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Light matter interactions in engineered structures: radiative thermal management & light-assisted assembly of reconfigurable optical matter
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Light matter interactions in engineered structures: radiative thermal management & light-assisted assembly of reconfigurable optical matter
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UNIVERSITY OF SOUTHERN CALIFORNIA
LIGHT MATTER INTERACTIONS IN ENGINEERED STRUCTURES:
Radiative Thermal Management & Light-Assisted Assembly of Reconfigurable Optical Matter
by
Shao-Hua Wu
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 (ELECTRICAL ENGINEERING)
May 2018
I
Dedication
To my parents, Chin-Chang Wu and Li-Fen Chen.
Thank you for all of your support and unconditional love along the way.
II
Acknowledgments
I would like to sincerely thank my PhD advisor, Professor Michelle Povinelli, for her
guidance, patience, and support throughout my time at USC. She has always been a
remarkable mentor and teacher. She is inspiring as a scientist, innovating as a pioneer, and -
guiding and supporting as a mentor. It was always a great pleasure to work and chat with
her.
I would like to express my gratitude towards many outstanding professors and faculty
members at USC. In regards to the study on cell membrane mechanics via dual-beam optical
traps, I thank Professor Noah Malmstadt for his support for my first research project at USC
and countless hours of reflecting, reading, revising my first academic journal paper. I would
like to thank Professor Chongwu Zhou for the research opportunity on graphere CVD
synthesis, Professor Aiichiro Nakano for his input on some of my simulation works, Professor
Wei Wu for useful discussions on Si microcone fabrication, and Professor Stephen Cronin for
the research opportunity on MoS
2
plasmonics. It was my privilege to sit in the class of
Professor Anupam Madhukar (Solid State), Professor Aluizio Prata Jr. (Advanced
Electromagnetics), Professor Aiichiro Nakano (Computational Phyics), Professor Tony Levi
(Engineering Quantum Mechains), and Professor Keith Jenkins (Optical Information
Processing). I would also like to thank Professor Noah Malmstadt, Professor Stephen Cronin,
Professor Aiichiro Nakano, and Professor Wei Wu for serving on my qualifying exam and
thesis defense committee.
I would also like to thank the former and current Povinelli Nanophotonics Group
members. Ningfeng Huang initially guided me into the GaAs nanowire solar cell modeling
project and the optical Brownian ratchets project; he constantly provided assistance, and
III
spent a lot of time training me on the cleanroom machines and the optical setup until his
graduation. Roshni Biswas taught me how to operate the dual-beam optical trap, and
showed me how to rebuild the system from bottom-up. I also enjoyed working with Eric
Jaquay and Duke Anderson; they brought much joy into our multi-cultural working
environment. Duke Anderson shared his projects insights with me. I would also like to thank
Chenxi Lin; his kindness really helped me smoothly fit in the group initially. I want to also
express my gratitude towards the current group members; Aravind Krishnan, an intelligent
and a good friend, who worked closely with me on the optical trapping project; Mingkun
Chen, an intelligent and diligent undergraduate scholar, who spent tremendous amount of
time working with me on the thermal homeostasis project; Ahmed Morsy, Elise Uyehara,
and Romil Audhkhasi, who always discussed their interesting projects with me.
I am also grateful to our clean room supervisor, Donghai Zhu; HPCC and its staff for
computational resources; and friendship with PhD students, Nirakar Poudel, Bingya Hou,
and Fanqi Wu. I also owe a debt of gratitude to my old friend, Li-Chen Cheng, who
encouraged me to pursue PhD.
Last, but not least, I would like to thank my parents, Chin-Chang Wu and Li-Fen Chen,
for their unconditional support, love, and encouragement. They are always there to support
me, and I dedicate this dissertation to them.
IV
Abstract
This dissertation work studies the use of nanostructures and microstructures to control
the flow of light in two application areas: radiative thermal management and near-field
optical manipulation, which are discussed in PART I and PART II, respectively.
The work of radiative thermal management focuses on understanding the radiative
heat transfer in nanowires, designing highly efficient thermal homeostasis devices, and
designing high contrast radiative thermal rectifiers. In both designing works, phase-change
material - vanadium dioxide (VO
2
), is used to achieve dramatic changes in optical properties.
In the thermal homeostasis device design, a novel mechanism for radiative thermal
management is proposed. The optimized device’s ability to dampen temperature
fluctuations can perform 20 times better than ordinary semiconductor materials, and 8
times better than perfect blackbody. In radiative thermal rectifier design work, the highest
reported value of rectifying coefficient (21.48) is achieved. The PART I of this dissertation
not only establishes the understanding of fundamental limits in radiative thermal
management, but also provides optimization approaches for high contrast thermal
rectification devices.
The work of near-field optical manipulation is based on the light-assisted, templated
self-assembly (LATS) technique developed in our group. Laser light is used to excite guided
resonant modes in the photonic crystal templates to create an array of optical traps. The
traps drive the particles into accurate periodic positions, and form self-assembly. The first
demonstration of near-field all-dielectric optical Brownian ratchets was achieved, resulting
in much higher ratcheting speed than previous works.
V
Table of Contents
Dedication ...................................................................................................................... I
Acknowledgments ........................................................................................................ II
Abstract........................................................................................................................ IV
List of Tables .............................................................................................................. VIII
List of Figures ............................................................................................................... IX
PART I Radiative Thermal Management 1
Chapter 1 Introduction .......................................................................................... 2
1.1 Radiative Heat Transfer.................................................................................................... 2
1.2 Optical Modeling Methods .............................................................................................. 3
1.2.1 Finite-Difference-Time-Domain Method .................................................................. 4
1.2.2 Transfer Matrix Method ........................................................................................... 5
1.3 Radiative Thermal Management ..................................................................................... 5
1.3.1 Radiative Cooling ...................................................................................................... 6
1.3.2 Thermal Homeostasis ............................................................................................... 7
1.3.2.1 Phase-Change Materials: VO
2
........................................................................... 9
Chapter 2 Solar Heating of GaAs Nanowire Solar Cells ......................................... 11
2.1 Thermal Management of GaAs Nanowire Solar Cells .................................................... 11
2.2 Modeling Approach ....................................................................................................... 12
2.3 Operating Temperature Rise ......................................................................................... 16
2.4 Spectral Emissivity ......................................................................................................... 18
2.5 Dependence of Nanowire Dimensions ......................................................................... 20
2.6 Dependence of Thermal Conductivity .......................................................................... 21
2.7 Effect of Convection ...................................................................................................... 21
2.8 Effect of Substrate Thickness ........................................................................................ 22
2.9 Discussion and Conclusions ........................................................................................... 24
VI
Chapter 3 Thermal Homeostasis Using Microstructured Phase-Change Materials 26
3.1 Thermal Management for Space Applications Using Thermal Homeostasis Materials . 26
3.2 Design of Structures for Thermal Homeostasis ............................................................ 28
3.3 Spectral Emissivity ......................................................................................................... 29
3.4 Radiated Thermal Power Results .................................................................................. 31
3.5 Thermal Homeostasis .................................................................................................... 32
3.6 Homeostatic Operating Range ...................................................................................... 34
3.7 Dependence on VO
2
Thickness and Fabrication Feasability ......................................... 35
3.8 General Considerations ................................................................................................. 37
3.9 Discussion and Conclusions ........................................................................................... 38
3.10 Radiated Thermal Power Calculation .......................................................................... 39
3.11 Thermal Modelling Approach ..................................................................................... 40
Chapter 4 Far-Field Thermal Rectifier and Applications ....................................... 42
4.1 Introduction .................................................................................................................. 42
4.2 Formulism for Far-field Thermal Rectifier ..................................................................... 44
4.3 Layered VO
2
Structures ................................................................................................. 45
4.3.1 Rectifying Coefficient Optimization Strategy ......................................................... 48
4.3.2 Broadband Perspective: Maximizing Emissivity Difference ................................... 49
4.3.3 Narrowband Perspective: Tuning Resonant Peaks ................................................ 50
4.4 Discussion and Conclusions ........................................................................................... 54
Chapter 5 Conclusion and Outlook ...................................................................... 57
5.1 Conclusions ................................................................................................................... 57
5.2 Outlook .......................................................................................................................... 58
PART II Light-assisted Assembly of Reconfigurable Optical Matter 60
Chapter 6 Introduction ....................................................................................... 61
6.1 Background ................................................................................................................... 61
6.2 Theory: Electromagnetic Force Calculation .................................................................. 62
6.3 Theory: Hydrodynamic Simulations .............................................................................. 63
VII
6.4 Photonic Crystal Device Fabrication ............................................................................. 64
6.5 Microfluidic Chamber Preparation ................................................................................ 65
6.6 Experimental Optical Setup ........................................................................................... 66
Chapter 7 Near-Field Optical Brownian Ratchets ................................................. 68
7.1 Introduction .................................................................................................................. 68
7.2 Brownian Ratchets ........................................................................................................ 69
7.3 Design of Asymmetric Optical Potential ....................................................................... 70
7.4 Device Characterization ................................................................................................ 72
7.5 Trapping Experiments ................................................................................................... 73
7.6 Ratchet Motion ............................................................................................................. 75
7.7 Transport Speed ............................................................................................................ 77
7.8 Discussion and Conclusions ........................................................................................... 78
7.9 Optical Setup and Beam Condition ................................................................................ 79
7.10 Particle Trajectories and Stiffness Analysis ................................................................. 79
Chapter 8 Reconfigurable Optical Matter ............................................................ 81
8.1 Introduction .................................................................................................................. 81
8.2 Photonic Crystal Design ............................................................................................. 82
8.3 Mode Characterization and Transmission Spectrum Measurement ......................... 83
8.4 Discussion and Conclusions ....................................................................................... 84
Chapter 9 Conclusions and outlook ..................................................................... 87
REFERENCES ................................................................................................................ 89
VIII
List of Tables
Table 4.1. Optimized multilayer thickness ( m) for proposed structures. ......................... 53
IX
List of Figures
Figure 1.1. Illustrations of thermal homeostasis in optics. ................................................... 2
Figure 1.2. The solar spectral irradiance of AM1.5G (peaked at 0.45 m), and the
blackbody radiance of 400 K (peaked at 7.6 m). ................................................................. 9
Figure 1.3. Complex permittivity of VO
2
. ............................................................................ 10
Figure 2.1. Schematic illustrations of the structures of interest. (a) Square array of GaAs
nanowires, embedded in optional BCB. The inset is the magnified top view of one unit cell;
a is the lattice constant for the nanowire array, and d is the nanowire diameter. Note that
the layer thicknesses are not drawn to scale. (b) Planar GaAs structure. (c) Boundary
conditions used to solve the 3D heat diffusion equation. ................................................... 15
Figure 2.2. (a) The temperature rise in a nanowire for the structure of Fig. 1(a), for a =
600 nm and d = 300 nm. The solid black line indicates the outline of the GaAs nanowire. (b)
The temperature rise in the top 3 m of the planar structure in Fig. 1(b). The heat input
for both (a) and (b) is set to be 900 W/m
2
. (c) Calculated temperature rise for different
structures as functions of heat input, Pin. Black, blue, and red curves represent the results
for planar, GaAs nanowire, and BCB-coated GaAs nanowire, respectively. ........................ 18
Figure 2.3. (a) Emissivity (or absorptivity) spectra of different solar cell designs. Results
are for normal incidence, averaged over polarization. For the nanowire structures, a = 600
nm and d = 300 nm. (b) The spectral blackbody radiance at different temperatures. ....... 19
Figure 2.4. F.O.M. for BCB-coated NW array as a function of the structural parameters;
=330 K. ................................................................................................................................. 20
Figure 2.5. Effect of nanowire thermal conductivity upon the temperature rise in a BCB-
coated NW structure at fixed heat input = 900 W/m
2
. The structural parameters are a =
600 nm and d = 300 nm. The reference bulk thermal conductivity is 54 W/m-K at 300 K.. 21
X
Figure 2.6. Effect of convection upon the temperature rise at fixed heat input = 900 W/m
2
.
(a) Temperature rise as a function of for fixed = 6 W/m
2
K. (b) Temperature rise as a
function of for fixed = 12 W/m
2
K. ................................................................................... 22
Figure 2.7. (a) Effect of substrate thickness on temperature rise at fixed heat input = 900
W/m
2
. (b) Emissivity spectra for a 3- m-tall nanowire with different radii: 150 nm (blue
curve), 200 nm (blue dashed curve), and 250 nm (blue dotted curve). a = 600nm. The
black curve represents emissivity for the 3- m thick planar GaAs solar cells. .................... 24
Figure 3.1. Illustrations of thermal homeostasis in optics. A surface that radiates much
more at higher temperature will help maintain the object at the target temperature, T
c
. 28
Figure 3.2. Design of structure for thermal homeostasis. (a) Square array of silicon
microcones with a conformal VO
2
coating, residing on silicon film. Note that layer
thicknesses are not drawn to scale. (b) Flat, VO
2
-coated silicon film. (c) Uncoated silicon
film. ...................................................................................................................................... 29
Figure 3.3. Emissivity spectra. (a) VO2-coated silicon microcones (b) VO
2
-coated flat silicon
film (c) uncoated silicon film. Results are for normal incidence, averaged over polarization.
............................................................................................................................................. 31
Figure 3.4. Radiated thermal power. (a) The arrows indicate the direction of heating or
cooling processes. The symbols represent the calculated values of thermal radiation for
metallic (hollow symbols) VO
2
or insulating (filled symbols) VO
2
structures at 330 K. Solid
curves represent temperature-dependent model for radiated power assuming a phase
transition width of 10 K. (b) Boundary conditions used to solve the heat equation. .......... 32
Figure 3.5. Thermal homeostasis. (a) Temperature variation for different structures with a
time-varying heat input flux. (b) Radiated power in extended temperature range. The
dotted-grey lines indicate the heat input range (150-550 W/m
2
), and the corresponding
steady-state temperature values for each structure. .......................................................... 34
Figure 3.6. Homeostatic operating range. (a-c) Temperature variation of the silicon
microcone structure for different heat inputs. (d) Reduction in temperature variation for
microcones with narrower hysteresis width. Yellow shade illustrates range of hysteresis
loop (homeostatic operating range). ................................................................................... 35
XI
Figure 3.7. Dependence on coating thickness. Radiated power at the phase transition for
flat, VO
2
-coated silicon film. ................................................................................................ 37
Figure 3.8. Emissivity spectra with a 1- m-thick gold mirror attached to the back of the
VO
2
-coated silicon microconest. .......................................................................................... 37
Figure 4.1. Schematic illustration of conductive thermal rectifier.. .................................... 43
Figure 4.2. Schematic illustration of far-field radiative thermal rectifier. ........................... 44
Figure 4.3. Layered structures under study. (a) single-layer VO
2
, (b) VO
2
sitting on-top of
an opaque substrate (here we use Si and sapphire), and (c) VO
2
sitting on-top of an
opaque substrate and a gold back reflector. ....................................................................... 46
Figure 4.4. Normalized radiated power for a single layer VO
2
In the insulating and metallic
states as a function of VO
2
thickness. ................................................................................. 47
Figure 4.5. Normalized radiated power for VO
2
structures. (a) VO
2
on 300- m sapphire. (b)
VO
2
on 300- m sapphire and a gold back reflector. (c) VO
2
on 300- m Si. (d) VO
2
on 300-
m Si and a gold back reflector. .......................................................................................... 48
Figure 4.6. (a) Schematics of simple thermal rectifier consisting of an active VO
2
multilayer
structure and a blackbody. (b) Thermal emissivity of the proposed structure. .................. 50
Figure 4.7. Schematic illustration of resonance tuning to achieve high contrast thermal
rectification. (a) A relatively temperature-independent spectral emissivity of one surface.
(b) A temperature-dependent spectral emissivity of the other surface. (c) The channeled
emissivity of the thermal rectifier in forward and reverse directions. ............................... 51
Figure 4.8. Spectral emissivities of (a) an Au|Si|Au multilayer structure, and (b) an
Au|VO2|Au multilayer structure. (C) Channeled emissivity of the proposed thermal
rectifier. ................................................................................................................................ 52
Figure 4.9. Optimized multilayer structures for thermal rectification................................ 53
XII
Figure 4.10. (a) Emissivity spectra of the proposed multilayer structures. (b) Magnified
view of (a) between =9.5 m and 10.5 m. (C) Channeled emissivity of the proposed
thermal rectifier. .................................................................................................................. 54
Figure 4.11. Infrared transparent materials choices (reprinted from ref. [119]). The unit
for wavelength at the bottom is m. ................................................................................... 56
Figure 6.1. Schematic of experimental set-up used to characterize samples and perform
assembly experiments. ........................................................................................................ 67
Figure 7.1. Basic operating principle of Brownian ratchets. (a) By modulating an
asymmetric external potential, the random, Brownian motion can be rectified in the
forward direction. Blue lines indicate potential; gray lines indicate particle probability
distribution. (b) A periodic array of optical traps generated by a photonic crystal slab.
Light is incident on the slab from below, perpendicular to the slab surface. The
asymmetric, modified triangular holes produce an asymmetric field distribution with
strong field intensity in the holes. Modulating the incident light results in sideways motion
of the particles or Brownian ratcheting. .............................................................................. 70
Figure 7.2. Design of a silicon photonic crystal device with asymmetric holes. (a) Simulated
electrical field intensity profile (|E
2
|) on resonance for y-polarized incident light
(polarization direction shown as red arrow). The white dashed line represents the location
of the hole. (b) Simulated transmission spectrum of the device. (c) Contact height,
simulated optical forces, and optical potential as a function of lateral position for a
particle in contact with the slab........................................................................................... 72
Figure 7.3. Fabricated device characterization. (a) SEM image of the device used in
experiments. (b) Measured transmission spectrum. ........................................................... 73
Figure 7.4. Microscopy-video analysis of ratcheting experiments. (a) Snapshot of particle
trapping. Colored circles label the initial position of four trapped particles. (b) Particle
ratcheting due to laser modulation. Trajectories are shown for the four labeled particles
over a 30 s time period. ....................................................................................................... 75
Figure 7.5. Mean displacement for ensemble of particles. (a,b) The mean displacements in
the x- and y-directions. The red curve represents the results for Brownian ratchet with 10
XIII
Hz modulation frequency, while the black dashed curve represents the results for
Brownian particles. .............................................................................................................. 76
Figure 7.6 Average transport speed of the particles. (a) 520 nm particles. (b) 780 nm
particles. ............................................................................................................................... 78
Figure 8.1 Schematic of LATS. (a) Normally incident light from backside of the photonic
crystal excites resonant modes. (b) and (c) show potential trapping sites within the
photonic crystal slab. ........................................................................................................... 81
Figure 8.2 Schematic of lattice basis for (a) hybrid triangular-graphite and (b) adjusted
hybrid triangular-graphite lattice. ........................................................................................ 83
Figure 8.3 (a) Resonant wavelength as a function of double-hole separation (hole
diameter). Four preferred resonant modes are monitored. (b)The electric field intensity
profiles for the four monitored modes. .............................................................................. 83
Figure 8.4 A design for the reconfigurable light-assisted assembly template and its
potential trapping pattern. .................................................................................................. 84
Figure 8.5 Fabricated devices for the reconfigurable light-assisted assembly. (a) SEM of
the fabricated device. (b) Measured transmission spectrum. ............................................. 85
Figure 9.1 Trapping selectivity tuning by changing the surfactant concentration. Data
taken from A. Krishnan, S.-H. Wu, M. L. Povinelli (manuscript in preparation). .. .............. 88
XIV
1
PART I
Radiative Thermal Management
2
Chapter 1.
Introduction
1.1 Radiative Heat Transfer
Thermal radiation or radiative heat transfer are commonly used to describe the
mechanism of heat transfer caused by electromagnetic waves emission and absorption.
Radiative heat transfer is fundamentally and technologically important. The peak thermal
radiation wavelength is predicted by Wien's law. The thermal radiation from a very hot
object has a very short wavelength. For instance, sunlight is the thermal radiation from the
sun at ~5800 K, and the light emitted from a candle flame is at ~1900 K. For terrestrial
temperature objects, the typical temperature is about 300 K, with a peak wavelength at ~10
m. In this temperature range, thermal radiation is a very important heat dissipation
mechanism. The terms radiative cooling is specifically used to describe that a hotter body or
surface cools its temperature down by emitting electromagnetic waves into a heat sink or
heat receiver. For instance, heat is radiated into outer space (heat sink) from the surface of
Earth.
To engineer and design the radiative heat transfer of a particular system, it is physically
intuitive and important to understand Planck’s law of blackbody radiation using general
terms that utilize fundamental contributions from photonic perspective. Blackbody radiance
can be expressed as follows,
2
5 1 4
2 1 1 8 1
,
4
1
1
B
B
BB hc hc
kT
kT
hc hc
I T c
e
e
(1.1)
3
where c is light speed, h is the Planck’s constant, and k
B
is the Boltzmann’s constant. In such
a case, it is possible to rewrite and express blackbody radiance as a product of following
terms: the (1
st
) term is the group velocity of the photons, the (2
nd
) term is the photon energy,
the (3
rd
) term is the statistical distribution of photons (e.g. the Bose-Einstein distribution),
the (4
th
) term is the density of states of photons at each wavelength interval, and the (5
th
)
term,
1
4
, corresponds to isotropic radiation case. The group velocity and the photonic
density of states are dependent on the photonic dispersion. In general, photonic dispersion
is dependent on the material optical properties, the morphology of the emitter (absorber),
and the coupling between the emitter (absorber) to the environment.
Therefore, in Part I of this thesis, we will explore the engineering and modification of
the photonic dispersion through the use of different geometrical designs and different
materials to evaluate their impacts on radiative heat transfer. Two topics will be presented
that one focuses on studying material impacts and other one focuses more on studying
geometrical designs. In Chapter 2, it will be theoretically shown that by coating the GaAs
nanowire solar cells with a transparent isolating polymer the radiative cooling power can be
increased by 2.2 times and the operating temperature can be lowered by nearly 7 K. In
Chapter 3, a temperature-dependent switchable thermal emitter will be modeled and
designed for space applications. In Chapter 4, potential applications of thermal diodes will
be explored and proposed.
1.2 Optical Modeling Methods
Radiative heat transfer and thermal radiation generally involves solving Maxwell’s
equations in presence of fluctuating current sources at random positions; thus the
simulation is quite complicated. For arbitrary geometry, general methods, including finite-
4
difference-time-domain (FDTD) method [1-3] and boundary element method [4], can
calculate thermal radiation by directly updating fluctuating current and volume integral.
These are called direct methods for calculating thermal radiation. Other methods derived
from solving electromagnetic wave equations without fluctuating terms are called indirect
methods. By Kirchhoff's law, the angular spectral emissivity equals the absorptivity. The
indirect method is commonly used for systems with symmetry, and it has been shown that
the results from indirect and direct methods are quantitatively identical [1, 2, 5, 6]. In the
following, we will discuss the methods that are used in this thesis for calculating radiative
heat transfer.
1.2.1 Finite-Difference-Time-Domain Method
Finite-difference-time-domain (FDTD) method is commonly used for solving full
Maxwell’s equations by discretizing time and space. FDTD is capable of simulating complex
geometries and broadband response in single simulation by using a narrow pulse excitation
source and Fourier-transforming the frequency signal in time domain. Both spatial and
spectral information can be obtained from FDTD simulation.
Full 3D electromagnetic wave FDTD simulations are performed using a commercial
software package, Lumerical FDTD. Lumerical FDTD solution supports several desirable
features for simulations involving dispersive materials and plasmonic structures. More
specifically, it uses a “multi-coefficient model” for a more versatile fitting of the
experimentally-determined material optical constants over a wide wavelength range. FDTD
solution also supports a graded, non-uniform meshing scheme for improved simulation
accuracy and reduced memory requirement, compared to the conventional uniform
5
meshing scheme. FDTD solution is readily parallelized and can be used on USC HPCC cluster
for large-scale simulations.
1.2.2 Transfer Matrix Method
The transfer matrix method (TMM) is utilized for calculating the optical response of the
proposed structures. The basic operating principle is to divide the structure into slices
(layers) along the light propagation direction, use plane-wave expansion to calculate the
eigenmodes in each layer, and match the boundary condition for electric and magnetic field
across the interfaces between layers. The frequency-domain nature of the method is ideal
for simulations involving dispersive materials, since the experimentally-determined optical
constants can be directly used as the input for the program. An advantage of this method is
that the memory requirement does not depend upon the thickness of each layer since the
height dependence is purely analytical. The source code we use for the calculating optical
absorptivity (emissivity) is ISU-TMM [7, 8].
1.3 Radiative Thermal Management
In this thesis, we use coupled thermal-optical approach to model the transient and
steady-state temperature of the systems we study. We model and calculated the optical
response of the systems first, and then feed the optical response results as either emitted or
absorbed power into heat diffusion equation solver to obtain the thermal response. Here,
we generally discuss two mechanisms of radiative thermal management, including radiative
cooling and thermal homeostasis.
6
1.3.1 Radiative Cooling
A hotter object can cool its temperature down by sending thermal radiation to a colder
object or a heat sink. Earth’s atmosphere has a main transmission window in the
wavelength range of 8-13 m [9, 10], which coincides with the wavelength region
contributing the most spectral thermal emission around the terrestrial temperature. An
object within Earth’s atmosphere can send thermal radiation to outer space through this
transmission window to effectively use the coldness of outer space as a heat sink and cool
its temperature down. This procedure has been known as radiative cooling, and has been
used for centuries. Recent studies have shown that subambient radiative cooling is
achievable for modern solar cell structures [11].
Here we can consider an arbitrary solar absorber object at temperature T
top
, and the
structure is exposed to a clear sky, where the object is subject to solar irradiance and
atmospheric irradiance corresponding to an ambient temperature T
amb
. The net radiative
cooling power can be written as
rad top cell top amb amb abs sun
P T P T P T P
(1.2)
where
cos , ,
cell top BB top
P T d d I T
(1.3)
is the cooling power flux per unit area radiating from the top surface to the ambient,
cos , , ,
amb amb BB amb atm
P T d d I T
(1.4)
is the power flux absorbed from the ambient,
1.5 abs sun AM G
P d I
(1.5)
is the absorbed incident solar power by the object per unit area. Here
,
BB
IT is the
spectral blackbody radiance,
, is the computed spectral IR emissivity,
is the
7
computed solar absorptivity,
1.5 AM G
I is the ASTM Air Mass 1.5 G solar irradiance, and
,
atm
is the angular emissivity spectrum of the ambient atmosphere. The object is
assumed to face the sun, so there is no angular dependence on the solar absorptivity. By
substituting equations (1.3) through (1.5) into equation (1.2), the net radiative cooling
power can be expressed explicitly with angular spectral IR emissivity and solar absorptivity.
1.3.2 Thermal Homeostasis
Homeostasis is the tendency of a system within an organism to actively maintain its
internal stability. For instance, humans and other warm-blooded mammals maintain their
body temperature within a narrow range by various processes. This ability to maintain an
internal temperature that is relatively insensitive to changes in the external environment or
heat load is vital for all the complex processes that sustain life.
Without the ability to regulate temperature, materials and devices that experience
large temperature gradients or temperature cycles are vulnerable to performance
degradation or even catastrophic failure. Thermal control akin to the way living organisms
achieve thermal homeostasis is particularly important in environments such as space, where
changing solar illumination and the absence of convective cooling can cause large
temperature variations. Spacecraft are potentially subject to large external temperature
variation, from 150 K to 400 K [12] due to the coldness of outer space and the varying sun
illumination. Under such a temperature variation, the performance and lifetime of general
electronics would be hugely reduced. Moreover, the internal temperature inside spacecraft
must be regulated near room temperature. Efficient thermal management of spacecraft or
space electronics, such as thermal homeostasis, is necessary. With a specific interest in
space applications where radiative heat exchange is the sole cooling mechanism, we model
8
thermal homeostasis materials using optical approaches to design temperature-dependent
switchable thermal emitter or solar absorber.
In the thermal equilibrium picture, the steady-state temperature of a system is
determined by power balance; the input power equals to the output power. The idea of
thermal homeostasis in optics can be illustrated in Fig. 1.1. We can consider absorbed solar
power (red) as a power input and the radiative cooling power (blue) as a power output in
the system. While the system is at low temperature, the system will passively increase the
optical absorption for solar spectral irradiance, and lower the thermal emission in the near-
infrared range (or vice versa) to regulate the temperature within a targeted range.
Figure 1.1. Illustrations of thermal homeostasis in optics.
Absorbing less solar and radiating more in thermal wavelength with increasing
temperature (or vice versa) is necessary to achieve temperature self-regulation. An optical
switch design based on environmental temperature can be used. AM1.5G solar spectra (left
axis) and blackbody radiation at 400 K (right axis) are depicted in Fig. 1.2. Ideally, we can
design a switchable material that has a close-to-unity absorptivity in the solar spectral range
and near-zero emissivity in the thermal wavelength range when the temperature of the
device is below the target temperature, T
c
(Fig. 1.2, blue curve). While the temperature of
9
the device is above T
c
, the device will have close-to-unity thermal emissivity and near-zero
solar absorptivity (Fig. 1.2, red curve).
Figure 1.2. The solar spectral irradiance of AM1.5G (peaked at 0.45 m), and the
blackbody radiance of 400 K (peaked at 7.6 m).
1.3.2.1 Phase-Change Materials: VO
2
In order to achieve thermal homeostasis, it is necessary to have dramatic changes in
optical properties in materials due to temperature change. Phase-change materials such as
vanadium dioxide (VO
2
) are known to exhibit significant changes in crystallographic
structures, and corresponding electrical and optical characteristics in response to
temperature change near the metal-insulator transition (MIT) temperature, T
c
[13, 14]. We
will leverage the phase-change properties to design microstructured phase-change
materials that optimize the desired thermochromic properties. Figure 1.3 shows the
complex permittivity of VO
2
below (blue curve) and above (red curve) the MIT temperature
[13].
10
Figure 1.3. Complex permittivity of VO
2
.
VO
2
has attracted much attention as a thermochromic material for use in many
different applications. The phase-transition can be controlled by heat, light, electrical
current, or laser beam [15, 16]. Its MIT temperature varies from 310 K to 360 K (usually
around 340 K), depending on the processing methods [15], metal doping [15, 17, 18], strain
[19, 20], and material quality. The VO
2
phase-transition exhibits a hysteresis loop center
around the MIT temperature and a width of 4 K to 15 K [15, 16, 21]. The hysteretic width
can be reduced by increasing material quality (annealing or depositing VO
2
onto a lattice-
match substrate [20]). During the phase transition, VO
2
exhibits a much larger specific heat
(5 times greater than either insulating or metallic VO
2
) due to the latent heat [22].
11
Chapter 2.
Solar Heating of GaAs Nanowire
Solar Cells
A version of the results in this chapter was published as Ref. [23]
2.1 Thermal Management of GaAs Nanowire Solar Cells
Nanowire structures have been the subject of intense research for application in
photovoltaics [24-29]. Compared to planar structures, optimized nanowire arrays provide
concentrated light absorption within a small volume of material [30-34]. Concentrated
absorption can both decrease material usage and provide certain advantages for carrier
collection [24, 35]. However, while a great deal of study has been devoted to the optical and
electrical modeling of nanowire solar cells [36-43], relatively little attention has been paid to
their thermal properties. A significant portion of the light absorbed by a solar cell is
converted to heat, rather than electricity. Heat generation raises the operating temperature,
degrading a cell’s electrical performance and reliability. Meanwhile, the thermal
conductivity of nanowires can be reduced by up to two orders of magnitude relative to bulk
[44-46]. It is thus important to consider whether the highly concentrated light absorption
and reduced thermal conductivity present within nanowire cells influence the operating
temperature.
In this chapter, we model the temperature rise in nanowire solar cells under solar
illumination. We focus on GaAs nanowires, which have been investigated for their promise
in single- [47-50] and multi-junction [51] solar cells. Our coupled thermal-optical approach
12
uses the spatial light absorption profile obtained from electromagnetic simulations as a heat
source in the 3D heat equation. The thermal model includes the effects of convection and
thermal emission. We accurately account for modification of thermal emission by the
nanowire structure via electromagnetic simulations at thermal infrared wavelengths. Our
results show that GaAs nanowire solar cells, despite their more concentrated light
absorption and lower thermal conductivity, heat up slightly less than planar cells.
Moreover, heating can be significantly reduced by coating the nanowires with
benzocyclobutene (BCB), a transparent polymer commonly used to provide electrical
isolation and mechanical support [50, 52, 53]. The addition of BCB significantly increases the
thermal emissivity of the structure, reducing the operating temperature by nearly 10K due
to radiative cooling.
2.2 Modeling Approach
Fig. 2.1a shows a schematic illustration of the nanowire structure used in this work. A
square array of GaAs nanowires rests on a GaAs substrate. The nanowire cross section is
hexagonal, typical of nanowires grown in experiment [50, 54-56]. There is an aluminum back
reflector underneath the substrate. The space between the nanowires is either infiltrated
with BCB or left empty. For the calculations below, the nanowire height is set to 3 m and
the substrate thickness to 300 m. For comparison, we consider the planar structure shown
in Fig. 2.1b.
Our modeling approach follows the procedures described in Granqvist's and Zhu's
works [57, 58]. To calculate the operating temperature of the structures, we solve the 3D
heat diffusion equation,
, , ; , , , , 0
x y z T T x y z Q x y z , (2.1)
13
where
, , ; x y z T is the thermal conductivity,
,, T x y z is the temperature profile, and
,, Q x y z is the heat source in units of W/m
3
. We obtain
,, Q x y z from the spatial light
absorption profile. The absorption profile is calculated using a finite-difference time-domain
electromagnetic solver (Lumerical Solutions, Inc.) assuming an incident 1 sun AM1.5G
spectrum (total incident optical power equal to 3.6 ×10
-10
W). The total input power of the
heat source is set to a fraction f =1- of the absorbed optical power, where represents the
solar cell efficiency.
Fig. 2.1c represents the boundary conditions applied to solve the heat equation. For
the top surface,
1 rad top top amb
top
T P T h T T , (2.2)
where the first term on the right hand side represents radiative cooling, and the second
term represents convective cooling.
top
T and
amb
T are the temperature at the top surface of
the cell and the ambient temperature, respectively. For the bottom surface,
2 bot amb
bot
T h T T . (2.3)
The convective heat transfer coefficient
1
h is chosen to be 12 W/m
2
-K, corresponding to a
wind speed of ~3 m/s [59]. We take
2
h to be half of
1
h , reflecting the fact that the wind
speed on the unexposed bottom surface is smaller than that on the exposed top surface.
amb
T is set to 300 K.
The radiative cooling term can be written as
rad top cell top amb amb
P T P T P T . (2.4)
The first term,
cell top
PT , is the cooling power flux per unit area radiating from the top
surface to the ambient [57, 58]. It can be written as
14
cos , ,
cell top BB top
P T d d I T
, (2.5)
where
,
BB top
IT is the spectral blackbody radiance, and
, is the computed IR
emissivity spectrum. We obtain
, via electromagnetic simulation, using the ISU-TMM
package [60, 61], an implementation of the plane-wave based transfer matrix method. The
second term in Eq. (2.4),
amb amb
PT , is the power flux absorbed from the ambient:
cos , , ,
amb amb BB amb atm
P T d d I T
, (2.6)
where
,
atm
is the angular emissivity spectrum of the ambient atmosphere, given by
1/ cos
,1
atm
t
, and
1/ cos
t
is the zenith-angle-dependent atmospheric
transmittance [10, 57]. The atmosphere has a main transmission window in the wavelength
range of 8-13 m, which coincides with the wavelength region contributing the most
spectral thermal emission around the terrestrial temperature. In this region,
atm
is low, and
terrestrial objects can be cooled down by sending thermal radiation into outer space. For
dry atmospheric conditions, a secondary atmospheric transmission window opens in the
wavelength range of 20-28 m and contributes some extra cooling. The wavelength range
for integration is chosen to be 3-30 m, from where the blackbody radiance is negligibly
small (around the terrestrial temperature) to where
,
atm
can be considered as unity for
wavelengths greater than 30 m [10, 57]. The spectral resolution and angular resolution for
the emissivity are 2 nm and 5 degrees, respectively.
We use COMSOL Multiphysics to solve Eq. (2.1) subject to the boundary conditions in
Eq. (2.2) and Eq. (2.3). The heat source profile
,, Q x y z is obtained from the Lumerical
simulation as described above and imported into COMSOL. The radiative cooling power,
15
rad top
PT , is calculated numerically using the TMM result as a function of temperature, and
then imported in tabular form to COMSOL.
Figure 2.1. Schematic illustrations of the structures of interest. (a) Square array of
GaAs nanowires, embedded in optional BCB. The inset is the magnified top view of
one unit cell; a is the lattice constant for the nanowire array, and d is the nanowire
diameter. Note that the layer thicknesses are not drawn to scale. (b) Planar GaAs
structure. (c) Boundary conditions used to solve the 3D heat diffusion equation.
The absorption profile is calculated using a finite-difference time-domain
electromagnetic solver (Lumerical Solutions, Inc.) assuming an incident 1 sun AM1.5G
spectrum. The total input power of the heat source is set to a fraction f=1- of the
absorbed optical power, where represents the solar cell conversion efficiency. The solar
cell conversion efficiency is defined by the assumption that each absorbed photon with
energy greater than the band gap produces one and only one electron-hole pair with energy
h c/λ
g
,
2500
1.5 1.5
280 280
g nm
AM G AM G
g nm nm
I d I d
, (2.7)
where λ is wavelength, I
AM1.5G
(λ ) is the solar spectral irradiance of AM1.5G, ( ) is the
absorptivity of normal incidence.
16
2.3 Operating Temperature Rise
Fig. 2.2a shows the rise in operating temperature for one unit cell of the GaAs
nanowire structure. The nanowires are coated by BCB. The total heat input power is taken
to be 900 W/m
2
(f = 90%). The calculation is performed for dry atmospheric conditions
(water vapor column 1.0 mm [10]). The average temperature rise in the nanowire is
approximately 33.97 K. Cooler regions are observed outside the nanowire near the top of
the cell. However, the overall heat variation is very small. The change in temperature along
the dotted line is only ~7 ×10
-5
K. The small heat variation is consistent with dimensional
analysis. In thermal equilibrium, the temperature difference across the structure can be
estimated by / T PL where P is the energy flux, L is the nanowire height, and is the
thermal conductivity. For L = 3 m, P = 192 W/m2, and a volume-averaged of ~8.2 W/m-
K, the temperature difference is ~7 ×10
-5
K, consistent with the FEM results.
For comparison, we show the rise in operating temperature for the planar structure in
Fig. 2.2b. The average temperature rise is approximately 40.7 K, assuming the same total
heat input power. Again, the temperature variation across the device is very small relative
to the average temperature rise. The variation is several times smaller than in Fig. 2.1a due
to the higher thermal conductivity (35 W/m-K for bulk GaAs) [62].
The spatially averaged temperature rise in the top 3- m GaAs region is plotted as a
function of heat input in Fig. 2.2c. It is clear that the BCB-coated GaAs nanowire array (red
curve) heats up substantially less than the planar structure (black curve). The reduced
heating can largely be attributed to BCB. A GaAs nanowire array without BCB (blue line) has
a very similar temperature rise to the planar structure. Under wetter atmospheric
conditions (water vapor column 5.0 mm [10]), the difference in temperature rise is even
17
smaller (~0.1 K at 900 W/m
2
). The results thus suggest that BCB provides strong radiative
cooling effects.
Radiative cooling effects can also be observed for a BCB-coated planar structure. For a
heat input of 900 W/m
2
, the temperature rise for a BCB-coated planar structure is 4.6 K
lower than for a bare, planar structure. This is 1.8 K higher than for BCB-coated nanowires.
Here, we have assumed the same total volume of BCB for the planar and NW cases.
Throughout this paper, we have compared the temperature rise in nanowire and
planar structures given fixed heat input. Nanowire structures have widely been studied for
their light-trapping benefits: optimized nanowires absorb more light across the solar
spectrum than a planar structure of the same height [30, 33]. The total heat input for a
nanowire device can thus be higher than for a planar structure. The relative temperature
rise will depend in detail on the device geometries and cell efficiencies. However, the main
physical insights gained in this paper will still apply: (i) the concentration of the heat source
in the nanowires does not itself significantly affect the temperature rise, and (ii) the addition
of BCB around the nanowires will decrease the temperature rise.
18
Figure 2.2. (a) The temperature rise in a nanowire for the structure of Fig. 1(a), for
a = 600 nm and d = 300 nm. The solid black line indicates the outline of the GaAs
nanowire. (b) The temperature rise in the top 3 m of the planar structure in Fig.
1(b). The heat input for both (a) and (b) is set to be 900 W/m
2
. (c) Calculated
temperature rise for different structures as functions of heat input, Pin. Black, blue,
and red curves represent the results for planar, GaAs nanowire, and BCB-coated
GaAs nanowire, respectively.
2.4 Spectral Emissivity
To understand the mechanisms behind radiative cooling, we plot the thermal emissivity
spectrum for the various structures in Fig. 2.3a. The black curve represents the emissivity
spectrum for the planar structure. Due to the transparent nature of GaAs in the mid-IR to
infrared range [63, 64], the spectrum is highly oscillatory from 3 m to 12.5 m. This
wavelength region coincides with the peak of the blackbody radiance, which is plotted in Fig.
2.3b for reference. The radiative cooling power depends on the product of the emissivity
and the blackbody spectrum via Eq. (2.4) through (2.6). We note that the cut-off in
oscillations at 12.5 m seen in Fig. 2.3a is due to a sharp change in the tabulated optical
constants at this point. Above 12.5 m, the absorption for GaAs increases dramatically due
to multiple phonon interactions [65].
For the nanowire structure, the emissivity (blue curve in Fig. 2.3a) increases
substantially over the broad wavelength range from 12.5-30 m, where GaAs is absorptive.
19
The emissivity increase can be attributed to the fact that the nanowire array acts as an anti-
reflection (AR) coating layer in this range, reducing reflectivity and increasing absorptivity.
However, the emissivity increase has little effect on the overall temperature rise, due to
poor overlap with the blackbody peak. In addition, we found that the angular dependence
of the IR emissivity (not shown) is stronger than for the planar structure, reducing radiative
cooling effects.
Infiltration of the nanowires with BCB (red line) increases the spectral emissivity over
whole thermal wavelength range. In the thermal IR, the BCB provides even better
antireflective properties than nanowires alone. Moreover, for wavelengths below 12.5 m
where GaAs is transparent, the BCB itself is optically absorptive, boosting emissivity. As a
result, the operating temperature of the BCB-coated nanowire structure is significantly
lower than either of the other two cases.
Figure 2.3. (a) Emissivity (or absorptivity) spectra of different solar cell designs.
Results are for normal incidence, averaged over polarization. For the nanowire
structures, a = 600 nm and d = 300 nm. (b) The spectral blackbody radiance at
different temperatures.
20
2.5 Dependence of Nanowire Dimensions
In order to investigate the dependence of thermal emission on nanowire dimensions,
we define a figure of merit (F.O.M.) as follows,
30
3
30
3
,
. . .
,
m
BB top
m
m
BB top
m
I T d
FOM
I T d
, (2.8)
where
is the emissivity for normal incidence. Fig. 2.4 shows the F.O.M. of BCB-coated
GaAs nanowire solar cells as a function of lattice constant a and diameter-to-lattice constant
ratio d/a at
top
T =330 K. There is minimal dependence on the lattice constant a. This result
may be expected, as a is much smaller than wavelengths in the thermal range. There is a
greater dependence of the F.O.M. on d/a. As d/a increases, the amount of infiltrated BCB
between nanowires decreases, reducing the emissivity at the wavelength where GaAs is
transparent and thereby decreasing the F.O.M..
Figure 2.4. F.O.M. for BCB-coated NW array as a function of the structural
parameters;
top
T =330 K.
21
2.6 Dependence of Thermal Conductivity
In the calculations above, the conductivity of the nanowire was set equal to the bulk
value of GaAs. Experiments have shown that nanowire conductivity strongly depends on
surface roughness and nanowire diameter and may vary from 0.7 W/m-K to 27 W/m-K [62].
To investigate the effect of thermal conductivity on operating temperature, we scale the
thermal conductivity inside the nanowire by a factor of 0.001 to 100. As shown in Fig. 2.5,
the spatially averaged temperature rise in the nanowire is fairly insensitive to thermal
conductivity. In thermal equilibrium, the overall temperature rise is determined by the
energy balance between the input heat source, convection, and radiative cooling and
depends only minimally on the thermal conductivity of the structure.
Figure 2.5. Effect of nanowire thermal conductivity upon the temperature rise in a
BCB-coated NW structure at fixed heat input = 900 W/m
2
. The structural
parameters are a = 600 nm and d = 300 nm. The reference bulk thermal
conductivity is 54 W/m-K at 300 K.
2.7 Effect of Convection
Convection coefficients depend, in general, on wind speed [59, 66]. To illustrate the
impact of convective cooling, the operating temperature rise T is plotted as a function of
22
the heat transfer coefficient,
1
h , in Fig. 2.6a for a fixed heat input of 900 W/m
2
. The overall
temperature rise decreases with
1
h for all the structures studied. The temperature
difference between the BCB-coated nanowire structure and the planar structure is largest
for zero convection (17 K for
1
h = 0), indicating the importance of radiative cooling in this
regime. The zero convection case corresponds to space solar power applications, where
thermal radiation provides the only cooling mechanism. With increasing
1
h , the separation
in T becomes narrower. Nevertheless, the increased radiative cooling in the BCB-
infiltrated nanowire strucure still provides a 1.5 K reduction in T for
1
h =60 W/m2-K.
Similar trends can be seen in Fig. 2.6b by varying
2
h .
Figure 2.6. Effect of convection upon the temperature rise at fixed heat input =
900 W/m
2
. (a) Temperature rise as a function of
1
h for fixed
2
h = 6 W/m
2
K. (b)
Temperature rise as a function of
2
h for fixed
1
h = 12 W/m
2
K.
2.8 Effect of Substrate Thickness
In the previous sections 2.2-2.7, the assumption is that the 3- m tall nanowire region
rests on a 300- m thick substrate. Here, we consider the effect of thinning the substrate. Fig.
2.7a shows the operating temperature as a function of the total height of the GaAs region.
23
Reduction in GaAs height, from 303 m to 3 m, has minimal influence on operating
temperature, increasing the temperature by ~ 2.6 K. The temperature rise of the BCB-coated
nanowire structure is far lower than for the other two structures, regardless of the substrate
height.
Fig. 2.7a shows that there is a small difference in temperature between the planar and
the nanowire structures. For heights above 6 m, the nanowires have a smaller temperature
rise than the planar structure due to their higher emissivity. For heights below 6 m, the
trend is reversed. In the limit of very thin structures, the total volume of thermally
absorptive material dominates the radiative cooling power and the planar structure has
higher emissivity. Fig. 2.7b shows the emissivity for 3- m-tall GaAs nanowires with various
radii (blue solid curve for nanowire radius of 150 nm, dashed curve for radius of 200 nm,
and dotted curve for radius of 250 nm) and a 3 m-thick GaAs slab (black curve). An increase
in nanowire radius results in higher emissivity, which can be attributed to the larger filling
ratio (more absorptive material). The low emissivity below 12.5 m is due to the transparent
nature of GaAs inside this wavelength region.
24
Figure 2.7. (a) Effect of substrate thickness on temperature rise at fixed heat input
= 900 W/m2. (b) Emissivity spectra for a 3- m-tall nanowire with different radii:
150 nm (blue curve), 200 nm (blue dashed curve), and 250 nm (blue dotted curve).
a = 600nm. The black curve represents emissivity for the 3- m thick planar GaAs
solar cells.
2.9 Discussion and Conclusions
While concentration of light absorption within the nanowires produces more localized
heating than in planar structures, we find that this has minimal effect on the temperature
rise under solar illumination. Because the characteristic length scale for temperature
variation is much larger than the nanowire dimensions, the temperature is nearly uniform
across the unit cell. We also find that reduced thermal conductivity in the nanowire has little
influence on temperature rise under thermal equilibrium picture. Varying the conductivity
by up to a factor of 100 results in less than a 0.04% change in the operating temperature.
The characteristic length of heat diffusion length is much larger than the nano- or micro-
scale devices.
Though the radiative cooling power in this work is particular to specific materials and
structures, the approach should be applicable to a variety of different cell designs. Other
materials that share the general features of BCB could also lead to a reduction of the solar
cell operating temperature. High absorptivity in the thermal IR is desirable for radiative
25
cooling. In addition, the coating material should ideally have low absorption and low
refractive index across the solar spectrum so as to maximize the light that reaches the
semiconductor.
26
Chapter 3.
Thermal Homeostasis Using
Microstructured Phase-Change
Materials
A version of the results in this chapter was published as Ref .[67].
3.1 Thermal Management for Space Applications Using Thermal Homeostasis Materials
Thermal control schemes for space have focused on emission control since the absence
of convection makes radiative emission the sole cooling mechanism. Radiators that emit
significantly more when heated than cooled can be designed to dampen temperature
fluctuations that arise from changes in solar illumination and from on-board heat generation
[12]. Solid-state approaches to emission control [68, 69] offer lightweight alternatives to
approaches based on mechanically-moving parts [70-73] or fluid-filled heat pipes [74, 75].
The majority of these schemes, however, require electrical power [68, 70-73], limiting their
application space. Here in this chapter, we present a novel, passive scheme for thermal self-
regulation. Our design uses micropatterned phase-change materials to achieve a 10x
difference in emissivity between high and low temperature states, resulting in a ~20x
reduction in temperature variation relative to ordinary materials.
Micropatterning has been the subject of intense research for applications in radiative
cooling [11, 76]. Recent work has shown that micropatterned materials can be designed to
27
achieve near-unity infrared (IR) emissivity and steady state radiative cooling [76]. To provide
passive temperature regulation, however, temperature-switchable emissivity is required.
Phase-change materials such as vanadium dioxide (VO
2
) display a dramatic change in optical
properties near their phase-transition temperature, T
c
[13, 17, 77, 78]. VO
2
has previously
been used to achieve switchable reflectivity and transmissivity in the IR [79, 80] and visible
range [15, 17]. IR emissivity tuning has also been demonstrated with this unique material
[81, 82]. None of these works, however, considered a passive, switchable IR emitter for
thermal self-regulation. Previous work on bulk perovskite manganese oxide used a metal-
insulator phase transition to provide switchable emission [69, 83, 84], however, the
maximum difference in emissivity between high and low temperature states was only ~0.5,
and the width of temperature range for the phase transition was as large as ~200 K [84]. As
we will see in the following sections, the width of the transition limits temperature
regulation. Chalcogenide phase-change materials such as GST can also provide switchable
optical properties [85-87]. However, their non-volatile nature – in which the phase
transition must be triggered by an energetic pulse – makes them nonideal for passive
thermal homeostasis applications.
In this chapter, we design a VO
2
-coated silicon microcone structure with a large
emissivity difference of 0.8 between low and high temperature states. We show that our
structure’s sharp change in emissivity at the phase-change temperature (330 K) provides
excellent thermal regulation capability due in part to the narrow width of the VO
2
insulator
to metal phase transition, which can be as small as 4 K for high material quality [15]. In
particular, we solve the time-dependent heat equation using a lumped capacitor approach
to obtain the transient temperature in response to a time-varying heat load. Our results
show a ~20x reduction in temperature variation relative to an uncoated silicon film.
28
3.2 Design of Structures for Thermal Homeostasis
The concept of thermal homeostasis is illustrated in Fig. 3.1. The ideal surface for
thermal homeostasis would have near-zero thermal emissivity below the design
temperature set point, T
c
(Fig. 3.1a), and close-to-unity thermal emissivity above (Fig. 3.1b).
In this case, fluctuations in temperature will be mitigated by changes in emissivity. When
the object gets too cold, heat loss to the environment is minimized (Fig. 3.1a); when the
object gets too hot, heat loss is enhanced (Fig. 3.1b).
Figure 3.1. Illustrations of thermal homeostasis in optics. A surface that radiates
much more at higher temperature will help maintain the object at the target
temperature, T
c
.
We have designed a structure with the temperature-dependent emissivity needed for
thermal homeostasis. Our design is shown in Fig. 3.2a. A square array of silicon microcones
is covered by a conformal layer of VO
2
. Cone arrays are known to exhibit strong anti-
reflection and to be relatively insensitive to angle of incidence, making them well suited for
absorber and emitter applications [88-91]. In the calculations below, we will take the height
of silicon microcones to be 40 m, the period to be 20 m, and the thickness of the coating
to be 200 nm. These dimensions were optimized by running particle swarm optimization [92]
to maximize broadband emissivity difference between the insulating and metallic states.
29
Lower and upper bounds on period, cone height, and VO
2
thickness were set to at 5 m-40
m, 5 m-40 m, and 0.2 m-1.0 m, respectively. For reference, we will also consider a flat,
VO
2
-coated silicon film (Fig. 3.2b) and an uncoated silicon film (Fig. 3.2c) and calculate
thermal emissivity for all three structures.
Figure 3.2. Design of structure for thermal homeostasis. (a) Square array of silicon
microcones with a conformal VO
2
coating, residing on silicon film. Note that layer
thicknesses are not drawn to scale. (b) Flat, VO
2
-coated silicon film. (c) Uncoated
silicon film.
3.3 Spectral Emissivity
We first calculated the infrared spectral emissivity for the VO
2
-coated Si microcones.
The results are shown in Fig. 3.3a. For T < T
c
, VO
2
is in the insulating phase. The emissivity of
the VO
2
-coated microcones is low (thin blue line). For T > T
c
, the VO
2
layer is metallic, and
the emissivity is high (thin red line). The VO
2
-coated microcones thus act as a switchable
thermal emitter, with a nearly 10x difference in emission between the insulating and
metallic states.
The difference in emission can be understood as follows. Consider infrared light
incident on the structure. The metallic state has a much larger imaginary part of the
permittivity than the insulating state, yielding strong attenuation in the thin VO
2
layer. From
30
Kirchoff’s law, the increased attenuation (absorption) corresponds to an increase in
emission. We note that the oscillatory features in Fig. 3.3a are due to reflection from the
backside of the sample, resulting from the negligibly small absorption in Si.
The emission from a microcone structure is far more switchable than from a planar film.
For the planar film, the difference in emissivity between metallic and insulating states is
smaller (Fig. 3.3b). Moreover, the emissivity for the metallic state (thin red line; Fig. 3.3b) is
much lower than for the microcones (thin red line; Fig. 3.3a). To understand this effect, we
again consider incident infrared light. In the metallic state, the planar structure is highly
reflective, and little light is absorbed in the VO
2
layer. In contrast, the microcones act as
impedance matching tapers and effectively serve as an anti-reflection coating, allowing light
to be better absorbed in the VO
2
. The emissivity for the insulator state of the planar film
(blue curve; Fig. 3.3b) is largely dominated by the properties of the silicon; above 10 m, the
spectrum of the VO
2
-coated film is nearly identical to that of the uncoated Si film (Fig. 3.3c).
We note that the sharp cut-off at 10 m seen in Fig. 3c is due to the transparent nature of Si
in this wavelength range (1 m to 10 m) [93].
We note the calculations shown in Fig. 3.3 are calculated from the coherent
absorptivity at normal incidence. Experiments may not resolve the fine-scale wavelength
features seen in the plots, and we have thus added smoothed lines as a guide to the eye
(thicker lines).
The calculated spectral resolution is 10 nm. The optical constants for VO
2
and Si are
obtained from semi-empirical fitted experimental [13] data and experiments [93],
respectively. We note that the measured optical constants for silicon in the infrared range
are obtained from intrinsic samples, and so the free carrier contribution is minimal.
31
Figure 3.3. Emissivity spectra. (a) VO
2
-coated silicon microcones (b) VO
2
-coated flat
silicon film (c) uncoated silicon film. Results are for normal incidence, averaged
over polarization.
3.4 Radiated Thermal Power Results
We next calculate the total radiated power in the insulating and metallic phases from
the angle-averaged emissivity of each structure. The values of radiated power at the
transition temperature are shown by the symbols in Fig. 3.4a. The microcones have a large
difference in radiated power between insulator (filled, green circle) and metallic (unfilled,
green circle) states. The VO
2
-coated flat film (magenta diamonds) has a smaller difference,
as expected from the smaller difference in thermal emissivity.
To model the temperature dependence of the radiated power, we assume a model (Eq.
3.2) that takes into account the hysteresis of the phase transition and the temperature
dependence of the blackbody spectrum (see 3.10 Radiated Thermal Power Calculation).
The full model of P
rad
(T) is shown by curves in Fig. 3.4a. The directions of heating and
cooling processes are indicated by arrows. For the microcone heating curve, the radiated
power increases sharply with temperature through the VO
2
phase transition (green curve;
upward arrow). This sharp rise is consistent with its function as a switchable emitter. When
the temperature is decreased, the radiated power also drops sharply, due to the change in
emissivity across the phase transition. These trends are much more pronounced than for the
32
planar film. The radiated power for the uncoated silicon film is shown for reference and
increases slowly across the entire range.
Figure 3.4. Radiated thermal power. (a) The arrows indicate the direction of heating
or cooling processes. The symbols represent the calculated values of thermal
radiation for metallic (hollow symbols) VO
2
or insulating (filled symbols) VO
2
structures at 330 K. Solid curves represent temperature-dependent model for
radiated power assuming a phase transition width of 10 K. (b) Boundary conditions
used to solve the heat equation.
3.5 Thermal Homeostasis
The large, sharp increase in radiated power across the phase transition helps regulate
the temperature of the microcones. Given a fluctuating heat input, the temperature
variation for the microcones is much smaller than for a Si film. To see this effect, consider
the time-varying heat input shown in the top panel of Fig. 3.5a. The value of P
in
oscillates
between 150 and 550 W/m
2
. Such an input could result, for example, from a time-varying
solar illumination or internal heat load. We demonstrate the thermal dynamics of the
system by solving the time-dependent heat equation for an isothermal mass (i.e. a "lumped
capacitor") [94] with an initial temperature of 330 K. We plot the system temperature as a
function of rescaled time t’= t/ CL
C
, where is the material density, C is the thermal
33
capacitance of the structure, and L
C
is the characteristic length scale (i.e. height) of the
structure (see 3.11 Thermal Modelling Approach for details).
For the bare silicon film, the temperature of the device strongly oscillates in response
to the input, shown by the dot-dashed black curve in Fig. 3.5a. The amplitude of the
variation is 219.3 K. The VO
2
-coated flat film reduces these fluctuations to 147.3 K (dotted,
magenta curve). However, the microcone structure has a nearly constant temperature
response: the fluctuation amplitude is reduced by nearly 20x relative to the silicon film, to
11.9 K (solid, green curve). We refer to this behavior as thermal homeostasis; by proper
design, the material can passively regulate its temperature far better than a bare silicon film.
Moreover, the material also regulates temperature better than a blackbody emitter.
Calculations show that the fluctuation amplitude of the microcone structure is
approximately 8x smaller than for a perfect blackbody.
The origin of thermal homeostasis can be understood from a power balance formalism.
We assume that the input power varies slowly enough for the device to reach steady state
at each step (increase or decrease in P
in
). The steady-state temperature is determined by a
balance between input and radiated power, shown schematically in Fig. 3.4b: P
in
(T) = P
rad
(T).
For convenience, we replot the radiated power curves from Fig. 3.4a over an extended
temperature range in Fig. 3.5b.
Starting with the uncoated Si (black curve), we determine that the temperature value
corresponding to P
in
= P
rad
= 550 W/m
2
is 749 K. For the lower power P
in
=P
rad
= 150 W/m
2
, T=
530K. The temperature fluctuation is indicated by the black arrows in Fig. 5b. For the flat
VO
2
-coated structure, a similar procedure gives a narrower temperature range, indicated by
the magenta arrows in Fig. 5b. For the microcone structure, however, the range of
temperature corresponding to powers between 150 and 550 W/m
2
is much smaller. To find
34
this range, we take into account the hysteresis in the curve. When P
in
is increased to 550
W/m
2
, the heating curve (right side of hysteresis loop) gives a steady-state temperature of
337 K. When P
in
is decreased to 150 W/m
2
, the cooling curve (left side) gives a temperature
of 325 K. The overall temperature fluctuation (green arrows) is thus much smaller than for
the other two structures. In summary, the design of the microcone structure, which yields a
steep dP
rad
/dT at the phase transition, provides strong thermal regulation behavior with
much smaller oscillation in temperature than a Si film.
Figure 3.5. Thermal homeostasis. (a) Temperature variation for different structures
with a time-varying heat input flux. (b) Radiated power in extended temperature
range. The dotted-grey lines indicate the heat input range (150-550 W/m
2
), and the
corresponding steady-state temperature values for each structure.
3.6 Homeostatic Operating Range
The ability of the VO
2
-coated microcone device to maintain thermal homeostasis is
limited by the width and height of the hysteresis loop associated with the insulator to metal
phase transition around T
c
. In Fig. 3.4a, the height of the loop (green curve) extends from 40
to 550 W/m
2
. The width of the loop is approximately 10 K. Fig. 6 shows the temperature
variation of the microcones for three different input power oscillations. In Fig. 3.6a, the
values of P
in
fall well within the range of the loop (shaded yellow). The resulting thermal
35
variation is 11.6 K, as in Fig. 3.5a (note change in y-axis scale). However, when the range of
P
in
is lowered below (Fig. 3.6b) or above (Fig. 3.6c) the range of the hysteresis loop, the
temperature variations over the cycle are larger. For optimal performance, the variations in
input power should therefore fall within the range of the hysteresis loop. However, we note
that for variations in input power larger than the range of the hysteresis loop, the
microcone structure still outperforms the flat film or uncoated Si film.
The width of the loop will determine the size of the temperature fluctuations. As the
width is reduced to zero, the fluctuations decrease as well, as shown in Fig. 3.6d.
Experimentally, the width of the hysteresis loop can be reduced via improvements in
material quality [15, 20, 77, 78], with some works showing hysteresis widths as low as 4 K
[20]. The best thermal regulation performance will thus be obtained by using material with
minimal hysteresis.
Figure 3.6. Homeostatic operating range. (a-c) Temperature variation of the silicon
microcone structure for different heat inputs. (d) Reduction in temperature
variation for microcones with narrower hysteresis width. Yellow shade illustrates
range of hysteresis loop (homeostatic operating range).
3.7 Dependence on VO2 Thickness and Fabrication Feasability
In our calculations, the VO
2
coating thickness was set to 200 nm for ease of
computation, but better performance may be possible using a thinner coating. While a full
36
optimization for the microcone structure is computationally prohibitive, we can easily
calculate the emissivity of the flat, VO
2
-coated silicon film as a function of VO
2
thickness. For
the best performance, the radiated power in the metallic and insulating states should be as
different as possible at T
c
. In Fig. 3.7, we plot P
rad
(T
c
), normalized by the radiated power at T
c
for a perfect blackbody. Fig. 3.7 shows that for a flat, VO
2
-coated film, the largest difference
between metallic and insulating states occurs for a thickness of 0.03 m, or 30 nm. For
insulating VO
2
(blue circles), P
rad
(T
c
) increases with increasing VO
2
thickness. Insulating VO
2
is optically absorptive in the IR range. As the amount of VO
2
increases, the emissivity is
increased at wavelengths where Si is transparent. The results suggest that a very thin layer
of VO
2
is sufficient to provide the maximum emissivity difference between metallic and
insulating states.
Our design is amenable to standard microfabrication techniques. Si cone arrays with
similar aspect ratios to our design have been fabricated by cryogenic, inductively-coupled
plasma reactive-ion etching [88, 90, 95, 96]. Thin VO
2
conformal coatings can be achieved by
using gas-phase reactions and deposition, such as sputtering deposition [13, 17, 18, 20, 77],
pulsed laser deposition [78, 97], and atomic layer deposition [21, 98-101]. The deposition of
conformal coatings on microscale structures is an ongoing area of research [101]. In this
work, we have assumed a perfect conformal coating for simplicity. However, further
calculations show that deviations from perfect conformality do not change the qualitative
difference in emissivity between metal and insulator states. Future work will design and test
the concept of thermal homeostasis in experiment.
37
Figure 3.7. Dependence on coating thickness. Radiated power at the phase
transition for flat, VO
2
-coated silicon film.
In the calculations above, we have considered a microcone structure surrounded by
vacuum on both sides for simplicity. We note that the addition of an opaque material as the
bottom boundary, e.g. a gold coating on the back surface of the Si substrate, has a minimal
effect on the emissivity spectrum (see Fig. 3.8).
Figure 3.8. Emissivity spectra with a 1- m-thick gold mirror attached to the back of
the VO
2
-coated silicon microconest.
3.8 General Considerations
In the discussion and calculations above, we have analyzed specific structures based on
VO
2
-coated microcones. We can abstract from our results to speculate on the ideal
conditions for thermal homeostasis.
38
First, the temperature at which homeostasis is obtained corresponds to the phase-
transition temperature of the material. For VO
2
, this temperature can be tuned between
310 K and 360 K [15, 17] by adjusting the processing method [15, 17, 20, 21, 97], doping [17,
18], or strain [19, 77]. For applications at other temperatures, one could hope to identify a
different phase-change material with a transition temperature in the target range.
When evaluating alternative materials, several considerations should be kept in mind.
First, the time scale for the phase change should be shorter than both the thermal response
time of the structure and the time scale for fluctuations in input power. For VO
2
,
experimental measurements of the phase transition time are in the ps range [16]. Second,
materials with large changes in permittivity across the phase transition will generally make it
easier to design a microstructure geometry that provides the desired change in emissivity.
The emissivity should be as close as possible to zero below the transition, and as close as
possible to the black-body above. The microcone structure presented here is optimized for
VO
2
; other materials will likely require different microstructures and/or metamaterial
designs. Third, the width of the phase transition should be as small as possible. As discussed
above, the residual temperature fluctuations for our material will be reduced as the width
of the hysteresis loop shrinks (Fig. 3.6d).
3.9 Discussion and Conclusions
In conclusion, we have proposed a route to thermal homeostasis using passive
microstructures. We have presented a specific design that uses a thin film of VO
2
conformally coated on Si microcone structures to yield switchable thermal radiation. The
design concept is based on a temperature-switchable thermal emitter: below the target
temperature, emission is minimized, whereas above the target temperature, emission is
39
maximized. This sharp change in emission helps to reduce the temperature variation of the
structure due to a time-varying heat load. The proposed thermal homeostasis structure has
a 10x difference in emissivity between the metallic and insulating states of VO
2
, resulting in
a nearly 20x reduction in temperature variation relative to Si film, and a 8x reduction
relative to a perfect black body. These numbers are obtained within a 1D heat-transfer
system in which radiation is the sole heat dissipation mechanism. Our results provide a light-
weight, completely solid-state thermal control mechanism particularly well suited for space
applications. The use of mechanically static structures, free of any moving parts, provides a
complementary alternative to existing MEMS-based approaches for thermal emission
control [102].
3.10 Radiated Thermal Power Calculation
The radiated thermal power can be written as
30
2.5
cos , ,
m
rad BB
m
P T d d I T
(3.1)
where
,
BB
IT is the spectral blackbody radiance, and
, is the computed
emissivity at 330 K. The angle resolution was 5 degrees. The calculated values of P
rad
(T
c
=330
K) for metallic and insulating VO
2
coated Si cone structures are 550 W/m
2
and 40 W/m
2
(as
shown in Fig. 3.4; green unfilled and filled circles), respectively.
Given the calculated values of P
rad
at 330 K (symbols in Fig. 3.4), we assume a model for
P
rad
(T) that takes into account the hysteresis of the phase transition and the temperature
dependence of the black-body spectrum (solid curves). Experimentally, the phase transition
in VO
2
exhibits a hysteresis loop with a width of 4 K to 15 K [13, 15, 17, 78]. The hysteretic
width can be reduced by annealing or depositing VO
2
onto a lattice-matched substrate to
40
improve VO
2
quality [15, 78]. We assume a smooth function that matches the calculated
values at 330 K and a hysteretic width of 10 K:
30
2.5
cos ,
1 1 1 1
, 1 , 1
2 2 2 2
m
rad BB
m
M c c I c c
P T d d I T
erf T T T erf T T T
(3.2)
where
,
BB
IT is the spectral blackbody radiance, ( , )
M
is the emissivity for metallic
VO
2
, ( , )
I
is the emissivity for insulating VO
2
,
C
T is the hysteretic width of 10 K, and
erf is the error function. The error function is used for convenience in interpolation;
substituting another smooth function will slightly change the shape of the temperature
response curves in Fig. 3.5 but will not alter their qualitative behavior. The + and – branches
of Eq. (3.2) give the cooling and heating branches of the P
rad
(T) loop.
3.11 Thermal Modelling Approach
We solve the time-dependent heat equation to obtain the transient temperature
resulting from a time-varying heat input. When the resistance to heat spreading in the
structure is small, the volume can be approximated as being isothermal, and we can neglect
the spatial distribution of the temperature. The entire layered structure can thus be treated
as a boundary, as shown in Fig. 3.4b. P
in
is the heat source in the system, and P
rad
is the
radiated thermal power. Such a lumped capacitor approach is valid for Biot numbers
/ 0.1
C rad
Bi L h k , where
rad
h is a radiative heat transfer coefficient, L
c
is the
characteristic length scale (e.g. the height of the structure in a one-dimensional heat flow),
and k is the thermal conductivity [94]. The radiative heat transfer coefficient can be written
as
3
~4
rad
hT , where is Stefan-Boltzmann constant, and is the effective emissivity
(P
rad
normalized by the radiated power for a perfect blackbody). Assuming a perfect
blackbody with T=800 K and L
c
=300 m, the Biot number can be calculated as
41
-4
8.34 10 0.1 Bi . Since the blackbody value is an upper bound for our structure, the
Biot number of our structure is smaller than this value.
The time-dependent heat equation can then be written as
in rad
dT t
CL P t P T
dt
, (3.3)
where ρ is the material density (kg/m
3
), C is the heat capacitance (J/K-kg), L
C
is the
characteristic length scale (m), P
in
(t) is the time-dependent heat source (W/m
2
), and P
rad
(T)
is the radiated thermal power (W/m
2
). By a change of variables, the rescaled time ( t’) can be
written as
'
C
t
t
CL
. (3.4)
Equation (3.3) can be further simplified to
'
'
'
in rad
dT t
P t P T
dt
. (3.5)
Here we assume for simplicity that C is the thermal capacitance of the structure itself. If the
structure is in thermal contact with an additional object, the time-dependent response will
depend on the lumped thermal capacitance [94] of the entire system.
42
Chapter 4.
Far-Field Thermal Rectifier and
Applications
4.1 Introduction
Conventionally, information is processed and carried by electrons. Electric flow and
heat flow are fundamental in the electron transport. Though the heat flow is the
counterpart of the electric flow, it is not as well controlled and out of reach as electric flow.
While the development of integrated circuits based on electronic devices has been
remarkably successful, there are emerging fields needing novel architectures for situations
where electronic devices don’t function, e.g. nanostructures with low thermal conductivity.
In analogue to electronic devices, similar functions in thermal or phononic devices, like
thermal rectifier [103-106], thermal diode [107, 108], thermal memory [109-111], and
thermal logics [110, 111], can be achieved to control the heat flow.
In recent years, much more attention has been attracted to the realization of thermal
rectifiers as the most fundamental component in thermal computing [103, 105, 106, 112-
116]. A general thermal rectification device consists of three basic components: an input
thermal terminal, an output thermal terminal, and a heat flux exchanging channel bridging
the two terminals. The channel’s conductivity depends on the direction of the heat flow. A
schematic of two-terminal device is depicted in Fig. 4.1. The two heat baths with
temperatures, T
h
and T
c
, are connected to the device. The heat flow between the two
terminals is altered when T
h
and T
c
are swapped. We can define the forward biased
43
direction as from left to right. The channel is highly conductive when it is under forward
biased condition, and the resulting heat flow
f
J is greater. In contrast, when the channel is
reverse biased (right to left), the heat flow
r
J is minimized. Thus we can define the
rectifying coefficient
th
R as the ratio of
f
J to
r
J ,
f
th
r
J
R
J
(4.1)
Figure 4.1. Schematic illustration of conductive thermal rectifier.
In addition to conductive thermal rectifiers, photon-based radiative thermal rectifiers
are fundamentally important. More attention has been given to near-field study of the
thermal rectifiers due to the possibility of achieving high rectification [103]. However, the
experimental realization is much more difficult. Far-field radiative thermal rectifiers are thus
attracting more interest [104, 109, 116, 117], especially in experimental demonstrations
[104, 109]. In this chapter, we theoretically study the far-field thermal rectification of
designed structures and propose two different approaches to achieve high rectification. As
shown in Fig. 4.2, a simple far-field radiative thermal rectifier consists of two parallel plates
separated by a distance much larger than the wavelength under consideration.
44
4.2 Formulism for Far-field Thermal Rectifier
Figure 4.2. Schematic illustration of far-field radiative thermal rectifier.
To calculate the rectifying coefficient of the far-field thermal rectifier, we need to first
calculate the radiative heat exchange between the two surfaces as a function of
temperature. The far-field radiative heat exchange between the two surfaces can be written
as [94]
ex 1 2 1 2 1 2
, cos , , , , ,
BB BB
P T T d d I T I T T T
(4.2)
where
BB
I is the blackbody radiance, T is the temperature for surface 1 or 2, is solid
angle, and is the channeled emissivity. The function
12
, , , TT represents the
effective emissivity in heat transfer between the two surfaces,
12
,
1 1 2 2
11
, , ,
2 1 , , 1 , , 1
TE TM
TT
TT
(4.3)
where stands for TE or TM polarizations. If surface 2 is a temperature-independent
blackbody,
12
, , , TT can be simplified to
1 1 1 1 2
1
, , , , , ,
2
TE TM
T T T
. (4.4)
Equation (4.4) is used for all the previous chapters to calculate the radiated power.
45
Since the geometry we consider for potential thermal rectification applications in this
chapter is a two-parallel-plate (surface) system, we can thus neglect the angular
dependence of the emissivity, perform the angular integral, and further simplify Eq. (4.2)
and Eq. (4.3) to
ex 1 2 1 1 1 2
1
, , , , ,
2
BB BB
P T T d I T I T T T
(4.5)
and
12
,
1 1 2 2
11
,,
2 1 , 1 , 1
TE TM
TT
TT
. (4.6)
If surface 2 is a temperature-independent blackbody,
12
,, TT can be simplified to
1 1 1 1 2
1
, , ,
2
TE TM
T T T
. (4.7)
For an opaque object, the emissivity can be attributed from its reflectivity
, 1 ,
i i i i
TT
. (4.8)
Equation (4.8) is commonly used to calculate the emissivity (absorptivity) for the cases with
perfect matching layer (PML), semi-infinite substrate, and a substrate with anti-reflection
coating.
4.3 Layered VO
2
Structures
In section 3.7 Dependence on VO2 Thickness and Fabrication Feasability, we have
shown that emissivity difference between hot temperature and cold temperature states can
be tuned by changing the VO
2
thickness. A potential thermal rectifier can be achieved by
simple layer stacking of VO
2
and other materials. Figure 4.3 shows schematic illustrations of
three simple layered structures under our study. Figure 4.3a shows a single layer VO
2
floating in air, this case is mechanically impossible, but it can provide insights about VO
2
IR
46
emissive properties. Figure 4.3b is a repeated study from 3.7 as a reference to Fig. 4.3c (a
gold back-reflector is added to the backside of the sample).
Figure 4.3. Layered structures under study. (a) single-layer VO
2
, (b) VO
2
sitting on-
top of an opaque substrate (here we use Si and sapphire), and (c) VO
2
sitting on-
top of an opaque substrate and a gold back reflector.
Normalized P
rad
(T
c
) for the three structures are shown in Fig. 4.4-4.5. To maximize
rectifying coefficient, normalized radiated power at T
c
in metallic and insulating states
should be as different as possible. For convenience, we treat normalized radiated power at
T
c
as effective emissivity
Metal
(or
Insulator
), and plot
Metal Insulator
in Fig. 4.4-4.5 (right y-
axis). Though the largest difference between metallic and insulating states (
Metal Insulator
)
occurs for a thickness of 0.02 m in Fig. 4.4a; the largest ratio ( ~ 290
Metal Insulator
) occurs
in the thinnest VO
2
thickness, 0.01 m. Insulating VO
2
is slightly absorptive in the IR range.
As the thickness and amount of VO
2
increase, the emissivity also increases. In the extreme
thin thickness scenario, the amount of thermally absorptive material (insulating VO
2
)
dominates the radiated power. For metallic VO
2
in the limit of very thin structure, the
thickness is less than the absorption length (tens of nanometers as shown in Fig. 4.4b), so
the plasmatic absorption is enhanced. Even when the thickness goes up to 0.03 m, the
single-layer VO
2
can still potentially be used as a thermal rectifier to achieve a rectifying
coefficient of ~50.
47
Figure 4.4. Normalized radiated power for a single layer VO
2
In the insulating and
metallic states as a function of VO
2
thickness.
Next we calculate the normalized radiated power in more feasible and reasonable
structures with substrates and back-reflector. In Fig. 4.5a-4.5b, we choose sapphire as
substrate, which is commonly used to grow high-quality VO
2
[78, 118], and gold as back-
reflector material. The largest rectifying coefficient can be achieved is only ~1.5. Gold back-
reflector enhances the emission for both metallic and insulating VO
2
structures when the
thickness is less 0.3 m, but reduces the rectifying coefficient. We note that sapphire is
optically absorptive in the entire wavelength range (2.5-30 m) we consider.
In Fig. 4.5c-4.5d, Si substrate is considered. Similar trends in normalized radiated power
can be observed as in Fig. 4.4a. For a simple VO
2
/ Si structure, a rectifying coefficient R
th
~7
can be achieved when VO
2
thickness is 20 nm.
48
Figure 4.5. Normalized radiated power for VO
2
structures. (a) VO
2
on 300- m
sapphire. (b) VO
2
on 300- m sapphire and a gold back reflector. (c) VO
2
on 300- m
Si. (d) VO
2
on 300- m Si and a gold back reflector.
4.3.1 Rectifying Coefficient Optimization Strategy
An optimized rectification is achieved due to a large contrast between the two surfaces’
thermo-optic properties. Thermo-optic properties depend on both choice of materials and
morphological effects (micro- or nano-patterning). VO
2
has been intensively studied and
used as thermal rectification devices in many works [103, 104, 107]. Changes in the
morphology or structure typically result in discrete optical modes. In the previous chapters
and sections, we focus mainly on the thermal emissivity from a broadband perspective;
explicitly, we consider the entire wavelength range 3-30 m, where the blackbody radiance
contributes the most to radiated power (around the room temperature). The microcone
structure in Chapter 3 is optimized to achieve this goal. From Eq. (4.6), we find that only the
49
overlapped area of the spectral emissivity between of the two surfaces contributes to the
channel for heat exchange. If we consider the emissivity of surface 2 to be relatively
temperature-independent, we can maximize the rectifying coefficient or the contrast ratio
of overlapped area in spectral emissivity by tuning the temperature-dependent emissivity of
surface 1. Here we propose two approaches: 1) broadband approach (will be discussed in
4.4.2), and 2) narrowband approach (will be covered in 4.4.3).
4.3.2 Broadband Perspective: Maximizing Emissivity Difference
In the broadband approach, ideal rectification scheme is such that the reverse
channeled emissivity is suppressed close to zero over the entire wavelength range we
consider. The proposed device structure consists of a simple multilayer structure sitting on a
semi-infinite Si substrate on one side, and a blackbody on the other side, as shown in Fig.
4.6a. The multilayer structure consists of a thin VO
2
film, Si film, and a gold back-reflector.
The thickness of gold back-reflector is fixed to be 100 nm, which is sufficient enough to
block radiation from the substrate (the reification results remain unchanged until the gold
thickness is smaller than 20 nm). Then particle swarm optimization [92] was performed to
optimize the VO
2
and Si thickness to achieve high rectifying coefficient. Lower and upper
bounds on VO
2
thickness and Si thickness were kept at 10-100 nm and 10-3000 nm,
respectively. Optimal thicknesses were found to be 10 nm and 700 nm for VO
2
and Si. The
spectral emissivities for insulating (blue line) and metallic (red line) VO
2
are shown in Fig.
4.6b. The spectral blackbody radiance at 300 K (shaded pink) is added in Fig4.6b as
reference.
When VO
2
is metallic, the multilayer structure acts like a broadband plasmonic emitter
(absorber). We monitor the power flux in each interface, and find that >91% of the power is
50
emitted (absorbed) in the thin metallic VO
2
layer. When VO
2
is insulating, most of the power
is reflected by the gold back-reflector. A rectifying coefficient of 21.48 can be achieved, and
it is the highest value so far all the far-field radiative rectifiers have achieved.
Figure 4.6. (a) Schematics of simple thermal rectifier consisting of an active VO
2
multilayer structure and a blackbody. (b) Thermal emissivity of the proposed
structure.
4.3.3 Narrowband Perspective: Tuning Resonant Peaks
An ideal thermal rectification scheme has a rectifying coefficient of infinity (one over
zero). This can be achieved by either broadband or narrowband spectral emissivity tuning. In
this section, the thermal rectification arises from alignment and misalignment of the
resonant peaks of the two surfaces in the thermal wavelength range. We suppose that the
forward direction is when the resonant peaks are spectrally aligned, while the reverse
direction is when the resonant peaks are spectrally misaligned or separated. An ideal
thermal rectification scenario is depicted in Fig. 4.7. For simplicity, we assume that one of
the two surfaces has relatively temperature-independent thermo-optic properties, e.g.
intrinsic semiconductors, and it has a narrow resonant peak in spectral emissivity as shown
51
in Fig. 4.7a (green curve). The other surface consists of phase-change materials, and is
designed to support a resonant mode as shown in Fig. 4.7b; the resonance is dramatically
shifted in the two temperature states (T
h
and T
c
). The emissivity of the temperature-
independent surface is also shown (dashed green line) in Fig. 4.7b. We note that the
emissivities in Fig. 4.7 are idealized as step functions with unity emissivity in a narrowband
around the resonance and zero emissivity outside resonance. Figure 4.7c shows the
channeled emissivity for this ideal case. In the forward biased direction (Fig. 4.7c; red line),
there is a certain amount of net heat transferred from the hot surface to the cold surface
due to the spectral emissivities overlap. In the reverse biased direction (Fig. 4.7c; blue line),
there is no overlap of the spectral emissivities, and hence there is no radiated power is
transferred or exchanged between the two surfaces. In such a scenario, the rectification is
perfect, and the rectifying coefficient is infinite.
Figure 4.7. Schematic illustration of resonance tuning to achieve high contrast
thermal rectification. (a) A relatively temperature-independent spectral emissivity
of one surface. (b) A temperature-dependent spectral emissivity of the other
surface. (c) The channeled emissivity of the thermal rectifier in forward and reverse
directions.
To implement the proposed concept, a simple device constituted by two multilayer
surfaces made of gold and semiconductor (Si and VO
2
) thin films is proposed as shown in Fig.
52
4.8. The proposed structures are made of three thin films: a relatively transparent layered
sandwiched by two metallic reflectors. A high contrast of refractive indices between the
multilayer structure and vacuum consequently collimates the thermal radiation within a
very narrow light cone leading to negligible angular dependence of the thermal radiation.
Figure 4.8a shows that Au|Si|Au multilayer structure emissivity exhibits a single resonant
peak at =3 m. The Au|VO
2
|Au multilayer structure emissivity is shown in Fig 4.8b.
Metallic VO
2
emissivity (red line) is slightly greater than insulating VO
2
emissivity (blue line)
in the wavelength range from 5 m to 30 m. The channeled emissivities for metallic VO
2
(red line) and insulating VO
2
(blue line) are shown in Fig. 4.8c. The resonant peak is far away
from the peak of blackbody radiance at 300 K (shaded pink; peaked at 10 m). While the
device is operating under usual temperature condition (close to the VO
2
phase-change
temperature ~330 K), the rectifying coefficient is only ~1.01.
Figure 4.8. Spectral emissivities of (a) an Au|Si|Au multilayer structure, and (b) an
Au|VO
2
|Au|Si multilayer structure. (C) Channeled emissivity of the proposed
thermal rectifier.
With an aim to improve the rectifying coefficient, we propose another multilayer
designs consisting of five Si|CsI double-layer (as shown in Fig. 4.9: surface 2); Si is swapped
to VO
2
in the third double-layer (as shown in Fig. 4.9: surface 1). An optimization was
53
performed to produce a narrow resonant peak around 10 m for both surfaces. Details on
designing layer thickness can be found in Table 4.1.
Figure 4.9. Optimized multilayer structures for thermal rectification.
Air Si CsI Si CsI Si CsI Si CsI Si CsI Si
0.8 1.22 0.95 1.48 1.31 1.21 1.05 1.49 0.91 1.08
Air Si CsI Si CsI VO
2
CsI Si CsI Si CsI Si
1.9 1.22 0.72 1.48 0.06 1.22 0.79 1.49 0.68 1.08
Table 4.1. Optimized multilayer thickness ( m) for proposed structures.
The resulting spectral emissivities of the two surfaces are shown in Fig. 4.10a. Multiple
peaks can be observed for the optimal Si|CsI multilayer (black line) and Si|CsI|VO
2
multilayer (blue and red lines) structure, and a sharp pronounced resonant peak can be seen
at around 10 m for Si|CsI (black line) and Si|CsI|insulating VO
2
(blue line) cases. Fig. 4.10b
is the magnified view of Fig. 4.10a centered at =10 m. When VO
2
is insulating, there is a
great portion of overlap between the black and blue lines. When VO
2
turns metallic (red
line), the resonance is shifted out of the window. This evolution would potentially induce a
high rectifying coefficient. Figure 4.10c shows the channeled emissivity of the optimized
thermal rectifier. When considering only the wavelength range (9.5-10.5 m) depicted in
54
4.10c, a rectifying coefficient of 5.25 can be achieved. However, if the entire wavelength
range is considered, the rectifying coefficient would be 1.51. This is expected due to the
multiple resonances within the thermal wavelength.
Figure 4.10c shows the channeled emissivity of the optimized thermal rectifier.
Figure 4.10. (a) Emissivity spectra of the proposed multilayer structures. (b)
Magnified view of (a) between =9.5 m and 10.5 m. (C) Channeled emissivity of
the proposed thermal rectifier.
4.4 Discussion and Conclusions
We study several VO
2
based thermal rectifier designs in this chapter. Both broadband
and narrowband perspectives are explored. A simple tri-layer broadband design is
investigated. The tri-layer consists of VO
2
, Si and gold thin films. As VO
2
undergoes phase-
change, the surface optical properties are dramatically changed. Thin metallic VO
2
film
contributes more than 91% of emission (absorption) while insulating VO
2
structure is highly
reflective – leading to a high degree of asymmetry in radiative heat transfer in the forward
and reserve biased directions between the proposed tri-layer design and a blackbody. The
system shows a rectifying coefficient value of 21.48, the highest reported in the literature in
VO
2
based far-field radiative thermal rectifier.
Narrowband thermal rectification arises from alignment and misalignment of the
resonant peaks of the two surfaces. Two initial multilayer structures are proposed and
55
investigated. However, no sufficient rectification is attained. Since the proposed structures
are based on spectrally tunable resonances, it is possible to eliminate the multiple resonant
features and further optimize results by tuning the stacking thicknesses or introducing
photonic crystal structures into the system.
Potential optimization of attaining an even higher rectification could be investigated in
future by introducing dielectric mirror with alternating layers or photonic crystal structures
in the system, and utilizing other IR transparent materials [119].
56
Figure 4.11. Infrared transparent materials choices (reprinted from ref. [119]). The
unit for wavelength at the bottom is m.
57
Chapter 5.
Conclusion and Outlook
5.1 Conclusions
In PART I of this dissertation, we use full-field electromagnetic simulations to
investigate the optical and thermal properties of proposed nanostructures and
microstructures. In specific, the radiative heat transfer properties in those structures. The
main contribution and discoveries of PART I of this dissertation can be characterized as
following.
Firstly, I used a coupled 3D thermal-optical model to estimate the thermal response of
a GaAs nanowire solar cell under solar illumination. I found that the radiative thermal
response of nanowire solar cells behaves very much like the planar counterpart, even with
highly concentrated light absorption and much more localized heating than planar
structures. I also found that reduced thermal conductivity in the nanowire has very little
effect on the operating temperature rise. These results can be attributed to that the
characteristic length scale for temperature variation under one sun condition is much larger
than the nanowire dimensions. Moreover, I also found that the infuriation of an isolating
polymer (BCB) can not only provide mechanical support to the nanowires, but also enhance
the radiative cooling power of the nanowire solar cell by a factor of 2.2 relative to the planar
structure.
Secondly, I proposed a new mechanism for radiative thermal management – thermal
homeostasis – utilizing the phase-change properties of VO
2
to minimize and dampen
temperature fluctuations. This novel mechanism shows that the residual temperature
58
fluctuations are reduced to the width of the hysteresis loop. An optimized design that uses a
thin film of VO
2
conformally coated on Si microcone structures is achieved to yield highly
switchable temperature-dependent thermal radiator. The Si microcone design is optimized
to exhibit strong anti-reflection effect and to be relatively insensitive to angle of incidence.
The optimized thermal homeostasis structure has a nearly 10x difference in emissivity
between the metallic and insulating states of VO
2
, resulting in a nearly 20x reduction in
temperature variation relative to ordinary semiconductor materials, and a nearly 8x
reduction relative to a perfect black body.
Thirdly, two approaches to design far-field rectifiers and maximize rectifying coefficient
were proposed and explored. A promising design was achieved; a rectifying coefficient R
th
=
21.48 of a far-field radiative thermal rectifier was achieved in this dissertation. This value is
the highest reported value in the literature.
5.2 Outlook
The theoretical work indicates a promising route to thermal homeostasis. A US patent
of the theoretical work and design was filed and submitted for review. Our collaborators at
Northrop Grumman Corp. and colleagues at our group will continue working on
experimental demonstration of thermal homeostasis.
On the Si microcone fabrication, we recently found a promising receipt (SF6:C4F8 = 33
sccm: 57 sccm) for Si ICP-RIE etching using a thicker photoresist (AZ5214E), resulting in a
selectivity of 15 between Si and photoresist. Alternatively, a thicker SiO
2
as the mask is
preferred due to an even higher selectivity under the same etching condition. On the optical
emissivity measurement, our colleagues were trained to operate the Fourier-transform
infrared spectroscopy (FTIR) at USC, and have measured promising results (lower reflectivity
59
and higher emissivity at higher temperature) for thin film VO
2
on Si substrate. Our
collaborators at Northrop Grumman Corp. will be responsible for the thermal response
measurement and thin film VO
2
deposition. I believe that the thermal homeostasis
experiments may yield interesting results.
In the far-field thermal rectification part, there is plenty space for improvement. More
sophisticated design and optimization work can be done in order to obtain a giant rectifying
coefficient.
60
PART II
Light-assisted Assembly of
Reconfigurable Optical Matter
61
Chapter 6.
Introduction
Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting
in random, Brownian motion. Optical fields induced forces on matter are capable of pulling
nano-objects into precise positions [120, 121]. Single-particle and multiple optical traps
based on this principle have been demonstrated for biological cells [122-124], dielectric
[125-130], and metallic nanoparticles [131, 132]. Optical traps have been adapted and
widely used in physics and biology.
In dielectric optical traps, the strong electromagnetic field gradient near a patterned
dielectric surface attracts particles to desired trapping locations near the surface. Resonant
enhancement of the optical near-field of the dielectric template strongly enhances the trap
stiffness [131-134]. The on-chip implementation of near-field optical traps and introduction
of dynamic optical manipulations would greatly facilitate applications in lab-on-a-chip,
microfluidic environments, from particle sorting to directed transport.
6.1 Background
The assembly of periodic arrays of nanoparticles resembles synthetic and
reconfigurable two dimensional (2D) optical matters. Traditional colloidal nanoparticle self-
assembly results in close-packed structures, which is limited by free energy minimization
constraints. By imposing an array of optical traps, free energetic constraints can be released.
In our group, the LATS (light-assisted templated self-assembly) technique which exploits
photonic-crystal slabs to create arrays of resonantly enhanced optical traps near the slab
62
surface has been demonstrated to assemble square arrays of polystyrene nanoparticles
[125], chains of gold nanoparticles [131], and hexagonal arrays of gold nanoparticles [132,
134]. The LATS technique paves a new way to fabricate optical matters at nanoscale from
bottom-up. By using different laser wavelengths, polarizations, and wave fields, complex
optical potential landscapes can be created near the dielectric surface, and thus generate
different arrays of trapping sites.
6.2 Theory: Electromagnetic Force Calculation
Whenever electromagnetic wave interacts with a material, there are always optical
forces. In general, electromagnetic forces originate from Lorentz force on a charge in an
electromagnetic field. The total electromagnetic force on this charge can be written as
q F E v B . (6.1)
Considering some volume of space with charge density ρ and current density J, the force
density can be rewritten as
f E J B . (6.2)
The local electromagnetic force on an object then can be readily calculated by the
volumetric integration
VV
dV dV
F = f E J B . (6.3)
Since the volumetric method requires 3D field information, it is computationally costly. It
can be shown that the Eq. (6.3) can be rearranged in the following form
ij
S
dS
F = T n . (6.4)
63
where i and j are one of the three primary coordinate directions (x, y or z), S is an arbitrary
surface around the object, n is the unit normal of S, and T
ij
is the Maxwell Stress Tensor
[135], which has the following form:
22
**
1
2
ij i j i j ij
EE H H T E H . (6.5)
The Maxwell stress tensor method can be used to calculate the forces on particles of any
size and shape in response to an electromagnetic field. Electromagnetic field is obtained by
finite-difference time-domain (FDTD) method (Lumerical Solutions, Inc.). In most of the
cases, Eq. (6.4) will be used to calculate the optical force acting on a trapped particle. Eq.
(6.3) will be used when the particle is close to the photonic crystal slab or when the particle
sinks into the holes on the photonic crystal slab.
6.3 Theory: Hydrodynamic Simulations
Typical trapping experiments are conducted in an aqueous solution and a microfluidic
chamber. The assembly of nanoparticles may depend on other non-optical forces, such as
fluidic drag forces, fluidic flows, and thermophoresic forces. The Langevin equation under
viscous limit has been used to predict the optically trapped nanoparticle behaviors [133, 134,
136]. A hydrodynamic simulator based on the Langevin equation was developed to model
our optical trapping system:
i
O F T R
d
dt
r
F F F F , (6.6)
where F
O
is the optical force
OO
U F , (6.7)
F
T
is the thermophoretic force
64
T
U
T
F , (6.8)
F
R
is the random force
2
RB
k T t F , (6.9)
and F
F
is the fluidic drag force,
6
F
R F v v . (6.10)
Here
O
U is the optical potential,
T
U is the thermal potential,
t is the random number
generator, v is the relative velocity between the medium and the particle, is the drag
coefficient, and is the viscosity of the medium. The expression for drag coefficient only
holds for spherical particles of radius R in a uniform medium. The presence of a surface
closely placed near a particle can alter the drag coefficient via Faxen’s Law:
2
2'
3 4 5
61
6
1
6
9 1 45 1
1
16 8 256 16
R
R
R
R R R R
H H H H
υ
F
F = v
, (6.11)
where
'
υ is the disturbance velocity, and H is the distance between the center of the
particle and the surface [134, 137, 138].
6.4 Photonic Crystal Device Fabrication
All devices will be fabricated at USC Keck Photonics microfabrication facility or UCLA
CNSI. Two types of silicon-on-insulator (SOI) wafer are used: 1) 250 nm Si device layer, 3 μm
buried oxide layer, 600 μm silicon handle layer, or 2) 340 nm Si device layer, 2 μm buried
oxide layer, 600 μm silicon handle layer.
65
At USC, PMMA 950K is used as the electron beam resist, and is spincoated onto the
wafer at 3,000 rpm for 60 seconds, resulting in a layer approximately 300 nm thick. The
sample is baked at 170 ° C for 70 minutes to evaporate the solvent. The sample is then
exposed in the Raith e-Line 150 system using an acceleration voltage of 30 kV and an
aperture of 10 μm, which produces a current of approximately 32 pA.
At UCLA, ZEP electron beam resist is used and spincoated onto the wafer at 2,500 rpm
for 60 seconds, resulting in a layer approximately 300 nm thick. ZEP is known to associate
with high resolution and excellent dry-etching resistance for device fabrication. The sample
is baked at 170 ° C for 2 minutes. The exposure requires only 10 - 20% the dose requirement
of PMMA. The sample is exposed in the VISTEC EBPG 5000+ system using an acceleration
voltage of 100 kV and an aperture of 10 μm, which produces a current of approximately 2
nA.
Etching is done in the Oxford DRIE system at USC using a modified Bosch process with
the following parameters: 33.0 sccm of SF
6
(etchant), 57.0 sccm of C
4
F
8
(polymer coating for
protecting sidewalls), 20 mT chamber pressure, 30 W inductively-coupled plasma (ICP)
power, 600 W reactive ion etching (RIE) power, 49 seconds etching time for 250 nm devices
(52 seconds for 340 nm devices).
6.5 Microfluidic Chamber Preparation
Microfluidic chambers are used to deliver particles to the trapping region. The
chambers are fabricated on a round glass coverslip 2 mm thick and 1 inch in diameter. After
cleaning, the glass is spincoated with AZ 4620 positive photoresist for 60 seconds at 3,000
rpm, resulting in a thickness of approximately 8 μm. The sample is baked on a hotplate at
100 ◦C for 10 minutes to evaporate the solvents, then exposed in the MJB3 aligner with a
66
dose of 300 μJ. The exposed resist is then developed using AZ400K for 5 to 6 minutes,
resulting in a square of photoresist in the center of the glass (this is the inverse of the
microfluidic chamber). A mixture of polydimethylsiloxane (PDMS), hexane, and a curing
agent is prepared. Then a conformal layer is spincoated on top of the glass with the square
shape of photoresist at 5,000 rpm for 60 seconds. The final thickness of the PDMS can range
from 200 nm to 5 μm depending on the ratio between PDMS and hexane. The sample is
then cured in a 65 ◦C oven over night, thereby solidifying the PDMS. The final step is to cut
away the square area above the photoresist using a razor blade and then to dissolve the
photoresist with acetone. Then the chamber is used to cover the SOI device. This results in a
microfluidic chamber in which the walls are made of PDMS, the ceiling is glass, and the floor
is the SOI sample.
6.6 Experimental Optical Setup
To characterize the device, the PhC sample is mounted on a glass slide with a 2 mm
circular hole at the center. A schematic of the optical setup is shown in Fig. 2.1. A tunable
laser with a wavelength range from 1500 nm to 1620 nm (Santec TSL-550) and a single-
mode fiber (mode diameter 10.4 ± 0.8 m) were used. A polarizer and a half-wave plate
allows for control over the polarization state of the beam. An aspherical lens (f = 11 mm and
NA = 0.25, Thorlabs C220 TME-C) was incorporated to collimate the beam. An achromatic
doublet (f = 30 mm, Thorlabs AC254) was then used to refocus the beam to the back side of
the sample. On the other side of the sample there is a second microscope objective for
collecting the transmitted light. In addition, this objective is used to image the particle
movement using a CMOS camera and a white light source. A second set of polarization
control optics is used to enable crossed-polarization measurements, which simplify the
67
alignment of the set-up and improve the characterization of the sample. A second collimator
is used to couple the light back to a single-mode fiber, which is connected to a germanium
detector. The operation of the laser and detector is controlled by a computer running
LabVIEW, which is also used to monitor and record the camera output.
Figure 6.1. Schematic of experimental set-up used to characterize samples and
perform assembly experiments.
68
Chapter 7.
Near-Field Optical Brownian
Ratchets
A version of the results in this chapter was published as Ref .[133].
7.1 Introduction
Brownian ratchets [139, 140] are of fundamental interest, and their understanding
yields insight into natural systems from protein motors [141-143] to far-from-equilibrium
statistical physics [144]. The realization of Brownian ratchets in engineered systems [139,
145-149] opens up the potential to harness thermal energy for directed motion and has
applications in transport and sorting of nanoparticles [145, 150] and DNA [151, 152].
Optically driven Brownian ratchets [153] offer opportunities for tuning and reconfiguration.
By using different laser wavelengths, polarizations, and wave fields, complex optical
potential landscapes can be created [154] and modulated in time [121]. Previous work
based on conventional and holographic optical tweezers [155, 156] has demonstrated
ratchet motion.
The on-chip implementation of optical Brownian ratchets would greatly facilitate
applications in lab-on-a-chip, microfluidic environments, from particle sorting to directed
transport. Optical ratchets [157] based on plasmonic traps [126, 158, 159] have been
proposed theoretically but not demonstrated. Here, we experimentally demonstrate an on-
chip optical ratchet based on an all-dielectric approach. In dielectric optical traps, the strong
electromagnetic field gradient near a patterned dielectric surface attracts particles to
69
desired trapping locations [124, 127, 128]. In our previous work, we have demonstrated the
creation of multiple, periodically spaced trapping sites using a silicon photonic crystal
template [125, 131, 132]. Resonant enhancement of the optical near field of the template
strongly increases the trap stiffness.
We show that by breaking the symmetry of an all-dielectric template, we can create
asymmetric optical potentials suitable for on-chip ratchets. We fabricate our template
design and experimentally demonstrate ultrastable optical trapping. For 520 nm diameter
polystyrene particles, our measured trap stiffness is 53 pN· nm
–1
·W
−1
, more than 25 times
stiffer than conventional optical tweezers [160] and >400 times higher than holographic
traps [161]. We demonstrate optical ratcheting with transport speeds of approximately 1
μm/s. These speeds are greater than previous optical Brownian ratchets [146, 153, 155, 156];
refs [155] and [156] demonstrated a transport speed of 0.01 μm/s for 1.53 μm diameter
particles, ref [153] demonstrated a transport speed of 0.095 μm/s for 1.5 μm diameter
particles, and ref [146] demonstrated a transport speed of 0.2 μm/s for 0.5 μm diameter
particles.
7.2 Brownian Ratchets
The basic principle of a Brownian ratchet involves the on–off modulation of a spatially
asymmetric potential (1), shown in Figure 7.1a. The particle probability distribution is shown
in gray and the potential in blue. Initially (top panel), the particles are trapped in the
potential minima. When the potential is turned off (middle panel), the particles start to
diffuse freely. The particle probability distribution becomes a set of broadened Gaussians
centered on the potential minima. Particles in the shadowed region of the Gaussian diffuse
past the potential maxima of the neighboring trap. When the potential is turned on again
70
(lower panel), these particles are captured by the neighboring trap, resulting in net motion
to the right. The asymmetry parameter of the potential is defined as = 1-
f
/ (
f
+
b
), where
(
f
+
b
) is the lattice constant of the potential. With higher asymmetry of the potential
(larger α), the rectification efficiency (probability of rightward motion during one cycle) is
larger.
Figure 7.1. Basic operating principle of Brownian ratchets. (a) By modulating an
asymmetric external potential, the random, Brownian motion can be rectified in
the forward direction. Blue lines indicate potential; gray lines indicate particle
probability distribution. (b) A periodic array of optical traps generated by a
photonic crystal slab. Light is incident on the slab from below, perpendicular to the
slab surface. The asymmetric, modified triangular holes produce an asymmetric
field distribution with strong field intensity in the holes. Modulating the incident
light results in sideways motion of the particles or Brownian ratcheting.
7.3 Design of Asymmetric Optical Potential
We consider a silicon PhC slab (n = 3.45) with a square lattice of modified triangular
holes. The lattice constant a is 960 nm, and the slab thickness is 250 nm. The slab rests on a
silica substrate (n = 1.45) and is covered by water (n = 1.33). The PhC slab is designed to
support a guided mode resonance[162] near a wavelength of 1550 nm. Figure 7.2a shows
the normalized electric field intensity profile (|E|
2
) on resonance for y-polarized incident
71
light, calculated using a 3D finite-difference time-domain (FDTD) electromagnetic solver
(Lumerical Solutions, Inc.). The white dashed line represents the position of the hole. The
field profile is clearly asymmetric with respect to the y-axis and mostly concentrated in the
hole. The simulated transmission spectrum is shown in Fig. 7.2b. A resonant wavelength
0
of 1555 nm and a quality factor Q of ~700 were obtained by fitting the spectrum to a Fano-
resonance line shape.
The optical forces acting on a dielectric nanoparticle due to the guided resonance
mode of the PhC slab is calculated next. We assume a 520 nm diameter polystyrene sphere
with n = 1.59. In previous work, we have observed that optical forces tend to pull particles
toward the PhC slab, causing the particles to sink slightly into the holes.[125, 131, 132] For a
particle in contact with the slab, the vertical height can be determined as a function of the
in-plane position using the geometrical constraints. The top panel of Fig. 7.2c shows the
height of the bottom edge of the particle (z) as a function of the in-plane x position, where z
= 0 is the top edge of the slab. We calculate the optical force on the particle along this (x,z)
contact path by numerical integration of the electromagnetic force density over the particle
volume [135]. The results are shown in Fig. 7.2c (middle). The optical forces are in
dimensionless units of Fc/P, where c is the light speed in vacuum, and P is the incident
power. The negative force in the z-direction indicates attraction toward the slab, while the
force in the x-direction tends to pull the particle toward the field intensity maxima. The
force in the y-direction is zero, as expected due to symmetry.
To visualize the optical potential experienced by the particle, we perform a line
integration of the optical force along the contact path. Figure 7.2c (lower) shows the optical
potential normalized to the room temperature thermal energy and the incident source
power flux. For a fixed coupled power flux of 100 W/m
2
, an optical potential energy shift of
72
57 k
B
T is achieved. There are two dips in the optical potential. The potential dip with lower
potential energy is a more stable trapping position and corresponds to the maximum field
intensity. The second dip results from the change in contact height when the particle sinks
into the hole. From simulations of the Langevin equation, we have observed that the double
dip shape reduces the effective trap stiffness within each unit cell. Using the deeper of the
two dips to calculate the asymmetry factor, we find a value of 0.8.
Figure 7.2. Design of a silicon photonic crystal device with asymmetric holes. (a)
Simulated electrical field intensity profile (E
2
) on resonance for y-polarized incident
light (polarization direction shown as red arrow). The white dashed line represents
the location of the hole. (b) Simulated transmission spectrum of the device. (c)
Contact height, simulated optical forces, and optical potential as a function of
lateral position for a particle in contact with the slab.
7.4 Device Characterization
To experimentally validate our near-field optical Brownian ratchet design, we
fabricated the PhC using a silicon on insulator (SOI) wafer with a 250 nm device layer and a 3
73
m buried oxide layer. A scanning electron microscopy (SEM) image of the device is shown
in Fig. 7.3a. The scale bar is 2 m, and the lattice constant is 960 nm.
To characterize the device, the PhC sample is mounted on an optical characterization
setup (see 7.9 Optical Setup and Beam Condition). The parallel-polarization transmission
spectrum of the device is shown in Fig. 7.3b. By fitting the spectrum to a Fano-resonance
line shape, the resonant wavelength
0
and quality factor Q were determined to be 1553 nm
and ~570, respectively. The Fabry-Perot fringes visible in the spectrum are due to reflection
from the backside of the sample. The difference in maximum transmission values between
the simulated and experimental transmission spectra is due to optical loss in the collection
optics (e.g., finite numerical aperture of the collection lens and loss in the fiber to free space
coupler).
Figure 7.3. Fabricated device characterization. (a) SEM image of the device used in
experiments. (b) Measured transmission spectrum.
7.5 Trapping Experiments
Optical trapping and Brownian ratchet experiments were conducted in a sealed
microfluidic chamber (~700 nm height) filled with dilute 520 nm diameter polystyrene
particle solution using a laser power of 100 mW. Heavy water (D
2
O) is used to minimize
74
heating effects in the system; its extinction coefficient k is 5.2×10
-6
(unitless) at 1550 nm, in
contrast with 1.4×10
-4
for water [163].
Optical trapping experiments were performed first. Multiple particles were trapped on
the sample surface, as shown in Fig. 7.4a. Taking into account the measured beam radius
(see 7.9 Optical Setup and Beam Condition), the maximum power per trap is ~160 W. We
followed the procedure described in our previous work [125, 131, 132] to analyze the trap
stiffness at each trap site (see xxx). We found that the mean stiffness in the y-direction (k
y
=
53 pN· nm
-1
·W
-1
) is 3 times greater than the stiffness in the x-direction (k
x
= 18 pN· nm
-1
·W
-1
).
The standard deviations of the measured values are ± 8 pN· nm
-1
·W
-1
and ± 3 pN· nm
-1
·W
-1
,
respectively. As mentioned above, the double-dip optical potential tends to reduce trap
stiffness along the x-direction.
75
Figure 7.4. Microscopy-video analysis of ratcheting experiments. (a) Snapshot of
particle trapping. Colored circles label the initial position of four trapped particles.
(b) Particle ratcheting due to laser modulation. Trajectories are shown for the four
labeled particles over a 30 s time period.
7.6 Ratchet Motion
To perform Brownian ratcheting, laser power modulation was initiated after tens of
particles had been trapped. The modulation frequency was 10 Hz and the duty cycle (on
time / total time) was 80%. The experiments were recorded and analyzed using microscopy-
video analysis. Particle positions were detected in each video image frame, and a nearest
neighbor algorithm was applied to link the particle trajectories. Fig. 7.4a shows four particles
with linked trajectories of at least 30 s (dashed circles). Fig. 7.4b shows the trajectories over
a 30 s time period. It is clear that the particles move preferentially to the right as the laser is
modulated, with some fluctuation in position.
76
To quantify the ratcheting behavior, we computed the mean displacement of 115
trapped particles from three experiments as a function of time. Fig. 7.5a shows the mean
displacement in the x-direction (red, solid line). The displacement increases linearly as a
function of time, with a ratcheting speed of approximately 0.9 m/s. In contrast, for
untrapped, Brownian particles (black, dashed line), the mean displacement fluctuates
around zero. Fig. 7.5b shows the mean displacements in the y-direction, which are both
close to zero. It is evident that our PhC with triangular holes creates an asymmetric, periodic
optical potential that rectifies the particle motion.
Figure 7.5. Mean displacement for ensemble of particles. (a,b) The mean
displacements in the x- and y-directions. The red curve represents the results for
Brownian ratchet with 10 Hz modulation frequency, while the black dashed curve
represents the results for Brownian particles.
77
7.7 Transport Speed
We further optimize the ratchet speed by varying the laser modulation frequency.
Ratcheting behavior is known to depend on the off-time of the laser [139, 153, 157]. In a
simple theoretical picture, the relation between the forward and backward ratcheting
probabilities and t
off
are [139]
1
4
2
f f off
P efrc l Dt
, (7.1)
1
4
2
b f off
P efrc l Dt
, (7.2)
where P
f
(P
b
) is the forward (backward) ratcheting probability, erfc is the complementary
error function, l
f
(l
b
) is the forward (backward) moving distance, and D is the diffusion
coefficient.
The transport speed can be expressed analytically as
f b f b off on
V P P l l t t . (7.3)
To determine the diffusion coefficient, we treated our system as an approximate 2D system
and analyzed the mean squared displacement of freely-moving Brownian particles as a
function of time. A linear, least-squares fit yielded a diffusion coefficient of 0.59 m
2
/s for
520 nm particles. Substituting the experimental value of t
off
, the estimated diffusion
coefficient, and the calculated asymmetry parameter of 0.8 in Equations 7.1 through 7.3, we
obtain the analytical prediction of the transport speed shown in Fig. 7.6a (black, dashed line).
The optimal average transport speed is ~1.0 m/s and is obtained at a modulation
frequency of 10 Hz. At higher frequencies, the speed decreases due to the increased
probability that a particle moves neither forward nor backward during one cycle.
78
We repeated the trapping and ratcheting experiment for different modulation
frequencies. The average transport speed as a function of modulation frequency is shown in
Fig. 7.6a (red squares). The error bars indicate the standard deviation of the speed. Data
was collected down to a frequency of 5 Hz. Below this frequency, too many particles tended
to diffuse away into solution. The experimental results agree very well with the analytical
prediction. The optimal modulation frequency was 10 Hz, and the average speed at this
value was 0.93 ± 0.14 μm/s (standard deviation). Similarly, we repeated the experiments for
780 nm polystyrene particles; the results are shown in Fig. 7.6b.
Figure 7.6 Average transport speed of the particles. (a) 520 nm particles. (b) 780
nm particles.
7.8 Discussion and Conclusions
In summary, we have presented the first demonstration of a near-field optical
Brownian ratchet device. Our approach uses a silicon PhC slab designed to support an
asymmetric optical potential. The optimal transport speed is 0.93 μm/s, which agrees well
with analytical prediction. The device can also be used to perform assembly of hundreds of
particles with ultrahigh trap stiffness of 18 and 53 pN· nm
–1
·W
–1
in the x- and y-directions.
The ability of our system to perform both steady and dynamic optical manipulation can
79
enable a variety of dynamic lab-on-a-chip applications. The sensitivity of the optical
potential to particle size and composition opens up a range of possibilities not provided by
flow control alone. We also expect that our system can be extended to batch processing and
delivery of biological objects, impacting the field of microfluidic manipulation.
7.9 Optical Setup and Beam Condition
To characterize the device, the PhC sample is mounted on a glass slide with a 2 mm
circular hole at the center. A tunable laser with a wavelength range from 1500 to 1620 nm
(Santec TSL-550) and a single-mode fiber (mode diameter 10.4 ± 0.8 μm) were used. An
aspherical lens (f = 11 mm and NA = 0.25, Thorlabs C220 TME-C) was incorporated to
collimate the beam. An achromatic doublet (f = 30 mm, Thorlabs AC254) was then used to
refocus the beam to the back side of the sample. The Gaussian beam diameter incident on
the sample was measured by the knife-edge method to be ∼27 μm. To identify the guided
mode resonance of the device, the transmission spectrum was first measured in cross-
polarization (resonance appears as a transmission peak) and then tuned back to parallel-
polarization (resonance appears as a transmission dip) and measured. The input power for
characterization was 0.1 mW while input power for trapping was 100 mW.
7.10 Particle Trajectories and Stiffness Analysis
The experiments were recorded using a 20× objective and a CMOS camera. The video
was recorded with exposure time of 1/30 s at 30 frames per second. Each pixel of the video
represents a 66 nm × 66 nm area of the sample. The particle positions were obtained by
detecting the highest brightness pixel for each particle [164]. The frame-by-frame particle
80
positions were linked to form trajectories using a nearest neighbor algorithm with maximum
movement step of 0.7 lattice constants between each frame.
After the assembly of tens of particles, videos were recorded with a fixed exposure
time of 1/30 s. Typical videos were 600 frames or more in length. For every trapped particle,
the measured variances were corrected for motion blur due to finite integration time of the
camera and detection error from the camera [165]. The trap stiffness k was then calculated
by equipartition theorem
2
B
i
i
kT
k
x
, (7.4)
where i indicates the direction of the displacement, and
2
i
x is the time-averaged and
motion-blur-corrected variance of observed particle positions away from the center of a
trap.
81
Chapter 8.
Reconfigurable Optical Matter
8.1 Introduction
As mentioned in the previous chapters, LATS technique can be utilized to achieve
realtime tunability of optical maters by turning on and off the laser. The reconfiguration of
an assembled nanoparticle array is proposed to further extend the degree of freedoms for
LATS tunability. By exciting different resonant modes of the photonic crystal template within
a targeted wavelength range, the realization of realtime reconfiguration of optical matters
and assembly of nanoparticles is possible.
A reconfigurable optical matter is of great importance and interest for the realtime
tunability which will bring various applications, such as the real-time all optical tunable filter
or dual wavelength bio-sensor. LATS technique can also be utilized to fabricate different
optical metamaterials within the same template from bottom-up.
Figure 8.1 Schematic of LATS. (a) Normally incident light from backside of the
photonic crystal excites resonant modes. (b) and (c) show potential trapping sites
within the photonic crystal slab.
82
The approach to achieve the reconfigurable light-assisted assembly would be based on
the photonic crystal design with different resonant modes (can be either different resonant
wavelengths or different mode polarizations) in the same photonic crystal template as
shown in Fig. 8.1.
8.2 Photonic Crystal Design
It has been shown that hybrid triangular-graphite photonic crystal (shown in Fig. 8.2a)
device can be designed to support high quality modes at -point [166, 167] (corresponding
to a zero in plane wave vector) which can be excited by normally incident light; such modes
are often referred to as coupled modes. Here we use an adjusted hybrid triangular-graphite
photonic crystal featuring a double-hole in the triangular lattice (shown in Fig. 8.2b). By
introducing the double-hole into the triangular lattice, the hexagonal symmetry can be
broken, and thus can separate the degenerate modes by exciting the modes using different
polarized light. An arbitrarily chosen geometry will result in very different resonant
wavelengths. A carefully design of the double-hole separation can bring the resonant
wavelengths within our tunable laser and EDFA wavelength range (1540 nm – 1560 nm).
Figure 8.3a shows the simulated resonant wavelength dependence on the hole
separation when the photonic crystal slab is excited by an incident plane wave source
polarized in y- (blue curves) and x-directions (red curves). The corresponding electric filed
profiles are shown in Fig. 8.3b. It is clear that x
1
and y
1
have much stronger dependence on
the hole separation. The slab thickness is 340 nm, the lattice constant a is chosen to be 700
nm, and the hole radius in the graphite lattice and the triangular lattice is 0.154a and 0.08a,
respectively.
83
Figure 8.2 Schematic of lattice basis for (a) hybrid triangular-graphite and (b)
adjusted hybrid triangular-graphite lattice.
Figure 8.3 (a) Resonant wavelength as a function of double-hole separation (hole
diameter). Four preferred resonant modes are monitored. (b)The electric field
intensity profiles for the four monitored modes.
Figure 8.4 shows a final design that has four resonant modes within our tunable laser
and EDFA wavelength range. The double-hole separation is 1.4 for this design, the lattice
constant is 700 nm, the hole radius in graphite lattice is 0.154a, and the hole radius in
triangular lattice is 0.08a. The simulated transmission spectrum is shown in the top panel.
The red and the blue curves are the transmission spectra when the device is excited with the
x- and y- polarized incident light, respectively. The expected modes and the trapping
patterns are shown in the bottom panel. For x
1
and y
1
modes, nanoparticles form triangular
84
lattice of either dimers or monomers. For x
2
and y
2
modes, nanoparticles form triangular
lattice of dimers with larger separation and different orientations.
Figure 8.4 A design for the reconfigurable light-assisted assembly template and its
potential trapping pattern.
8.3 Mode Characterization and Transmission Spectrum Measurement
Figure 8.5a shows the SEM of fabricated adjusted hybrid triangular-graphite photonic
crystal. The scale bar is 400 nm. The measured lattice constant is 710 nm. The resonant
modes can only be identified in the cross-polarization measurement [168] (shown in Fig.
8.5b). In the parallel transmission spectrum measurement (dip), only one resonant mode (y
1
)
can be identified. x
2
and y
2
are more TM-like modes, and can hardly be excite by normally
incident laser beam due to poor coupling between the incident light and the resonant
modes. The photonic crystal is fabricated from a SOI wafer (340-nm device layer, 2- m
85
silicon dioxide, and 600- m Si handle layer). From the calculation, around 40-60% of the
laser power is reflected by the handle layer. Moreover, the quality factor of the four modes
varies from 1,500 to 5,000 for the four modes. The resonant modes are highly sensitive to
the incident laser wavelength. Tuning the incident laser wavelength can result in even larger
reflection (Fabry–Pérot) from the Si handle layer. The power coupling between the incident
planewave and the guided resonant modes should be improved by releasing and
transferring the photonic crystal slab onto a glass slide.
Figure 8.5 Fabricated devices for the reconfigurable light-assisted assembly. (a)
SEM of the fabricated device. (b) Measured transmission spectrum.
No trapping was observed in the initial trapping experiment using resonant mode (y
1
).
The inability to trap particles may be due to the spatial variation of the mode concentrating
in the Si area between the two small holes. The area where the field intensity maximum
locates is extremely small (Fig. 8.4 y
1
), and there is no additional mechanical support to
stabilize the trapping.
8.4 Discussion and Conclusions
In order to achieve sufficient optical trapping, a re-designed photonic crystal template
may be required. Some suggestions are provided when designing the photonic crystal
86
templates: 1) TE-like modes are easier to excite from normal incidence in experiment, so TE-
like modes are preferred in the experiment. 2) Mode intensity maximum should be
concentrated in the hole region to provide extra mechanical support. 3) The resonance is
highly sensitive to the slab thickness. In order to have more TE-like modes within the target
wavelength range (smaller ), I suggest using a thicker Si slab.
87
Chapter 9.
Conclusions and outlook
The main discovery of the PART II of this dissertation is that a near-field optical
Brownian ratchet device was demonstrated for the first time. An asymmetrically patterned
photonic crystal was accurately designed and fabricated to demonstrate near-field optical
Brownian ratchets. The optimal ratcheting speed is 0.93 m/s, which agrees well with
analytical prediction. Ultrahigh trap stiffness of 18 and 53 pN· nm
–1
·W
–1
in the x- and y-
directions were also achieved in the same device. The ability of the system to perform both
dynamic and steady optical manipulation paves the way to various applications, including
nanoparticles sorting and delivery.
The photonic crystal near-field optical trapping system is an exciting and interesting
system with both practical and fundamental interest. From the practical side, The system
can be designed to be reconfigurable sensors. Assembly of nanoparticle (core-shell quantum
dots, nanodiamonds, or nanowires) array along with solidification of the array can yield a
new way of bottom-up process to fabricate metamaterials.
From the fundamental science side, the system contains a rich set of interacting
physical effects, including not only optical forces but also thermophoresis and thermal
convection, as mentioned in 6.3. In our recent study, we found that opto-thermophoretic
force plays an important role in our particle assembly. As shown in Fig. 9.1, the optical
trapping selectivity of 380 nm and 520 nm particles can be tuned from 100% selectivity to
no selectivity by controlling the surfactant (Triton- X-100) concentration.
88
Moreover, a mixed metallic nanoparticle system has not been studied yet. The optical
binding effect between different types of metallic particles should be very intriguing. By
tuning the environmental parameters (temperature, surfactant concentration, and chamber
height), a wide range of controlled experiment can be achieved to observe microscopic
optical epitaxial growth [132].
Figure 9.1 Trapping selectivity tuning by changing the surfactant concentration.
Data taken from A. Krishnan, S.-H. Wu, M. L. Povinelli (manuscript in preparation).
89
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Light matter interactions in engineered structures: radiative thermal management & light-assisted assembly of reconfigurable optical matter
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Abstract (if available)
Abstract
This dissertation work studies the use of nanostructures and microstructures to control the flow of light in two application areas: radiative thermal management and near-field optical manipulation, which are discussed in PART I and PART II, respectively. ❧ The work of radiative thermal management focuses on understanding the radiative heat transfer in nanowires, designing highly efficient thermal homeostasis devices, and designing high contrast radiative thermal rectifiers. In both designing works, phase-change material - vanadium dioxide (VO₂), is used to achieve dramatic changes in optical properties. In the thermal homeostasis device design, a novel mechanism for radiative thermal management is proposed. The optimized device’s ability to dampen temperature fluctuations can perform 20 times better than ordinary semiconductor materials, and 8 times better than perfect blackbody. In radiative thermal rectifier design work, the highest reported value of rectifying coefficient (21.48) is achieved. The PART I of this dissertation not only establishes the understanding of fundamental limits in radiative thermal management, but also provides optimization approaches for high contrast thermal rectification devices. ❧ The work of near-field optical manipulation is based on the light-assisted, templated self-assembly (LATS) technique developed in our group. Laser light is used to excite guided resonant modes in the photonic crystal templates to create an array of optical traps. The traps drive the particles into accurate periodic positions, and form self-assembly. The first demonstration of near-field all-dielectric optical Brownian ratchets was achieved, resulting in much higher ratcheting speed than previous works.
Tags
electronics
microphotonics
nanoelectronics
nanofabrication
nanophotonics
optical force
optical trapping
optics
photonics
semiconductor
solar cells
thermal management
Linked assets
University of Southern California Dissertations and Theses