Carrier transport in photorefractive multiple -quantum -well spatial light modulators

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Content CARRIER TRANSPORT IN PHOTOREFRACTIVE MULTIPLE- QUANTUM-WELL SPATIAL LIGHT MODULATORS By Ergun Canoglu A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY ELECTRICAL ENGINEERING December 1997 Copyright 1997 Ergun Canoglu Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3139260 Copyright 1997 by Canoglu, Ergun All rights reserved. INFORM ATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3139260 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS; I would like to express my sincere thanks to Dr. Elsa Garmire for providing a valuable chance to work on this project and for demonstrating how to improve problem solving skills. Her inspiring discussions allowed me to explain many complicated phenomenon described in this thesis in a much simpler way. I would also like to thank Dr. Steier and Dr. Gershenzon for serving in my dissertation committee. I would like to acknowledge Dr. Ching-Mei Yang and Dr. Daniel Mahgerefteh, who helped me to start the project. Their valuable contributions continued even after leaving the Center for Laser Studies (CLS). Furthermore, their initial guidance strengthened my laboratory skills and allowed me to enjoy the dark atmosphere of an photonics laboratory. I owe thanks to Kim Reid and Hermine Fermanian for taking care of all my office related needs (even when I was away from USC); I would also like to thank former CLS members and my friends Ashok Kanjamala, Maria Coleno and David Cohen. I also like to express my sincere gratitude to Akheelesh Abeeluck who was always willing to help me. His continuous help allowed me to set-up a new lab at Dartmouth College and take the data presented in Chapter-III. Without his contributions, I could not finish this dissertation. Without Robert H. Russell I could not have my lab equipment running. When I had problems in the lab, he was there (also Akheel) and helped me to fix the problems. In an photonics lab, obstacles were not only in the from electronics and optics, plumbing was a major concern. Bob’s unique guidance helped me to learn more about pluming and be self- sufficient. I would also like to thank Bob for teaching me how to survive on icy roads of New Hampshire. I would also like to thank Dr. Afshin Partovi at Lucent Technologies of AT&T Bell Laboratories, Dr. David Nolte and Indrajit Lahiri at Purdue University for providing samples for my experiments. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Finally, I would like to express my sincere thanks to my parents Ismail and Zekiye Canoglu and my brothers Aziz and Mustafa Canoglu for their endless support at every stage of my life. Their continuous support and encouragement allowed me to focus more on my studies and ignore the financial problems of the world outside the academic life. lU Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ergun Canoglu Eisa Garmire ABSTRACT CARRIER TRANSPORT IN PHOTOREFRACTIVE MULTIPLE-QUANTUM- WELL SPATIAL LIGHT MODULATORS In this thesis, we present theoretical and experimental analysis of PR-MQW operation, specifically carrier transport in PR-MQW structures. We study the carrier transport by illuminating the devices with a sinusoidal grating pattern and measuring the diffraction efficiency as a function of time. We begin by introducing the basic concepts and device structures. We then present the picosecond time-resolved four-wave mixing (TR-FWM) data on the first device structure and describe the tum-on and turn-off mechanisms in a PR-MQW structure. We show that holes contribute to the tum-on time as a slower rise o f the diffraction efficiency. Furthermore, the diffraction grating is dominated by either electrons or holes, depending on the applied polarity relative to the direction of illumination. The granting decays in 0.4-8.5 ns, depending on the grating spacing. We show that the decay is due to the lateral transport of carriers at the MQW/dielectric interfaces, where low-temperature-grown (LTG) layers can increase the diffraction efficiency and resolution. In the third chapter we investigate the carrier transport length as function of trap density. The trap density in a LTG-MQW structure was dynamically adjusted for optimum sensitivity and resolution by passivating some traps with photocarriers. We show that without pre-illumination, sensitivity and the transport length is 350 Â, however with the pre-illumination, sensitivity and the transport length increases by a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. factor of 10. We also calculate the trap density and the longitudinal mobility of electrons in the device. In our theoretical studies, we present a self-consistent numerical model that combines both the standard photorefractive material calculations and the carrier transport in MQW devices to represent the transient response of PRMQW devices. In the model we show that tum-on time of the device is mainly determined by carrier drift and escape from the quantum wells. We also show that the polarity dependence of the tum-on time is due to large absorption of the device combined with the difference between electron and hole escape and drift times. Numerieal simulation results also indicate that when highly trapped materials are used throughout MQW region, deviee sensitivity reduces. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS I. Photorefractive Multiple Quantum Well Spatial Light M odulators 1 I l Introduction_____________________________________________________________1 1.2 Background____________________________________________________________ 2 1.2.1 Semiconductor Quantum W ells___________________________________________________________ 2 1.2.2 Photorefractive Quantum W ells___________________________________________________________ 8 1.3 Our Contribution_______________________________________________________ 16 IL Carrier Transport in a Photorefractive Multiple Quantum Well device: Device-A, Experimental Results_________________________________________ 21 HI. Carrier Transport in a Low Temperature Grown Multiple Quantum W ell p-i-n Modulator: D evice-B______________________________________________ 31 111.1 Background__________________________________________________________ 31 111.2 Introduction__________________________________________________________ 32 111.3 Experimental Results___________________________________________________ 33 111.3.1 Device structure______________________________________________________________________ 33 111.3.2 Device sensitivity and longitudinal carrier transport_______________________________________35 111.3.3 Lateral carrier transport________________________________________________________________ 39 111.4 Discussion___________________________________________________________ 41 111.4.1 Longitudinal transport length and device sensitivity_______________________________________41 111.4.2 Effect of pre-illumination on resolution_________________________________________________ 53 111.5 Conclusion___________________________________________________________ 58 IV. Numerical Model fo r Cross-Well Carrier Transport in Photorefractive MQW D evices__________________________________________________________ 5 9 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV. 1 Previous Research on Carrier Transport Modeling in MQW Devices___________ 61 IV.2 Summary of Our Contribution___________________________________________62 IV.3 The Experimental Device Structures and the Model Results____________________ 63 IV.4 Device Model:________________________________________________________ 64 rV.4.1 Carrier capture by deep traps___________________________________________________________ 67 IV.4.2 Carrier transport in MQW region______________________________________________________ 71 IV.4.3 Rate Equations:______________________________________________________________________ 77 rv.5 Simulation results______________________________________________________ 79 rV.5.1 Non-uniform space charge buildup (Device-A):___________________________________________ 81 IV.5.2 Reduced sensitivity with LTG MQW region (Device-B)___________________________________ 90 V ll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIS T OF FIGURES Figure I-l Schematic diagram o f Franz-Keldysh effect: F is the applied field; is the bandgap o f the material, E ^ is the reduced bandgap due to the electric field.________ 6 Figure I-l Energy band diagram o f GaAs/Alg jGaQjAs MQW structure drawn to scale. Well width Lw =100 A, barrier width Lb = 35 A .___________________________________5 Figure 1-2 QW energy band diagram drawn to scale in a field o f 70 kV/cm. Transition wavelengths red-shifted under an applied field._________________________________7 Figure 1-3 Basic operation o f the Transverse-Geometry PR-MQW device. The final field distribution is the device is 18Œ out o f phase with the illumination.______________ 12 Figure 1-4 Generic Stark geometry PR-MQW d evice______________________________ 13 Figure 1-5 Operation o f Stark Geometry PR-MQW_________________________________14 Figure 11-1.Time-resolved four-wave mixing experimental geometry using a photorefractive M QW device consisting o / Cr-doped GaAs (100Â) QWs and AlO.2 9 GaO.7i As (35A) barriers with a region o f MQW grown at low temperature (LT). Uniform diode laser illumination is used to erase the grating between successive pulses._________________________________________________________________ 22 Figure 11-2. Picosecond time-resolved diffraction efficiency at A=50fJtm (fluence = 30 nJ/cm^, applied field = 68 kV/cm): small arrows in the inset show the magnitude and direction o f carriers; large arrows show the direction o f laser illumination. Experiment (a) : electrons drift to LT region at exit face; (b): holes drift to LT region at exit face; (c): electrons drift to N T MQW/dielectric interface; (d): holes drift to N T MQW/dielectric interface. The polarity is noted by +, - in the figure._____________ 26 Figure 11-3 Picosecond decay o f the diffraction efficiency as a function o f grating period in the geometry (case (a), fluence = 30 nJ/cmf , applied field = 68 kV/cm) where electrons dominate and travel to LT layer. The decay times are 8.5 ns, 3.5 ns and 0.46 n sfor grating periods o f 50 jjm,30 fjm and lOjdm.________________________ 29 Figure 111-1 Device-B structure_________________________________________________ 34 Figure 111-2 Timing diagram fo r pump/probe and four-wave mixing experiments (not to scale). _________________________________________________________________ 37 Figure 111-3 Transmission change measured at constant pump fluence and various pre illumination fluence. _____________________________________________________ 38 Figure 111-4 Transmission change measured at fixed time delays o f the probe pulse ( Before the pump pulse (t< 0 ), after the pump pulse (t> 0))____________________ 40 Figure 111-5 Time-resolved four-wave mixing diffraction efficiency at F^^p= 7.5 V/jJm and grating period o f 18 p m .__________________________________________________ 42 Figure 111-6 Screening field distribution in the MQW region________________________44 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure III-7 Comparison o f numerically calculated photo-voltage fo r exponential carrier distribution and the photo-voltage described by Eq.III-3 (uniform carrier distribution)46 Figure 111-8 Measured rise-time o f AT/T and calculated transport time (fi=6.72 cm^/(Vs), F,^^ = F ^ in E q .I I I - 9 ) ----------------------------------------------------------------------------- 49 Figure III-9 Residual AT/T : The solid curve is the plot of the estimated AT/T by using Eq. III-IO and Eq. 111-5______________________________________________________ 52 Figure 111-10 Schematic description o f screening field when the spatial carrier distribution is sinusoidal.____________________________________________________________ 54 Figure 111-11 Calculated lateral fie ld _____________________________________________55 Figure IV-1 Time-resolved four-wave mixing diffraction efficiency o f device-A. Data-A were obtained electrons towards the exit face (z = 2.1 pm plane). In Data-B holes were sent towards the exit face._____________________________________________65 Figure IV-2 Time-resolved four-wave mixing diffraction efficiency o f a device with LTG MQW region (device-B). Data C was obtained by reducing the trap density in the MQW region by pre-illumination (see Chapter-111). ___________________________ 66 Figure TV-3 Generic device structure used in simulation____________________________ 68 Figure lV-4 Schematic description o f carrier trapping: (a) before illumination (b) after illumination. While acceptors are shown fo r charge neutrality, they were ignored in the m odel.______________________________________________________________ 69 Figure TV-5 Schematic diagram fo r carrier transport in MQW region: (1) Carrier generation, (2) thermionic emission, (3) tunneling, (4) drift, (5) capture by QWs, (6) recombination___________________________________________________________ 70 Figure TV-6 Schematic description o f the variables in Eq. lV-6-11. H(F) is the effective barrier height fo r thermionic emission; H ’(F) is the effective barrier height fo r non resonant tunneling, H ”(F) is the energy mismatch o f the ground state and the first excited state o f the adjacent well.____________________________________________73 Figure TV-7 Carrier escape from a QW with x = 30% , 100 A, = 35 A. Calculations were made fo r the ,the electron thermionic emission time; f,,s,,hrm 4he electron resonant tunneling time; , the electron tunneling time; ,the hole thermionic emission time; an the hole tunneling tim e.______________________________ 74 Figure lV-8. Electron transport in the MQW region at various times, t (psec). Electron motion is towards z= 2.1 pm. The trapping layers are located 0<z< 0.1 pm and 2 < z < 2.1 pm ______________________________________________________________ 82 Figure TV-9. Hole transport in the MQW region fo r various times, t (psec). Hole motion is towards z = 0 pm. The trapping layers are located 0 < z< 0.1 pm and 2 < z< 2 .1 pm84 Figure TV-10 Charge distribution fo r various times, t (psec). Top inset show the details o f the trapping region at the entrance face; bottom inset shows the trapping region at the exit face o f the MQW region._______________________________________________86 ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure IV-11. Photogenerated field distribution in the MQW region fo r various times, t (psec)._________________________________________________________________ 87 Figure IV-12. Photo-voltage generated by the electron and hole transport (electrons are sent to the exit face o f the MQW region) as a function o f time._______________________88 Figure IV-13. Comparison o f photo-voltage obtained with dominant electrons (e— > z= 2.1 pm) and dominant holes (h— > z = 2.1 pm) configurations.____________________ 89 Figure lV-14 Electron distribution in a LTG MQW region at various times, t (psec). 93 Figure lV-15 Charge distribution in LTG M QW region at various times, t (psec). A majority o f holes are trapped where they were generated, while electron trapping takes place throughout the MQW region._________________________________________ 94 Figure TV-16 Photogenerated field distribution in the MQW region at various times t (psec). ________________________________________________________________________ 95 Figure TV-17. Photo-voltage created by electron transport in LTG MQW region (Device-B simulation). Hole contribution is negligible.__________________________________96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES: Table III-l Calculated transport length by using the data from Figure 0-4 (solid squares). 47 Table IV-1. Parameters used in the numerical simulation___________________________ 80 XI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I. Photorefractive Multiple Quantum Well Spatial Light Modulators 1.1 introduction Optical processing applications require high-resolution and high-sensitivity optically addressed spatial light modulators (OASLM) for performing high-speed correlation, spatial filtering, and other operations. Photorefractive multiple quantum well (PR-MQW) devices, satisfying the above requirements, have become the prime candidates for optical processing applications. High speed operation of PR-MQW comes from the fact that carrier mobility in these devices is much larger compared to standard photorefractive crystals. Large electro-optic coefficients, due to resonant excitonic nonlinearities, enable these devices to be as small as 1-2 pm, and operate with light inputs as low as 16 nJ/cm^ but still be able to create detectable absorption and refractive index changes that can be used for practical applications.[l] Since MQW devices rely on the resonant excitations of the excitons that remain bound at room temperature because of confinement within the quantum wells (QWs), the nonlinear effects are considerably large compared to bulk semiconductor devices. This enables MQW devices to be four orders of magnitude thinner (~1 pm) than their bulk counterparts (~1 cm). PR-MQW devices differ from the conventional MQW modulators because of their ability to spatially modulate the electro-optic properties of the medium without requiring any pixelation. In other words, PR-MQWs combine the large nonlinearities of MQWs and the parallelism of the photorefractive effect. This has been achieved by using semi- insulating regions in the MQW device. The semi-insulating regions enable spatial storage of the modulation by fixing the photo-charges at defect sites. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In general, depending on the applied field direction, PR-MQW devices can be categorized into two classes: field parallel to the QW layers (the transverse geometry) and field perpendicular to the QW layers (the Stark geometry). Although our experiments and analysis described in the following chapters are on the Stark geometry, we will briefly discuss the transverse geometry and describe its operation. In this chapter we will introduce the basic concepts that are important for understanding and designing PR-MQW devices. After a brief review of concepts, we will discuss the two geometries for PR-MQWs and compare their performances. 1.2 Background 1.2.1 Semiconductor Quantum Wells In bulk semiconductor, operating near the band-edge brings the advantage of band- edge nonlinearities such as the Franz-Keldysh effect [2].These bandedge nonlinearities are enhanced with the excitonic absorption due to the existence of excitons near the band edge. Excitons are electron-hole pairs forming a bound state similar to the hydrogen atom. At low temperatures they produce very sharp resonance peaks just below the bandgap (bandgap). Excitonic resonances in bulk semiconductors have been extensively investigated, but because of the low temperature operation requirements, their use for practical applications has been limited [3,4].Excitons in bulk materials are ionized at room temperature, preventing observation of excitonic nonlinearities. With the advances in crystal growth techniques, it is possible to observe excitonic features at room temperature in certain structures. This is achieved by confining the exciton in quantum wells created by growing alternating layers of materials with high and low bandgaps ( Figure I-l). The electron-hole pair in the QW (low gap layer) interact through the Coulomb interaction as in bulk materials, but in the QW the average distance between Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the two particles is reduced, and the excitonic binding energy is increased, resulting in enhanced excitonic effects that can be observed at room temperature [5]. However, it should be noted that the energy of the longitudinal-optic (LO) phonons is much larger than the binding energy, thus, excitons are ionized in less than 0.5 psec [6,7]. But this is long enough to produce excitonic absorption lines at room temperature. The excitonic nonlinear effects in QW devices have been extensively investigated in the literature. These include intensity related effects such as Coulomb screening, phase- space filling [8,9,7] and electric field effects such as field-induced broadening and quantum confined Stark effect (QCSE) [10,11,12,13]. Since the operation of the devices under consideration depends mainly on the electric field effects, we will limit our discussion to field-induced broadening of excitonic absorption and QCSE. 1 .2.1.1 Field-Induced Electro-Optic Effects in Quantum Wells The QW devices show large and fast effects on the absorption spectrum near the band edge when electric fields are applied. The principal effect is electroabsorption : electric fields modify the absorption spectrum and the excitonic transition leading to absorption and refractive index changes. Both effects are quadratic [11] and require large electric fields to obtain detectable electroabsorption for practical applications [14]. 1.2.1.1.1 Field-Induced Broadening In bulk semiconductors, electric field causes a slight shift of the absorption edge to lower photon energies, a process known as the Franz-Keldysh effect [2]. When an electric field F is applied, the conduction and valance bands tilt, and electrons, having an oscillating wave function above the bandgap prior to applying the field, can now tunnel into the forbidden bandgap with a decreasing probability, as shown in Figure 1-2. Owing to the extended tail of the electron-hole wave functions, the effective bandgap is reduced, resulting in a broadened edge in the absorption spectrum. In addition, experiments Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. performed at low temperatures show broadening of bulk excitonic resonances [15] as a result of the electric field, which is explained by the ionization of the excitons; immediately after their creation, excitons are by the strong electric field. Similar effects are observed in QW devices, but they can occur at room temperature unlike the case involving bulk semiconductors. In addition to the Franz-Keldysh effect, excitons progressively broaden and disappear when a strong and increasing electric field is applied parallel to the QW layers [9,14]. The combination of broadened band edge and excitonic resonances leads to absorption and refractive index changes that can be used for modulating the transmission and/or the phase of the incident light. 1.2.1.1.2 Quantum Confined Stark Effect The strongest electro-optic effect is obtained when the electric field is applied perpendicular to the QW planes. As in the Franz-Keldysh effect, the electric field introduces a linear potential to the QW potential and tilts the band. However, in this case the tilt is in the growth direction. In addition to reduced effective bandgap, the linear potential gives rise to triangular potential wells, reducing both the electron and the hole confinement energies and leading to a decrease in the transition energy (Figure 1-3). In this case, excitons shift to lower photon energies, with little or no broadening even at very high fields. This is because the potential barriers in the growth direction inhibit the field ionization of excitons, hence inhibiting the broadening mechanism [16]. Thus excitons continue to exist even at higher applied fields that would normally ionize them, resulting in larger Stark shifts. A 20 meV shift of the excitonic transition energy can be obtained for a field strength of 100 kV/cm [17]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.0 n 11 11111111 T -n 11111 I 11111111111111111 111111 11 1.5 , E g =35 meV- 1.0 a B 0 > c ( U D) T 5 ■ ë 0.5 c C O 0 Û 0.0 IM P eJ = 130 meV- ^ E ,,°=4m eV — 0.24 eV GaAs / Alg gGag^yAs i _42 eV t 0.15 eV “ A -0.5 I L . ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' I ' I ' ' ' ' I ' ' ' ^ -100 0 100 200 300 400 Position (A) Figure I-l Energy band diagram of GaAs/AlggGaoyyAs MQW structure drawn to scale. Well width Lw =100 Â, barrier width Lb = 35 Â. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1-2 Schematic diagram o f Franz-Keldysh effect: F is the applied field; is the bandgap o f the material, E is the reduced bandgap due to the electric field. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.0 Fapp=70 kV/cm > 0) p 0) c LU 1.326 eV 0) O ) "S 0.5 T 3 C (0 0 Û 0.0 -0.5 0 1 0 0 200 300 400 Position (A) Figure 1-3 QW energy band diagram drawn to scale in afield o f 70 kV/cm. Transition wavelengths red-shifted under an applied field. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.2.2 Photorefractive Quantum Wells The principal requirement for an optically addressed MQW-SLM is to be able to spatially modulate the absorption and/or the refractive index, and store the modulation during the processing time of an optical processor. In conventional MQW modulators that uses field-induced nonlinearities, modulation of the absorption spectrum is achieved by screening the applied field, a process that involves transport of the photogenerated carriers. However, since there is no mechanism to fix the photocarriers after they have screened the field, their motion either washes out the spatial modulation or they simply leave the device, causing the modulation to decrease [18] before it can be used by the optical processor. One solution to this problem is to introduce defect centers into the device, as in conventional photorefractive crystals or semiconductors, such that photocarriers can be fixed by the trapping processes. Historically, one of the major challenges in the fabrication of PR-MQWs was to introduce deep-level defects without destroying the excitonic features of the device. Glass et. al. [19] recognized that proton implantation could be used to make QWs semi-insulating without adversely affecting the lineshape of the exciton or its electroabsorption. Proton bombardment of the semiconductor knocks out some atoms from their original position in the lattice and create mid-gap defects [20,21]. The damage caused by proton implant consists of deep acceptors and deep donors which trap holes and electrons. The carrier lifetimes in proton-implanted GaAs vary from 500 psec to 500 fsec, depending on the radiation dose [14,22]. The limit of the radiation dose is determined by the maximum defect density at which excitonic features can still exist. An alternative way for creating deep-level traps in GaAs based structures is to grow the material at low substrate temperatures. The low-temperature-growth (LTG) GaAs was 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. first introduced to reduce the parasitic back-gating in GaAs integrated circuits [23,24,25]. At low temperature growth, excess arsenic is incorporated into the crystal [26]. If the device is not annealed, it becomes conductive [27,28] as a result of defect-band transport. However, a mild post-growth anneal makes the device semi-insulating [23,28]. Stronger post-growth anneal, at temperatures in the range of 700 °C to 900 °C for 30 seconds, allows the excess arsenic to form precipitates with well-controlled size and spacing [29]. The carrier lifetime varies from 90 fsec to 10 psec depending on the precipitate spacing and size [30,31,14]. Owing to their ultrafast carrier lifetime and fabrication techniques, LTG materials are ideal photorefractive MQW devices. 1 .2.2.1 Transverse Geometry The semi-insulating MQW (SIMQW) device is fabricated such that the applied field is parallel to the QW layers. This is achieved by evaporating gold electrodes (~1 mm apart) onto the SIMQW [32] (Figure 1-4). The device operation relies on the field ionization of excitons and the Franz-Keldysh effect. The field screening process is similar to the one in conventional photorefractive materials; drift and diffusion drive carriers from regions of high light intensity to regions of low light intensity, and these carriers are trapped by the defects, building up a space-charge field [33] (Figure 1-4). Typical applied voltages for these devices are in the range of 1-1.5 kV, producing field strengths of 10-15 kV/cm. Since excitons are easily ionized, applying higher fields is not followed by larger modulation. 1 .2 .2 .2 Stark Geometry In this geometry electric field is applied perpendicular to the QW layers in order to take advantage of large QCSE. The device structure resembles the Pockels readout optical modulator (PROM) [34,35,36]; an electro-optic region sandwiched between buffer layers and transparent electrodes (Figure 1-5). Electrons and holes, generated by the illumination. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. drift parallel to the field, and get trapped at the interface between the electro-optic MQW layer and the buffer layer. These trapped carriers screen the applied field in the illuminated regions, reducing the net field in these regions. When the illumination is spatially varying, the resulting net field experienced by the MQW region is spatially modulated, causing spatial modulation of the absorption spectrum through QCSE (Figure 1-6). The modulation of the absorption spectrum can be explained through field- dependent complex refractive index. The change in the complex refractive index due to the electric field is given by [32] Ah = ^ n ^ (r F + s F^) Eq. 1-1 where r is the linear electro-optic coefficient and s is the quadratic electro-optic coefficient which consists of real and imaginary parts ( s = Sj + iSj ) When the sample is illuminated with an interference pattern, as in Figure 1-6, the complex refractive index in the dark and bright regions of the MQW can be expressed as A n ,= in ;(r.F „+s.F i,) Eq. 1-2 and A a . = |n : ( i - ( F „ - F , ) + 5 - ( F „ - F „ ) “) Eq. 1-3 where F ^pp is the applied field and F ^^ is the space-charge field. If the light intensity is low such that F ^p p » F^^, then the peak value of the complex refractive index difference between dark and bright regions of the device becomes = a l , p p X ,, I _ 4 Thus the absorption change and refractive index change caused by the illumination can be 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. expressed as = S. F ap p F sc Eq. 1-5 and Eq. 1-6 Since at low intensities the generated space-charge field is directly proportional to the intensity, the magnitudes of the index and absorption changes created with the interference pattern are also directly proportional to the illumination intensity. In the case of a sinusoidal illumination, one can define a diffraction efficiency from the sinusoidal grating that has index and absorption variations described by Eq. 1-5 and Eq. 1-6. Because of the small thickness of the MQW region, the diffraction can be treated as Raman-Nath diffraction, and the output diffraction efficiency (defined as the ratio of the first order diffracted to zeroth order intensity) is given by [32]: 1 / A 2;r , An— d V A + ( Act Eq. 1-7 1 Eq. 1-8 Note that using Eq. 1-8, we can relate the measured diffraction efficiency to the space-charge field and investigate the dynamics of space-charge field build-up through electron-hole transport. 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Light i app T F + + + I I I I +i 1 “ 4 Î ! - ■ + { "app + + + Gold Contacts } SIMQW Figure 1-4 Basic operation o f the Transverse-Geometry PR-MQW device. The final field distribution is the device is 18(f out o f phase with the illumination. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. <x> i i - * A MQW Region Buffer Layers — Transparent Electrodes Figure 1-5 Generic Stark geometry PR-MQW device 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Input pattern [ i t vAn, A a Recorded pattern X . X . c d c An A a E u 1 ' '"-'"''"1I - -I \ i 1 1 I- : L Fapp : applied field Fgg: photo-generated field X q : opreating wavelength 830 835 840 845 850 Wavelength(nm) Figure 1-6 Operation o f Stark Geometry PR-MQW 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 .2.2.2.1 Stark Geometry related work Historically, the first demonstration of a PR-MQW device in the Stark geometry was reported by A. Partovi et. al. [37,38] from AT&T Bell Labs (Lucent Technologies). The device consisted of ion-implanted Cdg ^Zn^ ,Te/ZnTe QWs sandwiched between dielectric blocking layers and transparent electrodes. This device operated at 590 nm with a maximum diffraction efficiency of 0.25% [37]. Later, devices with Cr-doped AlGaAs/GaAs QWs with various barrier heights and thicknesses were introduced [39,40]. In addition to dielectric buffer layers, these devices also incorporated a LTG region to trap carriers. The CW diffraction efficiencies in these device approached 3%. However, the resolution (20 |im) of these devices was ten times smaller than the theoretically calculated resolution of 2 pm. [40,41]. The best performance (higher diffraction efficiency and higher resolution) is achieved when the QW structure is optimized for carrier transport [40]. The devices with improved LTG region pushed the resolution limit to 5 pm [42]. Improvement of resolution is achieved by using better trapping regions. In addition, with their work on intrinsic MQW devices, Rabinovich et. al. from Navy Research Labs showed that trapping in the MQW region is not required to obtain higher resolution [43]. The next family of devices was designed such that they could be fabricated monolithically. This required the replacement of dielectric blocking layers with highly trapping layers. The first all-semiconductor Stark Geometry device used LTG layers to sandwich the MQW region, with metal contacts placed in direct contact with the LTG layer [44]. The second design, introduced by a group at Purdue University [45,46], uses LTG MQW layer in the i-region of a p-i-n diode structure. These devices used the MQW layer both as a trapping region and an electro-optic region. The resolution limit for these LTG p- 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i-n devices was 7 |im. 1.3 Our Contribution Despite the new device designs, a detailed theory of PR-MQW operation did not exist in the literature. The models developed in recent years have concentrated on steady- state operation and/or analyzed the device operation from a bulk device point of view rather than as a QW device [47,48,49]. In addition, the causes for low resolution and low sensitivity had not been clearly investigated. In this thesis work, we have focused on the picosecond response of PR-MQW devices. We have investigated the picosecond electron-hole dynamics that are responsible for the grating build-up and decay in the devices. We show that the device response can be as short as 30-300 psec depending on the dominant carrier type. In addition, our data show that carrier drift at the MQW/ buffer layer interface is the dominant decay mechanism that causes low resolution. We also demonstrate that LTG materials reduce the effect of carrier drift at the interface. The experiments performed on the p-i-n diode structure with LTG MQW region show that device sensitivity is a strong function of the trap density. We describe a method in which adjusting the trap density gives higher sensitivities and resolution. We also discuss the trade-off between sensitivity and resolution of the device. The numerical model that is described in this thesis gives an insight into the transient response of the device. In contrast to earlier device models, our model includes every QW in the calculation, and self-consistently calculates the space-charge field and carrier distribution throughout the device. In addition, the processing time of our numerical analysis is considerably shorter, and requires only a standard personal computer with an inexpensive software package. Our numerical results, confirmed by the experiments, indicate that both electrons and holes contribute to the grating build-up. However, due to the non-uniform carrier excitation, one carrier type dominates. The modeling of carrier 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transport in LTG MQWs revealed that due to the highly trapping nature of the device, device sensitivity (quantum efficiency) is considerably small, and only the fast carriers contribute to the field screening. With the better understanding of the carrier dynamics, the results and models discussed in this thesis will improve the design of devices with higher sensitivity and better resolution. In addition, the experimental methods described in this thesis will enable high speed operation of these devices. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References: 1 E. Canoglu, C-M. Yang, D. Mahgerefteh, E. Garmire, A. Partovi, T.H. Chiu, and GJ.Zydzik, Appl. Phys. Lett. 69, 316 (1996). 2 V. W. Franz, Z. Naturforch, and L. V. Keldysh, Sov. Phys. JETP 7, 788 (1958). 3 E.I. Rashba and M.D. Struge, eds.. Modem Problems in Condensed Matter Science Series, North-Holland Pub. Co. Amsterdam (1982). 4 D.S. Chemla and A. Maruani, Prog, in Quantum Electron. 8, 1 (1983). 5 R. Dingle ,ed.. Devices and Circuit Applications o flll-V Semiconductor Supperlattices and Modulation Doping, Academic Press, N.Y. (1985). 6 J. S. Weiner, D.S. Chemla, D.A.B. Miller, T.H. Wood, D. Sico, and A Y. Cho, Appl. Phys Lett. 46, 619 (1985). 7 D. A. B. Miller, D.S. Chemla, D.J. Eilenberger, P.W. Smith, A C. Gossard, and W. T. Tsang, Appl. Phys. Lett 41, 679 (1982). 8 H. Haig and S. Schmitt-Rink, Prog. Quantum Electron. 9, 3 (1984). 9 D.S. Chemla, D. A. B. Miller, P.W. Smith, A C. Gossard, and W. Wiegmann, IEEE J. Quantum Electron. QE-20,265 (1984). 10 D. A. B Miller , D.S. Chemla, T.C. Damen, A. C. Gossard, and W. Weigman, Opt. Lett. 9, 567 (1983). 11 D. A. B. Miller , D.S. Chemla, T.C.Damen, A.C. Gossard, W. Weigman, T.H. Wood, and C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984). 12 T. Sizer, II. T.K. Woodward, U. Keller, K. Sauer, T.-H. Chiu, D.L. Sivco, and A.Y. Cho, IEEE J. Quantum Electron. 30, 399 (1994). 13 P. Debernardi and P. Fasano, IEEE J. Quantum Electron. 29, 2741 (1993). 14 D.D. Nolte, ed., Photorefractive Ejfects and Materials, Kluwer Academic Pub., Boston (1995). 15 J.D. Dow and D. Redfield, Phys. Rev, B :l, 3358 (1970). 16 D.S. Chemla, D. A. B. Miller and P.W. Smith, Opt. Eng. 24, 556 (1985). 17 D. A. B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W.Weigmann, T. H. Wood and C. A. Burrus, Phys. Rev. B:32, 1043 (1985). 18 D P. Norwood, H.-E. Swoboda, M. D. Dawson, A. Smirl, D R. Andersen, App. Phys. Lett., 59, 219 (1991). 19 A. M. Glass, D.D. nolte, D. H. Olson, G. E. Doran, D.S. Chemla and W. H. Knox, Opt. Lett., 15, 264 (1990). 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 B. Schwartz, L. A. Koszi, P.J. Anthony and R. L. Hartman, J. Electrochem. Soc. 131, 1703 (1984). 21 G.H. Kinchin and R.S. Pease Re. Prog.Phys., 18, 2 (1955). 22 Y. Silverberg, P.W. Smith, D.A. B. Miller, B. Tell, A.C. Gossard and W. Weigman, Appl. Phys. Lett., 46, 701 (1985). 23 F.W. Smith, A.R. Calawa, C. Chen, M.J. Mantra and L.J. Mahoney, IEEE Electron. Dev. Lett., EDL-9, 77 (1988). 24 B. Lin, J.-F. D P. Kocot, D.E. Mars and R. Jaeger, IEEE trans. Elec. Dev., ED-37, 46, (1990). 25 M R. Melloch, D.C. Miller, and B. Das, Appl. Phys. Lett., 54, 943 (1989). 26 M. Kaminska, Z. Lilionthal-Weber, E.R. Weber, T. george, B. Kotright, F. W. Smith, B.Y. Tsaur and A.R. Calawa, Appl. Phys. Lett., 54,1881 (1989). 27 D.C. Look, D.C. Walters, M O. Mansereh, J.R. Sizalove, C E. Stutz and K.R. Evans, Phys Rev. B, 42, 3578 (1990). 28 D.C. Look, D.C. Walters,G.D. Robinson, J.R. Sizalove, M.G. Mier and C E. Stutz, J. App. Phys., 74, 306 (1993). 29 M R. Melloch, N. Otuska, J.M. Woodall, A.C. Warren, and J.L. Freeouf, App. Phys. Lett. 57, 1531 (1990). 30 K.A. McIntosh, K.B. Nichols, S. Verhese and E.R. Brown, App. Phys. Lett., 70, 354 (1997). 31 E.S. Harmon, M R. Melloch, J.M. W oodall, D.D. Nolte, N. Otuska and C. L. Chang, App. Phys. Lett. 63, 2248 (1993). 32 Q. Wang, R. M. Brubaker, and D.D. Nolte, J. Opt. Soc. Am. B, 9, 1626 (1992). 33 D.D. Nolte, D.H. Oison, G.E. Doran, W.H. Knox, A.M. Glass, J. Opt. Soc. Am. B, 7, 1626 (1990). 34 S.L. Hou and D.S. Oliver, App. Phys. Lett., 18, 325 (1971). 35 D.S. Oliver and W.R. Buchan, IEEE Trans. Electron. Dev. ED-18, 769-773 (1971). 36 B.A. Horwitz and F.J. Corbett, Opt. Eng. 17, 353 (1978). 37 A. Partovi, A.M. Glass, D.H. Oison, G.J. Zydzik, K.T. Short, R.D. Feldman and R.F. Austin, App. Phys. Lett., 59, 1832 (1991). 38 A.Partovi, , A.M. Glass, D.H. Oison, G.J. Zydzik, K.T. Short, R.D. Feldman and R.F. Austin, Opt. Lett., 17, 655 (1992). 39 A.Partovi, , A.M. Glass, D.H. Olson, G.J. Zydzik, H.M. O’Brayn, T.H. Chiu and W.H. Knox, Appl. Phys. L ett, 62, 464 (1993). 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 A .Partovi,, A.M. Glass, D.H. Olson, G.J. Zydzik, H.M. O’Brayn, T.H. Chiu and W.H. Knox, Appl. Phys. Lett., 62, 3088 (1993). 41 Y. Owechko, A.R. Tanguay Jr., J. Opt. Soc. Am. A 1, 635 (1984). 42 S.R. Bowman, W.S. Rabinovich, C.S. Kyono and D.S. Katzer, App. Phys. Lett. 65, 956 (1994). 43 W.S. Rabinovich, S.R. Bowman, D.S. Katzer, C.S. Kyono,Appl. Phys. Lett. 66,1044, (1995). 44 C.S Kyono, K. Ikossi-Anastasiou, W.S. Rabinovich, S.R. Bowman and D.S. Katzer, App. Phys. Lett, 64, 2244 (1994). 45 I. Lahiri, K.M. Kwolek, D.D. Nolte, and M R. Melloch, Appl. phys. Lett., 67, 1408 (1995). 46 I. Lahiri, M. Aguilar, D.D. Nolte, and M R. Melloch, Appl. Phys. Lett.,68, 517, (1996). 47 S.L. Smith and L. Hasselink, J. Opt. Soc. Am. B 11, 1878, (1994). 48 V.V. Shuknov, and M. V. Zolotarev, J. Opt. Soc. Am. B. 12, 913 (1995). 49 D.D. Nolte, I. Lahiri, M. Aguilar, Opt. Comm. (1997). 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II. Carrier Transport in a Photorefractive Multiple Quantum Well device: Device-A, Experimental Results Multiple Quantum Well (MQW) photorefractive devices have become important for the implementation of fast and sensitive 2D optical information processing systems at wavelengths compatible with diode lasers. Recently, applications such as real-time optical image correlation [1] and time-space conversion [2] have been demonstrated. In initial CW experiments on a 2.2 |im thick GaAs/AlGaAs device, a 3% diffraction efficiency (relative to the transmitted signal) with a 20 p.m spatial resolution was obtained at 850 nm using 0.80 |iJ/cm^ energy density [1]. Higher spatial resolution of 5 jam has been obtained in a 1 |0,m thick device by improving material properties [3, 4]. Theoretically the resolution in an ideal device should be comparable to device thickness [5]. The lower resolution obtained in the experiments implies the existence of lateral carrier transport. In order to understand the role of charge transport on the resolution and diffraction efficiency, we made picosecond time-resolved measurements of grating build-up on the device used in Ref. 1. The photorefractive MQW device, shown in Figure II-1, is functionally divided into three regions: the photoconductive MQW region which also provides optical modulation, the low-temperature grown quantum well layer (LT layer) which efficiently traps carriers, and the dielectric layers which block the photocarriers from reaching the electrodes. Light absorbed in the MQW region generates electron-hole pairs that separate across the wells and partially screen the applied electric field. For a lateral sinusoidal intensity pattern, the space-charge field forms an absorption and refractive index grating in the MQW region through the quantum-confined Stark effect. In general, both electrons and holes contribute to the build-up of space-charge in a photoconductive MQW [6]. Here we are able to separate the contribution of electrons and 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vapp PUMP PROBE PUMP ERASING ILLUMINATION “ I DIFFRACTED ^OBE / LTMQW REGION -DIELECTRIC LAYERS -J TRANSPARENT ELECTRODES Figure II-1.Time-resolved four-wave mixing experimental geometry using a photorefractive MQW device consisting o f Cr-doped GaAs (IOOÂ) QWs and ^l0.29Ga0.7lAs (35Â) barriers with a region o f MQW grown at low temperature (LT). Uniform diode laser illumination is used to erase the grating between successive pulses. 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. holes in the same device by varying the experimental conditions. We show that one type of carrier dominates the growth rate and amplitude of the diffraction grating, depending on the polarity of the applied voltage relative to the direction of light incidence on the sample. We also show that electron-dominated gratings partially decay in times from 0.4 to 8.5 ns after they reach their maximum value; gratings with small spacing decaying faster. Since our sample has a LT layer on one side, we used this asymmetry to determine the effectiveness of the low-temperature grown layers in slowing down grating decay. We show that gratings formed mostly on the LT side last about ten times longer than those formed on the side grown at normal temperature (NT). The sample [1], grown by molecular beam epitaxy, consists of 155 periods of Cr- doped 100 Â GaAs wells and 35 Â Alo^gGag^yiAs barriers. The last 5 periods were grown at low temperature (380 °C). Device has a 2.1 |xm thick active region sandwiched between dielectric layers (2000 Â) and transparent electrodes. Grating build-up was monitored by picosecond time-resolved four-wave mixing, with two intense (15 nJ/cm^) pulsed ( ~2 psec) laser beams crossed in the sample so that the grating vector was in the MQW plane. The grating strength was monitored by diffracting a time-delayed weak probe beam from the sinusoidal grating. Both pump and probe beams were at 850 nm wavelength. We applied a single polarity pulsed voltage (22V) with repetition rate of 50 kHz across the quantum wells to ensure that the carriers always accumulate on the same interface after crossing the wells. Because of long carrier decay time (-200 msec) at the interfaces between the MQW and the dielectric blocking layers, a pulsed laser diode was used during the time when V = 0 to erase any residual charge grating before each picosecond laser pulse. To prevent saturation, the total writing 2 beam energy density was kept low (30 nJ/cm ). 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Since the device is highly absorptive [1], with an absorption length shorter than the device thickness (near the heavy-hole exciton peak a ‘'=1.25 pm), there is a non-uniform optically induced initial carrier distribution. The majority of photocarriers are generated near the entrance face. Hence, depending on the applied field polarity, only one carrier type crosses the majority of QW, while the other carrier type crosses few, traveling in the opposite direction. Since the diffracted signal measures the average refractive index and absorption change of the entire sample, the carrier type that passes the most QW dominates the dynamics of the grating build-up. Since the sweep-out times of the electrons and holes in this structure differ very much from each other, the contribution of each type of carrier could be identified in the diffraction efficiency by its own rise-time. Figure II-2 shows the grating diffraction efficiency as a function of probe delay for a grating with 50 pm spacing. In the figure, the data, shifted vertically for clarity, correspond to the four possible combinations of voltage polarity and direction of light incidence relative to the LT layer, as depicted in the inset. In experiment (a) electrons cross the most wells and dominate, while holes are the dominant carriers in experiment (b). The grating build-up has fast and slow components due to sweep-out of electrons and holes, respectively, across the quantum wells [6]. The curves in Figure II-2 are fit to % e ~ 34 ps ± 12 ps and rp - 285 ps ± 23 ps. The difference in sweep-out times is expected because our applied field of 68 kV/cm is near the resonant tunneling field for electrons through the relatively thin Alg^gGag^yiAs barriers [7]. In experiment (a), a larger component of the fast rise is observed ( -60%) which indicates the dominant electron contribution. However in experiment (b), the contribution from fast carriers decreases (-33% ), indicating that the grating is mostly formed by slower carriers (holes). Also the diffraction efficiency in A is 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. higher, indicating that electrons are more effective in traversing the quantum wells. When compared to Fox’s sweep-out time for a p-i-n device [7], the overall grating build-up time in our device is slower. This is due to the contribution of the slower carriers to the internal field screening. (Since the device used in Fox’s measurements had conductive p and n regions, the internal field recovered due to enhanced diffusion before slow carriers (holes) could contribute to internal field screening.) The data was fit to a model in which the carriers are assumed to be quickly swept from the MQW region and accumulate at the interfaces. The charge pattern is assumed to decay at a constant rate once it reaches the interface, yielding a time response that can be represented by a convolution of the charge build-up and decay functions. The grating build up times obtained from the curve fits of the data to the convolution of exponentially rising and decaying functions are in agreement with values obtained from a more rigorous numerical model, in which thermionic emission, tunneling, drift, and carrier capture by traps and subsequent quantum wells were included [8]. Our numerical simulation shows that rise times in this device are mostly determined by carrier drift, tunneling and thermionic emission. 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.25 > 0.20 « 0.15 E 0.10 2 0.05 500 1000 1500 Time (psec) Figure II-2. Picosecond time-resolved diffraction efficiency at A=50iJm (fluence = 30 nJ/cm^ , applied field = 68 kV/cm): small arrows in the inset show the magnitude and direction o f carriers; large arrows show the direction o f laser illumination. Experiment (a) : electrons drift to LT region at exit face; (b); holes drift to LT region at exit face; (c): electrons drift to N T MQW/dielectric interface; (d): holes drift to N T MQW/dielectric interface. The polarity is noted by +, - in the figure. 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The effect of the LT grown region was investigated by flipping the non-symmetric device and comparing the time-resolved diffraction efficiencies. In experiments (c) and (d ), dominant carriers (electrons and holes respectively) accumulate at the NT interface of the sample. When experiment (c) is compared to experiment (a) (electrons drifting to the LT region at the exit face), the diffraction efficiency is smaller and decays much faster. Comparison of experiments (b) and (d) gives the same result: the diffraction efficiency decays in 2-3 ns (much faster than in experiments (a) and (b)). Apparently carriers accumulated at the NT interface have a higher effective mobility than the LT region and move laterally to erase the grating faster in experiments (c) and (d). This data also shows that accumulating carriers at the LT side result in a higher diffraction efficiency. Figure II-3 shows the time-development of the diffraction efficiency as a function of probe delay for gratings of decreasing period. In these experiments the electrons are the dominant carriers and they accumulate on the LT side of the device, case (a) of Figure II-2. Gratings with smaller spacing decay faster, consistent with the reported decrease in CW diffraction efficiency of gratings with small spacing'. Since the carrier sweep-out time is -34 psec for electrons, the diffraction efficiency decays after carriers reach the MQW/dielectric interfaces. The grating decay is therefore assumed to be caused by the lateral motion of the photocarriers at the MQW/dielectric interface. However, the exact nature of this motion is not yet clear; diffusion alone cannot explain this fast decay. The diffusion time of a charge grating with spacing A^at a temperature T is '^ d iffu s io n = where fx^ is electron mobility, e is electric charge and kg is the Boltzman's constant [9]. Fitting decay times obtained from Figure II-3 to the equation gives fi^~ 9200 cm W s for electrons in the LT layer, unrealistically large. The mobility would have to be even larger for the NT interface, as the grating decays faster there (Figure II-2). Lateral transport of carriers at the interface may be drift due to the lateral component 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the space charge field [10]. Preliminary measurements of grating decay as a function of applied voltage in this device support this hypothesis. When normalized to constant carrier density, the transient diffraction efficiency obtained with picosecond pulses was measured to be 24 times larger than the diffraction efficiency reported in Ref. 1 which used a CW laser. Since in picosecond operation the writing time is only limited by the carrier sweep-out time (300 psec for slower carriers), the grating could be read and then erased with another picosecond pulse, resulting in a device operation at GHz frame rates. In conclusion, our data show that for sufficiently high applied fields, the grating builds up as fast as the carriers are swept out from the MQW region, in 30 ps for electrons and 300 ps for holes. Thus, for higher diffraction efficiency, trapping within the MQW region is not needed; in fact, having traps in the MQW region reduces the quantum efficiency of the device [3]. Lateral diffusion during transport across the quantum wells is not important. Charges move laterally at the MQW/dielectric interface after they have accumulated. Hence efficient trapping or removal of charges at the MQW/dielectric interface is the key to improving the spatial resolution. Although the LT grown layers slow down grating decay more than the NT side, gratings with small spacing still decay. Annealing the low-temperature grown layers may reduce their conductivity [11] and increase grating decay time. By efficiently trapping carriers at LT regions, a device with a resolution close to its thickness can be fabricated. In addition to this high resolution device, using picosecond mode-locked diode lasers instead of CW diode lasers in an optical image processing system will increase the diffraction efficiency and the frame rate. An alternative geometry for photorefractive quantum wells is to use LT grown material throughout the structure (see Chapter-Ill) [12,13]. Localized carrier trapping means elimination of lateral fields, which should lead to higher spatial resolution and efficient probe diffraction but lower pump sensitivity. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A=50 A= 30 |im 0.06 0.04 A=10 |im 0.02 0.00 1500 0 500 1000 Time(psec) Figure II-3 Picosecond decay o f the diffraction efficiency as a function o f grating period in the geometry (case (a), fluence = 30 nJ/cm^, applied field = 68 kV/cm) where electrons dominate and travel to LT layer. The decay times are 8.5 ns, 3.5 ns and 0.46 ns fo r grating periods o f 50 pm, 30 pm and 10pm. 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References : 1 A. Partovi, A.M. Glass, D.H. Olson, G.J. Zydzik, H.M. O'Brayn, T.H.Chiu and W.H.Knox, Appl.Phys.Lett. 62, 464 (1993). 2 M. C. Nuss,M. Li, T.H. Chiu, A.M. Weiner, A. Partovi, Optics. Lett. 19, 664 (1994). 3 W. S. Rabinovich, S. R. Bowman, Appl. Phys. Lett. 66, 1044 (1995). 4 S. R. Bowman, W. S. Rabinovich, C. S. Kyono, D. S. Katzer, and K. Ikossi- Anastasiou, Appl. Phys. Lett. 65, 956 (1994). 5 Y. Owechko, A. R. Tanguay Jr., J. Opt. Soc. Am. A 1, 635 (1984). 6 Ching-Mei Yang, D.Mahgerefteh, Elsa Garmire, L. Chen, K. Z. Hu and A. Madhukar, App. Phys. Lett., 65, 995 (1994). 7 A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunnigham, and W. Y. Jan, IEEE J. Quant. Electron. QE-27, 2281 (1991). 8 E. Canoglu, Ching-Mei Yang, D. Mahgerefteh and E. Garmire, to be published. 9 P. Gunter, J. P. Huignard, Photorefractive Materials and Their Applications-I, 25 (1988). 10 D. D. Nolte, Opt. Commun. 92, 199 (1992). 11 H.H. Wang, J.F. Whitaker, A. Chin, J. Mazurowski, and J.M. Ballingall, J. of Electronic Materials, 22, 1461 (1993). 12 I. Lahiri, K.M. Kwolek, D.D. Nolte, and M R. Melloch, Appl. Phys. Lett. ,67,1408 (1995). 13 I. Lahiri, Maria Aguilar, D.D. Nolte, and M R. Melloch, Appl. Phys. Lett., 68, 517 (1996). 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III. Carrier Transport In a Low Temperature Grown Multiple Quantum Well p-i-n Modulator: Device-B III.1 Background The poor resolution problem described in the previous chapter made researchers to concentrate more on the lateral transport and ways to reduce it. The major drawback of device-A, as described earlier, is that its single LTG trapping region was not capable of eliminating the lateral transport. The second problem was that, due to the dielectric layers, its non-monolithic structure required complicated fabrication processes such as deposition of dielectric layers and transparent electrodes. The desired monolithic device requires highly trapping semiconductor buffer layers to replace the dielectric layers. Such a device would consist of only semiconductor layers that are grown by molecular beam epitaxy. The first all-semiconductor device used low temperature growth (LTG) layers on either side of the normal grown MQW layer, both with metal contacts placed directly on the LTG layers [1] The disadvantage of this structure was that it required a lift-off technique in order to access the LTG layers, which was a limiting factor for large area device fabrication. The second design, introduced by Lahiri et al [2] from Purdue University, was a p- i-n structure with the LTG MQW in the i-region. The advantage of this p-i-n structure is that it did not required a laborious lift-off technique to make the electrical contacts. Also, in order to increase the spatial resolution, a large number of traps were introduced to the MQW region by growing at low substrate temperatures (320 °C). The highest resolution obtained from these devices was ~7 |im [3], which was a factor of three enhancement compared to the performance of device-A described in the previous chapter. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Although increased resolution can be achieved with LTG MQWs, the device sensitivity reduces due to the highly trapping nature of the active region of these p-i-n devices. In this chapter we discuss the effects of LTG MQW on device sensitivity and resolution. In addition, we describe an experimental method of dynamically optimizing device sensitivity and resolution. III.2 Introduction The device performance is characterized by its spatial resolution and sensitivity, both of which strongly depend on carrier transport. The spatial resolution decreases with increased lateral carrier transport, while the sensitivity increases with increased longitudinal transport. As described earlier, highly trapping materials fabricated with LTG techniques have been successfully used to increase the spatial resolution by reducing the lateral carrier transport. However, there is a trade-off between spatial resolution and sensitivity in the devices that use LTG MQW. Reduced lateral transport also means shorter longitudinal transport, so that the photocarriers do not travel very far along the field lines. As a result, the field screening created by the photocarriers is experienced by only few QWs, causing lower sensitivity. Thus, in an optimized device, just enough traps should be introduced so that higher spatial resolution can be obtained without reducing device sensitivity any more than necessary. Since it is difficult to fabricate a device with the optimum trap density that will satisfy the trade-off between sensitivity and the resolution, we start with a device (p-i-n structure with LTG MQW in the i-region) that has large trap density and we optically adjust the active trap density during operation by passivating some of the traps. We have found that spatially homogeneous illumination just before the experiment (a pre-illumination pulse) can increase the sensitivity of our device by a factor of twelve . In addition to increasing the device sensitivity, pre-illumination performs erasure of the modulation. 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which translate into several hundred MHz frame rate operation for optical image processing applications. We study the effects of LTG MQWs on sensitivity and resolution by using picosecond time resolved pump/probe and four-wave mixing experiments. From the time resolved transmission data, we calculate free-carrier lifetime, longitudinal mobility and transport length for electrons. The device resolution is investigated by four-wave mixing diffraction efficiency. Our four-wave mixing data indicate that higher diffraction efficiency with minimal decay can be obtained when the trap density is optimized. Using a simple model for lateral carrier transport, we discuss effects of traps on device resolution and estimate the lateral mobility of the electrons. III.3 Experimental Results III. 3.1 Device structure Device-B had a Alg jGao^As /GaAs LTG MQW structure grown on an n " * " GaAs substrate (Figure 1). Contact and etch-stop layers of n-type materials were grown on the n^ GaAs substrate at 600 C. This was followed by 120 periods of LTG (320 °C) MQW region consisting of 100 Â GaAs wells and 35 Â Alo jGao^As barriers. The LTG (320 °C) results in approximately 0.2 % excess arsenic in the MQW The LTG MQW region is sandwiched between 5000 Â LTG AlgjGaojAs buffer layers. A 2000 Â p-Alq^GagjAs (10^* cm'^) layer followed by a 1000 Â top p-GaAs (10^® cm'^) layer was grown at 450 °C on top of the Al^gGaggAs buffer layer. The 450 °C growth temperature for the p-doped layers acts as a weak in situ anneal of the previously grown LTG layers and results in the formation of As precipitates in the MQW region [4,5]. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 3 h f g 1 o I | v p I (3 2 I. r ô p-GaAs 1x10i9cm-3 1000 Â p-AI 0.3 6 8 0 . 7 As 1x10i9cm-3 2000 Â i-Alo.s Gao.sAs 5000 Â GaAs 100 A 1 2 0 period supperlattlce: 100 Â GaAs 35 À A! 0.3 6 8 0 . 7 As 0.2 % ex cess As i-AI 0.5 6 8 0 . 5 As 5000 A n-Alo.3 Gao.7 As 1x10i7cm-3 2000 A n-GaAs 1x10i8cm-3 3000 A n-Alo.5 Gao.oAs 1x10i8cm-3 5000 A n-AIAs 1x10i8cm-3 200 A n-GaAs 1x10''8cm-3 0.5 nm n+ GaAs Substrate Figure III-1 Device-B structure 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III. 3.2 Device sensitivity and longitudinal carrier transport The sensitivity measurements were carried out by using psec time-resolved pump/probe experiments. We measured the transmission change (AT/T) at constant pump power as a function of pre-illumination fluence (active trap density). In a reverse biased (5 V/|im) p-i-n diode, a strong (0.016 |iJ/cm^) pump pulse 3 psec long tuned to the heavy- hole excitonic absorption line created electrons and holes in the QWs. In the experiment, a time-delayed weak probe pulse monitored the transmission change caused by the strong pump pulse. Before each psec pump pulse (5 kHz repetition rate) a 50 jisec long pre illumination pulse (from a 850 nm laser diode) impinged uniformly onto the sample while the field in the QW region was zero (Figure III-2). The field was applied 25 |isec after the pre-illumination pulse and remained for 100 |xsec. The pump pulse is arrived 1 |isec after completion of the field rise. The fluence of the pump pulse was kept constant; only the fluence of the pre-illumination was changed for each set of time-resolved experiments. In Figure III-3, t = 0 represents the arrival of the pump pulse onto the sample, while t < 0 and t > 0 correspond to the measurement of AT/T before and after the pump pulse, respectively. The signal measured before the pump pulse (t < 0 ) remains from the previous pump pulse that arrived 200 |xsec earlier. When the pre-illumination fluence is zero, we obtain a DC-like signal in which the transmission change created by a single pump pulse is not clearly observed, indicating that the measured AT/T is due to an average accumulation of carriers from several pump pulses. This occurs because the trapped-carrier life-time is long ( -500 ^tsec). As the pre-illumination fluence is increased, the measured AT/T increases and the effect of a single pump pulse can be clearly observed in Figure III-3. The rise that is observed after t = 0 is due to the screening field of moving carriers that were created by a single pump pulse. In contrast to a QW device grown at normal temperatures, in which two rise-time constants exist [6], we observe a single rise-time, indicating that only one type 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of carrier is mobile and contributing to the field screening. From exponential rise-time fits, we observe that the rise of the AT/T signal takes a longer time as the pre-illumination fluence increases ( 29,47, 51 and 59 psec for pre-illumination fluences of 0.02, 0.03, 0.1 and 10 |0,J/cm^), indicating that carriers are traveling longer distances with increased pre illumination. We also measure non-zero AT/T when t < 0, indicating the existence of field screening before the pump pulse. This residual AT/T comes from the fact that there are some left-over charges that were created by the previous pump pulse. Since the trapped- carrier life-time (500 |xsec) is longer than the time interval (200 (xsec) of the pump pulses, some portion of the carriers created by the previous pulse, if not removed, continue to screen the applied field even 200 jisec after the pump pulse. Figure III-4 shows the measured values for AT/T before (t = -160 psec , circles) and after (t= 200 psec, triangles) the pump pulse for several pre-illumination fluences at constant pump fluence. The difference of AT/T before and after the pump pulse indicates the transmission change due to a single pump pulse (Figure 111-4, solid squares). At low pre-illumination fluences we observe that AT/T due to a single pulse (Figure III-4, solid squares) increases with pre-illumination fluence, indicating that the device sensitivity increases with the pre-illumination fluence. Increased sensitivity is believed to be due to increased carrier transport length. At low pre-illumination fluence, the residual AT/T ( Figure III-4, circles) also increases. However, when the pre-illumination reaches 0.104 (xJ/cm^, the residual AT/T decreases dramatically with increasing pre-illumination fluence, indicating that the screening field due to left-over carriers from the previous pulse is now being removed. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200 iLisec Eapp Pre- Illumination Psec Pump Psec Probe 50 |xsec psec 25 |xsec - 1 |isec Figure III-2 Timing diagram fo r pump/probe and four-wave mixing experiments (not to scale). 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.03 ^^/cm 14 12 10 0.02 /iJ/cm 6 1 0 //J /c m ‘ 4 0 fvJ/cm 2 0 1000 1500 0 500 Tim e (p s e c ) Figure III-3 Transmission change measured at constant pump fluence and various pre illumination fluence. 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III. 3.3 Lateral carrier transport Since pre-illumination has an effect on the device sensitivity by changing the longitudinal transport length, it is also expected to affect lateral earrier transport thus the device resolution. In order to obtain information on both longitudinal and lateral carrier transport as a function trap density, we have performed psec time-resolved four-wave mixing experiment. In this experiment, two strong picosecond-pulsed pump beams are crossed in the sample so that the grating vector is in the QW plane. This writes sinusoidal gratings (A=18 |im) so that the diffraction efficiency of a time-delayed probe pulse can be monitored. Figure III-5 shows the results for various pre-illumination energies, indicating that there is an optimum pre-illumination energy (0.1 (xJ/cm^) at which the diffraction efficiency is maximum with minimal decay. This pre-illumination energy corresponds to the minimum energy at which we obtain the highest sensitivity and reduced residual carriers (Figure III-4). When the pre-illumination energy is higher (10 pJ/cm^) than optimum, a rapid deeay of diffraction efficiency is observed, indicating that the trap density is low enough to allow carriers to move in lateral direction and reduce the grating strength. At low pre-illumination energy (0.02 pJ/cm^), smaller diffraction efficiency is obtained because the sensitivity decreased due to smaller longitudinal transport length. 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I 14 D ifferen ce 12 10 8 6 4 2 0 0.001 0.01 0.1 1 Pre-illumination Fluence (|iJ/cm ) Figure III-4 Transmission change measured at fixed time delays o f the probe pulse ( Before the pump pulse (t < 0), after the pump pulse (t> 0)) 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III.4 D i s c u s s i o n III. 4.1 Longitudinal transport length and device sensitivity In the pump/probe experiment, the pump pulse generates electron and hole pairs in the QWs. Due to the applied field, these carriers escape from the QWs and move toward the n and p regions, generating a screening field that reduces the total field in the illuminated area. Because of high trap density and the fast trapping time, the photocarriers are captured in the MQW layer before they reach the electrodes. The field change in the illuminated area causes absorption and index change due to the quantum confined Stark effect. Since the carriers are trapped throughout the MQW region, the screening field experienced by the QWs is not uniform. The screening field magnitude and distribution is determined by the carrier transport length (LJ. In the case of uniform carrier excitation, when both electrons and holes are mobile, the screening field distribution resembles a trapezoid that is defined by [7]: 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.12 0.1 0 |iJ/cm 0.10 10 ^J/cm 0 0.08 1 S 0.06 c o S 0.04 i 0.02 |xJ/cm 0.02 0.00 1500 1000 500 0 Time (psec) Figure 1 1 1 - 5 Time-resolved four-wave mixing diffraction efficiency at F^p^= 7.5 V/jJm and grating period o f 18 pm. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. L h + z 0 < z < Lg Lh + Le Lg < z < d - d + Lg — z d — L[j ^ z < d ///-7 where • —, with as the excited carrier density, q as the charge of the electron, e e as the dielectric constant. Also d is the MQW region length, and Lg and are electron and hole transport lengths. The measured AT/T in pump/probe experiments is related to the field screening through the total absorption change (AA) created by the reduced field: AT T -T g ^ g-AA ui-2 T 0 Where T^ is the transmission without the screening field and AA is the total absorption change defined by d AA = J Aa(z) • dz Eq. III-3 0 Assuming that the absorption change of the QW material has a linear field dependence (Aa = K F), the total absorption change created in the device becomes proportional to area of the field trapezoid, which is the photo-voltage generated by electrons and holes moving distances of Lg and Lj, respectively. Thus, for arbitrary Lg and L,, the total absorption change can be expressed as: d A A (L „ L j = j K F„(L.,L^,z) dz = K V ^ (L „ L ,) Eq. III-4 0 where the photo-voltage V pj, is related to the transport lengths by: 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. initial Carrier Distribution Electrons ^max — ■ Final Charge Distribution Screening Field Figure III-6 Screening field distribution in the MQW region 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V ^(k,L j = d-(Le + U)---(Le +U) Eq. m -5 Although Eq. 1II-5 is derived with the assumption of uniform carrier distribution, it can also be used to describe the photo-voltage for exponential carrier distribution when a d < l. Figure III-7 shows that the numerically calculated photo-voltage for an exponential carrier distribution (a = 8000 cm * , n„= 10*' cm '^, d = 1.63 |im and = 1^) is similar to the photo-voltage described by Eq. III-5. Thus the total absorption change of the MQW can be calculated by simply using Eq.III-4 and Eq. 1II-5, then related to the measured (AT/T) by: A A (L „ L j = - ln 1 + Eq. III-6 The maximum AA is obtained when all the carriers move to the MQW interfaces (L^ = 1^= d). In this case, the screening field is uniform and A A ^ = Aad. Note that A A ^ can also be obtained by electrically changing the field experienced by the QWs and measuring the (AT/T)„^. as a function of A P^pp. If only one carrier type is mobile (i.e. = 0), the transport length for that carrier type can be calculated by comparing the photogenerated AA obtained from the pump/probe experiment ( through Eq. III-6 ) and electrically generated A A ^: 1 - T 2 AA AA Eq. III-7 max y 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5 2.0 > 'S Ql non-uniform uniform 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Le,Lh (/;m) Figure IIÎ-7 Comparison o f numerically calculated photo-voltage fo r exponential carrier distribution and the photo-voltage described by Eq.III-3 (uniform carrier distribution) 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In our case, the experimental configurations were such that electrons were the dominant carriers in the field screening process [6]. Since the measured rise time (29-59 psec) of the AT/T signal is fast compared to hole sweep-out time, we can assume that the measured AT/T is due to electrons only [6]. Thus, the transport length of electrons can be calculated from Eq. III-7. When the applied field changed from 0 to 5 V/pm, we measured (A T/T)^ = 0.26. At low pre-illumination fluence ( 0.02 pJ/cm^ ), Figure III-4 (solid squares) shows (AT/T)p^ = 0.032. We find that the estimated electron transport length is 0.21 pm. Similar calculations are performed for 0 pJ/cm^, 0.03 pJ/cm^ and 10 pJ/cm^ are shown in Table III-l Pre-illumination Fluence (pJ/cm"^) Transport Length (pm) Number of QWs passed 0 0.03 ~2 0.02 0.21 ~ 16 0.03 0.35 - 2 6 10 0.41 - 3 0 Table III-l Calculated transport length by using the data from Figure III-4 (solid squares). The calculated transport length for 10 pJ/cm^ pre-illumination fluence is unreliable because the time resolved AT/T data has decay, indicating that the (AT/T)^^ value used to calculate the transport length is reduced. However comparison of transport lengths for 0 pJ/cm^ and 0.03 pJ/cm^ fluences show that the electron transport length is increased by a factor of 12. The increased transport length translates into enhanced device sensitivity (Eq. Ill-5). The limit for the increase in sensitivity is reached when the majority of traps are passivated. With too high pre-illumination fluence, free carriers are formed and photocarrier field screening is reduced by processes such as enhanced diffusion and lateral carrier transport. III. 4 .1 .1 Effective free carrier life time and longitudinal mobility: Information about the carrier transport length enables us to calculate the longitudinal electron mobility by using the measured rise-time values from time-resolved 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pump/probe experiments. Since the electron escape from the quantum wells at high fields is much shorter than the measured rise-times of AT/T data, we can assume instantaneous generation of free electrons in the conduction band. Then these free electrons drift towards the positive electrode until they are captured by traps. Since the screening field is a function of transport length, depending on their distribution, carriers experience a reduced field. The time required for carriers to drift from plane z to z+Az: At = Az V F - - F app 1 ^ max Eq. III-8 Thus the average transport time required for carriers to move a distance L, is az o p - ~ F ' app ^ * max P i F. log V d F Eq. III-9 app y As shown in Figure III-8, when = 6.72 cmV(Vs) is used for the longitudinal electron mobility, the calculated transport time agrees with the measured rise-time. Although the estimated electron mobility is much smaller than that of bulk GaAs, it is consistent with the low mobility of the LTG AlGaAs. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i — calculated (/v=6.72 cm’ /(V s)) ■ measured rise time 1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Transport Length (#/m) Figure III-8 Measured rise-time o f AT/T and calculated transport time (ii=6.72 cm^/(Vs), Pap, = in Eq. 111-9) 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Since the carrier transport length is much shorter than the device thickness, the rise time that we observe in pump/probe data is related to the trapping time or the free-carrier life-time rather than the transit-time. As long as carriers are free, they move and increase the photo-voltage {Eq. III-5). Since AT/T is proportional to photo-voltage, the rise in AT/T will stop when the carriers are trapped. Thus the measured rise-time can be considered the free- carrier lifetime. This also explains the increase in the measured rise-time with the pre illumination intensity. III. 4 .1 .2 Erasure with pre-illumination: The effect of pre-illumination on residual AT/T (Figure III-4, circles) can be better understood when we consider the carrier density at the MQW interface. Since electrons were the only mobile carriers in our experiments, we concentrate on a single carrier type. For simplicity, assume a uniform initial carrier distribution and, after excitation, carriers travel a distance L^ and get trapped. Although there are carriers trapped in the MQW region, the largest contribution to the screening field comes from the carriers that have moved to the MQW interface (assuming L, « d). The density of carriers at the MQW interface is proportional to the transport length (Figure III-6). In the pump/probe experiment, the applied voltage is turned off after the pump pulse, so that only the screening field created by the pump carriers exists. The carriers created by the pre-illumination pulse then move to reduce this space charge field; holes move to the MQW interface that contains the electrons created by the previous pump pulse. The existence of electrons and holes at the same location in the device increases the recombination rate of the carriers. In this case, the total electron density at the MQW interface can be expressed as: \ •exp ( t ] k " ^ e - h J Eq. 111-10 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T _ . = --------- Eq. III-l 1 7e-h • P pI where is the electron-hole recombination coefficient and Pp, is the density of holes created by the pre-illumination. In Eq. Ill-10, both L,and depend on pre-illumination. As the pre-illumination fluence increases, L, increases and x ^.^ decreases. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. e 8 6 4 2 0.001 0.01 0.1 1 10 Pre-illumination Fluence (nJ/cm ) Figure III-9 Residual AT/T : The solid curve is the plot o f the estimated AT/T by using Eq. Ill-10 and Eq. III-5 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The carrier density described by Eq. III-IO can be related to the residual AT/T ( Figure III-4, circles) by using Eq. III-4, Eq. III-5 and Eq. III-6. This can explain Figure III-9. At low pre-illumination fluences, due to the low density of Ppj, electron-bole recombination is not dominant. The residual AT/T increases with increasing pre illumination fluence because of increased carrier transport length. However, at higher pre illumination fluences, although L, increases, electron-hole recombination dominates, causing the residual AT/T to decrease because of reduced carrier density. Since the pre illumination pulses arrive onto the sample when the applied voltage is zero and since the photocarriers are captured by the traps well before the applied field rises, pre-illumination pulses do not directly contribute to the field screening. However, as shown in Figure III- 9, they play an important role removing the field created by the earlier pump pulses. III. 4.2 Effect of pre-illumination on resolution So far, our discussion has been concentrated on longitudinal transport pre illumination dependence of device sensitivity. When the trap density is changed by pre illumination, carriers can travel longer distances not only in the longitudinal direction but also in the lateral direction. If there is a lateral spatial distribution of carrier excitation, as in our four-wave mixing experiments, a lateral field arises from the spatial distribution of the carriers and forces carriers to drift in the lateral direction (Figure III-10). The magnitude of the lateral field is proportional to the carrier density at the MQW interfaces and inversely proportional to the grating period (assuming a sinusoidal distribution of charges at the MQW region interface). At the MQW interfaces, where the lateral screening field is maximum, the lateral field is [8] E,(x) = ^ • L, • tanhf — - I - S in f — ■ x l Eq. HI-12 e d ' lA lA J (Note that lateral field calculations in Ref. 10 had math errors. The error-free version is shown in Eq. Ill-12) 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -d/2 0 d/2 Figure 111-10 Schematic description o f screening field when the spatial carrier distribution is sinusoidal. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30x10 n^=5.4e11 cm L^=0.41 /vm E u > 2 o > LL. 2 V 5 100 0 20 60 80 40 Grating Period (|/m) Figure III-l 1 Calculated lateral field 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30x1 n^,=5.4e11 cm Lt=0.41 A /m 20 L L 0 20 60 100 40 80 Grating Period (|/m) Figure III-l 1 shows that the lateral field, E^, dramatically increases as the grating period becomes smaller. Due to large E^, free carriers drift to the dark regions in the sinusoidal grating, blurring the spatial distribution of the initial carrier distribution. In our time-resolved four-wave mixing experiments, blurring of the sinusoidal grating pattern shows up as the decay of the diffraction efficiency, which can be related to the lateral field through the decay-time by A 2 ^ -A r E , where |X ,i is the lateral mobility . Using the decay-time constant (Xj=4400 psec) obtained from the curve fitting of 10 |xJ/cm2 (Figure III-5) and Eq. 111-13, we calculate p,, = 11.8 cmV(Vs). Contrary to the large lateral mobility in normal temperature growth QWs, lateral electron mobility in LTG QWs is much smaller and similar to the longitudinal mobility, indicating that the low 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carrier mobility in the LTG MQW layers is mainly determined by the large defect density . When the drift time, described by Eq. III-l3, is shorter than the carrier trapping time, carriers move towards the dark regions until the lateral field is eliminated or they are captured by the traps. The trapping-time of the carriers can be described by: /tip ^^trp where y,^ is the trapping coefficient and is the available trap density. Thus, as the available trap density reduces, the trapping-time increases, enabling carriers to move longer distances. The decay of diffraction efficiency at large pre-illumination fluence (Figure III-5, 10 |H/cm^ data) was explained by Eq. III-I2, Eq. III-13 and Eq. III-I4. With larger pre illumination fluence, the lateral field increases and the drift-time becomes shorter, meanwhile the trapping-time becomes longer due to reduced active trap density. As a result, more carriers can move towards the dark regions, reducing the grating strength. The low diffraction efficiency at low pre-illumination fluence (Figure III-5, 0.02 |jJ/cm^ data) can be explained by low sensitivity of the device due to short longitudinal transport length. According to analysis described in the previous paragraph, we would expect no decay of the diffraction efficiency (high resolution) at low pre-illumination fluence. However, the 0.02 pJ/cm^ data in Figure III-5 has a decaying diffraction efficiency (the decay rate is slower than that of 10 pJ/cm^ data). We believe that the main reason for this decay is residual carriers. The density of residual carriers is higher at low pre-illumination fluence (no erasure of modulation after each pulse, Eq.III-IO)', thus the accumulation of residual carriers locally reduces the trap density, enabling lateral drift by increasing the trapping-time in the accumulation region. The maximum diffraction efficiency and minimal decay is obtained when the trade off between sensitivity and resolution is satisfied. The 0.10 pJ/cm2 data in Figure III-5 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. indicates that the trapping time, defined by Eq. Ill-12, is short enough to trap carriers before they reduce the grating strength considerably. Meanwhile the trapping time is long enough to let carrier travel 0.35 |xm in the longitudinal direction, enabling larger diffraction efficiency. IH.5 Conclusion We have described a method in which the carrier transport length can be calculated from the transmission change data. Also we have shown that the sensitivity and the resolution of a MQW device can be dynamically adjusted. This may relax the restrictions in device fabrication and provide a dynamic adjustment of device properties. Also using pre illumination for erasing purpose will increase the operation rate (frame rate) of image processing applications. Finally, our experimental results give information about effective carrier mobility and life time. 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References: 1 e s. Kyono, K. Ikossi-Anastaiou,W. S.Rabinovich, S. R. Bowman and D.S. Katzer, Appl. Phys. Lett., 64, 2244 (1994) 2 I. Lahiri, K.M. Kwolek and D.D. Nolte, Appl. Phys. Lett. 67,1408 (1995) 3 I. Lahiri, M. Aguilar, D.D. Nolteand M.R. Melloch, Appl. Phys. Lett., 68,517(1996) 4 M.R. Melloch, N. Otsuka, K. Mahalingam, C.L. Chang, J.M. Woodall, G. D. Pettit, P.D. Kirchner, F. Cardone, A C. Warren and D. D. Nolte, J. Appl. Phys. 72, 3509 (1992) 5 M.R. Melloch, N. Otsuka, J.M. Woodall, A.C.Warren abd J.L. Freouf, Appl. Phys Lett. 57, 1531 (1990) 6 E.Canoglu, C.-M. Yang, D. Mahgerefteh, E. Garmire, A. Partovi, T.H. Chiu, and G.J. Zydzik, Appl. Phys. Lett. 69, 316 (1996) 7 C.-M. Yang, E. Canoglu, E. Garmire, K. W. Goossen, J. E. Cunnigham, W. Y. Jan, submitted to IEEE JQE , Sept. (1996). 8 D. D. Nolte, Opt. Comm. (1993) 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.Numerical Model for Cross-Well Carrie* Transport in Photorefractive MQW Devices In the previous two chapters, experimental results from two device structures have been discussed. A more detail analysis of these experimental results, especially device response and sensitivity, relies on understanding the carrier transport. A rigorous carrier transport model will provide a clear picture of device operation and possible ways of enhancing its properties. IV. 1.Previous Research on Carrier Transport Modeling in MQW Devices The models for PRMQW response developed in recent years have concentrated mainly on steady state operation and analyzed the device operation from a bulk device point of view rather than as a QW device [1,2].Smith et al [1], in their steady state analysis, calculated the charge accumulation regions in the device and discussed the response assuming a bulk device with uniform trap distribution and weak absorption. In addition, weak absorption contradicts the highly absorbing nature of PRMQW that leads to a polarity dependent device response [2,3,4]. Although Shkunov et al. [5] discussed the QW nature of the device, due to large computational requirements they have avoided fully modeling the device response and therefore briefly discussed the response of the device in terms of the fastest carrier type. However, as shown experimentally [3], both types of carriers contribute to the field screening and this contribution is observed as a contribution of fast and slow rise of the time-resolved diffraction. A numerical model that discusses carrier transport in MQW has been presented by Hutchings et al. [6]. However, since their focus was on the enhanced diffusion process in p-i-n devices, the photorefractive nature of MQW was not discussed. Furthermore, since the enhanced diffusion process was much faster 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. than the contribution of slow carriers to the field screening, only the effects of fast carriers was observed as the result of the modeling [6]. IV.2 .Summary of Our Contribution Despite the increased complexity of the problem due to inclusion of QWs into the calculation, we show that by using an inexpensive software package such as MATLAB, carrier transport in complex MQW structures can be solved with relative ease and speed. With the SIMULINK toolbox of MATLAB, depending on the time-resolution of the simulation, 3-10 minute processing time on a standard personal computer is enough to calculate 1 nsec time evolution of the local field, carrier and trap density of a device containing 155 QWs. In this chapter, we present a self-consistent numerical model that combines both standard photorefractive material calculations and carrier transport in MQW structures to analyze the transient response of PRMQW devices. We compare the numerical simulation results with experimental picosecond time-resolved four-wave mixing (TR-FWM) diffraction efficiency. In the model we show that the tum-on time of the device is mainly determined by carrier drift and escape from the quantum wells. We also show that the polarity dependence [5] of the tum-on time is due to large absorption of the device combined with the difference between electron and hole escape and drift times. Numerical simulation results also indicate that when highly trapped materials are used throughout MQW region, the device sensitivity reduces and only fast carriers contribute to the field screening. 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.3 .The Experimental Device Structures and the Model Results Before discussing the details of the model, the experimental results that are going to be explained by the model have to be introduced. We concentrate our analysis on two specific PRMQW structures and consider the TR-FWM diffraction efficiency of these structures to verify the modeling results. The device-A [7] consists of a 155-period Cr-doped (35 Â) Alo^gGag^iAs/ (100 Â)GaAs MQW region sandwiched between dielectric blocking layers and transparent electrodes. The last 5 periods of the MQW region are low temperature grown (LTG) to introduce large number of trapping centers with ultrafast carrier capture time (details of the device structure and experimental procedure are discussed in Chapter-II). In device-B [8], the MQW region is completely made of LTG QWs and fabricated in a p-i-n structure ( see Chapter-Ill) As described earlier, in TR-FWM experiments, while a single polarity square wave voltage is applied, two strong pump pulses are crossed in the device to generate a sinusoidal pattern with the grating vector lying in the QW plane. The psec device response is obtained by monitoring the diffraction of a time delayed probe pulse. In the bright regions of the grating, electron and hole pairs generated by the psec pump pulses move toward the electrodes and screen the applied field, causing the absorption and the refractive index to change. Later, the time delayed probe pulse diffracts from the index and absorption grating created by the spatially modulated field. As a result, the time evolution of the space charge field in the device is obtained from the diffracted probe. The first issue that we are going to explain with our model is the time evolution of the space charge field. The second part of the modeling will discuss the effect of the highly 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. trapping MQW region. The TR-FWM results obtained from device A and B will be used to check the validity of the model. Figure IV-1 shows the experimental output diffraction efficiency when positive and negative fields (68 kV/cm) are applied to device-A. Data-A is obtained by applying a positive field ( electrons are sent to the exit face of the device). The polarity of the applied field is switched for data-B ( holes are sent to the exit face). Although the diffraction efficiency rises with two rise-time constants in both data sets, their relative contribution depends on the applied field direction. By calculating the space charge field for positive and negative applied fields, we will show that the two rise-time constants comes from electron and hole transport and the applied field direction determines the dominant carrier type. The results from device-B are used for to verify the model representing structures with LTG MQW region. When similar TR-FWM experiments (with 70 kV/cm applied field, 32 nJ/cm^ total pump fluence and 18 pm grating period) were performed on device- B, we observed that the diffraction efficiency had only the fast rising component (Figure IV-2). In addition, by reducing the active trap density with a pre-illumination pulse before each pump pulse, larger diffraction efficiency can be obtained [8]. Data-C in Figure IV-2 was obtained under the reduced trap density condition (see Chapter-3). IV.4.Device Model: We begin our analysis with a generic device model in which an intrinsic MQW region is sandwiched between highly trapping regions and dielectric blocking regions (similar to device-A). Later, the analysis will be improved by introducing trapping centers into the MQW region (similar to device-B). The generic device structure under consideration, shown in Figure IV-3, has 155 QW periods of 100 Â thick GaAs wells and 35 Â thick Alo2 9Gao7iAs barriers. The trapping centers that fix the photogenerated charges will initially be assumed to be located in a narrow region (5 QW periods) at both MQW/dielectric interfaces. At both edges of the MQW region, two perfect dielectric layers 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.10 LU - 0.04 Q 0.02 0.00 1500 1000 500 0 Time (psec) Figure IV-1 Time-resolved four-wave mixing diffraction efficiency o f device-A. Data-A were obtained electrons towards the exit face (z = 2.1 {jm plane). In Data-B holes were sent towards the exit face. 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.12 0.10 ô 0.08 y 0.06 ^ 0.04 £ LU 0.02 o 0.00 1500 1000 500 0 Time (psec) Figure IV-2 Time-resolved four-wave mixing diffraction efficiency o f a device with LTG MQW region (device-B). Data C was obtained by reducing the trap density in the MQW region by pre-illumination (see Chapter-Ill). 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. insulate the MQW region from the transparent electrodes. Our goals in numerical modeling are to conveniently easily calculate the transient device response while including all the QWs and self-consistently determining the space charge field. To simplify the analysis, the model is divided in two sections: (a) carrier capture by deep traps and (b) carrier transport in the MQW region. When combined, these two processes will describe the transient response of the device structure shown in Figure IV-3. IV.4.1. Carrier capture by deep traps Both device-A and B have trapping regions; in device-A the trapping regions are limited to 5 QW layers on both sides of the normally grown MQW region; in device-B, the MQW region is itself a trapping region. As seen in Figure 2, having a thick trapping region changes the device response and sensitivity. Thus when defining the carrier transport in MQW structures, inclusion of carrier capture by traps becomes necessary. The simple carrier trapping model described in this section is used to calculate the carrier capture rates in LTG MQW regions. As in standard photorefractive device models [9], trapping regions are assumed to be doped uniformly with deep single-level donor impurities (N^) which are compensated by shallow acceptors (N^) ( acceptors are just used for satisfying the charge neutrality of the device, they do not involve trapping process ) ( Figure IV-4(a)). The ionized donors act as trapping centers for electrons (N ^ + e — >N"[)) where as neutral donors act as trapping centers for holes ( > Ap) ( Figure IV-4(h)). The total trap density {N^ = N'^ + N° ^) is kept constant such that saturation of traps could be observed when large intensities are used. The electron and hole capture rates are then defined as: 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. <z> I MQW Region Buffer Layers — Transparent Electrodes — Figure TV-3 Generic device structure used in simulation 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ec Nq e _ _ e e_ e_ _ NA ^ ± 2 Î Ev (a) e e e e e e e e ( £ ) _ ^ 2 _ s _ e / 3 y N o h h h h h h h h (b) Figure IV-4 Schematic description o f carrier trapping: (a) before illumination (b) after illumination. While acceptors are shown for charge neutrality, they were ignored in the model. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ► Figure IV-5 Schematic diagram fo r carrier transport in MQW region: (1) Carrier generation, (2) thermionic emission, (3) tunneling, (4) drift, (5) capture by QWs, (6) recombination 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Electron Capture Rate = 7„ • « • Eg. IV -1 Hole Capture Rate = Jp - p -(Vg - Eq. IV-2 where Y e and are the capture coefficients for electrons and holes. Since the trap density is limited, the capture coefficients depends on the density of available traps: where are the capture rates for an infinite number of traps. Before photocarrier T" excitation, the initial values for y^ and Y h are calculated by considering Np = . IV.4.2.Carrier transport in MQW region In addition to carrier capture by deep traps, the processes that contribute to the cross-well motion of the carriers in the MQW can be described in several categories (Figure IV-5) [10]: (1)- Generation of confined carriers: The photocarriers are assumed to be generated in the QWs by an ultrashort pulse such that their distribution in the device is determined by the absorption of the MQW material. Since QW devices are highly absorptive at the band-edge, the initial carrier distribution after the excitation pulse is not uniform; QWs near the entrance face contain the most carriers. Thus the carrier generation rate G due to photon energy of hû) is: G(z) = lo ( l - R ) « e Eg. IV-5 h(0 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where is the incident pulse fluence; a is the absorption coefficient and R is the reflection of the front surface. (2-3)-Carrier escape from the wells: The transition from confined carrier into free carrier occurs because of escape mechanisms that allow carriers to leave the confined states in QWs and drift with the applied field. Although discussions about carrier escape mechanisms continue in the literature [11,12,13], for the purpose of simple calculations, we consider only the simplest form of thermionic emission and tunneling through barriers ( including resonant tunneling) [11,14]. At room temperature, the thermionic emission rate is mainly determined by the energy difference between the confined state of the carrier and an energy over the barriers. The thermionic emission rate can be expressed [15] as : 1 ^th m ,q ( k,T 1 r Hq(F)l •exp U m iq L ^ J kgT . Eq. IV-6 and H /F ) = AEq - - e • F • Eq. IV-7 where q stands for either electron or hole, Hq(F) is the field-dependent effective barrier height, AEq stands for conduction or valance band offset, E ^^”^ is the energy level of the n-th confined state relative to the center of the well and is the width of the quantum well. Due to smaller barrier height in the valance band, hole thermionic emission is magnitude of an order faster than electron thermionic emission (Figure IV-7). The tunneling time of carriers depends on the effective mass, and the QW’s barrier height and thickness, which can be approximated by the quantum mechanical transmission of particles through a finite potential. For a rectangular barrier, the tunneling rate from the n-th state is given by [14]: 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H(F) H'(F) AE, H"(F) Lw Lj, Figure IV-6 Schematic description o f the variables in Eq. IV -6-II. H(F) is the effective barrier height fo r thermionic emission; H ’ (F) is the effective barrier height fo r non resonant tunneling, H ”(F) is the energy mismatch o f the ground state and the first excited state o f the adjacent well. 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V) ( U E K ( Q a h.tun 9 0 e,thm 10 ........ h,thm 12 0 e,tun e,res 13 O ' 14 O ' 20 40 60 80 100 120 Field (kV/cm) Figure IV-7 Carrier escape from a QW with x = 30% , 100 A, = 35 A. Calculations were made fo r the ,the electron thermionic emission time; f^s.ihrm dhe electron resonant tunneling time; , the electron tunneling time; ,the hole thermionic emission time; an the hole tunneling time. 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T ttun.q nfiK ^ •exp n Eq. IV-8 and ( L . + W Hq (F) = AEq - Ej"’ - e • F • ' " Eq. IV-9 where Ly is the barrier thickness, and m^q is the carrier effective mass in the barrier. Due to their larger effective mass, hole tunneling times are expected to be much longer than electrons (Figure IV-7). In our model, carriers are assumed to become free after tunneling through the barrier (the high applied field approach) In the case of resonant tunneling, the tunneling rate dramatically increases when energy levels in adjacent QWs coincide, due to the applied field [16]. The resonant tunneling time can be approximated by [6]: ^9. IV-,0 where H' ’ (F) = E(') - E(°) - e • F • (L ^ + Ly) Eq. IV-11 Although resonant tunneling can be observed for both electrons and holes, experiments performed on double quantum wells show that the electron resonant tunneling time is in the several psec time scale, whereas the hole resonance tunneling time is longer than 100 psec [17]. Since hole resonant tunneling time is much longer than the thermionic emission time (Figure IV-7), hole escape will be dominated by thermionic emission allowing us to ignore the hole resonant tunneling. Combining thermionic emission, tunneling and resonant tunneling, carrier escape mechanisms can be described by a single term, as: = — -— + ^— Eq. IV-12 T T T T esc.q *'thrm,q *'tun,q *'res,q 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For X = 30% and Ly = 35 Â, electrons are the fastest carriers because of tunneling through thin barriers. Due to their larger effective mass, heavy holes mainly escape from the wells through thermionic emission (Figure IV-7). 4- Carrier drift: After escaping from the quantum wells, under the influence of the applied field, carriers move towards the electrodes. In the classical picture of carrier transport phenomena in bulk semiconductors, the drift velocity of carriers is proportional to the applied field. v,q=/Xq-F Eq. IV -13 where p is the carrier mobility and F is the field. The measured electron drift velocity in bulk GaAs saturates at 10’ cm/s when the applied electric field is greater than 10 kV/cm. Since our devices operate under large applied fields, in our model electrons are assumed to travel with a saturated velocity of 10’ cm/s. For the hole drift, we use the hole mobility to calculate the hole velocity. We obtain the hole mobility by comparing calculated rise time of the space charge field to the experimentally measured rise time. Using Pp=150 cm W s for hole mobility provides comparable rise-times to the experimental results. In general, the current density that describes the free carrier motion consists of carrier drift and diffusion. =ePx„fn'F + ^ V n f l , jJ = ep^pfp^F-^VpO Eq.IV-14 V e / p V c y Assuming the field experienced by carriers is large, the diffusion term in Eq. 14 can be ignored. Furthermore, in order to restrict the analysis to 2-D (time and cross-well longitudinal coordinate z), we assume only the cross-well carrier motion exist in the device and ignore the lateral motion. This approach is valid only when the gradient of the carrier density is small. 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5- Carrier capture by the wells: While drifting towards the electrodes, carriers may loose their energy and become confined in the QWs, due to carrier-phonon, carrier-impurity and carrier-carrier scattering. The dynamics of the carrier capture process has received considerable attention because of its relevance to the dynamics of quantum well lasers. Numerical calculations of electron and hole capture rates into quantum wells in MQW structures as well as laser structures have been performed by a number of groups [18,19]. These calculations show a periodic variation in capture rates with well thickness. Experimentally measured capture rates are on the order of 0.3-0.5 psec [18]. In our model we set the carrier capture time by quantum wells to a constant value x^p = 0.5 psec (for = 100 Â), in order to see its effect on the transient response of the MQW structure. 6-Carrier recombination: In GaAs/AlGaAs QW structures the electron-hole recombination time is 4-10 ns, which is much longer than the carrier transit time [20]. Thus in our model we ignore direct electron-hole recombination. IV.4.3.Rate Equations: Combining the contribution of each phenomenon described in the previous section, a set of coupled differential equations which describe the confined and free carrier population throughout the device is obtained: Confined carrier population ( n'(t, z) and p°(t, z)): ^ = G - — + —----- 7„ n" N^ Eq. IV -15 ^ ^esc ^cap 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ^ = G - ^ + ^ - y p . p = . ( N D - N + ) Eq.IV-16 ^esc ^cap Free carrier population (n^(t, z) and p^(t, z)): A _ = 2 ÎL_ + 1 v 7 ^ a e + -V J n - r „ - n '- N ; Eq. IV -17 = - 2 l _ ^ + l v j ; - y p . p '. ( N ^ - N + ) Eq.IV-18 ^esc ^cap ® Trapped carrier population (N'"g(t, z) and N°g(t, z)): ^ = r , ■ (p ' + p ') ■ (Nd - n ; ) - r . • (n ' + n'). N ; Eq. IV- 19 These coupled differential equations are solved self-consistently through Poisson's equation.: VF„ = - N* + (p‘ + p ') - (n‘ + n')) Eq. IV-20 where is the space charge field created by carrier transport. In order to solve the coupled differential equation system defined by Eq. IV -15-20, the variables n, p, Np, F,^ have been discretized in the longitudinal direction (z) such that each discrete point is defined at the center of each QW. Using the SIMULINK toolbox of MATLAB, the equation system is solved in 3-10 minutes on a standard personal computer with the time resolution of 0.05-.01 psec. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.5 .Simulation results The model discussed above allows one to estimate the time evolution of local space charge field (F,^(t, z)), carrier (n(t, z), p(t, z)) and trap density (N'^o(t, z)) for different device structures. In order to compare our results with the TR-FWM experiments, we have used a model device structure similar to the device used in the experiments. The parameters used in the first part of the simulation ( for modeling device-A) are shown in Table-1. Although calculating the local field is important in terms of understanding the device operation, results obtained from TR-FWM experiments depend on the small photo-voltage (Eq. IV-21). This is because in these experiments F^^ is derived from the diffraction of a probe beam that passes through all the QWs. Thus at the output of the device, the diffracted probe beam has the cumulative absorption and index change of each QW passed. In order to relate the simulation results to the experimental results, we calculate the total absorption change (AA) by integrating the local absorption change in the MQW. By using the Kramers-Kronig rule, the total phase change due to local refractive index modulation can also be calculated. Since the time evolution of both AA and the phase change are similar, calculating only AA will be enough to investigate the time dependence of the diffraction efficiency. When calculating A A, we have assumed the absorption change of the QW material is linear with the field (Aa = K F,J : d d AA(t) = JAa(t,z) • dz = K • jF ,,(t,z) • dz = K • Vp,(t) Eq. IV-21 0 0 where K is the proportionality constant, d is the length of the MQW region and Vp^ is the photo-voltage. This approach is valid when the photo-voltage is small. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. QW Structure: Band offset ratio: Total Number of QWs: Trap density in LTG QWs: LTG-QWs: Absorption coefficient (a): Excited carrier density (n, p): Electron drift velocity (v^ J: Hole mobility (|X p): Applied Field (Fapp): GaAs (100 Â)/ Alo 2 9Gao7iAs (35Â) 35/65 155 10*^ cm'^ 5 ( on both side of the MQW region) 8000 c m ' 10“ cm’^ 10’ cm/s 150 cm’/(Vs) 70 kV/cm Electron capture time of QWs (x ^ ^p j : 0.5 psec Hole capture time of QWs (x ^ ^p J : 0.5 psec Electron capture time of LTG-QWs: 5 psec Hole capture time of LTG-QWs: 5 psec Table IV-1. Parameters used in the numerical simulation 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.5.1, Non-uniform space charge buildup (Device-A): In order to easily observe the effect of each carrier type on the space charge field, Fapp = 70 kV/cm is chosen such that the electron escape from the QW is mainly due to the resonant tunneling. This provides the largest contrast between escape rates of electrons and holes. Figure 8 shows the electron density throughout the MQW region at various times after the excitation (for clarity, the electron distribution in the trapping layers is not shown). At t = 0 the electron distribution along the growth direction is determined by the absorption of the MQW region. After the excitation (t > 0), due to resonant tunneling, the majority of electrons become free in less then 1 psec {Eq. IV-10). The free electrons then start moving towards the end face with the saturated drift velocity, depleting the MQW region. Although the majority directly drifts to the MQW/dielectric interface, a small portion of electrons are captured by the QWs. For these electrons, escape and drift processes are repeated until they are captured in the trapping regions or reach the MQW/dielectric interface. This phenomenon is observed as the tail of the electron distribution. As shown in Figure IV-8, a majority of the electrons reach the MQW/dielectric interface in -20 psec without being trapped by the QWs. The lagging electrons complete their journey to the MQW/dielectric interface in 36 psec. 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.0x10 t=0 t=1.1 t=4 t=11 t=15 t=20 0.5 t=36. 0.0 0.5 1.0 2.0 1.5 z ium) Figure IV-8. Electron transport in the MQW region at various times, t (psec). Electron motion is towards z= 2.1 pm. The trapping layers are located 0<z< 0.1 pm and 2 < z< 2 .1 pm 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For holes the direction of motion is reversed; holes move towards z = 0 plane. Although the majority of holes travel a shorter distance (most of the holes are generated near the z = 0 plane), their transit time, when compared to electrons, is much longer. This is due to their longer escape time from the quantum wells. In addition, due to the screening field created by fast electron transport, holes experience a reduced field even before escaping from the wells, causing the hole escape rate and drift velocity to be much smaller. The depletion of holes from the MQW begins at the region close to the exit face ( z = 2 |im) (Figure IV-9). The depletion of holes is completed in -750 psec. The resulting space charge that occurs when the electron-hole transport is completed, is shown in Figure IV -10. Since there were no trapping centers in the MQW region, the region is charge-free. The charge distribution shown in Figure IV-10 is similar to the results obtained by Smith et. The two insets in Figure IV-10 show the charge distribution in the trapping layers on both sides of the MQW region at t = 0, t = 34 psec and t = 998 psec. Electrons accumulate at the region near z = 2 pm whereas holes accumulate near z = 0 plane. Due to the short length of the trapping regions, majority of the carriers reach the MQW/buffer layer interface without being trapped. However, since hole transport is much slower than electrons, more holes are trapped in the trapping region than the electrons (top inset in Figure IV-100; the trapping region near the z = 0 plane extends up to z = 0.9 pm). Figure IV-11 shows the buildup of F ^^ throughout the MQW region (for clarity, F,^ in the trapping layers are not shown). As shown in the figure, F,^ rises with a non-uniform spatial profile; at some distances the photogenerated field is higher. This non-uniform field distribution comes from the difference between electron and hole transport times and exists until all the photocarriers reach the trapping regions; then the field is uniform everywhere in the MQW region. 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.6x10 t=0 t=79 0.8 = 168 0.6 t=294 0.4 0.2 t=739 0.0 2.0 1.0 1.5 0.5 z ium) Figure IV-9. Hole transport in the MQW region fo r various times, t (psec). Hole motion is towards z = 0 pm. The trapping layers are located 0 < z< 0.1 pm and 2 < z < 2.1 pm 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If we were to send a probe beam through the device to monitor the absorption change due to and interpolate the field distribution through space, we would obtain AA(t) which is proportional to the photo-voltage (Eq. IV-21). As shown in Figure IV-12, the photo-voltage rises with two rise-time constants; the fast rise is due to electron contribution and slow rise for holes. Note that despite the equal electron and hole densities, their contribution to the photo-voltage is different. This inequality of contribution comes from the fact that because of large absorption coefficient of the material, most of the carriers are generated near the front surface of the MQW region. Thus, depending on the applied field direction, the carrier type that crosses the most QWs dominates the field screening. The simulation results shown in Figure IV-11-12 are obtained under an applied field that forces electrons to move to the exit face of the MQW, thus making them the dominant carriers in the field screening process. When the applied field direction is reversed, holes move towards the exit face of the MQW region. Since holes cross the most number of QWs, they become the dominant carrier type that determines the rise of the integrated field (or AA). A comparison of the V(t) obtained by sending electrons to the exit face and holes to the exit face is shown in Figure IV -13. Although contributions from both electrons and holes are observed, their ratio varies with the direction of the applied field, which is similar to the experimental data shown in Figure IV-1. IV. 5.1.1. Summary of simulation results for Device-A The simulation results confirm that the fast and slow rise-time components observed in TR-FWM experiments come from the electron and hole transport. In addition, our model also predicts the polarity-dependence due to different electron and hole contributions to the field screening. The simulation results also show that when the trapping region is thin, most of the carriers, specially the fast carriers, are not trapped. This reduces the effectiveness of the trapping regions in terms of fixing the carriers. 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 00 r t=998 O t=34 ; t=998 t=0 -20 \ 0 ) -40 •60 -50 : t=998 -80 - 1 0 0 x 1 0 2.0 1.0 1.5 0.5 0.0 z Ovm) Figure IV-10 Charge distribution fo r various times, t (psec). Top inset show the details o f the trapping region at the entrance face; bottom inset shows the trapping region at the exit face o f the MQW region. 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. t=998 20x1 G t=135 t=459 t=34 t=23 u_ t=1 1 CO t=0 2.0 0.5 1.0 1.5 z (/ym) Figure IV-11. Photogenerated field distribution in the M QW region fo r various times, t (psec). 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X 0 200 400 600 800 1000 Time (psec) Figure FV-12. Photo-voltage generated by the electron and hole transport (electrons are sent to the exit face o f the M QW region) as a function o f time. 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. g I 6 0.6 e > z= 2.1 //m I Q . 1 h-> z=2.1 jum I 0.2 0.0 1000 600 800 400 200 0 Time (psec) Figure IV-13. Comparison o f photo-voltage obtained with dominant electrons (e-> z = 2.1 pan) and dominant holes (h-> z = 2.1 pm) configurations. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV.5.2.Reduced sensitivity with LTG MQW region (Device-B) The second part of the simulation discusses the effects of using a highly trapping MQW region on the device response and sensitivity. The model discussed in the previous section is modified such that the whole MQW region becomes a highly trapping, as in device-B. In the simulation, this is achieved by increasing the number of trapping layers to become the total number of QW layers. In order to compare the simulation results from models with no trapping and highly trapping MQW regions, all the numbers in Table IV-1 remain the same except that the number of LTG QWs is changed to 155. Figure IV-14 shows the electron distribution throughout the MQW region (for clarity the accumulated electrons at z = 2.1 |im plane are not shown). As in the non trapping MQW model, after the excitation electrons escape from the wells and start moving towards the z = 2.1 pm plane. However, due to the highly trapping nature of the MQW region, with increasing time the electron density decreases dramatically when compared to the non-trapping MQW model (Figure IV-8). Thus the majority of the electrons cannot travel to the exit face, they are trapped somewhere in the MQW region. The transport length of electrons depends on their free-canier life-time, which is determined by the trapping time of the LTG material. Assuming a LTG trapping time of 5 psec and saturated electron velocity of 10^ cm/s, a simple calculation indicates that the average electron transport length is 0.5 pm (37 QW periods). Since the hole escape time is longer than the LTG trapping time, majority of the holes are captured by the deep traps before they escape from the wells. Thus, the average hole transport length is much shorter. This is clearly observed from the charge distribution shown in Figure IV -15. Note that there is a positive charge distribution inside the MQW region that is similar to the excitation intensity, that is also similar to the hole distribution at t = 0. This indicates that majority of the holes have been trapped before escaping from the 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wells. Contrary to the charge distribution in the non-trapping MQW model (Figure IV -10), the majority of the charges are distributed in the MQW region and not at the MQW/dielectric interface. (Also note that the charge density at the MQW/dielectric interfaces is 15 times smaller.) Figure IV-16 shows the space charge field throughout the MQW region. Note that the field distribution does not change after t = 20 psec (at least until ~1 ns) and keeps its non uniform distribution throughout the region. Since holes are captured before they screen the applied field, only electron transport affects the screening field buildup. Because a majority of electrons are captured in 5 psec, the screening field buildup slows down and attains its final form when the rest of the untrapped electrons reach the MQW-dielectric interface (in -20 psec). The maximum of the space charge field is located at z=0.5 pm, which is same as the average electron transport length. The relationship between the carrier transport length and the location of maximum Fsc also agrees with the simple model described in Chapter- Ill. The resulting photo-voltage, shown in Figure IV -17, has only a single rise-time constant, which is similar to the experimental results obtained from device-B. Moreover, the maximum Vp^(t) is 6.8 times smaller than the Vp^(t) of the non-trapping MQW model (Figure IV-12), which is also similar to the reduced sensitivity obtained from device-B (shown in Figure IV-2). Similar argument can be made for the quantum efficiency of the device: If one defines the 100% quantum efficiency for the case of all carriers traveling to the MQW/dielectric interfaces, th en , due to short transport length of carriers, the quantum efficiency of the devices with LTG MQW region will be smaller. 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV .5 .2 .1 .Summary of modeling results of device-B The simulation results obtained from a model with a highly trapping MQW region confirm that the observation of a single rise-time constant from the device is due to immobile holes. The hole contribution to field screening is negligible when highly trapping MQWs are used. Our results also show that, due to the short transport length of electrons in the LTG MQW region, the sensitivity ( absorption change or phase change per excited carrier) is smaller when compared to devices with non-trapping MQW regions. In addition, the numerical simulation results obtained in this section are in agreement with the simple model described in Chapter-Ill. 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.0x1 G t=2 LU t=1 5 t=6 0.5 0.0 0.5 1.0 2.0 1.5 z (fvm) Figure IV-14 Electron distribution in a LTG MQW region at various times, t (psec). 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 4 2 t=998psec 0 2 4 9 -6x10 0.0 0.5 1.0 1.5 2.0 z (//m ) Figure IV-15 Charge distribution in LTG MQW region at various times, t (psec). A majority o f holes are trapped where they were generated, while electron trapping takes place throughout the MQW region. 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 0 0 0 t=6.5- t=2 t=20 u. t= 988 2000 J C CO 1000 t=0 0.5 1.0 1.5 2.0 z (f/m) Figure IV-16 Photogenerated field distribution in the MQW region at various times t (psec). 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.6 0.5 0.3 £ 0.2 Q . 0.0 0 20 40 60 80 100 Time (psec) Figure IV-17. Photo-voltage created by electron transport in LTG M QW region (Device-B simulation). Hole contribution is negligible. 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References: 1 S.L. Smith and L. Hesselink, J. Opt. Soc. Am. B 11, 1878 (1994). 2 S. L. Smith, L. Hesselink and A. Partovi Appl. Phys. Lett. 68, 311 (1996). 3 E. Canoglu, C. M. Yang, E. Garmire, D. Mahgerefteh, A. Partovi, T.H. Chiu and G. J. Zydzik, Appl. Phys. Lett. 69, 310 (1996). 4 E. Canoglu, C.-M. Yang, E. Garmire, D. Mahgerefteh, A. Partovi, A. M. Glass, T. H. Chiu and G. J. Zydzik, CLE096, Anaheim, California, June 2-7 (1996). 5 V.V. Shkunov and M.V. Zolotarev, J. Opt. Soc. Am. B 12, 913,(1995). 6 D C. Hutchings, C. B. Park and A. Miller, Appl. Phys. Lett, 59, 3009 (1991). 7 A. Partovi, A.M. Glass, T. H. Chiu, and D. T. H. Liu, Opt. Lett. 18, 906 (1993). 8 E. Canoglu, E.Garmire, I. Lahiri, D.D. Nolte and M R. Melloch, submitted to Appl. Phys. Lett. (1997). 9 N. V. Kuhktarev, Sov. Tech. Phys. Lett. 2, 438 (1976). 10 C-M Yang, E. Canoglu, E. Garmire, K.W. Goossen, J. E. Cunnigham, and W.Y. Jan, Submitted to IEEE J.of Quantum Electron. (1996). 11 A. M Fox, D A. B Miller, G. 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Quantum Electron., QE-22,1799 (1986). 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Canoglu, Ergun (author)

Core Title Carrier transport in photorefractive multiple -quantum -well spatial light modulators

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program Electrical Engineering

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

Tag engineering, electronics and electrical,OAI-PMH Harvest,physics, condensed matter,physics, optics

Language English

Advisor Garmire, Elsa (committee chair), Gershenzon, Murray (committee member), Steier, William H. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-501139

Unique identifier UC11340199

Identifier 3139260.pdf (filename),usctheses-c16-501139 (legacy record id)

Legacy Identifier 3139260.pdf

Dmrecord 501139

Document Type Dissertation

Rights Canoglu, Ergun

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA