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Impact of Mechanical Stress on AlGaN/GaN HEMT Performance

Permanent Link: http://ufdc.ufl.edu/UFE0043630/00001

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Title: Impact of Mechanical Stress on AlGaN/GaN HEMT Performance Channel Resistance and Gate Current
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Koehler, Andrew D
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: factor -- gan -- gate -- gauge -- hemt -- leakage -- strain -- stress
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract: AlGaN/GaN high electron mobility transistors (HEMTs) stand out with superb advantages for high-power, high-temperature, high-frequency applications. Internal stress is inherent to state-of-the-art AlGaN/GaN HEMTs and has the potential to impact performance and reliability. Strain is an integral part of modern semiconductor technology and has been used to extend scaling of Si for nearly a decade, and the performance and reliability implications are well understood. Understanding the impact of mechanical stress on AlGaN/GaN HEMT channel resistance and gate current is crucial for continued improvements in device performance and reliability. Repeatable gauge factors of an AlGaN/GaN HEMT device were obtained after eliminating parasitic charge trapping effects. Over four orders of magnitude of variation in gauge factors are reported in literature. Charge traps are likely responsible for the huge discrepancy. By employing continuous sub-bandgap optical excitation, the effect of non-repeatable charge trapping transients was effectively minimized, allowing the gauge factor to be accurately measured. The measured gauge factor is compared to a simulated gauge factor, calculated from stress-induced changes in the 2DEG sheet carrier density and mobility. Stress-altered gate leakage currents in AlGaN/GaN HEMTs are measured as a function of constant applied reverse gate bias. Increasing reverse gate bias decreases the stress sensitivity of the gate leakage current. Poole-Frenkel emission dominates the gate leakage current for gate biases above threshold. Stress changes Poole-Frenkel emission by altering the trap activation energy, which also changes the compensation parameter. Reverse tunneling current which balances the forward Poole-Frenkel current at equilibrium is modeled to explain the experimental results. Tensile (compressive) stress decreases (increases) the trap activation energy, increasing (decreasing) the gate leakage current. Although below threshold, the electric field in the AlGaN barrier saturates in the middle of the gate, the electric field increases at the gate edges because of two-dimensional effects. For larger reverse gate bias much below threshold, the thickness of the AlGaN tunneling barrier decreases which causes Fowler-Nordheim tunneling at the gate edges to dominate the current transport.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Andrew D Koehler.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Thompson, Scott.
Local: Co-adviser: Nishida, Toshikazu.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043630:00001

Permanent Link: http://ufdc.ufl.edu/UFE0043630/00001

Material Information

Title: Impact of Mechanical Stress on AlGaN/GaN HEMT Performance Channel Resistance and Gate Current
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Koehler, Andrew D
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: factor -- gan -- gate -- gauge -- hemt -- leakage -- strain -- stress
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: AlGaN/GaN high electron mobility transistors (HEMTs) stand out with superb advantages for high-power, high-temperature, high-frequency applications. Internal stress is inherent to state-of-the-art AlGaN/GaN HEMTs and has the potential to impact performance and reliability. Strain is an integral part of modern semiconductor technology and has been used to extend scaling of Si for nearly a decade, and the performance and reliability implications are well understood. Understanding the impact of mechanical stress on AlGaN/GaN HEMT channel resistance and gate current is crucial for continued improvements in device performance and reliability. Repeatable gauge factors of an AlGaN/GaN HEMT device were obtained after eliminating parasitic charge trapping effects. Over four orders of magnitude of variation in gauge factors are reported in literature. Charge traps are likely responsible for the huge discrepancy. By employing continuous sub-bandgap optical excitation, the effect of non-repeatable charge trapping transients was effectively minimized, allowing the gauge factor to be accurately measured. The measured gauge factor is compared to a simulated gauge factor, calculated from stress-induced changes in the 2DEG sheet carrier density and mobility. Stress-altered gate leakage currents in AlGaN/GaN HEMTs are measured as a function of constant applied reverse gate bias. Increasing reverse gate bias decreases the stress sensitivity of the gate leakage current. Poole-Frenkel emission dominates the gate leakage current for gate biases above threshold. Stress changes Poole-Frenkel emission by altering the trap activation energy, which also changes the compensation parameter. Reverse tunneling current which balances the forward Poole-Frenkel current at equilibrium is modeled to explain the experimental results. Tensile (compressive) stress decreases (increases) the trap activation energy, increasing (decreasing) the gate leakage current. Although below threshold, the electric field in the AlGaN barrier saturates in the middle of the gate, the electric field increases at the gate edges because of two-dimensional effects. For larger reverse gate bias much below threshold, the thickness of the AlGaN tunneling barrier decreases which causes Fowler-Nordheim tunneling at the gate edges to dominate the current transport.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Andrew D Koehler.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Thompson, Scott.
Local: Co-adviser: Nishida, Toshikazu.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0043630:00001


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1 IMPACT OF MECH ANICAL STRESS ON ALGAN/GAN HEMT PERFORMANCE: CHANNEL RESISTANCE AND GATE CURRENT By ANDREW DANIEL KOEHLER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT O F THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011

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2 2011 Andrew Daniel Koehler

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3 To my family

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4 ACKNOWLEDGMENTS I would like to thank my advisor Dr. Scott E. Thompson. I have benefited from his advice and guidance during my studies. Also, I thank my co chair Dr. Toshikazu Nishida for his encouragement and guidance. I would also like to thank Dr. Ant Ural and Dr. Brent Gila for their assistance and serving on my committee. I also thank all of my current a nd past colleagues for their assistance and support: Amit, Eric, Guangyu, Hyunwoo, Jingjing, Ji Song, Kehuey, Lu Min, Nidhi, Onur, Sagar, Sri, Tony, Toshi, Ukjin, Uma, Xiaodong, Yongke, Younsung

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION AND OVERVIEW ................................ ................................ ....... 15 Overview of AlGaN/GaN HEMTs ................................ ................................ ............ 15 Stress in AlGaN/GaN HEMTs ................................ ................................ ................. 17 Stress in Semiconductor Technology ................................ ................................ ..... 18 Motivation ................................ ................................ ................................ ............... 19 Organization ................................ ................................ ................................ ........... 21 2 ALGAN/GAN HEMT AND WAFER BENDING BACKGROU ND ............................. 25 GaN Fundamentals ................................ ................................ ................................ 25 Spontaneous Polarization ................................ ................................ ................. 25 Piezoelectric Polarization ................................ ................................ ................. 26 Formation of 2DEG ................................ ................................ .......................... 28 Device Description ................................ ................................ ................................ .. 29 Mechanical Wafer Bending Experiment Setup ................................ ........................ 30 Four Point Bending ................................ ................................ .......................... 31 Bending Measurements of Small Samples ................................ ....................... 31 Summary ................................ ................................ ................................ ................ 33 3 EXTRACTION OF ALGAN/GAN HEMT GAUGE FACTOR IN THE PRESENCE OF TRAPS ................................ ................................ ................................ .............. 42 Introduction ................................ ................................ ................................ ............. 42 Effects of Trapped Charge ................................ ................................ ...................... 42 Experimental Setup ................................ ................................ ................................ 44 Elimination of Charge Trapping Effects ................................ ............................ 44 External Resistance Consideration ................................ ................................ .. 45 Results and Discussion ................................ ................................ ........................... 46 Gauge Factor Measurement ................................ ................................ ............. 46 Resistance Change with Stress ................................ ................................ ........ 47

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6 2DEG Change with Stress ................................ ................................ ................ 47 Electron Mobility Change with Stress ................................ ............................... 48 Simulated Gauge Factor ................................ ................................ ................... 49 Sum mary ................................ ................................ ................................ ................ 49 4 VERTICAL ELECTRIC FIELD IN THE ALGAN BARRIER ................................ ...... 62 Introduction ................................ ................................ ................................ ............. 62 Ideal 1D Calculation of E AlGaN ................................ ................................ ................. 63 1D Experimentally Measu red E AlGaN ................................ ................................ ....... 65 2D Simulation of E AlGaN ................................ ................................ ........................... 67 Simulation Details ................................ ................................ ............................. 67 Simulation Results ................................ ................................ ............................ 68 Summary ................................ ................................ ................................ ................ 69 5 FIELD DEPENDENT MECHANICAL STRESS SENSITIVITY OF ALGAN/GAN HEMT GATE LEAKAGE CURRENT ................................ ................................ ....... 84 Introduction ................................ ................................ ................................ ............. 84 Experiment ................................ ................................ ................................ .............. 85 Results and Discussion ................................ ................................ ........................... 86 Waf er Bending Results ................................ ................................ ..................... 86 Discussion ................................ ................................ ................................ ........ 87 Maximum com pensation ( r = 1) ................................ ................................ 90 Reduced compensation (1 < r < 2) ................................ ............................. 92 Reduced compensation (1 < r < 2) with reverse current ............................ 94 Summary ................................ ................................ ................................ ................ 96 6 CONCLUSION ................................ ................................ ................................ ...... 112 Overall Summary ................................ ................................ ................................ .. 112 Future Work ................................ ................................ ................................ .......... 114 LIST OF REFERENCES ................................ ................................ ............................. 116 BIO GRAPHICAL SKETCH ................................ ................................ .......................... 126

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7 LIST OF TABLES Table page 1 1 Key material parameters for high power high performance transistors ............... 23 4 1 List of parameters used in 1D E AlGaN calculation ................................ ................ 71 5 1 Key parameters extracted to match experimental data ................................ ...... 97

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8 LIST OF FIGURES Figure page 1 1 Cross section schematic of AlGaN/GaN HEMT on Si(111) substrate. ............... 24 2 1 GaN faced GaN crystal lattice, oriented along the <0001> direction. ................. 34 2 2 Polarizations in strained Al x Ga 1 x N (x = 0.26), relaxed GaN heterostructure. The strained AlGaN layer has larger spontaneous polarization than the GaN layer, as we ll as additional polarization from the piezoelectric effect. ................. 35 2 3 Conduction band schematic diagram of an AlGaN/GaN HEMT showing charge balance. ................................ ................................ ................................ .. 36 2 4 Cross section SEM of commercial devices characterized in this dissertation. Image from Nitronex [47]. ................................ ................................ ................... 37 2 5 Typical I D V G curve of a depletion mode AlGaN/GaN HEMT meas ured at V DS = 0.1 V. ................................ ................................ ................................ ............... 38 2 6 Mechanical wafer bending setup: showing (a) a photograph of Si wafer under ~1 GPa of stress, and (b) a schematic of wafer under four point bending. ......... 39 2 7 GaN wafer sample attached to heat treated high carbon stainless steel inserted in a four point bending setup. ................................ ............................... 40 2 8 Increasing and drecreas ing stress applied to a wafer mounted on a stainless steel strip. A strain gauge is used to determine the amount of applied stress. .. 41 3 1 Results of consecutive V GS = 2 to 0 V DS = 0.1 V meas urement sweeps resulting in charge trapping and detrapping. ................................ ...................... 51 3 2 V T measured in consecutive I D V G sweeps. In dark, | V T | can increase (decrease) from detrapping (trapping) of electrons, dep ending the device initialization. Under unfiltered UV illumination, V T does not fluctuate. ................ 52 3 3 A decrease in channel resistance of 15% observed during 1200 seconds of measuring after turnin g on the incandescent microscope light. .......................... 53 3 4 Unfiltered UV measurement (a) I D V G measurements in dark and under unfiltered UV light with a large increase in off state current and a decrease in subthreshold slope. (b) The spectral output of the unfiltered UV light. .............. 54 3 5 Filtered UV measurement (a) I D V G measurements in dark and UV light filtered by a 380 nm bandpass filter (b) The spectral output of UV light with 380 nm bandpass filter. ................................ ................................ ...................... 55

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9 3 6 Experimental setup for photoionizing trapped charge to measure the gauge factor. ................................ ................................ ................................ ................. 56 3 7 lluminating the device under test with UV light stabilized R CH to less than 0.02% variation for 1200 seconds of measurement. ................................ ........... 57 3 8 Normalized change in channel resis tance with incrementally increasing a nd decreasing uniaxial stress. ................................ ................................ ................. 58 3 9 R CH measurements at each time interval stress was held constant. Error bars represent a three standard deviation conf idence interval for the measurement. ................................ ................................ ................................ ..... 59 3 10 Schematic showing polarizations in AlGaN/GaN HEMTs as fabricated (left), and 1 GPa mechanically applied stress (right) generating additional P PE mec h similar in magnitude for both AlGaN and GaN layers. ................................ ........ 60 3 11 Simulated change in n s e and R CH with uniaxial stress shown in bands of uncertainty. The bands signify variations in numerical r esults due to uncertainty in elastic a nd piezoelectric coefficients. ................................ ........... 61 4 1 Energy band diagram schematic showing Ni/AlGaN/GaN interface ................... 72 4 2 Dependence of the 2DEG density ( n s ) with gate bias for the 1D case, with no interface trapped charge. Threshold is defined when n s is entirely depleted ( n s = 0). ................................ ................................ ................................ ............... 73 4 3 Idealisti c 1D calculation of E AlGaN assuming no interface trapped charge. E AlGaN increases linearly until the threshold voltage, then saturates. .................. 74 4 4 Bar diagram of the AlGaN/GaN interface charge fo r an ideal device with no trapped charge and an actual device. Trapped charge reduces the positive fixed sheet charge density at the AlGaN/GaN interface. ................................ .... 75 4 5 Capacitance Voltage measurement which is integrated in order to determine n s ( V ). ................................ ................................ ................................ .................. 76 4 6 1D ideal (no interface trapped charge) calculation and the experimental result from experimental parameters obtained by adjusting int and obtaining n s from C V ................................ ................................ ................................ ............. 77 4 7 Optimized grid for Sentaurus simulation of the AlGaN/GaN HEMT device. ........ 78 4 8 Experimental calcula tion of E AlGaN versus V G compared to 2D simulation results. ................................ ................................ ................................ ................ 79 4 9 Vertical cross section of electric field of the AlGaN/GaN HEMT at the (a) center of the gate and (b) drain edge of the gate. ................................ ............... 80

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10 4 10 Horizontal cross section of E AlGaN taken near the top surface of the AlGaN barrier 1 nm below the gate contact. ................................ ................................ .. 81 4 11 Hor izontal cross section of the electrostatic potential taken near the top surface of the GaN 0.5 nm below the AlGaN/GaN interface. .............................. 82 4 12 H orizontal component of E AlGaN at the (a) center and (b) edge of the gate. ........ 83 5 1 Electrical step stress measurement showing the breakdown of J G at the critical voltage. ................................ ................................ ................................ .... 98 5 2 Normalize d change in J G for incrementally increasing and decreasing uniaxial stress for (a) V G = 0.25 V and (b) V G = 4 V. ................................ ........ 99 5 3 J G ( )/ J G (0) averaged for all levels of compressive and tensile stress at V G = 0.25 V and 4 V. Uncertainty comes from three standard deviation from J G ( )/ J G (0) over the duration stress was held constant. 100 5 4 E xperimentally measured stress sensitivity of J G per 100 MPa of stress, as a function of reverse gate bias. ................................ ................................ ............ 101 5 5 Measured gate leakage current densit y versus gate voltage from T = 300 K to 400 K for unstressed AlGaN/GaN HEMT. ................................ ..................... 102 5 6 PF plot showing linear fit to the measured data for T = 300 K to 400 K. ........... 103 5 7 The slope of the PF plot ( m ) plotted versus 1/ T The slope of this plot ( m used to calculate ................................ ................................ ................. 104 5 8 The y intercept of the PF plot versus 1/ T The slope of this plot ( m to calculate the trap energy level. ................................ ................................ ..... 105 5 9 Schematic of change in E A with compressive and tensile stress. Compressive stress increases E A decreasi ng r increasing compensation, and reducing PF emission. The opposite is true for tensile stress. .................. 106 5 10 Simulated stress sensitivity of J G per 100 MPa of stress, including E A and r changing with stress, as a function of reverse gate bias. ................................ 107 5 11 Schematic of J G J PF and J R assuming J R is a bulk assisted mechanism driven by the PF emission current for V G = 2 V and other parame ters from Table 4 1. ................................ ................................ ................................ ......... 108 5 12 Measured J G ideal J PF obtained by linear extrapolation of the linear PF fit, and J R calculated by the difference between J PF and J G ................................ .. 109

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11 5 13 Simulated stress sensitivity of J G at 100 MPa of stress, including J R as a function of reverse gate bias. J R not changing with stress overestimates the stress sensitivity. However, J R ( )/ J G (0) = 1.5% matches e xperiment. ........... 110 5 14 Energy band diagrams showing the reduction in the AlGaN barrier thickness at the gate edges for V G well below V T ................................ ............................ 111

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12 LIST OF ABBREVIATION S DC Direct current FN Fowler Nordheim GF Gauge factor HEMT High electron mobility transistor MEMS Microelectromechanical systems MOCVD Metal organic chemical vapor deposition MOSFET Metal oxide semiconductor field effect transistor PF Poole Frenkel SEM Sca nning electron microscope UV Ultraviolet

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13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy IMPACT OF MECHANICAL STRESS ON ALGAN/GAN HEMT PERFORMANCE: CHANNEL RESISTANCE AND GATE CURRENT By Andrew Daniel Koehler December 2011 Chair: Scott E. Thompson Cochair: Toshikazu Nishida Major: Electrical and Computer Engineering AlGaN/GaN high electron mobility transist ors (HEMT s ) stand out with superb advantages for high power high temperature high frequency applications. Internal stress is inherent to state of the art AlGaN/GaN HEMTs and has the potential to impact performance and reliability. Strain is an integral part of modern semiconductor technology and has been used to extend scaling of Si for nearly a decade, and the performance and reliability implications are well understood. Understanding the impact of mechanical stress on AlGaN/GaN HEMT channel resistanc e and gate current is crucial for continued improvements in device performance and reliability Repeatable gauge factors of an AlGaN/GaN HEMT device were obtained after eliminating parasitic charge trapping effects. O ver four orders of magnitude of variat ion in gauge factors are reported in literature. C harge traps are likely responsible for the huge discrepancy By employing continuous sub bandgap optical excitation, the effect of non repeatable charge trapping transients was effectively minimized, allo wing the gauge factor to be accurately measured. The measured gauge factor is compared to a

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14 simulated gauge factor, calculated from stress induced changes in the 2DEG sheet carrier density and mobility. S tress altered gate leakage currents in AlGaN/GaN HE MTs are measured as a function of constant applied reverse gate bias. Increasing reverse gate bias decreases the stress sensitivity of the gate leakage current. Poole Frenkel emission dominates the gate leakage current for gate biases above threshold S tress changes Poole Frenkel emission by altering the trap activation energy which also changes the compensation parameter Reverse tunneling current which balances the forward Poole Frenkel current at equilibrium is modeled to explain the experimental re sults. Tensile (compressive) stress decreases (increases) the trap activation energy, increasing (decreasing) the gate leakage current. Although below threshold, the electric field in the AlGaN barrier satu rates in the middle of the gate the electric fi eld increases at the gate edges because of two dimensional effects For larger reverse gate bias much below threshold, the thickness of the AlGaN tunneling barrier decreases which causes Fowler Nordheim tunneling at the gate edges to dominate the current transport.

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15 CHAPTER 1 INTRODUCTION AND OVERVIEW Overview of AlGaN/ GaN HEMTs III V semiconductor devices show promise over Si metal oxide semiconductor field effect transistors (MOSFETs) for high speed circuits. The focus of e arly III V semiconductor rese arch was toward GaAs MOSFET technology however poor quality native oxide and high surface state density prevented channel electron accumulation. In 1980, Takashi Mimura from Fujitsu Laboratories developed a depletion mode high electron mobility transisto r (HEMT) with selectively doped n type AlGaAs barrier, eliminating issues associated with native oxides on GaAs [1] [2] Although Al x Ga 1 x N was historically used in optoelectronic devices because of its direct and tunable band gap, AlGaN/GaN HEMTs were developed in 1993 by M. Asif Khan of APA Optics for high temperature, high performance devices [3] Unique advantages associated with GaN make AlGaN/ GaN HEMTs desirable for high speed, high performance applications. Table 1-1 summarizes key material parameters for high power high performance devices, displaying benefits of GaN compared to other relevant semiconductors. Although the effective mass ( m* ) of GaN is larger than GaAs and InP, resulting in lower bulk effective low field electron mobility ( e ), the high conduction band density of states (DOS) and large saturation velocity ( v sat ) still permits large current densities. The l ow dielectric c onstant ( ) reduces capacitive loading and allows for large area devices, increasing RF current and power [4] The l arge band gap ( E G ) improves radiation resistance results in high intrinsic temperature and provid es a v ery large breakdown field ( E br ) necessary for handling high RF power.

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16 H eat dissipation benefits from the high thermal conductivity ( ), allowing for more efficient dissipation of heat away from the device. Mechanical strain resulting from lattice mismatch between the AlGaN and GaN layers induces piezoelectric polarization. This polarization increases the two dimensional electron gas ( 2DEG) sheet carrier density ( n s ) Benefitting from mechanical strain, AlGaN/GaN HEMTs are capable of achieving n s greater than 10 13 cm 2 without intentional doping. This is significantly higher than other III V systems due to strong piezoelectric polari zation in the Wurtzite GaN and AlN. Biaxial tensile stress in the AlGaN barrier results from the lattice mismatch between AlGaN and GaN increase polarization at the AlGaN/GaN interface and induces the mobile 2DEG. A cross section schematic of a n AlGaN/ G a N HEMT is shown in Figure 1 1. The combination of material and structural benefits allows AlGaN/GaN HEMTs to be suitable for various high power, high performance circuits. AlGaN/GaN HEMTs are attractive for expanding markets in communications, radar, s en sors and automotive for both military and commercial applications. Integration of GaN on Si(111) substrates improve s device performance and reliability while reducing cost [5 ] making AlGaN/GaN HEMT technology extremely attractive for commercial and military markets. Currently, several commercial vendors have AlGaN/GaN HEMT devices available such as Cree, Fujitsu, Nitronex, RFMD, Toshiba, and Triquint. An example AlGaN/GaN HEMT power transistors of current commercially availableoperate at 2.7 to 3.5 GHz range (S band) ,o utputting 240 W of power with a power added efficiency (PAE) of 60% [6] [7] In academia, an example of the current devices under investiga tion include Al 2 O 3 dielectric layer s form ing metal oxide

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17 semiconductor HEMT s provi ding transistors with a PAE of 73% at 4 GHz at a 45 V drain bias [8] Stress in AlGaN/GaN HEMTs Stress is an integral part of AlGaN/GaN HEMT devices. Large mechanical stress profiles ar e created during processing and are generated during operation. These stresses can impact device performance and reliability. In order for AlGaN/GaN HEMTs to be commercially competitive with Si alternatives, low cost large scale production must be achieved Si(111) substrates offer advantages of low cost, large size, and high quality over sapphire and SiC alternatives However, large differ ences in lattice constants (~17 %) and thermal ex pansion coefficients (TEC) (~56 %) between GaN and the Si(111) produce large strains, resulting in the formation of crystallographic defects [5] High quality GaN layers on Si, free of cracks and dislocations, have been fabricated through implementation of stress mitigation using transition layers [5] It is hypothesized that the l attice mismatch stress is primarily absorbed by the Al/Si interface, while the (Al, Ga) N transition layer absorbs the TEC mismatch stress, which occurs during processing [5] Another type of stress induced during processing is biaxial tensile str ess in the AlGaN barrier layer. The AlGaN barrier is pseudomorphically grown on the relaxed GaN channel/b uffer. L attice mismatch between AlGaN and GaN induces a biaxial tensile stress i n the AlGaN barrier. For an Al concentration of 26 %, the AlGaN barrier has ~3 GPa of biaxial tensile stress induced This stress is advantageous since Wurtzite GaN and AlN g rown in the (0001) orientation are both strongly piezoelectric [9] T he piezoelectric effect results in a polarization fixed charge at the AlGaN/GaN interface, inducing a mobile sheet charge layer which is termed a two dimensional

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18 electron gas ( 2DEG ) SiO 2 or Si 3 N 4 passivation possess residual stress which also has been shown to induce stress adding to the lattice mismatch stress and increasing the 2DEG [10 ] During operation the vertical electric field under the gate contact through the inverse piezoelectric effect induces additional stress in the AlGaN barrier This vertical field is the largest at the gate edges, where significant amounts of stress (50 0 MPa) can be generated in the AlGaN barrier during normal operation ( V GS = 30 V). It has been proposed that stress generated from the inverse piezoelectric effect can initiate defect formation leading to irreversible degradation [11] Stress is of particular importance to performance and reliability of AlGaN/GaN HEMTs and has been investigated extensively in Si MOSFET technology for improving performance. Stress in Semiconductor Technology Piezoresistance, or change in electrical resistance in the presence of external mechanical stress was first discovered in copper wires by Lord Kelvin in 1856 and first utilized in strain gauges in the 1930s [12] Twenty years later, theory was developed outlining the implications of stress on semiconductors based on energy shifts resulting from deformation of the crystal la ttice by Bardeen and Shockley [13] In 1954, the first piezoresistance measurements of n and p type conduction fo r both Si and Ge were published [14] The piezoresistive property of Si gave potential for Si pressure, flow, force, and accele ration sensors as well as reducing the channel resistance of Si MOSFETs In semiconductors, strain alters crystal symmetry and then alters the energy band structure by shifting bands, lifting band de generacies, and warping bands. As a result, strain alt ers the mobility through mass change and of scattering change

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19 Stress can be introduced in a semiconductor through lattice mismatched film growth in epitaxial heterostructures, deposited thin films, and applied external stress [15] In the early 1980s, successful in process i mplementation of beneficial strained epitaxial Si layers on relaxed Si 1 x Ge x demonstrated potential advantages of strain in Si technology [16], [17] In plane biaxial stress induce d i n the MOSFET channel results from mismatch in lattice constants between Si and SiGe. However, p rocess integration challenges and almost negligible pMOSFET performance gain s at typical operating voltages limited the usefulness of this technology [18], [19] Uniaxial stress reduces crystalline symmetry mor e than biaxial stress providing superior enhancement in carrier mobility In Si MOSFETs, t ensile stress is beneficial for nMOSFETs and compressive stress is beneficial for pMOSFETs. Developing a process to implement both stresses on a single wafer challenged the semiconductor industry, particularly since biaxial stress was traditi onally applied to entire wafer by grown ing strained Si on relaxed SiGe. These issues were overcome when the successful implementation of uniaxial stress in the CMOS process flow was achieved in the early 2000s the 90 nm node [20 22] Longitudinal tensile stress was generated by nitride capping films for nMOSFETs, and longitudinal compressive stress was created by SiGe source drain for pMOSFETs. Soon after, dual stress liners capable of applying both tensile and compressive stresses were developed to eliminate SiGe source/drain integration issues [23] Similar process induced strain techniques remain implemented in nearly all commer cial Si CMOS technologies to date. Motivatio n Although excellent AlGaN/GaN HEMT performance has been demonstrated, electrical stability and reliability issues of these devices remain obstacles to further

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20 development. Trapping centers at the AlGaN surface, AlGaN/GaN interface, and/or GaN bulk are co nsidered the main origin of GaN reliability issues. Degradation effects associated with traps are characterized by low frequency noise [24 26] transconductance frequency dispersion [24], [27] current collapse [28], [29] gate lag and drain lag transients [30 32] threshold voltage shift [33] increase d gate current [34] and light sensitivity [28], [30], [33] Charging and discharging of traps can limit device performance. G eneration of new traps can permanently degrade the device, eve n to breakdown. Understanding the degradation mechanisms is necessary for improving the performance and reliability of AlGaN/GaN HEMTs. One of the most widely accepted theories explaining AlGaN/GaN HEMT degradation is based on the inverse piezoelectric ef fect [11], [35] During operation, the large vertical field under the gate creates strain in the AlGaN barrier, adding to the limit (at the critical voltage) relaxation will occur through crystallographic defect formation. These generated defects act as trapping centers for electrons, degrading performance and reliability. Large amounts of mechanical strain can certainly cause cracks and defect s to form how ever even nondestructive amounts of strain also can impact performance and reliability of the device. Strain reduces crystal symmetry, reorienting the energy band structure resulting in lifting of band degeneracies, shifting band energies, warping bands [15] and even altering trap ene rgy levels [36] This can affect carrier mobility by changing conductivity effective mass, density of states, and scattering, as well as impacting reliability, by increasing gate curr ent, and increasing hot carrier effects [37]

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21 Since stress i s a major factor in the operation, performance, and reliability in AlGaN/GaN HEMT devices, a thorough understanding of the impact of stress on performance and reliability can lead to improvements in device design. The effects of strain in Si MOSFETs are w ell understood and used to improve the devices. Mechanical wafer bending is a cost effective method to study the effects of stress on semiconductor devices which has been extensively used to isolate and study the effect of stress in Si MOSFETs A systema tic study of the effects of externally applied mechanical stress on the AlGaN/GaN HEMT channel resistance and gate current can provide insights in to the physical mechanisms responsible for stress related performance and reliability issues. Organization The focus of this dissertation is to provide a n improved understanding of the impact of mechanical stress on AlGaN/GaN HEMT chan nel resistance and gate current which are key parameters for studying performance and reliability Previous studies have suggested that catastrophic failure can be related to stress [11], [35] Combining systematic mechanical wafer bending experiments and theory, physical models are presented to explain the incremental effect of stress on channel resistance and gate leakage current. Background information will be provided in Chapter 2, beginning with fundamentals of AlGaN/GaN HEMT operation. Then, a brief description of the characterization method is provided, followed by details on mechanical wafer bending. Chapter 3 prese nts experimental and theoretical details on the extraction of the AlGaN/GaN HEMT gauge factor in the presence of traps. A comprehensive investigation of the vertical electric field in the AlGaN barrier is given in Chapter 4 The

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22 electric field model and simulation results assist in the analysis of the effect of stress on the gate leakage current presented in Chapter 5. Chapter 6 concludes the study with an overall summary and suggestions for future work.

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23 Table 1 1. Key material parameters for high pow er high performance transistors Parameter Units GaN Si GaAs InP 4H SiC m* m 0 kg 0.22 [38] 1.56 [38] 0.06 [38] 0.07 [38] 0.58 [38] e cm 2 /Vs 1245 [38] 1750 [38] 9340 [38] 6460 [38] 1000 [38] DOS 10 18 cm 3 2.3 [39] 32 [39] 0.47 [39] 0.57 [39] 24 .9 [39] v sat 10 7 cm/s 1.4 [40] 1 [41] 0.72 [41] 0.67 [41] 0.33 [39] r 9.4 [4] 11.9 [4] 12.5 [4] 12.9 [4] 10.0 [4] E G eV 3.4 [4] 1.12 [38] 1.43 [38] 1.35 [38] 5.4 [38] E br 10 5 V/cm 20 [4] 3 [4] 4 [4] 4.5 [4] 35 [4] 1.12 [38] 1.56 [38] 0. 45 [38] 0.68 [38] 3.7 [38]

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24 Figure 1 1. Cross section schematic of AlGaN/GaN HEMT on Si(111) substrate.

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25 CHAPTER 2 ALGAN/GAN HEMT AND W AFER BENDING BACKGROUND GaN Fundamentals AlGaN/GaN HEMTs are depletion mode field effect transistors, benefit ing from large 2DEG sh eet carrier density obtained without intentional doping or applied gate bias The combination of s pontaneous polarization ( P SP ) and piezoelectric polarization ( P PE ) in the AlGaN and GaN layers create a macroscopic polarization which induces a 2DEG in the absence of electric field and intentional doping. Spontaneous Polarization There are two requirements for spontaneous polarization : lacking inversion symmetry and a bond between atoms that is not purely covalent This results in a built in dipole. In wu rtzite semiconductors such as GaN, s pontaneous polarization exists when the ratio c / a differs from the ideal value of where c is the height and a is the spacing as shown in Figure 2 1. In order to induce a 2 DEG of electrons desirable for AlGaN/GaN HEMT performance polarization must result in a net positive fixed charge at the AlGaN/GaN interface. T o achieve this, GaN is eptaxially grown in the direction normal to the (0001) basal plane, which lack s inversio n symmetry The t op atomic layer is intentionally fabricated to be GaN, or GaN faced. The direction or < 0001 > direction is defined as a vector originating from a Ga atom pointing to the nearest N atom as shown in Figure 2 1. In this orientation sp ontaneous polarization exists only in the direction therefore P SP = P SP In AlGaN, spontaneous polarization can be expressed in terms of AlN and GaN spontaneous polarization constants and the mole fraction x [2010] IEEE. Reprinted with permission from [A.D. Koehler, A. Gupta, M Chu, S. Parthasarathy, K.J. Linthicum, J.W. Johnson, T. N ishida, S.E. Thompson, Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, May 2010]

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26 ( 2 1 ) It is important to note that spontaneous polarization in AlN ( 0.081 C/m 2 ) is larger than in GaN ( 0.029 C/m 2 ) [9] Piezoelectric Polarization A crystal which becomes electrically polarized in the presence of applied mechanical stress is described as piezoelectric Piezoelectric polarization is observed in crystals lacking a center of invers ion such as GaN and AlGaN Piezoelectric polarization is described by the piezoelectric tensor [ e ] and strain tensor ( 2 2 ) The piezoelectric tensor is a 3 x 6 matrix and the strain vector can be written with six dimensional com ponents. In wurtite GaN, t he piezoelectric polarization is given by ( 2 3 ) In the case of a n AlGaN/GaN HEMT, the Ga N layer is significantly thicker relative to the AlGaN barrier layer, so the AlGaN barrier strains to lattice match the relaxed GaN layer. S train which i s genera ted from this lattice mismatch is i n t he out of plane di rection ( along the c axis ) defined by the lattice distortion as Also, an isotropic i n plane strain results, where where a and c are the strained and a 0 and c 0 are the unstrained lattice constants. The polarization induced by lattice mis match strain in AlGaN/ GaN HEMT devices grown along the < 0001 > direction only exists in the <0001> direction Therefore, th e piezoelectric polarization resulting

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27 from lattice mismatch strain in the AlGaN layer of an AlGaN/GaN HEMT can be expressed as : ( 2 4 ) Stress [ ] and ( 2 5 ) and analogously (2 6 ) T he stiffness tensor [ C ] and compliance tensor [ S ] = [ C ] 1 are 6x6 eleme nt tensors of the following form for hexagonal symmetry (2 7 ) (2 8 ) The polarization resulting from built in lattice mismatch stress in the AlGaN layer of a n AlGaN/GaN HEMT can be simplified in terms o f atomic distortion piezoelectric constants and stiffness constants, giving ( 2 9 )

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28 Formation of 2DEG The net positive fixed sheet charge at the AlGaN/GaN heterostructure i nterface ( int ) results from the polarization difference between AlGaN and GaN, which induces the mobile 2DEG Figure 2 2 shows a plot of the polarizations for a strained Al x Ga 1 x N ( x = 0.26) layer on relaxed GaN. The spontaneous polarization in AlGaN an d GaN as well as the piezoelectric polarizations in the AlGaN layer are oriented downward, toward the substrate The sum of spontaneous and piezoelectric polarizations, or the total polarization in the AlGaN layer ( ) is larger than the total polarizations in GaN ( ) The net polarization ( PZ = ) is equivalent to a positive fixed sheet charge density at the AlGaN/GaN interface. In a device with interface tra pped charge ( Q it ), the interface sheet charge is reduced by Q it ( 2 10 ) In actual devices, surface roughness, variations in Al composit ion, and strain gradients can alter the local polarization induced 2DEG but the total 2DEG density is nearly equal to the theoretical value [9] Free electrons accumulate at th e AlGaN/GaN interface to compensate the effective positive fixed sheet charge corresponding to the net polarization Unlike operation of Si MOSFETs, the conductive channel is not formed through inversion since in GaN, the intrinsic carrier density is low ( n i = 10 10 cm 3 ). Electrons originating from surface states on the surface of the AlGaN barrier accumulate at the AlGaN/GaN interface to form the 2DEG in the GaN, as described by [42] Figure 2 3 show s a schematic of the space cha rges for an ideal AlGaN/GaN. The 2DEG sheet carrier density ( n s ) is described by E quation 2 11.

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29 (2 1 1 ) The maximum 2DEG sheet car rier density ( n s0 ) occurs at V G = 0 V (2 1 2 ) Th e electronic charge is q the dielectric constant of AlGaN is the thickness of the AlGaN barrier is t A lGaN the Schottky barrier height of the ga te is the conduction band offs et in the AlGaN/GaN interface is and the Fermi level with respect to the GaN conduction band is E F At equilibrium, the Fermi level can be describ ed as, ( 2 1 3 ) where is given by ( 2 1 4 ) and m* is the effective mass of AlGaN. The parameters n s int E F0 E C and m* are a ll a function of the Al mole concentration. Device Description State of the art, commercially available AlGaN/GaN HEMTs [43] were characterized in this dissertation. Figure 2 4 shows a cross section scanning electron microscope ( SEM ) image of the devices. The GaN and Al x Ga 1 x N ( x = 0.26) layers were deposited through metalorganic chemical vapor deposition (MOCVD) on hi gh resistivity (111) Si substrates. The AlGaN barrier is 18 nm thick with a ~1.5 nm GaN cap and a 1 m GaN channel layer. Ti/Al/Ni/Au metal stack was used for the o hmic source and drain contacts. The wafers were passivated with a PECVD deposited SiN x passivation

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30 layer. In a separate lithography step, Ni/Au Schottky gates were formed G ate to source s pacing of s and gate drain spacing of gives The channel width is 50 The substrate was thinned to a thickness of 150 m using standard Si grinding techniques. Devices wi th and without field plates were analyzed. Typical DC I D V G characteristics are shown in Figure 2 5 for V DS = 0.1 V. Although these devices were fabricated on a 100 mm diameter wafer, the wafer was diced in approximately 1 cm 2 samples to maximize the num ber of usable devices for mechanical wafer bending experiment s used to study the effect of stress on the AlGaN/GaN HEMTs Mechanical Wafer Bending Experiment Setup M echanical wafer bending is a simple and cost effective way to investigate the underlying ph ysics of strain in semiconductors. Fabricating several wafers with varying amounts of process induced stress is expensive and it can be difficult to accurately quantify the amount of stress present in to the device Also, modifying the process flow to a lter the internal stress es can impact other characteristics of the device Therefore mechanical wafer bending is fundamental in performing controlled stress experiment s. Several methods have been used to externally apply external mechanical stress to sem iconductors. The first piezoresistance measurement s by Smith [14] w ere achieved by hanging weights from slabs of semiconductors. This method requires large samples therefore only bulk measurements can be taken and the maximum stress achieved in Bending of c antilevers, or beams anchored at one end is another possible way to apply stress. While cantilevers are often found in microelectromechanical systems (MEMS) for transducer and resonator applications, the stress profile is nonuniform along the length of th e beam making specification of the

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31 applied stress difficult. Three point bending can also be used, however, like cantilevers, estimation of stress is difficult since stress varies between the three point loads In this work, w e use a flexure based four point wafer bending system, capable of applying greater th an 1 GPa of uniaxial stress to Si wafer s [47] to isolate the effect of stress on AlGaN/GaN HEMT devices due to the significantly improved uniformity of stress in the region between the inner load points Four Point Bending In four point bending, a beam is supported by two anchored point s while being deformed by two driving loads as shown in Figure 2 7 Between the center two rods, the sample is bent with a constant radius of curvature resulting in uniform stress. Therefore, unlike cantilevers and three point bending, v ariation of devic e position does not affect the accuracy of the measurements The magnitude of uniaxial stress on the top surface of a homogenous material sample between the center two rods can be represented as [44] ( 2 1 5 ) w here, E t is the sample thickness, and L and a are rod spacing distances indicated in Figure 2 6 The magnitude of applied stress was calibrated by comparing the calculated stress to re adings from a noncontact fiber optical displacement system and strain gauge measurements [45] Bending Measurements of S mall S amples AlGaN/ GaN HEMT samples were diced into ~1 cm 2 size to maximize the number of measureable samples since wafer bending tests are potentially destruc tive and AlGaN/ GaN HEMT wafers are costly However, the sample s are smaller than the

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32 minimum size that can be directly bent in the four point wafer bending setup. So, to apply stress to these small samples w e developed a technique to bend small wafer sa mples in the standard flexure based wafer bending setup This technique of applying mechanical stress to a small AlGaN/ GaN HEMT wafer sample starts by attach ing the wafer sample to a heat trea t ed high carbon stainless steel plate (Figure 2 7 ). First, the steel strip was sanded with fine grit sand paper to remove oxidation and to provide a rough surface for adhesion. A thin layer of Epoxy Technology H74 two part epoxy was then applied to the middle of the steel strip. The wafer sample was placed on top of the epoxy and pressed down, and excess epoxy was wiped away. To eliminate air pocket formation during curing of the epoxy, a metal washer was placed on top of the wafer sample and the sample was clamped with a metal binder clip. Then, the sample was in serted into a 100 C oven for 5 minutes. The washer and metal binder were removed and th e sample was placed on a 150 C hotplate for 5 minutes to complete the curing process The sampl e atta ched to the steel plate was then inserted into the wafer bending s etup. Under the amount of stress applied (360 MPa) in the experiments, the stainless steel plate does not permanently deform. A strain gauge is mounted on the top of the III V wafer with epoxy to calibrate the stress. As shown in Figure 2 8 stress is ap plied and released to the sample. The amount of stress read from the strain gauge returns to the starting point verifying that stress applied to the sample is elastic. To characterize the impact of mechanical stress on the AlGaN/GaN HEMT devices, e lectri cal measurements need to be taken while simultaneously varying the amount of applied stress. In order to achieve this, wires were attached to the device

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33 bond pads. Standard ball and wedge wire bonding techniques resulted in delamination of bond pads dest roying the device Therefore a novel technique was developed to attach wires to the bond pads without the use of heat or ultrasonic energy. First, a ball was formed on the end of a 1 mil Au wire in a ball bonding machine Then, the wire was cut to appro ximately 1 cm length and removed from the ball bonder. A small amount of electrically conductive Epoxy Technol ogy EE 129 4 two part epoxy, was placed on the end of a probe tip. The probe tip was brought into contact with the end of the wire without the ba ll and cured for 24 hours at room temperature. The ball end of the wire was dipped in conductive epoxy and the probe tip was inserted into the micropositioner. Using the micropositioner, the ball end of the wire with conductive epoxy was landed on the de another 24 hours at room temperature. After the epoxy cured, the micropositioner was lowered to allow slack on the wire for displacement of the wafer while applying stress. Summary The b ackground on the fundamentals of AlGaN/GaN HEMT operation and the details of the wafer bending experiments were presented. The accumulation of mobile electrons to form the 2DEG is a result of a net positive charge at the AlGaN/GaN interface. This interface sheet charge is induced by th e difference in polarization between the AlGaN and GaN layers. The strained AlGaN layer has piezoelectric polarization as well as spontaneous polarization, whereas the relaxed GaN layer only has spontaneous polarization. To investigate the impact of mech anical stress on AlGaN/GaN HEMT devices, four point mechanical wafer bending is used. Wires are attached to the device bond pads to simultaneously take electrical measurements while the level of applied stress is varied.

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34 Figure 2 1. GaN faced GaN crys tal lattice, oriented along the <0001> direction.

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35 Figure 2 2. Polarizations in strained Al x Ga 1 x N (x = 0.26), relaxed GaN heterostructure. The strained AlGaN layer has larger spontaneous polarization than the GaN layer, as well as additional polariza tion from the piezoelectric effect. [Reprinted, with permission, from A.D. Koehler, et al., Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, Figure 3, May 2010]

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36 Figure 2 3. Conduction band schematic diagram of an AlGaN/GaN HEMT showing charge balance.

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37 Figure 2 4. Cross section SEM of commercial devices characterized in this dissertation. Image from Nitronex [46]

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38 Figure 2 5. Typical I D V G curve of a depletion mode AlGaN/GaN HEMT measured at V DS = 0.1 V.

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39 Figure 2 6 Mechanical wafer bending setup: showing (a) a p hotograph of Si wafer under ~1 GPa of stress and (b) a s chematic of wafer under four point bending showing tensile stress on the top and compressive stress on the bottom with a neutral axis in the middle

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40 Figure 2 7. GaN wafer sample att ached to heat treat ed high carbon stainless steel inserted in a four point bending setup.

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41 Figure 2 8. Increasing and d recreasing stress applied to a wafer mounted on a stainless steel strip. A strain gauge is used to determine the amount of applied stress.

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42 CHAPTER 3 EXTRACTION OF ALGAN/GAN HEMT GAUGE FACTOR IN THE PRESENCE OF TRAPS Introduction Sensitivity to change in electrical resistance with stress can be represented by a gauge factor (GF) or the normalized change in resistance ( R ) per mechanical strain ( ) R / R )/ ) Obtaining an accurate measurement of the gauge factor of AlGaN/GaN HEMTs is essential in understanding device degradation as well as improving design of piezoresistive sensors. A l arge discrepancy in gauge factors (GF) ranging from 4 to 40,000 for AlGaN/GaN HEMTs are reported in literatu re (E. Y. Chang, 2009; Eickhoff, Ambacher, Krotz, & Stutzmann, 2001; Gaska et al., 1998; Kang et al., 2005, 2004; Yilmazoglu, Mutamba, & Pavlidis, 2006; Zim mermann et al., 2006) This large disagreement likely result s from inaccuracies in resolving the applied stress and changes in the trapped charge density over the time elapsed during measurement. These past studies used three point bending [47 49] cantilevers [50], [52] complex lever mass system [51] and circular membranes [53] to apply stress, which can be difficult to accurately quantify the amount of stress applied to the devi ce and therefore extract the gauge factor W e use four point bending, while mitigating the effects of charge traps to experimentally characterize the effect of stress on AlGaN/GaN HEMT s. Effects of Trapped Charge The effect of charge trapping due to surf ace states, traps in the AlGaN barrier, or bulk traps can lead to measurable changes in device characteristics, such as current collapse [54] gate lag [55] drain lag [55] increased gate leakage [11] threshold [2010] IEEE. Reprinted with permission from [A.D. Koehler, A. Gupta, M Chu, S. Parthasarathy, K.J. Linthicum, J.W. Johnson, T. N ishida, S.E. Thompson, Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, May 2010]

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43 voltage shift [56] and l ight sensitivity [57] These traps can be formed during processing and crystal growth [58] or generated during device operation via th e inverse piezoelectric effect [11] or by hot carri ers [59] Trapped electrons between the source and drain can be modeled as a virtual gate in series with the actual metal gate, depleting channel electrons Therefore, the drain current is a function of both the mechanism supplying electrons t o the virtual gate as well as the external bias applied to the metal gate. Similar to many AlGaN/ GaN HEMTs described in literature the commercial devices characterized in this dissertation also exhibit charge t rapping effects The drain cu rrent and thres hold voltage depend strongly on the concentration of trapped charge in the device B iasing the device during measurement s can alter the concentration of trapped charge increasing or decreasing in the devi ces can be demonstrated by first initializing the device with a large V G pulse ( V G = 10 V held for 1 minute) filling available trap states with electrons (right side of Figure 3 1 ). Then, 40 consecutive V G sweep s from 2 V to 0 V were performed over 120 0 seconds in the dark These sweeps are unable to maintain the large charge density of trapped electron s which were filled from the large V G pulse This results in electrons thermally detrapping. This in turn, shifts the threshold voltage less negative. Shining the incandescent microscope light on a device without a field plate photoionizes trapped charges (left side of Figure 3 1 ). Consecutive sweeps of V G from 2 V to 1 V in the dark fills the available traps shifting the threshold voltage more n ega tive. The threshold was demonstrated to shift ~0.1 V during 1200 seconds of measurement as shown in Figure 3 2 Also, it was observed that simply turning on the incandescent

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4 4 microscope light during measurement causes a 15% reduction in channel resistance (Figure 3 3 ). In fact, although an enormous gauge factor of 40,000 was reported, the measured change in resistance was only 15% [53] which could easily res ult from a change in trapped cha r ge during the experiment To e limi nate parasitic charge trapping effects we developed a technique to expose the sample to continuous sub bandgap optical excitation to photoionize trapped charge in order to obtain an accur ate gauge factor measurement Experimental Setup Wafer samples were attached to heat treated high carbon steel plates with epoxy and stressed in a four point wafer bending setup Compressive and tensile uniaxial stress up to 360 MPa was applied longitudin al to the channel direction. To obtain an accurate measurement of the AlGaN/ GaN HEMT gauge factor p arasitic charge trapping transient s and external re sistances were addressed A fter the effects of charge trapping were eliminated, and external resistance s were accounted for an accurate gauge factor measurement was performed Elimination of Charge Trapping Effects To combat the instability issue associated with trapped charges the HEMT device was exposed to light with a photon energy near but below the band gap of GaN (~3.4 eV or 365 nm wavelength) to photoionize all trapped electrons influencing the resistance measurement without band to band generation of electron hole pairs. Initially, a mercury arc ultraviolet (UV) spotlight with peak wavelength of 377.7 nm or 3.284 eV was chosen to illuminate the device under test. A sweep of I D V G under UV spotlight illumination compared to dark (Figure 3 4 a ) showed a large increase in off state drain current and a decrease in subthreshold slope. The spectral int ensity of the

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45 light source was measured in a spectrometer. A significant portion of the photon energy was above the band gap of GaN (3.39ev ~ 365 nm) as shown in Figure 3 4 b Under illumination of above bandgap light, mobile electron hole pairs are photo generated An increase in off state current and a decrease in subthreshold slope are consistent with carrier photogeneration. A 380 nm band pass filter was measured to filter out wavelengths below 365 nm (Figure 3 5 b ). A horizontal shift in sub threshold slope and similar off state leakage current (Figure 3 5 a ) verifies a decrease in the effect of trapped charge without photogeneration of electron hole pairs A schematic of the experimental setup is shown in Figure 3 6 The standard wafer bending setup d escribed in Chapter 2 is illuminated by the UV light source. The band pass filter is mounted in a 4 inch thick polystyrene heat shield to block ambient heat from the mercury arc lamp and block nonfiltered light from illuminating the device. As shown in F igure 3 7 over 1500 seconds, the change of the measured channel resistance is less than 0.02%. Since the resistance measurement has been stabilized, it is now appropriate to apply stress to monitor the gauge factor. External Resistance Consideration The s tress dependence of the channel resistance ( R CH ) was measured at V GS = 1V and V DS = 0.1V, by excluding source/drain contact resistances The high conductivity of GaN 2DEG results in a small channel resistance, especially for the commercial devices char acterized with W/L ratio of 25. The measured resistance ( R meas ) is the sum of the channel resistance ( R CH ) source contact resistance ( R S ), drain contact resistance ( R D ), and external parasitic resistances ( R ext ) and was on the order of 100

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46 (3 1 ) The source and drain contact resistances ( R S = R D = 5 ) measured by transmission line measurements, are subtracted from the measured resistance and are assumed to have a negligible stress dep endence A four point Kelvin measurement is used to eliminate the effect of external resistances T w o wires were bonded to both the source and drain pad and one to the gate. One pair of source and drain contacts are used to supply a dc current via the f orce connections on the semiconductor parameter analyzer. The other pair of connections are used to sense the voltage drop across the source and drain pads Results and Discussion Gauge Factor Measurement Longitudinal uniaxial stress was varied in 60 MPa increments and held for 100 seconds at each interval. The normalized change in R CH was measured for incrementally applied compressive and tensile stress up to 360 MPa, which was then released incrementally to zero as shown by the dotted lines of Figure 3 8 Tensile stress decreases R CH while compressive stress increases R CH are seen by the solid experimental lines of Figure 3 8 At the maximum applied stress (360 MPa), the normalized resistance change was ~0. 83 % /10 0 MPa which is much smaller than what is observed in (001)/<110> silicon n MOSFETs of 3.2%/100 MPa [60] The resistance returned to the initial unstressed value after increasing and decreasing the compressive and tensile stress. This demonstrates that the ch ange in resistance observed is due to a reversible strain effect opposed to charge trapping/detrapping transients. The gauge factor was determined by averaging the R CH measurements over each time interval during which the stress was held constant (Figur e 3 9 ) Error bars

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47 represent a three standard deviation confidence interval for the measurement. The slope of a total least squares linear fit o f the averaged R CH versus strain curve was obtained to determine a gauge factor of 2.5 0.4 Total least squ ares analysis included uncertainty of the measurements. The determined gauge factor ( 2.5 0.4) is small relative to values in literat ure ranging from 4 to 40,000 [47 53] Resistance Change with Stress To provide understanding of the small measured gauge factor, the factors influencing the change in channel resistance with stress are investigated. T he channel resistance is inversely related to the 2DEG sheet ca rrier density and electron mobility ( e ) (3 2 ) w here the A is cross sectional area of the 2DEG. In the presence of stress, the normalized change in channel resistance can be written as: (3 3 ) T o evaluate the effect of stress on the channel resistance both the effect of stress on the 2DEG sheet carrier density and mobility needs to be considered. 2DEG Change with Stress To analyze the effect of stress on the 2DEG sheet carrier density the additional piezoelectric polarization induced by mechanical wafer bending must be analyzed. Mechanical wafer bending induces additional polarization in the < 0001 > direction. Stress resulting from uniaxial mechanical w afer bending is approximately equal in both the AlGaN barrier and the GaN layer because t he AlGaN barrier (18 nm) and GaN layer

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48 (1 m) are thin compared to the total thickness of the wafer (150 m). Therefore these two layers are near t he top surface of the sample, far from the neutral axis of bending and experience the same magnitude of stress Spontaneous polarization in both t he AlGaN and GaN remains unchanged by wafer bending since it is an intrinsic material parameter. As shown in Figure 3 1 0 for 1 GPa of uniaxial tensile stress mechanical wafer bending induced piezoelectric polarization ( P PE,mech. ) adds to the polarization in both the AlGaN and GaN layers [57] The magnitude of the mechanical wafer bending induced piezoelectric polarization is calculated for uniaxial stress where xx is the only nonzero element in the stress t ensor and The mechanical wafer bending induced piezoelectric polarization is similar for both AlGaN (0.00148 C/cm 2 ) and GaN (0.00143 C/cm 2 ) since the elastic and piezoelectric coefficients in GaN and AlGaN are similar for a small Al mole f raction ( 26% ) The total polarization at the interface under uniaxial mechanical stress is (3 4 ) Relating the total polarization at the interface to n s according to Ambacher et al. [61] gives an increase in n s ranging from 0.064% to 1% for 360 MPa of tensile stress. U nce rtainty of n s results from variation in stiffness constants and piezoelectric coefficients reported in literature [62 70] Electron Mobility Change with Stress Strain enhanced mobility can result from reduced average conductivity effective mass from carrier repopulation and band warping, suppression of i ntervalley scattering from subband splitting, and change in density of states with stress. Unlike Si, GaN is a direct semiconductor with a non degenerate conduction band minimum at the point.

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49 Therefore, stress induced change of the average effective mass due to electron repopulation and scattering can be neglected. Thus, the m obility change is dominated by a change in the effective mass through band warping Band warping can be simu lated using a tight binding model with a sp 3 d 5 basis [71] Since s train alters the ato mic positions and consequently the bond lengths and bond angles strain modifies the elements of the new Hamiltonian matrix. Solving for the eigenvalues of the strained matrix allows the strain effect on the effective mass to be calculated Mobility enhancement from a reduction in effective mass was determined to be 0.29% to 0.49% for 360 MPa of stress [72] Simulated Gauge Factor Figure 3 1 0 shows the experimental normalized change in R CH with stress (symbols) compared to the calculation (shaded bands). The change in 2DEG sheet carrier density and mobility is combined using E quation 3 3 to calculate the normalized change in resistance. Depending on the coefficient values used in the calculation, the change in R CH can range from 0.29% to 1.5% for 360 MPa of stress illustrated as shaded bands in Figure 3 1 1 This corresponds to a GF of 7.9 5.2. Comparing the experimental results with the model, the best fitting set of elastic and piezoelectric coefficients from literature is C ij (GaN) [73] C ij (AlN) [74] e ij (GaN) [75] e ij (AlN) [76] Summary Illuminating the AlGaN/GaN HEMT device with photon energy near but below the band gap of GaN provided a reliable gauge factor measurement. After eliminating trap charging effects, the gauge factor of the AlGaN /GaN HEMT was determined to be 2.8 0.4. A reliable gauge factor measurement The small gauge factor indicates a small stress dependence on the device resistivity. This is explained by small changes in the

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50 2DEG sheet carrier density and channel mobility. The experimental results were compared with simulated gauge factor ( 7.9 5.2) to determine the best fitting set of elastic and piezoelectric coefficients of GaN and AlN

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51 Figure 3 1 Results of c onsecutive V GS = 2 to 0 V DS = 0.1 V measurement sweeps resulting in charge trapping and detrapping

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52 Figure 3 2 V T measured in consecutive I D V G sweeps In dark, | V T | can increase ( decrease ) from detrapping ( trapping ) of electrons depending the device initialization Under unfiltered UV illumination, V T does not fluctuate

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53 Figure 3 3 A decrease in channel resistance of 15% observed during 1200 seconds of measuring after turning on the incandescent microscope light.

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54 Figure 3 4 Unfiltered UV measurement (a) I D V G measurements in dark and un der unfiltered UV light with a large increase in off state current and a decrease in subthreshold slope. (b) The spectral output of the unfiltered UV light.

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55 Figure 3 5 Filtered UV measurement (a) I D V G measurements in dark and UV light filtered by a 380 nm bandpass filter with a much smaller increase in off state current and n o subthreshold slope change (b) The spectral output of UV light with 380 nm bandpass filter.

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56 Figure 3 6 Experimental setup for photoionizing trapped charge to measure the gauge factor.

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57 Figure 3 7 Illuminating the device under test with UV light stabilized R CH to less than 0.02% variation for 1200 seconds of measurement.

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58 Figure 3 8 Normalized change in channel resistance with incrementally increasing and de creasing uniaxial stress. [Reprinted, with permission, from A.D. Koehler, et al., Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, Figure 2, May 2010]

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59 Figure 3 9 R CH measurements at each time interval stress was held constant. Error bars represent a three standard deviation confidence interval for the measurement. [Reprinted, with permission, from A.D. Koehler, et al., Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, Figure 4, May 2010]

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60 Figure 3 1 0 Schematic showing polarizations in AlGaN/GaN HEMTs as fabricated (left), and 1 GPa mech anically applied stress (right) generating additional P PE mech similar in magnitude for both AlGaN and GaN layers. [Reprinted, with permission, from A.D. Koehler, et al., Extraction of AlGaN/GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, Figure 3, May 2010]

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61 Figure 3 11 S imulated change in n s e and R CH with uniaxial stress shown in bands of uncertainty. The bands signify variations in numerical results due to uncertainty in elastic and piezoelectric coefficients. [Reprinted, with permission, from A.D. Koehler, et al., Extraction of AlGaN/ GaN HEMT Gauge Factor in the Presence of Traps IEEE Elec. Dev. Lett., vol. 31, pp 665 667, Figure 4, May 2010]

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62 CHAPTER 4 VERT ICAL ELECTRIC FIELD IN THE ALGAN BARRIER Introduction R eliability is a major concern with AlGaN/ GaN HEMTs and a systematic stud y of the impact of stress on gate leakage current is essential to gain physical insight in to the degradation mechanisms in order to improve device reliability Gate leakage currents for AlGaN and GaN Schottky interfaces in literature are significantly lar ger than what would be theoretically predicted based purely on the thermionic emission model [77] Determining the dominant g ate leakage transport mechanism through the AlGaN barrier in AlGaN/GaN HEMT is necessary for investigating the physic s behind the effect of stress on the gate leakage current A n accurate determination of the electric field in the AlGaN barrier ( E AlGaN ) is required to investigate the gate leakage models Several models have been proposed to explain the gate leakage mech anism in AlGaN/GaN HEMTs, such as trap assisted tunneling [34], [78 81] direct or Fowler Nordheim (FN) tunneling [78 80], [82] temperature assisted tunneling [78], [83] multi step trap assisted tunneling [84] thermionic trap assisted tunneling [82], [85 87] tunneling through a thin surface barrier [88] and Poole Frenkel (PF) emission [89 94] The dominant leakage mechanism is strongly de pendent on the materials and p rocessing conditions and the electric field in the AlGaN Barrier, E AlGaN To characterize the effect of mechanical stress on the state of the art commercial AlGaN/GaN devices, an accurate model for the leakage mechanism is ne cessary. To compare different leakage models to the experimental measurements an accurate calculation of E AlGaN is needed In past works, E AlGaN has been simplified to a linear relationship with the gate voltage [91] [89] simulated using Medici 2D simulations [95] and experimentally

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63 measured [96] The V DS = 0 state is of particular interest for exploring reliability since both the source and drain sides of the device gate are electrically stressed simultaneously A complete investigation of the electric field relationship as a function of V G at the V DS = 0 state will be presented. I deal 1D Calculation of E AlGaN A one dimensional (1D) calculation of E AlGaN provides insight in to the general relationship between voltage and field. In this condition the gate is assumed to be infin itely wide. Also, for simplicity, E AlGaN is assumed to be a constant throughout the entire thickness of the AlGaN barrier. Based on these assumptions, a simple expression for the electric field in the AlGaN barrier can be derived from the voltage drop across the AlGaN barrier ( V AlGaN ) from inspection of the e nergy band diagram (Figure 4 1). E AlGaN can be written as, ( 4 1 ) Recalling Equation 2 11 n s can be rewritten in terms of E AlGaN ( 4 2 ) Then the simple expression for E AlGaN is ( 4 3 ) In the expression for E AlGaN (E quation 4 3) only th e 2DEG sheet carrier density ( n s ) is a function of gate voltage. The total fixed charge density at the AlGaN/GaN interface ( int ) is assumed to be independent of bias because it is based on the polarization Charge trapped at the AlG aN/GaN interface is estimated to be constant

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64 with bias To analyze the dependence of n s with gate voltage, n s is re w ritten to include the contribution of V G in terms of the equilibrium 2DEG concentration n s0 ( 4 4 ) w here, is the AlGaN capacitance per unit area. At equilibrium, V G = 0 V and n s = n s0 which is the max imum induced 2DEG sheet carrier density. T he fixed positive charge at the AlGaN/GaN interface induces accumulation of electrons at the interface in the GaN The electrons that form the 2DEG originat e from the AlGaN surface [42] not from the source, drain and substrate as in a Si MOSFET inversion layer A negative bias applied to the gate depletes the 2DEG, decreasing n s linearly as shown by Equation 4 4 The threshold voltage for the depletion mode AlGaN/GaN HEMT is defined as t he voltage required on the gate to entirely deplete the 2DEG ( n s = 0 ). Since the AlGaN/GaN HEMT is a depletion mode device with a negative V T the device is considered to be turned off below threshold (| V G | > | V T |). Above threshold, the 2DEG is formed (| V G | < | V T |). Below threshold the 2DEG remains depleted. S ince the intrinsic carrier concentration of GaN is extremely low ( n i ~ 1 x 10 10 cm 3 at 300 K) hole accumulation at the surface is negligible. Figure 4 2 shows for an ideal device, without inte rface trapped charge, the 2DEG sheet carrier density plotted against V G T he charge at the AlGaN/GaN interface ( int = 2.2 x 10 6 C/cm 2 ) is only a result of the polarization differences between AlGaN and GaN Parameters described in T able 4 1 were used f or the calculation To express E AlGaN as a function of gate voltage, t he voltage dependent 2DEG equation (Equation 4 4) was incorporated in to the expression for E AlGaN ( Equation 4 3) to give,

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65 ( 4 5 ) For gate bias below threshold, E AlGaN saturates at Figure 4 3 shows E AlGaN increasing linearly with bias for gate biases above threshold 1D Experimentally Measured E AlGaN Estimation of E AlGaN for an actual AlGaN/GaN HEMT device based on the 1D model requires both int and n s to be experimentally measured T he t hreshold voltage determined by the standard l inear extrapolation m ethod ( V T = 1.4 V) is not consistent with the definition of V G = V T when n s = 0. A more appropriate threshold of 1.9 V is used based on the initial increase of the capacitance voltage curve (Figure 4 5) T rapped charge in the actual device reduces the amount of fixed charge at the AlGaN/GaN interface, shifting the threshold voltage more positive than the ideal value From Equation 4 4 and the definition of threshold ( V G = V T when n s = 0), t he 2DEG sheet carrier density at V G = 0 can be calculated from the measured V T ( 4 6 ) Which gives n s0 = 5 3 x 10 12 cm 3 for V T = 1.9 V. T he n, the fixed charge at the AlGaN/GaN interface can be estimated by solving for int in Equation 2 12 ( 4 7 ) Resulting in int = 1. 25 x 10 6 C/cm 2 which is nearly half the ideal value ( int = 2.2 10 6 C/cm 2 ) using the constants in Table 4 1 The i nterface trapped charge density is estimated from the su bthreshold slope ( SS ) measurements [97], [98]

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66 ( 4 8 ) The c apacitance associated with the interface trapped charge ( C it ) can be related to the density of interface traps by C it = qD it For the measured device with SS = 10 0 mV/dec, the interface trap density is D it = 1 92 x 10 1 2 cm 2 eV 1 Assuming all traps are full, integrating over the bandgap of AlGaN gives an interface trapped charge Q it = 1 2 x 10 6 C/cm 2 Figure 4 4 shows a bar chart of the charge density in the ideal device compared to the actual device. In the ideal device ( Q it = 0) pz = int However, in the actua l device, fixed charge at the AlGaN/GaN interface induced by polarization is reduced by negative trapped charge. To obtain E AlGaN for the actual device, the n s versus V G relationship needs to be obtained. A high frequen cy (1 MHz) capacitance voltage curve (Figure 4 5) was integrated from pinch off to voltage V The experimental bias range was limited to V G = 2 V to 0 V to avoid additional charge trapping from larger applied biases. The value of n s ( V ) is also shown in Figure 4 5. The experimentally obtained n s versus V G relationship is used in Equation 4 3 to calculate the experimentally obtained E AlGaN versus V G relationship. Implementing the experimentally determined int and n s versus V G relationship provides the experimentally determined 1D calculation of E AlGaN versus V G Figure 4 6 shows a comparison between the experimental and ideal 1D calculation for E AlGaN versus V G Since both methods are based on the 1D exp ression they have similar trends Above threshold, | E AlGaN | increases linearly with increasing reverse bias, and below threshold E AlGaN saturates at The presence of Q it reduces int and the magnitude of the saturated value of E AlGaN below threshold in the actual

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67 device compared to the ideal 1D calculation. In addition V T is shifted toward the positive direction by the negative Q it At V G = 0, the experimental | E AlGaN | is larger than the ideal 1D case becau se the experimentally extracted n s0 is lower than what is theoretically predicted making the numerator of Equation 4 3 larger 2D Simulation of E AlGaN Simulation Details The AlGaN/GaN HEMT structure was simulated using the Sentaurus d evice simulator. A t wo dimensional (2D) simulation was performed to gain a physical understanding of 2D effects on E AlGaN The thin (~1.5 nm) GaN cap layer was neglected in the simulation for simplicity. The device structure is quantized into a mesh or grid o f discrete elem ents. The grid was condensed in areas where large variations of carrier concentration are expected at short distances to optimize computational accuracy (Figure 4 7 ). At each point on the grid three variables are solved for simultaneously T he electro static potential electron concentration, and hole concentration are solved for and the electron and hole continuity equations respectively The b oundary conditions used to solve for the three variables are : the metal contact wo rk function difference, the o hmic contacts at the source and drain, and local conservation of charge. In the actual device, the high resistivity Si layer isolates the GaN layer from the back side of the wafer, leaving it electrically floating. The bulk i s left floating in simulation to model this. Shockley Read Hall recombination and generation were included in the calculation Also, a hydrodynamic model was used where the carrier temperature is not assumed to be equal to the lattice temperature. Elect ron mobility was modeled including d oping dependence, high field saturation, and

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68 temperature. Doping was introduced under the source and drain contacts to emulate metal spikes to provide an o hmic contact to the 2DEG [99] The p iezo electric effect is modeled by incorporating a fixed charge at the AlGaN/GaN interface equal to int and at the AlGaN surface equal to PZ to match experiment. The parameters used in the simulation are given in Table 4 1. Simulation Results The simulated dependence of E AlGaN versus V G at the center of the gate is compared to the 1D model with experi mentally determined parameters (Figure 4 8 ) In the simulation, int was matched to the experimentally obtained value of 1. 25 x 10 6 C/cm 2 The trend of the 2D sim ulated E AlGaN is similar to the 1D calculation. Above threshold | E AlGaN | increases until threshold with decreasing reverse gate bias B elow threshold | E AlGaN | tends to saturate Although int is matched, the saturation value of E AlGaN in the 2D simulation at the center of the gate is slightly lower than the experimentally determined curve. Since the simulated device has a finite gate width (1 ate for a comprehensive understanding of the E AlGaN versus V G relationship V ertical cross section plots of E AlGaN through the middle of the gate and d rain edge of the gate are shown in Figure 4 9 The AlGaN/GaN interface is referenced at y = 0 m and the AlGaN surface is at y = 0.018 m. In the middle of the gate E AlGaN remains essentially constant throughout the depth of the AlGaN layer for V G = 2 to 10 V As shown in Figure 4 5, t he magnitude of E AlGaN increases more above V T than below V T as a function of V G demonstrating the saturation of E AlGaN below V T However, at the gate edge E AlGaN varies with depth in the AlGaN barrier and E AlGaN co ntinues increasing with increasing reverse gate bias

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69 A horiz ontal cross section 1 nm below the gate contact in the AlGaN barrier shows a large increase in E AlGaN at the gate edges (Figure 4 10 ). At V G = 0 V, | E AlGaN | is lower directly under the Schottky gate than under the passivation layer This is a result of the negative polarization charge at the top surface of the AlGaN Under the nitride the surface polarization exists, however, the gate has control of the potential under the gate electrode To e xplain the large increase in E AlGaN at the gate edges, a plot of the potential at the GaN surface 0.5 nm below the AlGaN/GaN interface is shown (Figure 4 11 ) At large reverse gate biases there is a large horizontal potential drop in the GaN surface nea r t he gate edge s This potential drop results in a large horizontal electric field at the gate edge. T he horizontal field at the gate edge is much larger than in the center of the gate (Figure 4 12) The contribution of the horizontal electric field at the gate edge adds to the vertical electric field increasing the magnitude of E AlGaN increasing at the gate edges. Summary The relationship between E AlGaN and V G was cal culated for an ideal 1D device. It was experimentally matched to the actual device an d a 2D simulation was performed. A 1D model was used to investigate the dependence of E AlGaN with V G Adjusting int and n s based on experimental measurements provides an accurate relationship above threshold. The 1D model fails to capture the edge phys ics of a realistic device. 2D Sentaurus device simulation showed the 1D model is accurate above threshold, but below threshold, E AlGaN at the gate edges continues increasing. Above threshold, | E AlGaN | increase s linearly with increasing re verse gate bia s and the field is approximately constant throughout the depth of the AlGaN layer. Below threshold V G <

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70 V T 2D effects change the field profile. In the middle of the gate, E AlGaN s aturate s, but at the gate edges, E AlGaN increases With the relationship b etween E AlGaN and V G understood, this relationship can be used to explain the gate leakage transport mechanism in the AlGaN/GaN HEMT.

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71 Table 4 1. List of parameters used in 1D E AlGaN calculation Parameter Symbol Value Units Temperature T 300 K Intrin sic carrier concentration n i 10 10 cm 3 AlGaN thickness t AlGaN 18 nm Permittivity of GaN 9.5 Permittivity of AlN 8.5 Bandgap of GaN E G,GaN 3.4 eV Bandgap of AlN E G,AlN 6.13 eV Electron affinity of GaN 4.1 eV N i work function 5.27 eV Mass of GaN m* GaN 0.2* m 0 Mass of AlN m* AlN 0.48* m 0 Fixed charge at AlGaN/GaN interface int 2.2 x 10 6 C/cm 2

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72 Figure 4 1. Energy band diagram schematic showing Ni/AlGaN/GaN interface

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73 Figure 4 2. Dependence of the 2DEG dens ity ( n s ) with gate bias for the 1D case, with no interface trapped charge. Threshold is defined when n s is entirely depleted ( n s = 0).

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74 Figure 4 3. Idealistic 1D calculation of E AlGaN assuming no interface trapped charge. E AlGaN increa ses linearly until the threshold voltage, the n saturates.

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75 Figure 4 4. Bar diagram of the AlGaN/GaN interface charge for an ideal device with no trapped charge and an actual device. Trapped charge reduces the positive fixed sheet charge density at the AlGaN/GaN interface.

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76 Figure 4 5. Capacitance Voltage measurement which is integrated in order to determine n s ( V ).

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77 Figure 4 6. 1D ideal (no interface trapped charge) calculation and the experimental result from experimental parameters obtained by adjusting int and obtaining n s from C V

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78 Figure 4 7 Optimized grid for Sentaurus simulation of the AlGaN/GaN HEMT device.

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79 Figure 4 8. Experimental calculation of E AlGaN versus V G compared to 2D simulation results.

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80 Figure 4 9. Vertical cros s section of electric field of the AlGaN/GaN HEMT at the (a) center of the gate and (b) drain edge of the gate.

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81 Figure 4 10. Horizontal cross section of E AlGaN taken near the top surface of the AlGaN barrier 1 nm below the gate contact

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82 Figure 4 11 Horizontal cross section of the electrostatic potential taken near the top surface of the GaN 0.5 nm below the AlGaN/GaN interface

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83 Figure 4 12. Horizontal component of E AlGaN at the (a) center and (b) edge of the gate.

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84 CHAPTER 5 FIELD DEPENDENT MECHANICAL STRESS SENSITIVITY OF ALGAN/GAN HEMT GATE LEAKAGE CURRENT Introduction AlGaN/GaN HEMT s provide benefits over Si, SiGe, SiC and GaAs material systems for high frequency and high power applications. Unique advantages include a built in polarizati on and a wide bandgap which allow for high sheet charge carrier density and high voltage operation. However, the device reliability of AlGaN/GaN HEMTs still requires improvement. Particularly generation of defects during high bias operation has been sho wn to increase the gate leakage current density ( J G ), reducing the output power and power added efficiency (PAE), limiting its prolonged usefulness in high power applications [100] A systematic study of gate leakage transport mechanisms in the presence of defects is required. The p hysical breakdown of the AlGaN barrier has been shown to occur at voltages beyond the critical voltage ( V crit ) creating an irreversible increase in J G [11] To demonstrate this crucial AlGaN/GaN HEMT failure mode, a step voltage stress is applied and the gate current is monitored Figure 5 1 shows the results of V G step electrical stress on J G at the V DS = 0 V sta te showing a sudden increase in J G at V crit Th is type of degradation has been hypothesized to be related to the generation of crystallographic defects via the inverse piezoelectric effect [11] At large V G as seen from the Sentaurus 2D simulations in Chapter 4, increased vertical fi eld occurs at the gate edges This creates additional tensile stress in the AlGaN barrier through the invers e piezoelectric effect. This stress adds to the pre existing built in tensile stress resulting from lattice mismatch between the AlGaN barrier and the GaN layer. It has been suggested that when stress reaches the material critical limit defect to form i n

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85 order to relax the internal elastic energy [11] These defe cts cause a low resistance leakage path through the AlGaN barrier resulting in a sudden increase in J G A mechanical wafer bending experiment in literature showed a reduction of V crit with applied mechanical stress, however, only five pairs of devices were investigated in this study and a more comprehensive study is required [101] S ince s tress is inherent in AlGaN/GaN HEMTs, understanding the role of stress on J G is essent ial to improve reliability. However, there are discrepancies in the published literature explaining the gate leakage mechanism of unstressed devices Several transport mechanisms have been suggested to explain J G such as trap assisted tunneling [34], [78 81] direct or FN tunne ling [78 80], [82] temperature assisted tunneling [78], [83] multi s tep trap assisted tunneling [84] thermi onic trap assisted tunneling [82], [85 87] tunneling through a thin surface barrier [88] and PF emission [89 94] W e endeavor to resolve the mechanisms of gate leakage in AlGaN/GaN HEMT by varying external mechanical stress and reverse gate bias simultaneously, and discuss implications on the effect of mechanical stress on device degradation. Experiment Wafer samples were attached to heat treated high carbon steel plates with epoxy and stressed in a four point wafer bending setup Compressive and tensile uniaxi al stress up to 360 MPa was applied longitudinal to the channel direction. The stress dependence of the AlGaN/GaN HEMT J G was characterized at the V DS = 0 state, isolating the effect of electric field induced by the gate. Various r everse biases ( 0. 1 V t o 4 V) were applied to the gate and held constant until J G reached steady state to eliminate transient trapping effects before each measurement At each bias, mechanical stress was incrementally applied then released, while simultaneously

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86 measuring J G High temperature measurements were taken on a temperature controlled probe station using sample stage heaters. Results and Discussion Wafer Bending Results L ongitudinal stress up to 360 MPa, was incrementall y applied to the AlGaN/GaN HEMT device while J G was simultaneously measured over a period of 1800 seconds Averaging J G over 1800 seconds was done to account for random fluctuations in the measured current. It was found that a t ime duration of 1800 seconds while the stress was held constant was adeq uate to obtain a reasonable statistical confidence in the measured J G The normalized change in J G J G J G (0)) was measured for several constant applied gate biases ( V G = 0.1, 0.25, 0.5, 1, 2, and 4 V) using the above mentioned procedure Figure 5 2 shows results of J G J G (0) for V G = 0.25 V and 4 V. T he stress dep endence of J G was weaker at V G = 4 V than at V G = 0.25 V T ensil e (compressive) stress increased (decrease d ) J G for all applied gate biases At each bias a fter the compressive or tensile stress wa s applied to its maximum magnitude of 360 MPa then the stress was incrementally released. Upon releasing the stress to zero J G return ed to its initial unstressed value This demonstrates that the measured change in J G is purely a reversible consequence of the applied stress, and not a transient effect. A lso, it demonstrates that the applied mechanical stress (up to 360 MPa) does not induce permanent damage to the device To quantify the magnitude of the normalized change in g ate current density, J G ( )/ J G (0) for each applied gate bias and stress level, J G is averaged over the duration of time the stress was held constant. Fig ure 5 3 show s J G ( )/ J G (0) averaged for all levels of compressive and tensile stress at V G = 0.25 V and 4 V Error bars

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87 representing the uncertainty in the measurement of J G ( )/ J G (0) are t hree times the standard deviation of the J G measurement s over the duration when the stress was held constant The sensitivity of J G to stress defined as the normalized change in J G per stress J G ( )/ J G e weighted total least squares linear fit J G ( )/ J G (0) versus stress, including uncertainty in J G at each stress increment. The stress sensitivity of J G is plotted as a function of reverse gate bias in Figure 5 4. Increasing the reverse gate bias is o bserved to decrease the sensitivity of J G to stress. The sensitivity of J G to stress de creased from 1.7 0.3 %/100MPa at V G = 0.25 V to 0.6 0.1 %/100MPa at V G = 4 V as shown in Figure 5 4 To interpret th e decreasing sensitivity for increasing reverse gate bias the dominant gate leakage transport mechanism needs to be analyzed Discussion To understand the decreasing stress dependence of J G with increasing reverse gate bias and co mpare the measurements to gate leakage transport models, the experimenta lly determined 1D E AlGaN values discussed in Chapter 4 are used. Since the 2D edge effects complicate the E AlGaN profile under the gate for gate biases below V T the simple 1D model cannot be used. Therefore, we analyze the gate leakage mechanism only fo r V G above V T Simulations performed indicate that t hermionic emission, bulk trap assisted tunneling, and Fowler Nordheim ( FN ) tunneling models underestimate the magnitude of the experimental data [102] However, the Poole Frenkel ( PF ) emission model for gate leakage current closely matches the experimental data.

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88 PF emission refers to the lowering of the Coulombic potential barrier of a trapped electron due to a large electric field, increasing the probability for the electron to be emitted into the conduction band. The general expression for PF emission current considering c ompensation is [103 105] : ( 5 1 ) where ( 5 2 ) C is a constant related to mobility an d density of states E A is the trap activation energy is the vacuum permittivity, and is the relative permittivity of the AlGaN The compensation or slope parameter r ranges from 1 to 2 depending on the amount of acceptor concent ration and position of the Fermi energy with respect to E A [103 105] This compensation parameter is used as a first order model parameter to describe acceptor compensation. Often, the assumption of r = 1 is used to model PF emission data [93], [94] When r =1, the concentration of electrons excited up to the conduction band is small relative to the donor and acceptor densities When r = 2, t he concentration of acceptor levels is small compared to the number of donor levels and ex cited electrons The E A ext racted from the PF model represents the average trap energy level with respect to the conduction band of the traps contributing to PF current. Traps are distributed both in energy and space throughout the AlGaN barrier; the extracted E A only represents th e traps participating in emitting electrons to the conduction band via the PF effect Also, the trap levels are assumed to be located

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89 physically close to the top surface of the AlGaN layer under the gate, therefore the trap s are assumed to be filled, and only the emission is considered. To determine the dominate gate leakage mechanism of the experimentally measured devices, t he J G versus V G curves (Figure 5 5) were measured from 300 K to 400K Since PF emissio n is a thermal assisted process w hose efficie ncy increases at higher temperatures the gate current was measured at temperatures larger room temperature The temperature and field dependence of J G were plotted in a PF plot (plot of the natural logarithm of the gate current divided by the electric fi eld versus square root of the electric field ) as shown in Figure 5 6 When plotted in this manner, t he linear region of the PF plot signifies that PF emission dominates the gate leakage for that range of E AlGaN By taking the natural log of Equation 5 1 t he PF equation can be written as a linear equation y = m ( T ) x + b ( T ) The slope and y intercept of the PF plot are m ( T ) and b ( T ) respectively. ( 5 3 ) ( 5 4 ) ( 5 5 ) To analyze the stress results systematically, the data is assumed to fit the PF model beginning with an assumption of the limiting case of high compensation when r = 1 independent of stress. The n, a more physical fit to the PF model is used where r is determined by adjusting for a realistic value of the high frequency permittivity. Finally, a

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90 reverse tunneling current is included into the overall expression to satisfy the equilibrium condition, J G ( V G = 0) = 0 Maximum compensation ( r = 1) We begin the analysis by assuming the simple case where the maximum acceptor compensation level in the PF model is assumed ( r = 1 ) The permittivity is extracted including the entire range of measured temperat ures ( T = 300 K to 400 K) First, the slope of the PF plot is plotted against 1/T (Figure 5 7 ). The slope of the linear fit to the plot in Figure 5 7 with the y intercept forced to zero ( ) is ( 5 6 ) Then, the permittivity is calculated from ( 5 7 ) giving a value of 5.88 Including the uncertainty in the measured J G of 3.3% from a control measurement of 1200 simultaneous measurements, t he uncertainty in the e xtracted value of i s determined by including the error in the linear fit when calculating T he resulting uncertainty in is approximately 0. 16 So, for r = 1, = 5.88 0. 16 The n the trap activation ener gy is extracted using the y intercept of the PF plot (Equation 5 5 ) First, the y intercept of the PF plot is plotted against 1/T (Figure 5 8 ). The value of E A is calculated from the slope ( ) and ln( C ) is the y intercept of the linear fit to the plot in Figure 5 8 where ( 5 9 )

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91 Hence, ( 5 10 ) E A was determined to be 0. 37 eV and ln ( C ) = 14 23 The u ncertainty in E A and ln( C ) is e stimated by including the uncertainty of the linear fit when obtaining This gives an estimate for the error of 0.05 eV for E A and 1.55 for ln( C ) The s tress dependence of the PF current can be derived by first defining the unstressed PF current for r = 1 a s: ( 5 1 1 ) In the PF expression, only E A is assumed to be affected by mechanical stress. Stress has been known to change the trap activation energy level in Si/HfSiON devices dominated by PF tunneling through altering bond angle and lengths [106] [107] Although the nature of the trap is likely different in the AlGaN/GaN system than Si/HfSiON, similar physics will apply where stress changes the bond lengths and angles, which will in turn affect the trap activation energy. The compensation parameter permittivity, and other parameters are assumed to remain independent of stress. During four point bending, equal stress is applied to both the AlGaN and GaN layer since the AlGaN/GaN interface is located close to the top surface of the wafer, far from the neutral axis of bending. Therefore, E AlGaN will not be affected by the externally applied stress. Under these assumptions the PF cu rrent under stress is given by ( 5 1 2 )

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92 where E A ( ) is the chan ge in trap energy level due to the applied mechanical stress. The normalized change in PF cu rrent with stress is: ( 5 1 3 ) Based on Equation 5 1 3 the expected normalized change in PF current for a given amount of stress is constant independent of E AlGaN or V G However, t he experimentally J G ( )/ J G experiments decreases with increasing reverse gate bias. Therefore, the simplistic model ( r = 1 independent of stress) fails to capture the correct trend observed e xperimentally Reduced compensation (1 < r < 2) The permittivity used in the PF model should be the high frequency permittivity [103] This is because the trapping/detrapping effects are quick transients. T he high f requency permittivity of Al GaN is = 5.1 0.5, based on the high frequency permittivities of AlN ( 4.6) and GaN (5.3) [108] However, t he value of permittivity extracted from the PF model assuming the high compensation case with r = 1 was 5 88 0. 16 Since the extracted permittivity based on th e assumption that r = 1 does not match the required high permittivity value, the compensation factor r is adjusted. From Equation 5 4 using = 5.1 the value r = 1.0 7 0.0 2 is extracted in order to provide a more physical fit to the PF mode l. This value of r still signifies very high compensation. Since the r value is adjusted to match the high frequency permittivity of AlGaN the E A value is also adjusted B ased on Equation 5 5 including r = 1.0 7 0.0 2 t he value of E A becomes 0.4 0 0.05 eV and ln( C ) is 13.55 1.55 Since r is no longer fixed at the limit of maximum compensation, when E A changes with stress, r also will change with stress Figure 5 9 shows a schematic of the trap

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93 level chang e with stress, and how compensation affects PF emission When E A increases (compressive stress) the trap energy level moves farther away from the conduction band. The acceptor compensation increases while the probability of emission into the conduction band decreases. In the case of decreasing E A (tensile stress), the opposite is true. Including the change in E A and change in r r ) the PF current under stress is written as ( 5 1 4 ) The normalized change in J PF with stress is ( 5 1 5 ) Both E A and r are obtained by simultaneously solving for at two biases ( 0.5 and 1 V) These bias points were chosen because the gate leakage mechanism is primarily PF emission in this range. Incorporating uncertainties from E A and r gives E A = 0.26 0.07 meV/100 MPa and r = 0.001 7 0.0001 /100 MPa. Tensile stress decreases E A and compressive stress increases E A This result is unlike the S i/HfSiON system, where both tensile and compressive stress decreased the trap energy level, increasing J G [106] [107] In the Si/HfSiON device, the dielectric is unstressed Both compressive and tensile stress perturbs the bond angles and bond lengths from equilibrium reducing E A In the AlGaN/GaN HEMT, the AlGaN layer already has a large amount of tensile stress from lattice mismatch. Therefore, applied tensile stress will continue perturbing the bond angles and lengths decreasing E A and compressive stress will tend to return the bond angles and lengths back to equilibrium increasing E A

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94 Figure 5 10 shows the simula ted per 100 MPa calculated from Equation 5 1 5 compared to experiment. Although we use E AlGaN in simulation, for the purpose of plotting, the V G values are used to compare to experiment. Considering r changing with stress provi des a reasonable fit to experiment within the range of experimental uncertainty The V G range shown is from 0 to 2 V, since the experimentally obtained 1D E AlGaN values are only valid until ~ V T It can be observed that there is some small discrepancy in the fit at low V G We investigate the effect of reverse current in the following discussion. Reduced compensation (1 < r < 2) with reverse current At equilibrium, polarization creates a relatively large E AlGaN (0.75 MV/cm). This field should produce a s ignificant forward PF current. However, at V G = 0 V the net current must be zero. Therefore, to balance the PF current a rev erse current ( J R ) of equal and opposite magnitude should be prese nt to balance the PF current at equilibrium The exact transpo rt mechanism of the reverse current is not well understood at this time, however Yan, et al. proposed that in equilibrium J R 0 exp( 3/2 / E AlGaN ) where is a constant [94] Figure 5 1 1 shows a schematic diagram showing J PF and J R assuming J R is assisted by bulk traps. In the PF plot (Figure 5 6 ), the e xperimentally measured J G differs from the ideal linear fit. Th e difference between the idea l linear extrapolated PF plot and the measured data is assumed to be the reverse current. Figure 5 1 2 shows the ideal PF ( J PF ) current reverse current ( J R ) and the total measured gate current ( J G ), where ( 5 1 6 )

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95 The derived ex pression in Equation 5 1 5 describes the normalized change in PF current only, neglecting the reverse current. Therefore, to incorporate the reverse current in the normalized change in the total gate current, the expression for normalized change in PF curr ent is written as: ( 5 1 7 ) Solving for J G ( )/ J G ( 0 ) based on Equation 5 1 5 for J PF ( )/ J PF ( 0 ) gives ( 5 1 8 ) Excluding the last term J R ( )/ J G ( 0 ), this expression is straight forward to calculate. Since the exact mechanism of J R is not well characterized interpreting the stress d ependence of J R is also not clear. However, making some simple assumptions about J R ( )/ J G ( 0 ) can provide a better fit to the experimental stress results. Figure 5 1 3 shows the experimental fit including reverse current for two situations. First, the J R ( )/ J G ( 0 ) is neglected, but the calculation over estimates J G ( )/ J G ( 0 ) at low V G Then, J R ( )/ J G ( 0) is set to 1 .5 % to achieve a very good fit to the experimental data. It is likely that J R may depend slightly with stress, in particular at very low V G H owever, more measurements at lower reverse gate biases will be needed to make a definitive conclusion. The inclusion or o J R ( )/ J G ( 0 ) only affects the fit at low V G Once E AlGaN increases enough to cause J PF >> J R the first part of Equatio n 5 1 8 captures the physics of carrier transport.

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96 At voltages below threshold, E AlGaN at the gate edges continues to increase. Also, the thickness of the AlGaN potential barrier reduces as shown in Figure 5 1 4 This result s in the probability of FN tunne ling increasing. Around 3 MV/cm, the FN tunneling current becomes significant [102] The FN tunneling will occur at the gate edges, where E AlGaN is the largest in parallel with the PF tunneling in the middle of the gate At extreme ly large E AlGaN values where degradation occurs, the majority of J G will likely be dominated b y FN tunneling. The s tress dependence of FN tunneling will be dominated by the out of plane effective mass, which is relatively independent of stress [72] Hence, stress will not cause an incremental change in J G but can cause defect form ation. Summary We have developed a model to explain the gate leakage mechanism in an AlGaN/GaN HEMT. This model explains the experimentally observed de creasing stress dependence of J G with increasing reverse gate bias at a given stress. Tensile (compress ive) stress increases (decreases) J G for all applied gate biases ( V G = 0.1 to 4 V). We conclude, based on our model that b oth PF and a reverse current mechanism are present for V G > V T Table 5 1 sumarizes the key parameters extracted to match the exp erimentally measured data. Below V T E AlGaN at the gate edges increases due to 2D edge effects FN tunneling current likely dominates for very large reverse V G where E AlGaN > 3 MV/cm. At the critical voltage J G is dominated by FN tunneling at the edge s of the gate which will have negligible incremental stress dependence but defect formation can occur.

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97 Table 5 1. Key parameters extracted to match experimental data Parameter Maximum Compensation Reduced Compensation r 1 1.0 7 0.04 r 0.001 7 0.0001 /100 MPa E A 0.37 0.05 eV 0.4 0.05 eV E A 0. 26 0.07 meV/100 MPa AlGaN 5.88 0 16 5.1 0 ln (C) 1 4 23 1.55 13.56 1.55

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98 Figure 5 1. Electrical step stress measurement showing the breakdown of J G at the critical voltage.

PAGE 99

99 Figure 5 2. Normalized change in J G for i ncrementally increasing and decreasing uniaxial stress for (a) V G = 0.25 V and (b) V G = 4 V.

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100 Figure 5 3. J G ( )/ J G (0) averaged for all levels of compressive and tensile stress at V G = 0.25 V and 4 V. U ncertainty comes from three standard deviation from the J G ( )/ J G (0) over the duration stress was held constant.

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101 Figure 5 4 Experimentally measured s tress sensitivity of J G per 100 MPa of stress, as a function of reverse gate bias.

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102 Figure 5 5. Measured gate leakage current dens ity versus gate voltage from T = 300 K to 400 K for unstressed AlGaN/GaN HEMT.

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103 Figure 5 6 PF plot showing linear fit to the measured data for T = 300 K to 400 K.

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104 Figure 5 7 The slope of the PF plot ( m ) plotted versus 1/ T The slope of this plo t ( m is used to calculate

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105 Figure 5 8 The y intercept of the PF plot versus 1/ T The slope of this plot ( m to calculate the trap energy level.

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106 Figure 5 9 Schematic of change in E A with compressive and tensile stress. Compressive stress increas es E A decreasing r increasing compensation, and reducing PF emission. The opposite is true for tensile stress.

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107 Figure 5 10 Simulated s tress sensitivity of J G per 100 MPa of stress, including E A and r changing with stress, as a function of reverse gate bias.

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108 Figure 5 1 1 Schematic of J G J PF and J R assuming J R is a bulk assisted mechanism driven by the PF emission current for V G = 2 V and other parameters from Table 4 1.

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109 Figure 5 1 2 Measured J G ideal J PF obtained by linear extrapolatio n of the linear PF fit and J R calculated by the difference between J PF and J G

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110 Figure 5 1 3 Simulated s tress sensitivity of J G at 100 MPa of stress, including J R as a function of reverse gate bias. J R not changing with stress overestimates the str ess sensitivity. However, J R ( )/ J G (0) = 1 .5 % closely matches experiment.

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111 Figure 5 1 4 Energy band diagrams showing the reduction in the AlGaN barrier thickness at the gate edges for V G well below V T

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112 CHAPTER 6 CONCLUSION Overall Summary A system atic study of the effect of mechanical stress on AlG aN/GaN HEMTs was presented in this dissertation. Stress is inherent to AlGaN/GaN HEMTs and can be beneficial or detrimental to performance and reliability. The lattice mismatch stress between AlGaN and GaN benefits the device by creating the 2DEG inducing polarization, while stress generated via the inverse piezoelectric effect can induce degradation. To characterize the impact of stress on the performance and reliability of AlGaN/GaN HEMTs, a novel te chnique was developed to apply external stress to small (~1 cm 2 ) wafer samples while simultaneously taking electrical measurements A four point wafer bending setup applied stress to the small sample, which was attached to a hi gh carbon stainless steel st rip with epoxy To simultaneously conduct electrical measurements while varying the amount of mechanical stress, wires were attached to the bond pads with room temperature curing conductive epoxy. An enormous variation in AlGaN/GaN HEMT gauge factor mea surements (4 to 40,000) have been reported in literatu re (E. Y. Chang, 2009; Eickhoff et al., 2001; Gaska et al., 1998; Kang et al., 2005, 2004 ; Yilmazoglu et al., 2006; Zimmermann et al., 2006) and is likely a result of charge trapping effects After eliminating the charge trapping effects the measured gauge factor of the AlGaN/GaN HEMT was 2.8 0.4. Th is gauge factor indicates a small stre ss dependence on the device resistivity. This is explained by small changes in the 2DEG sheet carrier density and channel mobility. The experimental results were compared with a simulated gauge factor ( 7.9 5.2) to determine the best fitting set of elas tic and piezoelectric coefficients of GaN and AlN

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113 In order to determine the dominant gate leakage mechanism, a thorough investigation of the relationship between E AlGaN and V G was presented. In a simple model of an ideal 1D device, E AlGaN has a linear re lationship to V G above V T and saturates below V T Experimentally determined parameters were used in the 1D calculation to model the actual device. Adjusting int and n s based on experimental measurements provided an accurate V G versus E AlGaN relationshi p above threshold. Also, a comprehensive 2D simulation was performed to provide insight on E AlGaN for large reverse biases much below V T The 2D results proved the 1D model accurate for V G > V T However, below threshold, although E AlGaN saturates in the middle of the gate, at the gate edges, E AlGaN continues to increas e. PF conduction was proven to be the dominant gate leakage transport mechanism above threshold. Bias and stress dependence of J G was measured simultaneously A decreasing stress dependen ce of J G with increasing reverse gate bias was observed Tensile (compressive) stress increases (decreases) J G for all applied gate biases ( V G = 0.1 to 4 V). Compressive stress increases E A and tensile stress decreases E A Since stress shifts the tra p energy level the compensation parameter r is also affected by stress. A r everse tunneling curre nt was included in the model to balance the forward PF current at equilibrium. However, the reverse tunneling current only is important at extremely small g ate biases. A t very large increasing reverse bias es E AlGaN at the gate edges continues to increas e which decreases the tunneling barrier making FN tunneling more probable. W hen degradation occurs, the contribution to J G is dominated by FN tunneling at the edges of the gate.

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114 Future Work Mechanical stress has been shown to affect AlGaN/GaN HEMT channel resistance and gate current. The demand for improved performance and reliability of AlGaN/GaN HEMT devices requires further analysis into the role of mec h anical stress in degradation. A more comprehensive understanding of the reverse tunneling current will help to understand how stress affects the gate leakage current at very low reverse biases. J G ( )/ J G (0) data points need to be obta ined at low bias ( 0.1 V < V G 0 V) to see if reverse tunneling current is present, and if it has a stress dependence. Also, degradation experiments combining the effects of temperature, electrical stress, light, and mechanical stress will provide further i nsight in to the role of mechanical stress on device degradation. Since limitations on samples prevent a thorough statistical degradation investigation, experiments need to be designed to isolate the effect of stress on degradation. Gate current should be monitored to evaluate degradation as the device is incrementally stressed using temperature and electrical stress just prior to breakdown. Then, mechanical tensile stress can be applied to attempt to induce degradation. Then, a more direct relationship between stress and device failure can be obtained. Also, trap characterization under mechanical stress to directly measure the change in trap energy with stress will be extremely beneficial Using optical trap characterization methods will be best since t here is no body contact in the AlGaN/GaN HEMT devices making other characterization methods invalid A more direct

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115 measurement of the effect of stress on AlGaN/GaN HEMT traps can help to engineer more reliable, better performing devices.

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126 BIOGRAPHICAL SKETCH Andrew (Andy) Daniel Koehler was born in 1982 in Gainesville, Florida. He received his B. S. and M. S. degrees in electrical and computer engineering from the University of Florida in 2004 and 2007 respectively. He has been pursuing his Ph.D. degree in electrical and computer engineering under Dr. Scott E. Thompson and co supervised by Dr. Toshikazu Nishida since 2005 focusing on the impact of strain on novel device materials and structures. During his graduate studies, he also completed three internships with Intel Corporation. In 2006 he interned in Rio Rancho, New Mexico with Fab 11 Sort, optimizing testing of NOR flash devices for functional defects. In the summers of 2007 and 2008 he interned in Hillsboro, Oregon with Components Research exploring methods of fabricating semiconducting nanowire FETs and investigat ing the str ess dependence of III V devices. He received his Ph. D. from the University of Florida in the fall of 2011.