Silicon-Based Infrared Photodetectors for Low-Cost Imaging Applications

Home , Microbolometer

SILICON-BASED INFRARED PHOTODETECTORS FOR LOW-COST IMAGING APPLICATIONS

Dissertation

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Doctor of Philosophy in Electro-Optics

Joshua Duran, M.S.

Dayton, Ohio

May 2019

SILICON-BASED INFRARED PHOTODETECTORS FOR LOW-COST IMAGING APPLICATIONS

Name: Duran, Joshua

APPROVED BY:

______Andrew Sarangan, Ph.D. Michael Eismann, Ph.D. Advisory Committee Chair Committee Member Professor, Dept. of Electro-Optics & Photonics Chief Scientist, AFRL/RY

______Jay Mathews, Ph.D. Partha Banerjee, Ph.D. Committee Member Committee Member Assistant Professor, Department of Physics Professor, Dept. of Electro-Optics & Photonics

______David Forrai, M.S. Committee Member Program Manager, DARPA

______Robert J. Wilkens, Ph.D., P.E. Eddy Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean of School of Engineering Professor School of Engineering

ABSTRACT

SILICON-BASED INFRARED PHOTODETECTORS FOR LOW-COST IMAGING APPLICATIONS

Name: Duran, Joshua University of Dayton

Advisor: Dr. Andrew Sarangan

Infrared imaging is a powerful capability that has been technologically driven primarily by the defense industry over the past several decades. As a result, ultra-high-performance infrared imaging arrays with specialized functionality have been developed but at a relatively high cost. Meanwhile, economy of scale has driven the price of visible complementary metal- oxide-semiconductor (CMOS) image sensors down drastically while simultaneously providing greater on-chip capability and performance. Silicon-based infrared sensors have the potential to leverage modern CMOS advancements and cost, but poor performance has inhibited the widespread adoption of this technology. In this work, I explored the potential for novel silicon- based infrared sensors that exploit nanoscale structures to provide new methods of photodetection in silicon beyond the bulk bandgap response. Nanostructure fabrication developments and challenges were also investigated with the perspective of applying the underlying structure as a platform to detect infrared photons. Proposed solutions include improvement to existing detector technology (Schottky barrier photodiodes) as well as novel detector architectures (silicon quantum walls) that leverage the unique geometry of nanostructured silicon.

iii

ACKNOWLEDGEMENTS

I would like to first thank my advisor, Dr. Andrew Sarangan, for his guidance, mentorship and professional insight during this project and throughout my time as a graduate student. I first met Dr. Sarangan while working with him over the summer break on an undergraduate research project. I spent the summer working in the cleanroom with him, and he left a tremendous impression on me in that short time. That experience ultimately led to my decision to pursue graduate school, with the desire to continue working with and learning from him. I am grateful for the opportunity I’ve had to work with Dr. Sarangan and thankful he invited me to work with him that summer. I admire his ability to translate complex concepts into digestible pieces and his fearlessness and excitement when taking on a new challenge, regardless of the unknowns. I hope to continue our relationship through collaborative research efforts in the future.

I also have my committee members to thank, for their feedback from my prospectus, where they identified several missing elements of the project and helped me focus the variety of concepts I had into a more cohesive and manageable project. I want to also thank them for the time they spent reviewing and improving this document and for the guidance they’ve provided me throughout this process.

For the duration of this project, I’ve been employed by the Air Force Research

Laboratory as a research engineer focused on IR detectors for imaging applications. Many of my coworkers at AFRL have helped me both directly and indirectly on this project, too many to list

iv here. Having said that, I would like to highlight several people who have directly helped me on various aspects of this project: Jason Hickey for performing the metal depositions and for his help in calibrating the ultra-thin film deposition rate, Andy Browning for performing the PECVD processes, Kevin Leedy for teaching me about the ALD process and for training me on the tool,

Mike Eismann, who is also a committee member, for hosting several meetings with me to discuss my ideas and progress throughout the project, and Gamini Ariyawansa for his insightful discussions on the phenomenology of quantum wells and walls and for aiding me with the modeling section of Chapter 3.

Finally, I would like to thank my wife, parents, brother, sister, family and friends for their continued support. These people have all played a significant role in shaping me into the individual I have become. Any accomplishments I achieve, including the work written here, is a reflection of these people and the love and care they’ve given me throughout my life.

TABLE OF CONTENTS

ABSTRACT ...... iii

ACKNOWLEDGEMENTS ...... iv

LIST OF FIGURES ...... x

LIST OF TABLES ...... xix

EXECUTIVE SUMMARY ...... xx

CHAPTER 1 BACKGROUND AND MOTIVATION ...... 1

1.1 The Electromagnetic Spectrum ...... 3

1.1.1 Atmospheric Transmission ...... 4

1.1.2 Blackbody Radiation ...... 5

1.1.3 Additional Photon Sources ...... 6

1.2 Infrared Detector Array Architectures ...... 8

1.2.1 Hybrid Focal Plane Arrays ...... 9

1.2.2 Monolithic Infrared Focal Plane Arrays...... 14

1.3 Chapter 1 Summary ...... 20

CHAPTER 2 SILICIDE-BASED SCHOTTKY BARRIER PHOTODETECTORS ...... 22

2.1 Internal Quantum Efficiency ...... 25

2.2 Dark Current ...... 35

2.3 Device Fabrication ...... 40

2.4 Characterization Setup and Measurement Techniques ...... 45

2.4.1 Housing ...... 45

2.4.2 Dark Current ...... 47

2.4.3 Spectral Response ...... 49

2.4.4 External Quantum Efficiency ...... 53

2.4.5 Reflection, Transmission and Absorption ...... 57

2.5 Device Results ...... 74

2.5.1 Material Comparison ...... 74

2.5.2 Dark Current ...... 80

2.5.3 External Quantum Efficiency ...... 84

2.5.4 Optical Characterization ...... 85

2.5.5 Internal Quantum Efficiency ...... 91

2.5.6 Image Sensor Demonstration ...... 95

2.6 Engineering NiSi Schottky Barrier Photodiodes for Improved Quantum Efficiency ...... 99

2.7 Chapter 2 Summary ...... 105

CHAPTER 3 SILICON NANOSTRUCTURES FOR INFRARED PHOTODETECTORS ...... 108

3.1 Motivation and Device Concept ...... 108

3.2 Silicon Quantum Well Modeling ...... 112

vii

3.3 Heterostructure Materials ...... 125

3.4 Silicon Quantum Wall Fabrication ...... 127

3.4.1 MacEtch Process Overview ...... 127

3.4.2 PVD Self-Assembly for MacEtch ...... 128

3.4.3 Influence of Metal Geometry on MacEtch ...... 133

3.4.4 Suitable Metals for MacEtch ...... 139

3.4.5 Substrate Doping Impact on MacEtch ...... 142

3.4.6 Structural Integrity of Silicon Nanowalls ...... 143

3.4.7 Initial Demonstration of Conformal Coating with ALD ...... 145

3.5 Chapter 3 Summary ...... 146

CHAPTER 4 CONCLUSIONS AND FUTURE WORK...... 148

REFERENCES ...... 156

APPENDIX A Fabrication Process Followers ...... 167

A.1 Plasma-Enhanced Chemical Vapor Deposition (PECVD) SiO2 Process ...... 167

A.2 HMDS Coating ...... 167

A.3 AZ Electronic Materials AZ 5214 Image Reversal Process ...... 167

A.4 Shipley Microposit S1805 Process ...... 168

A.5 Solvent Cleaning ...... 168

A.6 Metal-Liftoff Process ...... 168

A.7 Metal Etchants ...... 169

viii

APPENDIX B Python Source Code ...... 170

LIST OF FIGURES

Figure 1. Schematic of generic pixel architecture for (a) CCD and (b) front-side illuminated CMOS image sensor ...... 2

Figure 2. Band diagram of p-n junction photodiode with no applied bias...... 2

Figure 3. Atmospheric transmission through a one nautical mile sea level path4 ...... 4

Figure 4. Blackbody spectral exitance for Sun (5778 K), incandescent light bulb (2400 K), human body (310 K) and room temperature (295 K) ...... 6

Figure 5. Spectral radiant sterance of night sky for various phases of the moon5...... 7

Figure 6. Schematic of hybrid FPA illustrating indium bump bonded detector array to silicon ROIC...... 9

Figure 7. Simplified process follower for hybridized FPA fabrication. (a) detector architecture growth/doping (b) mesa etch delineation (c) sidewall passivation (d) metal contact deposition (e) indium bump deposition (f) alignment and hybridization of detector array and ROIC (g) epoxy underfill for mechanical rigidity (h) substrate thinning/polishing (i) anti-reflection coating. Wafer-level processing includes steps (a-e) on the left and die-level processing includes steps (f-i) on the right...... 11

Figure 8. Illustration of interconnect strain induced by CTE mismatch. (a) hybridized detector at bonding temperature (b) hybridized detector at cooled operating temperature ...... 13

Figure 9. Band diagram of n-type blocked impurity band detector architecture under operating bias...... 15

Figure 10. Band diagram of PtSi/p-Si Schottky photodiode...... 16

Figure 11. Profile schematic of microbolometer pixel...... 17

Figure 12. Illustration of CCD shift register utilizing a 3-phase single-level gate40...... 19

Figure 13. Illustration of photoemission in p-type (a) and n-type (b) SBDs...... 22

illuminated detectors, green indicates plasmonic resonant detectors, red indicates waveguide integrated detectors and purple indicates resonant-cavity- enhanced detectors. The dashed line represents the theoretical maximum quantum efficiency based on the barrier height, assuming a sharp emission threshold34...... 24

Figure 15. Energy band diagram of photoemission process in SBDs (n-type semiconductor)...... 25

Figure 16. Illustration of escape cone (green shaded region rotated about 푘푥 axis) defined by escape momentum vector 푘푒, 푥 with solid angle Ω푠...... 27

Figure 17. Illustration depicting the energy loss and probability of emission per pass through the film...... 30

Figure 18. Predicted IQE for several different SBH (as labeled) using the Scales/Berini model as a function of L/t. Illumination wavelength is 1.55 μm. The flat portion of each curve for L/t near zero is the theoretical IQE for a thick device...... 31

Figure 19. Comparison of Scales/Berini and Vickers IQE models. Illumination wavelength is 1.55 μm, and SBH is 0.2 eV for all curves. The temperature used for Vickers’ model is 80 K, to simulate a sharp emission threshold as is assumed in Scales/Berini...... 34

Figure 20. Illustration of dark current mechanisms in SBDs...... 37

Figure 21. Illustration of scattering that can occur for frontside illuminated detectors with incomplete absorption. The thermal paste is used to provide good thermal conductivity between the package and device for temperature dependent measurements, but is a diffuse reflector...... 43

Figure 22. Schematic of FSI (a) and BSI (b) photodetectors. Detectors are square shaped ranging in width between 500 and 1000 µm. 100 µm square top contact bond pads and large area ground metal surrounding the detector are wire bonded to a ceramic chip carrier for device testing...... 43

Figure 23. Photographs of die packaging. (a) sample during wire bonding. (b) front view of FSI detector die packaged in chip carrier. (b) back view of BSI detector with hole-drilled package for illumination through the package. Die are silver epoxy bonded to the package to establish good thermal contact with the ceramic package...... 45

Figure 24. Photographs of pour-filled LN2 dewar for sample testing. (a) lid open with sample clamp holding the chip carrier in place for test. (b) lid closed and vacuum sealed for cryogenic temperature measurements. Electrical connections to wire bonded pads on the chip carrier are routed to the backside of the dewar for connecting to measurement equipment...... 46

Figure 25. Measured transmission of silicon window used for optical detector testing...... 47

Figure 26. Plot of measured temperature at the cold finger and in the chip package as the dewar warms from LN2 to room temperature from ambient heating. Only the cold finger measurement can be made during a device IV measurement, so this plot is to confirm the cold finger temp is an accurate measure of the chip temp...... 48

Figure 27. Illustration of grating spectrometer that can be used to obtain spectral response characteristics of photodetectors...... 50

Figure 28. Diagram of FTIR spectrometer configured for measuring transmission (a) and reflection (b) of a sample...... 50

Figure 29. Raw (a) and frequency corrected (b) normalized spectral response of DLaTGS using four different OPD velocities. Spectrum is valid for FTIR configured with white light source and quartz beam splitter. Spectrum is proportional to optical power (not photon flux) in both plots...... 53

Figure 30. Blackbody setup for measuring the EQE of infrared photodetectors...... 54

Figure 31. EQE spectral curve (grey) of NiSi SBD with superimposed filter measurements. The integral of the colored filters is equal to the blackbody EQE measurement obtained with the setup in Figure 30. The scaling of the grey EQE curve is determined by the average of the two scaling factors...... 57

Figure 32. (a) Transmission of 2 µm notch filter measured at 0 deg and 10 deg angle of incidence. (b) Transmission of Si wafer for angles ranging between 0—10 deg...... 58

Figure 33. Calculated reflectance using the index of refraction of Al100 and Au101...... 60

Figure 34. Illustration of standard spring-loaded clamp (a) and weighted ring clamp (b) used to position sample for reflection measurement. The ring clamp provides a sample surrounded by air, to aid modeling, and produces negligible reflection...... 61

Figure 35. Measured reflection, transmission and calculated absorption for (a) fused silica, (b) sapphire and (c) silicon windows. Absorption is calculated using both 0 and 10 degree transmission measurements to compare accuracy...... 61

Figure 36. Calculated transmittance of 500 µm thick silicon wafer using coherent and incoherent models over wide (a) and narrow (b) wavelength ranges...... 67

Figure 37. State diagram of refractive index fitting procedure ...... 69

Figure 38. Silicon wafer index fitting using only a reflection measurement to constrain the fitting. Modeled transmission doesn’t match measured as a result. This error can become worse for films with higher absorptance...... 73

Figure 39. Fitting of same silicon wafer data, this time using both the reflection and transmission measurements to compute residual error and better constrain the fitting for consistency between measurements...... 73

xii

Figure 40. Dark current characteristics of various SBDs to n-type Si. Zoom view of plot (a) is shown for just the reverse bias in (b)...... 74

Figure 41. Photo response of various SBDs to n-type Si. Response is normalized, but care was taken to preserve relative difference between devices. Zoom view of plot (a) is shown in (b) to better distinguish cutoff wavelengths and compare low signal devices...... 75

Figure 42. Reported external (square) and internal (diamond) quantum efficiency for various metal/metal-silicide Schottky-barrier photodetectors at 1.55 µm36,52- 60,62,63,65,66,79,84,88. Blue marker-fill indicates standard front-side or back-side illuminated detectors, green indicates plasmonic resonant detectors, red indicates waveguide integrated detectors and purple indicates resonant-cavity- enhanced detectors. The dashed line represents the theoretical maximum quantum efficiency based on the barrier height, assuming a sharp emission threshold34...... 77

Figure 43. Same collection of reported quantum efficiency values from Figure 42 but plotted as a function of the reported metal/metal-silicide thickness. In an effort to minimize the barrier height influence, the quantum efficiency is divided by the theoretical maximum (based on the barrier height). The marker color and shape are the same indicators as in Figure 42...... 78

Figure 44. Schematic of FSI (a) and BSI (b) photodetectors. Detectors are square shaped ranging in width between 500 and 1000 µm. 100 µm square top contact bond pads and large area ground metal surrounding the detector are wire bonded to a ceramic chip carrier for device testing...... 79

Figure 45. (a) Dark current density plot of all (90) detectors at room temperature. The inset is a zoom view of the reverse bias region to better distinguish the distribution of curves for each NiSi thickness. (b) Arrhenius plot of BSI device dark current measured between 290 K and 220 K using 1 V reverse bias...... 80

Figure 46. Room temperature dark current density of BSI 1 nm NiSi sample, color coded by device size, demonstrating negligible edge effects in this size regime. This size independence is consistent for all samples, but shown here using the devices from a single die for clarity...... 82

Figure 47. Modeled (dashed) and measured (solid) reverse-bias dark current density of BSI 1 nm NiSi device. The model is based on the thermionic emission model with field-dependent barrier lowering. These formulas along with all the supplemental formulas for calculating the field in silicon as a function of temperature are included in Section 2.2...... 83

Figure 48. QE spectra for the FSI (a) and BSI (b) devices at 1 V reverse bias. The inset in (a) shows the QE as a function of bias, illuminated through a 1.38 μm notch filter; the BSI devices are the higher grouping of values, while the FSI devices are the lower grouping in this inset. All measurements were performed at room

xiii

temperature. A detailed description of how I perform these measurements in included in Section 2.4.4...... 84

Figure 49. Transmission and reflection spectra of companion pieces used to characterize the index dispersion of various thin films used in fabrication of the devices. (a) plots the measurements of a bare DSP silicon wafer, (b) plots an SiO2 coated silicon wafer, (c) plots an SiO2 coated silicon wafer with aluminum backside mirror representative of FSI devices and (d) plots an SiO2 coated silicon wafer with Cr/Au backside mirror representative of BSI devices...... 86

Figure 50. Reflection and Transmission measurements and model fit for the 1 nm (a), 2 nm (b), 3 nm (c) and 4 nm (d) NiSi films. Measurements of simply the NiSi thin film on silicon, the completed FSI device and the completed BSI device are all included for each thickness...... 87

Figure 51. Example calculation of the per-layer absorption for the 2 nm NiSi device in the FSI (a) and BSI (b) configurations...... 88

Figure 52. (a) Fitted n (solid) and k (dashed) for 2 nm NiSi data modeled as 1, 2 and 3 nm. (b) The resultant absorption calculation of the 2 nm NiSi film in the BSI and FSI configurations, fitted as though the layer was 1, 2 and 3 nm thick...... 89

Figure 53. The real (solid) and imaginary (dashed) parts of the three TMM matrix elements: (a) 푐표푠훿, (b) 푗훾푠푖푛훿, and (c) 푗훾 − 1푠푖푛훿. The n and k values were derived from fitting the 2 nm NiSi data as though it were 1 nm, 2 nm, and 3 nm as labeled in the plots (refractive index dispersion plotted in Figure 52)...... 90

Figure 54. Calculated IQE spectra for all FSI and BSI devices (1 V reverse bias). IQE is calculated from the QE spectral measurement and absorption calculation based on the film FTIR measurements...... 91

Figure 55. (a) Fowler plot of 1, 2, 3 and 4 nm NiSi FSI photodetectors (b) quantum efficiency coefficient dependence on thickness for FSI and BSI devices, the 100 nm thick NiSi quantum efficiency coefficient value is included for reference as the grey dotted line and should not be interpreted as a function of thickness...... 92

Figure 56. Fowler plot IQE fitting of FSI (a) and BSI (b) NiSi devices using Casalino’s approximation of Vickers’ model...... 93

Figure 57. Simplified process follower for NiSi SBD hybridized FPA. (a) The process begins with deposition of 1 nm nickel (dark grey) and titanium (orange) for ground contact. The wafer is subsequently annealed, as before, to form NiSi. (b) A nominally quarter-wave SiO2 layer (blue) is deposited via PECVD. (c) The oxide is etched using BOE to reveal the ground contact and NiSi layers. (d) A 500 nm thick gold mirror is deposited (gold) with a thin chromium layer for adhesion to fill the etched plugs in the SiO2 and to provide reflection of light back onto the silicide layer. A backside SiO2 anti-reflection coating is also deposited at this stage. (e) 2 µm thick indium interconnects are deposited on each top and ground contact element. A 50 nm chromium layer is used as a

xiv

wetting layer for the indium. (f) The detector array is aligned to the ROIC and hybridized by compressing the chips with 2500 N force at room temperature...... 96

Figure 58. SWIR image of a man entering his truck, taken with a NiSi SBD FPA with 2 nm silicide layer. The image was taken through a second story window looking out on the loading dock below (overcast day), with a broadband SWIR/MWIR f/2.5 lens. The optical window is an uncoated silicon wafer with about 50% broadband transmission to block the silicon VIS/NIR reponse. This is a raw image with no image processing (apart from brightness/contrast and jpeg compression) or nonuniformity corrections. The FPA was cooled to 80 K to minimize ROIC noise...... 97

Figure 59. (a) Ratio between the measured IQE from Figure 54 and the theoretical maximum IQE, given the barrier height and illumination wavelength, for each BSI device. (b) Modeled IQE for various NiSi thin films (thickness defined by number of monolayers) using the mean hot carrier attenuation coefficient from Section 2.5.5. The theoretical max curve and measured IQE for the 1 nm NiSi BSI device is included for reference...... 99

Figure 60. Various FSI design concepts illustrating the minimal improvement afforded by designs more complicated than the very simplistic ASM design used in Section 2.5...... 101

Figure 61. Two BSI designs illustrating the ability to “filter” the absorption, but not increase beyond the relatively broadband nSAnM design used in Section 2.5...... 102

Figure 62. Process follower for thin SBD device fabrication. (a) Dielectric (green) and metal mirror (gold) layers are deposited on silicon-on-insulator (SOI) wafer. (b) Using metal as etch mask, top silicon (grey) device layer of SOI wafer is etched, revealing SiO2 (blue) layer. (c) Wafer is direct bonded to another silicon handle wafer coated with a metal suitable for low temperature direct bonding (Au, Ni, Cu, In, etc.). (d) SOI handle wafer is released by etching entire stack in BOE, which will undercut the device through the SiO2 layer. (e) Silicide is formed on remaining silicon device layer. (f) final dielectric (optional) and top contacts are deposited to finalize device...... 103

Figure 63. Various thin SBD designs which require substrate removal. The AhM design is the most simplistic, utilizing an SOI wafer with the silicon device layer chosen strategically to be a quarter-wave thickness. Another simple design, AsnM, uses an ultra-thin silicon device layer and lower index resonant reflector to broaden absorption. The resonant nhnHAnM design demonstrates a tradeoff of peak absorption and absorption bandwidth for thin SBD designs...... 104

Figure 64. Theoretical EQE for some of the optical designs discussed above. The IQE and index of refraction used to calculate these results were extracted from the 1 nm NiSi BSI device...... 105

Figure 65. Energy diagram of quantum confined semi-metal SBD. The confinement well is provided by the wide bandgap dielectric and Schottky barrier, producing an

asymmetric well. The semi-metal thickness should be designed such that the first excited state confinement energy is near the top of the Schottky barrier for efficient extraction...... 109

Figure 66. Generic conduction band diagram of a quantum well photodetector under bias...... 110

Figure 67. Conceptual SiQW detector illustrating an energy band diagram (a) and profile view of the device geometry (b). The quantum walls (vertical well) or posts (vertical wire) are composed of silicon, and connected directly to the substrate where a common contact is made. The conformally coated cladding forms an energy potential such that the silicon is a low energy well with confined energy states. The top contact is made to the low-energy collector material which should be doped to reduce series/contact resistance...... 110

Figure 68. GaAs/Al0.36Ga0.64As quantum well designs featuring bound-to-bound (a), bound-to-quasi-bound (b) and bound-to-continuum (c) confinement cases, calculated using the method described above. Confinement of first excited energy state is modulated by controlling the GaAs well width which are 40 Å, 46 Å and 55 Å respectively...... 115

Figure 69. Silicon quantum well designs for 1 eV (a), 0.5 eV (b) and 0.3 eV (c) cladding barrier heights. The transverse effective mass in silicon is used, and the cladding is modeled to have the same effective mass...... 116

Figure 70. Bound-to-quasi-bound silicon quantum well designs for 300 meV cladding barrier with effective masses of 0.1 m0 (a), 0.19 m0 (b) and 1.2 m0 (c). Well width is modulated to maintain bound-to-quasi-bound transition which are 32 Å, 27 Å and 26 Å respectively...... 117

Figure 71. Silicon quantum wells designed to absorb at 1.55 µm (a), 4 µm (b) and 9 µm (c). A constant effective mass of 0.19 m0 was used for all designs. Well widths for these bound-to-quasi-bound transitions are 14 Å, 22 Å and 34 Å respectively...... 118

Figure 72. Energy diagram and wavefunction for SiQW device with low-energy collector region. The bound-to-quasi-bound transition for this 27 Å well is 198 meV...... 119

Figure 73. Quantum mechanical tunneling probabilities of a single barrier (a) and double resonant barrier (b). The boundary material is GaAs and the barrier material is Al0.36Ga0.64As for both plots. The vertical dotted line indicates the barrier height energy. Insets for each plot illustrate the barrier potential used for the calculation...... 121

Figure 74. Tunneling SiQW design with absorption at 1.3 µm. (a) Energy diagram with superimposed eigen energies/wavefunctions (zero-energy reference chosen as silicon conduction band). (b) Tunneling probability through system with same energy reference as plot (a)...... 122

Figure 75. Tunneling SiQW design with absorption designed at 2.6 µm (transition between ground and first excited state). (a) Energy diagram with superimposed

xvi

eigen energies/wavefunctions (zero-energy reference chosen as silicon conduction band). (b) Tunneling probability through system with same energy reference as plot (a). Barrier and collector layers are identical as the design from Figure 74...... 123

Figure 76. Tunneling probability of 3.0 µm T-SiQW device from Table 5 using three different barrier widths...... 124

Figure 77. Conduction band offsets (relative to silicon) for various materials143-155. Each blue horizontal line represents a reported offset or electron affinity, with the shaded region highlighting the range. Electron affinity of silicon is taken to be 4.05 eV40...... 126

Figure 78. Illustration depicting an isometric view of the MacEtch fabrication process, (a) metal pattern on silicon before MacEtch and (b) resulting silicon structures after vertical MacEtch...... 128

Figure 79. Evolution of sputtered gold film formation on oxidized silicon. Arrows point from thinnest (~2nm) to thickest (~9nm) depositions. All images taken at the same zoom to maintain relative size comparison...... 129

Figure 80. SEM image of 10 nm silver film deposited on silicon wafer with oxide removed immediately prior to deposition...... 130

Figure 81. Comparison of 2 nm sputtered gold film on (a) silicon after BOE dip and (b) plasma oxidized silicon...... 131

Figure 82. Metal depositions of (a) 2 nm platinum and (b) 5 nm gold on oxidized silicon in the hole-filling phase...... 131

Figure 83. Sputtered gold films near the percolation thickness (a) 4 nm gold sputtered at room temperature (b) 16 nm gold sputtered at 200°C. Both depositions were performed on oxidized silicon...... 132

Figure 84. Illustration of particle MacEtch featuring (a) vertical etching and (b) curved etching...... 133

Figure 85. Comparison of metal pattern geometry, substrate crystal orientation, and solution stoichiometry on etch profile for select trials. (column 1) As deposited gold pattern, (column 2) 6:1 HF:H2O2, (column 3) 3:2 HF:H2O2, (column 4) 1:2 HF:H2O2, (rows 1&2) on [100] wafers and (rows 3&4) on [111] wafers. All 60 s etch duration...... 134

Figure 86. (a) Cropped SEM image of metal pattern used for MacEtch. (b) Segmented image after processing. Shading is used on the segmented image to highlight isolated particles. Once the image is segmented, the SEM scale bar can be used to calculate each particle’s area based on pixel count...... 135

Figure 87. Zoom view of (a) original SEM image post-etch (scale bar = 200 nm) and (b) image after edge detection and directionality correlation. The colors indicate

xvii

the edge directionality at that pixel location: 90-degree vertical (yellow), 0- degree horizontal (purple), +45-degree (turquoise) and -45-degree (red)...... 136

Figure 88. (a) Plot of etch anisotropy for numerous etch trials. Blue markers represent [100] wafers, red represent [111]. The size of the markers is proportional to the mean size of the metal particles on the substrate. (b) Plot of numerous etch trials highlighting size dependence. Edge angle near 90° is indicative of vertical etching, while lower angles indicate random etching for both plots...... 136

Figure 89. Etch process demonstrating a faithful pattern transfer; (a) original metal pattern (b) isometric view post etch (c) close-up detail highlighting ideal pattern transfer...... 137

Figure 90. SEM images of silicon nanostructures from (a) top and (b) profile views using a 3:2 HF:H2O2 8min MacEtch process with same Au film from Figure 89...... 138

Figure 91. MacEtch trial of 50 nm commercial gold nanoparticles (a) particles after deposition (b) ¾ view of substrate after MacEtch (c) profile view detail after MacEtch ...... 139

Figure 92. High resolution SEM image of silicon nanostructures formed by gold MacEtch with no indication of crystalline damage to the sidewall...... 140

Figure 93. (a) 10 nm silver island formation (b) profile view after 60 s MacEtch (c) profile view after 120 s MacEtch. Both etches used 2:1 HF:H2O2 solution...... 141

Figure 94. (a) 4 nm platinum film deposited on oxidized silicon at 250°C (b/c) profile view of substrate after etch indicating random etching direction and porous silicon formation...... 142

Figure 95. Profile view of (a) moderately p-type doped (1-10 Ω∙cm) and (b) highly p-type doped (1-5 mΩ∙cm) silicon nanostructures after 60s MacEtch in 2:1 HF:H2O2 solution ...... 143

Figure 96. Comparison of two metal patterns (top) and their resultant structures after MacEtch (bottom). The fully interconnected metal mesh pattern on the left results in isolated silicon nanostructures that collapse during the drying process while the island metal pattern on the right forms a structurally sound silicon nano-mesh...... 144

Figure 97. Comparison of (a) nitrogen blow dried and (b) CPD dried MacEtch samples from identical gold mesh metal patterns. Top images show top view of nanostructures and bottom images show profile view...... 145

Figure 98. ALD coating of silicon nanostructures with 40 Å of Al2O3. The wide view (a) demonstrates the uniformity of the coating, while the zoom view (b) reveals what appears to be a pinhole free film. The bright regions of the image are Al2O3 coated silicon, while the dark regions are crystalline silicon...... 146

xviii

LIST OF TABLES

Table 1. Material bandgap (temperature in parenthesis) and corresponding cutoff wavelength for commonly used compound semiconductors for infrared photodetectors. InGaAs bandgap is calculated for lattice matched condition to InP substrate...... 8

Table 2. List of Silicon material parameters used for SBD dark current calculations ...... 40

Table 3. Extracted Schottky barrier heights based on activation energy of Arrhenius plots (Figure 45 (b))...... 81

Table 4. Summary of measured and extracted parameters from NiSi SBDs. Φ퐵퐹, Φ퐵푉 and Φ퐵퐴 are the extracted SBH using the modified Fowler equation, Casalino’s Vickers approximation and Arrhenius analysis (IVT) respectively. All voltage dependent quantities, such as the quantum efficiency, are for a 1 V reverse bias...... 94

Table 5. Nominal parameters for T-SiQW designs that span the SWIR, MWIR and LWIR atmospheric windows. Barrier material is assumed to have equal effective mass to transverse mass in silicon. The wavelength column references the absorption wavelength expected from excitation from the ground state to first excited state energy of the well...... 124

xix

EXECUTIVE SUMMARY

In Chapter 1, I introduce several infrared (IR) imaging applications considering atmospheric transmission and photon sources. With these applications in mind, I discuss a variety of detector array architectures, both hybridized and monolithic, that are used for these applications. I build a case for building IR detector arrays monolithically, to leverage the technological advancements and low cost of complementary metal-oxide-semiconductor

(CMOS) image sensors designed for visible imaging.

The first research effort is described in Chapter 2 and is based on applying the concept of Schottky barrier detectors (SBDs), which is a proven approach to monolithic IR imaging on

CMOS image sensors. I reviewed the literature to determine state-of-the-art performance, and found that reported quantum efficiency (QE) of SBDs designed with a cutoff around 2 µm was poor relative to earlier research on SBDs designed with a cutoff around 5 µm (for thermal imaging applications). SBDs with the shorter cutoff wavelength are of particular interest for low cost IR imaging because they can be operated at or near room temperatures, in contrast to the longer cutoff wavelength designs which require expensive cryogenic cooling. To investigate this,

I performed the first thickness-dependent performance evaluation of nickel silicide (NiSi) SBDs, which feature a cutoff around 2 µm [4]. By investigating thicknesses near the percolation threshold of the NiSi film, I was able to demonstrate the highest reported QE of any silicide SBD with comparable cutoff wavelength to date. To fully characterize the tradeoff between absorption and internal quantum efficiency (IQE) of these devices, I developed a novel Fourier

xx transform infrared (FTIR) spectrometry-based measurement technique for measuring/modeling the absorption in these ultra-thin NiSi films accounting for all the parasitic losses of the substrate and mirrors in the structure. This unique approach was required for the analysis because standard measurement techniques, namely ellipsometry, are prone to error when performed on ultra-thin films. Using the absorption analysis and QE measurement, I extracted the IQE of the NiSi devices at each thickness and found the thinnest (1 nm) NiSi SBD had over an order of magnitude higher IQE than previously reported devices. I took this a step further by fitting the IQE spectrum to SBD IQE theory to extract the NiSi hot carrier attenuation length directly from device measurements, a first to my knowledge. With this information, I explored theoretical designs based on material parameters extracted directly from device measurements which show how resonant absorption designs and thinner NiSi layers could improve performance even further from what I demonstrated experimentally.

In Chapter 3, I introduce a second research effort based on a novel silicon-based quantum photodetector concept termed silicon quantum walls (SiQW). This architecture features vertically standing quantum wells or wires, which introduce discrete energy transitions in the IR that can be engineered for detection. I modeled the architecture using quantum mechanics and describe the theoretical performance advantages this architecture provides relative to other similar quantum devices that have been previously demonstrated. The primary impediment to demonstrating the SiQW devices is the fabrication of vertical quantum walls, which require lateral dimension < 8 nm. I investigated a promising top-down fabrication process known as metal-assisted chemical etching (MacEtch), which has previously been demonstrated to etch vertically for patterns > 50 nm. I found that shrinking the metal template dimensions altered the etch dynamics such that the etch directionality is dominated by the template geometry rather than the solution stoichiometry or crystal orientation, which are known to

xxi dominate the etch directionality for metal templates of larger dimension [2]. Using this knowledge, I developed a MacEtch fabrication process for creating vertical nanowalls/nanowires with lateral dimensions around 10 nm with excellent uniformity and reproducibility. While these structures fall short of reaching the SiQW dimension target of < 8 nm, the results provide a significant step toward realizing this promising detector architecture. In addition to this fabrication work, I perform an initial demonstration of atomic layer deposition for conformally coating these structures to realize the SiQW heterostructures.

The publications derived from this work include two peer-reviewed journal articles [2, 4] and two conference proceedings [1, 3], listed below.

[1] J. Duran and A. Sarangan, "Infrared absorption in MacEtch fabricated silicon quantum walls," in 2016 IEEE Photonics Conference (IPC), 2016, pp. 234-235: IEEE.

[2] J. M. Duran, A. Sarangan, Journal of Micro/Nanolithography MEMS, and MOEMS, "Fabrication of ultrahigh aspect ratio silicon nanostructures using self-assembled gold metal-assisted chemical etching," vol. 16, no. 1, p. 014502, 2017.

[3] J. Duran and A. Sarangan, "Internal Quantum Efficiency Dependence on Thickness of NiSi Schottky Barrier Photodetectors," in 2018 IEEE Photonics Conference (IPC), 2018, pp. 1- 2: IEEE.

[4] J. Duran and A. Sarangan, "Schottky-Barrier Photodiode Internal Quantum Efficiency Dependence on Nickel Silicide Film Thickness," 2019.

xxii

CHAPTER 1

BACKGROUND AND MOTIVATION

In the late 1960s, the complementary metal-oxide-semiconductor (CMOS) and charge- coupled device (CCD) were first introduced as new electronic devices with the potential to be used for solid-state imaging1. Several years later in 1975, Steve Sasson an electronics engineer working for Kodak, demonstrated the utility of the CCD by building the first prototype digital camera2. Nearly fifty years later, these two technologies are still the predominate components used for digital image capture. The persistence of these technologies can be largely attributed to the basis material they are fabricated from: silicon. Silicon comprises over a quarter of the earth’s crust by mass and is the primary material used in the over $300 billion semiconductor electronics industry3. This abundance and economy of scale has driven the cost of CMOS image sensors so low that even the most inexpensive cellular phones include one, while others include two or even three CMOS image sensors.

CCD and CMOS image sensors are not strictly photodetectors themselves, but rather architectures that convert incident light energy to electrical signal while also providing a mechanism for reading the resulting electrical signals from the imaging matrix. The photodetector element used in modern CCD and CMOS image sensors is the p-n photodiode. A generic pixel design for the CCD and CMOS image sensor architectures are shown in Figure 1.

Micro-Lens

Color Filter Amplifier, Reset, Column/Row Bus Transistors Metal or poly-Si

n-type n-type SiO2

p-type substrate p-type substrate

(a) (b)

Figure 1. Schematic of generic pixel architecture for (a) CCD and (b) CMOS image sensor (front-side illuminated)

The sandwiching of adjacent p-type and n-type doped regions in a p-n junction form a built-in energy potential and charge depleted region that prevents free majority carriers from either side of the junction from transporting across. This mechanism of blocking majority carriers serves to limit current through the device in the absence of light (i.e. reduce dark current). In contrast, minority carriers are free to transport across the junction (in one direction), which provides the basis for collection of photo-generated carriers in a photodiode.

Electron Built-in potential

Fermi-level

p-type Incident Light

n-type Hole

Figure 2. Band diagram of p-n junction photodiode with no applied bias.

Photons with sufficient energy can transfer their energy to bound charge carriers in the silicon lattice to generate an unbound electron-hole pair through the process of absorption. The minimum energy required for this type of absorption mechanism is defined by the material

2 bandgap (1.1 eV for silicon at 300 K). The wavelength of a photon is inversely proportional to the energy as defined by:

ℎ푐 1.24 퐸 = ⇒ 퐸(푒푉) ≅ (1) 휆 휆(휇푚) where 퐸 is the photon energy, ℎ is Plank’s constant, 푐 is the speed of light and 휆 is the photon wavelength. The bandgap energy of the material defines the wavelength sensitivity of a photodiode, limiting the detection of silicon photodiodes to wavelengths shorter than approximately 1.1 µm. This adequately covers the visual spectrum, which spans from about 400 nm (violet) to 700 nm (red). However, there is a growing need for image sensors with sensitivity beyond 1.1 µm, which requires a detector other than the perennial silicon photodiode.

1.1 The Electromagnetic Spectrum

The electromagnetic spectrum is the umbrella term that includes all known forms of radiant energy. This includes highly energetic ionizing radiation in the very short wavelength regime all the way to low-energy radio waves with wavelength measured in kilometers and beyond. While technically any wavelength regime can be imaged, this paper will focus on the visible and infrared portions of the spectrum. Humans are sensitive to the visual spectrum that roughly spans between the 400 nm and 700 nm wavelength range. This spectral sensitivity is an evolutionary response to the spectrum of light from the sun that illuminates the world around us, spanning the peak of the spectral output. This spectrum is governed by two primary factors: spectral emission of the sun and spectral absorption/scattering from the atmosphere. The infrared portion of the spectrum spans roughly between 700 nm and 1 mm, but not all regions of that spectrum are particularly useful for imaging. Suitable spectral bands for imaging require a photon source, low-loss transmission through the atmosphere, available optics for focusing and reasonably low-noise photodetectors; these requirements will be further discussed in the following sections.

1.1.1 Atmospheric Transmission

The earth’s atmosphere is composed of various gasses that absorb and scatter a significant portion of the electromagnetic spectrum. These gasses include H2O vapor, O2, CO2 and several others that govern the wavelength dependent transmission of the atmosphere

(Figure 3).

100 NIR SWIR MWIR LWIR 80

20 Transmission (%) Transmission

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Wavelength (µm)

Figure 3. Atmospheric transmission through a one nautical mile sea level path4

The spectral absorption gaps in the atmosphere are often referred to as windows due to their relative transparency. For imaging applications, the electromagnetic spectrum can be further delineated by these atmospheric windows into the following spectral bands of interest:

Visible (VIS): 0.4—0.7 µm

Near infrared (NIR): 0.7—1 µm

Short-wave infrared (SWIR): 1—2.7 µm

Mid-wave infrared (MWIR): 3—5 µm

Long-wave infrared (LWIR): 8—14 µm

While the atmospheric windows ultimately define the spectral bands of interest for imaging, the availability of photon sources and photodetectors further refines the imaging applications for these spectral bands.

1.1.2 Blackbody Radiation

The sun radiates because it is hot; in fact, all objects whose temperature is above absolute zero radiate. The precise temperature dependent emission spectrum of an idealized object, known as a blackbody (perfect absorber over all wavelengths), is described by Planck’s

Law.

2휋ℎ푐2 푀(휆, 푇) = (2) 휆5(푒ℎ푐⁄휆푘푇 − 1)

푀(휆, 푇) = spectral radiant exitance [W m-3]

휆 = wavelength of emission [m]

푇 = absolute temperature of blackbody [K]

ℎ = Planck’s constant [6.626 x 10-34 W∙sec2]

푐 = speed of light [2.998 x 108 m∙sec-1]

푘 = Boltzmann’s constant [1.381 x 10-23 W∙sec∙K-1]

The total power radiated (푃) from an object at a given temperature can be found by integrating

Planck’s Law over all wavelengths, resulting in the Stefan-Boltzmann Law:

2휋5푘4 푃 = 푇4 (3) 15푐2ℎ3 The peak emission wavelength can also be solved for by differentiating Planck’s Law and finding the root. The resultant expression is known as Wien’s Displacement Law:

휆푚푎푥푇 = 2898 휇푚 퐾 (4)

The above expressions provide a clear and simplistic relationship between an object’s temperature and its emission spectrum. As temperature increases, the total emission output power increases (at all wavelengths), while the peak emission shifts to shorter wavelengths. For a blackbody at 5778 K (surface temperature of the sun), the peak emission falls in the visible portion of the spectrum. For a blackbody at 295 K (room temperature), the peak emission falls in the infrared portion of the spectrum as shown in Figure 4 .

Figure 4. Blackbody spectral exitance for Sun (5778 K), incandescent light bulb (2400 K), human body (310 K) and room temperature (295 K)

The room temperature blackbody curve indicates the MWIR and LWIR spectral bands are ideal for imaging the natural radiant emission of objects, without the need for an external light source (such as the sun). For this reason, infrared radiation is often referred to as thermal radiation. Example applications for imaging in this portion of the infrared spectrum include night vision for military applications, medical imaging, climate studies and industrial monitoring of equipment and facilities.

1.1.3 Additional Photon Sources

Another natural photon source, provided by the atmosphere, is known as night glow or airglow. Night glow is a luminescence phenomenon driven by the excitation from cosmic rays, solar radiation and chemical reactions in the thermosphere. This luminescence shines brightest in the SWIR wavelength range as indicated in Figure 5.

1E-9

)

1 -

1E-10

2 -

1E-11

1E-12 Nightglow Only Nightglow + 0.25 Moon at 45° Altitude

Nightglow + 0.50 Moon at 45° Altitude Radiant (W Sterance cm Nightglow + 0.89 Moon at 45° Altitude

0.5 1.0 1.5 2.0 Wavelength (µm)

Figure 5. Spectral radiant sterance of night sky for various phases of the moon5.

Figure 5 indicates that the natural sky illumination due to night glow in the SWIR can provide comparable brightness to a full moon-lit night in the visible regime. Because night glow is independent of the moon phase, SWIR is an attractive alternative for lightweight night vision enhancement to replace image intensifiers that operate in the visible regime.

Photon sources discussed thus far have all been natural sources of light. Imaging systems that utilize these natural sources of light are categorized as passive imaging. Active imaging, in contrast, refers to imaging systems that include an artificial photon source. Lidar

(sometimes referred to as LiDAR, LIDAR or LADAR) stands for light/laser detection and ranging and is analogous to radar but utilizes the visible or infrared portions of the spectrum to improve resolution relative to radar systems that operate at radio frequencies. Lidar imaging systems with time-of-flight capability can capture not only the x and y spatial coordinates, but also the z

(depth) coordinate. For this reason, lidar is employed in topology mapping applications and is emerging in the consumer market for autonomous vehicle situational awareness.

Wavelength selection is an important aspect for lidar systems. Source/detector performance and cost, object reflectance, noise sources and eye safety are just some of the

7 considerations taken into account when developing a lidar system. Low cost detectors and sources exist in the VIS and NIR spectral bands, but range is ultimately limited for these systems due to eye safety requirements. Due to significant water and lens absorption, wavelengths beyond 1.4 µm can be used at higher powers with low risk of damaging the retina6. Higher source power enables longer range and higher signal-to-noise ratio (SNR) in lidar systems. Due to fiber communication technology for the telecommunication industry, sources at 1.55 µm are relatively cheap and efficient. These facts provide motivation for developing Lidar technology at longer wavelengths, but the major component missing for SWIR-based lidar is a low-cost image sensor.

1.2 Infrared Detector Array Architectures

To address the need for infrared imaging arrays, scientists and engineers have developed alternative architectures to the monolithic silicon photodiodes used in CMOS and

CCD arrays. One straightforward approach is to replace the silicon photodiode with a photodiode (or similar detector architecture) built in a narrow bandgap semiconductor.

Material Bandgap (eV) Cutoff Wavelength (µm)

7 In0.53Ga0.47As 0.75 (300 K) 1.65 InSb8 0.23 (77 K) 5.4 HgCdTe9 -0.261 – 1.61 (77 K) ≥ 0.77

Compound semiconductors with appropriate bandgaps for building photodetectors sensitive in the SWIR, MWIR and LWIR spectral bands exist and are commonly utilized for this purpose.

Notable materials include InGaAs for SWIR, InSb for MWIR and HgCdTe which can be tuned for

SWIR, MWIR or LWIR by controlling the material alloy composition. While fabrication of

8 photodiodes in these materials is relatively straightforward, integrating an array of these detectors to form an imaging architecture is where the challenge and cost grow, which is the subject of the next section.

1.2.1 Hybrid Focal Plane Arrays

The most common approach for fabricating an infrared imaging array is to build a silicon-based readout integrated circuit (ROIC) and hybridize it to a detector array made from an appropriate narrow bandgap semiconductor (Figure 6). The advantage of this approach lies in the performance benefits of utilizing high efficiency, low noise photodetectors with (potentially) full fill-factor to detect light, while also leveraging the mature silicon foundries for relatively low noise readout. The primary disadvantage of this approach is the cost and complexity of forming a hybrid array relative to low-cost monolithic arrays.

Detector Array

Silicon ROIC

Figure 6. Schematic of hybrid FPA illustrating indium bump bonded detector array to silicon ROIC.

Hybrid focal plane arrays (FPAs) begin with a substrate that is lattice matched (or closely matched) to the detector material of interest. The photodetector structure is grown epitaxially onto the substrate. This structure could be a simple p-n photodiode, a unipolar barrier structure10 or photoconductor, and can be composed of compound semiconductors (InGaAs,

InSb, HgCdTe) or quantum engineered materials (strained-layer superlattice, quantum well, quantum dot). Alternatively, for materials available in wafer format (e.g. InSb), the epitaxial

9 growth can be replaced with a thermal or implantation doping process directly into the wafer to form a homojunction photodiode. With the detector architecture in place, the wafer is then processed into an array of photodetectors which typically involves etch delineation, passivation and contact metal deposition. Indium interconnects are then deposited on each pixel and the array ground plane. Up to this point, all processes are done on the wafer scale, so many detector arrays can be processed in parallel. The detector wafer is then diced into individual detector arrays to finish the processing. Each detector array is individually aligned and mated to a silicon ROIC through (thermo-)compression bonding of the indium interconnects. Epoxy is wicked between the detector array and ROIC to provide mechanical rigidity, and the substrate is removed using diamond point turning and/or chemical/mechanical polishing. With the substrate removed, an anti-reflection (AR) coating is deposited on the remaining substrate. At this stage, the FPA is ready for packaging and integration into a camera system. A simplified example of a hybrid FPA process follower is illustrated in Figure 7.

(a) (f)

(b)

(g)

(c)

(h) (d)

(i) (e)

The hybrid FPA architecture has several performance benefits. Because the detector array is fabricated separately from the ROIC, each component can be individually optimized for maximum performance without compromise. The backside illumination geometry inherent in a hybrid FPA enables at or near 100% detector fill factor to maximize sensitivity. Finally, because no space on the ROIC unit cell needs to be dedicated to detector area, charge input capacity can be maximized, and additional space can be used in the unit cell of the ROIC to optimize performance.

The major downside of this approach is the cost. A commercial off-the-shelf 640x512

InSb FPA costs around $15ki. The ROIC component of that FPA can be purchased separately for

i Prices quoted in March 2016 from commercial manufacturer of IR FPAs, ROICs, and camera systems. ROIC cost based on price of a whole wafer divided by the number of good die.

11 about $650i. This indicates that the primary cost driver in hybrid FPA manufacturing is in the detector array fabrication and hybridization process. Considering a 3” InSb wafer can be purchased for around $1kii and can fit 30 detector arrays that are mostly processed in parallel, we can attribute a major component of the cost to yield and the significant die-level processing that must occur for each array. These processes include alignment and hybridization, substrate thinning and AR coating.

There are several technological and physical challenges related to the integration of narrow bandgap semiconductor detector arrays to silicon ROICs that has resulted in the persistence of indium bump flip-chip hybridization. Generally, smaller bandgap semiconductors are accompanied with greater thermally generated noise. To overcome this, infrared FPAs are cooled during operation to improve sensitivity. Cooling requirements are highest for LWIR, but are sometimes employed for SWIR arrays as well, depending on the application. A material’s coefficient of thermal expansion (CTE) describes the relative expansion/contraction of the material as a function of temperature. Because the CTE of silicon does not match the common semiconductors used for IR detector arrays, mechanical relief must be in place between the materials.

ii Price quoted in July 2010 from III-V substrate manufacturer.

Detector Array

Indium

ROIC

(a) (b)

Figure 8. Illustration of interconnect strain induced by CTE mismatch. (a) hybridized detector at bonding temperature (b) hybridized detector at cooled operating temperature

Indium is a highly malleable and ductile material that serves to provide both the necessary mechanical relief and electrical contact between the detector array and ROIC. A key parameter for accommodating the CTE stress is the physical distance between the detector array and ROIC, as the mechanical stress is inversely proportional to that distance11. This imposes a challenge as pixel pitch shrinks, because indium bump height must be maintained and therefore deposited at a higher aspect ratio. As a result, hybrid FPAs generally feature significantly larger pixels than can be achieved in monolithic arrays, further increasing the cost disparity between the two because overall chip area is a significant cost driver in the CMOS process.

Another important note about hybrid FPAs relates to innovation in ROIC technology. A

ROIC is essentially a CMOS imaging array without the space-consuming silicon photodiode; additionally, ROIC pixel pitch is around an order of magnitude larger than in CMOS imaging arrays. Theoretically, this should enable additional functionality and performance optimizations to fit in the unit cell of the ROIC. Unfortunately, these inherent benefits have not been leveraged. In fact, today’s commercial ROIC technology is significantly outdated relative to visible CMOS image sensors. Innovative technology introduced by the visible CMOS imaging array community includes: pixel-sharing12, record-breaking pixel count13, multiple exposure for wide dynamic range14, in-pixel digitization15, Tpixel/s readout16 and an industry-first stacked

CMOS image sensor with DRAM17.

1.2.2 Monolithic Infrared Focal Plane Arrays

While silicon photodiodes cannot be used for infrared sensing, alternative detector structures have been developed that are built on silicon wafers to enable monolithic IR FPAs.

These detector structures include photoemissive (Schottky barrier), extrinsic (impurity band) and thermal (micro-bolometer) detectors. These FPAs are significantly cheaper than hybrid

FPAs, but are limited by relatively low performance.

1.2.2.1 Impurity Doped IR Photodetectors

Impurity doped photodetectors operate on the principle that dopant impurities create localized energy states within the host material’s bandgap that require energy to be activated.

This energy is typically quite small (< 100 meV18), and therefore, dopants are readily activated by thermal excitations from the lattice, even at relatively low temperatures. Consequently, these detectors must operate at extremely low temperatures (< 20 K) where thermal excitation is not significant enough to ionize the impurities (known as freeze-out). The most basic impurity doped detector is a simple photoconductor which is commonly referred to as an extrinsic photodetector. These detectors are moderately doped, and therefore feature weak absorption, which requires employing abnormally thick detectors to obtain reasonable responsivity. To address this issue, blocked impurity band (BIB) detectors with significantly higher doping were developed19. BIB detectors feature a highly doped active region that enhances absorption, but also enables impurity band transport. To suppress dark current, the impurity band transport is blocked by employing a low doped “intrinsic” layer as illustrated in Figure 9. Because of the increased absorption, BIB detectors can be made reasonably thin (≤ 20 µm20) which improves optical cross talk in imaging arrays. BIB detectors have been demonstrated in Si:As21, Si:Ga22 and

Si:Sb23 among others.

Contact Impurity Band Absorber Intrinsic Blocking Layer

Contact

Figure 9. Band diagram of n-type blocked impurity band detector architecture under operating bias.

While these sensors do have a niche in a few applications requiring radiation-hardened, very long wavelength sensing, they are not widely used due to the extremely low temperature of operation.

1.2.2.2 Photoemissive Photodetectors

Photoemissive detectors are composed of an active absorbing emitter layer and a collector region. The active layer can be a highly-doped semiconductor semi-metal or metal layer. This architecture relies on a band misalignment between the emitter and collector region as the photo-collection mechanism. Highly doping a semiconductor will cause band gap narrowing,24 which introduces a band misalignment in the homojunction architecture. Another approach to designing the emitter-collector misalignment is through the use of a Schottky contact, which creates an electrical diode behavior25,26. The most widely explored Schottky photodiode is based on the PtSi/p-Si heterojunction27-30.

PtSi p-type Si

Figure 10. Band diagram of PtSi/p-Si Schottky photodiode.

The PtSi/p-Si Schottky photodiode has a convenient cutoff around 5 µm, making it appropriate for sensing across the MWIR spectral window, but requires cryo-cooling around 77

K. Monolithic PtSi arrays have been demonstrated with excellent uniformity and low noise at relatively low cost29-33. Despite these advantages, PtSi arrays have generally been replaced with

InSb and HgCdTe detector arrays because of their improved sensitivity, owed primarily to their superior quantum efficiency relative to PtSi arrays. There is an inherent tradeoff in engineering the PtSi layer thickness between maximizing absorption (thicker) and collection efficiency

(thinner). Modified Fowler emission theory can predict the quantum efficiency limit of PtSi detectors based on an optimized layer thickness for a given hot-carrier mean free path34. State of the art quantum efficiency resides around 1% at 4 µm with a resonant absorber35. Similar to

PtSi, IrSi has been demonstrated for use as a LWIR detector with cutoff wavelength between 9.4

– 12.4 µm depending on processing conditions36-38.

1.2.2.3 Thermal Detectors

Thus far, all of the previously discussed photodetectors can be broadly classified as photon detectors. The principle detection mechanism for these devices always employs the excitation of a charge carrier to overcome some barrier to conduction through direct energy transfer. The other broad classification of photodetectors is referred to as thermal detectors.

Thermal detectors rely on a physical property change in a material in response to a temperature

16 change. In contrast to photo detectors, thermal detector response is proportional to the incident power rather than the photon flux. Photon sensors feature a distinct cutoff wavelength that is associated with the barrier to conduction featured in these detectors (e.g. bandgap of a photodiode or Schottky barrier of a photoemissive detector). Thermal sensors, on the other hand, feature a characteristic “flat” spectral response over most wavelengths. A variety of techniques can be used to build thermal sensors, but the most commonly used for imaging arrays are bolometers (resistive), pyroelectric (capacitive) and cantilevers (mechanical).

Absorber Thermal Resistor Insulating Membrane Contact Reflector

ROIC

Figure 11. Profile schematic of microbolometer pixel.

Thermal detectors, regardless of type, share several commonalities that provide advantages relative to photon sensors. The thermal-sensitive materials used in these detectors do not need to be low-defect single crystals, unlike photon detectors. This enables inexpensive thin film deposition techniques to be used rather than expensive and lattice constrained epitaxial growth. Because there are no lattice matching constraints in thin film deposition processes, these detectors can typically be fabricated directly on silicon ROICs, which dramatically reduces cost relative to hybrid arrays. Another advantage of thermal sensors over photon sensors is their ability to provide acceptable performance without cooling. Photon sensors are highly susceptible to thermal noise and therefore must be cooled during operation.

Thermal sensors are typically operated uncooled or with temperature stabilization, which dramatically lowers the overall camera cost.

Because thermal sensors rely on temperature change in material(s), they must be fabricated with high thermal isolation, and their response time is therefore relatively slow. The thermal isolation requirement introduces challenging fabrication techniques involving suspended membranes using sacrificial layers. This complication has caused a disparity in array format size and pitch relative to arrays built from photon sensors. The relatively slow response time ultimately limits the practicality of using thermal detectors for applications that feature imaging of dynamic scenes. The time constant associated with heating and cooling the thermal detectors can create “streaking” or “tails” around moving objects in the scene. For platforms in constant motion, e.g. on an airplane, this streaking can render the camera unusable. Despite these disadvantages, the significant cost savings relative to photon sensors, due to the monolithic design and lack of cooling cost, has resulted in emergence of this technology in the consumer product space39; something that has not happened for other infrared imaging technologies.

1.2.2.4 Narrow bandgap CCD

Another approach to monolithic arrays is to completely abandon silicon in favor of a narrow gap semiconductor. The challenge of this approach is to incorporate the necessary logic, switching and amplification components associated with readout of charges generated by the detector array. Translating the CMOS process from silicon to another material system has major challenges and cost due to the significant optimization that has occurred over time in silicon.

CCDs, on the other hand, have shown some promise as a potential monolithic approach to imaging arrays in narrow bandgap semiconductors due to the relatively simplistic architecture.

The CCD architecture functions both as a photodetector and shift register, which provides a mechanism for converting photons to electrical charge and to subsequently transfer the matrix of generated charges out of the array. A metal-oxide-semiconductor (MOS) stack provides the

18 basic unit-cell architecture of a CCD which is operated in depletion mode. During exposure of the array, photo-generated charge accumulates at (surface channel) or near (buried channel) the semiconductor-oxide interfaces. During readout, gate voltages are modulated with clock sequences in appropriate phase to serially transfer charge out of the array through adjacent

MOS devices to the output register.

φ1 φ2 φ3 Poly-Si or Metal Insulator

p-type Silicon

Figure 12. Illustration of CCD shift register utilizing a 3-phase single-level gate40.

This relatively simplistic architecture has motivated investigation into the suitability of infrared sensitive materials such as InSb41,42 and HgCdTe43-46 for CCD imaging. Because charge is transferred through hundreds to thousands of pixels during readout, the primary metric of concern for a CCD is charge transfer efficiency (CTE). Silicon CCDs typically have CTE >

99.9995%47 which translates to a loss of about 1% for the distant corner of a 1k x 1k array. InSb

CCDs have been demonstrated with CTE as high as 99.5%,41 which translates to a loss of greater than 99.99% for the same far reaching corner. A better CTE of 99.9% has been demonstrated in

HgCdTe43, but that still results in an abysmal 86% loss for the furthest pixel in a 1k x 1k array.

The disparity in CTE between silicon and narrow bandgap CCDs can be attributed primarily to the superior oxide-semiconductor interface in silicon. While buried-channel CCDs reduce losses due to interface traps by pushing carriers away from the interface, inhomogeneities in the oxide morphology can create non-uniform fields that ultimately limit transfer efficiency41. The CTE limitation in narrow bandgap CCDs has prohibited its use for infrared imaging applications, and

19 research in this area has declined significantly since the early research in the late 1970s and early 1980s.

1.3 Chapter 1 Summary

Atmospheric transmission windows in the infrared define spectral bands that can be utilized for imaging applications. Within these bands, photon sources generally define the application space. The SWIR (1 – 3 µm) spectral band can be exploited for night vision based on night glow, irrespective of moon conditions. It is also a promising band of interest for lidar applications due to the availability of low cost, high performance sources and relative eye safety in contrast to shorter wavelengths. Because many molecules feature unique absorption features in this wavelength range, the SWIR spectral band is also useful for spectral interrogation for identifying/typing materials for medical, military and industrial applications.

The MWIR (3 – 5 µm) and LWIR (8 – 14 µm) bands are primarily useful for imaging the natural thermal emission of objects. Emission intensity is greatest in the LWIR for objects around room temperature; however, MWIR detectors can be fabricated with lower cooling requirements, and the shorter wavelength provides a resolution advantage for imaging systems. These imaging applications, primarily funded by the defense industry, have driven innovation primarily in hybrid FPAs due to their superior performance characteristics. While significant development effort has refined detector performance and hybridization reliability, ROIC technology simply does not provide feature/performance parity relative to visible CMOS imaging arrays.

Monolithic silicon arrays utilizing a variety of alternative detector architectures to the photodiode are an intriguing alternative to the comparatively expensive hybrid FPA. Arrays of this type can be developed to leverage innovations in visible CMOS image sensors quickly due to processing compatibility. The major weakness of these monolithic arrays is performance,

20 fueling the need for improved performance infrared photodetectors based on silicon technology.

CHAPTER 2

SILICIDE-BASED SCHOTTKY BARRIER PHOTODETECTORS

Schottky-barrier detectors (SBDs) based on silicide/silicon heterostructures is a proven low-cost solution for monolithically integrated infrared photodetectors on silicon. The inherent silicon compatibility of these heterostructures has driven the broad interest in these detectors for photonic integrated circuits and infrared imaging arrays. The photodetection process for

SBDs is illustrated in Figure 13. Carriers in the metal or silicide layer are excited by incident radiation. Hot carriers then transport through the metal and are emitted into the silicon if the kinetic energy and momentum of the carrier toward the barrier is sufficient.

ΦB

(a) (b)

Figure 13. Illustration of photoemission in p-type (a) and n-type (b) SBDs.

For an ideal metal/n-type semiconductor interface, the Schottky barrier height (Φ퐵) is dependent simply upon the metal work function (Φ푀) and semiconductor electron affinity (휒) by the Schottky-Mott rule: Φ퐵 = Φ푀 − 휒. Similarly, for an ideal metal/p-type semiconductor interface, the barrier height is given by: Φ퐵 = 퐸푔 − (Φ푀 − 휒), where 퐸푔 is the bandgap energy of the semiconductor. From this idealized relationship, it is apparent that any metal whose work function falls within the semiconductor bandgap will form a Schottky barrier to both n-

22 type and p-type doped surfaces and that the sum of those Schottky barriers will equal the semiconductor bandgap, i.e. 퐸푔 = Φ퐵푛 + Φ퐵푝. The Schottky-Mott rule also suggests that when

Φ푀 ≤ 휒, an ohmic contact between metal and n-type semiconductor should be formed; similarly, Φ푀 ≥ 휒 + 퐸푔 should form an ohmic contact to p-type semiconductor. Although it is often referenced, real semiconductor/metal interfaces almost never obey the Schottky-Mott rule and instead are governed by surface states at the interface40. In fact, no known metal forms an ideal ohmic contact to moderately doped n-type silicon, despite several metals having work functions that ought to satisfy this condition40,48-50. Silicon ohmic contacts are instead formed by pairing a highly doped silicon surface with a metal/silicide that forms a small Schottky barrier. In this configuration, the silicon depletion width formed by the Schottky barrier narrows significantly due to the high doping, and a tunneling ohmic contact is formed.

The most thoroughly studied material system in this class of detectors has been PtSi for thermal imaging applications in the MWIR band29-31,33,35,51, but several other metal/silicide material systems including those derived from the metals: Au52-58, Ni59-62, Cu63-65, Pd66,67, Co68,69 and Ir36-38,70,71 among others. An unfortunate commonality amongst all of these SBDs is poor external quantum efficiency (EQE or simply QE) that is typically < 1% across the spectral band if interest. In an effort to improve EQE, a variety of innovative device architectures such as detectors with plasmonic52-56,58,72-79 and photonic cavity65,80-84 resonant absorbers and integrated waveguide detectors53,56,58,60,62,63,77,85-87 have been explored. Despite these efforts, reported EQE falls between 0.001—1 % of theoretical maximum.

Figure 14. Reported external (square) and internal (diamond) quantum efficiency for various metal/metal-silicide Schottky-barrier photodetectors at 1.55 µm36,52- 60,62,63,65,66,79,84,88. Blue marker-fill indicates standard front-side or back-side illuminated detectors, green indicates plasmonic resonant detectors, red indicates waveguide integrated detectors and purple indicates resonant-cavity-enhanced detectors. The dashed line represents the theoretical maximum quantum efficiency based on the barrier height, assuming a sharp emission threshold34.

Figure 14 shows a collection of reported EQE (calculated from responsivity when necessary) for a variety of silicide Schottky barrier detectors operating at 1.55 µm. Barrier height in Figure 14 is based on the reported value (typically measured optically and/or electrically). Reports of SBDs that exhibited gain were purposely omitted from this chart, as gain obfuscates the EQE of a device.

The goal of this chapter is to describe the basic phenomenology that dictates the EQE of

SBDs, employ device characterization techniques to identify what the primary inefficiencies of a typical SBD are, and utilize that information to engineer SBDs with improved EQE.

Photodetector EQE is determined by the optical (absorption) and electrical (collection or internal quantum) efficiencies simply by

휂푒 = 퐴푎휂푖 (5) where 휂푒 is the EQE, 퐴푎 is fractional absorption in the active region of the detector and 휂푖 is the internal quantum efficiency (IQE). Maximizing EQE is therefore simply a matter of maximizing

24 absorption and IQE in the detector. In practice however, absorption and IQE are often coupled by the detector geometry in a contentious way; in many cases, for example, increasing the detector thickness increases absorption at the cost of decreasing IQE. This tradeoff between absorption and IQE is at the forefront of SBD design. Despite this important balance for optimization, IQE and absorption efficiency are rarely if ever reported in SBDs. This lack of reported data has created an uncertainty over which efficiency mechanism is primarily responsible for the large discrepancy between theoretical max and reported EQE of SBDs.

2.1 Internal Quantum Efficiency

To understand IQE of SBDs, first consider a thick metal/silicide film on a semiconductor.

In this configuration, the detector is illuminated through the semiconductor and into a mathematically infinite metal film. Practically, this occurs anytime the metal thickness is significantly greater than the skin depth and hot carrier attenuation length: 푡 ≫ δ, Le, Lh. For simplicity, the following discussion will focus on electrons in a metal/n-type SBD, but an analogous treatment can be made for holes in a metal/p-type SBD. The following derivation reproduces the work of Scales and Berini for thick and thin film SBDs34.

퐸1

퐸 ℎ Φ퐵

퐸퐹

퐸0

Figure 15. Energy band diagram of photoemission process in SBDs (n-type semiconductor).

In Figure 15, an electron is excited from initial energy state 퐸0 to excited state 퐸1 by a photon with energy ℎ휐. Because the average thermal energy (퐸푇 = 푘퐵푇 = 0.026 푒푉 at 300 K)

89 is insignificant relative to the Fermi energy (퐸퐹 = 4.35 eV for NiSi ) we can safely assume

25 electrons occupy all of the available energy states up to the Fermi energy. This implies the excited electron must have excess energy within the range: 0 < 퐸 < ℎ휐. For emission of the hot electron to occur, the momentum of the electron normal to the barrier interface must have a kinetic energy greater than or equal to the barrier height. Assuming the excess energy of the hot electron is purely kinetic, the following can be written

(ℏ푘 )2 퐸 = (6) 2푚 where ℏ푘 is the electron momentum and 푚 is the electron’s mass. From this relationship, the emission condition can be written

2 (ℏ푘 ) ,푥 > Φ (7) 2푚 퐵 where ℏ푘 ,푥 is the electron momentum in the x-direction (toward the barrier). The escape momentum ℏ푘푒,푥 is therefore

ℏ푘푒,푥 = √2푚Φ퐵 (8)

A hot electron in this system has equal probability of momentum in all spatial directions, but only the subset of momentum vectors with x-component equal to or greater than the escape momentum will emit over the barrier. This concept can be visualized as a k-space sphere of possible momenta, with a solid angle Ω푠 that defines the escape cone. A cross section of this sphere is illustrated in Figure 16.

푘

Escape Cone 푘Ω

Ω푠 푘푥 푘푒,푥

Figure 16. Illustration of escape cone (green shaded region rotated about 푘푥 axis) defined by escape momentum vector 푘푒,푥 with solid angle Ω푠.

The probability of emission 푝 for an electron with excess energy 퐸 is then given simply by a ratio of the escape cone solid angle Ω푠 to that of the whole sphere Ω푘.

2휋 Ω Ω ∫ ∫ sin휃푑휃푑휑 1 푠 0 0 푝 (퐸 ) = = = (1 − cosΩ) (9) Ω푘 4휋 2

Using the geometry from Figure 16 and Equations 6—9, it follows:

1 Φ퐵 푝 (퐸 ) = (1 − √ ) (퐸 > Φ퐵) (10) 2 퐸 which provides a simple formulation of the escape probability of a hot carrier as a function of the excess carrier energy and barrier height. IQE can be understood simply as a ratio between the number of energy states that result in emission 푁 and the total number of possible excited energy states 푁푇 initiated by absorption.

푁 휂푖 = (11) 푁푇

As discussed previously, excited electrons in the metal can have excess energy anywhere in the range between 0 and ℎ . It should be noted that this distribution of possible excited energy states is the first and fundamental limitation to IQE for photoemissive detectors without a bandgap in the absorber layer. In contrast, a detector with an absorber that has a bandgap prohibits excitation of carriers to an energy state within the gap, which forces absorption to

27 provide excess carrier energy of at least the bandgap energy. For this reason, the theoretical quantum efficiency limit of a Schottky barrier photodiode is fundamentally capped, while the theoretical quantum efficiency of detector with a bandgap can be 100% for excitation energies above the bandgap energy. This fundamental limit of Schottky barrier detectors is plotted in

Figure 14 for an excitation wavelength of 1.55 μm, which approaches 100% only for a vanishing barrier height relative to the excitation energy. Because there is no bandgap in the metal and

ℎ ≪ 퐸퐹, we can model the density of states 푔(퐸) as a constant over the energy range of interest:

ℎ휈 푁푇 = ∫ 푔푑퐸 = 푔ℎ (12) 0

To describe the number of emitted carriers, we consider only carriers with energy greater than the barrier and include the probability of emission:

2 ℎ휐 1 Φ 푁 = ∫ 푔푝(퐸 )푑퐸 = 푔ℎ휐 (1 − √ 퐵) (13) 2 ℎ휐 Φ퐵

Substituting Equations 12 and 13 into Equation 11 provides the following expression for the IQE of thick metal SBDs:

2 1 Φ 휂 = (1 − √ 퐵) (14) 푖 2 ℎ휐

It has been demonstrated that an improvement in the emission probability for SBDs can be achieved by employing thin metal layers51. If the metal film thickness is on the order of the hot carrier attenuation length or thinner, hot carriers experience multiple opportunities for emission due to reflections at the metal/semiconductor and metal/dielectric interfaces34,90. The following treatment of the hot carrier multi-pass process relies on several assumptions.

Absorption in the metal film is treated as uniform, which is reasonable considering the film

28 thicknesses of interest are partially transparent and rely on multiple passes to absorb the light.

In addition, the layer thickness is orders of magnitude smaller than the wavelength of light, so optical resonances will not occur within the film itself. As was assumed when deriving the IQE for thick films earlier, excited carriers are assumed to have excess energy 0 < 퐸 < ℎ that is isotopically distributed in momentum space. Carriers that are not emitted at the metal/semiconductor interface are assumed to be reflected, and carriers that reach the metal dielectric interface are also assumed to be reflected; these reflections are considered elastic and diffuse. This implies carrier reflection at the interface does not result in energy loss of the carrier, and incident carrier momentum has no influence on reflected carrier momentum. Hot carriers, as they traverse the metal film, will be reduced in numbers due to emission, while remaining carriers will have a reduction in energy as they experience collisions with phonons and other carriers during transport. If we assume, for simplicity, that a hot carrier with initial excess energy 퐸0 travels a distance of 2푡 for each round trip after reflection at the metal/semiconductor interface, we can write the excess energy 퐸푛 after 푛 round trips as:

2푛푡 − 퐸푛 = 퐸0푒 퐿 (15) where 푡 is the metal film thickness and 퐿 is the hot carrier attenuation length. The total number of possible round trips 푛 is determined by when the excess energy 퐸푛 = Φ퐵, given by the integer part of:

퐿 퐸0 푛 = ln ( ) (16) 2푡 훷퐵

The total emission probability grows with each round trip a hot carrier makes through the film, while the total population of hot carriers is reduced by the emission process itself. This process is illustrated in Figure 17. Using the probability 푝푘 of emission for a carrier with energy

퐸푘 from Equation 10, we can write the aggregate thin film probability of emission 푃0(퐸0) for a hot carrier with initial energy 퐸0 as:

푛−1

푃0(퐸0) = 푝0 + (1 − 푝0)푝1 + (1 − 푝0)(1 − 푝1)푝2 + ⋯ + 푝푛 ∏(1 − 푝푘) (17) 푘=0 퐸 0 −2푡 퐿 퐸0푒 푝0

−4푡 퐿 퐸0푒 (1 − 푝0)푝1

−2푛푡 퐿 퐸0푒 (1 − 푝 ) (1 − 푝 )푝 0 푛−1 푛

Figure 17. Illustration depicting the energy loss and probability of emission per pass through the film.

Following an analogous treatment as was described for the thick film case, we can write the IQE for the thin film condition as

1 ℎ휈 휂 = ∫ 푃 (퐸 )푑퐸 (18) 푖 ℎ 0 0 0 Φ퐵

ℎ휈 푛 푘−1 1 Φ퐵 Φ퐵 1 Φ퐵 휂푖 = ∫ (1 − √ ) + (∑ (1 − √ ) ∏ (1 + √ )) 푑퐸0 (19) 2ℎ 퐸0 퐸푘 2 퐸푗 푘=1 푗=0 Φ퐵

where 푃0 is given by Equation 17 and expanded along with 푝푘 from Equation 10 to form

Equation 19. The final expression is in the form of a definite integral of a sum of a cumulative product which can be computed numerically.

Figure 18. Predicted IQE for several different barrier heights (as labeled) using the Scales/Berini model as a function of L/t. Illumination wavelength is 1.55 μm. The flat portion of each curve for L/t near zero is the theoretical IQE for a thick device.

Figure 18 demonstrates how the IQE of SBDs increases with increasing hot carrier attenuation length, decreasing layer thickness or lowering Schottky barrier. The hot carrier attenuation length is the only parameter that increases IQE without penalty, but is generally considered a material property and has not been proven to be conducive to engineering.

Decreasing layer thickness has an absorption penalty, while lowering the Schottky barrier has a noise penalty in the form of increased dark current. The relationship of these tradeoffs directs the primary considerations for choosing a particular metal or silicide material for SBDs.

Favorable properties include high hot carrier attenuation length, thin percolation thickness and the lowest barrier height that meets the dark current requirements at the desired operation temperature.

The above treatment handles high-yield devices with theoretical consistency (i.e. IQE approaches the theoretical limit as the photon energy and L/t approach infinity). The limitation is in the predictability of low-yield devices (i.e. thick devices or small L/t). First, the predicted

IQE, particularly for thick SBDs, is much higher than reported values (see Figure 14).

Additionally, the IQE vs L/t plot shows an abrupt increase in the IQE as the theory transitions from IQE of a thick device to a “thin” device, rather than a gradual one as would be expected.

Finally, the thick device IQE does not depend on the hot carrier attenuation length, which should influence the IQE of thick silicide SBDs. To handle the treatment of low-yield devices, we can look at the most cited theoretical treatment of IQE for SBDs as given by Vickers90:

퐼푄퐸 = 퐹(Φ퐵) ∙ 푃(푡) (20)

푡 ∞ 푡 0.5 − 퐸 ( ) 푡 −푥푡 퐿 − 3 퐿 − 푒 푃(푡) = (1 − 푒 퐿 + 푒 퐿) ; 퐸 (푥) = ∫ 푑푡 (21) 푡 푛 푛 푡 1 − 퐸 ( ) 푡 2 퐿 1

∞ 2 2 ℎ휐−Φ 푖 1 (ℎ휐 − Φ퐵) 휋 1 퐵 2 푘퐵푇 퐹(Φ퐵) = ( + (푘퐵푇) ( + ∑ 2 (−푒 ) )) (22) 4퐸퐹ℎ 2 6 푖 푖=1 where 퐹 is known as the Fowler factor and 푃(푡) is the thickness-dependent scattering term.

The Fowler factor describes the fraction of hot carriers whose energy and momentum satisfy emission over the barrier. The scattering term describes the probability that carriers with sufficient energy are scattered off of phonons or the metal interfaces such that the momentum also satisfies emission before it collides with another carrier and loses its energy. It is from this term that the theory of increased collection efficiency with decreasing film thickness is quantified.

One issue with Vickers’ model is the unphysical results when the model is pushed to the limits of wavelength and 푡 퐿 ratio approaching zero (IQE grows unbounded); this limits the formulation to a low-yield solution. The model is also inconsistent with expectation for 푡 퐿 approaching infinity, as the modeled IQE continues to drop rather than saturate as expected.

Another issue with the model is the relative complexity of the formulas that comprise the model. The scattering term includes exponential integral formulas, and the Fowler factor includes a polylogarithm function. These functions are computationally expensive and inhibit

32 the fitting of experimental data to the model. The computational complexity of the model was addressed by Vickers originally with the following simplification:

푡 퐿 − 푡 푃(푡) ≈ √1 − 푒 퐿; ≥ 0.35 (23) 푡 퐿

2 1 (ℎ휐 − Φ퐵) lim 퐸퐹 ≈ (24) 푇→ 0 퐾 8퐸퐹 ℎ휐

1 In practice, the scattering and terms are often replaced with a constant known as the 8퐸퐹 quantum efficiency coefficient. This form is referred to as the modified Fowler equation and is by far the most common method for analyzing the quantum efficiency of SBDs. Extraction of the barrier height and quantum efficiency coefficient is accomplished by a linear fit of ℎ휐 vs

√퐼푄퐸 ∙ ℎ휐, known as a Fowler plot. Analysis using the modified Fowler equation is easy to implement and therefore popular, but is an empirical fit that doesn’t provide insight into the physical parameters that govern the IQE of the devices (i.e. the hot carrier attenuation length).

In addition, the modified Fowler equation is based on assumptions that aren’t valid at room temperatures and does a poor job fitting IQE near the cutoff (leading to underestimation of the barrier height).

Recently, Casalino has addressed the challenges with Vickers’ rigorous model by developing approximate formulas for the Fowler Factor and scattering term that significantly improve the accuracy relative to the approximations described above, while preserving the thickness-dependent scattering term91.

푡 푡 퐿 − −4.1 푃(푡) = (√1 − 푒 퐿 + 0.1 ∙ 푒 퐿) (25) 푡

2 2 ℎ휐−Φ ℎ휐−Φ 1 (ℎ휐 − Φ ) 휋 −1.07 퐵 −1.07 퐵 퐵 2 푘 푇 푘 푇 퐹(Φ퐵) = ( + (푘퐵푇) ∙ ( − 1.545 ∙ 푒 퐵 + 0.722 ∙ 푒 퐵 )) (26) 4퐸퐹ℎ휐 2 6

Using Equations 25 and 26 as inputs to Equation 20 provides a long but computationally efficient expression for the device IQE that can be used as a physical model for fitting. Despite all the terms, the only unknown variables in this expression are the NiSi Fermi energy 퐸퐹 (4.35

89 eV ), the SBH Φ퐵 and the hot carrier mean free path 퐿. This approximation to Vickers’ model has the same “low yield” limitation, but addresses the computational challenge of fitting the model to experimental data.

Figure 19 compares the IQE models between Scales/Berini and Vickers as a function of

퐿 푡. Because Vickers’ model includes an extra parameter (퐸퐹), the model is plotted for several different 퐸퐹 values for comparison. The models clearly disagree, the degree with which is dependent on 퐸퐹. While the Scales/Berini model is the most physically consistent, e.g. constant

IQE for small L/t and asymptotic approach to theoretical max as L/t approaches infinity, the

34 predicted IQE appears to be too high when compared to experimental results (see Figure 14).

Reviewing the Scales/Berini model critically, the primary weakness appears to be the predicted

IQE result of a thick silicide film (Equation 14), which doesn’t depend on the hot carrier attenuation coefficient, as expected. This formula predicts an IQE that is significantly higher than experimental results and likely needs adjustment to properly scale the model. Because this formula resides within the infinite series summation for the thin film case, the entire curve depicted in Figure 18 would drop with a corresponding correction to the thick film IQE formula.

For this reason, and because the Vickers’ model has been shown to be consistent with Monte

Carlo simulations92, I will use it (with Casalino’s approximation) for fitting experimental data to theory.

The inconsistencies outlined above highlight the challenge of accurately and confidently predicting SBD IQE performance as a function of thickness using existing models. This challenge is exacerbated by unavailable and otherwise often conflicting reports on the hot carrier attenuation length of various metal/silicide films. Because there is also an inadequate number of experimental reports of SBD IQE, particularly as the metal/silicide thickness approaches the film percolation threshold, it is important to investigate this experimentally.

2.2 Dark Current

Maximizing SNR is a primary consideration when designing any photodetector. For

SBDs, dark current represents the noise component of SNR. Dark current, as it sounds, is the current that flows through the device when no illumination is present. The noise associated with dark current arises from the statistical fluctuation of dark current over any period of time.

This statistical fluctuation is known as shot noise, or Poisson noise, and arises due to the discrete nature of the charges (electrons and holes) that comprise the dark current. The fluctuation of dark current over a given time period is therefore dependent upon the average number of

35 charges that arrive over that time period such that 휎 = √푁 where 휎 is the standard deviation and 푁 is the average number of charges. This statistical behavior indicates that dark noise increases as the square root of the average dark current, leading to the conclusion that reducing the dark current in a device translates to reducing the noise. It should be noted that “skimming” of the dark current by means of an electronic circuit does not reduce dark noise directly.

Skimming can, however, be practically useful for an imaging system with limited charge capacity by enabling longer integration time, which reduces relative dark noise via averaging. It should also be noted that the photo signal in photodetectors is subject to shot noise as well due to the discrete nature of photons and the photo-excited charges. Therefore, the photon shot noise in a detector increases as the square root of the number of photons collected as signal, while the relative noise decreases as the reciprocal square root of the collected photons. When photo signals are very high or dark current is sufficiently low, the photodetector can be said to be photon, background or signal shot noise limited, which all reference the same condition; under this condition, the only way to improve SNR is to integrate longer and/or improve quantum efficiency. Additional detector noise sources include amplifier gain excess noise, Johnson noise and 1/f (flicker) noise. These additional noise components are typically negligible relative to dark current and photon shot noises for SBDs in imaging systems.

The primary dark current processes in an SBD include thermal excitation of carriers that can transport over the barrier (thermionic emission) or tunnel through the barrier (quantum mechanical tunneling). The former process is primarily responsible for the reverse bias characteristics for moderately doped Si SBDs, while the latter process is significant in tunnel junction ohmic contacts (highly doped Si SBDs) and reverse bias characteristics of SBDs at low temperature operation, when thermionic emission probability is low.

Thermionic Emission

Quantum Tunneling

퐸퐹

Figure 20. Illustration of dark current mechanisms in SBDs.

Richardson and Dushman have derived the current voltage relationship due to thermionic emission93 as:

∗∗ 2 푞훷퐵 푞푉푏 퐽푅 = 퐴 푇 exp (− ) [1 − exp (− )] (27) 푘퐵푇 푘퐵푇

∗∗ where 푉푏 is the bias across the junction and 퐴 is known as the effective Richardson constant.

The effective Richardson constant is related to the probability of electron emission over a barrier in the presence of optical phonons. This “constant” depends on the electric field in the semiconductor but varies only slightly over the electric field range typical of SBD photodetector operation, which validates the treatment of this parameter as a constant. For electrons, 퐴∗∗ ≅

112 (A cm−2K−2) and for holes, 퐴∗∗ ≅ 30 (A cm−2K−2)40.

The Richardson Dushman equation is in a form similar to that of a pn junction diode, featuring a forward turn-on voltage and reverse saturation current. It is well known that SBDs do not exhibit strict reverse saturation current, instead featuring a gradual increase in current with increasing reverse bias. The soft reverse saturation current in SBDs can be explained by barrier lowering due to image-force charges and in some cases lowering due to a static dipole layer at the metal-semiconductor interface94. Image-force lowering is a result of charge in the semiconductor approaching the metal interface attracting charge of the opposite type in the metal. The induced charge in the metal creates a force of attraction to the incoming charge

37 from the semiconductor, in effect lowering the barrier for emission. The change in barrier height ΔΦ퐵퐼퐹 due to image-force lowering is dependent on maximum field 퐸푚 in the semiconductor and the permittivity of the semiconductor 휀푠.

푞퐸푚 ∆Φ퐵퐼퐹 = √ (28) 4휋휀푠

While image force lowering is present for all SBDs, static lowering is found in only some SBDs.

Static lowering occurs when the metal/semiconductor interface is free from any oxides or other contaminates, enabling the wavefunctions of electrons in the metal to penetrate the semiconductor. This effect creates an electrostatic dipole layer at the interface which creates a field-dependent lowering of the barrier. Because this effect is slight, it is common to use a first- order Maclaurin series approximation to describe the barrier lowering field dependence

ΔΦ퐵푆 ≈ 훼푠퐸푚 (29) where 훼푠 ≡ 푑Φ퐵0 푑퐸푚 and has units of length. With these two lowering terms, we can write the field-dependent Schottky barrier height as follows:

푞퐸푚 Φ퐵 = Φ퐵0 − √ − 훼푠퐸푚 (30) 4휋휀푠 where Φ퐵0 is the intrinsic barrier height. It is worth noting that the intrinsic barrier height is not the zero-bias barrier height, since the electric-field strength at zero bias for an SBD is nonzero.

Substituting Equation 30 into Equation 27 produces a more accurate expression for the current- voltage relationship of SBDs that models the soft reverse saturation current accurately. To implement this model however, we need to express the maximum electric field 퐸푚 in terms of known parameters such as applied bias, temperature, carrier concentration and bandgap.

The electric field metal semiconductor junction is similar to a one-sided abrupt pn junction, where the maximum field is located at the interface and decreases into the depletion region of the semiconductor. The maximum field strength can be written as:

2푞푁 푘퐵푇 퐸푚 = √ (휙푏푖 − 푉푏 − ) (31) 휀푠 푞 where 푁 is the doping concentration and 휙푏푖 is the built-in potential of the junction. Making the standard assumptions for deriving the Shockley equation (i.e. abrupt depletion region, the

Boltzmann approximation is valid, low minority carrier injection and no generation- recombination in the depletion region) we can write the built-in potential with reference to the difference between the Fermi-level and conduction band minimum 휙푛 (for n-type SBD):

푛 휙푏푖 = Φ퐵 − 휙푛 = Φ퐵 − (퐸푔 − 퐸푖 − 푘퐵푇ln ( )) (32) 푛푖 where 퐸푖 is the intrinsic Fermi level and 푛푖 is the intrinsic carrier concentration. These intrinsic parameters are both functions of the effective density of states:

퐸푔 푘퐵푇 푁푉 퐸푖 = + ln ( ) (33) 2 2 푁퐶

퐸푔 푛푖 = √푁퐶푁푉 exp (− ) (34) 2푘퐵푇

where 푁퐶 and 푁푉 are the conduction and valance band effective density of states respectively.

The effective density of states is dependent on temperature and is written as:

3 2휋푚 푘 푇 2 푁 = 2 ( 푒, ℎ 퐵 ) (35) 퐶,푉 ℎ2 where 푚 푒 and 푚 ℎ are the density-of-state effective masses of the conduction and valance bands respectively. To thoroughly account for all temperature effects, we can model the temperature dependence of the bandgap using an empirical formula:

훼푇2 퐸 (푇) = 퐸 (0) − (36) 푔 푔 푇 + 훽 where 훼 and 훽 are empirical fitting parameters. Equations 27–36 includes all of the formulas necessary to accurately model the current/voltage characteristics of SBDs under typical

39 operation conditions for imaging. Several material parameters are needed for this calculation and are listed in Table 2 for silicon.

Table 2. List of Silicon material parameters used for SBD dark current calculations

Parameter Value

퐸푔(0) 1.169 (eV) 훼 4.9E-4 (eV/K)

훽 655 (K)

휀푠 11.9 휀0 (C/V-cm)

푚 푒 1.08 푚0 (kg)

푚 ℎ 0.81 푚0 (kg)

2.3 Device Fabrication

There are several different methods for forming silicide/silicon heterojunctions including direct deposition of silicide, deposition of elemental metal and subsequent annealing and implantation of metal with annealing. I’ve chosen to use the elemental metal deposition followed by annealing process for several reasons: angstrom-level thickness control, ability to produce clean and abrupt interfaces, wide availability of metals, low cost, excellent uniformity and high purity. Because device IQE is a strong function of the silicide thickness, the angstrom- level thickness control of this method will be instrumental in exploring device performance of ultra-thin layers approaching the percolation thickness of the metal.

In the subsequent sections, I will discuss a variety of SBDs I fabricated and tested. I developed a general process follower that I used for all SBD fabrication, which I will outline here.

Fabrication of the SBDs begins with a double-side polished (DSP) Si wafer with resistivity between 1-10 Ω-cm. Wafers are first cleared of organic contaminates using a solvent cleaning procedure (Appendix A). An image reversal photolithography process using AZ 5214E resist

(Appendix A) is then used to define the liftoff pattern for the metal (to be formed into silicide)

40 deposition. The image reversal process produces a negatively tapered sidewall that is useful for liftoff processing. To clear the sample of any resist processing residues, the sample is exposed to an oxygen plasma in a barrel asher for 4 min (200 W). This clears the developed areas from residue but oxidizes the silicon surface. Immediately prior to loading the sample for metal deposition, the sample is dipped in a 10:1 volume ratio of deionized (DI) water:buffered oxide etchant (7:1 NH4F:HF) for 20 s. The sample is then immediately rinsed with DI water and thoroughly dried with a nitrogen blow gun. This pre-deposition acid dip completely clears the silicon of any oxide without creating any visible pitting of the surface that can form when exposing bare silicon to buffered oxide etchant (BOE) for too long. Metals are deposited using e-beam evaporation at a base-pressure of around 3 µTorr. Thickness control is provided by a quartz crystal thickness monitor calibrated to deposit at a rate of 0.5 Å/s. A metal liftoff process is then used to remove the unwanted metal and clear the wafer of resist (Appendix A). The metal patterned wafers are then annealed at a temperature appropriate for the silicide phase of interest. Annealing was typically performed using a rapid-thermal annealing oven in a nitrogen purged environment for 1 min. It was found that in some cases, for example nickel, the annealing process couldn’t be controlled at low enough temperature to achieve the desired silicide phase. In this case, annealing was performed on a hotplate under vacuum for 5 min. It should be noted that reported annealing temperature ranges for the formation of specific silicide phases in general do not directly translate for ultra-thin metal films. This phenomenon has been reported previously by Nava et al95. After silicide formation, a small amount of residual elemental metal can remain on the surface. To improve quantum efficiency, this residual elemental metal must be removed using an etchant that will etch the metal but not the silicide. The metal etchants used for the various silicides tested are included in Appendix A.

After removal of the residual elemental metal, the wafer is patterned again using the AZ 5214E

41 image reversal process to define the ground contact metal. For p-type silicon wafers, platinum was used as the ground contact metal while titanium was used for n-type wafers. These metals were chosen due to their relatively small Schottky barrier height. I found the barrier heights of these metals to be small enough to have a negligible impact on the reverse bias characteristics of the SBDs while providing a simplified process relative to tunneling ohmic contact formation that requires high doping of the silicon wafer in the ground contact region. Prior to deposition, the same barrel asher and acid dip are performed to clear the wafer of resist residue and remove oxide from the silicon surface. A 20 nm layer of ground contact metal is deposited using e-beam evaporation followed by another liftoff process. I use another AZ 5214 image reversal process to define a metal pattern used for wire-bonding the devices for characterization. The bonding metal stack consists of 10 nm titanium for adhesion, 20 nm of platinum to act as a diffusion barrier and 200 nm of gold for wire bonding. I again use e-beam evaporation to deposit the bonding metal stack, followed by another liftoff process. At this stage, the SBD is functional and could be packaged for operation. I determined experimentally, however, that illuminating the device from the frontside and leaving the backside uncoated leads to unreliable quantum efficiency measurements due to scattering of unabsorbed light from the backside as illustrated in Figure 21.

Silicide

Thermal Paste

To eliminate this effect and obtain accurate quantum efficiency measurements, two different illumination configurations are used.

Wire Bonds Cr/Au Mirror Wire Bonds SiO2 Silicide Silicide

n-Si n-Si

Al Mirror SiO2

(a) (b)

The frontside illuminated (FSI) configuration is completed by simply depositing a 200 nm aluminum layer on the backside of the wafer to act as a mirror. Because the backside of the silicon wafer is polished, the aluminum forms a high-quality mirror that eliminates scattering from the backside and enables an accurate and reliable quantum efficiency measurement. The

FSI configuration is useful because of its simplicity and relatively flat spectral absorption. To improve performance, however, I used the backside illuminated (BSI) configuration.

To finish the BSI configuration process, first I deposit an SiO2 layer using plasma- enhanced chemical vapor deposition (PECVD) (Appendix A). The thickness of this layer can be designed to maximize absorption over a wavelength range of interest. The ideal thickness

43 depends primarily on the index of refraction of the SiO2 layer and the peak wavelength of interest. A reasonable approximation for the ideal layer thickness is given by 휆0 4푛 where 휆0 is the peak wavelength of interest and 푛 is the real-part of SiO2 index of refraction. A rigorous determination of the ideal thickness includes the complex index of refraction of the silicide layers and all of the parasitic losses, such as substrate absorption and mirror losses. After the dielectric coating, an AZ5214E image reversal process with an hexamethyldisilazane (HMDS) adhesion process (Appendix A) is performed to define the backside mirror geometry. After lithography, the sample is exposed to oxygen plasma for 2 min prior to metal deposition. The backside mirror metal stack consists of a 2 nm chromium adhesion layer and 200 nm gold reflective layer. This metal stack was chosen over aluminum because of its resiliency to BOE. To reveal the bonding metal, the sample is placed in a 7:1 BOE bath until the oxide has been cleared. For this step, the backside mirror metal stack becomes a self-aligned etch mask for the

SiO2. Timing of the wet etch process was established with a bare companion piece from the

PECVD process. The typical etch rate was around 230 nm/min. To finish the process, the sample was cleaned thoroughly on the backside in preparation for anti-reflection coating. Again, a

휆0 4푛 approximation can be used to determine the ideal thickness of this layer, or it can be determined precisely using a transfer-matrix method analysis.

After fabrication, the sample is diced into individual die and packaged for testing.

Packaging consists of mounting the die in a ceramic chip carrier using a two-part thermally conductive epoxy (for temperature dependent measurements). BSI samples are mounted on specialized chip carriers with a hole cut through the center of the package, so light can pass through the package and onto the detectors when mounted upside down.

(a) (b) (c)

Figure 23. Photographs of die packaging. (a) sample during wire bonding. (b) front view of FSI detector die packaged in chip carrier. (b) back view of BSI detector with hole- drilled package for illumination through the package. Die are silver epoxy bonded to the package to establish good thermal contact with the ceramic package.

The epoxy is cured at 100 C for 1 hour in an oven. After mounting, individual detectors are wire bonded to the ceramic package to provide electrical connection between the device and testing instruments. After packaging, the device is ready for characterization.

2.4 Characterization Setup and Measurement Techniques

All of the devices were tested using the same characterization setup. Chip carriers were mounted in a liquid nitrogen pour-filled dewar (regardless of operation temperature) and connected to a variety of instruments for testing. This section will cover the basics of the measurement setup, but further details on the analysis and treatment of the measurements are included in subsequent sections along with the data.

2.4.1 Housing

To enable temperature dependent measurements, I used a liquid-nitrogen (LN2) pour- filled dewar as the housing for measuring detector samples. To maintain consistency, I used the dewar for testing samples even at room temperature.

The dewar features an LN2 reservoir connected to a cold finger that is used to cool the sample below ambient. The chip carrier can be mounted with the backside in contact to the cold finger for FSI samples, or upside down such that the shoulder of the chip carrier is in contact with the cold finger for BSI samples. An indium shim is used to provide good thermal conductivity between the ceramic chip carrier and cold finger. The chip carrier fits in a pressure mounted socket with electrical feedthroughs that provide contact to the chip carrier pins for electrical testing. A cold shield blocks stray light from entering the detector. Temperature control is provided by a resistive heater that is mounted to the cold finger along with a calibrated silicon diode temperature sensor and adjusted with a PID controller. After mounting the detector sample, the dewar can be vacuum sealed for low temperature measurements. A silicon window on the front of the dewar is used to reduce the primary silicon bandgap response of the detectors and provide a flat spectral transmission in across the SWIR/MWIR spectral range.

Figure 25. Measured transmission of silicon window used for optical detector testing.

2.4.2 Dark Current

Current-voltage (IV) measurements were made using an Agilent 4155C semiconductor parameter analyzer. For dark current measurements, the cold shield aperture was replaced with a completely closed aluminum shield to provide the sample with a 2π sr view of a cold thermal background with low emissivity. Dark current density is calculated using the detector area defined by the metal liftoff lithography process.

A useful technique in analyzing the dark current is to investigate its temperature dependence. Temperature dependent IV (IVT) curves can be used to determine the Schottky barrier height through an Arrhenius analysis40. When a device is mounted in the dewar, a dedicated connection to a temperature sensor attached to the cold finger can be monitored as a temperature reference, but a direct chip temperature measurement cannot be made. Because of thermal resistance, it is important not to assume the cold finger temperature matches the chip temperature perfectly. To analyze the temperature discrepancy between the cold finger measurement and the actual chip temperature, I mounted a calibrated silicon diode temperature sensor to one of the chip carriers I use for detector testing. I performed

47 temperature dependent measurements by cooling the dewar down to LN2 temperature (near

77K) and allowing the dewar to slowly warm to room temperature through ambient heating.

I’ve found that this method is significantly more accurate and straightforward than attempting to control the dewar temp with proportional-integral-derivative controller and heating element.

The plot in Figure 26 shows good agreement between the cold finger and chip temperature across the full temperature range.

IVT measurements were made by triggering the IV sweep once the cold finger reached the desired measurement temperature through ambient heating. Because ambient heating from base to room temperature takes around 12 hours, this measurement was performed programmatically.

Sze described how the Schottky barrier height can be determined from an IV or IVT measurement with Arrhenius analysis under forward bias40. The analysis involves a linear fitting and extraction of the SBH (activation energy) from:

퐼 푎푟푘(푉푏) 푞 푦 = Φ푏푥 + 푏 푦 = ln ( 2 ) ; 푥 = (37) 푇 푘퐵푇 where 퐼 푎푟푘 is the dark current at a bias 푉푏, and 푇 is the device temperature. This approach can directly determine the intrinsic barrier height because the lowering effects (static and image force) can be eliminated in forward bias when the junction field becomes negligible. Using the forward bias regime to determine the SBH requires a good ohmic contact for the ground plane of the detector however. The presence of even a relatively weak Schottky contact can lead to a significant error for this analysis. This is further complicated by the fact that small Schottky barrier contacts will behave ohmic at room temperature but reveal Schottky characteristics at low temperatures. For this reason, I performed Arrhenius analysis of the reverse bias IVT curves to determine the effective Schottky barrier height at the device operation bias. The effective

Schottky barrier height is more relevant to the device operation, as it represents the barrier height at the operation bias. It is important not to confuse the experimentally determined value to be the intrinsic barrier height for dark current models such as Equation 27; substituting the experimentally determined effective barrier directly into the model as the intrinsic barrier will lead to disagreement between experiment and model.

2.4.3 Spectral Response

Spectral response is a measure of the relative sensitivity of the detector as a function of the illumination wavelength. The most commonly used technique for performing this measurement with visible photodetectors is with a grating spectrometer. This basic configuration features a broadband source that illuminates a dispersive grating which separates the light spectrum spatially through diffraction. A narrow slit directly in front of the detector is used to isolate a narrow wavelength range for the response measurement. The grating is then rotated and the measurement repeated until narrow spectral measurements over the full range of interest have been measured.

Mirror Source Entrance Slit

Diffraction Grating

Detector Mirror

Exit Slit

Figure 27. Illustration of grating spectrometer that can be used to obtain spectral response characteristics of photodetectors.

While grating spectrometers for the infrared exist, another instrument known as a

Fourier transform infrared (FTIR) spectrometer offers many advantages. The basic configuration of an FTIR spectrometer is illustrated in Figure 28. The instrument is essentially a Michelson interferometer featuring a translating mirror, a broadband light source for sample illumination and a coaxial laser source for precision monitoring of the mirror position. A spectrum is measured using an FTIR by first recording an interferogram of the temporal signal and then performing a Fourier transform on that interferogram to obtain the spectrum.

Moving Moving Sample Mirror Mirror

Sample Detector Detector

Beam Beam Splitter Splitter

Source Source

(a) (b)

Figure 28. Diagram of FTIR spectrometer configured for measuring transmission (a) and reflection (b) of a sample.

One advantage of the FTIR configuration is signal throughput (Jacquinot’s96 advantage). A grating spectrometer requires the use of a narrow slit to define the measured spectrum, which severely limits signal flux on the detector. An FTIR, in contrast, simply requires a well collimated

50 beam, the diameter of which is limited by a much larger circular aperture. This results in significantly higher SNR for a given spectral resolution. Another advantage is spectral multiplex

(Fellgett’s97 advantage). While a grating spectrometer measures a “single wavelength” at any given moment through the exit slit, an FTIR measures an entire wavelength spectrum simultaneously. This results in a higher SNR for a given scan speed or faster scan speeds for a target SNR. Mathematically, for a spectrum with 푁 sample points, the relative SNR increase is

√푁. Another advantage is wavelength accuracy (Connes’98 advantage). Wavelength accuracy for an FTIR is dependent on precise relative positioning of the translational mirror. This positioning is monitored with high precision using a laser (with known wavelength) that is coaxially aligned with the source. This encodes a highly stable and accurate interferogram of the mirror position in time. The grating spectrometer wavelength accuracy is dependent on precise mechanical rotation of a grating with no interferogram feedback and is significantly less accurate. Another advantage afforded by the built-in positional interferogram, is the ability for an FTIR to continuously scan the translational mirror without compromising accuracy. This enables accurate averaging of multiple continuous scans to further improve scan speed/SNR. In practice, all of these advantages enable higher resolution spectral measurements with lower noise in significantly faster time than what is possible with a grating spectrometer. It should be noted that many of these SNR advantage assertions are based on the assumption that the system noise is not background shot noise limited (i.e. the system is detector noise limited); when the system is background shot noise limited, an FTIR can be inferior to a grating spectrometer from an SNR perspective.

For all FTIR measurements, I used a Thermo Scientific Nicolet 8700 FTIR spectrometer.

To test an external detector, I use a Keithley 428 current amplifier to bias and convert the photocurrent to voltage with calibrated gain connected to the external detector input of the

FTIR. A relative spectral response measurement using any spectrometer requires the acquisition of a system reference spectrum. The system reference spectrum is an aggregate of the spectral characteristics of every optical component in the system. For the FTIR, this includes the source, mirrors, beam-splitter, atmosphere, windows and detector. One technique in obtaining this reference spectrum is to use a detector with known spectral response. I took this approach by using a deuterated L-alanine-doped triglycine sulfate (DLaTGS) pyroelectric detector. The response of this detector is spectrally flat over a wide wavelength range (limited only by its window). However, the raw signal from the DLaTGS cannot be used to directly measure the reference spectrum because the FTIR encodes spectral information temporally, and the detector doesn’t have a flat frequency response across the modulation frequencies generated by the

FTIR. To correct for this, the frequency response of the pyroelectric detector must be characterized across the modulation frequencies generated by the FTIR. I did this by taking reference spectra with the DLaTGS detector at several different optical path difference (OPD) velocities. From the OPD velocity (푣푂푃퐷), the modulation frequency spectrum (푓푚(휆)) can be calculated using the simple relationship: 푓푚(휆) = 푣푂푃퐷 휆. The frequency response of a pyroelectric detector can be modeled simply as a bandpass transfer function with cut-on and cutoff frequencies:

1 푅 (휆, 푓) = 푅 (휆) 퐻(푓); 퐻(푓) = (38) 푝푦푟표 푝푦푟표 √ 2√ 2 1 + (푓1⁄푓) 1 + (푓⁄푓2) where 푅푝 푟표 is the pyro responsivity, 퐻 is the frequency response transfer function, 푓1 is the cut-on frequency and 푓2 is the cutoff frequency. I used a least-squares fitting procedure to experimentally determine the cut-on and cutoff frequencies of the DLaTGS detector from raw spectra at four different OPD velocities. Applying the frequency response transfer function to the raw spectra at various OPD velocities resulted in excellent agreement as shown in Figure 29.

(a) (b)

In addition to the frequency response correction, it is important to consider that a pyroelectric detector features a linear spectral response with respect to incident optical power. Since SBDs respond linearly to photon flux rather than optical power, the frequency corrected response spectrum should be divided by the photon energy to obtain a system reference spectrum that is proportional to photon flux. Dividing the raw external detector measurement by the system reference spectrum produces a relative spectral response curve for the detector under test.

2.4.4 External Quantum Efficiency

The method outline in the previous section generates a spectral response curve of arbitrary units. To scale the response curve to a physically meaningful parameter like EQE, an additional calibrated measurement is required. One obvious technique would be to replace the pyro detector measurement with a calibrated detector whose quantum efficiency spectrum has been independently characterized. There are several problems with this approach. First, availability of spectrally calibrated detectors is very limited across all infrared wavelengths-of- interest (especially limited beyond 2 µm). Second, accuracy of the measurement is reliant on accuracy of the original calibration of the reference detector. Finally, the output of the FTIR is

53 typically focused onto the detector to improve SNR, which is prone to misalignment between the detector under test and the reference detector. To avoid these issues, I followed a method outlined by Vincent99 for measuring the EQE of infrared detectors using a calibrated blackbody source.

Chopper Filter Detector Cavity Current Lock-In Blackbody Amp Amp

Figure 30. Blackbody setup for measuring the EQE of infrared photodetectors.

The setup I used (illustrated in Figure 30) includes an Infrared Systems Development

Corp. IR-563/301 cavity blackbody (with an integrated chopper wheel), a Keithley 428 current amplifier and a Stanford Research Systems SR850 DSP lock-in amplifier. The cavity blackbody provides a photon source with spectral irradiance that is predicted accurately by Planck’s law as discussed in the previous chapter. To limit the measurement to a finite wavelength range, a notch-band optical transmission filter is placed between the detector and blackbody source.

The incident photon flux on the detector can be derived simply from the geometry of the setup:

∞ Ω 휆 Φ = ∫ ∙ 푀(휆, 푇) ∙ ∙ 푇푓(휆) ∙ 푇푤(휆) ∙ 푀퐹 푑휆 (39) 0 휋 ℎ푐

Φ = photon flux [photons s-1 cm-2]

Ω = projected solid angle subtended at detector by the blackbody cavity aperture [sr]

푇푓 = transmission of optical filter

푇푤 = transmission of window

푀퐹 = modulation factor where the projected solid angle is used to account for the cosine dependence of emitted radiant intensity of the blackbody. To reduce the influence of small errors in measuring the distance between the detector and blackbody, I placed the detector relatively far from the source

(around 20 cm). For the case of a small detector coaxially aligned to a round source aperture, the projected solid angle simplifies to:

푟2 Ω = 휋 sin2 휃 = 휋 (40) 푑2 + 푟2 where 휃 is the subtended half angle defined by the aperture radius 푟 and distance 푑. The modulation factor 푀퐹 arises from the waveform of the modulated source. It is useful to modulate the source to reduce noise (by limiting bandwidth) and to remove the DC background component. This can be accomplished with a spectrum analyzer or lock-in amplifier. These instruments use electrical filters to reject frequencies outside of the fundamental component and measures the rms value of the filtered signal. Because quantum efficiency is defined as electrical output divided by optical input, we need to convert the calculated optical input to rms by multiplying by the modulation factor (dependent on the generated waveform). For a round aperture with a wheel of spinning radial teeth, the modulation factor can be written99:

√2 푁 푁 푑 2 푀퐹 = 퐹 (− , , 2, ( ) ) (41) 휋 2 2 퐷

퐹(푎, 푏, 푐, 푑) = hypergeometric function

푁 = number of tooth-slot pairs

푑 = aperture diameter

퐷 = pitch diameter of the chopper

I numerically evaluated the integral in Equation 39 by inserting Equations 2, 40 and 41 over a finite wavelength range defined by the notch filter transmission to calculate incident photon flux on the detector. Transmission of the filter and window were measured independently using the aforementioned FTIR. The measured quantum efficiency (푄퐸푚푒푎푠) is related to the photon flux simply as:

퐼푝ℎ 푄퐸 = 푚푒푎푠 qAΦ

55 where 퐼푝ℎ is the photocurrent and 퐴 is the detector area. Direct measurement of the photocurrent is accomplished with a current amplifier and lock-in amplifier. The current amplifier biases the detector for operation and converts the input current to an output voltage with a calibrated gain stage between 103—1010 V/A (valid to a specified cutoff frequency). To verify the gain stages were performing as expected, multiple gain stages were checked for consistency. The output of the current amplifier was connected to the input of the lock-in amplifier which is also connected to the reference frequency of the chopper wheel. The lock-in amplifier isolates the modulated voltage output of the current amplifier to suppress noise. The measured EQE value can be used to scale a relative spectral response curve to generate an EQE spectrum. When using a notch filter, the relative spectrum can be scaled to good approximation by simply scaling the spectrum to pass through the measured EQE value at the peak transmission wavelength of the notch filter. This approximation is valid when the notch filter is well behaved (simple gaussian or box top spectral shape) and when the detector response doesn’t vary significantly over the transmission bandpass of the filter. A more general expression for scaling the relative spectral response curve to the measured EQE is given by the following:

퐸푄퐸(휆) = 푀푅푟(휆) (42)

∞ ∫0 푇푓 푀 = 푄퐸푚푒푎푠 (43) ∞ ( ) ∫0 푇푓푅푟 휆

퐸푄퐸(휆) = external quantum efficiency spectrum

푅푟(휆) = relative spectral response curve of detector [a.u.]

푀 = scaling factor

푄퐸푚푒푎푠 = measured quantum efficiency over the bandwidth of the optical filter

The above expression makes no assumptions about the spectral shape of the filter or detector and is the method I used to generate all EQE spectra.

To validate consistency between the relative spectrum and the measured EQE values, I use multiple independent measurements with different notch filters to generate multiple scaling factors. These scaling factors were first checked for agreement (should be nearly identical) and then averaged as demonstrated in Figure 31.

2.4.5 Reflection, Transmission and Absorption

Reflection, transmission and absorption spectra can be obtained using an FTIR spectrometer. Transmission is the most straightforward and commonly used FTIR measurement. The measurement is performed by placing the sample of interest in the beam path preceding the detector (see Figure 28). This measurement provides a spectrum that includes the spectral characteristics of all components of the FTIR (source, beam splitter, mirrors, atmosphere, detector) as well as the sample itself. To extract the transmission, a second measurement without the sample was used as a reference. Ideally, a second

57 measurement should be a perfect reference, but practically there are some nonidealities that should be considered. First, the atmosphere between measurements can change. Typically,

FTIR spectrometers are nitrogen purged to minimize gas absorption peaks that exist throughout the IR spectrum, such as O2, CO2 and H2O vapor. Opening the sample chamber will disrupt that purge, and it can take a fairly long time to return to its previous state. If the absorptive gasses aren’t precisely equivalent between the sample and reference measurement, it will show up in the spectrum as an artifact. Another practical consideration is the adsorption of moisture in the sample. That moisture will also exhibit absorption peaks that come from the film, but aren’t a fundamental material characteristic of the film.

Another, less known nonideality, is the potential for reflected light from the sample to feed back into the system for a second pass through the spectrometer. Because this second pass is out of phase with the first, this can result in erroneous spectral characteristics. This effect is most readily observed when the sample has relatively high reflection, low absorption and is placed at normal incidence.

(a) (b)

Figure 32. (a) Transmission of 2 µm notch filter measured at 0 deg and 10 deg angle of incidence. (b) Transmission of Si wafer for angles ranging between 0—10 deg.

The measurements in Figure 32 demonstrate this feedback nonideality. Figure 32 (a) shows the transmission of a notch filter taken at normal and 10-degree incidence. The normal incidence

58 measurement features an erroneous replica of the transmission spectra in the block band of the filter (around 1 µm). This replica spectrum is a result of reflected light passing back through the system with a relative phase shift from the first pass. This effect can be eliminated by simply tilting the sample slightly off normal, as shown by the 10-degree measurement. It may be tempting, because the erroneous transmission peak is weak and out of band, to simply ignore that part of the spectrum and force transmission to zero for everything outside of the passband.

The limitation with this this approach is that it is ineffective for wide bandpass samples, such as a silicon wafer, as shown in Figure 32 (b). Measurements performed between 0 and 4 degrees feature an unexpected shape and aren’t consistent with one another (reflectance should be nearly constant at these angles for unpolarized light). In contrast, the 6-10 degree measurements agree within 0.2% of one another and provide a spectral shape consistent with what is expected of a semiconductor wafer. Measuring the sample transmission off-axis does have its own limitations, however. As the incident angle increases, the output beam will become slightly offset from the input due to beam walk off. When this offset becomes large enough to impact the amount of light collected on the detector, you can get artificially low signal not representative of the true sample transmission. It is therefore important to characterize the setup and determine the setup parameters (J-stop, incidence angle) that provide accurate results.

Reflection measurements require a sample holder designed to collect light reflected off the sample (see Figure 28 (b)). This sample configuration differs from the transmission measurement with respect to the reference spectrum. If the sample is removed from the sample holder in a reflection setup, the detector will simply receive no signal, so a reflectance standard must be used instead. No perfectly broadband reflector exists, but aluminum and gold feature relatively high and flat reflectance (>95%) in the infrared region.

Figure 33. Calculated reflectance using the index of refraction of Al100 and Au101.

Reflection is extracted by dividing the sample measurement by the reference measurement, but this time the reference must also be divided by the reflectance of the metal from which the standard was made to account for its imperfect reflection. It is common for FTIR reflection accessories to include a sample clamp with black rubber or foam backing to provide a little pressure to the sample when mounting, which helps maintain measurement consistency. This black backing is designed to be low reflectance and soft to prevent scratching of the sample.

Unfortunately, these pads have nonzero reflection, and because they are a diffuse surface, complicate modeling the reflection of a film stack on a thick substrate. To address this, I removed the built-in sample clamp and replaced it with a weighted ring that applies pressure to the edges of the sample around the aperture. The weighted ring provides an air interface on the backside of the sample, which is easy to model (provided the surface is clean and polished).

I capped the weighted ring with a highly absorbing surface away from the sample focal point, which produces negligible reflection (painted sandpaper).

Spring Loaded Clamp Weighted Ring Clamp

Foam Air Sample Sample

Figure 34. Illustration of standard spring-loaded clamp (a) and weighted ring clamp (b) used to position sample for reflection measurement. The ring clamp provides a sample surrounded by air to aid modeling, and produces negligible reflection (verified by measurement).

To validate consistency, I measured each sample at least twice. If the measurements disagreed, the sample and mount were cleared of any debris, checked for scratches, realigned and remeasured another two times. If the measurements agreed, it was considered a good indication the sample was mounted properly and accuracy of the data could be trusted.

For a sample with negligible scattering and no gain, the reflection, transmission and absorption add to unity. Therefore, the total sample absorption was extracted directly from reflection and transmission measurements.

(a) (b) (c)

To validate accuracy of the measurements, I measured the reflection and transmission of several low-loss windows (Figure 35). Because I know the absorption of sapphire and fused silica is nearly zero over a wide range of IR wavelengths, I used the calculated absorption to verify that reflection and transmission add to unity (zero absorption) to validate accuracy of the

61 measurements. The calculated absorption using transmission measurements at 10-degree incidence demonstrates exactly this, with calculated absorption of < 1% over the transparent range of the window. In contrast, calculating absorption using the normal incidence transmission measurement results in a dubious negative absorption. The negative absorption comes from the artificially high transmission that occurs when light is fed back into the system for a second pass as discussed above. For the silicon wafer, which has higher reflection in the transparent region, the feedback is stronger and the error is higher. The real absorption beyond the band edge was found to be around 3% for this wafer, which is attributed to free-carrier absorption due to substrate doping.

While useful, the total sample absorption provides limited information about the individual films of which a device sample is composed. For the characterization of photodetectors, per-layer absorption in a device stack provides the necessary information to extract the device IQE from an EQE measurement (Equation 5). For the case of SBD device engineering, I want to understand the precise tradeoff between absorption and IQE in order to design devices with optimized performance. To model the reflection, transmission and absorption of a material stack, we need to consider the wave-nature of light whenever the stack includes optically-smooth layers with thickness that are within a coherence length of the light source. The coherence length of a light source provides a nominal distance over which the phase of the light field is regular or periodic. This is important because the wave-nature of light creates interference effects between traveling waves of differing phase, which alters the sample transmission, reflection and absorption. The coherence length of a source is inversely proportional to the spectral bandwidth of the source, e.g. a blackbody can have a coherence length on the order of a couple microns while a laser can have a coherence length of over a km.

In practice, interference effects are usually observable by the FTIR for layer thicknesses that are

62 less than about 200-300 microns. This thickness range typically encompasses all layers of the device with the exception of the substrate. To model this type of material stack, we therefore need to model both coherent and incoherent layers.

For a planar stack of materials where scattering can be ignored and layers are coherent, the transfer-matrix method (TMM) can be used to precisely calculate reflection, transmission and per-layer absorption so long as the refractive index of each material is known102-105. The following formulation assumes all media are homogenous and non-magnetic. The electric field of an electromagnetic wave traveling in the 푥-푧 plane can be written as a superposition of its forward and backward traveling components:

푗풌푓∙풓 푗풌푏∙풓 푬(풓) = 푬풇푒 + 푬풃푒 (44)

2휋푛 2휋푛 풌 = (풛푐표푠휃 + 풙푠푖푛휃) 풌 = (−풛푐표푠휃 + 풙푠푖푛휃) (45) 푓 휆 푏 휆

푬(풓) = Electric field vector where 풓 is defined in the 푥-푧 plane

풌푓, 풌푏 = forward and backward angular wavevectors respectively

푬풇, 푬풃 = constant vectors dependent on light polarization and 휃

휃 = wave propagation angle with respect to normal

푛 = complex index of refraction

휆 = vacuum wavelength

TE-polarized light has an 푬-field in the 푦-direction while TM-polarized light has an 푯-field in the

1 푦-direction. From Maxwell’s equations, we know the relation: 푯 = 풌 × 푬, from which the 휇0휔 polarized fields can be written:

푬푓(푇퐸) = 퐸푓풚 푬푏(푇퐸) = 퐸푏풚 (46)

푯푓(푇퐸) ∝ 푛퐸푓(−푐표푠휃풛 + 푠푖푛휃풙) 푯푏(푇퐸) ∝ 푛퐸푏(푐표푠휃풛 + 푠푖푛휃풙) (47)

푬푓(푇푀) = 퐸푓(−푐표푠휃풛 + 푠푖푛휃풙) 푬푏(푇푀) = 퐸푏(−푐표푠휃풛 − 푠푖푛휃풙) (48)

푯푓(푇푀) ∝ 푛퐸푓풚 푯푏(푇푀) ∝ 푛퐸푏풚 (49)

Using boundary conditions of incident and transmitted fields while maintaining continuity of fields and their derivatives, a transfer matrix connecting tangential fields on both ends of a layer can be written: . . 푗푠푖푛훿푖 퐸 퐸 퐸푖−1 푐표푠훿 퐸푖+1 [ 0 ] = 푀 [ 푡 ] ⇒ [ ] = [ 푖 ] [ ] (50) 퐻 퐻 훾푖 0 푡 퐻푖−1 퐻푖+1 . 푗훾푖푠푖푛훿푖 푐표푠훿푖 . 2휋 훿 = 푑 푛 cos 휃 (51) 푖 휆 푖 푖 푖

푛푖 훾푖(푇퐸) = 푛푖 cos 휃푖 훾푖(푇푀) = (52) 푐표푠휃푖

퐸0, 퐻0 = incident fields

퐸푡, 퐻푡 = transmitted fields

퐸푖, 퐻푖 = fields in layer 푖

푑푖 = thickness of layer 푖

푛푖 = refractive index of layer 푖

휃푖 = propagation angle (with respect to normal) through layer 푖

To determine the propagation angle within each layer (휃푖), we refer to Snell’s law:

√푛2 − 푛2 sin2 휃 푖 0 푖 푛0 sin 휃0 = 푛푖 sin 휃푖 ⇒ cos 휃푖 = 2 (53) 푛푖 where 푛0 and 휃0 are the refractive index and propagation angle in the incident media

(technically doesn’t have to be incident media, but that is what is typically known). For an 푁 layer stack, the incident and transmitted fields are connected by matrix multiplication of each layer.

퐸0 퐸푡 퐸푡 [ ] = 푀1푀2 ⋯ 푀푁 [ ] = 푀푡표푡 [ ] (54) 퐻0 퐻푡 퐻푡

105 The reflection and transmission (Fresnel) coefficients can be extracted from 푀푡표푡 :

훾0푚11 + 훾0훾푡푚12 − 푚21 − 훾푡푚22 푟 = (55) 훾0푚11 + 훾0훾푡푚12 + 푚21 + 훾푡푚22

2훾0 푡 = (56) 훾0푚11 + 훾0훾푡푚12 + 푚21 + 훾푡푚22 where 훾0 and 훾푡 reference the incident and transmitting media respectively. The fraction of transmitted and reflected powers can be written:

[ ] [ ∗] 2 푅푒 푛푡푐표푠휃푡 2 푅푒 푛푡푐표푠휃푡 푇푇퐸 = |푡| 푇푇푀 = |푡| ∗ (57) 푅푒[푛0푐표푠휃0] 푅푒[푛0푐표푠휃0]

푅 = |푟|2 (58)

To calculate absorption within the material stack, the Poynting vector 푺 must be calculated. In this 1-D treatment, we are specifically interested in the normal component of the Poynting vector 푺 ∙ 풛.

1 푺 ∙ 풛 = 푅푒[풛 ∙ (푬∗ × 푯)] (59) 2

∗ ∗ 푅푒[(푛푖)(푐표푠휃푖)(퐸푓 + 퐸푏)(퐸푓 − 퐸푏)] 푺 ∙ 풛푇퐸 = (60) 푅푒[푛0푐표푠휃0]

∗ ∗ ∗ 푅푒[(푛푖)(푐표푠휃푖 )(퐸푓 − 퐸푏)(퐸푓 + 퐸푏)] 푺 ∙ 풛푇푀 = ∗ (61) 푅푒[푛0푐표푠휃0]

The above formulas are all that is needed to calculate the reflection, transmission and per-layer absorption in a coherent stack of materials. As discussed earlier, not all layers in a device sample can be treated as coherent, namely the sample substrate. The procedure for calculating this stack is to first reduce each coherent stack(s) to system transfer matrices which bound the incoherent layer(s). Then, a second series of transfer matrices which considers only the intensity of the forward and backward traveling waves computes the phase averaging effect of the coherent layer(s) from the reflectivity and transmissivity parameters of the coherent system

65 matrices. The forward and backward propagating intensities at an incoherent interface 푖 are connected by the transmissivity and reflectivity through the interface matrix:

2 1 −|푟 | 푖푛푡 1 푖,푖−1 푀푖−1,푖 = 2 [ 2 2 2 ] (62) |푡푖−1,푖| |푟푖−1,푖| (|푡푖−1,푖푡푖,푖−1| − |푟푖−1,푖푟푖,푖−1| ) where 푖 − 1 references the previous incoherent layer. In addition to the interface, we must consider the power attenuated through a lossy incoherent layer represented by the propagation matrix:

푝푟표푝 e훼푖 푖 0 4휋퐼푚[푛푖푐표푠휃푖] 푀 = [ ] 훼푖 = (63) 푖 0 푒−훼푖 푖 휆 which, for a lossless layer, reduces to the identity matrix as expected. For the example illustrated, we have three incoherent layers: the incident media, substrate layer 푚 and transmitting media. The system matrix of this example reduces to the following:

푖푛푐 푖푛푐 푖푛푐 푚11 푚12 푖푛푡 푝푟표푝 푖푛푡 푀푡표푡 = [ 푖푛푐 푖푛푐] = 푀0,푚푀푚 푀푚,푡 푚21 푚22

1 1 −푅푚,0 e훼푚 푚 0 1 −푅푡,푚 = [ ] [ −훼 ] [ ] (64) 푇0,푚푇푚,푡 푅0,푚 푇0,푚푇푚,0 − 푅0,푚푅푚,0 0 푒 푚 푚 푅푚,푡 푇푚,푡푇푡,푚 − 푅푚,푡푅푡,푚

2 2 where 푇푖,푗 and 푅푖,푗 are used to represent |푡푖,푗| and |푟푖,푗| respectively which are calculated in this example from the coherent stacks that bound the substrate layer. It may not be obvious simply by inspection of the matrices, but the final system matrix accounts for the infinite number of the passes through the incoherent layer 푚. To verify this, we can perform the system matrix multiplication which gives:

푖푛푐 1 푀푡표푡 = (65) 푇0,푚푇푚,푡

1 푅 − P 푅 푅 − 푡,푚 − 푅 P (푇 푇 − 푅 푅 ) 푃 m 푚,0 푚,푡 푃 푚,0 m 푚,푡 푡,푚 푚,푡 푡,푚 × 푚 푚 푅0,푚 푅푡,푚푅0,푚 + 푅푚,푡Pm(푇0,푚푇푚,0 − 푅0,푚푅푚,0) − + 푃푚(푇푚,푡푇푡,푚 − 푅푚,푡푅푡,푚)(푇0,푚푇푚,0 − 푅0,푚푅푚,0) [ 푃푚 푃푚 ]

−훼푚 푚 where 푃푚 is used as shorthand for 푒 . From the system matrix, we can extract the reflectivity and transmissivity:

푚푖푛푐 푇 푇 푅 푒−2훼푚 푚 푅 = 21 = 푅 + 0,푚 푚,0 푚,푡 (66) 푖푛푐 0,푚 −2훼푚 푚 푚11 1 − 푅푚,0푅푚,푡푒

−훼푚 푚 1 푇0,푚푇푚,푡푒 푇 = = (67) 푖푛푐 −2훼푚 푚 푚11 1 − 푅푚,0푅푚,푡푒 which are the exact forms of the sums of the infinite Airy geometric series for reflectivity and transmissivity103. While the example illustrated here represents the case of a single incoherent layer, the method can be applied to any number of incoherent layers by simply accounting for the interface and propagation matrices for each incoherent layer. The computation procedure is the same: compute system matrices for all coherent stacks, extract the reflectivity and transmissivity from those stacks as input for the generation of the incoherent matrices, and evaluate to a final system matrix from which the overall reflectivity and transmissivity can be extracted.

(a) (b)

Figure 36. Calculated transmittance of 500 µm thick silicon wafer using coherent and incoherent models over wide (a) and narrow (b) wavelength ranges.

Figure 36 demonstrates the importance of considering layer coherence for modeling

FTIR transmission and reflection measurements. Because the substrate is thick relative to the coherence length, the measured transmission features no oscillations. Included in the plot are

67 calculated coherent and incoherent models of the silicon substrate. Strictly speaking, coherency is a continuum ranging between the two extremes of coherent and incoherent. For treatment of partial coherence using TMM, see Katsidis and Siapkas103. Another common technique for handling incoherency is to vary the phase, thickness, angles, etc. in the incoherent layer. This requires the averaging of many TMM calculations to dampen the oscillations predicted by the coherent analysis. This method is equally valid and converges to the same results predicted by the above method, but is computationally more expensive. To calculate a reflectance spectrum, the TMM is called once for each wavelength, multiplied by the number of averages required to dampen the oscillations. In contrast, the above method calls the TMM once coherently and once incoherently for each wavelength. While this performance difference may be relatively inconsequential for a single simulation, I will be calling the TMM simulation routine potentially hundreds of times as part of a fitting procedure to determine material index of refraction dispersion curves. Because of this, the computationally efficient method is preferred over the programmatically simple method.

The method outlined above performs a forward calculation that converts a known index stack into a predicted reflectance and transmittance. Using an FTIR, I can measure the reflectance and transmittance, then I need to perform the reverse calculation to extract the refractive index stack (in order to obtain the per-layer absorption information). There is no transformation to directly perform the reverse calculation, so a fitting routine must be used to converge to a solution that satisfies the measurement and known parameters of the material stack. The fitting procedure is outlined by the state diagram in Figure 37.

Guess Calculate Compare to Good Refractive Index TMM Measurement Agreement?

No Yes New Index Done Guess

Figure 37. State diagram of refractive index fitting procedure

Within the confines of the state diagram in Figure 37, there are a number of choices to be made regarding the precise implementation of each step that will determine whether successful convergence will be achieved (and how quickly).

The fitting procedure can be approached as a point-by-point technique, where the initial guess is performed at a single wavelength, a refractive index is converged to and used as the initial guess at the next adjacent wavelength until an entire spectrum is fit. The primary challenge of this approach is that reflectance and transmittance values do not uniquely correspond to an index of refraction value when the index is complex (i.e. lossy). To address this, the initial guess should be reasonably close, and the fitting routine must check that the converged value is reasonable, i.e. verify convergence didn’t generate an unreasonably large discontinuity in the index with respect to the wavelength. It can be challenging to implement a discontinuity check that is effective in regions of both low dispersion (e.g. infrared wavelengths longer than a semiconductor bandgap) and high dispersion (e.g. band edge of a semiconductor) simultaneously. Decreasing the wavelength step can be an effective approach for handling this challenge but at expense of speed.

A more effective and computationally efficient technique is to use an appropriate refractive index model for the materials of interest. The disadvantage of this approach is the requirement of defining an index model that accurately describes all the spectral characteristics of the material. The advantages include faster and more reliable convergence with added flexibility in fitting specific material/film characteristics. Because the refractive index model

69 predicts the entire reflectance and transmittance spectra, the fitting procedure is performed just once, taking into consideration the quality of fit of all wavelengths simultaneously for each guess/consistency check iteration. In addition, because the shape of the dispersion curve is defined by the model, a much sparser wavelength sampling can be used for fitting while still maintaining convergence reliability. These two features can drastically improve the speed to convergence by significantly reducing the total number of TMM computations. Convergence reliability is improved because the model effectively constrains the fitting algorithm, unlike the point-by-point method. This is true in general, but it is especially apparent for spectral regions where the transmission drops near zero (e.g. wavelengths shorter than a semiconductor’s bandgap cutoff wavelength). Because the model fitting procedure includes information across a range of wavelengths, the film thickness can be used as a fitting parameter as well, something which cannot be done with the point-by-point method. Additionally, if only a subset of a material’s characteristics is unknown, then that subset can be selectively fit. For example, a series of silicon wafers with similar but not identical doping will differ only with regard to the free-carrier absorption, so only the model describing free-carrier absorption needs to be fit independently for each wafer.

A wide variety of refractive index models exist to describe various types of materials including metals, semiconductors and dielectrics. The models I will use for the various materials that comprise the device samples are summarized below.

2 2 퐵푖휆 푛 (휆) = 1 + ∑ 2 (68) 휆 − 퐶푖 푖

Equation 68 is the Sellmeier equation, which improves upon the original work of Augustin

Cauchy for modeling the dispersion of transparent media with improved accuracy from the UV through IR106. This model can accurately fit the index of refraction over a wide wavelength

70 range, so long as the material absorption is zero (or weak when used in conjunction with a lossy model). I used Equation 68 to model SiO2 as well as the real-part of the refractive index of silicon, in the infrared portion of the spectrum where absorption is weak.

ℎ푐 2 ℎ푐 2 ℎ푐 훼 (휆) = 퐶 ( − 퐸 + 퐸 ) + 퐶 ( − 퐸 − 퐸 ) ; ≥ 퐸 + 퐸 (69) 퐼퐵 1 휆 푔 푝 2 휆 푔 푝 휆 푔 푝

ℎ푐 2 ℎ푐 훼 (휆) = 퐶 ( − 퐸 + 퐸 ) ; 퐸 + 퐸 > > 퐸 − 퐸 (70) 퐼퐵 1 휆 푔 푝 푔 푝 휆 푔 푝 ℎ푐 훼 (휆) = 0; ≤ 퐸 − 퐸 (71) 퐼퐵 휆 푔 푝 Equations 69—71 are a piecewise model of the absorption coefficient of an indirect-bandgap semiconductor where 퐸푔 is the bandgap energy and 퐸푝 is the phonon energy that assists the absorption transition. The formula can be derived from band theory by approximating the band structure of the semiconductor to be parabolic40.

훾 훼푓푐(휆) = 퐶휆 (72)

Equation 72 is a model of the free-carrier absorption in a semiconductor. This absorption is dependent on the doping level (increases with doping) and results in nonzero absorption for wavelengths beyond the zero-cutoff wavelength defined by a semiconductor bandgap.

훼휆 푛 = 푛 + 푗휅 = 푛 + 푗 (73) 푟 푟 4휋 Equation 73 defines the relationship between the extinction coefficient 휅 and absorption coefficient 훼 for use in the TMM. The TMM formulations take the complex refractive index 푛 as input.

Another aspect of the fitting routine is the comparison between model and measurement. The most common procedure for finding a best-fitting curve given a set of points is by minimizing the sum of the squares of the offsets of the points from the curve. This is referred to as least-squares fitting (LSF) or minimization and is represented mathematically as:

푛 2 2 푅 = ∑ 푑푖 (74) 푖=1 where 푅 is singular value residual and 푑푖 represents the offset of each point of 푛 total data points. The square of the offsets is used rather than the absolute value, because the absolute value function has discontinuous derivatives which cannot be solved analytically and can result in unstable convergence. An unintended consequence of using the square of the residuals is disproportionate weighting of outlier points, which is generally not desirable. To address this issue, the Huber loss can be calculated instead:

1 2 푑푖 , |푑푖| ≤ 훿 퐿 = {2 (75) 푖 1 훿 (|푑 | − 훿) , |푑 | > 훿 푖 2 푖 which varies quadratically for small offset values and linearly for large offset values, defined by the loss parameter 훿.

The last component of the fitting procedure is the convergence algorithm. The purpose of the convergence algorithm is to find a local minimum in a multi-dimensional variable space.

These algorithms typically compute the Jacobian of the fitting function with respect to the variable space (vectorized), and use it to make an educated guess of what the optimized variable vector is that minimizes the function. Repeated application of the algorithm will ideally lead to convergence toward the function minimum. Convergence will depend on the convergence algorithm, nature of the fitting function and its derivatives, and the initial variable guess.

Examples of minimization algorithms include Nelder-Mead107, Powell108, Broyden-Fletcher-

Goldfarb-Shannon109, conjugate gradient110, truncated Newton111 and others. The method I used for fitting data in this paper is the trust region reflective method112 which is generally robust and can be implemented with bounds on the variables.

Figure 38 plots the results of fitting the refractive index of silicon using a single reflection measurement. After convergence, the model fits the measured reflection data accurately, but doesn’t do a satisfactory job of accurately predicting the transmission measurement of the same sample. This is due to inadequate constraining of model, and is particularly an issue when trying to fit lossy material. By simultaneously fitting both the reflection and transmission measurements, the model can be adequately constrained to converge to a self-consistent solution.

To maximize flexibility, the code I developed for this fitting procedure is written generally enough to fit any number of measurements that correspond to any configuration of material

73 stacks, with the ability to link layers between stacks that are identical, and to fit any number of the refractive index model parameters. This code, written in Python, is included in Appendix B.

2.5 Device Results

2.5.1 Material Comparison

Following the procedure outlined in Section 2.3, I fabricated a variety of silicide SBDs.

The purpose of this initial experiment is to identify a material system of interest for deeper investigation. The SBDs fabricated include PtSi/n-Si, AuSi/n-Si, NiSi/n-Si, MoSi/n-Si, TaSi/n-Si,

PdSi/n-Si and CrSi/n-Si. All of these devices were fabricated by evaporating 15 Å of metal, followed by thermal annealing between 400—600 C. The precise silicide phase was not verified for these detectors, for example, PdSi is used to simply reference palladium silicide and doesn’t distinguish between Pd2Si, PdSi, PdSi2, etc. My focus on n-type SBDs is based on the desire to investigate devices that operate at or near room temperature. The p-type SBDs formed using the same materials have lower SBH than the n-type, leading to high reverse bias dark current that requires cryogenic cooling for adequate dark current suppression.

(a) (b)

Figure 40. Dark current characteristics of various SBDs to n-type Si. Zoom view of plot (a) is shown for just the reverse bias in (b).

Figure 40 summarizes the room temperature current/voltage relationship for all of the fabricated SBDs (around 10 detectors for each sample). Uniformity for each sample is relatively

74 good, with the reverse saturation current (negative bias) providing an indicator of the SBH

(higher dark current for lower SBH).

(a) (b)

Figure 41 plots the photo response of the SBDs at room temperature. This plot demonstrates a clear performance difference with respect to the silicide material. This can be explained by differing SBH, hot carrier attenuation lengths and extinction coefficients among the silicide materials. Given two SBDs with differing SBH but otherwise equivalent material parameters, the SBD with the lower SBH will have higher quantum efficiency at all wavelengths of sensitivity. Keeping the influence of SBH on quantum efficiency in mind, we can conclude there is a significant performance advantage of some silicide materials over others. The CrSi device, for example, features a mid-range SBH but significantly lower response than the other devices, indicating it is a poor candidate for SBD photodetectors. The NiSi device has the highest overall quantum efficiency, and is therefore intriguing, but the longer cutoff wavelength also results in the highest dark current. The AuSi device, despite having the second smallest SBH, outperforms all other devices (except NiSi) at shorter wavelengths. This suggests the AuSi device may have a significantly longer hot carrier attenuation length than the other silicides

(assuming absorption isn’t dramatically different amongst the equally thick samples). This is also evidenced by the much steeper slope of the response curve relative to the other devices.

Since it is reasonable to expect relatively flat absorption over the response wavelength range for these front-side illuminated devices, the steepness of the response curve is indicative of the collection efficiency (and therefore the hot carrier attenuation length). It is possible the short cutoff wavelength of the AuSi device could be extended by incorporating a delta-doping layer at the surface to lower the SBH113-116, expanding its utility for longer wavelength applications. To simplify the analysis and fabrication development however, I have chosen to further investigate the NiSi device in more detail, leaving the AuSi development for future work.

In the beginning of this chapter, I introduced a plot that summarizes the reported quantum efficiency of various SBDs (reproduced below for discussion).

Figure 42. Reported external (square) and internal (diamond) quantum efficiency for various metal/metal-silicide Schottky-barrier photodetectors at 1.55 µm36,52- 60,62,63,65,66,79,84,88. Blue marker-fill indicates standard front-side or back-side illuminated detectors, green indicates plasmonic resonant detectors, red indicates waveguide integrated detectors and purple indicates resonant-cavity-enhanced detectors. The dashed line represents the theoretical maximum quantum efficiency based on the barrier height, assuming a sharp emission threshold34.

Figure 42 shows a collection of reported QE values at 1.55 µm for a variety of SBDs; purposely omitted from this collection are detectors featuring internal gain, which obfuscates the device

QE. When available, the internal quantum efficiency (IQE), which is analogous to collection efficiency here, is plotted. Included in this collection are novel structures designed to improve

QE by increasing absorption such as plasmonic resonators, waveguide integrated devices and photonic resonant cavities. Despite these novel device designs, reported QE and IQE values are often orders of magnitude below the theoretical maximum (hence the need for a logarithmic y- axis).

Figure 42 shows the general trend of increasing QE with decreasing SBH, as expected.

To normalize the barrier height dependence on QE, Figure 43 shows the QE divided by the theoretical maximum QE (based on the barrier height) as a function of silicide thickness. From this plot it becomes clear that silicide thickness is the most critical design parameter for maximizing the QE of SBDs. The highest performing SBDs to date feature very thin silicide layers, leading to relatively simple backside-illuminated architectures with incomplete absorption outperforming novel resonant and waveguide architectures. Improved QE in thin silicide layers was first reported by Kimata et al.51 in PtSi where they found a thin 9 nm silicide

(the thinnest device tested in that work) exhibited the highest QE. Higher performance was subsequently reported for PtSi layers as thin as 2 nm88. This improvement has been attributed to multiple interface reflections of hot carriers (as discussed in Section 2.1) when the silicide thickness is reduced below the hot carrier mean-free path. Despite the age of this fundamental knowledge, very few reports of SBDs with thickness below 10nm exist, and to my knowledge

78 thickness dependence on QE has been systematically studied and reported for PtSi alone (3—5

μm wavelength). The purpose of the remainder of this chapter, therefore, is to investigate the thickness dependence of QE for SBDs made from NiSi on n-type Si. Because IQE monotonically increases towards the theoretical limit with decreasing silicide thickness34, my goal is to fabricate and characterize devices that approach the minimum achievable film thickness (which is determined by the percolation threshold of NiSi).

I fabricated series of NiSi SBDs with silicide thicknesses of 1, 2, 3 and 4 nm in both the

FSI and BSI optical configurations as outlined in Section 2.3. For reference, I also fabricated a

100 nm thick BSI device. Because of the thickness, only the BSI configuration of the thick devices is of interest because optical generation of the FSI device will be too far away from the

Schottky junction for collection. In parallel with the device sample fabrication, I fabricated wide- area companion samples for optical characterization. These samples went through identical processing steps (with the exception of lithography), sharing the deposition chamber to guarantee identical material stacks between the device and optical characterization samples.

These samples will be used to measure reflection, transmission and calculate absorption in the devices.

Wire Bonds Cr/Au Mirror Wire Bonds SiO2 NiSi NiSi

n-Si n-Si

Al Mirror SiO2

(a) (b)

I used double-side polished (DSP) [100] n-type Si substrates with resistivity between 1—

10 Ω∙cm for all devices. Ni film thickness was controlled using a quartz-crystal microbalance to

79 be 0.5, 1, 1.5, 2 and 50 nm, which combine with silicon to be 1, 2, 3, 4 and 100 nm films of NiSi respectively after annealing at 400 C for 5 min117,118. Attempts to fabricate NiSi SBDs from Ni films thinner than 0.5 nm resulted in devices with performance characteristics that suggested discontinuous NiSi films were formed, i.e. dark current that didn’t scale with device area and absence of photo response. This suggests that the percolation threshold for NiSi is around 1 nm for the deposition and annealing conditions I used.

2.5.2 Dark Current

(a) (b)

Figure 45 (a) plots the collection of room temperature current/voltage measurements for all 90 fabricated detectors (10 of each thickness/optical configuration). The thick reference device (grey curves) has notably lower dark current than the thinner devices. It has previously been shown that ultra-thin silicides can feature a lower SBH than bulk films70,71. Because the increased dark current for thin devices is driven by a lowering of the Schottky barrier, this doesn’t necessarily translate to poorer SNR, because the QE and cutoff wavelength will also increase with barrier lowering (even before accounting for increased collection efficiency). The dark current uniformity amongst the collection of detectors is excellent, a favored characteristic

80 of SBDs. In contrast, a collection of 90 photodiodes or unipolar barrier detectors for example, would have significantly more spread of the measured reverse saturation currents. This characteristic is attributed to SBDs being a majority carrier driven device, that isn’t influenced by local nonuniformities of the minority carrier transport properties. Figure 45 (b) is an Arrhenius plot of the dark current for one detector from each thickness of the BSI devices. The effective

SBH can be extracted from the slope of a linear fitting as described in Section 2.4.2 and is summarized for all of the diodes in Table 3.

Table 3. Extracted Schottky barrier heights based on activation energy of Arrhenius plots (Figure 45 (b)).

Device Thickness FSI Φ퐵 (meV) BSI Φ퐵 (meV) 1 nm 607 610 2 nm 610 613 3 nm 610 612 4 nm 605 608 100 nm -- 640

A potential nonideality of photodetector dark current is via “edge leakage” current. For

SBDs, this effect is due to high fringing electric fields at the boundary of the device. The high field lowers the effective SBH around the perimeter of the device, leading to higher dark current in that region due to the reduced barrier, and thus higher dark current for smaller SBDs. This effect can be eliminated by effectively guarding the detector with a doped region of the opposite polarity40, which I have not done here. It is important to verify that these edge effects are negligible for the device sizes tested in the Arrhenius analysis, or the analysis will be invalid.

The size dependent dark current shown in Figure 46 indicates the dark current for devices in the

500—1000 μm range are consistent, with negligible edge effects.

Using the thermionic emission model from Section 2.4.2, I fit the unknown parameters to the reverse saturation device current over a range of temperatures.

Figure 47. Modeled (dashed) and measured (solid) reverse-bias dark current density of BSI 1 nm NiSi device. The model is based on the thermionic emission model with field- dependent barrier lowering. These formulas along with all the supplemental formulas for calculating the field in silicon as a function of temperature are included in Section 2.2.

The measured and modeled dark current show excellent agreement over the range of temperatures used for the measurement. At lower temperatures and higher bias, quantum mechanical tunneling can become an appreciable component of the dark current, and would have to be added as an additional current component to the model to widen the predictability.

The thermionic emission model does, however, adequately predict the device dark current over the range of biases and temperatures most applicable to real-world device operation. Using the model fitting, I extracted the intrinsic SBH to be 628 meV. I calculated the -1 V effective barrier height to be 616 meV, which agrees with the Arrhenius analysis to within 6 meV. The doping, determined by the fitting, came to be 8.5e14 cm-3, within the expected range of 4.5e14—4.5e15 cm-3 (1—10 Ω∙cm phosphorus-doped wafers). The experimental agreement with theory is remarkably good for these SBDs, which is an advantage when engineering novel device designs.

2.5.3 External Quantum Efficiency

The critical performance parameter of interest with regard to the silicide thickness is the quantum efficiency (both internal and external). Using the methods outlined in Sections 2.4.3 and 2.4.4, I have measured the EQE of all the devices. Like the dark current, the response of these detectors is extremely uniform, and thus, a single detector from each die is plotted for clarity.

(a) (b)

As expected, the EQE for BSI devices is higher than FSI due to expected higher absorption. The

FSI devices feature an optimum NiSi thickness between 1—2 nm, while the BSI devices feature an optimum NiSi thickness between 1—3 nm. This result highlights the relationship between the detector optical design architecture and optimum silicide layer thickness for SBDs. Each combination of silicide and optical architecture can have a unique optimal silicide thickness that maximizes QE whenever the absorption is incomplete (typical for thin silicide SBDs in an imaging configuration). This also implies that if a different optical configuration can be designed that features higher absorption than the BSI device configuration, that design will have a different optimal silicide layer thickness. Also evident in Figure 48 is the substantial improvement of all

84 sub 5 nm devices relative to the 100 nm reference device. The EQE of the 2 nm BSI NiSi device is the highest ever reported to date for any silicide SBD with a similar barrier height (0.44% at 1.55

μm), enabled by the ultra-thin silicide device design.

2.5.4 Optical Characterization

Considering the EQE results from Figure 48, it may be tempting to draw final conclusions from that data. It is clear from the plot that there is an optimum silicide thickness, but all of the sub 5 nm devices have similar EQE for a given optical configuration. What’s missing from this result however is an analysis on the precise nature of the inefficiencies amongst the various thickness devices. In other words, what fraction of the quantum “inefficiency” is due to incomplete absorption and what fraction is due to imperfect collection of absorbed carriers.

This analysis is rarely performed for SBDs, and is critical to the understanding of what fundamentally limits the performance of these devices. EQE is simply equal to the fractional absorption of light multiplied by the IQE (collection efficiency), so accurately obtaining the absorption spectrum of these devices is all that remains to obtain the IQE spectra.

Section 2.4.5 describes, in detail, the technique I used to model reflection, transmission and absorption of a material stack by fitting appropriate index models. Before attempting to characterize the silicide layers of interest, I fit a series of samples that are composed of the various materials used in the BSI and FSI devices.

(a) (b)

The index models were fit for the silicon wafer and PECVD SiO2 films shown in Figure 49 using models described in Section 2.4.5. Dispersion curves for the metals Al100, Cr119 and Au101 were taken from literature and well-established databases120. With all of the constituent materials modeled accurately to fit the FTIR measurements, final fitting of the NiSi layers can be performed. Each thickness is fit independently of one another because it is known that material refractive index dispersion changes with thickness in the ultra-thin film regime95,121. I used a polynomial of the following form to fit the NiSi index dispersion:

3 3 푛 + 푗푘 = 퐶1 + 퐶2휆 + 퐶3휆 + 푗(퐶4 + 퐶5휆 + 퐶6휆 ) (76)

To constrain the fitting procedure and improve accuracy, multiple FTIR measurements of the same silicide film in different optical configurations were fit concurrently. For each layer thickness, reflection and transmission measurements of the NiSi thin film on Si as well as reflection measurements of the BSI and FSI configurations were all used for fitting. All of this data along with the modeled fitting curves are plotted in Figure 50.

(a) (b)

By implementing a fitting procedure to model the complex index of refraction for each material, I am able to accurately account for the parasitic losses due to free-carrier absorption in

87 silicon and losses in the metallic mirror layers to extract absorption in the NiSi layer. Because the NiSi film absorption depends on the thickness, the parasitic losses are not constant amongst the samples/layers and must be modeled to account for those variations. In other words, it would be flawed to simply measure two samples, one with and one without silicide, and assume the absorption difference between the two is representative of the silicide absorption. The calculated absorption from each layer for both the FSI and BSI configurations is plotted for the

2nm NiSi film in Figure 51, demonstrating the appreciable parasitic losses of the silicon wafer and metallic mirrors.

(a) (b)

Figure 51. Example calculation of the per-layer absorption for the 2 nm NiSi device in the FSI (a) and BSI (b) configurations.

Using this LSF/TMM method, I extract the complex index of refraction spectra for each layer. It should be noted that the precision of determining the index spectra is dependent on the fidelity to which the layer thickness is known for incoherent layers, e.g. ultra-thin layers like the NiSi and thick layers like the Si substrate. Because the thickness of these layers is too large or too small to contribute to interference fringing effects, thickness information isn’t encoded in the measurement spectra and therefore cannot be determined without an independent measurement of the thickness. This limitation is analogous to the challenge of fitting the film index and thickness simultaneously using ellipsometry of ultra-thin films122. For these samples,

88 my independent measurement comes from a quartz-crystal thickness monitor during deposition. However, this limitation does not impact the method’s ability to accurately determine the absolute absorption in each layer. This is perhaps obvious for the case of the thick substrate, where an adjustment to the substrate thickness will result in a change in the absorption coefficient such that total absorption is equivalent. I have found the equivalent to be true for the ultra-thin film case as well. To demonstrate this, I repeated the LSF/TMM procedure using the same set of FTIR measurements of the 2 nm NiSi film assuming the film thickness was 1, 2 and 3 nm (an overestimation of the error bounds on the film thickness).

Figure 52 demonstrates that while the absolute value of the index dispersion changes for each fitting, the calculated absolute absorption does not.

(a) (b)

Because the goal of this fitting procedure is to extract an accurate representation of the absorption spectrum and not the refractive index dispersion, I find this method to be satisfactory despite its limitations. Again, considering the analogy of ellipsometry measurements of ultra-thin films, the ellipsometric quantities Δ, Ψ and ρ can be accurately determined readily from measurements while accuracy of the refractive index fitting is reliant

89 on input of an accurate film thickness derived from another independent measurement. From this perspective, the LSF/TMM technique is potentially more useful for characterizing devices such as SBDs that feature ultra-thin films over ellipsometry because the measurable parameters of reflection, transmission and absorption are physically meaningful to device performance, while the ellipsometric quantities are not. To understand this theoretically, we can look at the

TMM (Equation 50). The silicide layer is described optically by a 2x2 matrix with three different elements: 푐표푠훿, 푗훾푠푖푛훿 and 푗훾−1푠푖푛훿. The real and imaginary parts of these elements for each modeled thickness are plotted in Figure 53.

(a) (b) (c)

Figure 53. The real (solid) and imaginary (dashed) parts of the three TMM matrix elements: (a) 푐표푠훿, (b) 푗훾푠푖푛훿 and (c) 푗훾−1푠푖푛훿. The n and k values were derived from fitting the 2 nm NiSi data as though it were 1 nm, 2 nm and 3 nm as labeled in the plots (refractive index dispersion plotted in Figure 52).

The real part of the matrix elements is related to the field strength which fully describes the

Poynting vector used to calculate absorption, while the imaginary part describes the field phase which dictates interference phenomena. Figure 53 shows the real part of each matrix element agrees for all three modeled thickness, while the imaginary part disagrees. The interpretation of this result is the overall absorption of these modeled films are the same with some difference in phase. Because the film thicknesses are significantly less than the wavelength of interest, these overall phase differences aren’t significant enough to introduce appreciable differences in interference effects when the film is inserted in a film stack with resonances (e.g. the BSI optical configuration), consistent with Figure 52.

2.5.5 Internal Quantum Efficiency

Using the calculated absorption spectra from the LSF/TMM technique along with the

EQE spectra, I have calculated the device IQE for both the FSI and BSI device configurations which is shown in Figure 54.

Figure 54. Calculated IQE spectra for all FSI and BSI devices (1 V reverse bias). IQE is calculated from the QE spectral measurement and absorption calculation based on the film FTIR measurements.

Figure 54 clearly depicts a trend of increasing IQE with decreasing NiSi thickness. Unlike the EQE results, the IQE of FSI and BSI devices (of equal thickness) are in good agreement. This is the expected result when the silicide layer is thin enough such that absorption in the film is uniform

(i.e. no significant absorption gradients in the film). Considering seven independent measurements are used to generate each IQE curve, it is remarkable that the FSI and BSI IQE curves agree so closely for all four thicknesses tested; a testament to the accuracy of the measurements and validity/utility of the methodology.

As mentioned in Section 2.1, the modified Fowler equation is the most common method of characterizing the quantum yield of SBDs.

(ℎ휐 − Φ )2 퐼푄퐸 = 퐶 퐵 (77) ℎ휐

91 where 퐶 is the quantum efficiency coefficient (eV-1) and ℎ휐 is the photon energy. The Fowler equation therefore enables a simple linear fitting of the SBH as well as the quantum efficiency coefficient, which is independent of the photon energy, directly from a response measurement.

While it is common to use the QE when fitting to the Fowler plot, because absorption is rarely measured in SBD reports, ideally the detector IQE spectrum should be used because the modified Fowler equation does not consider absorption.

(a) (b)

The plot in Figure 55 (a) shows the devices fit the Fowler yield relationship well over a wide range of photon energies but deviates when the photon energy approaches the SBH. Because the Fowler quantum efficiency coefficient (퐶) is a wavelength-independent measure of the quantum yield, it is a useful parameter to compare as a function of the silicide thickness as shown in Figure 55 (b). From this plot we can see good agreement between the FSI and BSI quantum yield across the thickness range. The shape of the plot suggests that the quantum yield parameter is accelerating rather than saturating with decreasing thickness across the range tested. The implication of this result is that further improvement to the quantum yield should be realizable if the NiSi thickness can be reduced from what has been demonstrated here.

As discussed in Section 2.1, the modified Fowler fitting is simply an empirical relationship that doesn’t provide insight into the key material parameter responsible for the device performance (hot carrier attenuation length). To fit the experimental IQE data to theory,

I use Vickers’ model (approximated by Casalino).

(a) (b)

Figure 56. Fowler plot IQE fitting of FSI (a) and BSI (b) NiSi devices using Casalino’s approximation of Vickers’ model.

Using a least-squares fitting procedure, I am able to extract the SBH and 퐿 푡 ratio for each device using Casalino’s approximation to Vickers’ model as shown in Figure 56. A summary of all of all of the extracted device parameters is included in Table 4.

Modified Vickers’ Model Arrhenius Calculated from Measurement Fowler 퐶 Φ L Φ Φ QE IQE QE IQE Device 퐵퐹 L/t 퐵푉 퐵퐴 1.3μm 1.3μm 1.55μm 1.55μm (eV-1) (eV) (nm) (eV) (eV) (%) (%) (%) (%) 1 nm 0.43 0.59 72.5 72.5 0.595 0.607 0.67 6.05 0.26 2.41 (FSI) 5 1 nm 0.40 0.583 63.2 63.2 0.585 0.610 1.0 5.78 0.4 2.41 (BSI) 2 2 nm 0.24 0.599 32.7 65.4 0.603 0.610 0.66 3.22 0.25 1.23 (FSI) 4 2 nm 0.23 0.59 30.1 60.2 0.593 0.613 1.09 3.22 0.44 1.29 (BSI) 2 3 nm 0.17 0.599 19.9 59.7 0.602 0.610 0.58 2.28 0.22 0.88 (FSI) 3 3 nm 0.15 0.582 17.5 52.5 0.584 0.612 1.01 2.3 0.43 0.96 (BSI) 9 4 nm 0.14 0.596 15.3 61.2 0.598 0.605 0.55 1.95 0.22 0.77 (FSI) 5 4 nm 0.13 0.583 13.7 54.8 0.586 0.608 0.96 1.92 0.41 0.8 (BSI) 3 100 nm 0.01 0.639 0.53 58.0 0.645 0.640 0.09 0.14 0.03 0.04 (BSI) 4

As expected, the 퐿 푡 ratio monotonically increases with decreasing NiSi thickness. The average hot carrier mean-free path for the BSI and FSI devices was found to be 57.7 nm and 64.7 nm respectively. This result is consistent with the modified Fowler fit where the average quantum efficiency coefficient is slightly higher for the FSI devices than the BSI. While this could suggest the BSI device NiSi films have been degraded slightly, I am hesitant to draw that conclusion.

Both the modified Fowler fitting as well as the fitting to Casalino’s Vickers approximation lose accuracy as the photon energy approaches the barrier height. I found both methods underestimated the measured zero-crossing wavelength of the QE spectrum (over-estimation of

Φ퐵) which was found to be around 2.15 μm (Φ퐵 = 0.577 eV) for all devices. In addition, both models fit the SBH of BSI devices to be smaller than the FSI devices which is inconsistent with the Arrhenius analysis. Additionally, inspection of the measured IQE in Figure 54 and Table 4 suggests that the collection efficiency between FSI and BSI are quite similar. Discrepancies

94 between the IQE of FSI and BSI devices for a given thickness are not consistently in favor of one illumination configuration over the other when considering the full wavelength range. For this reason, we interpret the extracted 퐿 to be an approximation limited in accuracy by the approximate model used for fitting as well as the accuracy of the film thickness, which is difficult to measure with high precision in this thickness regime (in addition to typical measurement errors). Despite this limitation, I believe fitting SBD device performance to a physical model that includes 퐿 to be a more meaningful and insightful than simply using a fitting parameter, as is more typically done with these devices using the modified Fowler fit.

2.5.6 Image Sensor Demonstration

The improvement in EQE I demonstrated with ultra-thin NiSi SBDs is promising, but it is still relatively low when compared to bandgap-based photodiodes (which can achieve EQE above 80%). While the IQE results suggest that even higher EQE can be achieved with the thinnest 1 nm NiSi if absorption can be improved (which I will discuss in the next section), it would be interesting to observe the image quality provided by the best NiSi device tested thus far (2 nm BSI design).

The motivation for developing these NiSi SBDs is to demonstrate monolithic image sensors that will dramatically save on cost. One way to do this is by taking an image sensor designed for the visible spectrum and reverse engineering it to display photoresponse from the

SBDs that are integrated as a BEOL process; this has been demonstrated previously with both

CMOS and CCD image sensors31. Another approach would be to start with a ROIC that is designed specifically for this purpose and integrate the SBDs either during the CMOS process or as a BEOL process. Both of these approaches are valid but require a significant effort for the development of the SBD/readout integration process, which is beyond the scope of this work.

Instead, as a proof-of-concept image demonstration, I developed a hybridized detector array

95 process. This process involves fabricating an array of NiSi photodetectors in the BSI configuration and hybridizing that detector array to a ROIC with indium interconnects. While the cost of this process is significantly higher at industrial scale than the monolithic approaches I mentioned, it is a process I am familiar with and have the ability to execute in a reasonable timeframe.

(a)

(e) (b)

(c)

(f)

(d)

The fabrication process I developed is outlined in Figure 57. The detector array fabrication process is very similar to the BSI detector fabrication from Section 2.3, with some tweaks to the contacts for compatibility with the ROIC. The ROIC I used for this demonstration is the ISC0403 by FLIR. The ISC0403 is a 640x512 element array on 15 µm pitch that is designed for MWIR imaging. Because the ROIC is designed to operate in the MWIR, it is not an ideal chip

96 to be used for SWIR imaging. The ISC0403 features a direct-injection unit-cell amplifier that feeds a relatively large integration capacitor that can handle > 6.5 million electrons. These

- design elements drive the input referred noise specification to be 715 e RMS (which degrades as chip temperature is raised above 80 K123). These specifications are suitable for MWIR imaging applications which typically feature significantly larger photon flux than SWIR imaging applications. FLIR does manufacture a ROIC designed specifically for SWIR imaging systems, the

- ISC1202 (input referred noise < 30 e RMS), but the ISC0403 is the only suitable ROIC I had on hand for this demonstration.

A still image from a 60 Hz video taken with the NiSi SBD FPA is shown in Figure 58. To improve image quality, a nonuniformity correction and bad pixel substitution is typically performed on IR FPAs. In this image, I’ve performed no such corrections so the defects and

97 nonuniformities can be seen. There are a number of open pixels (black), including an entire row and column, which is attributed primarily to unoptimized array fabrication and hybridization.

There is some minor nonuniformity throughout the image which has a regular column/row pattern to it; this can be attributed to nonuniformity in the ROIC (usually driven by the unit cell amplifier and integration capacitor). There are some streaky patterns in the image, particularly on the right-hand side, which can be attributed to the fabrication process. Detector nonuniformity is typically manifested with no spatial coherence (akin to a white-noise image); this is because detector nonuniformity is often driven by material defects, which are randomly distributed spatially. This type of nonuniformity is not dominate in the image above, indicating excellent detector uniformity. In a commercial IR FPA made from a bandgap-based photodetector, detector nonuniformity will dominate such that the ROIC nonuniformity isn’t seen. The FPA device uniformity is consistent with my single element detector measurements from the previous sections and is a known favored characteristic of SBDs, which can have an order of magnitude better uniformity (< 1%) than IR detectors made from compound semiconductors31.

Despite the unoptimized imaging conditions (ROIC designed for MWIR, 50% window transmission and no nonuniformity/bad pixel corrections), the image quality in Figure 58 is reasonably good. This is a promising demonstration, indicating that the relatively low quantum efficiency of these detectors doesn’t prohibit their use for imaging applications. It is expected that image quality can be improved significantly by simply utilizing components optimized for

SWIR imaging. If EQE can be further improved by increasing absorption in the 1 nm NiSi SBD

(which had the highest IQE), image quality should improve even more; this is the topic of discussion for the next section.

2.6 Engineering NiSi Schottky Barrier Photodiodes for Improved Quantum Efficiency

Using results from the device analysis, I now have the required information to investigate what is possible, from an engineering perspective, with regard to QE performance of

NiSi SBDs. It is clear from Figure 59 (a) and the IQE analysis that reducing the silicide thickness significantly improves the IQE with plenty of room for improvement with respect to the theoretical maximum performance.

(a) (b)

In Figure 59 (b), I used the mean hot carrier attenuation length extracted from the Vickers’ model fitting (64.7 nm) to calculate the theoretical IQE of NiSi SBDs as the thickness is reduced to a single monolayer (taken to be ½ of the lattice constant: 5.2 Å124). Because I extracted the hot carrier attenuation coefficient directly from SBD performance measurements, I believe the predicted thickness-dependent performance is more likely to be accurate than simply using a reported value that was obtained using another measurement technique such as ballistic electron-emission microscopy125-129 which often characterizes hot electron energies much larger than those applicable to IR SBD operation. It is important to consider that the Vickers model used to generate these modeled curves is known to break down as the L/t ratio gets very large

(see Section 2.1). Experimentally, however, the model doesn’t appear to break down within the

L/t range tested and therefore can likely be used as a reasonable approximation to expected performance improvements if the NiSi thickness can be further reduced. While the percolation threshold of NiSi was found to be around 1 nm in my experimentation, it is possible that this could be reduced by investigating low energy deposition techniques or reducing the substrate temperature.

The IQE performance improvements I’ve reported thus far are promising, but absorption must also be improved, particularly for the thinnest SBDs with highest IQE, to further improve the EQE. The most straightforward and established approach to improving the absorption, even for the thinnest silicide layers, is to use a waveguide detector configuration. SBDs in a waveguide configuration can approach unity absorption across the entire wavelength sensitivity range of the detector, limited only by parasitic losses (input coupling, scattering and absorption within the waveguide itself) which exist regardless of the detector technology. The waveguide configuration isn’t easily compatible with an imaging array however, necessitating the need for alternative approaches for imaging applications.

The two most common techniques for improving absorption in SBDs configured for normal incidence (imaging configuration) is through plasmonic or cavity resonances. While both are valid approaches, I will present a range of cavity designs that have the advantage of not requiring nanoscale patterning (in contrast to plasmonic designs). For all of these designs, I will use the following shorthand to represent the layers that comprise the designs:

h = high index material (Silicon) of nominally quarter-wave thickness

H = high index material (Silicon) of nominally half-wave thickness

n = low index material (SiO2) of nominally quarter-wave thickness

N = low index material (SiO2) of nominally half-wave thickness

100

A = NiSi absorber (1 nm for “worst-case” absorption scenario with highest IQE)

s = Thin silicon layer (25 nm) used as the SBD collector when resonance with a high

index material is not desired for the design.

S = Thick silicon substrate (500 μm). For comparison purposes, the free carrier

absorption has been removed with the assumption that using lower doped silicon

wafers will significantly reduce silicon absorption beyond the bandgap.

M = Thick gold mirror

Figure 60. Various FSI design concepts illustrating the minimal improvement afforded by designs more complicated than the very simplistic ASM design used in Section 2.5.

Figure 60 shows a variety of FSI designs. The most basic design, featuring a simple broadband metallic mirror on the backside performs relatively well. Slight improvement can be made by replacing the metallic mirror with a dielectric mirror, which reduces absorption from the mirror.

Coating the front side of the silicide results in weak filtering of the transmission and doesn’t enhance absorption relative to the uncoated design.

101

Figure 61. Two BSI designs illustrating the ability to “filter” the absorption but not increase beyond the relatively broadband nSAnM design used in Section 2.5.

Absorption can be improved with the BSI configuration, because the mirror (in close proximity to the absorber) provides a resonant feedback. Relatively broadband absorption can be achieved by utilizing a simple low index material for the quarter-wave back reflector as shown in

Figure 61. A stronger resonance design can be used to narrow the absorption band but not to significantly increase the peak absorption. Designs based on the BSI configuration represent the highest achievable absorption in a standard imaging configuration when a thick silicon substrate is used. To further improve absorption, resonant feedback from both ends of the silicide layer must be introduced. Because this is impossible with a thick silicon substrate, the fabrication process must be altered to remove the substrate. Figure 62 illustrates a simplified fabrication process that could be used to create such a device.

102

(a) (d)

(b) (e)

The ability to fabricate thin SBDs enables new optical designs that significantly enhance absorption relative to the BSI and FSI designs on thick silicon substrates.

103

Leveraging feedback from both ends of the silicide layer enables higher broadband absorption than the BSI configuration in a very basic design consisting only a single dielectric layer and metallic mirror deposition. A resonant design with 95 % absorption at 1.55 μm requires deposition of only four dielectric layers and a metallic mirror. It is remarkable that such high absorption can be achieved at normal incidence with an ultra-thin 1 nm NiSi absorber. While this certainly does not represent every possible thin SBD design, it does illustrate the tradeoff between peak absorption and absorption bandwidth that is fundamental to this design trade space. It also demonstrates absorption improvement over the entire wavelength range of interest using the broadband design when compared to the FSI and BSI designs using thick silicon wafers. The optimized design will depend on the application and its light source(s).

Using the extracted IQE from Section 2.5.5 and designs from above, I can calculate the expected EQE spectrum for a variety of thin SBD designs and compare them to the thick designs as shown in Figure 64.

104

Figure 64. Theoretical EQE for some of the optical designs discussed above. The IQE and index of refraction used to calculate these results were extracted from the 1 nm NiSi BSI device.

While the plot in Figure 64 is theoretical, it is important to consider that the key parameters of interest (index of refraction and IQE) that go into the EQE calculation were extracted from device measurements and found to be consistent with two different optical designs already (FSI and BSI). I believe these predictive plots are a significantly more realistic representation of expected performance than one which relies on reported literature values for the key parameters of interest that are often inconsistent, rarely extracted from device measurements or simply unavailable.

2.7 Chapter 2 Summary

In this chapter, I’ve reviewed the literature to establish state-of-art performance of SBDs operating in the SWIR atmospheric transmission band. I identified a shortcoming among existing reports with regard to investigation of ultra-thin silicide layers to improve IQE in silicide material systems that don’t require cryogenic cooling. After comparing a variety of silicide materials, I identified NiSi/n-Si as a material system of interest due to its cutoff wavelength and initial EQE results. In an effort to characterize and fit experimental data to theoretical

105 performance models, I fabricated and tested four different silicide thicknesses in two different optical configurations (along with a thick silicide reference device). The uniformity of all the devices is excellent, and the dark current characteristics are well predicted by thermionic emission theory with bias-dependent barrier lowering. Using a novel LSF/TMM fitting technique, the precise absorption under normal incidence of the NiSi layer was determined for each device to enable extraction of the IQE. For each thickness, the extracted IQE of the FSI and

BSI devices were in excellent agreement, supporting the accuracy of the measurements and methodology. The measured EQE and IQE spectrum of these devices are the highest reported values to-date for any silicide SBD with comparable SBH. I reviewed two IQE performance models and identified the limitations of each. Using a close approximation to Vickers’ model, I fit the IQE spectra to extract the ratio of the hot carrier attenuation length to the silicide thickness for each device. This type of fitting is rarely performed and often replaced by an empirical fit to the modified Fowler equation which doesn’t provide insight to the physical process involved in hot carrier collection. Using the hot carrier attenuation length, I was able to theoretically predict the IQE for silicide layers down to a single monolayer thickness. Using the refractive index of the thinnest (1 nm) NiSi layer, I presented a variety of optical designs that demonstrate how absorption can be improved for normal incidence illumination by introducing thin device concepts. I quantified the trade space between absolute absorption and absorption bandwidth for the optical design and calculated the predicted EQE spectra for those designs.

The work presented here is the most thorough investigation into device performance of NiSi/n-

Si SBDs to-date. The methodology of characterization to obtain critical device performance parameters can be used as a template for further study of other SBD material systems which are rarely investigated in such detail. To provide a proof-of-concept demonstration of the image quality attainable using the NiSi SBDs investigated here, I mated an array of 2 nm NiSi SBDs to a

106

ROIC to obtain SWIR imagery. Despite several components of the image system not being optimized for SWIR, the image quality is reasonably good.

107

CHAPTER 3

SILICON NANOSTRUCTURES FOR INFRARED PHOTODETECTORS

3.1 Motivation and Device Concept

Although the measured and calculated performance improvements for the thinnest NiSi

SBDs from Chapter 2 are promising, there still remains a significant EQE performance gap relative to narrow-bandgap based photodetectors. I demonstrated how absorption can be dramatically improved for these devices, even for the thinnest silicide layers tested. Despite these results, the EQE is ultimately limited by two primary inefficiencies: photon energy transfer and excited carrier collection. Photon energy transfer limits the theoretical maximum IQE because absorption in a metal leads to excess hot carrier energy between zero and the photon energy above the metal Fermi energy. Excited carrier collection is poor because hot carriers in solids quickly relax (picosecond regime) to thermal equilibrium before they can travel a significant distance in the material. In contrast, the bandgap of a semiconductor forces excess energy to be greater than or equal to the bandgap energy and features excited energy lifetimes in the nanosecond-millisecond regime which improves extraction efficiency. One concept to marry the monolithic advantages afforded by the SBD architecture with the performance advantages of a narrow bandgap semiconductor is through quantum confined structures.

108

퐸1

퐸0 퐸퐹

Semi- Dielectric Silicon metal

Figure 65. Energy diagram of quantum confined semi-metal SBD. The confinement well is provided by the wide bandgap dielectric and Schottky barrier, producing an asymmetric well. The semi-metal thickness should be designed such that the first excited state confinement energy is near the top of the Schottky barrier for efficient extraction.

The diagram in Figure 65 shows a conceptual design of a Schottky-barrier photodiode that features a thin absorber with quantum confinement. To achieve the illustrated confined energy states, a semi-metal would need to replace the metal/silicide because the conduction/valance band overlap of a semi-metal is small enough that it can be separated to open a bandgap with quantum confinement130-132. This device, unlike a traditional design, features a unity theoretical maximum quantum efficiency above the energy gap introduced by confinement. The excited carrier lifetime should also be appreciably longer than the hot carrier lifetime in a metal. These features enable near unity extraction efficiency of excited carriers for well-designed bound-to-quasi-bound and bound-to-continuum quantum wells133. The primary limitation of this device design is the limited absorption afforded by a single quantum well.

Semiconductor-based quantum well infrared photodetector (QWIP) designs address the absorption issue by stacking several quantum wells in series, as shown in Figure 66.

109

Contact

Barrier

Well

Contact

Figure 66. Generic conduction band diagram of a quantum well photodetector under bias.

A major limitation of this approach is the lattice matching epitaxial growth requirement which inhibits monolithic imaging arrays. A novel conceptual device that circumvents the lattice matching requirements while improving absorption is a vertical quantum well design, which I will refer to as a silicon quantum wall (SiQW) architecture (illustrated in Figure 67).

Core-Shell Quantum Walls

Contacts

Wall Collector Cladding Cladding Collector Silicon Substrate

(a) (b)

Figure 67. Conceptual SiQW detector illustrating an energy band diagram (a) and profile view of the device geometry (b). The quantum walls (vertical well) or posts (vertical wire) are composed of silicon and connected directly to the substrate where a common contact is made. The conformally coated cladding forms an energy potential such that the silicon is a low energy well with confined energy states. The top contact is made to the low-energy collector material which should be doped to reduce series/contact resistance.

The SiQW architecture has several advantages over epitaxial QWIPs. By connecting quantum wells in series, as is done in QWIPs to improve absorption, carriers excited out of one

110 quantum well must “hop” past subsequent wells in order to be collected. A fraction of photoexcited carriers will be trapped by the low energy well, limiting the collection efficiency. As a result, an optimum number of wells, depending on recapture mean-free path, absorption and operating bias provides the highest quantum efficiency133. The SiQW architecture features quantum wells connected in parallel, eliminating this source of inefficiency because contacts are made directly to the cladding (through the doped collector) and well (through the substrate).

There is also a requirement to replenish extracted carriers back to the quantum well after collection. If this isn’t done, no confined carriers will be present to participate in absorption, and the wells will become transparent to the transition energy134,135. For QWIPs, this is accomplished by carrier injection from the emitter contact through the device in the form of a leakage current. A fraction of this leakage current will be trapped by the wells (just as photoexcited carriers are), thereby repopulating them for absorption. This process introduces additional dark current in the device, which is undesirable. Because contact is made directly to each well through the substrate in the SiQW architecture, wells can be populated directly from the contact without the need for leakage current. The doped contacts of a SiQW are designed to be at a lower energy than the well, so the thermionic emission current limit is designated by the excitation energy rather than the contact, as it is in QWIPs. This design characteristic of the

SiQW will create a reverse bias dependence analogous to SBDs, that features a “soft” saturation dark current, that will increase with bias only due to barrier lowering and tunneling effects.

QWIPs, in contrast, have a simple photoconductor-like dark current behavior which degrades

SNR relative to diode-like devices.

The advantages pointed out thus far have been related to dark current and collection efficiency. Another advantage of the SiQW architecture is an optical one, based on absorption.

Quantum wells feature a strong absorption dependence on optical polarization. The oscillatory

111 electric field of the incident light must be polarized in the confinement direction to be absorbed

(i.e. the electric field must be aligned such that it perturbs the confinement potential for absorption to occur). For epitaxially-grown QWIPs, this results in no absorption for normally incident light (typical imaging configuration). To address this, a variety of techniques have been employed to redirect normally incident light to satisfy the polarization selectivity rules of the quantum well in QWIPs136-139. The SiQW features vertical wells which are oriented for normal incidence absorption. The optical cross section of the SiQW is also significantly larger than for

QWIPs, due to the limited number of wells that can be grown in series.

The multitude of performance advantages afforded by the SiQW architecture form a compelling motivation for investigation. There exist, however, several major development hurdles that must be addressed before a SiQW device can be realized, including:

1. Modeling of silicon quantum wells to determine nominal well dimension and

cladding/collector band-offset requirements for intraband energy transitions in the

infrared regime.

2. Identification of potential cladding/collector materials with appropriate band-

offsets from (1).

3. Fabrication of quantum walls of those dimensions.

4. Conformal coating of relevant cladding/collector materials to fabricate

heterostructures.

The following chapter will discuss progress toward each one of these major milestones for the development of this promising device architecture.

3.2 Silicon Quantum Well Modeling

The following treatment will consider modeling of quantum walls (vertical wells) with 1-

D confinement. For quantum posts (vertical wires), the modeling should be adjusted to account

112 for 2-D confinement. In order to develop fabrication requirements, I must first model some notional quantum well designs, based on silicon material parameters, to determine target well dimensions and cladding/collector parameters. In quantum theory, a particle is described by its wavefunction and energy according to Schrödinger’s equation, written below in its 1-D time- independent form (assuming a constant particle mass):

ℏ2 휕2 − 휓(푧) + 푉(푧)휓(푧) = 퐸휓(푧) (78) 2푚∗ 휕푧2 where ℏ is Planck’s constant divided by 2휋, 푚∗ is the particle effective mass, 휓 is the particle wave function, 푉 is the 1-D potential and 퐸 is the particle energy. Given the effective mass and envelop function approximations, this can be rewritten as:

ℏ2 휕2 − 휓(푧) + [푉(푧) − 퐸]휓(푧) = 0 (79) 2푚∗ 휕푧2 Motivated by the desire to formulate a numerical approach to solving Equation 79, a finite difference approximation to the second derivative of a function (푓) can be written:

푑2푓 푓(푧 + Δ) − 2푓(푧) + 푓(푧 − Δ) ≈ (80) 푑푧2 Δ2 where Δ is a finite step in the 푧-dimension. Substituting Equation 80 into Equation 79 and rearranging produces:

2푚∗ 휓(푧 + Δ) = [ Δ2(푉(푧) − 퐸) + 2] 휓(푧) − 휓(푧 − Δ) (81) ℏ2 which is a convenient form where two known values of the wavefunction at points 푧 and 푧 − Δ can be used to calculate the wavefunction at the next point 푧 + Δ for any energy 퐸. In a quantum well system, discrete energy values result in stationary states which have wave functions which satisfy these boundary conditions:

113

휕 lim ⇒ 휓(푧) → 0, 휓(푧) → 0 (82) 𝑧⟶±∞ 휕푧 The eigen energy solutions can be solved for by taking an initial guess, calculating the resultant wavefunction, testing the boundary conditions and forming a new guess using a root finding algorithm until the boundary conditions are satisfied to some tolerance. This approach is known as the shooting method and is described in detail by Harrison140. The first two starting values of the wavefunction are still unknown and must be chosen based on knowledge of the system. It is known from the analytical solution to a simple rectangular well that the wavefunction exponentially decays toward zero at the boundaries. Using this knowledge, the starting conditions can be chosen as:

휓(0) = 0; 휓(Δ) = 1 (83)

While these starting values may initially appear strange, they are valid for any potential profile, as proven by convergence tests comparing this numerical approach to analytical solutions140.

Because of the arbitrary (albeit strategic) choice of 휓(Δ) = 1, the calculated wavefunction will be an arbitrarily scaled version of the real wavefunction. To properly normalize this scaled wavefunction, we can use the fact that the probability distribution function (equal to the square of the wavefunction) of the particle must be normalized to unity, i.e.:

∞ ∫ |휓(푧)|2푑푧 = 1 (84) −∞

The formulation described above, in particular Equation 81, is valid for the special case of a constant effective mass throughout the system. Real heterostructures will have a spatially defined effective mass that varies depending on the constituent material properties. Equation

79 can be reformulated, again using finite difference approximations, for the variable effective mass system to be140:

114

휓(푧 + Δ) 2Δ2 1 1 휓(푧 − Δ) = [ (푉(푧) − 퐸) + + ] 휓(푧) − (85) 푚∗(푧 + Δ⁄2) ℏ2 푚∗(푧 + Δ⁄2) 푚∗(푧 − Δ⁄2) 푚∗(푧 − Δ⁄2) where 푚∗(푧) is the spatially-dependent effective mass defined by the material heterostructure.

(a) (b) (c)

Figure 68 shows a series of GaAs/AlGaAs quantum wells that feature three different energy transitions: bound-to-bound (a) bound-to-quasi-bound (b) and bound-to-continuum (c).

Experimentation in the GaAs/AlGaAs system has demonstrated that absorption is strongest for the bound-to-bound transition and weakest for bound-to-continuum133. This can be understood by considering that the oscillator strength, which depends on the wavefunction overlap, is strongest for the bound-to-bound transition. Carrier extraction efficiency from the well, however, is worst for the bound-to-bound transition due the cladding barrier blocking transport out of the well. Extraction of a bound-to-bound transition generally requires a high applied bias to distort the cladding barrier until an appreciable tunneling probability occurs at the first excited state (which also increases dark current). In contrast, very little bias is required to achieve near unity collection efficiency for bound-to-continuum and bound-to-quasi-bound transitions133. Because the SiQW architecture has absorption advantages over QWIPs, the bound-to-quasi-bound and bound-to-continuum designs are therefore of most interest for this architecture due to their extraction efficiency advantage.

115

(a) (b) (c)

Figure 69 shows bound-to-quasi-bound designs for a silicon quantum well in the [100] crystal orientation for three different barrier heights of 1 eV (a), 0.5 eV (b) and 0.3 eV (c). The well widths required to design a bound-to-quasi-bound transition for these barrier heights are

15 Å, 21 Å and 27 Å, corresponding to energy transitions of 632 eV, 332 eV and 200 eV

(wavelength of 1.9 µm, 3.8 µm and 6.3 µm) respectively. You will notice that the well width for the 0.3 eV barrier is thinner than the corresponding quasi-bound transition in the GaAs/AlGaAs well from Figure 68 (2.7nm vs 4.6 nm). This is because the electron effective mass in silicon

(0.19 m0) is higher than GaAs (0.067 m0). Effective mass is generally anisotropic, dependent upon the potential profile of the crystal orientation. For silicon, like many materials, the effective mass features an ellipsoidal constant energy surface which has isotropic effective mass in two crystal dimensions with a different (usually higher) effective mass in the third. These effective masses are referenced as the transverse and longitudinal effective masses respectively.

The longitudinal electron effective mass in silicon is 0.98 m0 in the [100] crystal direction. This implies the lowest effective mass for confined electrons in silicon is realized by lateral confinement on a [100] wafer defined by the transverse effective mass (condition modeled above). Because lower effective mass translates to wider quantum wells, the most technologically interesting crystal orientation for SiQW is indeed the [100] wafer, which is

116 conveniently the most commonly available and produced orientation. To determine the impact of cladding effective mass on the design, I designed a series of wells with equal barrier height but different cladding effective mass as shown in Figure 70.

(a) (b) (c)

Higher cladding effective mass results in stronger confinement, leading to higher energy transitions and narrower wells for a given barrier height.

It is obvious that the transition energy depends on the barrier height, but an interesting result is that the quasi-bound transition energy is approximately a constant fraction of the barrier height depending on the relative difference in effective mass between the cladding and well. For the wells in Figure 69, an equal effective mass results in the quasi-bound transition energy always equaling 66-67% of the barrier height. For the higher and lower effective masses modeled in Figure 70, the energy transitions are 81% and 64% of the barrier height respectively.

This useful relationship enables an engineer to quickly determine the ideal barrier height for a given wavelength of interest assuming the material effective masses are known.

117

(a) (b) (c)

Using this principle, I designed three silicon quantum wells with transition energies that correspond to absorption in atmospheric transmission windows of interest for imaging applications (Figure 71). While a constant effective mass was used for these designs, if the cladding effective mass is known, similar wells can be designed just as easily.

Thus far, basic rectangular wells have been used to mock a SiQW device (from an energy transition perspective). A SiQW device features a cladding surrounded by a low energy region for collecting extracted carriers from the well as shown in Figure 67. A potential profile that features a low energy well surrounded by higher energy cladding (as in the rectangular well), forces an evanescent wave function at the boundaries, which assists in the convergence toward the eigen energies of the system. The SiQW device, with its low energy collector boundary, doesn’t force an evanescent wavefunction at the boundary, and therefore, doesn’t converge as naturally as the rectangular wells modeled thus far. Nevertheless, to determine the effect the collector region has on the confined states, I modeled the bound and quasi-bound energy states for the same well design from Figure 69 (c) as a SiQW with defined collector regions (Figure 72).

118

Figure 72. Energy diagram and wavefunction for SiQW device with low-energy collector region. The bound-to-quasi-bound transition for this 27 Å well is 198 meV.

The quasi-bound energy transition defined by the SiQW structure agrees with the basic rectangular well model to within 2 meV, validating the use of the simple rectangular well for design purposes.

While bound-to-quasi-bound and bound-to-continuum designs are proven designs demonstrated by multi-well QWIPs, it requires specific barrier heights to achieve specific wavelength sensitivity. For the GaAs/AlGaAs system, this is accomplished readily by tuning the aluminum fraction of the ternary alloy. While it is possible such an analogous material system with tunable barrier height exists for silicon, it is advantageous to come up with a device design that doesn’t require a precise barrier height for a given wavelength sensitivity of interest. This can be accomplished by leveraging quantum mechanical tunneling.

Sarangan141 describes how the tunneling probability can be numerically calculated using the shooting method for an arbitrary potential profile. In a tunneling problem, the potential profile is bounded by low-energy materials (in contrast to the high-energy cladding in a potential well). This potential profile forms traveling waves in the low-energy boundary regions. This can be seen in the SiQW design from Figure 72 by the oscillatory wavefunction in the boundary

119 regions of the first excited state. The traveling wavefunction can be written in terms of the incident (휓푖), reflected (휓푟) and transmitted (휓푡) components:

푗푘푧𝑧 −푗푘푧𝑧 푗푘푧𝑧 휓푖(푧) = 퐴𝑧푖푒 ; 휓푟(푧) = 퐴𝑧푟푒 ; 휓푡(푧) = 퐴𝑧푡푒 (86)

√2푚∗(퐸 − 푉) 푘 = (87) 𝑧 ℏ where the 퐴𝑧푖,푟,푡 terms are the respective amplitudes of the traveling wave components. The shooting method for calculating the tunneling probability requires different initial conditions than those in found in Equation 83. Because the transmitted side features a traveling wave in only one direction, the initial conditions are chosen to be:

휓(0) = 1; 휓(Δ) = 푒−푗푘푧Δ (88) and the shooting method is deployed in reverse through the potential profile from the transmitted side toward the incident. Unlike in the previous method, where eigen states are converged to iteratively, the tunneling problem simply calculates the wavefunction at the given energy and uses that wavefunction to determine the probability of tunneling (transmission) through the potential profile. The tunneling probability (푃푡) is simply a ratio of the transmitted and incident wave amplitudes.

2 2 퐴𝑧푡 1 푃푡 = | | = | | (89) 퐴𝑧푖 퐴𝑧푖

All that remains to calculate the tunneling probability, therefore, is calculating the incident amplitude of the wavefunction (since the transmitted amplitude was chosen to by 1 in the boundary conditions). The last two calculated points of the wavefunction are the are on the incident side and can be written:

120

−푗푘푧푁Δ 푗푘푧푁Δ 휓(푁Δ) = 퐴𝑧푟푒 + 퐴𝑧푖푒 (90)

−푗푘 (푁−1)Δ 푗푘 (푁−1)Δ 휓((푁 − 1)Δ) = 퐴푧푟푒 푧 + 퐴푧푖푒 푧 (91)

Equations 90 and 91 can be used to calculate the reflection and incident amplitudes by substitution.

휓((푁 − 1)Δ)푒푗푘푧Δ − 휓(푁Δ) 퐴𝑧푟 = (92) 푒−푗푘푧푁Δ(푒2푗푘푧Δ − 1)

−푗푘푧푁Δ −푗푘푧푁Δ 퐴𝑧푖 = 푒 (휓(푁Δ) − 퐴𝑧푟푒 ) (93)

Calculation of the tunneling probability is therefore done by shooting the finite difference approximation to Schrödinger’s equation (Equation 85) using the boundary conditions from

Equation 88, normalizing the resultant wavefunction according to Equation 84, calculating the incident wavefunction amplitude using Equation 93 and using that amplitude to calculate the tunneling probability using Equation 89. The tunneling probabilities for a single rectangular barrier and double barrier, calculated using the shooting method, are shown in Figure 73.

(a) (b)

The utility of tunneling for detector design is the provided by the flexibility to tune energy levels to conduct through the system, even if the barrier height would classically prohibit such conduction. Because of this, barriers with relatively high energy (> 1 eV) can be used to design

121 detectors sensitive to much lower energies in the infrared. One such design is illustrated in

Figure 74.

(a) (b)

This tunneling quantum wall (T-SiQW) detector utilizes the tunneling phenomena to selectively collect carriers that are excited from the ground state of the quantum well to the first excited state. The T-SiQW uses the same layers as the SiQW design from Figure 72, but the band-offsets and layer thicknesses are chosen differently. In the SiQW design, the barriers are designed relatively thick to eliminate tunneling of the ground state energy directly to the collector. The T-SiQW design, in contrast, has relatively thin tunneling barriers, and the collector band offset is designed to be higher than the ground state confinement energy to eliminate direct tunneling to the collector. A convenient feature of the T-SiQW architecture is the barrier and collector band offsets don’t have to be precise for operation. In fact, a single barrier/collector design can be used for a range of wavelengths. To demonstrate this, another

T-SiQW designed to operate at 2.6 µm using the same collector and barrier from Figure 74 is shown in Figure 75.

122

(a) (b)

Figure 75. Tunneling SiQW design with absorption designed at 2.6 µm (transition between ground and first excited state). (a) Energy diagram with superimposed eigen energies/wavefunctions (zero-energy reference chosen as silicon conduction band). (b) Tunneling probability through system with same energy reference as plot (a). Barrier and collector layers are identical as the design from Figure 74.

The only difference between the designs in Figure 74 and Figure 75 is the silicon wall width (14 Å and 27 Å respectively). This implies that if the silicon wall fabrication process forms walls with a distribution of widths between 14 Å and 27 Å, the aggregate response should be one that is broadband and spans the SWIR atmospheric transmission band. Because these quantum walls are oriented vertically, a single pixel could be composed of thousands to millions of quantum walls, connected in parallel, with an overall response that is a summation of each individual well. Broadband photo response is an important feature for most passive imaging applications, so the ability to produce a broadband T-SiQW response with a common barrier and collector coating is extremely useful. Like the two SWIR designs above, T-SiQWs can be designed for the MWIR and LWIR atmospheric windows as well. A summary of nominal layer thicknesses and band offsets for T-SiQW designs that span all three atmospheric transmission windows is given in .

123

Wavelength Well Width Barrier Width Barrier Offset Collector Offset (µm) (Å) (Å) (meV) (meV) 1.3 14 25 1500 450—600 2.6 27 25 1500 450—600 3.0 30 25 1500 380—500 5.0 41 25 1500 380—500 8.0 54 25 1500 160—180 12.0 68 25 1500 160—180

While a single barrier design can be used to create functional detectors across all three atmospheric transmission windows as is shown in Table 5, there is some engineering that should be done to determine the optimal barrier width. Figure 76 shows the tunneling probability of a

3.0 µm sensitive T-SiQW device with three different barrier widths.

Figure 76. Tunneling probability of 3.0 µm T-SiQW device from Table 5 using three different barrier widths.

From Figure 76, it is clear that modulating the barrier width doesn’t significantly impact the resonance energy levels. Thicker barriers produce narrower tunneling resonances and also suppress lower tunneling probabilities for off-resonance energy levels. In the extreme case of

124 very thick barriers, the tunneling resonance will be completely “pinched” off and will not produce appreciable tunneling at the eigen state of the well (SiQW condition). This indicates that the barrier thickness for T-SiQW designs will likely form an optimization trade space between extraction efficiency and dark current in the device.

3.3 Heterostructure Materials

The heterostructure designs modeled in Section 3.2 require conformal coating of silicon quantum walls, with specific conduction band offsets to silicon and precise uniformity. Before identifying materials of interest, it is important to consider what fabrication process(es) are capable of conformally coating these high density and high aspect ratio structures with acceptable uniformity. The most promising deposition technique for this challenging task is atomic layer deposition (ALD). The ALD process consists of sequential exposure of the sample to gas precursors that react with the surface in a self-limiting manner. Only one precursor gas is introduced to the sample at a time, unlike other chemical vapor deposition (CVD) processes.

Typically, two precursor gasses are used in the following sequence: expose precursor I – purge – expose precursor II – purge; this sequence is referred to as one ALD cycle. A thin film is formed through repeated ALD cycles, which enables precise control over layer thickness. The self- limiting surface reaction enables conformal and uniform coating of dense, high aspect ratio structures. A growing variety of materials can be deposited by ALD, including dielectric, semiconductor and conductor layers (reviewed extensively by Miikkulainen et al.142 in 2013).

With this in mind, I’ve performed a literature search for materials with promising band offsets that have already been demonstrated by ALD growth. These materials can be broadly classified as large band offset materials (for barriers in T-SiQW architecture), low to moderate band offset materials (for quasi-bound and bound-to-continuum SiQW cladding or T-SiQW collectors) and negative band offset materials (for collector layer in SiQW). Because ALD films are generally

125 polycrystalline, and the conformal layer thickness of the heterostructure designs are in the range of 1—6 nm based on the modeling in Section 3.2, it isn’t critical to find materials that are lattice matched. This greatly widens the list of suitable materials for designing SiQW and T-

SiQW heterostructures.

Al2O3

HfO2 ZrO2

GaN GaP ZnS ZnTe Ta2O5 Ga2O3 TiO2 ZnSe ZnO

Figure 77 depicts a range of reported band offsets for materials of interest with respect to silicon. Several materials exist within each category, which provides a promising outlook that a functioning heterostructure can be achieved with enough development time. A particularly interesting set of materials is ZnTe and ZnO. ZnTe features a nominal conduction band offset around 550 meV, while ZnO has a negative conduction band offset (i.e. the conduction band of

ZnO is lower in energy than Si). This implies that the ternary alloy of ZnOXTe1-X has the potential to provide an alloy-fraction tunable band offset to silicon (characterized by a bowing parameter

148) analogous to the GaAs/AlGaAs material system. Other ternary materials with the potential to provide an alloy fraction with tunable band offset include ZnOXS1-X and InGaXN1-X. It is also apparent from Figure 77 that the band alignment of these materials relative to silicon is not precisely known at this time based on the spread in reported values. Many of these offsets are

126 predicted from Anderson’s rule, which is based entirely on the electron-affinities of the materials. Analogous to how the Schottky-Mott rule often doesn’t accurately predict the

Schottky barrier height between a semiconductor and metal (as discussed in Chapter 2),

Anderson’s rule only approximates the expected band offset between two materials. Precise determination of the band offsets will likely require experimental validation.

3.4 Silicon Quantum Wall Fabrication

There are generally two classifications of fabrication methods for forming vertical quantum nanostructures (posts or walls): bottom-up (growth) and top-down (etching). The bottom-up approach consists of starting with a seed template of some sort and epitaxially growing silicon nanostructures that preferentially grow according to the template. The bottom- up approach has been extensively studied in silicon156. The top down approach consists of starting with a silicon wafer and selectively etching to reveal nanostructures. Because the motivation for these devices is for low-cost IR image sensors, the bottom-up approach isn’t as promising as the top-down, which has more potential for low-cost wide area fabrication. One such method for fabrication of top-down silicon nanostructures is known as metal-assisted chemical etching (MacEtch)157 and is the fabrication approach I chose to investigate further.

3.4.1 MacEtch Process Overview

MacEtch is an electroless galvanic corrosion of silicon in the presence of a noble metal catalyst which produces dramatic etch contrast in a wet chemical solution. The solution is

157-159 typically composed of HF and an oxidizing agent such as H2O2 or HNO3 . In this process, metal patterns bore themselves into the silicon substrate leaving behind a structure with lateral dimensions defined by the initial metal pattern holes or gaps.

127

(a) (b)

Figure 78. Illustration depicting an isometric view of the MacEtch fabrication process, (a) metal pattern on silicon before MacEtch and (b) resulting silicon structures after vertical MacEtch.

MacEtch has been demonstrated on both lithographic160-162 and self-assembled158,159,163-167 metal patterns. Extremely thin, vertical silicon nanostructures have been demonstrated by several research groups168,169. The resultant silicon structures formed through the MacEtch process are striking. The extremely high aspect ratio, crystalline structure, room temperature synthesis and low-cost fabrication are unique and appealing features to provide a platform for innovative optoelectronic devices.

3.4.2 PVD Self-Assembly for MacEtch

As mentioned in the previous section, MacEtch has been demonstrated to reliably produce silicon nanostructures using a variety of metal patterning approaches. The most

164,167,171-174 common process utilizes a metal salt bath such as AgNO3 where the etch geometry is defined by silver dendrite formation from the wet-chemical solution. While modest control over the geometry has been demonstrated172, the resultant silicon nanostructures have generally been larger than 50 nm. These structures are too large to exhibit quantum confinement, so a process for producing smaller feature sizes must be developed to fabricate vertical SiQWs.

128

One method for forming self-assembled metal patterns < 10 nm in size is with ultra-thin metal films near the film percolation threshold formed by physical vapor deposition (PVD). It is known that metal films deposited onto (semi)insulating substrates evolve to a thin-film state through a morphological sequence: compact islands, elongated islands, percolation, hole filling and finally, the thin-film state;175 this evolution is captured in a series of SEM images shown in

Figure 79 for various Au films I’ve deposited on oxidized silicon. The sizes of these islands (and spacing between them) are dependent on a number of factors including the substrate composition, substrate temperature, surface quality and metal type. In the following sections, I will investigate utilizing the metal patterns from this morphological sequence as the catalyst for the MacEtch process with the goal of producing silicon nanostructures in the quantum confinement regime. This PVD method of forming metal patterns is particularly attractive because of its wide availability, uniformity, cost and purity.

129

3.4.2.1 Substrate Prep (Native Oxide)

One way to alter the wettability (and hence island formation) of metal on silicon is surface oxidation; in general, metals will not wet an oxidized silicon surface as well as a silicon surface with oxide removed. I found, experimentally, that stripping the native oxide of silicon with a BOE solution immediately prior to metal deposition resulted in continuous films for depositions as thin as 2 nm for both gold and platinum evaporation. In contrast, I found silver films formed patterned structures for depositions as thick as 14 nm.

Figure 80. SEM image of 10 nm silver film deposited on silicon wafer with oxide removed immediately prior to deposition.

Because the wettability of silver on silicon is relatively poor, a wide range of thicknesses form metal patterns suitable for MacEtch. Since the metal pattern serves as an etch catalyst for

MacEtch, the spacing between these metal structures defines what would be the resultant silicon nanostructure geometry post-etch. It is clear from the scanning electron microscope

(SEM) image in Figure 80 that these silver patterns will produce silicon structures that are far too large for the SiQW designs discussed earlier.

130

(a) (b)

Figure 81. Comparison of 2 nm sputtered gold film on (a) silicon after BOE dip and (b) plasma oxidized silicon.

To reduce the wettability of the substrate for platinum and gold films, I exposed silicon substrates to an O2 plasma barrel asher (200 W for 2 min) after a buffered oxide etch (BOE) dip to form a uniformly oxidized surface. I verified surface oxidation by testing that the substrate was hydrophilic. With the introduction of this critical processing step, I was able to achieve nanoscale gold and platinum PVD patterns at room temperature (Figure 82).

(a) (b)

Figure 82. Metal depositions of (a) 2 nm platinum and (b) 5 nm gold on oxidized silicon in the hole-filling phase.

These depositions produced smaller structures than the silver films, with platinum forming the smallest features. It should be noted that as the thickness decreases below 4 nm, repeatable

131 and uniform control of the PVD process becomes more challenging due to the extremely short deposition time.

3.4.2.2 Substrate Temperature

Another technique for altering the wettability of a metal to silicon surface is by controlling the substrate temperature during deposition. In general, a low substrate temperature will allow for the thin film state to be reached at a lower thickness threshold than at high temperature. In other words, large feature sizes over a wider thickness window should be producible at elevated temperatures, while smaller features over a narrower thickness window should be producible at lower substrate temperatures.

(a) (b)

Figure 83. Sputtered gold films near the percolation thickness (a) 4 nm gold sputtered at room temperature (b) 16 nm gold sputtered at 200°C. Both depositions were performed on oxidized silicon.

Figure 83 shows two metal films around the percolation thickness threshold for different substrate temperatures. It is clear that the elevated substrate temperature increases the percolation thickness threshold significantly. These results suggest that substrate temperature could be leveraged as a process control parameter for altering the feature sizes of PVD self- assembled metal patterns. Presumably, the percolation thickness threshold would be reduced if the substrate temperature is cooled below ambient, but I did not explore this because the deposition tools I used do not have substrate cooling.

132

3.4.3 Influence of Metal Geometry on MacEtch

I already highlighted that the metal pattern geometry used for MacEtch is important because the negative space between metal directly defines the resultant silicon structure post etch. Additionally, we know from the literature that metal geometry plays some role in the etch characteristics. For example, it is well known that the MacEtch process does not occur at an appreciable rate when wide-area metal patterns are used, which can be attributed to limited hole diffusion161,176. Hildreth et al.162 have demonstrated catalyst shape can be designed, in conjunction with etchant composition, to control MacEtch direction to fabricate complex 3D nanostructures. In this work, metal shapes with dimensions smaller than 25 nm were not studied, so an investigation into how ultra-fine metal patterns behave during MacEtch needs to be explored. Precisely vertical etching is paramount to high density nanoscale silicon structures; any deviation, even slightly from normal, will cause undercutting of the silicon structures to form a roughened silicon surface as illustrated in Figure 84.

(a) (b)

Figure 84. Illustration of particle MacEtch featuring (a) vertical etching and (b) curved etching.

Previous work suggests solution composition, crystal orientation, as well as geometry plays a role in etch characteristics.168 To better understand the role each of these plays in the nanoscale regime, I performed a design-of-experiments with varying solution ratio (by volume):

6:1, 3:1, 2:1, 3:2, 1:1 and 1:2 HF:H2O2, crystal orientation: [100] and [111] and with a variety of

133 different patterns around the percolation thickness of the metal film. A subset of these experimental results is shown in Figure 85.

Figure 85. Comparison of metal pattern geometry, substrate crystal orientation and solution stoichiometry on etch profile for select trials. (column 1) As deposited gold pattern, (column 2) 6:1 HF:H2O2, (column 3) 3:2 HF:H2O2, (column 4) 1:2 HF:H2O2, (rows 1&2) on [100] wafers and (rows 3&4) on [111] wafers. All 60 s etch duration.

Figure 85 suggests that pattern geometry plays a dominant role in etch direction; small isolated nanoscale particles etch relatively unpredictably while small interconnected nanoscale mesh structures etch vertically (generally independent of crystal orientation and solution stoichiometry). These results are in contrast from previous studies that used larger particles, where it was found that solution composition and crystal orientation are the primary predictors of etch direction158,160,163,171-173.

134

To systematically quantify this result and analyze a large number of etches, I developed some image processing algorithms to analyze the metal patterns and post etch profile SEM images. To quantify the particle sizes of the metal patterns, I passed top view SEM images of the metal patterns through a Gaussian filter and segmented the image using thresholding. After segmentation, I can calculate each particle’s area using the SEM scale bar and counting the pixels of each segment.

To quantify etch direction, I need to analyze the post etch profile views of the silicon structures. I used canny edge detection to first isolate the etch paths of the particles. I then performed a 2-D correlation between the resultant edge image and 5-pixel vertical, horizontal and ± 45-degree structuring elements at each edge-pixel location. The strongest correlation among the structuring elements was used to define the approximate etch path direction at that pixel location.

135

(a) (b)

Figure 87. Zoom view of (a) original SEM image post-etch (scale bar = 200 nm) and (b) image after edge detection and directionality correlation. The colors indicate the edge directionality at that pixel location: 90-degree vertical (yellow), 0-degree horizontal (purple), +45-degree (turquoise) and -45-degree (red).

I used the mean of the absolute value of all path directions along every edge pixel to quantify the path angle for each etch process.

Vertical Etches

Random Etches

Size Threshold

(a) (b)

Figure 88 features the analysis of over 30 etch trials with varying metal patterns, crystal orientation and solution stoichiometry. Figure 88 (a) confirms no major dependence of etch direction on solution stoichiometry or crystal orientation for metal features in the nanoscale

136 regime. Figure 88 (b) indicates a strong dependence of etch direction with particle size. The plot suggests a threshold size between 300—600 nm2; etching of particles below this threshold results in random etch direction while etching of particles above this threshold is vertical. This analysis quantitatively supports what was indicated observationally in Figure 85.

(a) (b) (c)

Figure 89. Etch process demonstrating a faithful pattern transfer; (a) original metal pattern (b) isometric view post etch (c) close-up detail highlighting ideal pattern transfer.

In Figure 89, a gold film in the hole filling stage was used as a MacEtch template. This image set demonstrates faithful pattern transfer of the metal etch template. A “stress test” of the etch verticality is to perform a very long etch. Any deviation from vertical etching will result in undercutting of the silicon nanostructures which becomes more significant as the etch depth increases.

137

(a) (b)

Figure 90. SEM images of silicon nanostructures from (a) top and (b) profile views using a 3:2 HF:H2O2 8min MacEtch process with same Au film from Figure 89.

The etch result of this “stress test” is shown in Figure 90. The preservation of the silicon nanostructures for an etch depth of 38 µm indicates nearly ideal vertical etching. Using the SEM image of the original metal template from Figure 89, I estimate the width of the silicon nanowalls to vary between 5—20 nm. Using that dimension, I estimate the aspect ratio of the nanowalls fabricated in Figure 90 to be between 1400—7200:1. To my knowledge, this is the largest aspect ratio achieved by a top-down etching of high-density structures, by a significant margin164.

As a separate experiment, the etching characteristic of 50 nm gold nanoparticles is shown in Figure 91. These nanoparticles have a faceted spherical shape in contrast to PVD islands which have a more pancake-like shape. The 50 nm nanoparticles, despite having a footprint greater than the experimentally determined 300—600 nm2 threshold, do not etch as vertically as PVD islands of similar size. This suggests that not only the overall size, but the shape of metal catalyst determines the etch directionality in the ultra-fine particle regime.

138

(a) (b) (c)

Figure 91. MacEtch trial of 50 nm commercial gold nanoparticles (a) particles after deposition (b) ¾ view of substrate after MacEtch (c) profile view detail after MacEtch

This behavior can be attributed to the increased influence of momentum transfer for smaller particles from expelled gaseous byproducts from the etch process. As the particle size and surface contact area decreases, the forces imparted by these byproducts begins to compete with van der Waals forces that keep the metal particle in contact with the substrate177. This explains not only the size dependent etch characteristics, but it also explains the discrepancy between etching with colloidal and PVD particles because the contact area (and hence van der

Waals force) of a colloidal nanoparticle is much smaller than the flattened pancake-shaped features formed by PVD islands178. I published the detailed methodology and analysis on the role of geometry in governing MacEtch characteristics for ultra-thin gold films in the Journal of

Micro/Nanolithography, MEMS and MOEMS179.

3.4.4 Suitable Metals for MacEtch

The results discussed in the previous section were demonstrated exclusively with gold, but several other metals are known to function as a MacEtch catalyst including gold, silver, platinum, palladium, etc.157,159,167,180-182. It has been shown previously that etch characteristics, such as etch rate and morphology of the resultant silicon structures, are dependent on the metal catalyst used167,182. Additionally, the percolation threshold of a metal film depends on the metal type. Metals with thinner percolation thresholds on silicon will form finer mesh

139 structures, which could translate to finer silicon nanostructures post etch. Results from the previous section indicate that gold is an excellent metal for producing crystalline silicon nanostructures in the 5-20 nm size range. The resultant silicon morphology appears to be highly crystalline without significant sidewall damage as indicated by the SEM image in Figure 92.

Figure 92. High resolution SEM image of silicon nanostructures formed by gold MacEtch with no indication of crystalline damage to the sidewall.

Silver is another commonly used metal for MacEtch. Previously, I demonstrated that silver has a significantly thicker percolation threshold than gold on silicon (with or without native oxide). These structures would create a crystalline silicon structure with high surface area to footprint ratio, to increase the absorber volume of silicide-based SBDs for example.

140

(a) (b) (c)

Figure 93. (a) 10 nm silver island formation (b) profile view after 60 s MacEtch (c) profile view after 120 s MacEtch. Both etches used 2:1 HF:H2O2 solution.

Figure 93 (a) shows that silver PVD island patterns can be used to etch crystalline silicon nanostructures larger than those fabricated from gold islands. The silicon sidewalls appear smooth post etch, suggesting good crystalline quality remains. The etch process appears to progress vertically, but it can be seen in Figure 93 (b) that longer etch durations highlight slight deviation from vertical etching, unlike with gold mesh patterns. This can be attributed to the

163 fact that silver etches slowly in H2O2. As silver patterns bore into the silicon substrate, they will also break into smaller particles which etch chaotically. This phenomenon is depicted in

Figure 93 (middle) where the etch begins vertically but alters course after enough time exposed to the etchant solution.

From a geometry perspective, platinum is an intriguing MacEtch catalyst because of it has an ultra-thin percolation threshold on silicon. Nano-mesh platinum patterns with voids in the 1 – 4 nm range can be achieved at room temperature. In practice however, platinum has been found to produce porous silicon structures.

141

(a) (b) (c)

Figure 94. (a) 4 nm platinum film deposited on oxidized silicon at 250°C (b/c) profile view of substrate after etch indicating random etching direction and porous silicon formation.

It is clear from Figure 94 that MacEtch using a platinum catalyst produces porous silicon around the etch location. While porous silicon has been shown to feature characteristics indicative of quantum confinement183-186, exploiting this for practical photodetector fabrication is difficult in practice due to the complex 3D matrix that is formed in the silicon. My experimentation with platinum MacEtch has also revealed a tendency for the platinum layer to release from the substrate when placed in the wet chemical solution. It is likely that a combination of the thin platinum layer and high etch rate, relative to gold and silver, increases the likelihood of metal liftoff during etching. Dilution of the etch chemistry could potentially improve this characteristic, but maintaining the crystalline integrity of the resultant silicon structures may not be possible. Li et al.180 suggests the metal work function plays a key role in MacEtch rate.

Platinum has a relatively high work function that can efficiently inject holes into silicon that could cause etching some distance away from the interface site via hole diffusion.

3.4.5 Substrate Doping Impact on MacEtch

Doping concentration and polarity are critical design parameters for any semiconductor device, including photodetectors. For example, moderately p-doped silicon wafers are typically used for MWIR PtSi photodetectors because highly doped substrates can lead to barrier lowering due to tunneling and therefore, high dark current115,187. QWIPs generally feature

142 moderate to high doping, because the absorption mechanism in quantum wells increases with carrier density133.

(a) (b)

Figure 95. Profile view of (a) moderately p-type doped (1-10 Ω∙cm) and (b) highly p-type doped (1-5 mΩ∙cm) silicon nanostructures after 60s MacEtch in 2:1 HF:H2O2 solution

Experimental results for both p-type and n-type silicon wafers at high and medium doping levels indicate that substrates with either doping polarity behave similarly for gold

MacEtch. Moderately doped wafers appear to preserve the crystalline integrity of the silicon nanostructures (Figure 95 (a)), while heavily doped wafers result in the formation of porous silicon (Figure 95 (b)). Because of this, any photodetector designs requiring high doping of the silicon nanostructures will need to be doped post etch. Similar results regarding the impact of doping on MacEtch have been reported in the literature188.

3.4.6 Structural Integrity of Silicon Nanowalls

The diminutive and high aspect ratio nanostructures formed by MacEtch are sensitive to mechanical stress, so care must be taken to maintain the structural integrity of the nanostructures during processing. The primary mechanical stress imposed by common semiconductor processing for these structures is the drying process.

143

Because of the porous nature of nanostructured silicon, the standard nitrogen-drying process imparts surface tension as capillary forces draw fluid out of the sample pores. When the silicon nanostructures are physically isolated from one another, the surface tension causes collapsing of the structures as shown in Figure 96. The common technique to mitigate surface tension induced structural collapsing during drying is critical point drying (CPD), also known as supercritical drying. The “critical point” of a substance refers to a pressure and temperate at which the liquid and vapor phases of the substance have equal density. If the liquid and vapor phases have equal density, surface tension is eliminated. Drying nanostructures under these conditions can therefore preserve their structural integrity. Few substances have a nominally room temperature critical point at reasonable pressure, so CO2 with a critical point of 31.1 °C and 1072 PSI, is almost exclusively used for this application.

144

(a) (b)

As shown in Figure 97, the CPD process eliminates structural collapsing of MacEtch fabricated silicon nanostructures. Maintaining the vertical alignment of these structures will be important for subsequent steps in the photodetector fabrication process, particularly heterostructure material growth. Collapsed structures can “pinch off” access to processes gasses used for material deposition, for example.

3.4.7 Initial Demonstration of Conformal Coating with ALD

To demonstrate the feasibility of utilizing ALD for conformal and uniform coating of silicon nanowalls, I utilized an Al2O3 recipe designed for high aspect ratio structures.

145

The SEM images in Figure 98 demonstrate highly uniform and conformal coating of high-density silicon nanowalls. This coating demonstrates the feasibility of using ALD to fabricate SiQW heterostructures. To demonstrate actual device performance, further shrinking of the nanowall geometry into the quantum confinement regime is required.

3.5 Chapter 3 Summary

Using motivation provided by device results and theory of SBDs in Chapter 2, I proposed a novel

SiQW detector architecture with promising performance advantages over SBDs. I modeled a variety of SiQW designs which provided a target wall width between 14—68 Å for wavelength sensitivity that spans 1.3—12 µm. Based on confinement calculations in quantum wells, I identified the [100] crystal orientation as preferred due to the relatively low transverse effective mass for vertical quantum wells. I developed a rule-of-thumb for identifying an ideal barrier height for a given wavelength sensitivity (for quasi-bound designs) and quantified how the barrier effective mass effects this rule. I also proposed a more advanced resonant tunneling design (T-SiQW), which enables the use of high potential barriers and eliminates the requirement of precise cladding energy offsets for a specific wavelength sensitivity. In an effort

146 to fabricate low cost silicon nanowalls in the dimensions of interest for SiQW detectors, I investigated the MacEtch process as a top-down approach. Utilizing a self-assembled gold nano- mesh, I fabricated silicon nanowalls with confinement dimension between 50—200 Å, an order of magnitude smaller than previously demonstrated. This development was realized by discovering that metal nanoparticles don’t etch with the same crystal orientation preference as larger metal particles179. Although a further shrinking of the nanowall dimension is required to realize SiQW devices, this progress represents a significant step toward its development. I briefly reviewed the literature to identify a variety of materials-of-interest for the design of

SiQW heterostructures and demonstrated conformal coating of silicon nanowalls with Al2O3 via

ALD. Additional investigation will be required to fabricate and test a functioning SiQW detector, but the progress from this chapter shows promise that the conceptual design is feasible from a fabrication and modeling perspective and worthy of further investigation.

147

CHAPTER 4

CONCLUSIONS AND FUTURE WORK

In Chapter 1, I reviewed some basic principles of infrared imaging in all three atmospheric transmission windows (SWIR, MWIR and LWIR). I compared these windows with respect to their photon sources, availability of photodetectors and operating temperature of those photodetectors. I presented motivation to develop monolithic imaging sensors in these wavelength bands, to reduce cost relative to hybridized focal plane arrays. I reviewed a number of monolithic focal plane array architectures including: impurity doped IR detectors, photoemissive detectors, thermal detectors and narrow gap CCDs. Of these architectures, I identified silicide-based SBDs, a subset of photoemissive detectors, to be of particular interest because they can be fabricated at low cost, can operate at room temperatures (depending on the cutoff wavelength) and can be designed to operate in all three of the atmospheric transmission windows. The primary inhibitor preventing the widespread adoption of SBD technology for IR imaging has been the poor performance of these detectors (in particular, quantum efficiency). I therefore chose to further investigate silicide-based SBDs to better understand their performance limitations with the goal of improving quantum efficiency.

I reviewed the physical models that govern the signal (IQE and absorption) and noise

(thermionic emission driven dark current) for SBDs and presented them in Chapter 2. I determined that the thermionic emission dark current model for SBDs can be used to predict the detector dark current, as a function of temperature and bias, accurately over several

148 magnitudes of current using only a few accessible input parameters. I also reviewed two IQE models (Vickers and Scales/Berini) and found that not only were the two models inconsistent with one another, but Vickers model isn’t physically meaningful under some conditions (IQE above theoretical maximum), while Scales/Berini overestimates the IQE for most reported SBDs.

Both of these models are characterized by a material-dependent parameter known as the hot- carrier attenuation length (or hot-carrier mean free path), which hasn’t been reported for most silicides and varies significantly in metals where it has been reported. Therefore, modeling the

IQE of SBDs is not easily done using lookup parameters from literature reports (in-contrast to dark current models which have excellent performance predictability). It is no surprise, given the above, that SBD IQE models are rarely used to corroborate measurements. Instead, an empirical fit to the modified Fowler equation (which is derived from a loose approximation to

Vickers’ model) is usually used to characterize SBD quantum efficiency performance. I also presented the TMM for the calculation of absorption in SBDs. Because the devices are composed of several optically thin layers on an optically thick substrate, I used a generalized two-step matrix computation method that can handle both coherent and incoherent layers.

Computation of the absorption using this method is limited in accuracy only by how precise the refractive index is known for each constituent material in the device. Refractive index data on silicides is rather limited, which is compounded by the fact that a material’s refractive index can change when it is made to be ultra-thin (thickness of interest for SBDs). This leads to the inability to accurately calculate absorption of silicides in SBDs using reported parameters from the literature.

The combination of unpredictable absorption and internal quantum efficiency for silicide-based SBDs led me to experimentally investigate the quantum efficiency and absorption characteristics of these devices with the goal of better characterizing these processes, improving

149 the overall performance and developing “practical limits” to that performance. I performed some initial measurements by fabricating a variety of silicide SBDs with cutoff wavelengths in the SWIR. I focused on SBDs with a SWIR cutoff wavelength because the cutoff wavelength also dictates the required operation temperature to manage dark current, and this range can be operated at room temperatures or with a low-cost thermo-electric cooler. Because of its relatively promising quantum efficiency and cutoff wavelength, I decided to further investigate

NiSi SBDs. Based on IQE models, I know that the IQE of SBDs monotonically increases with decreasing silicide thickness. This led me to investigate SBDs with NiSi thicknesses down to the percolation threshold, which I determined to be 1 nm for the deposition conditions I used. I measured the EQE of these ultra-thin NiSi SBDs and found the highest performing device to be a

2 nm NiSi SBD configured for backside illumination. The EQE of this device is the highest reported to-date for any silicide-based SBD with comparable barrier height. While the EQE was highest for the 2 nm device, I expected the IQE of the 1 nm device to be higher. To obtain the

IQE, I calculated the absorption of the NiSi thin films using a novel method based on FTIR reflection and transmission measurements. Using a fitting approach similar to what is commonly used in ellipsometry, I developed an algorithm to fit the silicide refractive index from several reflection and transmission measurements. This fitting procedure enabled me to accurately calculate the absorption in the NiSi layer, accounting for the parasitic losses due to absorption in the silicon (free-carrier) and metal mirror. Using the calculated absorption, I was able to determine the IQE spectrum for each NiSi thickness and found the 1 nm device to improve on the previously highest reported IQE by a factor of 16.7 at 1.55 µm. I also used an approximation to Vickers model that enabled me to fit the IQE results to theory, from which I extracted the hot carrier attenuation length. I believe this to be the first time SBD device measurements were used to directly extract the hot carrier attenuation length, which is the

150 primary unknown parameter in predicting the IQE of these devices. Using parameters extracted from the device results, I was able to establish some practical limits of performance. I presented a fabrication technique that could be used to remove the thick silicon substrate from the optical stack of the SBD and showed how near unity absorption can be achieved using the 1 nm NiSi layer in a cavity resonant configuration. I also show how broadband absorption can also be improved and calculated the expected EQE for these designs. I also used the hot-carrier attenuation length to predict the IQE performance improvements possible by taking the NiSi layer thickness down to a single monolayer. These predictive results are of practical interest, because they’ve been derived from SBD device measurements. These results also provide two avenues of future research for these detectors: integration of resonant absorption with ultra- thin silicide layers to improve EQE, and reduction of the silicide percolation threshold using low- energy deposition techniques to improve the IQE of SBDs.

A significant source of inefficiency for SBD QE performance can be attributed to the lack of a band gap in the silicide absorber. A band gap in the absorber of a photodetector forces the excess energy of an excited carrier to be greater than or equal to the bandgap energy. In contrast, the gapless absorber in an SBD allows excess energy of an excited carrier to be anywhere between the photon energy and zero. This is why, fundamentally, SBDs do not have unity theoretical maximum quantum efficiency. While materials with bandgaps appropriate for making photodetectors in the SWIR, MWIR and LWIR exist, they require expensive epitaxial growth methods that don’t form high quality material layers unless they’re grown on a lattice matched substrate (of which silicon is not). One way to introduce a narrow bandgap using materials of higher bandgaps is through quantum confinement via heterostructures. A well- known detector architecture for leveraging quantum confined heterostructures for infrared sensors is known as quantum well infrared photodetectors (QWIPs). QWIPs are generally

151 fabricated from the lattice-matched GaAs/AlGaAs material system using epitaxial growth methods. The QWIP architecture introduces an intraband gap by shrinking an energy potential until the states residing in that potential well are discretized. Because this work is focused on low-cost silicon-based IR detectors, I introduce a similar concept to QWIPs in silicon I refer to as silicon quantum walls (SiQWs), which is the subject of Chapter 3. The use of the term walls is used to describe how the geometry of these potential wells extend vertically with respect to the substrate, rather than planar as they are in QWIPs. In Chapter 3, I cover a variety of theoretical advantages SiQWs have over QWIPs, based on their geometry including: absorption, collection efficiency and dark current. Using a numerical approach to solving Schrödinger’s equation known as the shooting method, I modeled theoretical SiQW detectors and proposed designs for all three atmospheric transmission windows. I also propose quantum wall designs that leverage quantum mechanical tunneling (T-SiQW) to allow for fine tuning the wavelength response of these devices without the need for fine tuning the heterojunction energy offset (which may be limited depending on the availability of suitable materials). This modeling provides targets for the wall lateral dimension (depending on the operation wavelength) and heterojunction energy offset ranges to produce functional designs in all three atmospheric transmission windows. A review of the literature for band offsets of a variety of materials that can be conformally grown on vertical nanostructures revealed several potential materials that could be used as heterostructure building blocks of SiQW and T-SiQW devices.

With the wall dimension targets defined by the modeling in mind, I investigated a top- down fabrication process known as metal-assisted chemical etching (MacEtch) for forming silicon quantum walls. MacEtch is a process of silicon galvanic corrosion in a wet etch chemistry that is highly catalytic in the presence of metal and negligible without. I chose this process because it can be performed uniformly over an entire wafer and is extremely low cost, requiring

152 nothing more than a metal source and a wet-chemical bench for processing. I reviewed the

MacEtch literature and found existing reports focused on forming silicon structures between 1

µm and 80 nm. Because the metal template defines the geometry of the silicon heterostructures, I investigated the self-assembly process of metal thin films near their percolation threshold to serve as the template. This technique is very low cost, highly uniform and is capable of producing feature sizes below 10 nm. I investigated a variety of metals under varying substrate and deposition conditions and found several suitable metal templates that could be fabricated using the self-assembly process. Faithfully transferring this template geometry into silicon nanostructures proved more challenging. I found some metals, such as platinum, formed ideal metal templates but broke apart and left behind a porous silicon during

MacEtch. I also found that isolated nanoscale metal islands will not etch directionally regardless of the substrate crystal orientation or etchant stoichiometry used. In contrast, metal islands 300 nm2 and larger, like those that have been studied more extensively, show strong etch direction dependence with crystal orientation and etchant stoichiometry. I found that I could use a metal nano-mesh geometry, rather than a nano-islands, to faithfully transfer the metal template into the silicon. This approach resulted in highly uniform silicon nanowalls with lateral dimension between 5—20 nm. While this dimension range isn’t ideal for SiQW detectors, it represents significant progress toward reaching that goal. One approach to further shrinking the silicon nanowalls into the quantum wall dimension regime is to investigate low energy deposition techniques to lower the percolation threshold of gold on SiO2 (the metal/substrate combination used to produce the most uniform nanowalls). I showed how heating the substrate can create larger nano-mesh structures, so lowering the substrate temperature should have the opposite effect (smaller nano-mesh structures). Another approach would be to fabricate the nanowalls as described in this work and further shrink the dimensions post-etch using a second etch

153 process. One way to accomplish this would be to use a very slow but nonzero wet etch chemistry that would uniformly etch the nanowalls in all dimensions. If the etch rate can be uniformly controlled, this could be one straightforward method. Another method is by atomic- layer etching (ALE). Like atomic layer deposition, atomic layer etching involves at least two self- limiting processes to carry out the etch process in a step-by-step fashion. A reasonable approach to atomic layer etching of these structures would be to uniformly oxidize the nanowalls in an oxygen environment at a set temperature (known to be a self-terminating oxidation process). Then, the oxide can be removed using a wet etch that will selectively preserve the silicon (BOE for example). Each cycle of the ALE process will result in a uniform and controlled removal of some silicon from the nanowalls. By controlling the number of cycles and the parameters of each cycle, it should be possible to shrink the nanowalls so they could be used for SiQW detectors.

The work presented here demonstrates that significant improvement to silicon-based IR detectors can be achieved relative to current state-of-the-art. Working with SBD technology that has been studied for decades, I was able to improve performance by simply paying close attention to detail about the physical mechanisms that govern operation of the device. While novel SBD designs with plasmonic and cavity resonances have been reported elsewhere extensively, I showed that a simple BSI device could outperform those designs by simply shrinking the silicide layer thickness near the percolation threshold of the film. Improved performance can be achieved by marrying these two concepts, which I modeled here but left experimentally as future work. I also laid the framework for a conceptual device (SiQW) that leverages quantum physics to alter the optical properties of silicon from a transparent material in the infrared, to one which is absorptive and can be functionalized as a photodetector. While I was unable to demonstrate the performance of this conceptual device experimentally, I

154 modeled these devices to establish fabrication goals and made significant progress on one of the most challenging aspects of this design: fabrication of the silicon quantum wall. The silicon industry has an often repeated saying: “if it can be done in silicon; it will be done in silicon.” I believe that is true for infrared image sensors as well. While hybridized image sensor arrays composed of separately optimized detector arrays and readout integrated circuits will likely always provide the highest performance, I believe the market for low-cost infrared image sensors that leverage the manufacturing scale and reproducibility of the silicon industry has untapped potential.

155

REFERENCES

1 Boyle, W. S. & Smith, G. E. CHARGE COUPLED SEMICONDUCTOR DEVICES. Bell System Technical Journal 49, 587-+ (1970). 2 Estrin, J. Kodak’s First Digital Moment. The New York Times (2015). . 3 Corathers, L. A. Vol. I Silicon (ed U.S. Department of the Interior) (U.S. Geological Survey, Reston, VA, 2011). 4 Department, A. 328 (Naval Air Warfare Center Weapons Division Technical Publication, Point Mugu, CA, 2013). 5 Vatsia, M. L., Stich, U. K. & Dunlap, D. (ed U.S. Army Electronics Command) 31 (Night Vision Laboratory, Fort Belvoir, VA, 1972). 6 Commission, I. E. in Section three - User's Guide: Maximum permissible exposures 49- 53 (Geneva, Switzerland, 1993). 7 Swaminathan, V. & Macrander, A. Materials aspects of GaAs and InP based structures. (Prentice-Hall, Inc., 1991). 8 Kruse, P. W. Indium antimonide photoconductive and photoelectromagnetic detectors. Semiconductors and Semimetals 5, 15-83 (1970). 9 Hansen, G., Schmit, J. & Casselman, T. Energy gap versus alloy composition and temperature in Hg1− x Cd x Te. Journal of Applied Physics 53, 7099-7101 (1982). 10 Klipstein, P. in 34th Conference on Infrared Technology and Applications. (Spie-Int Soc Optical Engineering, 2008). 11 Jiang, J. T., Tsao, S., O'Sullivan, T., Razeghi, M. & Brown, G. J. Fabrication of indium bumps for hybrid infrared focal plane array applications. Infrared Physics & Technology 45, 143-151, doi:10.1016/j.infrared.2003.08.002 (2004). 12 Seo, M. W., Kawahito, S., Yasutomi, K., Kagawa, K. & Teranishi, N. A Low Dark Leakage Current High-Sensitivity CMOS Image Sensor With STI-Less Shared Pixel Design. Ieee Transactions on Electron Devices 61, 2093-2097, doi:10.1109/ted.2014.2318522 (2014). 13 Canon, I. Tokyo, Japan (http://global.canon/en/news/2015/sep07e.html, 2015). 14 Mase, M., Kawahito, S., Sasaki, M., Wakamori, Y. & Furuta, M. A wide dynamic range CMOS image sensor with multiple exposure-time signal outputs and 12-bit column- parallel cyclic A/D converters. Ieee Journal of Solid-State Circuits 40, 2787-2795, doi:10.1109/jssc.2005.858477 (2005). 15 Fowler, B., Elgamal, A. & Yang, D. X. D. A CMOS AREA IMAGE SENSOR WITH PIXEL-LEVEL A/D CONVERSION. 1994 Ieee International Solid-State Circuits Conference - Digest of Technical Papers 37, 226-227 (1994). 16 Tochigi, Y. et al. A Global-Shutter CMOS Image Sensor With Readout Speed of 1-Tpixel/s Burst and 780-Mpixel/s Continuous. Ieee Journal of Solid-State Circuits 48, 329-338, doi:10.1109/jssc.2012.2219685 (2013).

156

17 Corporation, S. S. S. Tokyo, Japan (https://www.sony.net/SonyInfo/News/Press/201702/17-013E/, 2017). 18 Sclar, N. PROPERTIES OF DOPED SILICON AND GERMANIUM INFRARED DETECTORS. Progress in Quantum Electronics 9, 149-257, doi:10.1016/0079-6727(84)90001-6 (1984). 19 Petroff, M. D. & Stapelbroek, M. G. (Google Patents, 1986). 20 Szmulowicz, F. & Madarsz, F. L. BLOCKED IMPURITY BAND DETECTORS - AN ANALYTICAL MODEL - FIGURES OF MERIT. Journal of Applied Physics 62, 2533-2540, doi:10.1063/1.339466 (1987). 21 Venzon, J., Lum, N., Freeman, S. & Domingo, G. in Conference on Infrared Detectors and Instrumentation for Astronomy. 34-40 (Spie - Int Soc Optical Engineering, 1995). 22 Hogue, H., Guptill, M., Lin, A., Besser, P. & Scott, R. Gallium-Doped Silicon Blocked- Impurity-Band Detectors. (DTIC Document, 1999). 23 Huffman, J. E., Crouse, A. G., Halleck, B. L., Downes, T. V. & Herter, T. L. SI-SB BLOCKED IMPURITY BAND DETECTORS FOR INFRARED ASTRONOMY. Journal of Applied Physics 72, 273-275, doi:10.1063/1.352127 (1992). 24 Lanyon, H. P. D. & Tuft, R. A. BANDGAP NARROWING IN MODERATELY TO HEAVILY DOPED SILICON. Ieee Transactions on Electron Devices 26, 1014-1018, doi:10.1109/t- ed.1979.19538 (1979). 25 Henisch, H. K. RECTIFYING SEMICONDUCTOR CONTACTS. Journal of the Electrochemical Society 103, 637-643, doi:10.1149/1.2430178 (1956). 26 Schneide.Mv. SCHOTTKY BARRIER PHOTODIODES WITH ANTIREFLECTION COATING. Bell System Technical Journal 45, 1611-& (1966). 27 Roosild, S. A., Shepherd, J. F. D., Yang, A. C. & Shedd, W. M. (Google Patents, 1975). 28 Petersson, S., Mgbenu, E., Norde, H. & Tove, P. A. EVALUATING PTSI FRONT CONTACT TO SURFACE-BARRIER DETECTORS. Nuclear Instruments & Methods 143, 525-535, doi:10.1016/0029-554x(77)90242-7 (1977). 29 Akiyama, A. et al. 1040X1040 INFRARED CHARGE SWEEP DEVICE IMAGER WITH PTSI SCHOTTKY-BARRIER DETECTORS. Optical Engineering 33, 64-71, doi:10.1117/12.162277 (1994). 30 Kimata, M., Denda, M., Yutani, N., Iwade, S. & Tsubouchi, N. A 512 X 512-ELEMENT PTSI SCHOTTKY-BARRIER INFRARED IMAGE SENSOR. Ieee Journal of Solid-State Circuits 22, 1124-1129, doi:10.1109/jssc.1987.1052863 (1987). 31 Kimata, M., Ozeki, T., Tsubouchi, N. & Ito, S. in Conference on Imaging System Technology for Remote Sensing. 2-12 (Spie-Int Soc Optical Engineering, 1998). 32 Shoda, M., Yamada, H., Yamanaka, H. & Akagawa, K. in Infrared Technology and Applications Xxiv, Pts 1-2 Vol. 3436 Proceedings of the Society of Photo-Optical Instrumentation Engineers (Spie) (eds B. F. Andresen & M. Strojnik) 184-193 (Spie-Int Soc Optical Engineering, 1998). 33 Yeh, R. N. et al. in Infrared Imaging System - Design, Analysis, Modeling, and Testing IX. 148-154 (Spie-Int Soc Optical Engineering, 1998). 34 Scales, C. & Berini, P. Thin-Film Schottky Barrier Photodetector Models. Ieee Journal of Quantum Electronics 46, 633-643, doi:10.1109/jqe.2010.2046720 (2010). 35 Kosonocky, W. F., Shallcross, F. V., Villani, T. S. & Groppe, J. V. 160X244 ELEMENT PTSI SCHOTTKY-BARRIER IR-CCD IMAGE SENSOR. Ieee Transactions on Electron Devices 32, 1564-1573, doi:10.1109/t-ed.1985.22165 (1985). 36 Tsaur, B. Y., Weeks, M. M., Trubiano, R., Pellegrini, P. W. & Yew, T. R. IRSI SCHOTTKY- BARRIER INFRARED DETECTORS WITH 10-MU-M CUTOFF WAVELENGTH. Ieee Electron Device Letters 9, 650-653, doi:10.1109/55.20425 (1988).

157

37 Tsaur, B. Y., McNutt, M. J., Bredthauer, R. A. & Mattson, R. B. 128X128-ELEMENT IRSI SCHOTTKY-BARRIER FOCAL PLANE ARRAYS FOR LONG-WAVELENGTH INFRARED IMAGING. Ieee Electron Device Letters 10, 361-363, doi:10.1109/55.31757 (1989). 38 Tsaur, B. Y., Chen, C. K. & Nechay, B. A. IRSI SCHOTTKY-BARRIER INFRARED DETECTORS WITH WAVELENGTH RESPONSE BEYOND 12-MUM. Ieee Electron Device Letters 11, 415- 417, doi:10.1109/55.62974 (1990). 39 Metz-Porozni, K. (FLIR Systems Inc., Wilsonville, OR, 2014). 40 Sze, S. M. & NG, K. K. Physics of Semiconductor Devices. 3rd edn, (John Wiley & Sons, Inc., 2007). 41 Thom, R. D., Koch, T. L., Langan, J. D. & Parrish, W. J. FULLY MONOLITHIC INSB INFRARED CCD ARRAY. Ieee Transactions on Electron Devices 27, 160-170, doi:10.1109/t- ed.1980.19835 (1980). 42 Thom, R., Eck, R., Phillips, J. & Scorso, J. in Proc. CCD Applications Conf. 31. 43 Koch, T. L., Deloo, J. H., Kalisher, M. H. & Phillips, J. D. MONOLITHIC N-CHANNEL HGCDTE LINEAR IMAGING ARRAYS. Ieee Transactions on Electron Devices 32, 1592-1598, doi:10.1109/t-ed.1985.22168 (1985). 44 Roberts, C. G. HGCDTE CHARGE-TRANSFER DEVICE FOCAL PLANES. Proceedings of the Society of Photo-Optical Instrumentation Engineers 443, 131-143 (1984). 45 Kim, M. E. et al. CHARGE-COUPLED-DEVICES IN EPITAXIAL HGCDTE-CDTE HETEROSTRUCTURE. Applied Physics Letters 39, 336-338, doi:10.1063/1.92713 (1981). 46 Kinch, M. A., Chapman, R. A., Simmons, A., Buss, D. D. & Borrello, S. R. HGCDTE CHARGE- COUPLED DEVICE TECHNOLOGY. Infrared Physics 20, 1-20, doi:10.1016/0020- 0891(80)90002-0 (1980). 47 Hardy, T., Murowinski, R. & Deen, M. J. Charge transfer efficiency in proton damaged CCD's. Ieee Transactions on Nuclear Science 45, 154-163, doi:10.1109/23.664167 (1998). 48 Werner, J. H., Spadaccini, U. & Banhart, F. LOW-TEMPERATURE OHMIC AU/SB CONTACTS TO N-TYPE SI. Journal of Applied Physics 75, 994-997, doi:10.1063/1.356425 (1994). 49 Zhu, J. G., Yang, X. L. & Tao, M. Low-resistance titanium/n-type silicon (100) contacts by monolayer selenium passivation. Journal of Physics D-Applied Physics 40, 547-550, doi:10.1088/0022-3727/40/2/031 (2007). 50 Tao, M., Shanmugam, J., Coviello, M. & Kirk, W. P. Suppression of silicon (001) surface reactivity using a valence-mending technique. Solid State Communications 132, 89-92, doi:10.1016/j.ssc.2004.07.031 (2004). 51 Kimata, M. et al. PLATINUM SILICIDE SCHOTTKY-BARRIER IR-CCD IMAGE SENSORS. Japanese Journal of Applied Physics 21, 231-235, doi:10.7567/jjaps.21s1.231 (1982). 52 Knight, M. W. et al. Embedding Plasmonic Nanostructure Diodes Enhances Hot Electron Emission. Nano Letters 13, 1687-1692, doi:10.1021/nl400196z (2013). 53 Goykhman, I., Desiatov, B., Khurgin, J., Shappir, J. & Levy, U. Locally Oxidized Silicon Surface-Plasmon Schottky Detector for Telecom Regime. Nano Letters 11, 2219-2224, doi:10.1021/nl200187v (2011). 54 Sobhani, A. et al. Narrowband photodetection in the near-infrared with a plasmon- induced hot electron device. Nature Communications 4, 6, doi:10.1038/ncomms2642 (2013). 55 Nazirzadeh, M. A., Atar, F. B., Turgut, B. B. & Okyay, A. K. Random sized plasmonic nanoantennas on Silicon for low-cost broad-band near-infrared photodetection. Scientific Reports 4, 5, doi:10.1038/srep07103 (2014).

158

56 Berini, P., Olivieri, A. & Chen, C. K. Thin Au surface plasmon waveguide Schottky detectors on p-Si. Nanotechnology 23, 9, doi:10.1088/0957-4484/23/44/444011 (2012). 57 Chen, W. J., Kan, T., Ajiki, Y., Matsumoto, K. & Shimoyama, I. NIR spectrometer using a Schottky photodetector enhanced by grating-based SPR. Optics Express 24, 25797- 25804, doi:10.1364/oe.24.025797 (2016). 58 Akbari, A., Tait, R. N. & Berini, P. Surface plasmon waveguide Schottky detector. Optics Express 18, 8505-8514, doi:10.1364/oe.18.008505 (2010). 59 Roy, S., Midya, K., Duttagupta, S. P. & Ramakrishnan, D. Nano-scale NiSi and n-type silicon based Schottky barrier diode as a near infra-red detector for room temperature operation. Journal of Applied Physics 116, 6, doi:10.1063/1.4896365 (2014). 60 Zhu, S. Y., Yu, M. B., Lo, G. Q. & Kwong, D. L. Near-infrared waveguide-based nickel silicide Schottky-barrier photodetector for optical communications. Applied Physics Letters 92, 3, doi:10.1063/1.2885089 (2008). 61 Harrison, T. R., Johnson, A. M., Tien, P. K. & Dayem, A. H. NISI2-SI INFRARED SCHOTTKY PHOTODETECTORS GROWN BY MOLECULAR-BEAM EPITAXY. Applied Physics Letters 41, 734-736, doi:10.1063/1.93659 (1982). 62 Li, S. X., Tarr, N. G. & Berini, P. in Conference on Photonics North 2010. (Spie-Int Soc Optical Engineering, 2010). 63 Casalino, M. et al. Cu/p-Si Schottky barrier-based near infrared photodetector integrated with a silicon-on-insulator waveguide. Applied Physics Letters 96, 3, doi:10.1063/1.3455339 (2010). 64 Aboelfotoh, M. O., Cros, A., Svensson, B. G. & Tu, K. N. SCHOTTKY-BARRIER BEHAVIOR OF COPPER AND COPPER SILICIDE ON N-TYPE AND P-TYPE SILICON. Physical Review B 41, 9819-9827, doi:10.1103/PhysRevB.41.9819 (1990). 65 Casalino, M., Coppola, G., Iodice, M., Rendina, I. & Sirleto, L. Critically coupled silicon Fabry-Perot photodetectors based on the internal photoemission effect at 1550 nm. Optics Express 20, 12599-12609, doi:10.1364/oe.20.012599 (2012). 66 Elabd, H., Villani, T. & Kosonocky, W. PALLADIUM-SILICIDE SCHOTTKY-BARRIER IR-CCD FOR SWIR APPLICATIONS AT INTERMEDIATE TEMPERATURES. Electron Device Letters 3, 89-90, doi:10.1109/edl.1982.25490 (1982). 67 Shepherd, F. D. & Yang, A. C. in Electron Devices Meeting, 1973 International. 310-313 (IEEE). 68 Roca, E., Larsen, K. K., Kolodinski, S. & Mertens, R. Infrared response of epitaxial and polycrystalline CoSi2 Schottky diodes. Materials Science and Technology 14, 1303-1306, doi:10.1179/mst.1998.14.12.1303 (1998). 69 Buchal, C., Loken, M., Lipinsky, T., Kappius, L. & Mantl, S. Ultrafast silicon based photodetectors. Journal of Vacuum Science & Technology A 18, 630-634, doi:10.1116/1.582239 (2000). 70 Worle, D. et al. Amorphous and crystalline IrSi Schottky barriers on silicon. Applied Physics a-Materials Science & Processing 66, 629-637, doi:10.1007/s003390050724 (1998). 71 Mahlein, K. M., Woerle, D., Hierl, T. & Schulz, M. in SPIE Conference on Infrared Technology and Applications XXIV. 138-147 (Spie-Int Soc Optical Engineering, 1998). 72 Qi, Z. Y. et al. Au nanoparticle-decorated silicon pyramids for plasmon-enhanced hot electron near-infrared photodetection. Nanotechnology 28, 9, doi:10.1088/1361- 6528/aa74a3 (2017).

159

73 Hashemi, M., Farzad, M. H., Mortensen, N. A. & Xiao, S. S. Enhanced Plasmonic Light Absorption for Silicon Schottky-Barrier Photodetectors. Plasmonics 8, 1059-1064, doi:10.1007/s11468-013-9509-y (2013). 74 Grajower, M. et al. Optimization and Experimental Demonstration of Plasmonic Enhanced Internal Photoemission Silicon Schottky Detectors in the Mid-IR. Acs Photonics 4, 1015-1020, doi:10.1021/acsphotonics.7b00110 (2017). 75 Desiatov, B. et al. Plasmonic enhanced silicon pyramids for internal photoemission Schottky detectors in the near-infrared regime. Optica 2, 335-338, doi:10.1364/optica.2.000335 (2015). 76 Akbari, A. & Berini, P. Schottky contact surface-plasmon detector integrated with an asymmetric metal stripe waveguide. Applied Physics Letters 95, 3, doi:10.1063/1.3171937 (2009). 77 Olivieri, A., Akbari, A. & Berini, P. Surface plasmon waveguide Schottky detectors operating near breakdown. Physica Status Solidi-Rapid Research Letters 4, 283-285, doi:10.1002/pssr.201004245 (2010). 78 Lee, Y. K. et al. Surface Plasmon-Driven Hot Electron Flow Probed with Metal- Semiconductor Nanodiodes. Nano Letters 11, 4251-4255, doi:10.1021/nl2022459 (2011). 79 Knight, M. W., Sobhani, H., Nordlander, P. & Halas, N. J. Photodetection with Active Optical Antennas. Science 332, 702-704, doi:10.1126/science.1203056 (2011). 80 Casalino, M. et al. Back-illuminated silicon resonant cavity-enhanced photodetector at 1550 nm. Physica E-Low-Dimensional Systems & Nanostructures 41, 1097-1101, doi:10.1016/j.physe.2008.08.049 (2009). 81 Casalino, M. et al. Cavity Enhanced Internal Photoemission Effect in Silicon Photodiode for Sub-Bandgap Detection. Journal of Lightwave Technology 28, 3266-3272, doi:10.1109/jlt.2010.2081346 (2010). 82 Casalino, M. et al. Fabrication and Characterization of a Back-Illuminated Resonant Cavity Enhanced Silicon Photo-Detector Working at 1.55 mu m. Fiber and Integrated Optics 29, 85-95, doi:10.1080/01468031003596861 (2010). 83 Casalino, M., Coppola, G., Iodice, M., Rendina, I. & Sirleto, L. Near-Infrared All-Silicon Photodetectors. International Journal of Photoenergy, 6, doi:10.1155/2012/139278 (2012). 84 Casalino, M. et al. Silicon resonant cavity enhanced photodetector based on the internal photoemission effect at 1.55 mu m: Fabrication and characterization. Applied Physics Letters 92, 3, doi:10.1063/1.2952193 (2008). 85 Zhu, S. Y., Lo, G. Q., Yu, M. B. & Kwong, D. L. Low-cost and high-gain silicide Schottky- barrier collector phototransistor integrated on Si waveguide for infrared detection. Applied Physics Letters 93, 3, doi:10.1063/1.2970996 (2008). 86 Zhu, S. Y., Lo, G. Q., Yu, M. B. & Kwong, D. L. Silicide Schottky-Barrier Phototransistor Integrated in Silicon Channel Waveguide for In-Line Power Monitoring. Ieee Photonics Technology Letters 21, 185-187, doi:10.1109/lpt.2008.2009946 (2009). 87 Zhu, S. Y., Chu, H. S., Lo, G. Q., Bai, P. & Kwong, D. L. Waveguide-integrated near- infrared detector with self-assembled metal silicide nanoparticles embedded in a silicon p-n junction. Applied Physics Letters 100, 3, doi:10.1063/1.3683546 (2012). 88 Chen, C. K., Nechay, B. & Tsaur, B. Y. ULTRAVIOLET, VISIBLE, AND INFRARED RESPONSE OF PTSI SCHOTTKY-BARRIER DETECTORS OPERATED IN THE FRONT-ILLUMINATED MODE. Ieee Transactions on Electron Devices 38, 1094-1103, doi:10.1109/16.78384 (1991).

160

89 Biswas, N., Gurganus, J. & Misra, V. Work function tuning of nickel silicide by co- sputtering nickel and silicon. Applied Physics Letters 87, 3, doi:10.1063/1.2115072 (2005). 90 Vickers, V. E. MODEL OF SCHOTTKY BARRIER HOT-ELECTRON-MODE PHOTODETECTION. Applied Optics 10, 2190-&, doi:10.1364/ao.10.002190 (1971). 91 Casalino, M. Internal Photoemission Theory: Comments and Theoretical Limitations on the Performance of Near-Infrared Silicon Schottky Photodetectors. Ieee Journal of Quantum Electronics 52, 10, doi:10.1109/jqe.2016.2532866 (2016). 92 Mooney, J. M. & Silverman, J. THE THEORY OF HOT-ELECTRON PHOTOEMISSION IN SCHOTTKY-BARRIER IR DETECTORS. Ieee Transactions on Electron Devices 32, 33-39, doi:10.1109/t-ed.1985.21905 (1985). 93 Dushman, S. Thermionic emission. Reviews of Modern Physics 2, 381 (1930). 94 Andrews, J. M. & Lepselter, M. P. REVERSE CURRENT-VOLTAGE CHARACTERISTICS OF METAL-SILICIDE SCHOTTKY DIODES. Solid-State Electronics 13, 1011-+, doi:10.1016/0038-1101(70)90098-5 (1970). 95 Nava, F. et al. ELECTRICAL AND OPTICAL-PROPERTIES OF SILICIDE SINGLE-CRYSTALS AND THIN-FILMS. Materials Science Reports 9, 141-200, doi:10.1016/0920-2307(93)90007-2 (1993). 96 Jacquinot, P. THE LUMINOSITY OF SPECTROMETERS WITH PRISMS, GRATINGS, OR FABRY-PEROT ETALONS. Journal of the Optical Society of America 44, 761-765, doi:10.1364/josa.44.000761 (1954). 97 Fellgett, P. Theory of infra-red sensitivites and its application to investigations of stellar radiation in the near infra-red, University of Cambridge, (1951). 98 Connes, J. & Connes, P. NEAR-INFRARED PLANETARY SPECTRA BY FOURIER SPECTROSCOPY .I. INSTRUMENTS AND RESULTS. Journal of the Optical Society of America 56, 896-&, doi:10.1364/josa.56.000896 (1966). 99 Vincent, J. D. Fundamentals of infrared detector operation and testing. (Wiley, 1990). 100 Ordal, M. A., Bell, R. J., Alexander, R. W., Newquist, L. A. & Querry, M. R. OPTICAL- PROPERTIES OF AL, FE, TI, TA, W, AND MO AT SUBMILLIMETER WAVELENGTHS. Applied Optics 27, 1203-1208, doi:10.1364/ao.27.001203 (1988). 101 Olmon, R. L. et al. Optical dielectric function of gold. Physical Review B 86, doi:10.1103/PhysRevB.86.235147 (2012). 102 tmm.py v. 0.1.7 (2017). 103 Katsidis, C. C. & Siapkas, D. I. General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference. Applied Optics 41, 3978-3987, doi:10.1364/ao.41.003978 (2002). 104 Byrnes, S. J. Multilayer optical calculations. arXiv:1603.02720v2 (2016). 105 Chilwell, J. & Hodgkinson, I. THIN-FILMS FIELD-TRANSFER MATRIX-THEORY OF PLANAR MULTILAYER WAVEGUIDES AND REFLECTION FROM PRISM-LOADED WAVEGUIDES. Journal of the Optical Society of America a-Optics Image Science and Vision 1, 742-753, doi:10.1364/josaa.1.000742 (1984). 106 Jenkins, F. A. & White, H. E. Fundamentals of optics. (Tata McGraw-Hill Education, 1937). 107 Nelder, J. A. & Mead, R. A SIMPLEX-METHOD FOR FUNCTION MINIMIZATION. Computer Journal 7, 308-313, doi:10.1093/comjnl/7.4.308 (1965). 108 Powell, M. J. An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Computer Journal 7, 155-162 (1964). 109 Fletcher, R. Practical methods of optimization. (John Wiley & Sons, 2013).

161

110 Hestenes, M. R. & Stiefel, E. METHODS OF CONJUGATE GRADIENTS FOR SOLVING LINEAR SYSTEMS. Journal of Research of the National Bureau of Standards 49, 409-436, doi:10.6028/jres.049.044 (1952). 111 Grippo, L., Lampariello, F. & Lucidi, S. A TRUNCATED NEWTON METHOD WITH NONMONOTONE LINE SEARCH FOR UNCONSTRAINED OPTIMIZATION. Journal of Optimization Theory and Applications 60, 401-419, doi:10.1007/bf00940345 (1989). 112 Branch, M. A., Coleman, T. F. & Li, Y. Y. A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. Siam Journal on Scientific Computing 21, 1-23, doi:10.1137/s1064827595289108 (1999). 113 Lin, T. L., Park, J. S., Gunapala, S. D., Jones, E. W. & Delcastillo, H. M. DOPING-SPIKE PTSI SCHOTTKY INFRARED DETECTORS WITH EXTENDED CUTOFF WAVELENGTHS. Ieee Transactions on Electron Devices 42, 1216-1220, doi:10.1109/16.391201 (1995). 114 Loh, W. Y. et al. Effective Modulation of Ni Silicide Schottky Barrier Height Using Chlorine Ion Implantation and Segregation. Ieee Electron Device Letters 30, 1140-1142, doi:10.1109/led.2009.2031828 (2009). 115 Lousberg, G. R. et al. Schottky-Barrier height lowering by an increase of the substrate doping in PtSi Schottky barrier source/drain FETs. Ieee Electron Device Letters 28, 123- 125, doi:10.1109/led.2006.889045 (2007). 116 Lin, T. L., Park, J. S., Gunapala, S. D., Jones, E. W. & Delcastillo, H. M. TAILORABLE DOPING-SPIKE PTSI INFRARED DETECTORS FABRICATED BY SI MOLECULAR-BEAM EPITAXY. Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers 33, 2435-2438, doi:10.1143/jjap.33.2435 (1994). 117 Gonchond, J. P. et al. in 5th Conference on Characterization and Metrology for ULSI Technology. 182-186 (2005). 118 De Keyser, K. et al. Phase formation and thermal stability of ultrathin nickel-silicides on Si(100). Applied Physics Letters 96, 3, doi:10.1063/1.3384997 (2010). 119 Rakic, A. D., Djurisic, A. B., Elazar, J. M. & Majewski, M. L. Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics 37, 5271-5283, doi:10.1364/ao.37.005271 (1998). 120 Polyanskiy, M. N. Refractive index database, ( 121 Brahmi, H. et al. Electrical and optical properties of sub-10 nm nickel silicide films for silicon solar cells. Journal of Physics D-Applied Physics 50, 10, doi:10.1088/1361- 6463/50/3/035102 (2017). 122 Ibrahim, M. M. & Bashara, N. M. PARAMETER-CORRELATION AND COMPUTATIONAL CONSIDERATIONS IN MULTIPLE-ANGLE ELLIPSOMETRY. Journal of the Optical Society of America 61, 1622-&, doi:10.1364/josa.61.001622 (1971). 123 FLIR. ISC0403 Standard 640x512 ROIC (15umx15um Pixel) Specifications, (2005). 124 Mao, Z. G., Kim, Y. C., Lee, H. D., Adusumilli, P. & Seidman, D. N. NiSi crystal structure, site preference, and partitioning behavior of palladium in NiSi(Pd)/Si(100) thin films: Experiments and calculations. Applied Physics Letters 99, 3, doi:10.1063/1.3606536 (2011). 125 Lee, E. Y., Sirringhaus, H., Kafader, U. & Vonkanel, H. BALLISTIC-ELECTRON-EMISSION- MICROSCOPY INVESTIGATION OF HOT-CARRIER TRANSPORT IN EPITAXIAL COSI2 FILMS ON SI(100) AND SI(111). Physical Review B 52, 1816-1829, doi:10.1103/PhysRevB.52.1816 (1995). 126 Niedermann, P., Quattropani, L., Solt, K., Maggioaprile, I. & Fischer, O. HOT-CARRIER SCATTERING IN A METAL - A BALLISTIC-ELECTRON-EMISSION MICROSCOPY

162

INVESTIGATION ON PTSI. Physical Review B 48, 8833-8839, doi:10.1103/PhysRevB.48.8833 (1993). 127 Ventrice, C. A., LaBella, V. P., Ramaswamy, G., Yu, H. P. & Schowalter, L. J. Hot-electron scattering at Au/Si(100) Schottky interfaces measured by temperature dependent ballistic electron emission microscopy. Applied Surface Science 104, 274-281, doi:10.1016/s0169-4332(96)00215-2 (1996). 128 Garramone, J. J. et al. Measurement of the hot electron attenuation length of copper. Applied Physics Letters 96, 3, doi:10.1063/1.3299712 (2010). 129 Balsano, R., Matsubayashi, A. & LaBella, V. P. Schottky barrier height measurements of Cu/Si(001), Ag/Si(001), and Au/Si(001) interfaces utilizing ballistic electron emission microscopy and ballistic hole emission microscopy. Aip Advances 3, 20, doi:10.1063/1.4831756 (2013). 130 Huber, T. E., Nikolaeva, A., Gitsu, D., Konopko, L. & Graf, M. J. Quantum confinement and surface-state effects in bismuth nanowires. Physica E-Low-Dimensional Systems & Nanostructures 37, 194-199, doi:10.1016/j.physe.2006.09.004 (2007). 131 Piepenbrock, M. O. M., Stirner, T., Kelly, S. M. & O'Neill, M. A low-temperature synthesis for organically soluble HgTe nanocrystals exhibiting near-infrared photoluminescence and quantum confinement. Journal of the American Chemical Society 128, 7087-7090, doi:10.1021/ja060721j (2006). 132 Villaflor, A. B., Shimomura, K., Kawamura, K., Belogorokhov, A. I. & Kimata, M. MOLECULAR-BEAM EPITAXY-GROWN CDTE/ALPHA-SN/CDTE SINGLE-QUANTUM-WELL STRUCTURES. Journal of Crystal Growth 150, 779-784, doi:10.1016/0022- 0248(95)80046-f (1995). 133 Levine, B. F. QUANTUM-WELL INFRARED PHOTODETECTORS. Journal of Applied Physics 74, R1-R81, doi:10.1063/1.354252 (1993). 134 Rosencher, E., Luc, F., Bois, P. & Delaitre, S. INJECTION MECHANISM AT CONTACTS IN A QUANTUM-WELL INTERSUBBAND INFRARED DETECTOR. Applied Physics Letters 61, 468- 470, doi:10.1063/1.107887 (1992). 135 Bandara, K., Levine, B. F., Leibenguth, R. E. & Asom, M. T. OPTICAL AND TRANSPORT- PROPERTIES OF SINGLE-QUANTUM-WELL INFRARED PHOTODETECTORS. Journal of Applied Physics 74, 1826-1831, doi:10.1063/1.354789 (1993). 136 Chen, C. J., Choi, K. K., Tidrow, M. Z. & Tsui, D. C. Corrugated quantum well infrared photodetectors for normal incident light coupling. Applied Physics Letters 68, 1446- 1448, doi:10.1063/1.116249 (1996). 137 Lundqvist, L., Andersson, J. Y., Paska, Z. F., Borglind, J. & Haga, D. EFFICIENCY OF GRATING-COUPLED ALGAAS/GAAS QUANTUM-WELL INFRARED DETECTORS. Applied Physics Letters 63, 3361-3363, doi:10.1063/1.110145 (1993). 138 Sarusi, G. et al. OPTIMIZATION OF 2-DIMENSIONAL GRATINGS FOR VERY LONG- WAVELENGTH QUANTUM-WELL INFRARED PHOTODETECTORS. Journal of Applied Physics 76, 4989-4994, doi:10.1063/1.357209 (1994). 139 Sarusi, G., Levine, B. F., Pearton, S. J., Bandara, K. M. S. & Leibenguth, R. E. IMPROVED PERFORMANCE OF QUANTUM-WELL INFRARED PHOTODETECTORS USING RANDOM SCATTERING OPTICAL COUPLING. Applied Physics Letters 64, 960-962, doi:10.1063/1.110973 (1994). 140 Harrison, P. & Valavanis, A. Quantum wells, wires and dots: theoretical and computational physics of semiconductor nanostructures. (John Wiley & Sons, 2016). 141 Haus, J. W. Fundamentals and applications of nanophotonics. (Woodhead Publishing, 2016).

163

142 Miikkulainen, V., Leskela, M., Ritala, M. & Puurunen, R. L. Crystallinity of inorganic films grown by atomic layer deposition: Overview and general trends. Journal of Applied Physics 113, 101, doi:10.1063/1.4757907 (2013). 143 Chen, Z. W. et al. Band alignment of Ga2O3/Si heterojunction interface measured by X- ray photoelectron spectroscopy. Applied Physics Letters 109, 105-108, doi:10.1063/1.4962538 (2016). 144 Hinuma, Y., Grueneis, A., Kresse, G. & Oba, F. Band alignment of semiconductors from density-functional theory and many-body perturbation theory. Physical Review B 90, doi:10.1103/PhysRevB.90.155405 (2014). 145 Robertson, J. Band offsets of high dielectric constant gate oxides on silicon. Journal of Non-Crystalline Solids 303, 94-100, doi:10.1016/s0022-3093(02)00972-9 (2002). 146 Bersch, E., Rangan, S., Bartynski, R. A., Garfunkel, E. & Vescovo, E. Band offsets of ultrathin high-kappa oxide films with Si. Physical Review B 78, 10, doi:10.1103/PhysRevB.78.085114 (2008). 147 Robertson, J. Band offsets of wide-band-gap oxides and implications for future electronic devices. Journal of Vacuum Science & Technology B 18, 1785-1791, doi:10.1116/1.591472 (2000). 148 Ting, M. et al. Electronic band structure of ZnO-rich highly mismatched ZnO1-xTex alloys. Applied Physics Letters 106, 5, doi:10.1063/1.4913840 (2015). 149 Sayan, S. et al. Valence and conduction band offsets of a ZrO2/SiOxNy,/n-Si CMOS gate stack: A combined photoemission and inverse photoemission study. Physica Status Solidi B-Basic Solid State Physics 241, 2246-2252, doi:10.1002/pssb.200404945 (2004). 150 Mayer, M. A. et al. Band Gap Engineering of Oxide Photoelectrodes: Characterization of ZnO1-xSex. Journal of Physical Chemistry C 116, 15281-15289, doi:10.1021/jp304481c (2012). 151 Mohamed, M. et al. Schottky barrier height of Au on the transparent semiconducting oxide beta-Ga2O3. Applied Physics Letters 101, 5, doi:10.1063/1.4755770 (2012). 152 Shan, W. et al. Effect of oxygen on the electronic band structure in ZnOxSe1-x alloys. Applied Physics Letters 83, 299-301, doi:10.1063/1.1592885 (2003). 153 Grabowski, S. P. et al. Electron affinity of AlxGa1-xN(0001) surfaces. Applied Physics Letters 78, 2503-2505, doi:10.1063/1.1367275 (2001). 154 Swank, R. K. Surface properties of II-VI compounds. J Physical Review 153, 844 (1967). 155 Perfetti, P. et al. EXPERIMENTAL-STUDY OF THE GAP-SI INTERFACE. Physical Review B 30, 4533-4539, doi:10.1103/PhysRevB.30.4533 (1984). 156 Fan, H. J., Werner, P. & Zacharias, M. Semiconductor nanowires: From self-organization to patterned growth. Small 2, 700-717, doi:10.1002/smll.200500495 (2006). 157 Li, X. & Bohn, P. W. Metal-assisted chemical etching in HF/H(2)O(2) produces porous silicon. Applied Physics Letters 77, 2572-2574, doi:10.1063/1.1319191 (2000). 158 Chartier, C., Bastide, S. & Levy-Clement, C. Metal-assisted chemical etching of silicon in HF-H2O2. Electrochimica Acta 53, 5509-5516, doi:10.1016/j.electacta.2008.03.009 (2008). 159 Lee, C.-L., Tsujino, K., Kanda, Y., Ikeda, S. & Matsumura, M. Pore formation in silicon by wet etching using micrometre-sized metal particles as catalysts. Journal of Materials Chemistry 18, 1015-1020, doi:10.1039/b715639a (2008). 160 Chern, W. et al. Nonlithographic Patterning and Metal-Assisted Chemical Etching for Manufacturing of Tunable Light-Emitting Silicon Nanowire Arrays. Nano Letters 10, 1582-1588, doi:10.1021/nl903841a (2010).

164

161 Zahedinejad, M. et al. Deep and vertical silicon bulk micromachining using metal assisted chemical etching. Journal of Micromechanics and Microengineering 23, doi:10.1088/0960-1317/23/5/055015 (2013). 162 Hildreth, O. J., Lin, W. & Wong, C. P. Effect of Catalyst Shape and Etchant Composition on Etching Direction in Metal-Assisted Chemical Etching of Silicon to Fabricate 3D Nanostructures. Acs Nano 3, 4033-4042, doi:10.1021/nn901174e (2009). 163 Kim, J. et al. Au/Ag Bilayered Metal Mesh as a Si Etching Catalyst for Controlled Fabrication of Si Nanowires. Acs Nano 5, 3222-3229, doi:10.1021/nn2003458 (2011). 164 Zhang, M.-L. et al. Preparation of large-area uniform silicon nanowires arrays through metal-assisted chemical etching. Journal of Physical Chemistry C 112, 4444-4450, doi:10.1021/jp077053o (2008). 165 Huang, Z. et al. Extended arrays of vertically aligned sub-10 nm diameter 100 Si nanowires by metal-assisted chemical etching. Nano Letters 8, 3046-3051, doi:10.1021/nl802324y (2008). 166 Scheeler, S. P., Ullrich, S., Kudera, S. & Pacholski, C. Fabrication of porous silicon by metal-assisted etching using highly ordered gold nanoparticle arrays. Nanoscale Research Letters 7, 1-7, doi:10.1186/1556-276x-7-450 (2012). 167 Yae, S., Morii, Y., Fukumuro, N. & Matsuda, H. Catalytic activity of noble metals for metal-assisted chemical etching of silicon. Nanoscale Research Letters 7, 1-5, doi:10.1186/1556-276x-7-352 (2012). 168 Huang, Z., Geyer, N., Werner, P., de Boor, J. & Goesele, U. Metal-Assisted Chemical Etching of Silicon: A Review. Advanced Materials 23, 285-308, doi:10.1002/adma.201001784 (2011). 169 Li, X. Metal assisted chemical etching for high aspect ratio nanostructures: A review of characteristics and applications in photovoltaics. Current Opinion in Solid State & Materials Science 16, 71-81, doi:10.1016/j.cossms.2011.11.002 (2012). 170 Peng, K. Q. et al. Metal-particle-induced, highly localized site-specific etching of Si and formation of single-crystalline Si nanowires in aqueous fluoride solution. Chemistry-a European Journal 12, 7942-7947, doi:10.1002/chem.200600032 (2006). 171 Huang, Z. et al. Oxidation Rate Effect on the Direction of Metal-Assisted Chemical and Electrochemical Etching of Silicon. Journal of Physical Chemistry C 114, 10683-10690, doi:10.1021/jp911121q (2010). 172 Chen, C.-Y., Wu, C.-S., Chou, C.-J. & Yen, T.-J. Morphological Control of Single-Crystalline Silicon Nanowire Arrays near Room Temperature. Advanced Materials 20, 3811-+, doi:10.1002/adma.200702788 (2008). 173 Chen, H., Wang, H., Zhang, X.-H., Lee, C.-S. & Lee, S.-T. Wafer-Scale Synthesis of Single- Crystal Zigzag Silicon Nanowire Arrays with Controlled Turning Angles. Nano Letters 10, 864-868, doi:10.1021/nl903391x (2010). 174 Qu, Y. et al. Electrically Conductive and Optically Active Porous Silicon Nanowires. Nano Letters 9, 4539-4543, doi:10.1021/nl903030h (2009). 175 Yu, X., Duxbury, P. M., Jeffers, G. & Dubson, M. A. COALESCENCE AND PERCOLATION IN THIN METAL-FILMS. Physical Review B 44, 13163-13166, doi:10.1103/PhysRevB.44.13163 (1991). 176 Geyer, N. et al. Model for the Mass Transport during Metal-Assisted Chemical Etching with Contiguous Metal Films As Catalysts. Journal of Physical Chemistry C 116, 13446- 13451, doi:10.1021/jp3034227 (2012).

165

177 Lai, C. Q., Cheng, H., Choi, W. K. & Thompson, C. V. Mechanics of Catalyst Motion during Metal Assisted Chemical Etching of Silicon. Journal of Physical Chemistry C 117, 20802- 20809, doi:10.1021/jp407561k (2013). 178 Bardeen, J. The image and van der Waals forces at a metallic surface. Physical Review 58, 727-736, doi:10.1103/PhysRev.58.727 (1940). 179 Duran, J. M. & Sarangan, A. Fabrication of ultrahigh aspect ratio silicon nanostructures using self-assembled gold metal-assisted chemical etching. Journal of Micro- Nanolithography Mems and Moems 16, 8, doi:10.1117/1.jmm.16.1.014502 (2017). 180 Li, X. P. et al. Influence of the Mobility of Pt Nanoparticles on the Anisotropic Etching Properties of Silicon. Ecs Solid State Letters 2, P22-P24, doi:10.1149/2.010302ssl (2013). 181 Yae, S., Tashiro, M., Abe, M., Fukumuro, N. & Matsuda, H. High Catalytic Activity of Palladium for Metal-Enhanced HF Etching of Silicon. Journal of the Electrochemical Society 157, D90-D93, doi:10.1149/1.3264643 (2010). 182 Asoh, H., Arai, F. & Ono, S. Effect of noble metal catalyst species on the morphology of macroporous silicon formed by metal-assisted chemical etching. Electrochimica Acta 54, 5142-5148, doi:10.1016/j.electacta.2009.01.050 (2009). 183 Cullis, A. G. & Canham, L. T. VISIBLE-LIGHT EMISSION DUE TO QUANTUM SIZE EFFECTS IN HIGHLY POROUS CRYSTALLINE SILICON. Nature 353, 335-338, doi:10.1038/353335a0 (1991). 184 Lehmann, V. & Gosele, U. POROUS SILICON FORMATION - A QUANTUM WIRE EFFECT. Applied Physics Letters 58, 856-858, doi:10.1063/1.104512 (1991). 185 Yoffe, A. D. LOW-DIMENSIONAL SYSTEMS - QUANTUM-SIZE EFFECTS AND ELECTRONIC- PROPERTIES OF SEMICONDUCTOR MICROCRYSTALLITES (ZERO-DIMENSIONAL SYSTEMS) AND SOME QUASI-2-DIMENSIONAL SYSTEMS. Advances in Physics 42, 173-266, doi:10.1080/00018739300101484 (1993). 186 Bisi, O., Ossicini, S. & Pavesi, L. Porous silicon: a quantum sponge structure for silicon based optoelectronics. Surface Science Reports 38, 1-126, doi:10.1016/s0167- 5729(99)00012-6 (2000). 187 Lin, T. L. et al. LONG-WAVELENGTH PTSI INFRARED DETECTORS FABRICATED BY INCORPORATING A P+ DOPING SPIKE GROWN BY MOLECULAR-BEAM EPITAXY. Applied Physics Letters 62, 3318-3320, doi:10.1063/1.109057 (1993). 188 Qi, Y. Y. et al. Electron transport characteristics of silicon nanowires by metal-assisted chemical etching. Aip Advances 4, 6, doi:10.1063/1.4866578 (2014).

166

APPENDIX A

Fabrication Process Followers

A.1 Plasma-Enhanced Chemical Vapor Deposition (PECVD) SiO2 Process

RF Power: 25 W

Process Pressure: 900 mTorr

Substrate Temperature: 300 C

Chamber Wall Temperature: 60 C

SiH4 Flow: 160 sccm

N2O Flow: 900 sccm

Nominal DC Bias: 9 VDC

Deposition Rate: 49 nm/min

A.2 HMDS Coating

Used to promote adhesion between resist and substrate. Particularly important when coating

SiO2 surface.

Dehydration Bake: 4 min @ 250 C

Spin Coat HMDS: 30 s @ 4000 RPM (required on oxide)

Soft Bake: 75 s @ 110 C

A.3 AZ Electronic Materials AZ 5214 Image Reversal Process

HMDS Coating

Spin Coat AZ 5214: 30s @ 4000 RPM (film thickness ~1.4 µm)

167

Soft Bake: 75 s @ 110 C

Align Mask and Expose: 2 s (no filter 10.5 mW/cm2)

Reversal Bake: 120 s @ 110 C

Flood Exposure: 20 s (no filter 10.5 mW/cm2)

Puddle Develop: 60 s (Microposit 351 developer 1:5 with DI water)

DI Water Spray Rinse: 20 s

Nitrogen Blow Dry: 30 s

A.4 Shipley Microposit S1805 Process

HMDS Coating (critical for patterned BOE etch of SiO2)

Spin Coat S1805: 30s @ 4000 RPM (film thickness ~0.5 µm)

Soft Bake: 75 s @ 110 C

Align Mask and Expose: 5 s (no filter 10.5 mW/cm2)

Puddle Develop: 30 s (Microposit 351 developer 1:5 with DI water)

DI Water Spray Rinse: 20 s

Nitrogen Blow Dry: 30 s

A.5 Solvent Cleaning

Spin Wafer: 500—1000 RPM

Pressure Spray Acetone: 30 s

Bottle Spray Acetone: 10 s

Bottle Spray Methanol: 10 s

Bottle Spray Isopropyl Alcohol: 20 s

Nitrogen Blow Dry: 30 s

A.6 Metal-Liftoff Process

Secure wafer with vacuum chuck

168

Apply wafer dicing tape to deposition surface, pressing firmly with roller to minimize air bubbles

Peel dicing tape from surface and recycle precious metal (repeat tape process if necessary)

Perform solvent cleaning process with extended acetone pressure spray (60 s)

A.7 Metal Etchants

The following etchants were used to remove residual metal after silicide formation. This process was found to improve device quantum efficiency and had no appreciable effect on dark current.

Chromium: Chromium Etchant TFE

Gold: Gold Etchant TFA

Nickel: Nickel Etchent Type I

Molybdenum: HNO3:HCl 1:3 (aqua regia)

Palladium: Nickel Etchent Type I

Platinum: HNO3:HCl 1:3 (aqua regia)

Tantalum: HF:NH4F 1:7 (BOE)

169

APPENDIX B

Python Source Code

# -*- coding: cp1252 -*- #======# # IMPORTS # #======import os, sys, fnmatch, copy, time import numpy as np from matplotlib import pyplot as plt from scipy import optimize, interpolate, integrate scriptPath = os.path.dirname(sys.argv[0]) parentDir = os.path.dirname(scriptPath) sys.path.insert(0,parentDir) from tmm.tmm_core import * from TMM import tmmCalc as tm #======# # MATH CONSTANTS # #======centi = .01 milli = .001 micro = 1e-6 nano = 1e-9 pico = 1e-12 kilo = 1000 mega = 1e6 tera = 1e9 c = 2.998e8 # m/s speed of light in vacuum h = 6.626e-34 # J·s Planck constant hbar = h/(2*np.pi) # J·s reduced Planck constant kB = 1.381e-23 # J/K Boltzmann constant q = 1.6e-19 # C elementary charge eV = q meV = milli*eV m0 = 9.1e-31 # kg electron mass e0 = 8.854e-12 # F/m inch = .0254 #Conversion to meters deg = np.pi/180 #Conversion to radians #======# # HELPER FUNCTIONS # #======def iround(val): """Round (val) to nearest integer and return as int""" return int(round(val)) def carray(start, stop, num=101, step=0): """Create a numpy array between (start) and (stop) with specified number of steps (num) or specified step value (step).

return: numpy array""" if step: divisions = abs(start-stop)/step if abs(1.0-divisions/iround(divisions)) < .000000001:

170

num = iround(divisions + 1) else: num = np.floor(divisions) + 1 stop = start + (num-1)*step return np.linspace(start,stop,num) def listT(listOfLists): """Transpose list from list of rows to list of columns or vice versa and return""" if len(listOfLists)==1: newlist = [[val] for val in listOfLists[0]] else: newlist = map(list, map(None, *listOfLists)) return newlist def findFilesR(directory, pattern): """Find files in (directory) that match (pattern) recursively""" fileList = [] for root, dirnames, filenames in os.walk(directory): for filename in fnmatch.filter(filenames, pattern): fileList.append(os.path.join(root, filename)) return fileList #======# # FTIR TMM FITTING FUNCTIONS # #======def stackTMM(stack, wl, pol, theta, layerAbs=False): """Performs TMM calculation on stack of materials whose relevent parameters to the calculation are given by keys of a dict. TMM calculation is performed by tmm_core.py which is written by Steve Byrnes. the source code for the TMM calculation can be found on his website: https://sjbyrnes.com.

stack: list of dicts representing material layers dict has following format: n (req): number or function (of wl and optional kwargs) representing complex index t (req): thickness of layer (meters) c (req): 'c' for coherant and 'i' for incoherant layer kwargs (opt): for calculting n function such that n(wl,**kwargs) produces index array for wl range wl: wavelength range [m] pol: 's','p', or 'u' polarization theta: angle of incidence [radians] layerAbs: whether or not to calculate % absorp in each layer

return: data dict of following format: r: reflection t: transmission a: absorption alayer: per layer absorption (only output when layerAbs=True)""" dlist = [s['t'] for s in stack] #list of layer thicknesses clist = [s['c'] for s in stack] #list of layer coherance/incoherance nwlList = [] # list of layer nk vs wl vals for mat in stack: #populate nk vs wl lists for each layer if type(mat['n'])==np.int or type(mat['n'])==np.float: nwl = np.repeat(mat['n'],len(wl)) else: if mat.has_key('kwargs'): nwl = mat['n'](wl,**mat['kwargs']) else: nwl = mat['n'](wl) nwlList.append(nwl) nLists = listT(nwlList) #Calculate r, t, and a using coherant/incoherent TMM method data = {'r':[],'t':[],'a':[]} if layerAbs: alists = [] for i,w0 in enumerate(wl): if pol=='s' or pol=='p': d = inc_tmm(pol,nLists[i],dlist,clist,theta,w0) data['r'].append(d['R']) data['t'].append(d['T']) data['a'].append(1.-d['R']-d['T']) if layerAbs: alists.append(inc_absorp_in_each_layer(d)) else: ds = inc_tmm('s',nLists[i],dlist,clist,theta,w0) dp = inc_tmm('p',nLists[i],dlist,clist,theta,w0) data['r'].append((ds['R']+dp['R'])/2.) data['t'].append((ds['T']+dp['T'])/2.) data['a'].append(1.-(ds['R']+dp['R'])/2.-(ds['T']+dp['T'])/2.) if layerAbs: alistspol = inc_absorp_in_each_layer(ds) alistppol = inc_absorp_in_each_layer(dp)

171

alist = (np.array(alistspol) + np.array(alistppol))/2. alists.append(list(alist)) if layerAbs: data['alayer'] = listT(alists) return data

def optFTIRModelFit(guess,stacks,dataDicts,wl='All',numpoints=101,rstandard=False): """Calculates the residuals between measured data (dataDicts) and model (calculated from stacks) Model parameters are either predifined in dataDicts, or fit using values from guess vector. Meant to be used in combination with a minimization function such as optimize.leastsq().

guess: vector of fitting parameter guesses. The order of this vector is defined by guessToStacks() and guessFromStacks() stacks: a list of material stacks (see stackTMM for dictionary description) The order of stacks should be same order as FTIR data from dataDicts dataDicts: List of ftir data dictionaries. Format of dictionary defined by importFile() and normalizeData() wl: should be 'All' or numpy array. if 'All', full measured data range will be fit, otherwise only fit wavelength values defined by numpy array numpoints: used in conjunction with 'All' to define number of data points to fit to save computation time. rstandard: if the reflectance of standard is known, set this parameter to function call such that rstandard(wl) returns fractional reflection at wl. (for example, set to gold reflectance if gold mirror is used as reflection standard). If False, simply use reflectance of 1.""" residuals = [] wl0 = copy.deepcopy(wl) print '======Fitting Parameters ======' newstacks = guessToStacks(stacks,guess) for i, stack in enumerate(newstacks): if type(wl0) == str and wl == 'All': wl=carray(dataDicts[i][0]['wl'].min(),dataDicts[i][0]['wl'].max(),numpoints) else: wl = copy.deepcopy(wl0) print '======End ======' for data in dataDicts[i]: if data['meas']=='r' and rstandard: m = rstandard(wl) else: m = 1. modelData = stackTMM(stack, wl, 'u', data['theta']) residual = modelData[data['meas']] - m*data['normf'](wl) residuals.append(residual) return np.array(residuals).flatten() def guessFromStacks(stacks,getBounds=False,tbounds=(0,5*micro)): """Vectorizes guesses from list of material stacks (stacks). This function is intended to be used with optFTIRModelFit() and optimize.leastsq(). This function handles the exchange of fitting parameters between those functions and the material stacks. Material uniqueness is defined by the 'label' key of the each material in the stacks. Identical labels indicates identical films, so single set of fitting parameters is used for every instance of that film in (stacks). The order of this vector works in tandem with guessToStacks()

stacks: list of list of material dicts defined by stackTMM() getBounds: whether to return bounds on fitting parameters in (guess) if bounds are requested but not defined by material dict key 'bounds', a default bounds of -inf to inf is used for that parameter. tbounds: thickness bounds when thickness is fit.

specialized keys from materials in each stack used by this function include: fitThick: whether thickness of film is fit fitArgs: list of keywords that serve as arguments to refractive index model defined by 'n' function bounds: list of parameter bounds for each argument fit (length should match fitArgs)

return: guess vector and (optional) bounds (list of tuples)""" guess = [] bounds = [] fitList = [] # list of material labels that share fitting parameters for stack in stacks: for i,mat in enumerate(stack): if mat.has_key('fitThick'): if mat['fitThick']: guess.append(mat['t']) if mat.has_key('tbounds'):bounds.append(mat['tbounds']) else:bounds.append(tbounds) if mat.has_key('fitArgs'): if mat['fitArgs'] and not(mat['label'] in fitList): fitList.append(mat['label']) if mat['fitArgs']=='All': keylist = mat['kwargs'].keys() else: keylist = mat['fitArgs']

172

for key in keylist: guess.append(mat['kwargs'][key]) if mat.has_key('bounds'): if mat['bounds'].has_key(key): bounds.append(mat['bounds'][key]) else: bounds.append((-np.inf,np.inf)) else: bounds.append((-np.inf,np.inf)) if getBounds: bounds = listT(bounds) return guess, (np.array(bounds[0]),np.array(bounds[1])) else: return guess def guessToStacks(stacks,guess,dec=4,stdout=True): """Takes a vector of fitting parameters (guess), and inserts them into a list of material stacks (stacks). This function is intended to be used with optFTIRModelFit() and optimize.leastsq(). This function handles the exchange of fitting parameters between those functions and the material stacks. Material uniqueness is defined by the 'label' key of the each material in the stacks. Identical labels indicates identical films, so single set of fitting parameters is used for every instance of that film in (stacks). The order of this vector works in tandem with guessFromStacks().

stacks: list of list of material dicts defined by stackTMM() guess: vector of fitting parameters that goes between optFTIRModelFit() and optimize function. stdout: whether to print fitting parameters whenever function is called (for monitoring fitting). dec: integer decimal places to print when stdout=True""" guess = list(guess) fitList = dict() if stdout: print '------Material Params ------' for stack in stacks: for i,mat in enumerate(stack): if mat.has_key('fitThick'): if mat['fitThick']: t = guess.pop(0) mat['t'] = np.abs(t) if mat.has_key('label'): label = mat['label'] else: label = 'Layer '+str(i) if stdout: print label+' thickness: '+str(t/nano)+' nm' if mat.has_key('fitArgs'): printList = [] if mat['fitArgs'] and mat['label'] in fitList.keys(): for keyval in fitList[mat['label']]: mat['kwargs'][keyval[0]] = keyval[1] printList.append("'"+keyval[0]+"':"+format(keyval[1],'.'+str(dec)+'g')) if mat['fitArgs'] and not(mat['label'] in fitList.keys()): fitparams = [] if mat['fitArgs']=='All': keylist = mat['kwargs'].keys() else: keylist = mat['fitArgs'] for key in keylist: val = guess.pop(0) mat['kwargs'][key] = val fitparams.append((key,val)) printList.append("'"+key+"':"+format(val,'.'+str(dec)+'g')) fitList[mat['label']] = fitparams printList.sort() print mat['label']+' Parameters:' print '{'+','.join(printList)+'}\n' return stacks

def importFile(path): """Import .csv FTIR file (path) and return dict. The .csv file is expected to be two columns of data, with the first being wavenumber (cm-2) and the second being the detector signal from the FTIR.

returns: dict of following format: label: filename without extension sig: raw FTIR signal from measurement sigf: function such that sigf(wl) gives interpolated value of signal at wavelength (wl) wn: wavenumber values from measurement wl: wavelength values calculated from measurement path: path to measurement file""" label = os.path.basename(path)[:-4]#Use filename as data label wn, sig = np.loadtxt(path, delimiter=',',unpack=True) wl = 10000./wn sigf = interpolate.interp1d(wl*micro,sig,fill_value=1,bounds_error=False) return {'label': label, 'sig':sig, 'sigf':sigf, 'wn': wn/centi, 'wl':wl*micro, 'path':path} def importFolder(directory): """Import all .csv from (directory) and return list of dicts""" filelist = findFilesR(directory,'*.csv')

173

dataList = [] for path in filelist: data = importFile(path) dataList.append(data) return dataList def normalizeData(dataList, refName=''): """Take list of data dicts (dataList) and normalize to refrence spectrum with label (refName). If none provided, guess reference based on signal level (highest average signal). Data dict format is defined by importFile(). Add normalized data list to dict as "norm' and interpolation function as 'normf'""" if refName=='': refName = guessRef(dataList) for i, data in enumerate(dataList): if data['label']==refName: ref = dataList.pop(i) for data in dataList: data['norm'] = data['sig']/ref['sig'] data['normf'] = interpolate.interp1d(data['wl'],data['norm']) return dataList def guessRef(dataList): """Guess which data in (dataList) is reference spectrum based on signal level across spectrum. used by normalizeData()""" points = len(dataList[0]['wl']) indices = [] for i in range(points): signals = [] for data in dataList: signals.append(data['sig'][i]) maxsigindex = signals.index(max(signals)) indices.append(maxsigindex) refindex = max(set(indices),key=indices.count) return dataList[refindex]['label'] def importMeasFolder(folder,meas,theta): """Import data from measurement folder using auto-normalize from normalizeData(). return dict with keys according to importFile() and normalizeData() with added keys 'meas' and 'theta' which represent the type of measurement (r or t) and the angle it was measured at""" data = normalizeData(importFolder(folder)) for d in data: d['meas'] = meas d['theta'] = theta return data

#======# # QUANTUM MODELING FUNCTIONS # #======def matMesh(matStack, dx, ezero='Auto'): """Takes a stack of materials (matStack) and outputs relevant calculation parameters in a mesh format defined by dx step size.

matStack: should be a list where each element of the list is a tuple of the form: (matdict, thickness). matdict should have keys: 'chi' which is the electron affinity of the material, and 'me' which is the electron effective mass. dx: step size of mesh ezero: zero energy reference (relative to vacuum). If set to 'Auto', lowest energy in system is used.

returns: x: position vector materials: list that contains material dict for each position in x. me: effective mass as function of position x. v: potential profile as function of position x.""" matMesh = [] for mat in matStack: matMesh.append([mat[0]]*iround(mat[1]/dx)) materials = [i for s in matMesh for i in s] # Flatten list if ezero == 'Auto': ezero = max([mat['chi'] for mat in materials]) x = np.cumsum(np.repeat(dx,len(materials))) me = np.array([mat['me'] for mat in materials]) v = np.array([-mat['chi']+ezero for mat in materials]) return [x, materials, me, v] def shootSchrodinger(x, me, v, eguess, de=1e-8*meV, tol=1e-5*meV,output=True): """Iteratively shoots Schrodinger's equation starting with eguess until convergence to nearest eigen- state.

174

x: position vector me: effective mass as function of position v: potential energy profile eguess: initial guess of eigen state de: energy difference used for finite difference calculation in Newton/Rapson method tol: precision of energy convergence output: whether to print convergence characteristics to standard output

returns: eguess: eigen energy after convergence phinorm: normalized wavefunction after convergence eguesses: list of eguesses during convergence process""" eguesses = [eguess] t1 = time.clock() dx = x[1]-x[0] for i in range(100): phi = [0,1] dphi = [0,1] me = np.append(me,me[-1]) for j in range(2,len(x)): mef = (me[j]+me[j+1])/2 meb = (me[j]+me[j-1])/2 dphi.append((2*mef*dx**2/(hbar**2)*(v[j]-eguess-de)+1.+mef/meb)*dphi[j-1]-dphi[j-2]*mef/meb) phi.append((2*mef*dx**2/(hbar**2)*(v[j]-eguess)+1.+mef/meb)*phi[j-1]-phi[j-2]*mef/meb) phiprime = (dphi[-1]-phi[-1])/de enext = eguess-phi[-1]/phiprime eguesses.append(enext) if len(eguesses) > 2: if (np.abs(eguesses[-2]-eguesses[-3]) <= tol) & (np.abs(eguesses[-1]-eguesses[-2]) <= tol): t2 = time.clock() if output: print len(eguesses)-2, ' Newton Iterations in ',np.round(t2-t1,4), ' seconds' phi = np.array(phi) break eguess = enext phinorm = phi/np.sqrt(np.sum(phi**2)*dx) return eguess, phinorm, eguesses def shootTunnel(x, me, v, energies): """Shoots Schrodinger's equation for an array of energies and returns the tunneling probability for each energy.

x: position vector me: effective mass as function of position v: potential energy profile energies: vector of energies to calculate tunneling probability

returns: prob: vector of calculated tunneling probabilities at each energy in energies phis: calculated wavefunction at each energy in energies""" t1 = time.clock() dx = x[1]-x[0] me = np.append(me,me[-1]) phis = [] prob = [] for e in energies: kt = np.sqrt(2*me[-2]*(e-v[-2])/hbar**2) phi = [1.,np.exp(-1j*kt*dx)] for j in range(2,len(x)): mef = (me[j]+me[j+1])/2. meb = (me[j]+me[j-1])/2. phi.append((2*mef*dx**2/(hbar**2)*(v[j]-e)+1.+mef/meb)*phi[j-1]-phi[j-2]*mef/meb) phi = np.array(phi) pdist = np.absolute(phi*np.conjugate(phi)) phi = phi/np.sqrt(np.sum(pdist)*dx)

azr = (phi[-2]*np.exp(1j*kt*dx)-phi[-1])/(np.exp(-1j*kt*x[-1])*(np.exp(2j*kt*dx)-1.)) azi = np.exp(-1j*kt*x[-1])*(phi[-1]-azr*np.exp(-1j*kt*x[-1]))

prob.append(1.-np.absolute((azi/azr)*np.conjugate(azi/azr))) phis.append(phi) return np.array(prob), np.array(phis) def plotSol(x,v,phi,en,phiscale=.333): """Plots energy potential (v), eigen energy (en) and superimposed wavefunction (phi). scale of wavefunction is defined by (phiscale) as a fraction of the total potential height.""" phiheight = (v.max()-v.min())*phiscale phinorm = phi*phiheight/(phi.max()-phi.min()) plt.plot(x/nano,v/meV, color='dimgrey')

175

phicolor = 'black' ecolor = 'indianred' plt.plot(x/nano, (phinorm+en)/meV, color=phicolor) plt.plot(x/nano, np.repeat(en/meV,len(x)), color=ecolor,linestyle='--') plt.xlim([x[0]/nano, x[-1]/nano]) plt.xlabel('Position (nm)') plt.ylabel('Energy (meV)') print 'Energy (meV): ',en/meV

#======# # EXAMPLE CALCULATIONS (HOW TO USE ABOVE FUNCTIONS) # #======

#------# Build a material stack, calculate transmission, reflection and plot the result

# Cauchy model for transparent media def cauchyn(wl,cn1,cn2,cn3): wl=wl/micro return np.abs(np.abs(cn1) + cn2/(wl)**2 + cn3/(wl)**4) air = {'label':'air','n':1.,'t':inf,'c':'i'} sio2cauchyparams = {'cn1':1.447, 'cn2':0.366, 'cn3':0} sio2film = {'label':'SiO2','n':cauchyn,'kwargs':sio2cauchyparams, 't':600*nano,'c':'c'} stack = [air, sio2film, air] wl = carray(1,3,501)*micro s = stackTMM(stack, wl, 's',0) plt.plot(wl/micro, s['t'],label='Transmittance') plt.plot(wl/micro, s['r'],label='Reflectance') plt.show()

#------# Fit refractive index model to reflection and transmission measurements from FTIR (quartz window)

# Cauchy model for transparent media def cauchyn(wl,cn1,cn2,cn3): wl=wl/micro return np.abs(np.abs(cn1) + cn2/(wl)**2 + cn3/(wl)**4) rdatapath = 'reflection data path' tdatapath = 'transmission data path' rdata = importMeasFolder(rdatapath,'r',10*deg) tdata = importMeasFolder(tdatapath,'t',10*deg) ftirdata = [rdata,tdata] air = {'label':'air','n':1.,'t':inf,'c':'i'} quartzcauchyparams = {'cn1':1.447, 'cn2':0.366, 'cn3':0} quartzwafer = {'label':'quartz','n':cauchyn,'kwargs':quartzcauchyparams, 'fitArgs':'All', 't':500*micro, 'c':'i'} wlfit = carray(1,3)*micro stack = [air, quartzwafer, air] stacks = [stack, stack] #Reflection and transmission stacks are identical in this case guess = guessFromStacks(stacks) opt = optimize.leastsq(optFTIRModelFit, guess, maxfev=100, args=(stacks,ftirdata,wlfit)) model = stackTMM(stack,wlfit,'u',10*deg) plt.plot(wlfit/micro, model['r'],'--',color='black') plt.plot(wlfit/micro, model['t'],'--',color='black') plt.plot(rdata[0]['wl']/micro,rdata[0]['norm'],label='Reflectance') plt.plot(tdata[0]['wl']/micro,tdata[0]['norm'],label='Transmittance') plt.show()

#------# Find eigen-states of potential well and plot

# Define Material Parameters well = {'chi':4.*eV, 'me':0.2*m0} barrier = {'chi':3.6*eV, 'me':0.3*m0}

176

# Define quantum well stack matstack = [(barrier,8*nano), (well,3*nano), (barrier,8*nano)] # Find eigen states for each eguess and plot solution eguesses = [100*meV, 300*meV] for i, eguess in enumerate(eguesses): x, mats, me, v = matMesh(matstack, .01*nano) en, phi, eguesses = shootSchrodinger(x, me, v, eguess) plotSol(x,v,phi,en) plt.show()

#------# Calculate tunneling probability of double barrier well = {'chi':4.*eV, 'me':0.2*m0} barrier = {'chi':3.6*eV, 'me':0.3*m0} # Define double barrier material stack matstack = [(well,8*nano), (barrier,2*nano), (well,3*nano), (barrier,2*nano), (well,8*nano)] # Calculate Tunneling Probability energies = carray(1*meV,500*meV,1001) x, mats, me, v = matMesh(matstack, .01*nano) prob, phis = shootTunnel(x, me, v, energies) plt.semilogy(energies/meV, prob) plt.show()

177