University of Southern California Dissertations and Theses

Diamond surface chemistry for NV quantum sensing

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Diamond surface chemistry for NV quantum sensing

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Content DIAMOND SURFACE CHEMISTRY FOR NV QUANTUM SENSING
by
Laura Cecilia Mugica Sanchez
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMISTRY)
May 2023
Copyright 2023 Laura Cecilia Mugica Sanchez
A mis padres, hermanos y peque˜ na Lau
ii
Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
Chapter 1:Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Defects in diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 NV-based ESR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2:EPR Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Electron Zeeman Interaction . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Nuclear Zeeman Interaction . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Zero-field splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Nuclear Quadrupole Interaction . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Continuous Wave-EPR . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 Pulsed ESR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7.1 Rabi Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.2 Free Induction Decay (FID) . . . . . . . . . . . . . . . . . . . 22
2.7.3 Spin Echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7.4 Inversion Recovery . . . . . . . . . . . . . . . . . . . . . . . . 28
iii
2.7.5 Double Electron-Electron Resonance (DEER) . . . . . . . . . . 30
2.7.6 Electron Nuclear DOuble Resonance (ENDOR) . . . . . . . . . 32
2.7.7 ELDOR-Detected NMR (EDNMR) . . . . . . . . . . . . . . . 34
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 3:Surface Chemistry of Diamond . . . . . . . . . . . . . . . . . . . . 39
3.1 Nanodiamond Functionalization . . . . . . . . . . . . . . . . . . . . . 46
3.1.1 FTIR Characterization . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Diamond Substrate Functionalization . . . . . . . . . . . . . . . . . . . 51
3.2.1 XPS characterization . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Chapter 4:Effect of surface spins on spin relaxation times in single NV cen-
ters in diamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 Nitrogen Vacancy Center in Diamond . . . . . . . . . . . . . . . . . . 72
4.2 NV fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4 Optically Detected Magnetic Resonance (ODMR) . . . . . . . . . . . . 77
4.5 Characterization of NV Spin Relaxation . . . . . . . . . . . . . . . . . 81
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Chapter 5:Electron-electron double resonance detected NMR spectroscopy
using ensemble NV centers at 230 GHz and 8.3 Tesla . . . . . . . 90
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 Methods and Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Chapter 6:Microwave AC voltage induced phase change in Sb
2
Te
3
nanowires 106
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2 Methods and Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
iv
List of Tables
2.1 Effective nuclear g-factors for common nuclei used in NMR . . . . . . 11
3.1 Quantification of surface atoms at different reaction steps. The atomic
percentages were calculated using Eqs. 3.5 and 3.6, they represent the
average of five different areas analyzed on the substrates. The numbers
in parenthesis corresponds to the standard deviation. D43 is a type IIa
diamond, D51 is and electric grade (EG) (111) diamond, and D41 is an
EG (100) diamond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2 Quantification of surface coverage. The density of bromine and nitrogen
for silanization and azide steps were calculated using Eq. 3.7 and they
represent the average of five different areas analyzed on the substrates.
The numbers in parenthesis corresponds to the standard deviation. . . . 63
4.1 Summary of analysis for NVs discussed within text. Analysis was per-
formed in Matlab using eq. 4.2 as summarized in the text. Values in
parantheses represent the 95% confidence intervals. . . . . . . . . . . . 81
5.1 State identification and energy values determined from Eq. 5.1 . . . . . 100
5.2 Simulated transition energies calculated from Table 5.1 . . . . . . . . . 101
v
List of Figures
2.1 Illustration of the g ellipsoid wheng
⊥
>g
∥
. . . . . . . . . . . . . . . . 10
2.2 cwEPR spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Energy level diagram for an electron spin S = 1/2 coupled to a nuclear
spin I = 1/2 system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Rabi Oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5 Free Induction Decay experiment . . . . . . . . . . . . . . . . . . . . . 24
2.6 Bath Spin Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Spin Echo Decay experiment . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 Inversion Recovery Experiment. . . . . . . . . . . . . . . . . . . . . . 29
2.9 Double Electron-Electron Resonance Experiment. . . . . . . . . . . . . 31
2.10 Double Resonance Electron Nuclear pulse sequences. . . . . . . . . . . 35
3.1 The phase diagram of carbon. . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Surface atomic geometries of diamond. . . . . . . . . . . . . . . . . . . 43
3.3 Surface atomic geometries of diamond with oxygen or hydrogen termi-
nation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Two-step nanodiamond surface homogeneization. . . . . . . . . . . . . 47
3.5 Introduction of azide groups via silanization. . . . . . . . . . . . . . . . 48
3.6 Click chemistry step. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 FTIR characterization of ND. . . . . . . . . . . . . . . . . . . . . . . . 51
3.8 Reaction schemes for diamond substrates. . . . . . . . . . . . . . . . . 52
3.9 Scheme of (3-Bromopropyl)trichlorosilane, used for the silanization step
of the diamond surface . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 XPS Characterization of HTHC vs LTLC reaction schemes. . . . . . . . 59
3.11 XPS Characterization of D43 plasma. . . . . . . . . . . . . . . . . . . 64
3.12 XPS Characterization of D51 plasma. . . . . . . . . . . . . . . . . . . 66
3.13 XPS Characterization of D41 LTLC. . . . . . . . . . . . . . . . . . . . 68
4.1 The NV
− center in diamond. . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Overview of the NV ODMR experimental setup. . . . . . . . . . . . . . 76
4.3 NV center fabrication and imaging. . . . . . . . . . . . . . . . . . . . . 77
4.4 High spectral resolution ODMR (NV8). . . . . . . . . . . . . . . . . . 79
4.5 Autocorrelation experiment on NV8. . . . . . . . . . . . . . . . . . . . 81
vi
4.6 Rabi experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.7 NV SE Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.8 NV FID experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.9 Effect of surface spins in diamond on spin relaxation times in single NV
centers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1 EDNMR Experimental Setup at 230 GHz . . . . . . . . . . . . . . . . 93
5.2 Ensemble ODMR at 230 GHz . . . . . . . . . . . . . . . . . . . . . . 96
5.3 NV detected EDNMR at high field. . . . . . . . . . . . . . . . . . . . . 98
5.4 NV detected EDNMR of at 8.3 Tesla . . . . . . . . . . . . . . . . . . . 102
6.1 SEM image of a contacted single Sb
2
Te
3
nanowire along with the mea-
surement circuit diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Imaging of Sb
2
Te
3
NWs. . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Electrical resistance measurements at first forward AC voltage sweeps
from 10 MHz to 4 GHz with 0.33 s DC integration time. . . . . . . . . 112
6.4 Subsequent continuous backward and forward AC voltage sweep results
for NW2 at∼ 1µ W power level. . . . . . . . . . . . . . . . . . . . . . 113
6.5 Resistance switches under passive heating steps on NW2 at room tem-
perature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.6 Temperature dependent resistance measurements during warm up from
77 K to 300 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.7 AC sweeps of the NW segment between electrodes 2-3 after the NW
segment switches and saturates at the high resistance state after contin-
uous sweeps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.8 Resistance measurements of NWs. . . . . . . . . . . . . . . . . . . . . 118
6.9 Segment of NW5 between electrodes 4-5, before and after AC sweeps . 119
6.10 TEM cross-sectional analysis of NW5 after AC sweeps. . . . . . . . . . 119
6.11 TEM cross-section image of area A indicated in Fig. 6.10(b) shows a
layered structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.12 Consistent EDX Spectra of NW segments. . . . . . . . . . . . . . . . . 121
6.13 EDX lines scan of NW5 at the segment between contacts 4-5. . . . . . . 122
14 XPS Characterization of functionalized glass using the HTHC method. . 145
15 XPS Characterization of functionalized glass using the LTLC method. . 146
16 XPS Characterization of stability of silane in glass using the LTLC method.146
17 XPS survey scan of glass functionalized with 4-hydroxy-TEMPO and
kept in storage under different conditions and time. . . . . . . . . . . . 147
vii
Abbreviations
AC Alternating Current
AOM Acousto-optic modulator
ASF Atomic Sensitivity Factors
APD Avalanche photo-diode
AWG Arbitrary Waveform Generator
BE Binding Energy
cw-ESR continuous wave Electron Spin Resonance
CVD Chemical Vapor Deposition
DAQ Digital to analog converter
DC Direct Current
DEER Double Electron Electron Resonance
EDX Energy Dispersive X-Ray Spectroscopy
EDNMR Electron-electron Double Resonance detected NMR
EG Electric Grade
ENDOR Electron-nuclear DOuble Resonance
ESEEM Electron Spin Echo Envelope Modulation
ESR Electron Spin Resonance
EPR Electron Paramagnetic Resonance
EZ Electron Zeeman
FID Free Induction Decay
FFT Fast Fourier Transform
viii
FL Fluorescence
FTIR Fourier-Transform Infrared Spectroscopy
FWHM Full Width at Half Maximum
HF Hyperfine Interaction, High Field
HTA High turning angle
HTLC High Temperature Low Concentration
HPTH High Pressure High Temperature
LTLC Low Temperature Low Concentration
MRI Magnetic Resonance Imaging
MW Microwave
MQ milli-Q
ND Nanodiamond
NMR Nuclear Magnetic Resonance
NV Nitrogen-Vacancy
NQ Nuclear Quadrupole
NW Nanowire
NZ Nuclear Zeeman
O-U Ornstein-Uhlenbeck
PELDOR Pulsed Electron DOuble resonance
PCM Phase Change Materials
PCRAM Phase Change Random Access Memory
PL Photoluminescence
SEM Scanning Electron Microscopy
TEM Transmission Electron Microscopy
TI Topological Insulator
TOA Takeoff Angle
XPS X-Ray Photoelectron Spectroscopy
XRD X-Ray Diffraction
ZFS Zero-Field Splitting
ix
List of Physical Constants
β e
9.27400968× 10
− 24
kg m
2
s
− 2
T
− 1
or J T
− 1
s Bohr magneton
β n
5.050783699× 10
− 27
kg m
2
s
− 2
T
− 1
or J T
− 1
s Nuclear magneton
e 1.602176634× 10
− 19
A S Elementary charge
g 2.00231930436256(35) g-factor of free electron
h 6.62606957× 10
− 34
kg m
2
s
− 1
or J s Plank constant
k
B
1.38066× 10
− 23
kg m
2
s
− 2
K
− 1
or J K
− 1
s Boltzmann constant
µ 0
4π × 10
− 7
N A
− 2
or T MA
− 1
s Permeability of free space
ρ C
1.76× 10
23
atoms/cm
3
Number density of carbon atoms
in diamond
x
List of Units
dB Decibel
eV electron V olt (1.602× 10
− 19
J)
µ L Microliter (1× 10
− 6
L)
mL Milliliter (1× 10
− 3
L)
µ M Micromolar concentration (1× 10
− 6
M)
mM Millimolar concentration (1× 10
− 3
M)
M Molar concentration
mW Milliwatt (1× 10
− 3
W)
kW Kilowatt (1× 10
3
W)
kHz Kilohertz (1× 10
3
Hz)
MHz Megahertz (1× 10
6
Hz)
GHz Gigahertz (1× 10
9
Hz)
THz Terahertz (1× 10
12
Hz)
Ω Ohm
T Tesla
W Watt
xi
List of Symbols
A Hyperfine interaction tensor (components A
xx
,A
yy
, andA
zz
)
A
j
XPS Peak area
A
⊥
Transverse hyperfine interaction
A
∥
Parallel hyperfine interaction
a
iso
Isotropic hyperfine interaction
a
dip
Dipolar hyperfine interaction
α Alpha state
B Pseudosecular hyperfine interaction
⃗
B Static magnetic field vector
(components Bx, By,and Bz and magnitudeB
0
)
⃗
b
m
Electromagnetic field vector
(magnitudeb
m
, frequencyω, and phaseϕ )
⃗
B
RF
Radiofrequency field vector
(magnitudeB
RF
, frequencyω
0
, and phaseϕ p
)
β Beta state
˜
b
j
Magnetic field of the j-th spin
β p,ENDOR,ELDOR
Tipping angle for different pulse experiments
D Electron zero-field interaction tensor (components D
xx
,D
yy
, andD
zz
)
∆ Variance in the magnetic field due to the Ornstein-Uhlenbeck process.
∆ E Energy difference
δ Resonance offset
∆ ω Width of the frequency distribution
δϕ Phase accumulation
E Electron strain interaction
E
n
Eigenenergy of state n
xii
g Electron g-tensor (with components gx, gy, and gz)
g
2
(τ ) Second order correlation function
γ 1
(γ 2
) Characteristic decay time of state 1 (state 2)
γ e
Gyromagnetic ratio for an electron
γ n
Gyromagnetic ratio for a nuclei
g
n
Nuclear g-factor
H Rotating frame Hamiltonian
H
0
Static spin Hamiltonian
H
dip
Dipolar interaction Hamiltonian
H
EZ
Electron Zeeman interaction Hamiltonian
H
HF
Electron-nuclei hyperfine interaction Hamiltonian
H
NQ
Nuclear quadrupole interaction Hamiltonian
H
NZ
Nuclear zeeman interaction Hamiltonian
H
ZFS
Electron zero-field interaction Hamiltonian
I
n
Signal Intensity of specified process n
I Nuclear spin angular momentum quantum value with nuclear spin
numberm
I
ˆ
I Nuclear spin angular momentum vector operator
(components Ix, Iy, and Iz)
λ C
Inelastic mean free path of electrons in diamond
L(ξ ;∆ ω) Intrinsic lineshape
Ω Rabi Frequency
ω
0
Electron precession frequency
P Pressure
P Nuclear quadrupole Tensor (componentsP
xx
,P
yy
, andP
zz
)
P
|n⟩
Probability of a state transition wheren=αorβ state
|ψ ⟩ Wavefunction of a pure state
|ψ (0)⟩ Wavefunction at the initial time
q Electric field gradient
Q Nuclear quadrupole moment
R DC electrical resistance
⃗ r Vector between two spins, with magnitude r
ˆ
R
n
Rotation operator (nϵx,yorz )
S Electron spin angular momentum quantum value with spin numberm
s
ˆ
S Electron spin angular momentum vector operator
xiii
(components Sx, Sy, and Sz)
S
j
Atomic sensitivity factor for the j-th element
σ j
Spin state of the j-th bath spin
t Time
T Temperature
T Anisotropic Hyperfine Interaction Tensor
T
1
Spin-lattice relaxation
T
2
Spin-spin relaxation
T
∗ 2
Intrinsic spin dephasing
τ Pulse delay time
τ c
Correlation time due to the Ornstein-Uhlenbeck process.
t
p
Pulse time
ˆ
U Unitary transformation operator
ξ Relative intensity of bunching and antibunching
ζ Nuclear quadrupole assymetry parameter
ζ s
Selectivity parameter
ζ mix
Mixing parameter
xiv
Acknowledgements
I would like to thank financial support from the National Science Foundation (NSF)
(Nos. DMR-1508661, CHE-1611134 and CHE-2004252 with partial co-funding from
the Quantum Information Science program in the Division of Physics) and the National
Institute of Health (NIGMS T32-GM118289).
xv
Abstract
Quantum sensing utilizes principles from quantum phenomena to interrogate a system
and obtain the most detailed information about a system to date. The applications are
countless, ranging from mapping of individual protein molecules in biological processes
to improved metrological standards, nanophotonics and information technology. Sen-
sors in the atomic scale are the key to achieving high sensitivity and spatial resolution.
The paramagnetic defect in diamond known as the nitrogen vacancy or NV center has
shown to be one of the most promising sensors thus far.
NV centers possess unique optical and electronic properties that allow magnetic
field, temperature and transport mechanisms detection at the nanoscale level. NV cen-
ters present stable photoluminescence signals, long decoherence times and the ability to
perform optically detected magnetic resonance spectroscopy at room temperature. The
fundamental principle of NV based detection of a target molecule is via dipolar coupling
between them. Thus, close proximity of the molecule of interest and the NV is critical
to achieve higher sensitivity.
An innovative approach to develop NV based techniques through the detection of
electron spin resonance (ESR) signals is to position the molecule of interest on the dia-
mond surface. Highly efficient covalent attachment of molecules on the diamond surface
xvi
has been developed. However, a deeper understanding of the surface properties of dia-
mond is necessary to optimize the positioning, proximity and concentration of the target
molecule as well as the NV properties, mainly spin relaxation times. Longitudinal and
transverse relaxation times are crucial to the development of NV-ESR utilizing hyperfine
double electron resonance techniques.
Furthermore, to increase the spectral resolution and extract precise information on
the nature and specific conformation of a molecule, NV-ESR techniques at higher mag-
netic fields must be developed.
This dissertation presents the author’s approach to tackle the challenges presented
on the understanding of the diamond surface to develop NV quantum sensing. In Chap-
ter 1, an overview of current approaches in the field and motivation of the present work
is introduced. Chapter 2 describes electron paramagnetic resonance principles neces-
sary for discussion and analysis of experimental results presented in subsequent chap-
ters. Chapter 3 introduces the surface chemistry of diamond and its functionalization
where different surface preparation methods are investigated and discussed. In Chapter
4, NV spin relaxation properties after diamond surface cleaning and functionalization
is analyzed. Chapter 5 presents the first performance of NV detected nuclear magnetic
resonance at 8.3 Tesla. Chapter 6 discusses a new approach to tuning phase changes in
Sb
2
Te
3
nanowires using frequency control.
xvii
Chapter 1: Introduction
The first quantum revolution and the origin of the term quanta revealed that light comes
in packets and that the size of the packet depends on the frequency of the vibration. It
also demonstrated that photons or light particles can sometimes behave like waves. Ever
since, new technologies able to measure the discrete character of the quantum world’s
properties (e.g. photons, angular momentum quanta) such as magnetic resonance, semi-
conductors, photo-induced electron transfer, lasers, communications, and many more
were developed.
The second quantum revolution is based on the superposition principle of quantum
states. With it, information can be stored and processed as a result of its quantum en-
tanglement properties. Quantum sensing exploits quantum phenomena to achieve the
highest level of sensitivity and spatial resolution. Increasing our control on suitable sen-
sors and developing tunable and reproducible techniques is a requirement for broader
and routine application of the technology.
The features of a promising quantum sensor reside in their atomic size and proximity
to the target molecule to enhance sensing interaction and an initialization and readout
mechanism that maximizes resolution while minimizing noise and detection limits. De-
fects in diamond offer different quantum sensor candidates.
1
1.1 Diamond
Diamond has long-since been recognized for its beauty as a gemstone and since its
discovery it has been valued because of their strength and brilliance, and for their ability
to refract light and engrave metal. An estimated US $13 billion worth of rough diamonds
are produced per year, from which about 30% are of gem quality and the remaining
70% of diamonds are sold for industrial applications.
1
Synthesis of diamond utilizing
HPHT conditions was first shown in 1954 by General Electric.
2
Later, chemical vapor
deposition was also introduced as an industrial process to fabricate diamond crystals.
Lab grown diamonds became attractive candidates in research applications since
they can be engineered to target specific applications based on the amount of impurities.
For instance, the majority of natural diamonds are classified as type I which contain 100-
3000 ppm nitrogen content. This type is sub-classified as type Ia for nitrogen present in
the form of aggregates and type Ib where nitrogen is present as a single substitutional
defect as in HPHT crystals. Type II diamonds have less than 5 ppm nitrogen content
with type IIa having nitrogen as the major impurity like in CVD diamonds; and type IIb
with boron as the major impurity.
3
CVD diamonds are the most typical type of diamond
crystal enginnered with ultrahigh purity for quantum optics and electronics.
During the fabrication process, the diamond crystal is either grown or cut and pol-
ished along one of its principal axes. Diamond is chemically inert with respect to most
acids or alkalis, however, their surface termination can be modified to attach a molecule
of interest. Diamond nanoparticles are fabricated by milling of the synthesized diamond
crystals. Functionalization of nanodiamond surface has found numerous applications in
biomedicine where they are used as nanocomposites, for drug delivery, protein mim-
ics, tissue scaffolds and surgical implants. Diamond crystals have also been utilized
2
as (dye-sensitized) solar cells,
4
in photocatalysis,
5
as a probe for protein binding,
6
and
single molecule applications. The latter conveying quantum sensing is the most innova-
tive and challenging, and only few reports have been published since 2015.
7–9
For this
reason, having a better understanding of the surface chemistry of diamond will lead to
greater control over their properties and establish quantum sensing methods.
1.2 Defects in diamond
Natural diamonds are rich in impurities, and even gem-quality stones of high purity
have been shown to contain identifiable impurities. Amongst the different alternatives
of quantum sensors, the nitrogen vacancy (NV) defect in diamond is the most devel-
oped quantum technology so far. However other defects such as silicon vacancy (SiV)
center
10
and germanium vacancy (GeV)
11
center are also being explored.
SiV center is formed by a silicon atom in between two vacancies forming a D
3d
.
The emission spectra of SiV shows a very sharp zero phonon line around 739 nm
12
and a weak phonon sideband at room temperature. SiV has stable optical properties
featuring bright, narrowband emission, allowing for fast, accurate measurements which
are consistent between emitters.
13
SiV center shows stable photoluminescence centers
and can be used as a single photon source.
14
The SiV center emits around 70-80%
luminescence into the zero phonon line which is a huge advantage as compared to the
NV center (∼ 5%),
12, 15
however the reported 9% quantum efficiency of SiV is lower
than NV center.
16
These optical properties and spin resonance make SiV a suitable
candidate for experiments in quantum communications and quantum optics.
Germanium vacancy (Ge-V) centers present a D
3d
symmetry as SiV centers. A sharp
zero phonon line at 602 nm and low sideband is observed in photoluminescence spectra
at 300 K.
11
Ge-V centers can be created with ion implantation and annealing similar
3
to NV centers. The ZPL contains about 60% of the total emission spectra, due to its
brightness and higher quantum yield than NV center, nano-waveguide system based on
GeV for interferometry are under developments.
16
The NV center is composed of a substitutional nitrogen atom neighbouring with a
vacancy in the diamond crystal lattice.
17
They are created via nitrogen ion implantation
and annealing in diamond crystals
18
and are known to exist in the neutral (NV
0
)
19
and
negatively charged (NV
− )
20
state. The identifying features of NV
− and NV
0
are their
optical zero phonon lines (ZPLs) at 1.945 eV (637 nm))
21
and 2.156 eV (575 nm),
22
respectively.
The negatively charged state has got extensive attention compared to NV
0
. The main
reason for this is the ability to use the photoluminescent properties of NV
− for quantum
sensing, although more studies on NV
0
that explain NV
− properties such as intercon-
version and control of nuclear spin coherence are investigated.
23
Within this text, we
refer to NV
− and NV interchangeably. The NV center is a S = 1 defect that can be
polarised into them
s
= 0 ground state and a characteristic zero field splitting (ZFS) of
2.87 GHz.
20
This unique characteristic makes it possible to readout its resonance fre-
quency through optically detected magnetic resonance. The NV ZFS is highly sensitive
to magnetic field fluctuations with nanoscale resolution.
The electronic structure of SiV and GeV is still under investigation and SiV shows to
be a strong candidate for quantum sensing thanks to its stability and sharp ZPL. Despite
being widely investigated and used, room temperature nanoscale magnetometry using
the NV center in diamond remains an inaccessible technique. Therefore we aim to
establish a systematic method to control NV properties and utilize them to investigate a
molecule of interest.
4
1.3 NV-based ESR
Electron spin resonance (ESR) spectroscopy is a powerful tool for structural biology
where conformation and conformational dynamics of biological molecules are probed
via ESR signals of spin labels (e.g. nitroxide radicals) or paramagnetic centers in bi-
ological molecules.
24–27
The vast range of applications for NV centers is also due to
the versatility of their fabrication as a diamond plate or nanodiamonds. The unique
electronic configuration of the NV center in diamond provides a means to modulate the
fluorescence intensity dependent on the magnetic interactions of the single electron spin.
This effect is known as Optically Detected Magnetic Resonance (ODMR) which pro-
vides nanoscale magnetometry sensitivity (pT).
28, 29
This enables the detection of spins
localized within a few nanometers of NV centers. ODMR signal in NV centers has been
proven to be sensitive to different physical quantities such as temperature,
30–33
pressure
21
and, electric fields.
34, 35
In addition, spin relaxometry of the NV center has also been uti-
lized to monitor ion concentrations.
36–39
The integration of nanodiamonds within living
cells has also opened the door to detect membrane potentials
40
and nanoscale thermom-
etry.
32, 33
NV centers can also be used to achieve atomic scale resolution in scanning
probe microscopy. Recently, scanning magnetometry with nanometer resolution has
been achieved
40–42
as well as the detection of magnetic nanostructures.
42
Currently,
challenges involving the fabrication of the nanoscale tip that incorporated the single NV
center remain to reach the ultimate resolution limit. Nanoscale NMR spectroscopy using
NV centers is another ambitious application that will unlock the door to atomic struc-
ture determination and associated dynamics of proteins and other complex biological
5
molecules. Furthermore, the combination of NV nanoscale sensitivity with high mag-
netic field spectral resolution will unravel crucial information at the single molecule
level.
6
Chapter 2: EPR Spectroscopy
Electron Paramagnetic Resonance (EPR) spectroscopy is a magnetic resonance tech-
nique used to investigate systems containing unpaired electrons. In EPR, the magnetic
moments of the unpaired electrons within molecules are detected conventionally in a
continuous wave (CW) EPR spectrum. The analysis of EPR spectra provides insight
into the electronic properties of a system such as structural information, detection of
short-lived species, enzymes, point defects in solids, and more. EPR is utilized to detect
the presence of different paramagnetic species and deduce electronic configurations or
infer magnetic coupling between centres through g values.
However, the technique is not limited to the detection of paramagnetic species. EPR
spectroscopy is also utilized on diamagnetic species through spin labeling with a para-
magnetic compound. The different types of interactions that arise between the unpaired
electron and different nuclei within the molecule can be investigated with the use of
pulse techniques. For instance, the detection of the interstitial atom in the complex
structure of nitrogenase MoFe cluster was shown upon labelling with
13
C and investi-
gated via ESEEM (Electron Spin Echo Envelope Modulation).
43
Time-resolved EPR
in combination with ENDOR (Electron Nuclear DOuble Resonance) has been used to
measure molecular wires.
44
Finally, Double Electron-Electron Resonance (DEER) and
Pulsed ELectron DOuble Resonance (PELDOR) spectroscopies are used for molecular
distance measurements.
45–50
7
The spin Hamiltonian is a useful mathematical construction to describe a spin sys-
tem. In EPR the following interactions are considered: i) the electron Zeeman (EZ)
interaction, caused by the electron spin interacting with an applied static magnetic field;
ii) the nuclear Zeeman (NZ) interaction produced by the nuclear spin interacting with
an applied static magnetic field; iii) the hyperfine (HF) interaction caused by the elec-
tron spin interacting with the nuclear spins; iv) the zero-field splitting (ZFS) caused by
electron spin-electron spin interactions in systems with more than one unpaired electron
(S > 1/2); and iv) nuclear quadrupole (NQ) interactions caused by the nuclear spin in-
teracting with electric field gradients in the nucleus for nuclear spin quantum number (I
> 1/2). Therefore, the complete spin Hamiltonian for a system with an electron spin (S
> 1/2) coupled to a nuclear spin (I> 1/2) in the presence of a static external magnetic
field is described by,
ˆ
H
0
=
ˆ
H
EZ
+
ˆ
H
NZ
+
ˆ
H
HF
+
ˆ
H
ZFS
+
ˆ
H
NQ
(2.1)
In the following sections we describe in more detail the composition of each term in Eq.
2.1.
2.1 Electron Zeeman Interaction
In magnetic resonance experiments a static external magnetic field B is applied to the
system. The simplest example for EPR discussions is that with one unpaired electron (S
= 1/2). In the absence of a magnetic field the two electron spin states ( m
S
=± 1/2) are
degenerate. In the presence of B, the magnetic dipoleµ e
arising from the electron spin
will then interact with it. B is commonly applied parallel to the magnetic dipole axis
8
and the energy levels are lifted. The energy of the magnetic dipole (U) can be defined
in terms of its scalar product with B,
U =− ⃗
B
T
· ⃗ µ e
=−| µ e
B|cosθ (2.2)
where the superscript T used to represent the transpose and θ is the angle between
⃗
B
and⃗ µ e
. From Eq. 2.2 it is clear that the lowest energy level corresponds to the magnetic
moment aligned parallel to the applied field ( θ = 0
o
) and the high energy state is aligned
in the opposite direction (θ = 180
o
). By convention in EPR the magnetic field is applied
along the z-direction and B
z
is referred to as B
0
. The splitting of the energy of levels of
this system is known as the electron Zeeman interaction (EZ) and can be described by
the EZ spin Hamiltonian,
ˆ
H
EZ
=γ e
B
0
· ˆ
S (2.3)
in which γ e
= g
e
µ B
is the electron gyromagnetic ratio, g
e
is the g-factor. For a free
electron the g-factor is 2.00231930436256(35)
51
and µ B
= µ e
is the Bohr magneton
constant. From Eq. 2.3, we can see that the magnitude of the energy levels are pro-
portional to B
0
and characterized by the m
S
quantum numbers (Fig. 2.3 EZ section).
The g values of bound electrons generally differ from g
e
since they are dependent on
the orientation of the molecule center with respect to B
0
. The main reason for this
orientation-dependent g value shift is the presence of spin-orbit coupling which mixes
the excited and ground states in a compound. In this case, we can represent the effective
value of the g-factor as follows:
g
eff
(ϕ,θ )=
q
g
2
x
sin
2
θ cos
2
ϕ +g
2
y
sin
2
θ sin
2
ϕ +g
2
z
cos
2
θ (2.4)
9
x
y
z
g
II
B
0
g
T
θ
φ
Figure 2.1: The main axis of the g tensor is rotated with respect toB
0
byθ and
ϕ .
whereϕ andθ represent the angle between magnetic field with respect to principle axis
of g tensor as shown in Fig. 2.1. The transverse components are commonly denoted as
g
⊥
while the parallel component is denoted asg
∥
. So Eq.2.4 may be written as:
g
S
(θ )=
q
g
2
⊥
+g
2
∥
+cos(2θ )(g
2
∥
− g
2
⊥
)/2 (2.5)
If anisotropy of the g tensor is significant, the z axis in Eq. 2.4 is tilted from the di-
rection of the magnetic field. This effect is more prominent in solid state sample and
for transition metal ions or rare earth ions. In systems with axial symmetry like Cu
2+
,
g
x
= g
y
̸= g
z
; and in systems with rhombic symmetry like the superoxide ion O
2− ,
g
x
̸=g
y
̸=g
z
.
2.2 Nuclear Zeeman Interaction
The presence of nuclei with magnetic spin I adds further magnetic interactions to the
spin system. The NZ Hamiltonian (Eq. 2.6) is analogous to Eq. 2.3 as the degeneracy of
10
Nucleus Spin g
N
1
H 1/2 5.5854
2
H 1 0.8574
13
C 1/2 1.4042
14
N 1 0.4036
31
P 1/2 2.2610
Table 2.1: Effective nuclear g-factors for common nuclei used in NMR
the energy levels of a nuclear spin (m
I
) is lifted in the presence of an external magnetic
field.
ˆ
H
NZ
=γ N
B
0
ˆ
I (2.6)
in whichγ N
= g
N
µ N
is the nuclear gyromagnetic ratio, g is the g-value of the nucleus
and µ N
is the nuclear magnetic moment. Analogous to the g-factor of the electron,
a shift in the actual resonance frequency of the nucleus is observed. In contrast with
g
S
, this effect arises from the induced orbital angular momentum in the electron cloud
around the nucleus by the external magnetic field which partially shields the nucleus
from the external magnetic field. In NMR, this is known as the chemical shift repre-
sented byδ . Table 2.1 provides the nuclear g-factor values for some commonly observed
isotopes in NMR.
It is important to note that the energy gap given by the NZ interaction is much smaller
than the gap for EZ interaction. This is caused by the much smaller value ofµ N
which
is proportional to the particle’s mass. (Fig. 2.3 NZ section).
11
2.3 Hyperfine Interaction
In the presence of a nuclear spin, the electron spin experiences local magnetic field fluc-
tuations originated from the nearby nuclei magnetic dipole moments. The interaction
between an electron spin and nuclear magnetic moments is known as the hyperfine in-
teraction. This is a weaker type of interaction compared to EZ and NZ, so its effect
acts more like a perturbation to the energy levels split by Zeeman interaction terms. The
magnitude of the HF interaction is given by the hyperfine coupling tensor A, therefore
the HF Hamiltonian can then be expressed as:
ˆ
H
HF
=
ˆ
S
T
· A· ˆ
I (2.7)
The hyperfine coupling tensor is composed of an isotropic ( a
iso
) and an anisotropic (T)
component,
A=a
0
· 1+ T (2.8)
in which 1 is the identity matrix. The isotropic HF interaction also known as Fermi
contact is a direct measure of the interaction between the electron and nuclear magnetic
dipole moments as a result of the small but finite probability that the unpaired electron
will enter the nuclear volume. The Fermi contact interaction is isotropic and is encoun-
tered also in systems with unpaired electrons in p, d, or f orbitals. The isotropic HF
coupling constant in energy units, is given by:
a
iso
=
2
3
µ 0
gµ B
g
N
µ N
|Ψ(0) |
2
(2.9)
12
in which|Ψ(0) |
2
is the square of the absolute value of the unpaired electron wavefunc-
tion evaluated at the nucleus.
The anisotropic HF interaction arises from the the dipole-dipole interaction due to
the magnetic field produced by the nuclear magnetic dipole moment at the position of
the electron’s dipole and is given by,
a
dip
(r)=− µ 0
4π
µ T
B
· µ N
r
3
− 3(µ T
B
· ⃗ r)(µ N
· ⃗ r)
r
5

(2.10)
in which superscript T indicates the transpose,⃗ r is the vector relating the electron and
nuclear positions, and r is the electron-nucleus distance. Replacing the magnetic mo-
ments with their corresponding quantum mechanical operators yields the anisotropic
dipolar interaction Hamiltonian,
H
dip
(r)=− µ 0
4π gµ B
g
N
µ N
"
ˆ
S
T
· ˆ
I
r
3
− 3(
ˆ
S
T
· ⃗ r)(
ˆ
I· ⃗ r)
r
5
#
(2.11)
where g andg
N
are taken to be isotropic. Expanding the tensors in Eq. 2.11 we obtain,
H
dip
(r)= − µ 0
4π gµ B
g
N
µ N
×
ˆ
S
x
ˆ
S
y
ˆ
S
z

· 







r
2
− 3x
2
r
5
− 3xy
r
5
− 3xz
r
5
r
2
− 3y
2
r
5
− 3yz
r
5
r
2
− 3z
2
r
5








· 







ˆ
I
x
ˆ
I
y
ˆ
I
z








=
ˆ
S
T
· T · ˆ
I
(2.12a)
in which T is an axially symmetric traceless tensor. A can be diagonalized in the Carte-
sian coordinate system as:
13
A=








A
xx
A
yy
A
zz








(2.13)
Analogous to g, A provides insight into the molecular symmetry of the nucleus with
respect to the unpaired electron. So the transverse (A
⊥
) and parallel (A
∥
) terms are de-
fined and we can separate the HF interaction into the axial A = A
∥
cos
2
θ , and nonaxial
B =(A
∥
− A
⊥
)cosθ sinθ components.
2.4 Zero-field splitting
The dipole-dipole interaction between two unpaired electrons is analogous to the
anisotropic contribution to the HF interaction. The difference is that in this case, ZFS
arises from the effect of the magnetic field created by one electron spin on the other. the
corresponding ZFS Hamiltonian is given by,
ˆ
H
ZFS
=
ˆ
S
T
1
· D· ˆ
S
2
(2.14)
in which
ˆ
S
1
and
ˆ
S
2
are the spin operators for electrons 1 and 2, repectively, ⃗ r is the
vector connecting them, and D is the dipolar tensor. Diagonalization of D results in two
independent parameters: D = (3/2)D
zz
and E = (1/2)(D
xx
− D
yy
). Expanding Eq.
2.14 with the definitions of D and E results in:
ˆ
H
ZFS
=D
x
ˆ
S
2
x
+D
y
ˆ
S
2
y
+D
z
ˆ
S
2
z
=D

ˆ
S
2
z
− 1
3
S(S +1)

+E(
ˆ
S
2
x
− ˆ
S
2
y
) (2.15)
14
In triplet states with
ˆ
H
ZFS
̸= 0 the degeneracy is broken in the absence of a magnetic
field leading to two different energy transitions. D and E contain information about
the local symmetry of the spin system. For instance in systems with axial symmetry
D
xx
= D
yy
and hence E=0, in cubic symmetry D=E=0. Therefore, D is sometimes
called an axial ZFS parameter and E is called the rhombic ZFS parameter.
2.5 Nuclear Quadrupole Interaction
In nuclei withI >1/2, the assymetric charge present at the nucleus creates a quadrupole
moment (P). The quadrupole moment interacts with the electric field gradients at the nu-
cleus created by the surrounding electron cloud. In this case the spin states are described
by the NQ Hamiltonian,
ˆ
H
NQ
=
ˆ
I· P· ˆ
I (2.16)
in which P is the quadrupole tensor. In the principal axis system, Eq. 2.16 can be written
as:
ˆ
H
NQ
=
e
2
qQ
4I(2I− 1)
h
3
ˆ
I
z
− I(I +1)+η (
ˆ
I
2
x
− ˆ
I
2
y
)
i
(2.17)
in which e is the charge of the electron, q is the electric field gradient and η an asymmetry
parameter defined as η = (P
xx
− P
yy
)/P
zz
with P
zz
≡ e
2
qQ/4I(2I− 1) and|P
zz
| >
|P
yy
| > |P
xx
|. The dimensionless asymmetry parameter η provides a measure of the
field gradient deviation from uniaxial symmetry ( η = 0 for uniaxial symmetry). Eq.
2.17 we see that the electron spin is not included, thus NQ interaction sometimes creates
only small second-order perturbations to allowed EPR transitions. For instance, the
strenght of the Zeeman interaction ranges from 10
7
- 10
9
Hz while the quadrupolar
15
interaction ranges from 10
3
- 10
7
Hz.
52
NQ interactions may become dominant and
appear as first-order perturbations in more advanced EPR techniques such as double
resonance electron-nuclear spectroscopy.
2.6 Continuous Wave-EPR
Experimentally, we observe EPR transitions using a continuous wave (CW) EPR tech-
nique in which a continuous source of microwave (MW) radiation at a fixed frequency
is applied to a sample. For simplicity, we use a two-level system (TLS)S = 1/2 model
and only consider EZ interactions with isotropic g andB
0
= B
z
(spin system collinear
with the z -axis). In this case the Hamiltonian can be written as:
ˆ
H =gµ B
(B
x
ˆ
S
x
+B
y
ˆ
S
y
+B
z
ˆ
S
z
) (2.18)
Using the Zeeman basism
s
=+1/2=|α ⟩=

1
0

,m
s
=− 1/2=|β ⟩=

0
1

we obtain
the spin matrices:
ˆ
S
x
=
1
2

0 1
1 0

,
ˆ
S
y
=
1
2i

0 1
− 1 0

, and
ˆ
S
z
=
1
2

1 0
0 − 1

. Diagonalization
of Eq. 2.18 yields the following energy values E
n
= ± (gµ B
/2)B
z
with n = 1 = |α ⟩
and n = 2 = |β ⟩. Absorption occurs when the energy of the external magnetic field
hν matches the energy level difference (∆ E = E
2
− E
1
) (Fig. 2.2(a)). The careful
implementation of a small additional oscillating magnetic field given by,
⃗
b
m
(t)=Ω h
ˆ
S
x
cos(ωt+ϕ )+
ˆ
S
y
sin(ωt+ϕ )
i
(2.19)
in which Ω =
1
2
γ e
b
m
is known as the Rabi frequency.
⃗
b
m
(t) is the Hamiltonian that
represents the modulation field. CW EPR spectroscopy often utilizes a phase-sensitive
detection to enhance the sensitivity. The field modulation is applied orthogonal to the
external magnetic field at a frequency of 20 kHz with an amplitude of 0.02 Gauss for
16
Δ μ E = g B
B 0
B
0
MW
E = h
photon
υ
|α⟩
|β⟩
E
B
0
B
0
1
2
I
1
I
2
b =20 kHz
m
output
(a)
(b)
A
pp
Figure 2.2: (a) Upon application of an external magnetic field B
0
, the spin
states are split into two|α ⟩ and|β ⟩. When the energy of the MW excitation
(E
photon
) equals the energy gap∆ E, absorption occurs and an absorption EPR
spectrum (b) is observed. (b) A 20 kHz modulation field ( b
m
) is applied on the
magnetic field and the output intensity only detects signals with the same modu-
lation increasing the signal to noise ratio (SNR). The observed EPR spectrum is
recorded as the derivative of the absorption spectrum in which the peak-to-peak
amplitude approximates the gradient of the absorption curve.
our home-built setup. As b
m
increases from point 1 to point 2 in Fig. 2.2(b), the de-
tector output increases from I
1
to I
2
. The output yields a peak-to-peak amplitude that
approximates the gradient of the absorption curve, leading to a first derivative profile.
Let’s consider the case of a system in which one electron spin (S = 1/2) is coupled to a
nuclear spin (I = 1/2) described by,
ˆ
H =γ e
B
0
· ˆ
S +γ N
B
0
· ˆ
I +
ˆ
SA
ˆ
I (2.20)
17
Magnetic Field (B )
0
m = 1/2
s
m = - 1/2
s
g
m = 1/2
I
EZ NZ
E
4
m = 1/2
I
m = -1/2
I
m = -1/2
I
E
3
E
2
E
1
EPR I
EPR II
NMR I
NMR II
HF
Energy
Figure 2.3: Upon the application of the magnetic field, the EZ interaction splits
them
s
=± 1/2 state into two. The energy gap depends on the value of g. The
NZ interaction further splits the EZ manifold into four spin states|± m
s
,± m
I
⟩.
The isotropic hyperfine interaction brings the states in the NZ manifold closer
or further apart according to Eq. 2.21. The allowed EPR and NMR transitions
are shown in pink and green, respectively.
in which a isotropic HF coupling constant andg
N
> 0 is considered. The energy levels
are given by,
E
1
=− (1/2)g
e
µ B
· B− (1/2)g
N
µ N
· B− (1/4)a
iso
(2.21a)
E
2
=− (1/2)g
e
µ B
· B+(1/2)g
N
µ N
· B+(1/4)a
iso
(2.21b)
E
3
=+(1/2)g
e
µ B
· B− (1/2)g
N
µ N
· B+(1/4)a
iso
(2.21c)
E
4
=+(1/2)g
e
µ B
· B+(1/2)g
N
µ N
· B− (1/4)a
iso
(2.21d)
Fig. 2.3 shows the corresponding energy diagram for Eq. 2.20. The order of them
I
levels within each NZ manifold is determined by the sign ofg
N
. In EPR spectroscopy,
18
the transitions with higher probability (allowed EPR transitions) are those corresponding
to∆ m
S
=± 1 and∆ m
I
= 0. This represents a change of the electron spin state only,
the nuclear spin state must remain the same. And, ∆ m
S
= 0 and ∆ m
S
± 1 represent
allowed NMR transitions.
2.7 Pulsed ESR spectroscopy
In a pulsed experiment, a radio-frequency (RF) field is applied via short pulses. The RF
field is resonant with the precession of the spin to allow it to accumulate over time. This,
induces a change in spin polarization that can be utilized to separate weak interactions
(i.e. hyperfine interactions) and obtain more detailed information about the spin system
that is being investigated. The spin system is commonly oriented along the external
static magnetic field which is taken as the z coordinate of the lab frame. The polarization
of an RF pulse with phaseϕ p
is applied along the x or y axis of the lab frame, orthogonal
to the static magnetic field, B
o
and is described by,
⃗
B
RF
(t)=B
RF
sinθ RF
(e
z
cosθ RF
+e
x
cos(ω
0
t+ϕ p
)+e
y
cos(ω
0
t+ϕ p
)) (2.22)
whereθ RF
is the angle betweenB
o
andB
RF
ande
n
with n = x,y,z represent the cartesian
orthonormal vectors. The total Hamiltonian for the system is given by,
ˆ
H(t)=
ˆ
H
EZ
+
ˆ
H
RF
(t) (2.23)
in which the static field Hamiltonian
ˆ
H
EZ
is described by Eq. 2.3 and the time-
dependent RF Hamiltonian is described by,
ˆ
H
RF
=− γB
RF
[
ˆ
S
x
cos(ω
RF
t+ϕ p
)+
ˆ
S
y
sin(ω
RF
t+ϕ p
)] (2.24)
19
where the definition of B
RF
with θ = 0 and the definitions of the spin operators were
used. The properties of the rotation operators may be used to rewrite Eq. 2.24 as follows,
ˆ
H
RF
=− Ω ˆ
R
z
(ϕ p
)
ˆ
S
x
ˆ
R
z
(− ϕ p
) (2.25)
where the nutation frequency Ω = γB
RF
is a measure of the RF field amplitude and
ˆ
R
z
(− ϕ p
) is the rotation operator around the z-axis with a phase equal to ϕ p
. Next we
transform Eq. 2.22 to phase modulated frame utilizing equation 9 in 6.4.
ˆ
H(t)=(ω
o
− ω)
ˆ
R
z
(− Φ PM
)
ˆ
S
z
ˆ
R
z
(Φ
PM
)+Ω ˆ
R
z
(− Φ PM
+Φ p
)
ˆ
S
x
ˆ
R
z
(Φ
PM
− Φ p
) (2.26)
in whichΦ PM
=ωt +ϕ PM
andΦ p
=ωt +ϕ p
Eq. 2.26 can be further simplified knowing
that
h
ˆ
S
z
,
ˆ
R
z
i
=0. Assuming thatϕ PM
= 0 and the utilizing the properties of the rotation
operators we obtain the rotating frame Hamiltonian;
ˆ
H =δ ˆ
S
z
+Ω[
ˆ
S
x
cos(ϕ p
)+
ˆ
S
y
sin(ϕ p
)] (2.27)
It is standard convention to set the phase of the RF radiationϕ p
= 0 for a pulse applied
along the x-axis. The differenceδ =ω
o
− ω is defined as the resonance offset.
2.7.1 Rabi Oscillations
The action of an x-pulse in a spin-system can be described by considering a two-level
system (TLS) in the Zeeman basis (|α ⟩,|β ⟩). Commonly, the pulse is applied exactly on
resonance with the Larmor frequency. In this case using Eq. 2.27, the Hamiltonian with
an x-pulse is:
ˆ
H =Ω ˆ
S
x
(2.28)
20
MW
t
p
|α⟩
|β⟩
Ω π = 
x
y
z
(a)
(c)
(b)
Ω μ t ( s)  
p
π
1.0
0.0
0.5
π/2
P α
P β
Figure 2.4: (a) The pulse sequence consists of a rectangular microwave pulse
of variable length t
p
. (b) The initial state|α ⟩ is aligned along +z axis in the
Bloch sphere. A pulse of length Ω t
p
= π flips the spin state into |β ⟩ aligned
along -z axis in the Bloch sphere. (c) The probability of|α ⟩ and|β ⟩ given by
Eq. 2.32.
The pulse of lengtht
p
is considered to be perfectly rectangular (Fig.2.4(a)). The evolu-
tion of the spin states can be obtained by direct integration of the Schr¨odinger equation
yielding Eq. 2.29
|ψ f
⟩=
ˆ
R
x
(t
p
)|ψ o
⟩ (2.29)
in which,
ˆ
R
x
(t
p
) = exp[− i(Ω
ˆ
S
x
)t
p
] and|Ψ o
⟩ ≡ | α ⟩ is the initial state. We define the
tipping angleβ p
= Ω t
p
of the pulse which by definition is always positive. The matrix
representation of the rotation operator
ˆ
R
x
(t
p
) is:
ˆ
R
x
(t
p
)=




cos

Ω tp
2

− isin

Ω tp
2

− isin

Ω tp
2

cos

Ω tp
2





(2.30)
The final state then becomes:
|ψ f
⟩=cos(Ω t
p
)|α ⟩− isin(Ω t
p
)|β ⟩ (2.31)
21
and the probability of the population being in theα orβ states,P
|α ⟩
andP
|β ⟩
respectively,
is given by,
P
|α ⟩
=cos
2
(Ω t
p
)=
1
2
(1+cos(Ω t
p
)) (2.32a)
P
|β ⟩
=sin
2
(Ω t
p
)=
1
2
(1− cos(Ω t
p
)) (2.32b)
The evolution of the spin states using Eq. 2.32 is seen in Fig. 2.4(b). The spin state
oscillates between the|α ⟩ and|β ⟩ spin states with a characteristic nutation frequency
defined by Ω . From this graph we see thatβ p
= π/ 2 generates a superposition of states
andβ p
=π induces a spin population inversion (Fig. 2.4(c)).
2.7.2 Free Induction Decay (FID)
Detailed information of a spin system can be obtained with the use of pulse sequences
that filter out specific signals. For instance, in addition to the static field applied, each
spin experiences a local, time-varying magnetic field b(t) which originates from cou-
pling to nearby spins. An experiment utilizing the an FID pulse sequence may be used
to detect these smaller magnetic field fluctuations. An FID experiment allows time for
a spin to interact with its environment. The model that describes this interaction can
be obtained by calculating the free evolution of the state under the fluctuating magnetic
field. For this model we use a TLS and prepare the state into the transverse x-y plane by
applying an RF pulse withβ p
= π/ 2 and let the state evolve for a finite amount of time
τ (Fig. 2.5). The final state is then described by,
|ψ f
⟩=
ˆ
U
1
(τ )
ˆ
R
x
(π/ 2)|ψ o
⟩ (2.33)
22
where the free evolution operator is defined
ˆ
U
n
(t) = exp(− i
R
tn
t
n− 1
γb (t
′
)
ˆ
S
z
dt
′
). After
applying aπ/ 2 pulse over the initial state|ψ o
⟩≡| α ⟩, we obtain a superposition of states
1
√
2
(|α ⟩− i|β ⟩). Now, we can rewrite Eq. 2.33 as follows:
|ψ f
⟩=
1
√
2
(exp(ϕ 1
)|α ⟩− iexp(− ϕ 1
)|β ⟩) (2.34)
In Eq. 2.34, we applied the definition of
ˆ
S
z
and defined ϕ n
(t
n
− t
n− 1
) =
− i/2
R
tn
t
n− 1
γb (t
′
)dt
′
) as a phase factor. The transverse components are obtained by find-
ing the expectation values
ˆ
S
x
and
ˆ
S
y
given by,
⟨ψ f
|
ˆ
S
x
|ψ f
⟩=− i
4
[exp(− 2ϕ 1
)− exp(2ϕ 1
)]=− 1
2
sin
Z
τ 0
γb (t
′
)dt
′

(2.35a)
⟨ψ f
|
ˆ
S
y
|ψ f
⟩=
1
4
[exp(− 2ϕ 1
)+exp(2ϕ 1
)]=
1
2
cos
Z
τ 0
γb (t
′
)dt
′

(2.35b)
After the free evolution time, each spin accumulates a phase proportional to its mag-
netic field offset. A Gaussian frequency distribution with a width ∆ ω and b(t) is a
symmetrically distributed variable. So the accumulated phase dependent on the fluctu-
ating magnetic field ω = γb (t
′
) is averaged over all possible frequencies and Eq. 2.35
may be expressed as:
⟨
ˆ
S
x
⟩=− 1
2
Z
∞
−∞
sin(ωt)
1
∆ ω
√
2π exp

− ω
2
2∆ ω
2

=0 (2.36a)
⟨
ˆ
S
y
⟩=
1
2
Z
∞
−∞
cos(ωt)
1
∆ ω
√
2π exp

− ω
2
2∆ ω
2

=
1
2
exp

− t
2
∆ ω
2
2

(2.36b)
in which ∆ ω =
2πµ 0
ℏ
9
√
3
γ A
γ B
n
B
represents the dipolar coupling between spins A and
B with their respective gyromagnetic ratios and n
B
represents the concentration of an
ensemble average of B spins.
53
⟨
ˆ
S
x
⟩ is averaged to zero and⟨
ˆ
S
y
⟩ gives an exponential
decay.
23
MW
τ
(1/ 2)( ) √ | | α β ⟩- ⟩ i
π/2
x
y
z
x
y
z
τ
Figure 2.5: The spin is rotated into the transverse plane by aπ/ 2 x-pulse. This
generates a superposition of|α ⟩ and|β ⟩. The state freely evolves over t = τ and accumulates a phase proportional to the magnetic field offset given by the
resonance frequencies offset of the spin bath.
In a general description, the electron spin bath governs the coherence decay. The
bath is treated as a classical noise field which is modeled by the Ornstein - Uhlenbeck
(O-U) process which is stationary (⟨b(t
′
) = 0⟩).
54, 55
The O-U correlation function
is ⟨b(0)b(t
′
) = b
2
exp(− t/τ
c
)⟩, in which the variance b
2
relates the amplitude of the
magnetic noise that arises from the coupling strength of the spin to the bath given by
b
2
=γ e
q
P
j
˜
b
2
j
. In this equation
˜
b
2
j
is is a magnetic field described by,
˜
b
2
j
=gµ 0
µ B
(1− 3cos
2
θ j
)σ j
/(4πr
3
j
) (2.37)
in which the magnetic field produced by a j-th bath spin at a central spin at a distance
given by ⃗ r
j
(r
j
,θ j
) and, σ j
is a spin state of the j-th bath spin (σ j
= ± 1/2). The cor-
relation time τ C
is the characteristic time for a flip or flop of a given spin in the en-
vironment. In the O-U approximation the averaging over all possible realizations of
b(t) is represented by the characteristic function⟨e
ikx
⟩ = exp

P
∞
n=1
(ik)
n
n!
c
n
(x)

. In
the case of the Gaussian variable, only the first two cumulants are non-zero. There-
fore, the characteristic function of the Gaussian variable x, is given by ⟨e
ikx
⟩ =
24
x
y
z
spin probe
flip
flop
bath spin
slow dynamics
fast dynamics
Figure 2.6: The magnetic field and thus the dephasing that the spin probe expe-
riences is affected by the dynamics of the spin bath. Bath spins can rotate down
(flip) or up (flop) within the experiment time at a slow or fast rate.
exp

ik⟨x⟩− k
2
2
(⟨x
2
⟩−⟨ x⟩)
2

, where k =
R
t
0
σ (t
′
)b(t
′
)dt
′
. Applying this property to
Eq. 2.35b and evaluating the integral
56
we obtain,
⟨
ˆ
S
y
⟩=
1
2
exp[− b
2
τ 2
C
(t/τ
C
+e
− t/τ
C
− 1)] (2.38)
Eq. 2.38 describes the magnetization in the transverse plane after the free evolution
time. Typically, FID signals are characterized by a decay rate Γ ∗ 2
or dephasing time
T
∗ 2
= 1/Γ ∗ 2
that arises from the dipolar interaction of the spin with the spin bath and
intra-bath dipolar coupling,
57
as described previously. Therefore, the FID signal that
represents the transverse magnetization is phenomenologically described by,
FID(t)=exp(− (t/T
∗ 2
)
n
) (2.39)
The value of n in Eq. 2.39 depends on the environment’s regime. For instance, spins
in the spin bath undergo a flip-flop process driven by dipolar interaction as shown in
Fig. 2.6. The spin bath can undergo fast spectral diffusion (rapid flip-flops) in which
τ C
>> t. This is known as the motional narrowing regime where n = 1.
58, 59
On the
opposite case, when the spin bath dynamics is slow or practically static, τ C
<< t and
the spin bath is said to be in a quasi-static regime where n = 2.
55
25
MW
τ
π/2
x
y
z
τ
π
τ
τ π
x
y
z
x
y
z
x
y
z
δφ ≠ 0
echo
Figure 2.7: The spin is rotated into the transverse plane by aπ/ 2 x-pulse. This
generates a superposition of|α ⟩ and|β ⟩. The state freely evolves over t = τ dephasing from the -y axis into the transverse plane. The spin is then rotated by
a π pulse and let evolve for t = τ to recover the phase. In the experiment the
spin accumulates a phase proportional to the magnetic field offset given by the
resonance frequencies offset of the spin bath which is detected att = 2τ as an
echo signal.
2.7.3 Spin Echo
The effect of local static magnetic field components discussed in the previous section
can be filtered by inverting their contribution. This is performed in a spin echo (SE)
measurement where an additional rotation
ˆ
R
x
(π ) in the transverse plane is performed.
To fully remove static magnetic contributions, the spin is allowed to revert the magne-
tization over the same free evolution time as in the first half of the pulse sequence as
shown in Fig.2.7(a). The remaining decay of the spin-echo signal is now only due to
dynamic magnetic field contributions.
To model SE signals, we follow a similar procedure as the one used in section 2.7.2
using the SE sequence shown in Fig. 2.7.3(a). The state is prepared in the transverse
plane by aπ/ 2 pulse, allowed to evolve duringτ , then inverted by aπ pulse and allowed
to evolve again for anotherτ . The final state is described by,
|ψ f
⟩=
ˆ
U
2
(τ )
ˆ
R
x
(π )
ˆ
U
1
(τ )
ˆ
R
x
(π/ 2)|ψ o
⟩ (2.40)
26
The result of Eq. 2.40 for the first half of the sequence is the same as the one obtained
in Eq. 2.34. The effect of theR
x
(π ) is to invert the magnetization or phase. Therefore,
the state after the pulse is given by,
|ψ f
⟩=− ˆ
U
2
(t)

1
√
2
(exp(− ϕ 1
)|α ⟩+exp(ϕ 1
)|β ⟩)

(2.41)
During the second half of the sequence, the spin accumulates an additional phase and
Eq. 2.41 can be rewritten as,
|ψ f
⟩=− 1
√
2
(exp(ϕ 2
− ϕ 1
)|α ⟩+iexp(ϕ 1
− ϕ 2
)|β ⟩) (2.42)
in whichδϕ = ϕ 1
− ϕ 2
= 1/2(
R
τ 2
τ b(t
′
)dt
′
− R
τ 0
b(t
′
)dt
′
) is the total phase accumulated
during2τ . The transverse components of SE are given by,
⟨ψ f
|
ˆ
S
x
|ψ f
⟩=− i
4
[exp(− δϕ )+ exp(δϕ )]=
− 1
2
sin
Z
2τ τ γb (t
′
)dt
′
− Z
τ 0
γb (t
′
)dt
′

⟨ψ f
|
ˆ
S
y
|ψ f
⟩=
1
4
[exp(− δϕ )+ exp(δϕ )]=
+
1
2
cos
Z
2τ τ γb (t
′
)dt
′
− Z
τ 0
γb (t
′
)dt
′

(2.43a)
Now, we model the spin bath by an OU process as done for FID. Averaging Eqs. 2.43a
and 2.43a over all possibleb(t
′
), the SE signal is now described by Eq. 2.44 Moreover
the SE decay function is modeled by the stretched exponential function,
54, 60
SE(2τ )=exp

−
2τ T
2

n

, (2.44)
27
where T
2
is the decoherence time and the exponent n depends on the environment’s
regime. The hyperfine interaction between an electron spin and a nuclear spin ( I
j
) can
create modulations on a SE signal, so-called electron spin echo envelope modulations
(ESEEM).
61–63
After preparing the state into the transverse place|ψ o
⟨=
1
√
2
(|α ⟨− i|β ⟨),
it becomes entangled with the nuclear spin state at a rate determined by the magnetic
fields experienced by I
j
. The magnetic field components depend on the spin state,
namely,
− − →
B
j
ms
=
− →
B
j
+m
s
− →
A
j
/µ
n
. As the electron spin becomes entangled with the nu-
clear spin, the spin-echo signal diminishes; when it gets disentangled, the signal revives.
The resulting SE signal thus exhibits periodic reductions in amplitude with modulation
frequencies f
ms
associated with the spin-dependent magnetic field (
− − →
B
j
ms
). By consid-
ering the unitary evolution associated with the pulse sequence and a hyperfine-coupled
Hamiltonian, the coherence of the spin is given by,
S
j
(2τ )=1− 2Csin
2

πf
j
0
(2τ )
2
!
sin
2

πf
j
− 1
(2τ )
2
!
, (2.45)
whereC =|
− →
B
j
0
× − − →
B
j
− 1
|
2
/[|B
j
0
|
2
|B
j
− 1
|
2
]∈[0,1] andf
ms
is a Larmor frequency of the nu-
clear spin when the spin state ism
s
. When multiple nuclear spins couple, the coherence
becomesS =Π j
S
j
.
61
2.7.4 Inversion Recovery
Pulse experiments such as SE and FID described in the previous sections, are limited by
the transverse spin relaxation since the spin-state evolves in the transverse plane. Pulse
sequences that allow the detection of other nuclear or electron spins via dipolar coupling
(e.g. DEER, EDNMR, ENDOR, etc.) highly rely on the longitudinal relaxation time
(T
1
). The characteristic time T
1
describes the amount of time required for the spin to
28
MW
t
|β⟩
x
y
z
π
(a) (b)
(c)
time ( s) μ
0.0
1.0
signal intensity
1.0 10.0
Figure 2.8: (a) The pulse sequence involves a π pulse that flips the spin into
the -z axis shown in (b), the spin is allowed to relax back to its original position
after a given amount of time. The characteristic relaxation time is known as
longitudinal relaxation time T
1
. (c) Normalized inversion recovery of a spin
withT
1
=1µs (shown by green dashed lines).
relax back into equilibrium. Inversion recovery is an experiment designed to measure
T
1
relaxation. In this process the spin is flipped from |α ⟩ to|β ⟩ (Fig. 2.8(b)) via a π pulse, and allowed to relax back to its original position during free evolution time. The
final state given by the pulse sequence in Fig. 2.8 given by,
|ψ f
⟩(t)=
ˆ
U
1
(t)
ˆ
R
x
(π )|ψ o
⟩ (2.46)
The final magnetization is given as a function of the time delay t and proportional to
the population of the final state, P
α = |⟨α |ψ f
⟩|
2
. The relaxation process follows an
exponential decay rate, and the recovered magnetization in the z-direction shown in Fig.
2.8(c) is obtained bym
z
(t)=gµ B
⟨ψ f
|
ˆ
S
z
|ψ f
⟩ yielding,
m
z
(t)=m
0
(1− exp(− t/T
1
)) (2.47)
in whichm
0
=gµ B
/2 is the thermal magnetization.
29
2.7.5 Double Electron-Electron Resonance (DEER)
This technique takes advantage of the dipolar coupling between two spins where one
spin is used as probe and the other one is a target spin (Fig. 2.9(b)). As seen in section
2.7.3 using a spin-echo sequence, the spin probe can i) be decoupled from static mag-
netic noise and ii) accumulate a phase proportional to the time-varying magnetic field.
DEER uses SE sequence to readout additional magnetic fields like the one induced by
a dipole during the second half of the sequence. The dipolar field is externally induced
by a second microwave π pulse on the target spin (Fig.2.9(a)). Therefore, during the
second half of the DEER sequence, the target spin will cause an additional accumula-
tion of phase proportional to its dipolar field. The magnetic field that the spin probe
experiences is now expressed asb
DEER
(t
′
)=b
j
(t
′
)+b
t
; in whichb
j
(t
′
) is the magnetic
field component produced by a j-th bath spin andb
t
is the field contribution of the target
spin induced by the flip of the spin.
If we consider b
DEER
(t
′
) and that the target spin is S = 1/2, the final state of the
spin probe follows a similar construction as Eq. 2.42 is given by,
|ψ f
⟩=
1
√
2
exp

iγ

− Z
2τ τ b
j
(t
′
)dt
′
+b
t
/2+
Z
τ 0
b
j
(t
′
)dt
′
+b
t
/2

|α ⟩
+
i
√
2
exp

iγ

+
Z
2τ τ b
j
(t
′
)dt
′
− b
t
/2− Z
τ 0
b
j
(t
′
)dt
′
− b
t
/2

|β ⟩
(2.48)
In Eq.2.48, the sign of b
t
is reversed on the second half of the sequence as induced by
the second microwaveπ pulse. Ifb
j
(t
′
) is assumed constant, Eq. 2.48 is reduced to:
|ψ f
⟩=
1
√
2
[exp(iγb
t
τ )|α ⟩+iexp(− iγb
t
τ )]|β ⟩ (2.49)
30
MW 1
τ
π/2 π
τ
MW 2
π
x
y
z
target spin
spin probe
x
y
z
target spin
spin probe
(MW 2) π
r r
(a)
(b)
x
y
z
τ τ π
x
y
z
x
y
z
x
y
z
δφ  
α
b
t
 
δφ  
α
b
t
 
0.5
1.0
SE
DEER
contrast
time
signal intensity
(c)
θ θ
Figure 2.9: (a) The SE pulse sequence is used as a reference of the spin probe
to reduce static field noise. The dipolar field of the target spin is reversed using
a second MW π pulse and the SE signal is readout. The signal intensity com-
pared to the reference contains an additional phase factorδϕ proportional to the
magnetic dipolar field of the target spin b
t
. (b) The spin probe and the target
spin are separated by a distance set byr and and angleθ . A second microwave
π pulse in resonance with the target spin is applied inverting its dipolar field.
The spin probe selectively senses the target spin. (c) The contrast between the
SE and DEER signal over time is changed by b
t
. The maximum contrast de-
pends on the signal intensity of SE at the specified τ , in which a shorterτ will
provide a higher contrast. This is ultimately limited by the transverse relaxation
timeT
2
.
Following a similar procedure as for Eqs. 2.43a and 2.43a, the expectation values for
the DEER experiment are given by,
⟨
ˆ
S
x
⟩=
1
2
sin(2γb
t
τ ) (2.50a)
⟨
ˆ
S
y
⟩=
1
2
cos(2γb
t
τ ) (2.50b)
31
The phase accumulation during DEERδϕ = iγb
t
τ in Eq. 2.50b now contains informa-
tion about the target spin. this is readout as a contrast to the original SE signal shown
in Fig. 2.9 (c). It is useful to consider the DEER signal of an ensemble of spins. In this
case, the signal intensity is dependent on the different configurations of the target spins
in space. The phase accumulation during DEER δϕ = iγb
t
τ has different degrees of
freedom. For instance, the distance between spinsR(r
j
) = 1/r
3
j
, the angle between the
probe and target spins,Θ( θ j
)=3cos
2
θ j
− 1, and the frequency offset distribution mod-
eled by a Lorentzian function, L(ξ ) =
Ω 2
(ξ j
− ωt)
2
+Ω
2

t
p2
2
p
(ξ j
− ω
t
)
2
+Ω 2

. Averaging
over all the possible orientations of the target spins, the effective population inversion is
given by,
64
P
α ↔β (ω;t
p2
,Ω ,∆ ω)=
Z
∞
−∞
Ω 2
Ω 2
+(ω− ξ )
2
sin
2

t
p2
2
q
(ξ j
− ω
t
)
2
+Ω 2

L(ξ,δω )dξ
(2.51)
in which L(ξ,δω ) represents the intrinsic ESR lineshape with linewidth given by ∆ ω.
The length of the DEER pulse is given byt
p2
and the Rabi frequency is given byΩ . A
NV-ESR signal readout atP(m
s
=0) is given by,
I
NV− ESR(ω)
=
I
o
2
cos(2CN
τ P
α ↔β (ω))+
1
2
(2.52)
in whichI
o
is the SE intensity without the DEER pulse, C is a constant, N is the number
of DEER pulses, andτ is the total evolution time.
2.7.6 Electron Nuclear DOuble Resonance (ENDOR)
In ENDOR, electron and nuclear spin transitions are induced through the application
of two irradiating frequencies. This experiment uses the higher sensitivity of the EPR
32
signal to enhance the detection of NMR signals over conventional NMR techniques.
The basic principles can be explained by reference to a TLS (S = I = 1/2). In section
2.3 we showed four possible energy levels according to Eq. 2.21 for isotropic hyperfine
coupling constant A. To model double resonance signals, we consider an anisotropic A
and the energy levels are now given by,
NMR :ν α,β
=
s

ν n
± A
2

2
+
B
2
4
(2.53a)
EPR :ν 1→3,2→4
=ν e
± 1
2
(ν α − ν β ) (2.53b)
ELDOR :ν 1→4,2→3
=ν e
± 1
2
(ν α +ν β ) (2.53c)
in which ν e
= γ e
B
0
is the electron Larmor frequency, ν n
= γ n
B
0
is the nuclear Lar-
mor frequency and, the definitions of A = A
∥
cos2θ + A
⊥
sin2θ and B = (A
∥
− A
⊥
)cosθ sinθ for an axially symmetric A tensor have been used. The energy diagram
for this system is shown in Fig. 2.10. Two additional transitions are considered: E
1
=
|− 1/2,+1/2⟩→E
4
=|+1/2,− 1/2⟩ andE
2
=|− 1/2,− 1/2⟩→E
3
=|+1/2,+1/2⟩
which are known as electron double resonance (ELDOR) transitions since both quan-
tum numbersm
S
andm
I
are changed. Pulsed ENDOR is used to independently select
pulse lengths and delay times to optimize the induced transition rates. The Davies EN-
DOR pulse sequence shown in Fig. 2.10(a) uses a MWπ pulse to drive one of the EPR
transitions, for example between E
1
and E
3
Fig. 2.10(c). This is followed by an RF
π pulse that to induce an NMR transition and invert the nuclear spin populations be-
tween E
3
and E
4
(Fig. 2.10 (d)) resulting in electron spin saturation (Fig. 2.10 (e)).
The second half of the sequence corresponds to SE detection sequence, in which an
increase in the SE signal will be observed as a result of the spin saturation caused by
33
the nuclear spin population inversion. The detection sequence used may also be FID,
this is useful for shorterT
2
times. An important requirement of Davies ENDOR is that
the first MW π pulse is selective by only exciting one of the allowed EPR transitions of
each spin packet. Therefore, the inversion bandwidth (∆ ν = 1/t
p
) ofπ MW
is related to
the isotropic hyperfine splitting a
0
through the selectivity parameter,η = (a
0
t
MW
)/2π .
When η > 1 the preparation pulse is selective and an ENDOR spectrum will be ob-
served, and whenη < 1 (non-selective pulse) the ENDOR spectrum will be suppressed.
Thus, the ENDOR intensity will depend ont
MW
which is described by,
65
I(η )=I
o
√
2η η 2
+

√
2
2
2
(2.54)
in which I
0
is the maximum ENDOR intensity. From Eq. 2.54, we see that I
0
is re-
stricted by the value of η which corresponds to
√
2η η 2
+
√
2
2

2
= 1. A valid solution exists
when

η − √
2
2

2
is positive. Therefore, length oft
MW
that will provide the maximum
ENDOR intensity will be whena
0
t
MW
=
√
2π .
2.7.7 ELDOR-Detected NMR (EDNMR)
Electron-electron double resonance (ELDOR)-detected nuclear magnetic resonance
(EDNMR) is another double resonance-based hyperfine spectroscopy where a NMR
signal is detected through a population change on an EPR transition induced by exci-
tation of an EPR forbidden transition. The forbidden transitions are driven through the
application of two MW frequencies. The first MW frequency utilizes a high-turning
angle (HTA) pulse at a frequency (ν 1
) to excite a forbidden EPR transition (ELDOR),
then an FID or SE sequence at a fixed frequency, ν 0
is used to measure the change in the
echo intensity. When ν 1
− ν 0
= 0, the observed signal is diminished; this is known as
34
MW1( ) ν
0
τ
π/2 π
τ
HTA
(a)
δφ αI
 EDNMR
 
E
4
E
3
E
2
E
1
|+1/2, +1/2⟩
|+1/2, -1/2⟩
|-1/2, +1/2⟩
|-1/2, -1/2⟩
E
4
E
3
E
2
E
1
E
4
E
3
E
2
E
1
MW
RF
(b)
(c)
(d)
MW
τ
π/2 π
τ
RF
π
δφ α I
 ENDOR
 
π
(e)
MW2( ) ν
1
Figure 2.10: (a) In the Davies-ENDOR sequence a first MW pulse is used to
excite one of the two allowed EPR transitions (TLS) as shown in (d), then an
RF pulse is applied to drive an NMR transition and saturate the EPR transition
(e). The ENDOR intensity is detected by a SE sequence in which the intensity is
proportional to the increase in the SE signal. (b) In an EDNMR sequence a HTA
pulse at a fixed frequency ( ν 1
) is used to excite a forbidden (ELDOR) transition
indicated by the blue arrow in (e). As another MW source of frequency ν 0
is swept, the SE intensity at ν 1
= ν 0
will be reduced as the population has
been transferred to a higher energy level. (c) TLS energy diagram shows two
EPR allowed transitions in pink, two allowed NMR transitions in green, and 2
forbidden (ELDOR) transitions in blue (dashed).
the central hole and defines the zero frequency in the EDNMR experiment. Considering
a rectangular MW pulse of length t
p
and amplitude ω
1
, the excitation function of the
zero frequency is given by,
66
f =(ω
1
/ω
eff
)
2
sin
2
(w
eff
t
p
/2) (2.55)
in which ω
2
eff
= ∆ ω
2
+ω
1
, and ∆ ω = 2π (ν 1
− ν 0
). The probability of a forbidden
transition is increased by mixing the states with a small misalignment between the ex-
ternal magnetic field and the hyperfine axis. The corresponding normalized transition
probabilities of the allowed and forbidden EPR transitions are given by,
67
35
I
EPR
=
|ν 2
e
− 1
4
(ν α − ν β )
2
|
ν α ν β (2.56a)
I
ELDOR
=
|ν 2
n
− 1
4
(ν α +ν β )
2
|
ν α ν β (2.56b)
in whichν α,β
are given in Eq. 2.53c. Eq. 2.56 shows that the intensities of the transi-
tions depend on the strength of the hyperfine splitting and the electron ( I
EPR
) or nuclear
(I
ELDOR
) Larmor frequencies, with the first being the largest one. In addition, the in-
tensity of the signal is affected by the efficiency of the change in polarization with the
application of a resonant forbidden transition represented by the flip angle β ,
β EPR
=ω
1
t
HTA
p
I
EPR
(2.57a)
β ELDOR
=ω
1
t
HTA
p
I
ELDOR
(2.57b)
The product β 0
= ω
1
t
HTA
determines the efficiency of the HTA pulse and for the par-
ticular case of β 0
= π , the polarizations of the two allowed transitions are reduced to
zero while the polarization of the second forbidden transition remains unchanged. Each
EDNMR signal is selectively detected by pumping an ELDOR transition and detecting
on the corresponding EPR transition. For instance, the E
1
→ E
4
ELDOR transition is
detected on theE
1
→ E
3
EPR transition. These two contributions to the EDNMR line
intensity can be described by,
67
I
EDNMR
=1− I
EPR
cos

β 0
p
I
ELDOR

− I
ELDOR
cos

β 0
p
I
EPR

(2.58)
36
In the experiment, relaxation processes such asT
1
andT
2
will also determine the length
of the HTA. When T
1
>> T
2
, an exponential decay with non-periodic signal will be
observed. In this case, Eq. 2.58 is described by,
I
EDNMR
=A
0
[1− cos(2πν ELDOR
t
HTA
)exp(− t
HTA
/T
2
)] (2.59)
2.8 Summary
In this chapter, fundamentals on EPR relevant to the present thesis are presented. EPR
spectra are modeled by the Hamiltonian which is constructed based on interactions be-
tween electron spins and nuclear spins with the applied external magnetic field, between
electron spins, between nuclear spins and between electron-nuclear spins. The origin
of each interaction is presented in separate sections. An example of a simple system is
presented to obtain the energy levels and to present how EPR transitions occur utilizing
conventional cw-EPR are also described in detail. The basis for specialized ESR tech-
niques presented in subsequent chapters is also described in section 2.7. The interaction
of the electron spin with a static external magnetic field and and oscillating RF field
is considered. The transformation of the lab frame Hamiltonian to the rotating frame
Hamiltonian using the resonance frequency of the system as the reference frequency is
utilized to simplify interpretation of pulse measurements. Precise information about the
system can be obtained using pulse measurements such as the nutation frequency of the
spin by performing a Rabi experiment. The dephasing timeT
∗ 2
, which correlates to the
intrinsic linewidth of the system can be extracted by performing an FID experiment.
The longitudinal (T
1
) and transverse (T
2
) spin relaxation times can be extracted by per-
forming an inversion recovery and spin echo experiment, respectively. Finally, double
37
resonance techniques are utilized to detect a target spin by taking advantage of the inver-
sion of the dipolar field induced by an inversion pulse (DEER), by inverting nuclear spin
populations to induce NMR transitions and readout using an EPR transition (ENDOR)
or by using a HTA pulse to induce forbidden transitions and detect NMR transitions
(ENDOR). NV ODMR spectroscopy has the same foundations as those of EPR spec-
troscopy. The models used for NV ODMR are shown in section 4.4 and experimental
applications are presented and discussed in chapters 5 and 6.
38
Chapter 3: Surface Chemistry of
Diamond
Carbon forms very stable and strong crystals such as graphite (sp
2
) and diamond (sp
3
).
The pressure/ temperature (P/T) diagram of carbon is shown in Fig. 3.1.
2, 68, 69
Car-
bon forms two stable solids: graphite and diamond and exists as a liquid above 5000
K. The gaseous phase of carbon also exists above 5000 K but occurs at pressures too
low (0-0.15 GPa) for the scale of Fig. 3.1. The boundary between graphite and dia-
mond runs from 1.7 GPa and 0 K to the graphite/diamond/liquid triple point at about
12 GPa and 5000 K (point A). The melting line of graphite extends from point A to
the graphite/liquid/vapor triple point at 0.011 GPa and 5000 K and from point A to
higher temperature and pressure values. Recent work has shown a diamond instability
zone from 55 to 115 GPa where diamond formation ceases and the already formed di-
amonds turn into carbon onions.
69
Once the carbon bonds form into one mode, a huge
amount of activation energy is required to transition between modes. For this reason,
graphite and diamond can both persist in metastable forms far into the P/T region of
thermodynamic stability of the other (graphite-diamond equilibrium line). Diamonds
naturally form deep on earth (down to 120 km below the surface) where high pressure
and temperature (HPHT) conditions are reached. Research to grow diamonds in the lab
replicating HPHT conditions led to the first report of a synthetic diamond in 1954 by
39
General Electric.
2
Their method mixed FeS and graphite at 7.5 GPa and 1600
◦ C using
a belt apparatus. Region I in Fig. 3.1 is the P/T region now utilized for commercial
HPHT grown diamonds from graphite. In greater detail, the transition from graphite to
diamond via HPHT takes place in a small capsule inside an apparatus capable of gener-
ating very high pressures (few GPa). Within the capsule, a carbon starting material, such
as high purity graphite, dissolves in a molten flux of metal catalyst such as iron, nickel
or cobalt, which lowers the temperature and pressure needed for diamond growth. The
carbon material then migrates through the flux towards the cooler diamond seed and
crystallizes on it to form a synthetic diamond crystal.
68
Crystallization occurs over a
period of several days to weeks to grow one or several crystals. Material grown this way
typically has a yellow hue, as a consequence of nitrogen incorporation into the diamond
lattice from the atmosphere and growth materials.
3
Synthesis of diamond at lower temperatures using chemical vapor depostion (CVD)
techniques was also explored by Union Carbide in 1953 but their results were announced
well after the HPHT method was announced by GE.
70
CVD involves a chemical reaction
inside a gas-phase as well as a deposition onto a substrate surface. The CVD conditions
for diamond growth rely on a faster nucleation and growth rate than graphite. The
work by Lander
71
and Hibshman
72
revealed that hydrogen-terminated diamond retains
the unreconstructed (111) surface structure up to 1300
o
C
71
favoring its growth. The
breakthrough result in CVD growth was published in 1978 by Fedoseev, Uspenskaya,
Varnin, and Vnukov
73
describing diamond deposition on high surface area diamond
powder. In this paper, the authors showed that the presence of atomic hydrogen gas has
a critical role on CVD growth of diamond as it inhibits critical graphite nucleation.
The commercial exploration and exploitation of CVD diamonds was possible only
after researchers at the National Institute for Research in Inorganic Materials in Japan
40
0 1000 2000 3000 4000 5000
20
40
60
80
100
120
 
 
Diamond
Onions with sp
2
and sp bonds
3
Diamond
Pressure (GPa)
Graphite
Temperature (K)
Liquid
A Region I
Figure 3.1: The graphite-diamond equilibrium was calculated from thermody-
namic energy values (Diamond: H = 2900 J/mol, V = 3.417 cm
3
/mol, S = 2.38
J/mol K and Graphite: V = 5.298 cm
3
/mol, S = 5.74 J/mol K). The diamond
instability zone was reproduced from Blank et. al.,
69
and the solid-liquid equi-
librium was reproduced from Bundy et. al.
2, 68
published a series of papers describing several methods of low-pressure diamonds. For
instance, the growth conditions of CVD diamonds are created by thermal dissociation of
hydrogen, and a gaseous source of carbon in plasma, with a gas temperature above 2000
o
C.
74, 75
The nucleation and growth of continuous diamond requires a substrate with
refractory characteristics, stable carbide formation and a low thermal expansion coeffi-
cient.
3, 76
The type of energy supply used for CVD diamond growth has a great impact
on the temperature distribution, solubility and internal energy of carbon. Microwave in-
duced plasma enhanced the commercial synthesis of CVD diamonds
77–79
thanks to the
availability of high power microwave sources at 2.45 GHz.
80
41
Diamond substrates are grown or cut into one of their epitaxial axis, most commonly
(100), (111), and (110). Computer simulation has been applied to study the structure,
reconstruction, energetics, and chemical composition of these different planes. The
surface composition of different diamond cuts has been shown to attain a stable config-
uration after undergoing reconstruction under different surface termination types.
81
For
instance, the ideal structure of the (100) surface presents atoms with two dangling bonds
(2 db) (Fig. 3.2(a)). Such a condition is strongly unfavourable from an energetic point
of view, and the surface undergoes a 2× 1 reconstruction
82
(Fig. 3.2(b)). The surface
unit cell is doubled with respect to the bulk one. This condition allows the formation
of surface C-C dimers, so that each surface atom realizes a distorted, unsaturated, sp
3
-
like coordination, thus reducing the number of dangling bonds and lowering the total
energy.
82, 83
In addition, when O and OH are present, a completely terminated diamond
(100) surface is most probably composed of ketone adsorbates.
82
The (111) diamond surface can have one or three dangling bonds. The (111) sur-
face with one dangling bond per surface atoms shown in Fig. 3.2(c) undergoes a strong
2× 1 reconstruction
84
yielding the surface shown in Fig. 3.2(d). The main consequence
of this type of reconstruction is the formation of “zig-zag” chains of C atoms at the
surface, featuring a geometry very close to that of graphite. This configuration allows
for the formation of a delocalizedπ -bond along the surface atoms, which stabilizes the
surface.
83, 85
In contrast, the (111) surface with three dangling bond per C atom main-
tains a 1× 1 unreconstructed surface and it is the least stable (Fig. 3.2(e)). However,
the (111) 1× 1 surface is the most stable when the diamond is terminated with hydrogen
upon treatment or growth with hydrogen plasma
84, 86
(Fig. 3.3(b)) In addition, mono-
valent hydroxyl groups binding upon oxygen-water etching are favored over the 2× 1
reconstruction
87, 88
(Fig. 3.3(c)).
42
(a)
(b)
(c)
(d) (e)
Figure 3.2: (a) (100) 1× 1-unreconstructed, (b) (100) 2× 1-reconstructed, (c)
(111) 1× 1-unreconstructed (1 db), (d) (111) 2× 1-unreconstructed (1 db) and
(e) (111) 1× 1-reconstructed (3 db). Reproduced from Ref
83
Diamond crystals on the nanometer size can be obtained by mechanical grinding of
HPHT crystals. This method uses the rotation or vibration of a ball mill to make the
hard particles strongly impact, grind, and agitate the raw material to crush the samples
into nanoscale particles. NDs prepared by ball milling (especially the precursors are
diamond particles synthesized by HPHT method) are small in size (within 100 nm) and
have high fluorescence defects, which makes them widely used in bioimaging and drug
delivery.
89
Nanodiamonds (NDs) received great attention thanks to their high biocompatibil-
ity,
90
optical properties and fluorescence.
91
These have been possible thanks to the pho-
toluminescence (PL) properties of NDs and their surface chemistry. Therefore we focus
on the understanding of the diamond surface and its tunability for specific applications.
Nanodiamond suspensions tend to form aggregates as large as 1-2 microns in diameter.
43
(a)
(b) (c)
Figure 3.3: (a) (100) relaxed geometry with ketone termination (oxygen atom is
shown in blue) Adapted from Ref.,
82
(b) (111) 1× 1 unreconstructed terminated
with a hydrogen atom (black) Adapted from Ref.,
84
(c) (111) 1× 1 unrecon-
structed terminated with a hydroxyl group. Adapted from Ref.
87
Commonly suspensions of nanodiamonds show a dependence on variation in size based
on the composition and pH of the media they are dispersed in. This means that nan-
odiamonds interact with each other via the functional groups that exist on their surface.
The nanodiamond particle core is a perfect spherical diamond crystallite with a poly-
hedral shell shape. The truncated octahedral structure presents 76% of the (111) faces
that are partially graphitized and 24% of the (100) faces that retain a diamond surface
structure.
91
X-ray diffraction studies have shown that NDs represent a mixture of dia-
monds (sp
3
) and graphite (sp
2
) and that treatment with acids can reduce graphite and
metal impurities.
92
Three of the most common oxygen-related terminating species shown to exist on
the diamond surface are a hydroxyl group and oxygen in either a ketone or an ether
position.
85
In addition, chemisorbed functional groups such as carbonyl (C=O), lactone
[(C=O)O], carboxylic acid [(C=O)OH], cyclic ether (COC), and carboxylic anhydride
[(C=O)O(C=O)] were found on diamond surfaces.
88
To functionalize the surface with a
44
specific molecule, it is important to begin with a homogeneous surface. Homogeniza-
tion methods include hydrogen plasma,
93
fluorinated plasma,
94–96
acid treatments,
97
and
annealing.
Conversion from a hydrogen fluorine or oxygen terminated surface to hydroxyl
groups is a crucial step for grafting of a desired molecule as the nucleophilic charac-
ter of -OH groups helps further reactions with electron-deficient molecules occur more
easily. In addition, its amphoteric character allows it to simultaneously act as a weak
base or a weak acid. A widely used method for molecular attachment on nanoparticles
and substrates is via silanization. Silanes are attractive molecules as they have the ca-
pacity to self-conjugate on a hydroxyl terminated surface. The hydroxyl groups attack
the alkoxy or halogen groups and displace them to form covalent siloxane groups (Si-
O). Silanes are usually composed of silicon and substituents (Si-R
4
) in which R may
be organic, inorganic or a combination of both. The introduction of a nucleophile via
silanization allows to further conjugate any molecule of interest, for instance, via click
chemistry. The azide-alkyne cycloaddition is a modular click chemistry approach in
which very high yields are achieved, they are highly selective for a single product, and
the reaction operates under simple reaction conditions in a benign solvent.
98
In this
work we utilize a bromine terminated silane to perform a nucleophilic acyl substitution
to introduce an azide group and perform click chemistry reactions.
In the following sections, we describe the functionalization and characterization of
nanodiamonds and diamond substrates with different molecules. We investigate the
parameters that affect the substrate functionalization such as crystal cut, and homoge-
nization procedures. We demonstrate the grafting of 4-hydroxy-TEMPO on different
45
diamond substrates via the characterization of the triazole ring using XPS. Crucial in-
sight into the diamond surface termination that can be utilized to introduce different
linkers and that may apply to other substrates is also discussed.
3.1 Nanodiamond Functionalization
Nanodiamond functionalization with nitroxide radicals has been previously shown and
the reader is referred to Romanova et.al.
99
for reaction details. Here we present an
overview of the reaction scheme to characterize the reaction upon ND functionalization
with different species.
The reaction scheme for ND surface homogeneization is shown in Fig. 3.4. For each
reaction batch, 250 mg of 50 or 100 nm Engis Hyprez (R) diamonds were used. The
nanodiamonds were transferred into a 50 mL round bottom flask with a teflon cap, then
dispersed in 20 mL of an acid mixture of H
2
SO
4
/HNO
3
(1:3) and stirred at 75
◦ C for
72 h. Upon reaction completion, the nanodiamonds were recovered via centrifugation
then dispersed in 40 mL of a 0.1 M NaOH solution and stirred at 90
◦ C for 2 h. The
nanodiamonds were recovered via centrifugation then dispersed in 20 mL of a 0.1 M HCl
solution and stirred at 90
◦ C for 2 h. The nanodiamonds are recovered via centrifugation
and rinsed with MQ water following a centrifugation/re-dispersion process until the
pH of the supernatant remains unchanged. The nanodiamonds were lastly rinsed with
filtered acetone and let dry overnight in a dessicator under a gentle nitrogen flow.
The dry acid-treated nanodiamonds (ND-acid) are transferred into a 50 mL round
bottom flask with a teflon cap, dispersed in 30 mL of tetrahydrofuran and stirred at 60
◦ C, then 6 mL of a 1.0 M solution of borane in tetrahydrofuran (THF) is added dropwise
and the dispersion is stirred for ∼ 24 h. The dispersion is hydrolyzed with a 2.0 M
HCl solution and bubbling is observed. The nanodiamonds are then rinsed with MQ
46
O
O
H
OH
O
H
O
OR
Nanodiamond
Surface
O
O
OH
O
Nanodiamond
Surface
OH
OH
OH
HNO /H SO
3 2 4
75 C / 72 h
o
O
OH
Nanodiamond
Surface
OH
OH
OH
OH
OH
OH
BH -THF
3
60 C / 24 h
o
Acid-treated (ND-acid) Hydroxylated (ND-OH)
Figure 3.4: The nanodiamonds are treated with a mixture of acids at high
temperature to oxidize existing surface functional groups into carboxylic acid
groups yielding ND-acid. The surface is then hydroxylated by utilizing borane
as a reducing agent to further reduce ketones into OH groups.
water following a centrifugation/re-dispersion process until the pH of the supernatant
remains unchanged. The nanodiamonds are lastly rinsed with filtered acetone and let
dry overnight in a dessicator under a gentle nitrogen flow.
The hydroxylated nanodiamonds (ND-OH) are transferred into a 50 mL round bot-
tom flask with a rubber cap and dispersed in 20 mL of dry toluene. The solution is
stirred in an inert environment and 1 mL of 3-bromopropyltrichlorosilane is added drop-
wise. The flask is sealed and stirred at 60
o
C for 24 h. Upon reaction completion, the
nanodiamonds are rinsed four times with toluene and once with acetone following a
centrifugation/re-dispersion process. The nanodiamonds are let dry overnight in a dessi-
cator under a gentle nitrogen flow.
The bromine-terminated nanodiamonds (ND-Br in Fig. 3.5) are transferred into a
50 mL round bottom flask with a teflon cap, dispersed in 30 mL of a saturated solution
of sodium azide in dimethyl formamide (DMF) and stirred at 80
o
C for 24 h. The
nanodiamonds are rinsed four times with MQ water and once with acetone following
a centrifugation/re-dispersion process. The nanodiamonds are let dry overnight in a
dessicator under a gentle nitrogen flow.
The azide-terminated nanodiamonds (ND-N
3
in Fig. 3.5) are transferred into a 50
mL round bottom flask with a teflon cap, dispersed in 30 mL of acetonitrile with 80 mg
47
sat. NaN solution
3
DMF 80 C / 24 h
o
N
3
N
3
N
3
ND-N
3
Figure 3.5: The oxygen atom in the hydroxyl groups on the nanodiamond sur-
face as strong nucleophiles displaces the chlorine groups on the silane com-
pound. The hydrogen atom originally attached to the hydroxyl group leaves
forming HCl. The bromine terminated silane attached to the nanodiamond sur-
face forming ND-Br. Sodium azide in DMF is used to displace the bormine
atom introducing an azide group (ND-N
3
).
of alkyne-terminated 4-hydroxy-TEMPO radical dissolved in 1 mL of triethylamine and
80 mg of Cu(I). The reaction is stirred at RT for 24 h. The nanodiamonds are rinsed four
times with acetonitrile and once with acetone following a centrifugation/re-dispersion
process. The nanodiamonds are let dry overnight in a dessicator under a gentle nitrogen
flow to yield nitroxide functionalized diamonds (NDs-TEMPO) (Fig. 3.6).
For the attachment of the tetrathiatriarylmethyl (TAM-trityl) radical, 20 mg of NDs
were dispersed in acetonitrile, 0.5 mg of Cu(I) and 0.5 mg of the clickable TAM (Fig.
3.6) radical were added to the reaction flask. After 24 h, the NDs were rinsed with
acetonitrile at least 4 times yieldgin ND-TAM.
3.1.1 FTIR Characterization
The functionalized nanodiamonds (ND-TEMPO and ND-TAM) were characterized us-
ing FTIR. The infrared spectra were collected with a Bruker Vertex 80v FTIR spectrom-
eter with 32 scan averaging and 4 cm
− 1
resolution. Solid pellets of NDs were prepared
by using∼ 1 mg in∼ 99 mg of KBr. The solids were crushed and mixed using an agate
mortar. The solid mix was placed in a 25 mm pellet press set and a pressure of 2× 10
4
psi is applied for 10 min. The residual moisture is extracted with a pump.
48
N
3
N
3
N
3
ND-N
3
ND-TEMPO
N
N
N
N O
_
N
3
N
3
ND-TAM
N
N
N
N
N
N
N O
_
N
N
N
N O
_
TAM
Clickable
TAM =
Alkyne terminated
4-hydroxy-TEMPO
Cu(I) + TEA (RT / 24 h)
Cu(I) + TEA (RT / 24 h)
Figure 3.6: A copper catalyzed azide-alkyne cycloaddition is used to introduce
nitroxide (a) or trityl (b) radicals. An alkyne group is introduced to the radicals
to conjugate with the existing azide group in NDs froming a triazole ring form-
ing ND-TEMPO (a) and ND-TAM (b).
The NDs surface contains several functional terminations such as -CH, -CO, -C=O,
-COOH amongst others. The purpose of acid cleaning with a mixture of strong acids is
to reduce some of these terminations to obtain hydroxyl groups (-OH). This latter type
of functional groups is essential for the introduction of a reactive group via silaniza-
tion. Silanes are favorite candidates since they easily bind to the –OH groups by auto-
condensation. A bromine terminated silane is selected as it can be effectively substituted
by and azide group. The nanodiamond surface is now functional and additional groups
such as alkyne terminated compounds can be introduced via the copper catalyzed click
49
chemistry reaction. Fig. 3.7(a) shows the transmission spectra of NDs at different reac-
tion steps.
A big prominent feature from 3000 to 3600 cm
− 1
is always observed. Whereas, the
NDs surface is expected to contain hydroxyl groups, it is very likely that the asymmetric
stretching of the OH groups in this region corresponds to moisture captured by the KBr
in the pellet or adsorbed on the surface of the NDs. Carbonyl groups located at 1800
cm
− 1
and 1086 cm
− 1
are also observed. These correspond to unreduced groups on the
ND surface. The peak at 1098 cm
− 1
corresponds to the C-Si-O linkage formed by the
silane. The success of the step ND-Silane to ND-Azide, however, is determined by the
appearance of the asymmetric stretching peak of the azide group at 2100 cm
− 1
.
The intensity of the azide peak is reduced as the reaction proceeds because of the
linkage of the alkyne radical through a triazole. The reduction of the peak can be used
as a reference of the yield of the reaction from ND-Azide to ND-Nitroxide or ND-Trityl.
In Fig. 3.7(b), the azide region of these three spectra are plotted with the same reference
line. It can be observed that the reduction of the azide peak is greater for the reaction
with the trityl radical. By analyzing the peak reduction and areas, the reaction yield for
the nitroxide radical is obtained to be 99% and for the trityl radical is 78%.
The main difference in the reaction yield of trityl compared to nitroxide where high
yields is believed to be due to the bulky aryl groups on the trityl molecule. In spite of the
click chemistry reaction being fast and successful, it may be strongly hindered by steric
impediment between trityl molecules. Thus, the number of unreacted azide groups is
expected to be larger decreasing the yield of the reaction as compared to the nitroxide
radical.
50
4000 3500 3000 2500 2000 1500 1000
 
 
% Transmission
Wavenumber (cm )
-1
2020 2060 2100 2140 2180
 
 
 
Wavenumber (cm )
-1
ND-OH
ND-Br
ND-N
3
ND-TEMPO
ND-TAM
(a) (b)
ND-N
3
ND-TEMPO
ND-TAM
-OH
-N
3
-C=O
-C-Si-O Figure 3.7: (a) FTIR spectra of 100 nm NDs at every step of the reaction.
The dashed black lines identify the modes of different groups. (b) The reaction
yield is based on the reduction of the azide peak at 2100 cm
− 1
after the click
chemistry step.
3.2 Diamond Substrate Functionalization
Here we present the complete methodology to successfully attach nitroxide radicals on
a diamond substrate. In the development of the diamond substrate reaction scheme,
we started following the procedure previously used for nanodiamonds.
99
However, we
realized that the reaction conditions have to be further optimized: i) to reduce the con-
tact time of the diamond surface with strong acids during surface homogenization to
avoid deep surface etching, ii) to achieve higher yields in every step of the reaction (See
Appendix), and iii) for the type of diamond substrate utilized. For the project, the dia-
mond substrates used were purchased from Element Six: D43, D48 and D50 are type
IIa diamonds, D51 is and electric grade (EG) (111) diamond, and D41 is an EG (100)
diamond. The proposed reaction conditions utilized for these diamonds are summarized
in Fig. 3.8.
The overall reaction scheme consists of three major sections: (a) surface preparation,
(b) silanization and (c) functionalization of a radical via click-chemistry procedure. The
51
surface preparation consists of the surface homogenization with hydroxyl (-OH) groups.
The aim is to control the number of -OH groups available for higher reaction yields.
As shown in Fig. 3.8(a), the hydroxylated diamond surface can be obtained through
cleaning with acidic (piranha) solution followed by plasma etching or reduction with
borane to achieve higher OH densities.
piranha
RT, 10 min
1 mM silane
o
(dry toluene, -10 C, 48 h)
NaN sat. solution
3
(DMF, RT, 24 h)
CF plasma
4
F
F
F
F
F
F
F F F F
F F
(20 sscm, RT, 2 min)
3 M silane
o
(dry toluene, 80 C, 24 h)
LTLC
HTHC
Plasma etching
Borane Reduction
Acid cleaning
(a)
(b)
Silanization
Click Chemistry
H O (vap)
2
2 o
(0.085 ft /h, 500 C, 1 h)
BH ‑THF
3
o
(60 C, 24 h)
TEMPO + Cu(I)
(TEA, RT, 24 h)
(c)
Figure 3.8: (a) Surface preparation. The as purchased diamond is acid cleaned
in piranha solution at RT for 10 min. D-acid is then hydroxylated via plasma
etching (pink path) or via borane reduction (green path). (b) Silanization. The
HTHC method is performed at a high silane concentration (3 M) and high tem-
perature (80
o
C). The LTLC method is performed at low silane concentration
(80µ M) and low temperature (-10
o
C). (c) Click Chemistry step. All the reac-
tion schemes follow the same procedure to replace the bromine group with an
azide group and a copper catalyzed azide-alkyne cycloaddition.
52
For surface preparation, acid cleaning of the diamond substrate is shown in Fig.
3.8(a) in black and performed as follows. The diamond crystal (3× 3× 0.5 mm) is im-
mersed in 10 mL of piranha solution H
2
O
2
/H
2
SO
4
(1:3) and stirred at room temperature
for 10 min. The diamond is rinsed with MQ water under sonication for 10 min three
times and dried with dust-free tissue to yield D#-acid.
The borane reduction option shown in Fig. 3.8(a) in green is performed by transfer-
ring the dry acid-treated diamond (D#-acid) into a flask with 30 mL of tetrahydrofuran.
A stirring bar magnet is used to stir the solvent to create a vortex. Then 6 mL of a 1.0
M solution of borane in tetrahydrofuran (THF) is added dropwise and the dispersion
is stirred at 60
◦ C for∼ 24 h. The solution is hydrolyzed with a 2.0 M HCl solution
and bubbling is observed. The diamond substrate is then rinsed with MQ water under
sonication for 10 min three times and dried with dust-free tissue to yield D#-OH.
For the plasma etching option shown in Fig. 3.8(a) in pink a fluorine gas is utilized.
Fluorine has shown to protect the diamond surface from oxidation and its low adsorption
energy makes it possible to create monolayers with high stability.
100
The plasma etching
procedure is performed by mounting the acid treated diamond (D#-acid) onto a silicon
wafer using photoresistant solution and further exposed to a 20 sscm gas flow at 100 W
for 2 min at ambient temperature. After the process is finished the diamond is cleaned
with acetone in a sonication bath overnight to remove any photoresistant solution yield-
ing D#-F. Next, to exchange the fluorine atoms water vapor annealing is performed.
93
The exchange of fluorine by hydroxyl groups has been studied before on silicon sur-
faces.
96, 97
Carbon possesses similar bonding properties as silicon since they belong to
the same group. Therefore, we propose the following reaction scheme:
− C− F
(substrate)
+H− OH
(vap)
→− C− OH
(susbtrate)
+HF ↑ (3.1)
53
Following the method of Yoshida, et al.,
93
the fluorinated surface is exposed to a water-
vapor annealing treatment to create hydroxyl groups yielding D#-OH. For this step, a
flask is filled with MQ water, sealed with a septum, and the air inside the flask was
replaced with nitrogen after bubbling for 30 min. The diamond crystal was placed in a
furnace and connected to the flask. A steady nitrogen flow of 0.085 ft
2
/h was applied
while keeping the pressure inside the quartz below 0.02 MPa. The nitrogen flow was
let pass through the system for 30 min to evacuate any oxygen remaining inside the
chamber furnace. Then, bubbling of water is applied for another 30 min until the flow
stabilized. The furnace is ramped to 100
o
C and allowed to stabilize for 30 min. A
second ramp to 300
o
C over 30 min is applied and then a third one up to Tf = 500
o
C.
Tf is applied for 60 min and the furnace is ramped back down to RT according to the
furnace’s manual procedure.
The silanization procedure is performed either at high temperature high concen-
tration (HTHC) or low temperature low concentration (LTLC) conditions as shown in
Fig. 3.8(b). In the HTHC method the hydroxylated diamond (D#-OH) is immersed in
20 mL of dry toluene. The solvent is stirred in an inert environment and 1 mL of 3-
bromopropyltrichlorosilane is added dropwise. The flask is sealed and stirred at 60
o
C
for 24 h. Upon reaction completion, the diamond is rinsed four times with toluene and
once with acetone under sonication for 10 min (each) and dried with dust-free tissue to
yield D#-Br. In the LTLC method the acid clean diamond (D#-acid) is further immersed
in a solution containing 80µ L of 3-aminopropyltriethoxysilane in 1 mL of toluene and
let react at -10
◦ C for 2 days. The diamond is rinsed with toluene, followed by a mixture
of toluene and acetone and a last time with acetone in a sonication bath for 10 min with
each solvent. The grafted silane is allowed to stabilize on the diamond surface for two
54
days in which the diamond is kept on a sealed container under an inert atmosphere to
yield D#-Br.
Finally, the functionalization with nitroxide radicals shown in Fig. 3.8(c) is per-
formed by immersing the bromine-terminated diamond (D#-Br) in 30 mL of a saturated
solution of sodium azide in dimethyl formamide (DMF) and stirred at 80
o
C for 24 h.
The diamond is rinsed four times with MQ water and once with acetone under sonica-
tion for 10 min (each) and dried with dust-free tissue. The azide-terminated diamond
(D#-N
3
) is immersed in 30 mL of acetonitrile, 80 mg of alkyne-terminated 4-hydroxy-
TEMPO radical, 1 mL of triethylamine, and 80 mg of Cu(I). The reaction is stirred at
RT for 24 h. The diamond is rinsed four times with acetonitrile and once with acetone
under sonication for 10 min (each) and dried with dust-free tissue to yield D#-TEMPO.
3.2.1 XPS characterization
Next, we discuss the characterization of the grafted substrates by X-Ray Photoelectron
Spectroscopy (XPS). The measurements were performed in a Kratos Axis Ultra instru-
ment. A low energy ion beam gun was used for all the measurements to compensate
the surface charge of the insulating substrates. A monochromatic Al Kα X-Ray source
with∼ 300µ m spot size and a 0
o
takeoff angle (TOA). The TOA is defined as the angle
between the sample surface normal and the axis of the XPS analyzer lens. The sur-
vey measurements were collected with an analyzer pass energy of 120 eV (single scan)
whereas the high-resolution measurements were taken using an analyzer pass energy of
40 eV (5 scans). Binding energies (BEs) were referenced to the hydrocarbon C 1s peak
at 285 eV . Two to four spot areas of each sample type and replicates were analyzed. In
addition an acid cleaned sample was used as a reference for measurements (D48-acid).
55
Quantitative analysis can be determined by curve-fitting and measuring the areas of
the appropriate peaks. The number of photoelectrons per second in a specific spectra
peak is given by,
101
I =nfσθyλAT (3.2)
in which n is the number of atoms of the element per cubic centimeter of the sample, f
is the x-ray flux in photons/cm
2
-sec, σ is the photoelectric cross-section for the atomic
orbital of interest in cm
2
,θ is an angular efficiency factor for the instrumental arrange-
ment based on the angle between the photon path and the detected electron, y is the
efficiency in the photoelectric process of the normal photoelectron energy, λ is the mean
free path of the photoelectrons in the sample, A is the area of the sample from which
photoelectrons are detected, and T is the detection efficiency for electrons emitted from
the sample. Eq. 3.2 can be rewritten in terms of the element density:
n=I/fσθyλAT (3.3)
The denominator in Eq. 3.3 is known defined as the atomic sensitivity factor, S. If we
consider a strong line from each of two elements, then:
n
1
n
2
=
I
1
/S
1
I
2
/S
2
(3.4)
It is certainly true that quantities such as σ and λ vary somewhat from material to ma-
terial, but the ratio of each of the two quantities remains nearly constant. Thus for any
spectrometer, it is possible to develop a set of relative values of S for all of the elements.
56
A general expression for determining the atomic percentages of any constituent in a
sample can be written as an extension of Eq. 3.3
x
j
=
A
j
P
n
j=1
(A
j
/S
j
)
(3.5)
in whichA
i
represents the peak areas andS
i
represents the atomic sensitivity factors for
the j-th element. To avoid counting the contribution of the carbon atoms in the aliphatic
tail of the silane molecule, the Si 2p peak was used as a reference. The reason for this is
that the ratio within the silane molecule of Si:C
aliphatic
is 1:3 which must be preserved
(Fig. 3.9). So the atomic percentage of carbon is determined by,
%C =
A
C1s
S
C1s
− 3
A
Si2p
S
Si2p
(3.6)
Figure 3.9: Scheme of (3-Bromopropyl)trichlorosilane, used for the silaniza-
tion step of the diamond surface
Furthermore, for an assumed monolayer coverage, there is negligible scattering
within the adsorbed surface layer. In this case, the number density can be obtained
by,
102
N
X
=ρ C
λ C

S
X
S
C

A
X
A
C

cos(θ ) (3.7)
in whichρ C
is the number density of carbon atoms in diamond (1.76× 10
23
atoms/cm
3
),
λ C
is the inelastic mean free path of electrons in diamond at different electron energies
57
calculated by interpolation of the values obtained by Tanuma et. al.
103
S
C
and S
X
are
the instrument specific atomic sensitivity factors (ASF) of the element “X” and carbon,
A
X
andA
C
are the measured integrated peak areas of the element “X” and carbon and
θ is the take off angle defined as the angle between the analyzer and the surface normal
(in our case,θ = 0).
3.2.2 Results and Discussion
The HTHC method was implemented as a variation of the reaction scheme and con-
ditions used for nanodiamonds. Prior to functionalization of diamond substrates, we
tested the HTHC method on glass substrates shown in Appendix 6.4. We did not ob-
serve a successful functionalization of the bromine terminated silane nor azide. Whilst
the surface termination of glass has a higher density of hydroxyl groups, the surface in-
teraction might have an easier molecule access for a smoother surface such as diamond.
For this reason, we functionalized D50 up to the azide step (D-N
3
) shown in Fig. 3.8
(green path). As seen in Fig. 3.10(a), the survey spectrum shows the C 1s and O 1s
peaks expected from a clean diamond surface. No signals around 400 eV or 200 - 50 eV
were observed even in different areas. The high-resolution Si 2p spectrum (Fig. 3.10(b))
confirms the non-existence of Si atoms on the diamond surface.
Surface functionalization of glass and silicon substrates has been successfully per-
formed previously,
96, 104, 105
and in most cases the use of strong acids is sufficient to
homogenize the surface with hydroxyl groups. However, the silanization step is highly
dependent on temperature, silane concentration and the molecule size.
106
In nanoparti-
cles, surface areas can be very large due to smaller particle size or porosity, so the use
of high silane concentrations is commonly implemented.
107
In contrast, the functional
58
0 600 500 400 300 200 100
 
 
98 100 102
 
Binding Energy (eV)
Binding Energy (eV)
Signal Intensity (a.u.)
D50 - N (HTHC)
3
D43 - Br (LTLC)
Si 2p
 
D50 - N (HTHC)
3
D43 - Br (LTLC)
O 1s
C 1s
silane
(a) (b)
 
 
 
 
 
 
 
 
404 402 400 398 396 394 392
 
 
74 72 70 68 66 64
D43 - Br (LTLC)
Br 3d
Binding Energy (eV)
Binding Energy (eV)
(c) (d)
D43 - N (LTLC)
3
N 1s
D43 - N (LTLC)
3
Expected Signal
D43 - N (LTLC)
3
N 1s
Signal Intensity (a.u.)
Figure 3.10: (a)Survey XPS of D50 up to azide step following the HTHC re-
action method and D43 up to silane (light blue) and azide (dark blue) steps
following the LTLC reaction method. Oxygen and carbon signals are observed
for both samples. The silane signals are shown in the 200-50 eV region for D43
and the nitrogen region indicated by a red arrow. (b) High resolution scan for Si
2p. A clear peak is observed for D43 at 100 eV . (c) High resolution Br 3d region
of D43 shows the appeareance of bromine upon silanization (D43-Br) and the
reduction of Br peak for D43-N
3
(d) High resolution N 1s scan for D43-N
3
. A
single peak is observed for the functionalized crystal. A dashed red line shows
the expected bimodal signal of an azide species.
area in substrates is much smaller (∼ 4 - 8 orders of magnitude). Therefore, we de-
cided to optimize the reaction conditions using glass substrates (see Appendix 6.4). The
use of a lower silane concentration and temperature avoids close contact between silane
molecules hindering their capacity to self-condense and polymerize. Longer reaction
time compensates for the slow molecule movement and allows longer interaction of the
59
silane molecules with the substrate. For this reason we referred to the second method
as low temperature low concentration (LTLC). After observing a successful functional-
ization of glass (see Appendix 6.4), we functionalized D43 up to the silane step (D-Br)
shown in the main reaction scheme in Fig. 3.8 (black arrows).
The halogen terminations (chlorine and bromine) of the silane were used as a refer-
ence of the condensation of the silane on the diamond surface and the yield of the silane
to azide step. Fig. 3.10(a) shows the survey spectrum for the silanization step. The full
condensation of the silane on the surface of the substrate is easily recognizable by the
absence of the chlorine atoms and the appeareance of silicon and bromine signals in the
lower BE region (200 - 50 eV). Additionally, the high-resolution Si 2p and Br 3d spec-
trum (Fig. 3.10(b) and (c)) show strong signals with a Br/Si ratio of∼ 1:1. These signals
are observed across different areas in the diamond substrate. The stability of the silane
molecule was studied in glass substrate under different conditions. The silane molecule
showed the best stability under storage in contact with air.
Upon successful observation of the silane molecule in the diamond surface, the
bromine was exchanged with the azide group. Fig. 3.10(a) shows the disappearance
of the bromine peaks in the survey spectrum but two peaks corresponding to Si 2s and
Si 2p. This confirms the exchange of the terminal group (bromine) only while preserving
the -C-O-Si link. The survey spectrum also shows only a trace of signal in the nitrogen
region (∼ 400 eV), and the N 1s high resolution spectrum (Fig. 3.10(d)) confirms this
signal. At the same time, the bromine peak intensity (Fig. 3.10(c)) is reduced 82%.
Upon further analysis of the nitrogen signal on Fig. 3.10(d), we overlap the charac-
teristic lineshape of the azido group (red dashed line)
104, 108–110
to our data. Even though
the atomic percent of nitrogen is almost 1% of the total surface groups, the azide sig-
nal is not well defined. The azido group forms two different stable configurations upon
60
linkage to an R-group (R-N
3
), in which either of the outer nitrogen atoms can bear a
negative charge at a given time (R - N
− = N
+
= N or R - N = N
+
= N
− ) while the middle
nitrogen bears a positive charge. The difference in electronegativity that each nitrogen
atom carries at a given time, gives rise to two different types of nitrogen species which
are observed at different binding energies in the XPS spectrum. However, an unlinked
azide group will exist as a single structure in which the outer nitrogen atoms bear a
negative charge (each) at all times [N
− = N
+
= N
− ]
− .
For D43-N
3
(LTLC), five different sample areas were analyzed and the nitrogen sig-
nal was observed consistently suggesting that a molecule containing nitrogen is present.
At this stage the loss of definition of the azide signal can be due to a degradation of
the azide molecule under continuous X-Ray exposure which has been previously ob-
served,
104
or to the presence of adsorbed azide to the surface rather than linked. The
presence of a nitrogen signal is accompanied by a reduction of the bromine peak which
suggests that the bromine was displaced. From previous experiments in glass, we ob-
served that the silane molecule has an excellent stability so the replacement of bromine
is most likely due to a nucleophilic substitution. Nonetheless, the nitrogen density is at
least one order of magnitude lower than the density reported for azide molcules attached
to substrates,
108, 111
which shows overall a low concentration of azide molecules.
Therefore, we seek to improve the nitrogen density. To achieve this, it is necessary
to begin with a large amount of hydroxyl groups. While acid treatment of the diamond
oxidizes some of the functional groups, not all of them are fully oxidized into -OH.
Mild plasma etching treatments have shown to homogenize the diamond surface with
a desired functional group like hydrogen.
93
The advantage of etching treatments with
61
Reaction Step %C %Br %N %F %O
D43-Br (LTLC) 96(0.9) 1.1(0.2) - - -
D43-N
3
(LTLC) 97(1.0) 0.2(0.3) 0.9(0.2) - -
D43-F (plasma) 76(0.5) - - 21(3.5) 6.8(0.8)
D43-OH (plasma) 87(0.8) - - - 13(0.8)
D43-Br (plasma) 85(5.6) 4.8(2.7) - -
D43-N
3
(plasma) 94(1.0) 0.8(0.3) 1.6(0.6) - -
D41-Br (LTLC) 23(6.3) 26(7.1) - - -
D41-N
3
(LTLC) 74(5.2) 2.9(1.3) 4.9(1.2) - -
D51-F (plasma) 32(0.2) - - 59(3.1) 9(3)
D51-OH (plasma) 56(9.3) - - - 44(9.3)
D51-Br (plasma) 83(5.5) 17(5.5) - - -
D51-N
3
(plasma) 93(5.0) 1.3(0.7) 5.6(4.2) - -
Table 3.1: Quantification of surface atoms at different reaction steps. The
atomic percentages were calculated using Eqs. 3.5 and 3.6, they represent the
average of five different areas analyzed on the substrates. The numbers in paren-
thesis corresponds to the standard deviation. D43 is a type IIa diamond, D51 is
and electric grade (EG) (111) diamond, and D41 is an EG (100) diamond.
plasma is that the creation of monolayers is possible upon adjustment of the etching con-
ditions. Here we propose plasma etching of the diamond surface to introduce fluorine
groups (Fig. 3.8 pink pathway). The experimental details are provided above.
We performed plasma etching on D43 and D51 to fluorinate the diamond surface.
Figs. 3.11(a) and3.12(a) shows the survey XPS spectrum of the fluorinated diamonds in
pink. The F 1s high resolution spectrum (Figs. 3.11(b) and 3.12(b)) show a single peak
at 686.7 eV . The atomic percentages (Table 3.1) show a 4:1 and 1:2 carbon to fluorine
ratio D43-F and D51-F, respectively. In the case of D51, two additional carbon species
are also observed in Fig. 3.12(c). The peak at 284.6 eV corresponds to the signal of
62
Reaction Br density N density
Step (atoms/cm
2
) (atoms/cm
2
)
D43-Br (LTLC) (7± 3)× 10
13
D43-N
3
(LTLC) (7± 1)× 10
12
(7± 5)× 10
13
D43-Br (plasma) (4± 3)× 10
14
D43-N
3
(plasma) (6± 2)× 10
13
(3± 2)× 10
14
D41-Br (LTLC) (1.2± 0.5)× 10
16
D41-N
3
(LTLC) (2± 1)× 10
14
(7± 3)× 10
14
D51-Br (plasma) (1.5± 0.6)× 10
15
D51-N
3
(plasma) (1.1± 0.7)× 10
14
(9.4± 7.7)× 10
14
Table 3.2: Quantification of surface coverage. The density of bromine and
nitrogen for silanization and azide steps were calculated using Eq. 3.7 and they
represent the average of five different areas analyzed on the substrates. The
numbers in parenthesis corresponds to the standard deviation.
aliphatic carbon (C-C), and the peaks located at 288.9 and 291.2 eV are assigned to -C-
F and -C-F
2
, respectively. Fluorine, as the most electronegative element has a marked
effect on the core level binding energy of the atom to which it is linked. This effect
leads to an important displacement toward higher binding energies. The assignment of
the peaks is based on the difference in binding energies,∆ E, with respect to the aliphatic
carbon. The∆ E for the peaks observed in the C 1s spectrum in Fig. 3.12(c) from right
to left are 4.4 eV and 6.7 eV . These values are in excellent agreement with previously
reported values for fluorine plasma exposed surfaces
102
where∆ E = 4.4 eV is assigned
to –C-F and∆ E = 6.7 eV to -C-F
2
, both cases when the fluorine is covalently attached
to the surface.
Next, we proceed to expose the crystals to water vapor annealing to exchange the flu-
orine groups. In both cases, the complete disappearance of the fluorine peak is observed
(Figs. 3.11(b) and 3.12(b)), indicating a full -C-F to -C-OH conversion. In addition for
63
 
 
 
 
 
 
 
0 800 600 400 200 675 695 690 685 680
78 74 70 66 415 410 405 400
(a) (b)
(c) (d)
Signal Intensity (a.u.) Signal Intensity (a.u.)
Binding Energy (eV)
Binding Energy (eV) Binding Energy (eV)
Binding Energy (eV)
Br 3d
N 1s
F 1s C 1s
N 1s
silane
F 1s
 
 
 
D43 - N
3
D43 - OH
D43 - Br
 
 
D43 - F
 
D43 - OH
 
D43 - F
 
 
D43 - N
3
D43 - Br
 
D43 - N
3
ΔE = 3.76 eV
D43-TEMPO
D43-TEMPO
Figure 3.11: (a) Survey XPS of every step of the reaction. Fluorine signal is
observed after plasma etching (peak∼ 690 eV in pink). The silane signals are
shown in the 200-50 eV region and the nitrogen region indicated by a red arrow.
(b) F 1s high-resolution spectrum. The fluorine signal disappears after anneal-
ing with water vapor. (c) Br 3d high-resolution spectrum. Bromine signal is
observed after silanization and the peak amplitude is monitored for subsequent
reaction with azide. (d) N 1s high-resolution spectrum. Two peaks with a sepa-
ration of 3.76 eV is observed. This signal is characteristic of azide as different
resonant structures exist when linked to diamond (see text for full explanation).
D51-OH, the disappearance of -C-F
2
and -C-F groups covalently attached to the sur-
face proves the cleavage between carbon and fluorine (Fig. 3.12(c)). Surprisingly, we
observed a 6x increase atomic percent of oxygen for D51-OH(plasma) as compared to
D43-OH (plasma) after the same procedure, suggesting a higher density and potentially
higher surface coverage. To determine the actual coverage, we proceed to silanize the
surface of both crystals. Figs. 3.11(a,c) and 3.12(a,d) show the successful linkage of
the silane molecule to the surface as silicon and bromine peaks are observed. However,
the bromine percent of D51 is∼ 3.5x higher than for D43, and the bromine density is an
64
order of magnitude higher. In addition, the standard deviation shows a more homoge-
neous distribution for D51. This verifies a higher coverage of the diamond surface with
bromine groups for D51 as suggested by a higher oxygen percent on the previous step
for the same crystal.
Upon exchange of bromine with azide, we observe a decrease of the bromine signal
(Figs. 3.11(c) and 3.12(d)), and the characteristic azido feature is observed in Figs.
3.11(d) and 3.12(e). In agreement with a lower surface coverage, D43-N
3
(plasma) has a
lower nitrogen density but it is important to note that the reaction yield is also lower, 86%
compared to 93% for D51-N
3
(plasma). The difference in surface morphology between
D43 and D51 demonstrates to play a crucial part for diamond surface functionalization.
D43 is a CVD grown (100) type IIa diamond while D51 is an EG (111) diamond. This
is consistent with the availability and transformation of groups at the surface of (100)
and (111) diamonds. For instance (111) diamonds have almost 3x more carbon atoms
available at the surface, and the formation of three bonds versus two bonds per carbon
as compared to (100). Additionally, in comparison with the LTLC method, we see that
plasma etching of D43 helped creating a more homogeneous surface and improve the
bromine coverage. However, based on the C:F atomic percents, the surface was not fully
covered yielding lower coverage for subsequent reaction steps.
To further understand the dependence of the surface termination on diamond, we
functionalized D41 following the LTLC method. Fig. 3.13(a) shows a successful func-
tionalization with bromine groups and over a 100 fold increase on the bromine percent
with respect to D43-Br(LTLC) (Table 3.1). This result shows an additional dependence
of the surface termination based on the diamond purity. D41 is an electric grade dia-
mond with < 10
14
cm
− 3
N impurities and low point defect material. The latter is very
65
 
 

(a) (b)
408 404 400 396
72 70 68 66 64
Binding Energy (eV)
(c)
(d)
C 1s
N 1s
silane
F 1s
0 800 600 400 200
Binding Energy (eV)
Binding Energy (eV)
675 695 690 685 680
F 1s C 1s
Binding Energy (eV)
-C-F2
-C-F
-C-C
292 288 284 280 294
 
 
 
D51-N 3
D51-Br
 
D51-F
412
D51-OH
D51-TEMPO
 
 
D51-F
D51-OH
 
 
D51-F
D51-OH
 
 
 
D51-N 3
D51-Br
D51-OH
D51-TEMPO
 
 
 
D51-N 3
D51-Br
D51-OH
D51-TEMPO
Br 3d N 1s
Binding Energy (eV)
(e)
Signal Intensity (a.u.)
Signal Intensity (a.u.)
Figure 3.12: (a) Survey XPS of every step of the reaction. Fluorine signal is
observed after plasma etching (peak∼ 690 eV in pink). The silane signals are
shown in the 200-50 eV region and the nitrogen region indicated by a red arrow.
(b) F 1s high-resolution spectrum. The fluorine signal disappears after anneal-
ing with water vapor. (c) C 1s high-resolution spectrum shows different types of
carbon linked to fluorine. (d) Br 3d high-resolution spectrum. Bromine signal is
observed after silanization and the peak amplitude is monitored for subsequent
reaction with azide. (e) N 1s high-resolution spectrum. The characteristic azide
signal is clearly observed (dark blue) for D51-N
3
. These signals disappear and
a new nitrogen signal appears at∼ 403 eV after click-chemistry step suggesting
the complete linkage of the TEMPO radical to the diamond surface.
important as point defects directly impact the atomic arrangement affecting the num-
ber of available groups at the surface. This is consistent with the results obtained for
%N for D51 since both crystals are electric grade. It is not surprising that the slightly
higher N percent for D51 may be attributed to the higher atomic availability as dis-
cussed previously. It has been previously shown that wet chemical oxidation increases
surface roughness
112
which may reduce the interaction between the silane molecule and
the surface due to geometrical impediment.
66
Subsequent functionalization with azide shows a 90% reduction of the bromine per-
cent and a total nitrogen density one order of magnitude larger than D43-N
3
(LTLC).
These values are still higher than the ones obtained for D43-Br and D43-N
3
(plasma),
demonstrating that the surface atomic homogeneity and the availability of functional
groups is extremely important for diamond functionalization. However, we observe that
the nitrogen percent is not proportional to the peak reduction on D41-Br(LTLC) nor
the exchange seen from D43-Br(plasma) to D43-N
3
(plasma). One possible explana-
tion is that some of the silane molecules polymerized and adsorbed to the surface upon
interaction with the attached silane molecules and these were washed away after the
subsequent reaction step with sodium azide. Thus, even if there was a Br-N
3
exchange,
only molecules covalently attached contribute to XPS signal in Fig. 3.13(b) (D41-Br)
It is also possible that if the nearby surface carbon atoms are not occupied by a silane,
the hydrolised groups in silane interact with the surface charges. The width of the Br 3d
peak in Fig. 3.13(b) is 5 eV as opposed to the widths for all previous samples of 3 eV .
The broadening in the XPS signal is mainly caused by differences in electronegativities
between atoms and these can also be caused by electrostatic interactions.
Next, we proceed to perform the click chemistry step for samples D43(plasma),
D51(plasma), and D41(LTLC). The survey spectrum for D51 (Fig. 3.12(a)) and D41
(Fig. 3.13(a)) show that the N 1s peak remained almost intact, however for D43 (Fig.
3.11(a)) no signal is observed. The N 1s high-resolution spectrum (Fig. 3.11(e)) reveals
a single peak at 405 eV . The lineshape change suggests that the azide molecule is no
longer present. This change is expected, as the azide molecule links to the radical form-
ing a 1,2,3 triazol ring (Fig. 3.8 D-TEMPO). The triazol ring has an even distribution of
charge across the ring so the three nitrogen atoms possess the same binding energy. If
67
 
404 400 396 410 394 0 600 500 400 300 200 100
Binding Energy (eV)
 
Binding Energy (eV) Binding Energy (eV)
 
 
D41-N 3
D41-Br
D41-TEMPO
 
 
D41-N 3
D41-Br
 
 
D41-N 3
D41-Br
D41-TEMPO
74 72 70 68 64 62

(a) (b) (c)
Signal Intensity (a.u.)
Figure 3.13: (a) Survey XPS of every step of the reaction. The silane signals
are shown in the 200-50 eV region and the nitrogen region indicated by a red
arrow. (b) Br 3d high-resolution spectrum. Bromine signal is observed after
silanization and the peak amplitude is monitored for subsequent reaction with
azide. (c) N 1s high-resolution spectrum. The characteristic azide signal is
clearly observed (dark blue) for D51-N
3
. These signals dissapear and a new
nitrogen signal appears at∼ 400 eV after click-chemistry step suggesting the
complete linkage of the TEMPO radical to the diamond surface.
only a few TEMPO molecules had undergone the azide-alkyne cycloaddition, the sur-
face would contain a mixture of azide and TEMPO terminations. Even though these
signals overlap, the N 1s high-resolution spectrum would show a convolution of the
two azide peaks and an additional peak corresponding to TEMPO as previously seen in
functionalized silicon.
104
This is not the case for our samples since a clear unique peak
is observed (Figs. 3.12(e) and 3.13(c)) demonstrating that the reaction fully proceeded.
A small increase in the nitrogen percent would be expected for the D-TEMPO samples
as an additional nitrogen is introduced in the surface, however, a quantitative analysis of
the nitrogen density and reaction yield is challenging since both species in the D-N
3
→
D-TEMPO step contain nitrogen.
68
3.3 Conclusions
The functionalization of 4-hydroxy TEMPO on a diamond substrate is successfully
demonstrated by XPS characterization. Atomic percentages and densities of the termi-
nal bromine atom in a silane molecule and subsequent exchange with azide were used
to analyze the reaction yield or coverage in the different reaction steps. The main aspect
observed and discussed with respect to diamond surface functionalization is the initial
surface atomic density which is dependent upon the crystal cut and its purity and surface
roughness. The crystal cut and purity will determine the homogenization method. For
instance, (111)-1× 1 (3db) termination will have a much higher coverage than (100)-
2× 1 (2db) due to the increased surface atomic availability. The crystal cut has a smaller
dependence on coverage for higher purity crystals (EG), with these most likely having
theoretical surface atomic arrangements.
Wet chemical methods may be used for practicality on EG diamonds but are still
not preferred as they increase surface roughness and may hinder the interaction between
molecules and the surface. In addition, (100) surfaces would require special control on
the conversion to hydroxyl groups as their intrinsic surface reconstruction favors the for-
mation of ketones lowering the surface coverage. To increase coverage on crystals with
>1 ppm nitrogen content (e.g. type IIa, Ib) an initial plasma treatment is required to ho-
mogenize the surface. The type of gas used for this process may be selected depending
on subsequent application of the diamond. For instance, fluorine termination provides a
full and stable coverage with the potential to create atomically flat surfaces.
100, 113
In ad-
dition, fluorine termination provides positive electron affinities for both (100) and (111)
crystals
113
which favors the density and stability of unique defects used for magnetom-
etry such as the negatively charged vacancy centre (NV
− ).
69
Water vapor treatment was shown to entirely remove the fluorine termination and it
has been previously demonstrated that hydroxyl groups are created maintaining an exist-
ing atomically flat surface.
93
It was also shown that silane condensation on the diamond
surface occurred at low silane concentration and low temperature. The acyl exchange
with azide was monitored via the reduction of the bromine atom in the silane molecule
and a clear identification of the azide molecule using XPS was observed. Finally, the
click reaction step was qualitatively characterized by the observation of the triazole ring
which causes a change in lineshape of the N 1s high resolution XPS spectrum in agree-
ment with the previous works.
104, 108
Direct characterization of the nitroxide radical on the diamond surface is not possible
using XPS as the molecule decomposes under continuous X-Ray excitation. However,
this functionalization procedure may be applied to substrates containing atomic sensors
like silicon vacancies in Si or NV
− centers in which the coupling between the sensors
and the target molecule is observed via ESR, EDNMR or ENDOR.
70
Chapter 4: Effect of surface spins on
spin relaxation times in single NV
centers in diamond
The nitrogen-vacancy (NV) center in diamond is a promising quantum system for appli-
cations of nanoscale magnetic sensing because of its unique properties including stable
photoluminescence (PL) signals,
114
long spin decoherence times
62, 115–118
and the ability
to perform optically detected magnetic resonance (ODMR) spectroscopy using a single
NV center.
114, 119
Although NV-ESR spectroscopy of biological molecules is an attractive approach to
drastically improve the ESR sensitivity for biological molecules, there are only few re-
ports of NV-ESR studies of spin-labeled biological molecules so far.
7–9
These examples
show the importance of nanoscale positioning of target molecules near NV centers with
long spin coherence, and particularly critical for studies of biomolecules in aqueous
solutions.
8
The technique of relaxometry exploits the sensitivity of individual quantum spin
systems to minute variations in the magnetic environment. In contrast to conventional
magnetic resonance techniques, where variations in the T
1
spin relaxation processes
between different macroscopic regions form the basis for contrast, detection through
71
measuring the decoherence of a single spin probe is inherently nanoscopic due to the 1/r
3
fall-off of the dipole interaction. NV-ESR relaxometry utilizes magnetic resonance on a
single spin probe qubit to indirectly detect an individual spin or few spins surrounding
the probe.
The transverse and longitudinal relaxation time have been previously used to study
coupling to nearby spins including external spins in NV center ensembles in nanodi-
amonds
39
and diamond crystals
36, 38, 120, 121
Recently, highly efficient covalent attach-
ment of molecules on the diamond surface has been developed. For instance, nitroxide
radicals have been grafted on the diamond surface using Cu(I) catalyzed click chem-
istry.
99
The diamond surface can also be functionalized by ligands to enhance bio-
compatibility.
122
Moreover the spin labeled DNA grafted on the diamond surface main-
tains functionality.
123
Here we utilize single NV centers to detect covalently attach nitroxide radicals to the
diamond surface via relaxometry. We perform the Cu(I)-catalyzed azide/alkyne click
chemistry reaction to minimize the sensor-molecule distance. Covalent binding should
be maintained in aqueous solutions, preserving molecular functionality. While prior
ESR work has been reported on nitroxide radicals covalently bonded to the diamond
surface,
124
our work investigates and systematically characterizes the effect of sample
preparation on the NV properties.
4.1 Nitrogen Vacancy Center in Diamond
NV centers are point defects with C
3v
symmetry in diamond consisting of a substitu-
tional nitrogen atom adjacent to a carbon lattice vacancy pair oriented along the [111]
crystalline direction (Fig. 4.1(a)). An electron is donated from the lattice to form the
negatively charged species.
125
NV centers exist in diamonds as a product of radiation
72
damage and annealing during the CVD growth process.
126
They can also be created via
ion implantation and annealing.
127
m = 1
s
± 
m = 0
s
 
m = 1
s
± 
m = 0
s
 
Optical
Excitation FL
Non-radiative
decay
1.42 GHz
2.87 GHz
N
V
3
E
3
A
2
1
A
1
Energy (GHz)
0
20 40 60 80 100
1
3
5
Magnetic Field (mT)
(a) (b)
(c)
Figure 4.1: (a) Schematic of the NV center defect in the diamond lattice in
the [111] crystallographic orientation. The nitrogen atom (pink), subsequent
vacancy (light blue) and, neighbouring carbon atoms (dark gray). (b) Electronic
structure of the NV center. Them
s
= 0 andm
s
=± 1 sub-levels are separated by
ZFS = 2.87 GHz in the GS (
3
A
2
) and 1.42 GHz in the ES. The transition from
GS→ ES is driven by green laser light (575 nm) and fluorescence is collected
at 637 nm. The ES undergo an additional non-radiative decay pathway into
the dark state
1
A
1
at different rates allowing spin polarization of the NV center
into the m
s
= 0 state. (c) NV energy diagram. The m
s
= ± 1 spin states are
split under an applied external magnetic field driving two possible transitions
indicated by the yellow arrows.
The versatility of NV
− with S = 1 is attributed to its unique optical properties.
Fig. 4.1(b) shows the electronic structure consisting of an
3
A
2
ground triplet state (GS),
an optical
3
E excited triplet state (ES) and dark states (
1
A
1
and
3
E). The NV
− center
presents a ZFS at 2.87 GHz
128
(GS) and 1.42 GHz
129
(ES) between the m
s
= 0 and
m
s
=± 1 spin states. The GS maintain optical spin selection rules (∆ S =0,∆ m
s
=0)
and result in optical spin-conserving transitions. The electronic transitions are driven
from GS→ ES at 575 nm with different decay pathways. For instance, them
s
=0 spin
73
state population relaxes back to the GS by FL emission at 637 nm which corresponds to
the center’s ZPL. Both ES sub-levels undergo an additional non-radiative decay pathway
via intermediate dark states (
1
E→
1
A
1
).
17, 130
However, the decay rate from the ES into
the
3
E is slower for the m
s
= 0 than for m
s
= ± 1 and, the non-radiative decay rate
out of the dark states into
3
A
2
is similar for both spin sub-levels.
130, 131
Therefore, a spin
polarization is induced into them
s
=0 state upon a few cycles of optical excitation.
The spin polarisation of the NV center into the m
s
= 0 GS allows optical readout
of the spin states. For instance, by applying MW excitation in resonance with the gap
between spin sub-levels, the population fromm
s
= 0 can be driven intom
s
=± 1. The
PL collected fromm
s
= 0 will be reduced upon MW excitation. Optical laser pumping
is optimized using spin polarization to a few microseconds, and readout of them
s
=± 1
spin states upon manipulation with MW excitation is achieved by projecting them into
m
s
= 0. Furthermore, the degeneracy of the m
S
= ± 1 states can be split upon the
application of an external magnetic field and a lower and higher resonance transitions
may be driven fromm
s
=0→m
s
=− 1 orm
s
=0→m
s
=+1, respectively.
4.2 NV fabrication
To create the near-surface NV centers, a⟨100⟩-cut electronic-grade diamond plate (El-
ement 6) was implanted with 5 KeV N
+
ions with a dose of 10
9
ions/cm
2
. The mean
depth of the implanted nitrogen ions was expected to be 8± 3 nm.
132
Subsequently the
plate was cleaned in a fuming sulfuric acid and potassium nitrate mixture and annealed
in vacuum at 400
◦ C for 4 hours, then 800
◦ C for two hours, with a 30 minute ramp in
between. After verifying NV creation via PL measurements, the sample was vacuum-
annealed at 1100
◦ C for two hours with one hour ramps, which is believed to reduce the
concentration of vacancy-related paramagnetic defects inside the diamond.
133
Lastly,
74
the diamond was annealed in atmosphere at 465
◦ C for 36 hours and cleaned in a 1:1:1:
mixture of sulfuric, nitric, and perchloric acid to remove graphitic carbon, restore oxy-
gen surface termination and reduce spurious surface fluorescence. For spin relaxometry
experiments, the diamond crystal was cleaned in piranha solution at 80
o
C. The function-
alization with nitroxide radicals was performed following the HTHC method discussed
in chapter 3. The mean depth of NV centers fabricated for this diamond is 8 nm as
calculated from SRIM mesurements, and the distance of the nitroxide radical from the
surface is expected to be 1.8 nm as calculated from previous studies.
123
4.3 Experimental Setup
Fig. 4.2 shows an overview of the experimental setup used for optically-detected mag-
netic resonance (ODMR) spectroscopy of nitrogen-vacancy (NV) centers in diamond
and double electron-electron resonance (DEER) spectroscopy for NV-detected electron
spin resonance (NV-ESR) experiment. The setup based on a confocal microscope sys-
tem and a microwave access consists of a continuous-wave diode-pumped solid-state
laser (Crystalaser), an acousto-optic modulator (AOM; Isomet), a microscope objec-
tive (Nikon), avalanche photo diodes (APDs; Pacer), a XYZ piezo stage (Thorlabs),
microwave sources (MW 1 and 2; Stanford research and Synth NV) and optics.
The 532 nm laser is focused into a diffraction-limited spot using the microscope
objective. Photoluminescence (PL) signals of the NV center are collected by the same
microscope objective, and then isolated from the laser excitation using a dichroic mirror
and a fluorescence filter. Finally the PL is detected by the APD detector. AOM is used
for pulsed ODMR experiments. To conduct autocorrelation measurements, the FL beam
is split with a beam splitter and the outputs of the two APD detectors (APD1 and APD2
75
Microscope
objective
Beam splitter
Dichloic mirror
XYZ piezo stage
Diamond
sample
Magnetic
field
Au wire
Fluorescence filter
APD1
532 nm
laser
APD2
Laser filter
SW
SW
Comb.
AOM
MW1
Pulse Blaster
MW2
I Q
Attn. Attn.
Amp.
Figure 4.2: ATT is a microwave attenuator. SW is a p-i-n switch. COMB is a
microwave combiner. AMP is a microwave amplifier.
in Fig. 4.2) are connected to a time-correlated single photon counting (TCSPC) unit
(Picoharp 300).
The sample position is controlled by the XYZ piezo stage. For ODMR spectroscopy,
a microwave excitation generated by the microwave source (MW1) is applied to the
NV center through the microwave transmission line (a small gold wire) placed on the
diamond surface. A phase of MW1 outputs is controlled by square pulses applied to the
I and Q channels of the MW1 system. Additionally the system has capability to use two
microwave sources (MW 1 and 2) for NV-ESR experiment. A magnetic field is applied
using a permanent magnet. Timing for pulsed ODMR is controlled by a pulse generator
(SpinCore).
76
4.4 Optically Detected Magnetic Resonance (ODMR)
The fabricated NV centers were first characterized by employing PL imaging. As shown
in Fig. 4.3(b) and (c), many PL spots were imaged only after the NV fabrication process.
To systematically characterize our sample, we begin by imaging one of the diamond
corners shown in Fig. 4.3(a). We identified individual PL spots and marked NV centers
after ODMR characterization.
(a) (b)
(c)
Figure 4.3: (a) Diamond sample crystal with a scratch on the bottom edge
used as a reference to image the bottom left corner (yellow circle). (b) Image
of the diamond crystal as received. (c) Image of the bottom left corner of the
diamond after implantation (white dashed line). The studied NVs are marked
and indexed.
The ODMR spectra were collected by applying a narrow bandwidth pulse to re-
solve the NV center’s hyperfine splitting. As seen in Fig. 4.4, both the lower
|m
s
=0⟩ ↔ |m
s
=− 1⟩ and upper|m
s
=0⟩ ↔ |m
s
=+1⟩ transitions each contain
77
two peaks(
15
N;I =1/2). The spectrum was simulated by considering the NV’s hamil-
tonian in the [1 1 1] crystalline orientation.
ˆ
H
NV
=D· ˆ
S
z
2
+
gµ B
h
B
0
(
ˆ
S
x
sinθ +
ˆ
S
z
cosθ )+A
⊥
(
ˆ
S
x
ˆ
I
x
+
ˆ
S
y
ˆ
I
y
)+
ˆ
S
z
A
∥
ˆ
I
z
(4.1)
The first term describes the zero field splitting ( g = 2.0029, D = 2.87 GHz), the
second term describes the Zeeman splitting where B
0
is an external magnetic field
and θ the polar angle between B
0
and the NV axis. The third term describes the
15
N hyperfine coupling with A
∥
= 3.03 MHz and A
⊥
= 3.65 MHz.
134
The ex-
perimentally observed signal was then calculated with a sum of Gaussian functions
Y(ω) =
P
4
n=1
A
n
exp(− (
ω− Cn
∆ ω
)
2
/2) for each resonance position (C
n
). The values of
C
n
are calculated with Eq. 4.1, and the amplitude (A
n
) and width (∆ ω) were set to
match the observed signal. The applied magnetic field strength B
0
and the polar angle
θ was then determined using a least square fit in MATLAB.
As shown in Fig. 4.4, the observed signals agree well with ODMR signals calculated
using Eq. 4.1. Each ODMR consists of two peaks split by∼ 3 MHz. This is due to the
hyperfine coupling between the NV S=1 electron spin and
15
N nuclear spin in the NV
center. Therefore, the observation of the 3 MHz splitting confirmed that the detected
NV was fabricated by the
15
N implantation process and it is expected to be located
near the surface. The observed ODMR signals were at frequencies of 2098.11 MHz and
2101.21 MHz for the|0⟩→|− 1⟩ transition and 3640.19 MHz and 3643.10 MHz for the
|0⟩→|+1⟩ transition. From the analysis of these ODMR frequencies, we determined
the magnetic field strength to be 27.532 ± 0.003 mT and the angle between the NV axis
and the magnetic field orientation to be 2.47 ± 0.09 degrees.
Next, we performed autocorrelation measurement to identify single NV centers. The
autocorrelation experiment was performed using a Hanbury Brown-Twiss interferometer
78
MW
(a)
Init RO
PL
t
π
(b)
Figure 4.4: Collected data is shown in teal and simulation using Eq. 4.1 is
shown in red. Left panel: Transition from |0⟩ → |− 1⟩ shown around 2100
MHz. Right panel: Transition from|0⟩→|+1⟩ shown around 3640 MHz.
with a TCSPC unit.
135
The autocorrelation function (g
(2)
(τ )) was obtained by correlat-
ing the arrival times (τ ) of photons detected at each APD as shown in Fig. 4.2. For
each NV ,g
(2)
(τ ) was measured continuously until sufficient photons were accumulated
for satisfactory signal-to-noise. Analysis of the autocorrelation function was based on a
previously introduced model of the photodynamics of NV centers.
136
For a single NV
center at zero time delay (τ = 0), an emitted photon may only be detected at one APD.
Therefore single NV centers exhibit antibunching with g
(2)
(0) < 0.5. The autocorre-
lation function exhibits a characteristic growth rate, γ 1
, that is dependent on the rate
of fluorescence and strength of laser excitation ( k
12
). NV centers also exhibit photon
bunching due to the existence of a metastable state with a long lifetime relative to the
excited state. Shelving of the electron from the excited state to the metastable state
79
acts to “trap” the electron and cause g
(2)
(τ ) > 1.0 with increased driving rate, k
12
. At
longer times, the population on the metastable state decays with a characteristic rate,γ 2
,
until the photons are completely uncorrelated at long delay times (ie, g
(2)
(τ ) ≈ 1.0).
The intensity of antibunching and bunching signals is dependent on the state popula-
tion and is therefore dependent on the strength of laser excitation relative to the decay
rates. The relative intensity of the corresponding signals is represented by β . This is
distinguished from incoherent background photons through the usage of an additional
parameter,ζ , and is the ratio of NV fluorescence (S) to total fluorescence (S+B) (i.e.,
ζ = S/(S +B)). The autocorrelation function is then described using the following
model:
136
g
(2)
(τ )=1+ζ 2
(− βe
−| τ |γ 1
+(β − 1)e
−| τ |γ 2
) (4.2)
Using this model, we analyze the photodynamics of the studied NV centers. The FL
lifetime of the excited state is given byτ FL
= 1/(γ 1
− k
12
). For all AC measurements
in this work, the laser power was set below 1 mW. Based on the previous study,
136
k
12
is
smaller than observed error values and τ FL
≈ 1/(γ 1
). Furthermore, the lifetime of the
metastable state is given byτ MS
=β/γ
2
.
Figure 4.5 shows the result of an autocorrelation measurement with NV8. As can be
seen, g
(2)
(0) = 0.28± 0.08 where the uncertainty was given from the 95% confidence
intervals, therefore, the experiment proves that the observed FL signal is from a single
photon emitter.In addition, by fitting with Eq. 4.2, values of τ FL
= 10.7± 0.3 ns,
τ MS
=344± 8 ns, andζ =0.85± 0.01 were obtained.
A summary of parameters extracted using eq. 4.2 for some NVs seen in Fig. 4.3
are included below. Parameters were calculated as described in the text with 95% confi-
dence intervals calculated using error propagation.
80
Figure 4.5: The green line is experimental data. The red solid line is the fit
result using Eq. 4.2. The red dashed line represents the 95% confidence interval
of the fit result.
NV g
2
(0) τ FL
[ns] τ MS
[ns] ζ 3 0.26 (0.15) 11.7 (1.0) 310 (20) 0.86 (0.03)
4 0.27 (0.14) 12.3 (1.0) 300 (20) 0.86 (0.03)
5 0.26 (0.12) 11.5 (0.9) 320 (20) 0.86 (0.03)
6 0.26 (0.12) 11.7 (0.9) 300 (20) 0.86 (0.03)
8 0.28 (0.16) 12.7 (1.1) 300 (20) 0.85 (0.03)
10 0.28 (0.15) 12.8 (1.2) 290 (30) 0.85 (0.03)
16 0.33 (0.13) 11.9 (0.6) 344 (18) 0.82 (0.02)
19 0.26 (0.22) 12.4 (0.9) 361 (29) 0.86 (0.03)
Table 4.1: Summary of analysis for NVs discussed within text. Analysis was
performed in Matlab using eq. 4.2 as summarized in the text. Values in paran-
theses represent the 95% confidence intervals.
4.5 Characterization of NV Spin Relaxation
For subsequent pulse measurements, an accurate characterization of the tipping angle
(t
π ) is crucial. This can be obtained by performing a pulsed measurement at the central
frequency of the|0⟩→|− 1⟩ transition (2174.00 MHz). After NV initialization, an x-
pulse of variable length (t
p
) is applied to the system (Fig. 4.6(a). The evolution of the
81
population transfer is readout and Rabi oscillations are observed (Fig. 4.6). The model
that describes the population transfer was previously derived yielding Eq. 2.32. The
Rabi frequency (Ω = t
π ) was obtained by fitting the data to Eq. 2.32. A t
π = 40.04± 0.04 ns was obtained.
MW
t
p
(a)
Init RO
PL
(b)
Figure 4.6: (a) The pulse sequence uses a pulse of variable length. (b) The data
is normalized toP(m
s
= 0) according to Eq. 10. The solid line is the fit result
using Eq. 2.32 witht
π = 40.04 ns.
Next, we obtain the transverse relaxation time by performing SE experiment. As
discussed in section 2.7.3, SE signals can be modeled by an exponential function that
considers the spin bath dynamics. In addition, hyperfine coupling between an electron
spin and a nuclear spin can create ESEEM which contributes to the SE signal (Eq.
2.45). In an NV , the coherence of the state after a pulse sequence is applied is detected
as P(m
s
= 0), therefore, the SE signal is given by SE(2τ ) = (1+S)/2. Based on
the alignment and strength of the magnetic field, the NV electron spin can entangle with
82
15
N nuclear spin in the NV and
13
C bath spins, and also experience spin decoherence
from its environment. Therefore, using Eq. 2.45, the SE signal can be expressed by,
SE(2τ )=
1
2
+
1
2
S
15N
S
13C
S
d
(4.3)
in which S
d
= exp(− (t/T
2
)
n
) is the decoherence term. The coherence influenced the
15
N hyperfine coupling is given by,
S
15N
(2τ )=1− 2C
1
sin
2

πf
N
0
(2τ )
2

sin
2

πf
N
− 1
(2τ )
2

(4.4)
in whichf
N
0
=γ N
B
N
(γ N
is the gyromagnetic ratio of
15
N andf
N
0
=γ N
B
N
− 1
.
For
13
C bath spins, the hyperfine couplings ( A) are much weaker than the magnetic
field in the present case. Therefore, f
C
− 1
≃ f
C
0
= γ C
B (γ C
is the gyromagnetic ratio of
13
C). The coherence influenced the
13
C hyperfine coupling is given by,
S
13C
(2τ )=Π j

1− 2C
j
sin
4

πf
C
0
(2τ )
2

≃1− 2C
2
sin
4

πf
C
0
(2τ )
2

, (4.5)
in whichC
2
=Σ j
C
j
andC
j
sin
4
(πf
C
0
(2τ )/2)≪ 1.
Fig. 4.7(a) shows the pulse sequence used for this experiment and results for two
NVs. NV6 (Fig. 4.7(b)) shows a decoherence time T
2
of 30.6± 1.1µ s compared to
T
2
= 4.2± 0.6µ s for NV8 (Fig. 4.7(c)). The longer decoherence time of NV6 allows
to observe ESEEM signals which provides insight into the local bath dynamics. For
instance, NV 8 with n closer to 1 shows a signal governed by a single exponential decay
characteristic of a quasi-static regime. NV6 with n> 1 shows a regime approaching the
motional narrowing regime in which the bath spin undergoes a faster dynamics.
83
MW
(a)
Init RO
PL
(b) (c)
π/2 π/2
τ
π
τ
Figure 4.7: (a) The pulse sequence uses aπ/ 2 pulse to prepare the state into the
transverse plane. The spin evolves overt = τ and the dephasing is inverted by
a π pulse. The spin rephases over another t = τ and the spin states is mapped
back onto them
s
= 0 state by aπ/ 2 pulse. (b) SE data for NV6 performed at
27.524± 0.002 mT. ESEEM modulations are observed. T
2
to be30.6± 1.1µ s
andn = 1.59± 0.14 is found using Eq. 4.3. (c) SE data for NV8 performed at
27.532± 0.003 mT andT
2
to be4.2± 0.6µ s andn = 1.08± 0.14 is found using
Eq. 4.3.
Additionally, we perform FID experiment to obtain T
∗ 2
. FID signals are readout by
an additionalπ/ 2 pulse (Fig.4.8(a)) that brings the state back to its initial position along
B
z
, and the population of the state that is measured is equal top
0
(t)=(1+cos(2β ))/2.
This value is averaged over all possible magnetic contributions including the staticγb
i
,
and dynamicγ R
τ 0
b(t
′
)dt
′
components. The averaging of Eq. 2.39 for a given hyperfine
couplingA
z
is given by,
FID(t)=
1
2
− 1
2n
n
X
1
cos[(∆ ω+A
z
m
n
)t]exp(− (t/T
2
∗ )
n
) (4.6)
in which∆ ω = ω
0
− ω
MW
1
the summation runs over the number of spin states, n, (n =
2 form
I
= 1/2, n = 3 form
I
= 1, etc.) andm
n
gives the magnetic spin number.
84
We then consider the two
15
N hyperfine peaks from the nitrogen atom in the NV
center (ω
0
+A
z
/2 andω
0
− A
z
/2) and a Gaussian distribution of the resonance frequency
with a full-width at half-maximum (FWHM) of2
√
2ln2/T
∗ 2
∼ 2.36/T
∗ 2
. Eq. 4.6 may
be rewritten as,
FID(t)=
1
2
− 1
4

cos

δω +
A
z
2

t

+cos

δω − A
z
2

t

e
− (t/T
∗ 2
)
2
, (4.7)
in whichδω =ω
0
− ω
MW1
. A
z
=3.03 MHz for the
15
N hyperfine coupling constant.
134
The experiment was performed using the pulse sequence shown in Fig. 4.8(a). Eq. 4.7
considers a mismatch between the resonance frequency and the MW1 frequency set by
δω . Fig. 4.8(b) and (c) shows an excellent agreement of the model used for two different
NV centers (NV 6 and NV8). The experiment was performed at a MW1 frequency of
2100 MHz for both NVs. We obtainedT
∗ 2
= 1.06± 0.21µ s for NV6 andT
∗ 2
= 1.21± 0.17µ s for NV8.
Finally, we obtained T
1
by performing an inversion recovery experiment and fitting
the data to Eq. 2.47. The transverse relaxation time is sensitive to the presence of bath
spins (e.g.
13
C,
14
N) in addition to external spins. However, it has been observed that the
longitudinal relaxation time (T
1
) has a higher sensitivity to external spins over T
2
.
137, 138
For this reason, we tracked changes in T
1
as well. Fig. 4.9(a) shows the characterization
of T
2
times for eight labeled (Fig. 4.3) single NVs in the diamond sample. Fig. 4.9(b)
and (c) shows the characterization of T
1
for the same NVs. The initial blue bar corre-
sponds to the diamond surface initially cleaned with piranha solution (Acid cleaned-1).
Next, the diamond was functionalized with TEMPO and the same NVs were localized
for characterization of their spin relaxation properties. Overall, a decline in the relax-
ation times is observed for both T
1
and T
2
cases. It is important to mention that for some
measurements the T
2
data (NVs 5, 8,and 16) was unreliable even after averaging due to
85
MW
(a)
Init RO
PL
(b) (c)
π/2 π/2
τ
Figure 4.8: (a) The pulse sequence uses a π/ 2 pulse to prepare the state into
the transverse plane. The spin evolves overt = τ and the spin states is mapped
back onto them
s
= 0 state by aπ/ 2 pulse. (b) FID data for NV6 performed at
27.524± 0.002 mT and T
∗ 2
= 1.06± 0.21 µ s is found using Eq. 4.7. (c) FID
data for NV8 performed at 27.532± 0.003 mT andT
∗ 2
1.21± 0.17µ s is found
using Eq. 4.7.
high background. Next, the diamond was cleaned a second time with piranha solution
(Acid cleaned-2) and only T
2
times were extracted. In this case, a recovery in the re-
laxation time was not observed. The overall trend observed is that the relaxation time
remained similar to that of the functionalized sample (TEMPO-1) with the exception of
a slight increase in relaxation time observed only for NV10. A second round of func-
tionalization with TEMPO was performed and a further decrease in T
2
was observed.
Fig. 4.9(a) shows T
2
times ranging from 5 to over 20 µ s and only one NV with T
2
longer than 70 µ s. Fig. 4.9(b) shows that in a clean surface most NV centers have T
1
values of up to 5 ms. Even though this might be an indication of the relative depth of an
NV center with respect to the surface and hence their stability, it has been observed that
some shallow NVs can still maintain long decoherence times.
124
There is also no cor-
relation between both types of spin relaxation as NVs with similar T
2
values (e.g. NV3
86
vs NV 19 and NV4 vs NV5). However, after the first functionalization, we observed
a decrease in T
1
and T
2
for most NVs studied. The largest decrease in T
1
, by almost
∼ 80% was observed for NV9 and NV19 although their T
2
values before and after the
functionalization remained similar. This result implies that both NVs experienced a
strong coupling to external spins with NV9 providing more reliable results according to
its 95% confidence interval. In contrast, NV10 and NV16 experienced a reduction in
both spin relaxation times with NV10 having the largest decrease in T
2
.
0
10
20
30
40
50
60
70
80
T ( s)
2
μ
NV3 NV4 NV5 NV8 NV10 NV16 NV19 NV9
Acid cleaned-1
TEMPO-1
Acid Cleaned-2
TEMPO-2
0
50
100
150
200 200
250
300
350
0
1000
2000
3000
4000
5000
6000
NV3 NV4 NV5 NV10 NV16 NV19 NV9
T ( s)
1
μ
T ( s)
1
μ
Acid cleaned
TEMPO
Acid cleaned
TEMPO
(a)
(b) (c)
Figure 4.9: (a) Transverse relaxation time of single NVs upon two cycles of
consecutive surface functionalization with nitroxide radicals and acid cleaning.
(b),(c) Longitudinal relaxation time of single NVs before and after functional-
ization.
Because surface treatments only affect the final atomic layer in diamond, differences
in T
2
should mainly originate by differences in the diamond surface. In comparison with
NV9 and NV19 for which only a large decrease in T
1
was observed, it is inferred that
87
NV10 and NV16 should have a stronger coupling to external spins. DEER measure-
ments were performed on these NVs to confirm the presence of such spins, however
no signal was observed (data not shown). Previously, DEER measurements on exter-
nal spins have been performed in which the distance from the NV sensor to the target
radical is between 3-10 nm.
8, 124
The NV centers in the present sample lie on the upper
limit of this range. This means a weaker coupling compared to previous studies and
longer experimental times to reduce the signal to noise ratio for which a normalized
signal of only 0.05 is expected.
8
Long laser exposure is detrimental to nitroxide radicals
leading to their decomposition and hindering the capacity of readout through a DEER
experiment.
Nonetheless, we cleaned the diamond a second time and characterized the same NV
centers. Fig. 4.9 shows in light blue the T
2
values of some NV centers. For NV3 and
NV4, these values remained similar to those for a functionalized sample, implying that
there were no changes to the surface. Even though acid treatments remove linkers such
as silanes,
124
they can also etch the diamond creating additional surface impurities. This
is particularly observed for NV10 for which the T
2
value was deteriorated compared to
the initial cleaning treatment. Finally, a second functionalization was performed on the
diamond surface and again a decrease in T
2
values was observed. This subsequent series
of cleaning and functionalization confirms that the decrease in spin relaxation of the NV
center is due to the presence of surface spins even after undergoing a deterioration of
their decoherence properties after a second acid cleaning treatment.
4.6 Conclusions
We established a systematic method to study properties of the same NV centers in a
diamond crystal upon sequential functionalization and acid cleaning treatments. This
88
systematic control is important as the sensitivity of single electronic spins heavily de-
pends on the distance between the NV and the target molecule but wet treatments ran-
domly place the target molecule in the diamond surface. In addition, a single diamond
crystal may be utilized to study different systems, for this reason it is important to under-
stand how the NV properties are affected after sequential functionalization or cleaning
treatments.
We have shown that the NV spin relaxation times of NV centers located at a mean
distance of 8 nm below the surface are both sensitive to external spins and provide evi-
dence of their presence. Both types of spin relaxation can be used for different purposes,
for instance tracking changes in T
2
results useful when longer T
1
values are observed.
This can significantly reduce experiment time and noise levels.
However, for direct recognition of external spins through the NV center it is crit-
ical to reduce the distance between the NV sensor and the target molecule. This can
be achieved by creation of NV center utilizing lower implantation energies or by the
creation of diamond nanopillars which have also been shown to reduce ESR detection
time.
8
Finally, complementary surface characterization methods of the reaction scheme can
be utilized to further verify and optimize the covalent attachment of target molecules.
This can be helpful to increase the surface density coverage since the probability of
finding a single molecule in the NV center’s detection area (10 nm apart from target
molecule) is only 14%.
8
89
Chapter 5: Electron-electron double
resonance detected NMR spectroscopy
using ensemble NV centers at 230 GHz
and 8.3 Tesla
Materials presented in this chapter can also be found in the article titled Electron-
electron double resonance detected NMR spectroscopy using ensemble NV centers at
230 GHz and 8.3 Tesla by Benjamin Fortman, Laura Mugica-Sanchez, Noah Tischler,
Cooper Selco, Yuxiao Hang, Karoly Holczer, and Susumu Takahashi in Journal of Ap-
plied Physics 130, 083901 (2021).
We have described the characterization of the diamond surface and the effect of sur-
face impurities and different functional groups on single NV centers. We also described
the use of hyperfine double resonance techniques that may be utilized to identify the na-
ture of the target spins with great precision. One of the key aspects of quantum sensing
is the coupling strength between the NV and the target spins. This results extremely
challenging for single NV experiments as the positioning of the NV with respect to the
target spin cannot be controlled.
90
An alternative is to utilize a larger amount of sensors like an NV ensemble to increase
the detection volume. This enables the optimization of diamond sample preparation
with NV properties such as spin coherence time and depth for the ultimate detection
of external spins. In addition, the implementation of higher magnetic fields provides
an increase in spectral resolution that enables a more fine characterization of molecules
with many similar nuclei, low gyromagnetic ratios, and low natural abundance.
5.1 Introduction
In this chapter we describe the development of NMR detection utilizing NV centers
in diamond for applications of high field NMR. NV centers possess unique properties
such as optical initialization and readout of the spin state ,
114, 119
long coherence times
62, 115–118
and nanoscale sensitivity to external magnetic fields.
29, 139, 140
NV-detected NMR has been widely used at low magnetic fields ( < 0.1 T) such
as for NV depth estimation, liquid state NMR, two-dimensional NMR, hyperpolarized
NMR, nanodiamond based NMR, and even for selective spin manipulation in a 10-
qubit quantum register .
141–145
The implementation of NV detected NMR offers new
insights into molecules with many similar nuclei, low gyromag- netic ratios, and low
natural abundance, such as for
17
O NMR in pharmaceutical com- pounds and biomacro-
molecules.
146, 147
Hyperfine spectroscopic techniques like electron spin echo envelope modulation
(ESEEM), electron-nuclear double resonance (ENDOR), and electron-electron double
resonance detected NMR (EDNMR) are primarily used for the development of NV-
detected NMR. ESEEM works efficiently when the energies of the hyperfine coupling
and nuclear Larmor frequency are comparable. This requirement makes this technique
unfeasible at high magnetic fields. ENDOR and EDNMR rely on the detection of the
91
population difference of an ESR transition via a pulsed RF or off resonance MW radi-
ation, respectively, used to drive polarization transfer. Both techniques are limited by
the longitudinal relaxation time, T
1
, instead of the transverse relaxation time, T
2
. The
T
1
relaxation time for NV ensembles has been shown to extend dramatically (up to min-
utes) at low temperature. In comparison to ENDOR, EDNMR has been proven to have
a higher sensitivity and resiliency against RF related artifacts .
148
In addition, EDNMR utilizes a high turning angle (HTA) pulse to drive population
transfer of forbidden transitions and does not require the implementation of additional
RF power amplifier or tuned RF circuit. In this work, we demonstrate optically de-
tected magnetic resonance (ODMR) on the NV center at the highest field and frequency
to date, 8.3 T, corresponding to the NV’s Larmor frequency of 230 GHz (proton Lar-
mor frequency of 350 MHz). We successfully implement EDNMR using ensemble NV
centers and detect
13
C nuclear bath spins in the diamond crystal. Since the EDNMR
technique is limited by T
1
, not T
2
, NV-detected NMR based on EDNMR can take ad-
vantage of the NV center’s longT
1
to perform measurements with a long HTA pulse.
5.2 Methods and Materials
A home-built, high field (HF) ODMR spectrometer operating in the band of 215-240
GHz was used. An overview of the experimental setup is shown in Fig. 5.1. The di-
amond sample was mounted at the center of a variable field 12.1 T superconducting
magnet (Cryogenic Limited). Microwave (MW) excitation was produced by a solid
state source (Virginia Diodes) and directed through quasioptics to the sample stage. The
output power of both channels from the source was 115 mW at 230 GHz. Laser ex-
citation was produced from a solid-state single mode laser (Crystalaser) and directed
92
Quasioptics
Dichroic
Mirror
Photodiode
Lenses
Corrugated
Waveguide
Fast Steering
Mirror
Tx
12.1 T
Magnet
Microscope
Objective
Sample
x24
B
0
Signal
Integrator
Laser
AOM
Central Computer
PB-500 & DAQ
PIN MW1
PIN MW2
Figure 5.1: Overview of the experimental setup. The transmission (Tx) setup
consists of two independently controllable frequency sources (MW1 and MW2)
that pass through PIN switches to a frequency multiplication chain. High
frequency MW excitation is propagated through quasioptics and a corrugated
waveguide to the sample stage within a 12.1 Tesla variable field magnet. Pulsed
laser excitation is directed through an acousto-optic modulator (AOM) and an
optical fiber to a system of lenses, a fast steering mirror, and the sample stage.
At the sample stage, a microscope objective directs laser intensity and collects
sample fluorescence. The fluorescence is redirected through a dichroic mirror
to a photodiode where it is integrated using either gated boxcar integrators or
a fast oscilloscope. The MW components, laser, and boxcar integrators are all
controlled through a central computer equipped with a fast TTL logic board and
digital to analog converter (DAQ). The magnetic field ( B
0
) is aligned with the
optical axis. Reproduced from Ref.
149
with the permission of AIP Publishing.
through an acousto-optic modulator (Isomet), single mode fiber (Thorlabs), and micro-
scope objective (Zeiss100X, NA=0.8) before reaching the sample stage. The excitation
beam position was controlled using a fast steering mirror (Newport) and a system of
lenses below the microscope objective. Fluorescence (FL) collected at the objective was
directed back through a dichroic mirror and fluorescence filters (Omega Optics) before
93
being detected using a photodiode (Thorlabs 130A2). The typical excitation spot size
was a few µ m
2
. Typical laser excitation of ∼ 4 mW at the sample stage resulted in
1-2 µ W of detected FL. The output of the photodiode was directed to a signal integra-
tor. Integration was performed using either a pair of analog boxcar integrators (Stanford
Research Systems SR250) or a fast digitizing oscilloscope (Tektronix MSO64B). The
analog output of the boxcar integrators was digitized using a fast DAQ (National Instru-
ments PCIe-6321). Gate timing was controlled using a gated TTL logic board (SpinCore
Technologies PB-500). Additional details of the HF-ESR/ODMR spectrometer have
been described previously.[ref] For this study, two samples were used. Sample 1 was a
2.0× 2.0× 0.3 mm
3
size, (111)-cut high pressure, high temperature type Ib diamond
from Sumitomo Electric Industries. Sample 2 was a hexagonal 4.4× 3.9× 0.5 mm
3
size, (111)-cut high pressure high temperature type-Ib diamond obtained from Element
Six. Both diamonds had previously been subjected to high energy (4 MeV) electron
beam irradiation and were exposed to a total fluence of 1.2× 10
18
e
− /cm
2
followed by
an annealing process at 1000
o
C. This treatment produced a NV concentration greater
than 1 ppm.[ref]
5.3 Discussion
We begin by performing pulsed ODMR on ensemble NV centers. For pulsed ODMR,
the relative FL intensity was monitored while a MW pulse was varied in frequency.
As seen in Fig. 5.2(a), clear reductions in FL intensity were resolved at 229.953 GHz
and 235.687 GHz, corresponding to the lower (|m
S
=0⟩ ↔ |m
S
=− 1⟩) and upper
(|m
S
=0⟩↔|m
S
=+1⟩) transitions of a [111] oriented NV with a polar offset angle
of1.50± 0.02 degrees. Next, Rabi oscillations were recorded by fixing the frequency of
MW1 at229.953 GHz (|m
S
=0⟩↔|m
S
=− 1⟩ transition) and varying the pulse length
94
as seen in Fig. 5.2(b). From these measurements, damped oscillations and a π pulse
length of 1.9 µ s was observed. Next, the NV ensemble’s spin-lattice relaxation time,
T
1
, was recorded. For this measurement, the duration between the laser initialization
and readout pulse (τ ) was varied (see Fig. 5.2 (c). Two sequential measurements were
performed by varying the spacing between initialization and readout with and without a
MWπ pulse before normalization. AT
1
time of3.9± 0.2 ms was found by fitting to a
single exponential decay.
Next we perform EDNMR using the NV center. As shown in Fig. 5.3(a), EDNMR
is a form of high field hyperfine spectroscopy that utilizes two microwave frequencies,
MW1 (ν 0
) and MW2 (ν 1
). EDNMR measurements vary the frequency (ν 1
) of a HTA
MW2 pulse, while MW1 applies a detection pulse sequence, such as Hahn echo, at
ν 0
to measure the spin polarization of an ESR transition.
151
As the frequency of ν 1
is
swept, the frequency shifts on resonance with transitions below the central transition
(ν 1
< ν 0
) due to weakly coupled hyperfine nuclei, as seen in Fig. 5.3(b). These tran-
sitions are generally forbidden as they involve a flip of both the electron and nuclear
spin (∆ m
S
= 1,∆ m
I
= 1). The forbidden transitions become weakly allowed with
partial state mixing, leading to polarization transfer and a reduction in the ESR signal
intensity. This change is detected as an EDNMR signal. Application of a long HTA
pulse improves the likelihood of population transfer, but the total length of the HTA
pulse must be short relative to T
1
in order to maximize the observable contrast. As ν 1
approaches the central allowed transition (∆ m
S
=1,∆ m
I
=0) there is significant pop-
ulation transfer leading to a highly intense change and the so-called ”central blind spot”.
Since the central blind spot highly distorts EDNMR signal, in practice the measurement
is performed at a frequency range outside of the central blind spot. After passing the
central blind spot, ν 1
then induces forbidden transitions from hyperfine coupled nuclei
95
0
t [ms]
T
1
= 3.9 ± 0.2 ms
0.5
0.0
1.0
Relative
Contrast [a.u.]
MW1
Laser
Init RO
p
t
5 10
Exp.
Fit
0 2 4 6
MW1
t
p
t
p
[ms]
0.2
0.4
0.0
Contrast [%]
8
(b)
(a)
(c)
Contrast [%]
229.94 229.96 235.68
Exp.
Fit MW1
t
p
Laser
Init RO
0.1
0.2
0.0
0.3
0.4
MW1 Frequency [GHz]
235.70
Figure 5.2: Ensemble ODMR at 230 GHz. (a) Pulsed ODMR data. For all
ODMR measurements, laser pulses of20µ s and15µ s were used for initializa-
tion (Init) and readout (RO), respectively. After initialization, a MW1 pulse (t
p
)
of1.9µ s was applied and varied in frequency. Clear reductions in FL intensity
were resolved at 229.953 GHz and 235.687 GHz, corresponding to the lower
(|m
S
=0⟩↔|m
S
=− 1⟩) and upper (|m
S
=0⟩↔|m
S
=+1⟩) transitions of
the NV center. The magnetic field was found to be 8.306 T with a polar angle
of 1.50± 0.02
◦ . Fitting was performed using nonlinear least squares regres-
sion and the NV center Hamiltonian (S = 1,D = 2870 MHz,g = 2.0028).
118
(b) Measurement of Rabi oscillations. The frequency of MW1 was set at the
lower resonance and the pulse length was varied. From the observed oscilla-
tions, aπ pulse length of1.9µ s was found. (c) Measurement ofT
1
relaxation.
Measurements were performed with (Sig1) and without (Sig2) a π pulse. The
difference (Sig2-Sig1) was normalized and then fit to a single exponential de-
cay.
150
Data was collected using (a) 10 scans, (b) 18 scans, and (c) Sig1 and
Sig2 were measured sequentially with 5 scans each. Reproduced from Ref.
149
with the permission of AIP Publishing.
96
with a positive frequency offset (ν 1
> ν 0
) relative to the central transition. For NV
detected EDNMR, the spin population can be directly detected via optical spin state
readout, eliminating the need for an echo detection sequence. EDNMR with the NV
center has an advantage over conventional EDNMR, as optical initialization of the NV
center ensures high spin polarization and improves EDNMR sensitivity. The usage of
optical initialization shortens the measurement time by eliminating the need for long
cycle delays between subsequent experiments (typically≫ T
1
).
As shown in Fig. 5.3(a), we perform the experiment by applying an initialization
laser pulse, MW2 HTA pulse at frequencyν 1
, MW1π pulse at frequencyν 0
, and laser
readout pulse. During the experiment ν 1
is varied while ν 0
is fixed at the lower NV
resonance. When the HTA pulse drives a transition, the population of the |m
S
=0⟩
spin state is reduced before the MW1π pulse transfers the population to the|ms=− 1⟩
state. Therefore, when the HTA pulse is in resonance with a transition, an increase in
the FL intensity is observed. For the present experiment, a HTA pulse length of500µ s
was chosen. In principle, longer length pulses, up to T
1
, can be applied. Figure 5.3(c)
shows the result of the experiment and we observe signals at± 88,− 64,− 30,+28, and
+65 MHz. The strong change in the FL intensity at 0 MHz corresponds to the central
blind spot. The signals at− 64 and +65 MHz give the hyperfine coupling constant of
129 MHz, consistent with nearest neighbor
13
C hyperfine interaction ( 126-130 MHz)
splitting the allowed ESR transition.
152–154
The reduced intensity relative to the central
transition corresponds to the low natural abundance of
13
C (∼ 1.1%) and low probability
of nearest neighbor locality.
97
MW1 (n
0
)
p
MW2 (n
1
) HTA
Laser Init RO
m
s
= 0, m
I
=+
m
s
= 0, m
I
=-
m
s
= -1, m
I
=-
m
s
= -1, m
I
=+
ESR (n
0
)
Forbidden
ESR (n
0
)
n
1
> n
0
n
1
< n
0
-100
Frequency Offset [MHz]
-50 0 50 100
Exp.
(a) (c)
(b)
n
1
< n
0
n
1
> n
0
13
C
13
C
14
N
14
N
1
0
2
3
EDNMR Intensity [%]
Figure 5.3: NV detected EDNMR at high field. (a) Pulse sequence used in
the NV-detected EDNMR experiment. In the experiment, a HTA pulse was
applied with MW2 at frequencyν 1
before aπ pulse was applied with MW1 at
frequency ν 0
. The frequency of ν 0
was set to match the lower transition. The
application of a π pulse increases the sensitivity by isolating the FL of [111]
oriented NV centers from non axial orientations. (b) Energy level diagram.
Nuclei coupled via weak hyperfine interaction are represented by m
I
= + and
m
I
=− . During the experiment, the frequency of the HTA pulse is swept from
below (ν 1
< ν 0
) to above (ν 1
> ν 0
) the central ESR resonance. Population
is transferred when the HTA pulse is in resonance with the difference between
coupled states, resulting in an increase in the observed FL. Due to the length
of the HTA pulse and state mixing induced by the hyperfine interaction, this
occurs for both allowed and forbidden transitions. The intensity of the central
blind spot is due to the allowed transitions. (c) Experimental spectra. The data
are shown with reference to the MW frequency offset (ν 1
− ν 0
) and normalized to
the intensity of the central blind spot. In the present case,ν 0
= 229.9528 GHz.
A 500 µ s HTA pulse and 1.9 µ s π pulse were used. The length of the HTA
pulse was chosen to minimize the influence of T
1
relaxation after population
transfer. EDNMR signals due to forbidden transitions involving
14
N and
13
C
are indicated. Grey stars are used to indicate peaks due to allowed transitions
from nearest neighbor
13
C lattice sites. For (c), data was collected using 20
scans over a period of 11 hours. Reproduced from Ref.
149
with the permission
of AIP Publishing.
Next we discuss signals at± 88 MHz. In order to understand the signals we discuss
the following Hamiltonian:
H
NV
=µ B
g
NV
⃗
B
0
· ⃗
S +D
⃗
S
z
2
+H
N
+H
C
, (5.1)
98
where D = 2.87 GHz, g
NV
= 2.0028, and
⃗
S is the electronic spin operator.
118
H
N
andH
C
represent the Hamiltonians of hyperfine coupled nitrogen in the NV center and
surrounding
13
C bath spins. The nuclear spin Hamiltonians may be written as:
H
N
=− γ 14
N
⃗
B
0
· ⃗
I
1
+
⃗
S· ⃗
A14
N
· ⃗
I
1
+PI
2
1z
, (5.2a)
H
C
=− γ 13
C
⃗
B
0
· ⃗
I
2
+
⃗
S· A13
C
· ⃗
I
2
, (5.2b)
where γ nuc
represents the gyromagnetic ratios (3.077 and 10.708 MHz/T for
14
N and
13
C, respectively),
⃗
I
1
(
⃗
I
2
) is the
14
N (
13
C) nuclear spin operator,
⃗
A
nuc
is the hyperfine
interaction (
14
N: A
⊥
=− 2.14 MHz, A
∥
=− 2.70 MHz), and P represents the nuclear
quadrupole interaction (− 5.0 MHz).
134
We focus our study on weakly coupled
13
C
nuclear bath spins. Using Eq. 5.1, we determine all eigenvalues based on the observed
magnetic field. The observed states and energies are listed in Table 5.1.
From Table 5.1, it is seen that the m
S
= 0 states are not evenly spaced around
zero. This spacing is induced by partial field misalignment and nuclear quadrupole
interaction that mixes the states and results in twelve non degenerate energy levels. We
next calculate allowed transitions (∆ m
S
=1,∆ m
I
=0) and double quantum transitions
(∆ m
S
= 1, ∆ m
I
= 1) involving a simultaneous electron and nuclear spin flip. We
tabulate the allowed transitions and double quantum transitions involving
13
C and
14
N
spin flips in Table 5.2. As seen in Table 5.2, the allowed ESR transitions are spaced by
the axial hyperfine coupling to
14
N, contributing to the central blind spot. As shown
in the inset of Fig. 5.4(a), the signals at− 30 and+28 MHz are in excellent agreement
with the predicted peak positions for
14
N predicted in Table 5.2. The proximity to the
central spot makes identification of the peaks at − 18 and20 MHz difficult, but a dip at
− 18 MHz is in agreement with the expected peak position. The polarity inversion of
the signals is under further investigation. The observed signals are not symmetric due
99
Table 5.1: State identification and energy values determined from Eq. 5.1 based
on a magnetic field of 8.306 Tesla with an offset angle of 1.5 degrees and
A13
C
= 1 kHz. The nuclear magnetic spin value of
14
N (
13
C) is shown as
m
I1
(m
I2
).
State|m
S
,m
I1
,m
I2
⟩ Energy [MHz]
-1, +1, +1/2 -230023.7
-1, 0, +1/2 -229995.3
-1, -1, +1/2 -229976.9
-1, +1, -1/2 -229934.8
-1, 0, -1/2 -229906.3
-1, -1, -1/2 -229887.9
0, +1, +1/2 -73.1
0, 0, +1/2 -42.5
0, -1, +1/2 -21.9
0, +1, -1/2 15.9
0, 0, -1/2 46.4
0, -1, -1/2 67.0
to the nuclear quadrupole interaction. The main graph of Fig. 5.4(a) shows the signals
at± 88 MHz in excellent agreement with double quantum transitions for
13
C bath spins
and are well spaced from the central blind spot. We next repeat the measurements on
additional locations to confirm the observed signals. We adjust the mirror to position
2,∼ 50µm from position 1, and repeat EDNMR measurements. We also include data
from a separate experimental run as position 3. For position 3, the sample was removed
from the setup and replaced, resulting in a different sample location. Fig. 5.4(a) shows
13
C EDNMR signals at ± 88 MHz for all positions in excellent agreement with the
simulation.
We next investigate the linewidth of the
13
C signals in more detail. We plot the sig-
nals related to double quantum transitions in Fig. 5.4 and show the transitions as a stick
spectrum. The calculated three transition frequencies are ranged by 4.3 MHz, which
100
Table 5.2: Simulated transition energies calculated from Table 5.1. The states
involved in the transition are listed in the left and central columns, while the
calculated difference is shown in the right column. For clarity, the transition
relative to the central transition (ν sim.
− ν obs.
) was tabulated (ν obs.
= 229.9528
GHz). Allowed transitions (∆ m
S
= 1, ∆ m
I
= 0) are shown in the top panel.
The middle and bottom panel show double quantum transitions (∆ m
S
= 1,
∆ m
I
= 1) involving a simultaneous electron and nuclear spin flip. The middle
panel shows transitions involving
14
N and the bottom panel shows transitions
involving
13
C.
|0,m
I1
,m
I2
⟩ |− 1,m
I1
,m
I2
⟩ ∆ E [MHz]
+1, +1/2 +1, +1/2 -2.1
+1, -1/2 +1, -1/2
0, +1/2 0, +1/2 0.0
0, -1/2 0, -1/2
-1, +1/2 -1, +1/2 2.1
-1, -1/2 -1, -1/2
+1, +1/2 0, +1/2 -30.6
+1, -1/2 0, -1/2
0, +1/2 -1, +1/2 -18.4
0, -1/2 -1, -1/2
-1, +1/2 0, +1/2 20.6
-1, -1/2 0, -1/2
0, +1/2 +1, +1/2 28.4
0, -1/2 +1, -1/2
+1, +1/2 +1, -1/2 -91.1
0, +1/2 0, -1/2 -88.9
-1, +1/2 -1, -1/2 -86.8
+1, -1/2 +1, +1/2 86.8
0, -1/2 0, +1/2 88.9
-1, -1/2 -1, +1/2 91.1
is comparable to the observed linewidth. In general, the EDNMR linewidth is depen-
dent on a variety of factors, including both intrinsic properties, such as spin relaxation
times, and experimental parameters, such as the HTA pulse length and intensity.
148
In
101
(a)
Sample 1
Sample 2
(b)
-40 -20 0 20 40
0
1
Freq. Off. [MHz]
EDNMR [%]
-40 -20 0 20 40
0
1
Freq. Off. [MHz]
EDNMR [%]
Frequency Offset [MHz]
80 100 -80 -100
Pos.3 Pos.2
Pos.1 Sim.
13
C
14
N
Pos.3
Pos.2
Pos.1
13
C
14
N
EDNMR Intensity [%]
EDNMR Intensity [%]
-90 90
Frequency Offset [MHz]
-100 -90 -80 90 80 100
0
1
2
3
4
5
0
1
2
4
5
6
3
Figure 5.4: NV detected EDNMR at 8.3 Tesla (a) NV detected EDNMR from
sample 1. EDNMR detection of
13
C is shown in the main graph and EDNMR
detection of
14
N is shown in the inset. Data is offset for clarity. The pre-
sented data is from three areas: positions 1 and 2 were spaced∼ 50µ m apart,
position 3 was taken after removing and replacing the sample. The data for
position 3 was integrated with boxcar integrators, all other measurements were
integrated using the fast oscilloscope. For position 3, variations in the exper-
imental setup resulted in slightly different parameters: the magnetic field was
8.298 T with a polar offset angle of 1.9± 0.1
o
. Rabi oscillations showed a
π pulse length of 1.6 µ s. The change in magnetic field resulted in a small
(∼ 0.1 MHz) shift in the transition frequencies. The stick spectrum shows
double quantum transitions from Table 5.2. A simulation based upon
13
C cou-
pling to the NV center is shown in red. The red line shows a simulation of
L(ω;∆ ω,ω
i
) = A/π
P
ω
i
∆ ω/(∆ ω
2
+4(ω− ω
i
)
2
) where A is an amplitude
and the sum runs over the resonance positions (ω
i
). A nitrogen spin concentra-
tion of 70 ppm (∆ ω =3.2 MHz) was used in agreement with sample properties.
Nonlinear regression of L(ω;∆ ω,ω
i
) was used to determine ∆ ω from the ex-
perimental data (fits not shown). ∆ ω was measured to be2.3± 0.3,2.9± 0.4,
and3.7± 0.8 MHz for positions 1, 2, and 3 respectively. (b) NV detected ED-
NMR from sample 2. EDNMR detection of
13
C is shown in the main graph and
EDNMR detection of
14
N is shown in the inset. Data is offset for clarity. The
presented data is from three areas: position 1, 2 and 3 were spaced∼ 50 µ m
apart from each other. The stick spectrum shows the position of double quan-
tum transitions. For sample 2,∆ ω was measured to be2.7± 0.3,2.9± 0.3, and
2.5± 0.3 MHz for positions 1, 2, and 3 respectively. Reproduced from Ref.
149
with the permission of AIP Publishing.
the present case, the observed linewidth was observed to be constant when HTA pulse
lengths from 300− 1000 µ s were used, suggesting that the linewidths are broadened
by internal dynamics. Therefore, we focus our discussion on magnetic dipole coupling
102
from surrounding spins which can contribute to the observed linewidth. In general, the
magnetic field at an “A” spin fluctuates due to the interaction with random spin flips of
dipolar-coupled “B” spins. When the concentration of “B” spins is sufficiently dilute,
this interaction broadens the linewidth of the “A” spin by inducing a distribution of Lar-
mor frequencies. In this case, the Larmor frequency fluctuations ( ∆ ω), at an “A” spin
from the j-th dipolar coupled “B” spins may be written as:
∆ ω
j
=γ a
δb
j
=
µ 0
γ a
γ b
ℏ
4π (1− 3cos
2
θ j
)m
j
r
3
j
, (5.3)
where γ a
(γ b
) is the gyromagnetic ratio of the “A” (“B”) spin, µ 0
is the permeability
of free space, and ℏ is the reduced planck constant. The spin state of the j-th spin is
given bym
j
(m
j
=± 1/2 for anS = 1/2 spin) withθ j
representing the angle between
the vector joining the spins, r
j
, and the applied magnetic field. Now by considering
that “B” spins are randomly distributed and the populations of the up- and down-states
of “B” spins are equal, we can average ∆ ω
j
by considering the probability of finding
a spin at the j-th position and integrating over possible angles and spin states.
54, 155, 156
The integral gives the full-width at the half-maximum of the Lorentzian function as a
linewidth (∆ ω), which may be written as:
∆ ω =
X
j
∆ ω
j
=
2πµ 0
ℏ
9
√
3
γ a
γ b
n, (5.4)
where n is the concentration of “B” spins in units of spins per cubic meter. In the case
of the present EDNMR study, “A” spin is the NV center and “B” spins are surrounding
paramagnetic spins such as P1 centers and
13
C nuclear spins. The concentration of
nitrogen in the present sample was estimated to be∼ 70 ppm from a 230 GHz pulsed
ESR measurement of the P1 center’sT
2
(T
2
=1.07± 0.01µ s; data not shown).
64
Using
103
70 ppm for the concentration of P1 centers, we obtained ∆ ω = 3.2 MHz. As shown
in Fig. 5.4, the simulated peaks with the three resonance frequencies and ∆ ω gives
excellent agreement with the observed data. Furthermore, the observed linewidth is in
excellent agreement with the linewidth of the lower NV resonance (Fig. 5.2 (a)) and
with previous work on type-Ib diamonds.
64
The use of high purity, isotopically purified
diamonds with low concentrations of paramagnetic spins can be used to further improve
the spectral resolution and is the subject of current work. For example, we note that
Eq. 5.4 predicts∆ ω∼ 0.2 MHz from dipolar broadening due to natural abundance
13
C.
We next discuss measurements on sample 2. All measurements previously discussed
were repeated on sample 2. From measurement of both the lower and upper ODMR
transitions, the magnetic field was determined to be 8.306 T with a polar offset angle of
1.88± 0.03
o
. Rabi oscillations showed aπ pulse length of1.6µ s and theT
1
relaxation
time was measured as3.8± 0.3 ms (data not shown). As seen in Fig. 5.4(b), EDNMR
was measured at three different locations on sample 2, with EDNMR signals from
13
C
resolved at± 88 MHz in each location. The observed signals are in excellent agreement
with the expected peak positions. The slight variation in the observed height and width
from sample 1 indicates small sample to sample variation. The inset shows EDNMR
signals resolved from
14
N. Clear signals are resolved at− 31 and+28 MHz in excellent
agreement with the simulated peak positions and sample 1.
5.4 Summary
We have demonstrated pulsed ODMR on an ensemble system of NV centers at 8.3 Tesla
and 230 GHz. Ensemble NV centers were utilized to perform pulsed EDNMR with
optical readout of the spin population. EDNMR signals were resolved from
13
C bath
spins with the linewidth limited by the concentration of paramagnetic impurities. This
104
work provides a clear demonstration of NV center detected EDNMR, and establishes
groundwork for the implementation of NV-detected NMR at higher magnetic fields,
with shallow NV centers, and for the study of nuclei with a variety of gyromagnetic
ratios. EDNMR can resolve spins whose gyromagnetic ratios shift the resonance from
the central blind spot. Nuclei with large gyromagnetic ratios, such as
1
H and
19
F , are
excellent candidates for future research. Signals from bath
13
C spins were resolved in
this work. From previous measurements, it is known that weakly coupled
13
C hyper-
fine interaction is on the order of 10− 100 kHz.
145, 157
Based on a dipolar calculation,
a hyperfine coupling of more than 10 kHz is expected for surface protons within 8 nm
of NVs. With the fabrication of NVs with T
1
times of a few ms, stable photolumines-
cence, and a depth of at least 8 nm,
158–160
NV-NMR of protons at the diamond surface
will be detectable with the presented EDNMR technique. Chemical functionalization
techniques can be used to bring spins of interest within close proximity of shallow NV
centers.
99, 123
Furthermore, the described technique is limited by the comparative length
of the HTA pulse relative to T
1
relaxation. As T
1
can be extended up to several sec-
onds at cryogenic temperatures, this technique can utilize a long HTA pulse to perform
measurements at higher fields and frequencies where microwave power is often lim-
ited.
118, 150
With the development of suitable pulsing techniques, this method will enable
measurements in higher magnetic fields, such as those in the National High Magnetic
Field Laboratory.
161, 162
105
Chapter 6: Microwave AC voltage
induced phase change in Sb
2
Te
3
nanowires
Materials presented in this chapter can also be found in the article titled Microwave AC
voltage induced phase change in Sb
2
Te
3
nanowires by Pok-Lam Tse, Fugu Tian, Laura
Mugica-Sanchez, Oliver R¨uger, Carsten Ronning, Andreas Undisz, George M¨othrath,
Susumu Takahashi, and Jia Grace Lu in ACS Nano Letters 12, 8668–8674 (2020).
Another realm in the development and characterization of nanoscale materials is
their application in quantum computing and optoelectronics. Topological insulators (TI)
are electrical insulators in the bulk with conducting surfaces owing to their topological
order. TIs like Sb
2
Te
3
have gained increased attention thanks to their matchless prop-
erties such as narrow band gap, protected conducting surface edges states, saturable
absorber character, very high damage threshold, low saturable optical intensity, easily
synthesize and low cost.
163
Thus far, the behavior of TIs has been tuned by temperature
changes. Achieving easy tuning of the phase change of Sb
2
Te
3
nanowires by varying the
frequency range provides an accessible path to their implementation in supercomputing
systems. Furthermore, in combination with superconductors, TIs could lead to a new
architecture for topological quantum bits.
106
6.1 Introduction
Non-volatile memory cells with high read/write speed have been the quest in the past
decades for superior performance in computing and communication electronics.
164–166
Phase change materials (PCM) have evolved into the industrial development stage when
the traditional technologies decelerate. PCM demonstrates a competitive read/write
speed compared to flash and embedded memories in solid state drives.
167–169
With their
high speed and remarkable cycling endurance, PCM in nanostructured forms is consid-
ered as a potential replacement for storage- class memory with exceptional computing
performance and reduced power consumption. Ge
2
Sb
2
Te
5
has been extensively studied
by slow passive heating and annealing
165–170
to judiciously separate out the amorphous,
cubic and hexagonal crystalline phases.
171, 172
In comparison, the binary Sb
2
Te
3
com-
pound has similar phase change properties but a lower melting temperature
173
than that
of Ge
2
Sb
2
Te
5
. This implies reduced power requirement for information encoding, and
thus relieves the heating problem on an integrated device chip. In addition, Sb
2
Te
3
attracts increasing research interests due to the existence of linearly dispersed surface
states
174
in the band structure, which could bring new perspectives from quantum me-
chanics in future device designs.
Conventional operation of phase change random access memory (PCRAM) is based
on the transition between the crystalline and amorphous phase, which can yield several
orders of magnitude difference in the electrical resistance.
167, 171, 175
In such a design,
applying a direct current (DC) voltage pulse in a single step to memory cells is the most
common method to switch memory states.
171, 176
In our work, we present alternate cur-
rent (AC) voltage sweep measurements from radio frequency to microwave range on
Sb
2
Te
3
nanowires, which reveal a systematic stepwise increase in DC resistance at∼ 3
107
GHz. The samples are cross-investigated by transport measurements, as well as high res-
olution electron microscopy analysis on segments with and without undergoing the AC
voltage sweeps. This unique phenomenon suggests that one can change the resistance
with an AC frequency knob. This extra degree of freedom for memory state switching
can lead to innovative developments in PCRAM for neuromorphic computation. It pro-
vides a futuristic technique to control the amount of phase change in the material, which
can be utilized to obtain the optimum crystalline-amorphous ratio in order to reach a
targeted resistance as an intermediate memory state. Consequently, such intermediate
states pave the way to a new frame of applications of multi-level storage with a simple
device, which is very difficult to be achieved with the traditional heating or application
of voltage pulses.
6.2 Methods and Materials
Sb
2
Te
3
nanowires (NWs) were synthesized by Au-catalyzed chemical vaporized depo-
sition (CVD) enabling the vapor-liquid-solid growth mechanism.
177
First, the Si/SiO
2
substrate was coated with 0.1 wt% poly-L-lysine to enhance the Au nanoparticle adhe-
sion, then a solution with Au particles having diameters of about 30 nm was dispersed
onto the substrate surface. Afterward, the CVD process was carried out in a quartz tube
inside a horizontal furnace setup. The source material of 0.6 g Sb powder was placed
in the center of furnace, 1 g Te powder at 13.5 cm away from center at upstream; and
the Au nanoparticle coated Si/SiO
2
substrate was set at 10.5 cm downstream from cen-
ter. Argon was used as a carrier gas at a flow rate of 80 standard cubic centimeters
per minute (sccm) at 2.67 - 5.33 mbar partial pressure. The process began with heating
up the quartz tube to 430
o
C in 20 minutes, then maintaining the temperature for 6 h.
108
Figure 6.1: Reproduced from Ref.
178
with the permission of ACS Publishing.
Pristine NWs on the as-grown substrates were then transferred to new substrates by son-
ication in isopropyl alcohol, and subsequently pipetted onto proper substrates for device
fabrication and microscopy analysis. The NW devices with 100 nm Au electrodes on
a 5 nm Ti adhesion layer were fabricated by photolithography and the device with Nb
electrodes was fabricated by e-beam lithography. In the AC sweep measurements, the
source and drain contacts of the devices were connected to bias-Ts at the source elec-
trode to mix DC signals from a DC analyzer (Agilent hp4156p) and AC signals from
a microwave (MW) source (SRS SG380); and at the drain electrode, to separate DC
signals to ground and AC signals to MW power detector (Windfreak SynthNV).
Fig. 6.1 shows the circuit diagram of one NW device on a Si/SiO
2
substrate. Coaxial
cables were used to minimize AC signal loss and the power detector was in place to
ensure minimum MW power transmission at -49 dBm (1.26 x 10
− 8
W). The device was
cooled down to about 77 K in high-vacuum (1.0 x 10
− 7
mbar) in order to ensure that
thermal effects were only dependent on the MW input power. The AC sweeps were
conducted between 10 MHz and 4 GHz at 10 to 20 MHz steps; I-V sweeps from -150
nA to +150 nA were carried out at each frequency step, and the differential resistance
was calculated for the nanowire at each corresponding frequency. Both forward and
109
backward sweeps between 10 MHz and 4 GHz were conducted to probe the reversibility
of the MW responses.
In order to investigate the temperature dependence of the electrical resistance, mea-
surements were done during cooling down and warming up from 75 to 300 K. A ref-
erence pristine sample (NW4), without undergoing any AC sweep, was measured sep-
arately in the same temperature range to compare the temperature dependence of the
resistance. For electron microscopy analysis, cross-sections were taken from one single
nanowire at two different parts: one segment was subject to AC sweeps, whereas the
second segment did not. The specimen were prepared using a focused ion beam system.
Briefly, a Pt protective layer was first deposited on the targeted NW segment by electron
beam induced decomposition of molecules. Then the substrate material in the surround-
ing area was sputtered away using the focused ion beam. After that, the lamella was
lifted off from the substrate and transferred to the omni-probe copper grid. Finally, the
thickness of the lamella was thinned down to about 50 nm for high-resolution transmis-
sion electron microscopy (TEM) analysis using a CS-corrected JEOL NEOARM 200
F. The TEM analysis was performed with 80 keV electrons at low currents in order not
to induce any phase change or degradation by the impact of electron beam, which was
correspondingly checked upon the analysis.
6.3 Results and Discussions
Sb
2
Te
3
has a bulk band gap of 0.28 eV and simple surface states consisting of a single
Dirac cone in the band gap. The pristine crystalline structure of Sb
2
Te
3
thin films and
nanowires is hexagonal, and the primitive cell is rhombohedral (R3m). Our previous
studies on the nanowires have revealed the single crystalline structure with repeating
quintuple layers of (Te-Sb-Te-Sb-Te) with an interlayer distance of 0.309 nm.
174, 179–182
110
Figure 6.2: (a) SEM image of a Sb
2
Te
3
NW on a Si/SiO
2
substrate. Images (b)
and (c) illustrate the EDX color mappings of the respective Sb and Te elements.
(d) EDX spectra and (e) XRD spectra of Sb
2
Te
3
nanowires. The peaks fit with
the rhombohedral structure of Sb
2
Te
3
(PDF # 00-015-0874). (f) TEM image
with lower right SAED inset showing the hexagonal crystalline structure; and
upper left cross-section HRTEM inset displaying the stacked quintuple layers
(QL). Reproduced from Ref.
178
with the permission of ACS Publishing.
We have also in the past performed low temperature magnetoresistance measurements
and angle resolved photoemission spectroscopy on the nanowires synthesized by the
same setup as presented in this work. The observed periodic Aharonov-Bohm type
oscillations are attributed to transport in topologically protected surface states in the
p-type Sb
2
Te
3
nanowires, with a Fermi level that situates around 40 meV below the
Γ -point.
174
The scanning electron microscope (SEM) image in Fig. 6.2(a) shows a single
Sb
2
Te
3
nanowire on a Si/SiO
2
substrate. Energy dispersive X-ray (EDX) spectroscopy
mapping for Sb and Te are displayed in Fig. 6.2(b) and Fig. 6.2(c), respectively. The
mappings of Sb and Te illustrate uniform elemental distributions along the nanowire.
From the EDX spectra in Fig. 6.2(d), the atomic ratio of Sb:Te is calculated to be
2:3. Powder X-ray diffraction (XRD) (Rigaku Ultima IV diffractometer) is carried out
in θ /2θ mode with a scan speed of 4
o
/min. The crystal structure is confirmed to be
rhombohedral (PDF# 00-015-0874), as shown in Fig. 6.2(e). A TEM image of the top
view of the nanowire is displayed in Fig. 6.2(f), showing that the growth direction is
111
Figure 6.3: Consistent increases occur at 3 GHz for all three NW samples.
Forward sweep results for samples NW1, NW2 and NW3 are separately shown
in (a), (b) and (c). In (c), the resistance rise at 3 GHz jumps out of the preset
range of DC measurement. Reproduced from Ref.
178
with the permission of
ACS Publishing.
along [110]. The lower right inset depicts the corresponding SAED pattern, verifying its
single crystalline hexagonal/rhombohedral nature. The upper left inset of Fig. 6.2(f) is
the crosssection TEM image of a NW, manifesting the repeating quintuple layers (QL).
Three NW samples have been investigated at 77 K for MW responses, with their
results plotted separately in Fig. 6.3 Clearly, the common phenomenon for all three
NWs is the increase in the electrical resistance sharply around 3 GHz, independent of
the geometry or material of the electrodes contacting the NWs. NW1 with Nb electrodes
at 1 µ m apart has an initial resistance of about 2800 Ω . Its AC sweep measurement is
112
Figure 6.4: The sweep directional arrows with color correspond to the data
plot in the same color. Reproduced from Ref.
178
with the permission of ACS
Publishing.
plotted in Fig. 6.3(a), indicating a resistance jump to 3350 Ω at 3 GHz in the first
forward sweep from 10 MHz to 4 GHz. Similar results are observed in NW2 ( 6.3(b))
and in NW3 (Fig. 6.3(c)), both fabricated with Ti/Au source and drain electrodes at 2
µ m apart. It has been shown from the comparison of 2-probe and 4-probe measurement
that the contact between either Nb or Ti/Au to the nanowire is of ohmic nature with
negligible contact resistance (data not shown).
NW2 sample was selected for subsequent continuous backward and forward AC
sweeps at a power level around -30 dBm (1µ W) after the initial forward sweep displayed
in Fig. 6.4. For the first three sweeps shown (backward in black line, forward in red
line and backward in blue line), the resistance starts to slightly increase between 2.8
and 3 GHz for both forward and backward direction. Then at the subsequent sweeps,
the resistance change becomes much more pronounced when the frequency reaches 3
GHz. The final sweep spikes the resistance to a saturation level of 108 Ω at 3 GHz, as
illustrated in the green line.
113
Figure 6.5: : 60 s (step 4, 6, 8 and 10) and 5 s (step 5, 7 and 9). Reproduced
from Ref.
178
with the permission of ACS Publishing.
NW2 was further investigated for the resistance change by passive heating to verify
that the resistance change originated from a phase change and not due to other artifacts
such as oxidation or decomposition. Short 5 s heating and long 60 s heating steps were
imposed by placing the NW sample on a piece of aluminum block in the center of a
heat plate at 130
o
C. Upon long 60 s heating on the heat plate at 130
o
C, the resistance
of NW2, which was driven to a saturation level by the AC voltage sweep, switched
back to crystalline phase with resistance in the 103Ω range. And with short 5 s passive
heating followed by quick quench to room temperature, the nanowire was switched to
the amorphous state, resulting in a resistance increase to 105 Ω range. Passive heating
results in Fig. 6.5 show that the reversible resistance change: decrease to ∼ 4 – 6
kΩ after applying 60 s long heating, and increase to∼ 105 Ω after 5 s short heating.
The reversibility of high and low resistances in alternating short and long heating steps
verifies that the sample after AC sweeps had gone through phase transition.
After the two samples (NW2& NW3) reached the saturation levels, the resistances
were measured from 77 K to room temperature. It was found that the resistances of both
114
samples first increased and peaked at ∼ 100 K (as shown in Fig. 6.6(a) and (b)]), then
they decreased exponentially with increasing temperature. Arrhenius semi-log fittings
oflnR vs1/(k
B
T) (whereR is DC electrical resistance,k
B
is Boltzmann constant, and
T is temperature), between 110 K and 300 K are plotted, as shown in the insets. The
results reveal that the transport is governed by thermal excitation conduction with two
distinct regions between 110 – 220 K and 220 – 300 K, and with respective activation
energy around 48 meV and 100 meV .
These values are close to the thermal activation energies attributed to phonon-
assisted hopping of small polarons, i.e. localized charges that are “self-trapped” within
potential wells produced by distorting the surrounding atoms.
183
The exact transport
mechanism is by itself a fascinating topic, which requires additional studies with See-
beck and Hall measurements. In contrast to NW2 and NW3 samples, the pristine refer-
ence sample NW4, which did not undertake microwave sweeps, keeps a linear relation
of resistance-temperature (R–T) with R (Ω ) ∝ 0.95(Ω /K)· T(K), as shown in Fig.
6.6(c)], manifesting a metallic behavior as in the initial state with a typical temperature
coefficient estimated to be ∼ 0.0014 /K.
The next investigation was to find out whether one can achieve segment-wise en-
coding along one nanowire sample, i.e. to obtain different resistance states in desired
segments of one single wire. Four electrodes were fabricated across a long nanowire
over 10µ m (NW5, as shown in the inset of Fig. 6.8(a)). The segment of NW between
contacts 2-3 undertook AC sweeps to get switched from low resistance to high resis-
tance state; whereas the segment between electrodes 4-5 was afloat, not connected to
either the DC analyzer or the MW power source. Fig. 6.8(a) shows the AC sweeping
results of the segment between electrodes 2-3 at 77 K. The first sweep at -26 dBm MW
power did not induce a resistance change at 3 GHz, whereas the second sweep at -24
115
Figure 6.6: (a) NW2, inset: corresponding Arrhenius semi-log plot with linear
fittings, showing two regions of thermal activated transport; (b) NW3, inset:
corresponding Arrhenius correlation, suggesting two regions with respective
activation energy of∼ 48 and∼ 100 meV . (c) NW4 reference sample with linear
regression fit in red demonstrating metallic behavior. Reproduced from Ref.
178
with the permission of ACS Publishing.
dBm MW power increased the resistance sharply at 3 GHz. After continuous forward
and backward sweeping at 77 K at -24 dBm, the NW reached and saturated at a high
resistance state.
To verify any further resistance changes, additional forward and backward AC
sweeps of NW5 segment between contacts 2-3 saturates at high resistance state were
performed. Fig. 6.7 shows the AC sweep result of the segment after it gets switched
116
Figure 6.7: Reproduced from Ref.
178
with the permission of ACS Publishing.
to high resistance state. The resistance of this segment of NW saturates at∼ 2× 10
6
Ω throughout the range of AC forward and backward sweeps at -24 dBm.
The R–T relation of this segment between electrodes 2-3 is plotted in Fig. 6.8(b) and
Fig. 6.8(c) upon cooling down and upon warming up after the AC sweeps, respectively.
The linear relation during cool down indicates that the initial low resistance state has
metallic behavior, consistent with the reference NW4 sample shown in Fig. 6.3(c). Af-
ter reaching the high resistance state, the resistance decays exponentially with increasing
temperature (Fig. 6.8(c). The inset in Fig. 6.8(c) shows the Arrhenius semi-log fitting,
confirming the two ranges of thermal activation transport as that of NWs 2 and 3.
Fig. 6.9 shows that the segment between electrodes 4-5 in NW5 maintained a linear
R–T relation after the AC sweeps on the other segment between electrodes 2-3. These
results demonstrate that the AC sweeps can change locally the resistance of a single
nanowire, which renders a blue print of selective phase change based nanowire bit-train.
High-resolution TEM analysis on the two segments in NW5 after AC sweep was
performed to examine the microstructure. Fig. 6.10(a) shows the SEM image of the
117
Figure 6.8: (a) AC voltage sweep at 77 K across electrodes 2-3 of NW5. Re-
sistance starts to increase sharply at 3 GHz for -24 dBm sweep (red line). Inset:
optical image of NW5 with four electrodes. (b) R–T plot at cool down for NW
segment 2-3 before AC sweeps, showing linear metallic conducting behavior.
(c) R–T plot at warm up stage after MW switching to high resistance state,
showing exponential drop in resistance with increasing temperature. Inset: Ar-
rhenius plot confirming the two thermal activation energies agreeable with NW2
and NW3. Reproduced from Ref.
178
with the permission of ACS Publishing.
to- be-carved-out regions for cross-section TEM analysis, as indicated by yellow and
blue arrows. Fig. 6.10(b) shows the cross-section TEM image in the segment between
contacts 2-3, which has been subject to AC sweeps. Fig. 6.10(d) and (f) are the high
resolution TEM and FFT images, respectively, with hazy ring patterns, indicating that
the region D is predominantly amorphous, corresponding to the high resistance and
semiconducting behavior.
Region B shows the same structural features; whereas, regions A and C show a lay-
ered structure, likely to be in transition to amorphous state (Fig. 6.11). In contrast, Fig.
6.10(c) shows the cross-section TEM image of the segment between contacts 4-5, which
has not been subject to AC sweeps. Apart from the amorphous and layered structures
respectively shown in region E and F, region G reveals a polycrystalline structure with
clear diffraction spots, as shown in the high-resolution TEM image and FFT image (Fig.
6.10(e) and (g)).
This region contributes dominantly to the low resistance and metallic conduction
behavior. Furthermore, the Sb and Te elemental composition and stoichiometry are
118
Figure 6.9: carried out in electrodes 2-3, maintains the low resistance metallic
state, indicating that information encoding can be done segment-wise along one
nanowire. Inset: optical microscope image of the NW5 sample. Reproduced
from Ref.
178
with the permission of ACS Publishing.
Figure 6.10: (a) SEM image of NW5 after AC sweep measurements. Yellow
and blue arrows indicate the segments selected for TEM cross-section imaging:
between contacts 2-3 (underwent AC sweep) and between contacts 4-5 (without
AC sweep). (b) TEM cross-section image of a slice of NW5 segment between
contacts 2-3, with high resolution TEM and FFT analysis indicating an amor-
phous phase, as shown in (d and f). (c) TEM cross-section image of a slice of
NW5 segment between contacts 4-5, with high resolution TEM and FFT analy-
sis indicating a polycrystalline phase, as shown in (e and g). Reproduced from
Ref.
178
with the permission of ACS Publishing.
119
Figure 6.11: Reproduced from Ref.
178
with the permission of ACS Publishing.
measured by EDX in the center of NW5 (Fig. 6.12). The elemental composition com-
parison of NW5 was illustrated by carrying out SEM EDX on segments with and without
going through AC sweeps. Fig. 6.12(a) shows the SEM image of the cross-section of
NW segment between contacts 2-3 which underwent AC sweeps and the EDX measure-
ment at the region marked by the yellow cross is shown in Fig. 6.12(b). Fig. 6.12(c)
shows the SEM image of the cross-section of NW segment between contacts 4-5 with-
out AC sweeps and Fig. 6.12(d) shows the corresponding EDX spectrum. Fig. 6.12(e)
shows the overlap of these two EDX spectra, indicating that the two spectra are similar
in the signal intensity related to Sb and Te. The results demonstrate that both segments
preserve the Sb
2
Te
3
composition and with no oxidation or decomposition.
The atomic ratio of the NW is also measured by the TEM EDX line scan. Fig.
6.13(a) shows the TEM image of the NW segment between contacts 4-5 and the red
dash line indicates the region of line scan. Fig. 6.13(b) is the atomic ratio plot along
the scan line, showing the atomic percentage of Sb around 40% and Te about 60%,
120
Figure 6.12: (a) and (b) SEM image of the cross- section of the NW segment
between contacts 2-3 and the corresponding EDX spectrum. (c) and (d) SEM
image of the cross-section of the NW segment between contacts 4-5, and its
EDX spectrum. (e) Overlap of the two EDX spectra, showing similar Sb and Te
contents. Reproduced from Ref.
178
with the permission of ACS Publishing.
confirming the 2:3 of Sb:Te stoichiometry. This result also reveals that the nanowire has
minimal oxidation or composition change from the AC sweep measurements.
Thus far we have observed reproducible sharp increases in resistance at∼ 3 GHz as
a result of AC sweeps on single Sb
2
Te
3
nanowires. The low to high resistance switch by
6 - 7 orders of magnitude at∼ 77 K is accompanied by a change of metallic to semicon-
ducting conduction characteristic, and correspondingly from crystalline to amorphous
structure. At first glance, one may deduce from these evidences that the MW power at
about 1µ W may have induced a phase change within the Sb
2
Te
3
nanowire, via dielec-
tric heating, comparable to that in the 2.45 GHz microwave oven since the dielectric
constant of Sb
2
Te
3
at 77 K is on the same order of magnitude with that of water at room
temperature. Refer to the heat capacity equation from Pashinkin et al.,
184
a rough cal-
culation of the energy required for a 2.5 µ m long, 200 nm in radius NW segment, to
be heated up from 77 to 403 K (130
o
C) is∼ 0.1 nJ. Thus, the 1 µ W (-30 dBm) AC
121
Figure 6.13: (a) SEM image of the cross-section of the segment, the dash line
indicates the line scan region. (b) Atomic ratio along the line scan, with the Sb:
Te = 2:3. Reproduced from Ref.
178
with the permission of ACS Publishing.
voltage could easily provide enough energy to heat up and amorphize the NW. Indeed,
such heating has even caused morphology changes shown in NW5 (Fig. 6.10(a)). Nev-
ertheless, this interpretation fails to address the facts that the transition occurs only∼ 3
GHz, and also the phase change is concentrated locally in a segment within a wire.
Such sharp transition at a resonant frequency signals that the mechanism is of an
electronic transition nature. Recent work on bonding calculations and simulations
185–187
suggests that the transition from low resistance to high resistance state in PCMs origi-
nate from the change of chemical bonding. Wuttig et al. has proposed a new state of
matter for materials, such as Sb
2
Te
3
, Ge
2
Sb
2
Te
5
, GeTe, etc., so called “incipient met-
als”.
185, 188, 189
Their unique metavalent bonding goes beyond the characteristic param-
eters for conventional solid state bonding, and possesses bonding mechanism between
those of covalency and metallicity, but at the same time, distinctly different from both.
We believe that the origin of the phase transition we have observed is induced by the
distortion in bonds under charge shuffling resonating at 3 GHz, such as in the resonance-
like bonds formed between Sb and Te layers by 5p electrons. As a result, it leads to the
transition from delocalized to localized electron distributions,
190–192
rendering self-trap
potential wells,
171, 193
and exhibiting thermally activated transport as shown in the trans-
port measurements. In depth investigations are required to elucidate the nature of the
atomistic bonding mechanisms.
122
6.4 Summary
Reproducible resistance increases in Sb
2
Te
3
nanowires are observed at∼ 3 GHz during
radio frequency to microwave AC voltage sweeps. The resistance jump is evidenced
by a transition from crystalline metallic to amorphous semiconducting phase. This the
low to high resistance change is accompanied by a phase change from a rhombohedral
crystalline to an amorphous disordered structure, which is verified by high-resolution
electron microscopy analysis performed at nanowire segments with and without AC
sweeping measurements. Correspondingly, the resistance change manifests in a metal-
lic to semiconducting transition, which is demonstrated in the temperature dependent
conductance measurements. This new phenomenon of microwave AC voltage induced
amorphization of crystalline phase change material is of fundamental interest for both
experimentalists and theorists to elucidate the physical nature of the phase change, espe-
cially from the perspective of bonding mechanisms. In addition, it is also unknown what
role the surface states play in the phase change in the Sb
2
Te
3
nanowire, which is known
to have topological surface state conduction. On the other hand, this discovery could
bring technology innovation for neuromorphic computing devices. With an additional
AC frequency control, one can envision potential multi-state information bit encoding
and discrimination along a single nanowire,i.e. a phase change nanowire based bit train.
123
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Appendix A
Conversion of Lab Frame to Phase Modulated Frame
The relationship between the lab frame (LF) and the phase modulated (PM) frame is the
following:
|Ψ PM
⟩=
ˆ
R
z
(− Φ PM
(t))|Ψ LF
⟩ (1)
Φ PM
(t) is a time dependent angle. We consider the case where the frame rotates
with a constant frequencyω
PM
around the z-axis.
Φ PM
=ω
PM
t+ϕ PM
(t) (2)
Let’s consider the time derivative of |Ψ ⟩
PM
. Using the chain rule we obtain the
following:
d
dt
|Ψ PM
⟩=
d
dt
(
ˆ
R
z
(− Φ PM
))|Ψ ⟩
LF
+
ˆ
R
z
(− Φ PM
)
d
dt
|Ψ LF
⟩ (3)
The first term corresponds to the time derivative of the rotation operator:
d
dt
(
ˆ
R
z
(− Φ PM
))|Ψ LF
⟩=
d
dt
exp(− iωt
ˆ
S
z
)|Ψ LF
⟩=iω
ˆ
S
z
exp(− iωt
ˆ
S
z
)|Ψ LF
⟩=
iω
ˆ
S
z
ˆ
R
z
(− Φ PM
)|Ψ LF
⟩ (4)
141
By using Eq. 1, Eq.4 becomes:
iω
ˆ
S
z
ˆ
R
z
(− Φ PM
)|Ψ LF
⟩=iω
ˆ
S
z
|Ψ PM
⟩ (5)
The second term of Eq. 3 may be obtained by the time dependent Schrodinger
equation:
ˆ
R
z
(− Φ PM
)
d
dt
|Ψ PM
⟩=− i
ˆ
R
z
(− Φ PM
)
ˆ
H
LF
|Ψ PM
⟩ (6)
From the inverse relationship of Eq. 1: |Ψ ⟩
LF
=
ˆ
R
z
(− Φ PM
(t))|Ψ PM
⟩, Eq. 6
becomes:
ˆ
R
z
(− Φ PM
)
d
dt
|Ψ PM
⟩=− i
ˆ
R
z
(− Φ PM
)
ˆ
H
LF
ˆ
R
z
(Φ
PM
)|Ψ PM
⟩ (7)
The final expression of the time derivative of the PM frame is obtained by adding
Eq. 5 and Eq.7
d
dt
|Ψ PM
⟩=− i
ˆ
H
PM
|Ψ PM
⟩ (8)
where,
ˆ
H
PM
=
ˆ
R
z
(− Φ PM
)
ˆ
H
LF
ˆ
R
z
(Φ
PM
)− ω
ˆ
S
z
(9)
142
Appendix B
Conversion of FL intensity to P(m
s
= 0)
In this section we describe the analysis of the pulse measurements based on the
P(m
s
=0). The collection of the data includes a 5µ s pulse to initialize the NV into the
|m
s
=0⟩ state, next a pulse sequence with MW application is performed to manipulate
the quantum coherent states of the NV . Finally the states are mapped to the|m
s
=0⟩
state and a readout fluorescent pulse is collected. The FL intensity was then converted
toP(m
s
=0) as follows:
P(m
s
=0)=
I
MW
− I(|m
s
=− 1⟩)
I(|m
s
=0⟩)− I(|m
s
=− 1⟩)
(10)
I
MW
is the fluorescence intensity of the spin state during the MW application,
I(|m
s
=0⟩) is the fluorescence intensity of the initialization pulse, and I(|m
s
=− 1⟩) is
the fluorescence intensity of the NV dark state readout with an additional channel with
the application of aπ pulse during the pulse sequence. The FL traces of|m
s
=− 1⟩ and
|m
s
=0⟩ were fit to a polynomial (n=3) to avoid further increase in the noise level to the
processed data intoP(m
s
= 0). The error propagation forP(m
s
= 0) is then obtained
as:
s
2
P(ms=0)
=

∂P(m
s
=0)
∂I
MW

2
s
2
I
MW
+

∂P(m
s
=0)
∂|− 1⟩

2
s
2
p(|− 1⟩)
+

∂P(m
s
=0)
∂|0⟩

2
s
2
p(|0⟩)
(11)
143
wheres
2
p(|− 1⟩)
ands
2
p(|0⟩)
correspond to the standard deviation of the polynomial fit to
the data of the|m
s
=− 1⟩ and|m
s
=0⟩ states, respectively. Ands
2
I
MW
is the standard
deviation of the fluorescence signals from I
MW
.
144
Appendix C
Functionalization and Characterization of Glass Slides
Prior to functionalization of diamond, the HTHC method discussed in Chapter 3 was
applied to glass slides. Fig. 14(a) shows the survey spectrum for glass functionalized
with silane in which the distinct silane peaks are observed on the 200-50 eV region.
Upon exchange of the surface bromine atom with azide we observe the disappearance
of the bromine peaks and no trace of nitrogen signal is observed (Fig. 14(b)). This
suggests that the silane molecule was most likely adsorbed to the surface rather than
linked through a covalent bond.
 
 
 
405 400 395 410 390
Binding Energy (eV)
 
G-N
3
G-Br
N 1s

(a)
(b)
 
 
0 600 500 400 300 200 100
 
Binding Energy (eV)
G-N
3
G-Br
G-OH
Signal Intensity (a.u.)
C 1s silane C 1s silane
Figure 14: (a) Survey XPS of glass up to azide step. The silane signals are
shown in the 200-50 eV region. (b) High resolution scan for N 1s.
We proceed to optimize the reaction conditions by implementing the LTLC method.
Fig. 15(a) shows the XPS survey spectrum of the glass slide functionalized up to the
azide step and in this case we observe a reduction in the bromine peak (Fig. 15(b)).
While no trace of nitrogen is observed on the survey spectrum for G-N
3
, a clear azido
signal is observed in the N 1s high resolution spectrum (Fig. 15(c)).
145

(a) (b) (c)
Br 3d
Binding Energy (eV)
76 74 76 74 78 72 70 68 405 400 395 410 390
Binding Energy (eV)
 
 
G-N 3
G-Br
N 1s
 
 
G-N 3
G-Br
0 600 500 400 300 200 100
Binding Energy (eV)
 
G-N
3
G-Br
G-OH
Signal Intensity (a.u.)
C 1s
silane
Figure 15: (a) Survey XPS of glass up to azide step. The silane signals are
shown in the 200-50 eV region. (b) High resolution scan for Br 3d showing a
reduction of the peak after functionalization with azide. (c) N 1s high-resolution
scan shows the characteristic azido lineshape for G-N
3
.
It has been suggested that siloxane bonds stabilize under storage after a few days
or after an annealing process.
106
For this reason, we study the stability of the silane
molecule under storage for five days under different conditions. The first one in direct
contact with air, the second stored in a furnace at 60
o
C and finally stored in DMF. Fig.
16(a) shows the XPS survey spectrum of silanized glass after five days. It is seen that the
silane is stable in all of these conditions and not a remarkable difference in the bromine
content is observed.
78 76 74 72 70 68 66 64
 
 
 
 
G-Br(air)
G-Br(furnace)
G-Br(DMF)
Binding Energy (eV)
Signal Intensity (a.u.)
 
 
 
 
 
 
G-Br(air)
G-Br(furnace)
G-Br(DMF)
 
0 500 400 300 200 100
 
Binding Energy (eV)
Signal Intensity (a.u.)
Br 3d
 
(a)
(b)
C 1s
Br 3s
Br 3p
Br 3p 1/2
Br 3p 3/2
Si 2s
Si 2p
Br 3d
Figure 16: (a) Survey XPS of glass up to silanization step kept under three
different conditions for five days. (b) Br 3d high resolution scan for G-Br shows
a slight peak reduction for Br 3d kept in DMF.
146
Finally, we study the stability of the triazole ring formed after the click reaction
step. It can be seen in Fig. 17 that the The N 1s signal remains intact under different
conditions. We conclude that storage of TEMPO in air at RT for up to 48 h does not
cause degradation of the triazole ring.
 
 
 
 
 
 
0 600 500 400 300 200 100
 
Binding Energy (eV)
G-TEMPO (DMF - 24 h)
G-TEMPO (air 60 C - 24 h)
o
G-TEMPO (air RT - 48 h)
G-TEMPO (air RT - 24 h)
Signal Intensity (a.u.)
Si 2p
Si 2s
C 1s
N 1s
Figure 17: The nitrogen signal remains intact.
147

Abstract (if available)

Abstract Quantum sensing utilizes principles from quantum phenomena to interrogate a system and obtain the most detailed information about a system to date. The applications are countless, ranging from mapping of individual protein molecules in biological processes to improved metrological standards, nanophotonics and information technology. Sensors in the atomic scale are the key to achieving high sensitivity and spatial resolution. The paramagnetic defect in diamond known as the nitrogen vacancy or NV center has shown to be one of the most promising sensors thus far. NV centers possess unique optical and electronic properties that allow magnetic field, temperature and transport mechanisms detection at the nanoscale level. NV centers present stable photoluminescence signals, long decoherence times and the ability to perform optically detected magnetic resonance spectroscopy at room temperature. The fundamental principle of NV based detection of a target molecule is via dipolar coupling between them. Thus, close proximity of the molecule of interest and the NV is critical to achieve higher sensitivity.
An innovative approach to develop NV based techniques through the detection of electron spin resonance (ESR) signals is to position the molecule of interest on the dia- mond surface. Highly efficient covalent attachment of molecules on the diamond surface has been developed. However, a deeper understanding of the surface properties of diamond is necessary to optimize the positioning, proximity and concentration of the target molecule as well as the NV properties, mainly spin relaxation times. Longitudinal and transverse relaxation times are crucial to the development of NV-ESR utilizing hyperfine double electron resonance techniques. Furthermore, to increase the spectral resolution and extract precise information on the nature and specific conformation of a molecule, NV-ESR techniques at higher magnetic fields must be developed.
This dissertation presents the author’s approach to tackle the challenges presented on the understanding of the diamond surface to develop NV quantum sensing. In Chapter 1, an overview of current approaches in the field and motivation of the present work is introduced. Chapter 2 describes electron paramagnetic resonance principles necessary for discussion and analysis of experimental results presented in subsequent chapters. Chapter 3 introduces the surface chemistry of diamond and its functionalization where different surface preparation methods are investigated and discussed. In Chapter 4, NV spin relaxation properties after diamond surface cleaning and functionalization is analyzed. Chapter 5 presents the first performance of NV detected nuclear magnetic resonance at 8.3 Tesla. Chapter 6 discusses a new approach to tuning phase changes in Sb2Te3 nanowires using frequency control.

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Creator Mugica Sanchez, Laura C. (author)

Core Title Diamond surface chemistry for NV quantum sensing

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2023-05

Publication Date 01/23/2023

Defense Date 01/12/2023

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag diamond,nanowires,NV center,OAI-PMH Harvest,quantum sensing,surface chemistry

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Contributor Electronically uploaded by the author (provenance)

Advisor Takahashi, Susumu (committee chair), Benderskii, Alexander (committee member), Pianud, Fabien (committee member)

Creator Email lauramugicasanchez@outlook.com,mugicasa@usc.edu

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Type texts

Source 20230126-usctheses-batch-1003 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu