IMPACT OF MECHANICAL 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
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2011

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© 2011 Andrew Daniel Koehler

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To my family

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 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 and 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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 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 BACKGROUND ............................. 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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 2DEG Change with Stress................................................................................ 47
Electron Mobility Change with Stress ............................................................... 48
Simulated Gauge Factor................................................................................... 49
Summary ................................................................................................................ 49

4 VERTICAL ELECTRIC FIELD IN THE ALGAN BARRIER ...................................... 62

Introduction ............................................................................................................. 62
Ideal 1D Calculation of EAlGaN ................................................................................. 63
1D Experimentally Measured EAlGaN ....................................................................... 65
2D Simulation of EAlGaN ........................................................................................... 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
Wafer Bending Results ..................................................................................... 86
Discussion ........................................................................................................ 87
Maximum compensation (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

BIOGRAPHICAL SKETCH .......................................................................................... 126

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 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 EAlGaN calculation ................................................ 71

5-1 Key parameters extracted to match experimental data ...................................... 97

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 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 AlxGa1-xN (x = 0.26), relaxed GaN heterostructure.

The strained AlGaN layer has larger spontaneous polarization than the GaN
layer, as well 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 ID-VG curve of a depletion mode AlGaN/GaN HEMT measured at VDS
= 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 drecreasing 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 VGS = -2 to 0 VDS = 0.1 V measurement sweeps

resulting in charge trapping and detrapping. ...................................................... 51

3-2 VT measured in consecutive ID – VG sweeps. In dark, |VT| can increase

(decrease) from detrapping (trapping) of electrons, depending the device
initialization. Under unfiltered UV illumination, VT does not fluctuate. ................ 52

3-3 A decrease in channel resistance of 15% observed during 1200 seconds of

measuring after turning on the incandescent microscope light. .......................... 53

3-4 Unfiltered UV measurement (a) ID-VG 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) ID-VG 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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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 RCH to less than
0.02% variation for 1200 seconds of measurement............................................ 57

3-8 Normalized change in channel resistance with incrementally increasing and

decreasing uniaxial stress. ................................................................................. 58

3-9 RCH measurements at each time interval stress was held constant. Error
bars represent a three standard deviation confidence 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 PPE,mech
similar in magnitude for both AlGaN and GaN layers. ........................................ 60

3-11 Simulated change in ns, μe and RCH with uniaxial stress shown in bands of
uncertainty. The bands signify variations in numerical results due to
uncertainty in elastic and piezoelectric coefficients. ........................................... 61

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

4-2 Dependence of the 2DEG density (ns) with gate bias for the 1D case, with no
interface trapped charge. Threshold is defined when ns is entirely depleted
(ns = 0). ............................................................................................................... 73

4-3 Idealistic 1D calculation of EAlGaN, assuming no interface trapped charge.

EAlGaN increases linearly until the threshold voltage, then saturates. .................. 74

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. .................................... 75

4-5 Capacitance-Voltage measurement, which is integrated in order to determine

ns(V). .................................................................................................................. 76

4-6 1D ideal (no interface trapped charge) calculation and the experimental result
from experimental parameters obtained by adjusting σint and obtaining ns
from C-V ............................................................................................................. 77

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

4-8 Experimental calculation of EAlGaN versus VG 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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4-10 Horizontal cross-section of EAlGaN taken near the top surface of the AlGaN
barrier 1 nm below the gate contact. .................................................................. 81

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. .............................. 82

4-12 Horizontal component of EAlGaN at the (a) center and (b) edge of the gate. ........ 83

5-1 Electrical step stress measurement showing the breakdown of JG at the

critical voltage. .................................................................................................... 98

5-2 Normalized change in JG for incrementally increasing and decreasing

uniaxial stress for (a) VG = -0.25 V and (b) VG = -4 V. ........................................ 99

5-3 ΔJG(σ)/JG(0) averaged for all levels of compressive and tensile stress at VG
= -0.25 V and -4 V. Uncertainty comes from three standard deviation from
the measurement of ΔJG(σ)/JG(0) over the duration stress was held constant. 100

5-4 Experimentally measured stress sensitivity of JG per 100 MPa of stress, as a

function of reverse gate bias............................................................................. 101

5-5 Measured gate leakage current density 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’) is
used to calculate .................................................................................. 104

5-8 The y-intercept of the PF plot versus 1/T. The slope of this plot (m’’) is used
to calculate the trap energy level. ..................................................................... 105

5-9 Schematic of change in EA with compressive and tensile stress.

Compressive stress increases EA, decreasing r, increasing compensation,
and reducing PF emission. The opposite is true for tensile stress. .................. 106

5-10 Simulated stress sensitivity of JG per 100 MPa of stress, including EA and r
changing with stress, as a function of reverse gate bias. ................................. 107

5-11 Schematic of JG, JPF, and JR assuming JR is a bulk-assisted mechanism

driven by the PF emission current for VG = -2 V and other parameters from
Table 4-1. ......................................................................................................... 108

5-12 Measured JG, ideal JPF obtained by linear extrapolation of the linear PF fit,
and JR calculated by the difference between JPF and JG................................... 109

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5-13 Simulated stress sensitivity of JG at 100 MPa of stress, including JR, as a
function of reverse gate bias. JR not changing with stress overestimates the
stress sensitivity. However, ΔJR(σ)/JG(0) = 1.5% matches experiment............ 110

5-14 Energy band diagrams showing the reduction in the AlGaN barrier thickness
at the gate edges for VG well below VT. ............................................................ 111

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 LIST OF ABBREVIATIONS

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 Scanning electron microscope

UV Ultraviolet

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 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 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

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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.

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 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 early III-V

semiconductor research 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 transistor (HEMT) with selectively doped n-type AlGaAs barrier,

eliminating issues associated with native oxides on GaAs [1][2]. Although AlxGa1-xN

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

(μe), the high conduction band density of states (DOS) and large saturation velocity (vsat)

still permits large current densities. The low dielectric constant ( ) reduces capacitive

loading and allows for large area devices, increasing RF current and power [4]. The

large band gap (EG) improves radiation resistance, results in high intrinsic temperature,

and provides a very large breakdown field (Ebr) necessary for handling high RF power.

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Heat dissipation benefits from the high thermal conductivity (κ), 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 (ns). Benefitting from

mechanical strain, AlGaN/GaN HEMTs are capable of achieving ns greater than 1013

cm-2, without intentional doping. This is significantly higher than other III-V systems due

to strong piezoelectric polarization 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 an AlGaN/GaN 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, sensors, and automotive for

both military and commercial applications. Integration of GaN on Si(111) substrates

improves 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) ,outputting 240 W of power with a

power-added efficiency (PAE) of 60% [6][7]. In academia, an example of the current

devices under investigation include Al2O3 dielectric layers forming metal-oxide-

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semiconductor HEMTs, providing 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 are 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 differences in lattice constants (~17%) and thermal

expansion 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

lattice 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 stress in the

AlGaN barrier layer. The AlGaN barrier is pseudomorphically grown on the relaxed

GaN channel/buffer. Lattice mismatch between AlGaN and GaN induces a biaxial

tensile stress in 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 grown in the (0001) orientation are both strongly piezoelectric [9].

The 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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electron gas (2DEG). SiO2 or Si3N4 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 (500 MPa) can

be generated in the AlGaN barrier during normal operation (VGS = 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 lattice by Bardeen and Shockley [13]. In 1954, the first

piezoresistance measurements of n and p type conduction for both Si and Ge were

published [14]. The piezoresistive property of Si gave potential for Si pressure, flow,

force, and acceleration 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 degeneracies, and warping bands.

As a result, strain alters the carrier’s mobility through mass change and of scattering

change.

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 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 implementation of beneficial strained

epitaxial Si layers on relaxed Si1-xGex demonstrated potential advantages of strain in Si

technology [16], [17]. In-plane biaxial stress induced in the MOSFET channel results

from mismatch in lattice constants between Si and SiGe. However, process integration

challenges and almost negligible pMOSFET performance gains at typical operating

voltages limited the usefulness of this technology [18], [19]. Uniaxial stress reduces

crystalline symmetry more than biaxial stress providing superior enhancement in carrier

mobility. In Si MOSFETs, tensile 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 traditionally applied to entire wafer by growning 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, extending Moore’s Law beyond

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

commercial Si CMOS technologies to date.

Motivation

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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development. Trapping centers at the AlGaN surface, AlGaN/GaN interface, and/or

GaN bulk are considered 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], increased gate current [34],

and light sensitivity [28], [30], [33]. Charging and discharging of traps can limit device

performance. Generation of new traps can permanently degrade the device, even 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 effect [11], [35]. During operation, the

large vertical field under the gate creates strain in the AlGaN barrier, adding to the

existing strain from lattice mismatch. Once the strain surpasses the material’s critical

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 defects to

form, however 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 energy 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 current, and increasing hot-carrier effects [37].

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 Since stress is 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 well 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 systematic study of the effects of externally applied

mechanical stress on the AlGaN/GaN HEMT channel resistance and gate current can

provide insights into the physical mechanisms responsible for stress-related

performance and reliability issues.

Organization

The focus of this dissertation is to provide an improved understanding of the

impact of mechanical stress on AlGaN/GaN HEMT channel 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 presents 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

21
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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Table 1-1. Key material parameters for high power high performance transistors
Parameter Units GaN Si GaAs InP 4H-SiC
m* m0*kg 0.22 [38] 1.56 [38] 0.06 [38] 0.07 [38] 0.58 [38]
μe cm2/V·s 1245 [38] 1750 [38] 9340 [38] 6460 [38] 1000 [38]
DOS 1018 cm-3 2.3 [39] 32 [39] 0.47 [39] 0.57 [39] 24.9 [39]
vsat 107 cm/s 1.4 [40] 1 [41] 0.72 [41] 0.67 [41] 0.33 [39]
εr 9.4 [4] 11.9 [4] 12.5 [4] 12.9 [4] 10.0 [4]
EG eV 3.4 [4] 1.12 [38] 1.43 [38] 1.35 [38] 5.4 [38]
5
Ebr 10 V/cm 20 [4] 3 [4] 4 [4] 4.5 [4] 35 [4]
κ W/˚K·cm 1.12 [38] 1.56 [38] 0.45 [38] 0.68 [38] 3.7 [38]

23
 GaN Cap 1.5 nm
Strained AlGaN (x = 0.26) Barrier 18 nm

2DEG
Relaxed GaN Channel and Buffer 1 μm

Stress Mitigating Transition Layer

Si(111) Substrate

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

24
 CHAPTER 2
ALGAN/GAN HEMT AND WAFER BENDING BACKGROUND

GaN Fundamentals

AlGaN/GaN HEMTs are depletion mode field effect transistors, benefiting from

large 2DEG sheet carrier density, obtained without intentional doping or applied gate

bias. The combination of spontaneous polarization (PSP) and piezoelectric polarization

(PPE) 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 wurtzite semiconductors such as GaN, spontaneous polarization exists

when the ratio c/a differs from the ideal value of 8 / 3 , where c is the height and a is the

spacing as shown in Figure 2-1. In order to induce a 2DEG of electrons desirable for

AlGaN/GaN HEMT performance, polarization must result in a net positive fixed charge

at the AlGaN/GaN interface. To achieve this, GaN is eptaxially grown in the direction

normal to the (0001) basal plane, which lacks inversion symmetry. The top 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, spontaneous polarization exists only in the ̂

direction, therefore PSP = PSP ̂. 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. Nishida, 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]

25
 ( ) ( ) (2-1)

It is important to note that spontaneous polarization in AlN ( -0.081 C/m2) is

larger than in GaN ( -0.029 C/m2) [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 inversion, 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 components. In wurtite GaN, the piezoelectric polarization is given by,

[ ] [ ] . (2-3)

[ ]

In the case of an AlGaN/GaN HEMT, the GaN layer is significantly thicker relative

to the AlGaN barrier layer, so the AlGaN barrier strains to lattice match the relaxed GaN

layer. Strain which is generated from this lattice mismatch is in the out-of-plane

direction (along the c-axis) defined by the lattice distortion as ( ) . Also, an

isotropic in-plane strain results, where ( ) , where a and c are the

strained and a0 and c0 are the unstrained lattice constants. The polarization induced by

lattice mismatch strain in AlGaN/GaN HEMT devices grown along the <0001> direction

only exists in the <0001> direction. Therefore, the piezoelectric polarization resulting

26
from lattice mismatch strain in the AlGaN layer of an AlGaN/GaN HEMT can be

expressed as:

( ). (2-4)

Stress [σ] and can be related by Hooke’s law, where,

, (2-5)

and analogously

(2-6)

The stiffness tensor [C] and compliance tensor [S] = [C]-1 are 6x6 element 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

an AlGaN/GaN HEMT can be simplified in terms of atomic distortion, piezoelectric

constants, and stiffness constants, giving

( ) (2-9)

27
Formation of 2DEG

The net positive fixed sheet charge at the AlGaN/GaN heterostructure interface

(σint) 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 AlxGa1-xN

(x = 0.26) layer on relaxed GaN. The spontaneous polarization in AlGaN and 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 (σPZ = ) is equivalent to a positive fixed

sheet charge density at the AlGaN/GaN interface. In a device with interface trapped

charge (Qit), the interface sheet charge is reduced by Qit,

( ) . (2-10)

In actual devices, surface roughness, variations in Al composition, 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 the 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 (ni = 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

Ibbetson’s surface donor model [42]. Figure 2-3 shows a schematic of the space

charges for an ideal AlGaN/GaN. The 2DEG sheet carrier density (ns) is described by

Equation 2-11.

28
 ( ) (2-11)

The maximum 2DEG sheet carrier density (ns0) occurs at VG = 0 V.

( ) (2-12)

The electronic charge is q, the dielectric constant of AlGaN is , the thickness of

the AlGaN barrier is tAlGaN, the Schottky barrier height of the gate is (

) , the conduction band offset in the AlGaN/GaN interface is , and the Fermi

level with respect to the GaN conduction band is EF. At equilibrium, the Fermi level can

be described as,

, (2-13)

where is given by

, - (2-14)
√

and m* is the effective mass of AlGaN. The parameters ns, σint, , EF0, ΔEC, , and

m* are all 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 AlxGa1-xN (x = 0.26) layers were

deposited through metalorganic chemical vapor deposition (MOCVD) on high resistivity

(111) Si substrates. The AlGaN barrier is 18 nm thick with a ~1.5 nm GaN cap and a 1

μm GaN channel layer. Ti/Al/Ni/Au metal stack was used for the ohmic source and

drain contacts. The wafers were passivated with a PECVD deposited SiNx passivation

29
layer. In a separate lithography step, Ni/Au Schottky gates were formed. Gate-to-

source spacing of 1.0 μm, gate lengths of 0.5 μm and 1 μm, and gate-drain spacing of

3.2 μm, gives a total channel length of 4.7 μm. The channel width is 50 μm. The

substrate was thinned to a thickness of 150 μm using standard Si grinding techniques.

Devices with and without field plates were analyzed. Typical DC ID-VG characteristics

are shown in Figure 2-5 for VDS = 0.1 V. Although these devices were fabricated on a

100 mm diameter wafer, the wafer was diced in approximately 1 cm2 samples to

maximize the number of usable devices for mechanical wafer bending experiments

used to study the effect of stress on the AlGaN/GaN HEMTs.

Mechanical Wafer Bending Experiment Setup

Mechanical wafer bending is a simple and cost effective way to investigate the

underlying physics 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 alter the internal stresses can impact other characteristics of the device. Therefore

mechanical wafer bending is fundamental in performing controlled stress experiments.

Several methods have been used to externally apply external mechanical stress to

semiconductors. The first piezoresistance measurements by Smith [14] were 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

Smith’s study is 10 MPa. Bending of cantilevers, 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 the beam, making specification of the

30
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, we use a flexure based four-point wafer bending system, capable of applying

greater than 1 GPa of uniaxial stress to Si wafers [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 points 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, variation of device 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]

(2-15)
( )

where, E is Young’s modulus, 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 readings from a noncontact fiber optical

displacement system and strain gauge measurements [45].

Bending Measurements of Small Samples

AlGaN/GaN HEMT samples were diced into ~1 cm2 size to maximize the number

of measureable samples since wafer bending tests are potentially destructive and

AlGaN/GaN HEMT wafers are costly. However, the samples are smaller than the

31
minimum size that can be directly bent in the four-point wafer bending setup. So, to

apply stress to these small samples, we developed a technique to bend small wafer

samples in the standard flexure based wafer bending setup.

This technique of applying mechanical stress to a small AlGaN/GaN HEMT wafer

sample starts by attaching the wafer sample to a heat treated 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 inserted into a 100°C oven for 5 minutes. The

washer and metal binder were removed and the sample was placed on a 150°C

hotplate for 5 minutes to complete the curing process. The sample attached to the steel

plate was then inserted into the wafer bending setup.

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 applied

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, electrical measurements need to be taken while simultaneously varying the

amount of applied stress. In order to achieve this, wires were attached to the device

32
bond pads. Standard ball and wedge wire-bonding techniques resulted in delamination

of bond pads destroying 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 approximately 1 cm length and removed from the ball bonder. A small amount of

electrically conductive Epoxy Technology EE129-4 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 ball 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 device’s bond pad and left to cure for 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 background 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 the 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 mechanical 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.

33
 <0001> a Ga

x y

Figure 2-1. GaN-faced GaN crystal lattice, oriented along the <0001> direction.

34
 0.08
Strained AlGaN
0.06
Polarization (C/cm2)

PPE,lattice
0.04

0.02 PSP

0.00

0.06 Relaxed GaN

0.04

0.02
PSP
0.00
© [2010] IEEE

Figure 2-2. Polarizations in strained AlxGa1-xN (x = 0.26), relaxed GaN heterostructure.

The strained AlGaN layer has larger spontaneous polarization than the GaN
layer, as well as additional polarization 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]

35
 Ni Gate AlGaN Barrier GaN

EC

   PZ

2DEG
surf

Qint qns
 
PZ

-30 -25 -20 -15 -10 -5 0 5 10

X (nm)
Figure 2-3. Conduction band schematic diagram of an AlGaN/GaN HEMT showing
charge balance.

36
 AlGaN
2DEG GaN

Figure 2-4. Cross-section SEM of commercial devices characterized in this dissertation.

Image from Nitronex [46].

37
 30
VDS = 0.1 V
JD (mA/mm) 25

20

15

10

-2.0 -1.5 -1.0 -0.5 0.0

VG (V)
Figure 2-5. Typical ID-VG curve of a depletion mode AlGaN/GaN HEMT measured at
VDS = 0.1 V.

38
 a.

b.

Figure 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, showing tensile stress on the top and compressive stress on the
bottom with a neutral axis in the middle.

39
 Probe tip Conductive
epoxy

Gold wire

GaN HEMT wafer

under stress High carbon
Epoxy steel strip
Steel rods
Figure 2-7. GaN wafer sample attached to heat treated high carbon stainless steel
inserted in a four-point bending setup.

40
 70
60
Stress (MPa) 50
40
30
20
10
0
0 1 2 3 4 5 6 7 8

Graduation of Stress (#)

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

41
 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 (ε)

(GF = (ΔR/R)/ε). 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 large discrepancy in gauge factors (GF)

ranging from -4 to -40,000 for AlGaN/GaN HEMTs are reported in literature (E. Y.

Chang, 2009; Eickhoff, Ambacher, Krotz, & Stutzmann, 2001; Gaska et al., 1998; Kang

et al., 2005, 2004; Yilmazoglu, Mutamba, & Pavlidis, 2006; Zimmermann et al., 2006).

This large disagreement likely results 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 device and therefore

extract the gauge factor. We use four-point bending, while mitigating the effects of

charge traps to experimentally characterize the effect of stress on AlGaN/GaN HEMTs.

Effects of Trapped Charge

The effect of charge trapping due to surface 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. Nishida, 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]

42
voltage shift [56], and light sensitivity [57]. These traps can be formed during

processing and crystal growth [58], or generated during device operation via the inverse

piezoelectric effect [11], or by hot carriers [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 to 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 trapping effects. The drain

current and threshold voltage depend strongly on the concentration of trapped charge in

the device. Biasing the device during measurements can alter the concentration of

trapped charge, increasing or decreasing the device’s threshold voltage. This instability

in the devices can be demonstrated by first initializing the device with a large VG pulse

(VG = -10 V held for 1 minute), filling available trap states with electrons (right side of

Figure 3-1). Then, 40 consecutive VG sweeps from -2 V to 0 V were performed over

1200 seconds in the dark. These sweeps are unable to maintain the large charge

density of trapped electrons which were filled from the large VG 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 VG from -2 V to 1 V in

the dark fills the available traps, shifting the threshold voltage more negative. 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

43
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 result from a

change in trapped charge during the experiment. To eliminate 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 accurate 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 longitudinal to the channel direction. To obtain an

accurate measurement of the AlGaN/GaN HEMT gauge factor, parasitic charge

trapping transients and external resistances were addressed. After the effects of

charge trapping were eliminated, and external resistances 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 ID-VG under UV

spotlight illumination compared to dark (Figure 3-4a) showed a large increase in off-

state drain current and a decrease in subthreshold slope. The spectral intensity of the

44
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 3-4b. Under

illumination of above bandgap light, mobile electron-hole pairs are photogenerated. 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 3-5b). A horizontal shift in subthreshold slope and

similar off-state leakage current (Figure 3-5a) 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 described 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 Figure 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 stress dependence of the channel resistance (RCH) was measured at VGS = -

1V and VDS = 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 characterized with W/L ratio of 25. The measured resistance

(Rmeas) is the sum of the channel resistance (RCH), source contact resistance (RS), drain

contact resistance (RD), and external parasitic resistances (Rext) and was on the order of

100 Ω.

45
 (3-1)

The source and drain contact resistances (RS = RD = 5 Ω), measured by transmission

line measurements, are subtracted from the measured resistance and are assumed to

have a negligible stress dependence. A four-point Kelvin measurement is used to

eliminate the effect of external resistances. Two 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 force 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 RCH 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 RCH, while compressive stress increases RCH 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%/100 MPa, which is much smaller than what

is observed in (001)/<110> silicon nMOSFETs 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 change in resistance observed is due to

a reversible strain effect, opposed to charge trapping/detrapping transients.

The gauge factor was determined by averaging the RCH measurements over each

time interval during which the stress was held constant (Figure 3-9). Error bars

46
represent a three standard deviation confidence interval for the measurement. The

slope of a total least squares linear fit of the averaged RCH versus strain curve was

obtained to determine a gauge factor of -2.5 ±0.4. Total least squares analysis included

uncertainty of the measurements. The determined gauge factor (-2.5 ±0.4) is small

relative to values in literature 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. The channel

resistance is inversely related to the 2DEG sheet carrier density and electron mobility

(μe).

(3-2)

where 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)

To 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 wafer bending is approximately equal in both

the AlGaN barrier and the GaN layer because the AlGaN barrier (18 nm) and GaN layer

47
(1 μm) are thin compared to the total thickness of the wafer (150 μm). Therefore, these

two layers are near the top surface of the sample, far from the neutral axis of bending,

and experience the same magnitude of stress. Spontaneous polarization in both the

AlGaN and GaN remains unchanged by wafer bending since it is an intrinsic material

parameter. As shown in Figure 3-10 for 1 GPa of uniaxial tensile stress, mechanical

wafer bending induced piezoelectric polarization (PPE,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

σxx is the only nonzero element in the stress tensor, and . The mechanical

wafer bending induced piezoelectric polarization is similar for both AlGaN (0.00148

C/cm2) and GaN (0.00143 C/cm2) since the elastic and piezoelectric coefficients in GaN

and AlGaN are similar for a small Al mole fraction (26%). The total polarization at the

interface under uniaxial mechanical stress is

( ) ( ) (3-4)

Relating the total polarization at the interface to ns according to Ambacher et al. [61]

gives an increase in ns ranging from 0.064% to 1% for 360 MPa of tensile stress.

Uncertainty of ns 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 intervalley 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 Γ-point.

48
Therefore, stress-induced change of the average effective mass due to electron

repopulation and scattering can be neglected. Thus, the mobility change is dominated

by a change in the effective mass through band warping. Band warping can be

simulated using a tight-binding model with a sp3d5 basis [71]. Since strain alters the

atomic 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 3-10 shows the experimental normalized change in RCH with stress (symbols)

compared to the calculation (shaded bands). The change in 2DEG sheet carrier density

and mobility is combined using Equation 3-3 to calculate the normalized change in

resistance. Depending on the coefficient values used in the calculation, the change in

RCH can range from 0.29% to 1.5% for 360 MPa of stress illustrated as shaded bands in

Figure 3-11. 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 Cij(GaN) [73] Cij(AlN) [74] eij(GaN) [75] eij(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 measurementThe small gauge factor indicates a small

stress dependence on the device resistivity. This is explained by small changes in the

49
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.

50
 40 Consecutive VGS = -2 to 0 VDS = 0.1 V measurements (1200 s)
2
Large VG pulse (VG = -10 V for 1 minute)

Dark Light 1.5

ID (mA)
trapping

detrapping 1

0.5
Gate AlGaN GaN
Gate AlGaN GaN
0
-2 -1.5 -1 -0.5 0
VG (V)
Figure 3-1. Results of consecutive VGS = -2 to 0 VDS = 0.1 V measurement sweeps
resulting in charge trapping and detrapping.

51
 -1.2
-1.2

Detrapping
-1.3
-1.3
initialized by VGS = -10 V for 1 minute
(measured in dark)
VT (V)
VT (V)

-1.4
-1.4

initialized by UV light (1 min) Trapping

(measured in dark)
-1.5
-1.5
Stable
measured under UV light
-1.6
-1.6
00 200
200 400
400 600
600 800
800 1000
1000 1200
1200
Time (s)
Time (s)
Figure 3-2. VT measured in consecutive ID – VG sweeps. In dark, |VT| can increase
(decrease) from detrapping (trapping) of electrons, depending the device
initialization. Under unfiltered UV illumination, VT does not fluctuate.

52
 Microscope Light ON
0
(%) VDS = 0.1 V
VGS = -1 V
/RCH(%)
-5
15% change in RTOT
15%
CHTOT

from detrapping
ΔR/R

-10
RTOT

-15
0 200 400 600 800 1000

Time
Time(s)
(s)
Figure 3-3. A decrease in channel resistance of 15% observed during 1200 seconds of
measuring after turning on the incandescent microscope light.

53
 -3
a. b.
10
Wavelength (nm)
-4
420 400 380 360 340 320
10 Under UV

≈
EG(GaN)

Intensity (au)
10
-5
10
ID (A)

Large
Increase Dark
-6 5
10

10
-7
0
3.0 3.2 3.4 3.6 3.8
-2.0 -1.8 -1.6 -1.4 -1.2 -1.0

VG (V)
Energy (eV)

Figure 3-4. Unfiltered UV measurement (a) ID-VG 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
a. b.
10 Wavelength (nm)
420 400 380 360 340 320
-4
10 0.4

≈
Under UV
EG(GaN)

Intensity (au)
0.3
-5
10 Under UV
ID (A)

with filter 0.2

Dark
-6
10 0.1
Much Smaller
Increase
0.0
-7
10 3.0 3.2 3.4 3.6 3.8
-1.6
Energy (eV)
VG (V)

Figure 3-5. Filtered UV measurement (a) ID-VG measurements in dark and UV light
filtered by a 380 nm bandpass filter with a much smaller increase in off-state
current and no subthreshold slope change. (b) The spectral output of UV light
with 380 nm bandpass filter.

55
 Polystyrene heat shield
Probe tip Conductive
epoxy

Gold wire

UV source

Band-pass filter

GaN HEMT wafer

under stress High carbon
Epoxy steel strip
Steel rods
Figure 3-6. Experimental setup for photoionizing trapped charge to measure the gauge
factor.

56
 UV Light
Filtered

ON

OFF

VGS = -1 V, VDS = 0.1 V

1.43
Sample A
1.42
((Ω)
)

1.41
ΔR
ΔR CH<< 0.02%
TOT 0.02%
CH

1.40
TOT
RΔR

1.39

1.38
0 500 1000 1500 2000

Time (s)
Figure 3-7. Illuminating the device under test with UV light stabilized RCH to less than
0.02% variation for 1200 seconds of measurement.

57
 -600
0.3

Stress Magnitude (MPa)

-400
0.2
(%)

-200
/RCH(%)

0.1
Compression
TOTCH TOT

0.0 0
/R

-0.1 Tension
RΔR

200

-0.2
400
-0.3 © [2010] IEEE
600
0 500 1000 1500
Time (s)
Figure 3-8. Normalized change in channel resistance with incrementally increasing and
decreasing 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]

58
 0.4

0.2
RCH/RCH (%)

0.0

-0.2

-0.4

-400 -300 -200 -100 0 100 200 300 400

Stress (MPa) © [2010] IEEE

Figure 3-9. RCH 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]

59
 As-Fabricated Mechanical Bending
0.08 0.08
AlGaN AlGaN
0.06 0.06 PPE,mech.
PPE,lattice
Polarization (C/cm2)

Polarization (C/cm2)
PPE,lattice
0.04 0.04

0.02 PSP 0.02 PSP

0.00 0.00

0.06
GaN 0.06
GaN

0.04 0.04
PPE,mech.

0.02 0.02
PSP PSP
0.00 0.00
© [2010] IEEE

Figure 3-10. Schematic showing polarizations in AlGaN/GaN HEMTs as fabricated

(left), and 1 GPa mechanically applied stress (right) generating additional
PPE,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]

60
 0.4

RCH
0.2
Change (%)

0.0
nS
-0.2 μe

-0.4

-400 -300 -200 -100 0 100 200 300 400

Stress (MPa) © [2010] IEEE

Figure 3-11. Simulated change in ns, μe and RCH 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]

61
 CHAPTER 4
VERTICAL ELECTRIC FIELD IN THE ALGAN BARRIER

Introduction

Reliability is a major concern with AlGaN/GaN HEMTs, and a systematic study of

the impact of stress on gate leakage current is essential to gain physical insight into the

degradation mechanisms in order to improve device reliability. Gate leakage currents

for AlGaN and GaN Schottky interfaces in literature are significantly larger than what

would be theoretically predicted based purely on the thermionic emission model [77].

Determining the dominant gate leakage transport mechanism through the AlGaN barrier

in AlGaN/GaN HEMT is necessary for investigating the physics behind the effect of

stress on the gate leakage current. An accurate determination of the electric field in the

AlGaN barrier (EAlGaN) is required to investigate the gate leakage models.

Several models have been proposed to explain the gate leakage mechanism 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 dependent on the materials and

processing conditions and the electric field in the AlGaN Barrier, EAlGaN. 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 necessary. To compare different

leakage models to the experimental measurements, an accurate calculation of EAlGaN is

needed. In past works, EAlGaN has been simplified to a linear relationship with the gate

voltage [91][89], simulated using Medici 2D simulations [95], and experimentally

62
measured [96]. The VDS = 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 VG at the VDS = 0 state will be presented.

Ideal 1D Calculation of EAlGaN

A one-dimensional (1D) calculation of EAlGaN provides insight into the general

relationship between voltage and field. In this condition, the gate is assumed to be

infinitely wide. Also, for simplicity, EAlGaN 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 (VAlGaN) from inspection of the energy band diagram

(Figure 4-1). EAlGaN can be written as,

( )
(4-1)

Recalling Equation 2-11, ns can be rewritten in terms of EAlGaN,

( ) (4-2)

Then, the simple expression for EAlGaN is

(4-3)

In the expression for EAlGaN (Equation 4-3), only the 2DEG sheet carrier density

(ns) is a function of gate voltage. The total fixed charge density at the AlGaN/GaN

interface (σint) is assumed to be independent of bias because it is based on the

polarization. Charge trapped at the AlGaN/GaN interface is estimated to be constant

63
with bias. To analyze the dependence of ns with gate voltage, ns is rewritten to include

the contribution of VG in terms of the equilibrium 2DEG concentration ns0.

( ) ( ) (4-4)

where, is the AlGaN capacitance per unit area. At equilibrium, VG = 0 V

and ns = ns0, which is the maximum induced 2DEG sheet carrier density. The fixed

positive charge at the AlGaN/GaN interface induces accumulation of electrons at the

interface in the GaN. The electrons that form the 2DEG originate 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 ns linearly, as

shown by Equation 4-4. The threshold voltage for the depletion mode AlGaN/GaN

HEMT is defined as the voltage required on the gate to entirely deplete the 2DEG (ns =

0). Since the AlGaN/GaN HEMT is a depletion mode device with a negative VT, the

device is considered to be turned off below threshold (|VG| > |VT|). Above threshold, the

2DEG is formed (|VG| < |VT|). Below threshold, the 2DEG remains depleted. Since the

intrinsic carrier concentration of GaN is extremely low (ni ~ 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

interface trapped charge, the 2DEG sheet carrier density plotted against VG. The

charge at the AlGaN/GaN interface (σint = 2.2 x 10-6 C/cm2) is only a result of the

polarization differences between AlGaN and GaN. Parameters described in Table 4-1

were used for the calculation.

To express EAlGaN as a function of gate voltage, the voltage dependent 2DEG

equation (Equation 4-4) was incorporated into the expression for EAlGaN (Equation 4-3)

to give,

64
 ( )
( ) (4-5)

For gate bias below threshold, EAlGaN saturates at ( ). Figure 4-3

shows EAlGaN increasing linearly with bias for gate biases above threshold.

1D Experimentally Measured EAlGaN

Estimation of EAlGaN for an actual AlGaN/GaN HEMT device based on the 1D

model requires both σint and ns to be experimentally measured. The threshold voltage

determined by the standard linear extrapolation method (VT = -1.4 V) is not consistent

with the definition of VG = VT when ns = 0. A more appropriate threshold of -1.9 V is

used based on the initial increase of the capacitance-voltage curve (Figure 4-5).

Trapped 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 (VG = VT when ns = 0), the 2DEG

sheet carrier density at VG = 0 can be calculated from the measured VT.

(4-6)

Which gives ns0 = 5.3 x 1012 cm-3 for VT = -1.9 V. Then, the fixed charge at the

AlGaN/GaN interface can be estimated by solving for σint in Equation 2-12.

( ) (4-7)

Resulting in σint = 1.25 x 10-6 C/cm2, which is nearly half the ideal value (σint = 2.2

10-6 C/cm2) using the constants in Table 4-1. The interface trapped charge density is

estimated from the subthreshold slope (SS) measurements [97], [98]

65
 [ ] (4-8)

The capacitance associated with the interface trapped charge (Cit) can be related

to the density of interface traps by Cit = qDit. For the measured device with SS = 100

mV/dec, the interface trap density is Dit = 1.92 x 1012 cm-2eV-1. Assuming all traps are

full, integrating over the bandgap of AlGaN gives an interface trapped charge Qit = 1.2 x

10-6 C/cm2. Figure 4-4 shows a bar chart of the charge density in the ideal device

compared to the actual device. In the ideal device (Qit = 0) σpz = σint. However, in the

actual device, fixed charge at the AlGaN/GaN interface induced by polarization is

reduced by negative trapped charge.

To obtain EAlGaN for the actual device, the ns versus VG relationship needs to be

obtained. A high-frequency (1 MHz) capacitance-voltage curve (Figure 4-5) was

integrated from pinch-off to voltage V. The experimental bias range was limited to VG =

-2 V to 0 V to avoid additional charge trapping from larger applied biases. The value of

ns(V) is also shown in Figure 4-5. The experimentally obtained ns versus VG

relationship is used in Equation 4-3 to calculate the experimentally obtained EAlGaN

versus VG relationship.

Implementing the experimentally determined σint and ns versus VG relationship

provides the experimentally determined 1D calculation of EAlGaN versus VG. Figure 4-6

shows a comparison between the experimental and ideal 1D calculation for EAlGaN

versus VG. Since both methods are based on the 1D expression, they have similar

trends. Above threshold, |EAlGaN| increases linearly with increasing reverse bias, and

below threshold EAlGaN saturates at ( ). The presence of Qit reduces

σint and the magnitude of the saturated value of EAlGaN below threshold in the actual

66
device compared to the ideal 1D calculation. In addition, VT is shifted toward the

positive direction by the negative Qit. At VG = 0, the experimental |EAlGaN| is larger than

the ideal 1D case because the experimentally extracted ns0 is lower than what is

theoretically predicted, making the numerator of Equation 4-3 larger.

2D Simulation of EAlGaN

Simulation Details

The AlGaN/GaN HEMT structure was simulated using the Sentaurus device

simulator. A two-dimensional (2D) simulation was performed to gain a physical

understanding of 2D effects on EAlGaN. 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 of

discrete elements. 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. The

electrostatic potential, electron concentration, and hole concentration are solved for

through Poisson’s equation and the electron and hole continuity equations respectively.

The boundary conditions used to solve for the three variables are: the metal-contact

work function difference, the ohmic 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 is 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. Electron

mobility was modeled including doping dependence, high field saturation, and

67
temperature. Doping was introduced under the source and drain contacts to emulate

metal spikes to provide an ohmic contact to the 2DEG [99]. The piezoelectric effect is

modeled by incorporating a fixed charge at the AlGaN/GaN interface equal to σint and at

the AlGaN surface equal to σPZ to match experiment. The parameters used in the

simulation are given in Table 4-1.

Simulation Results

The simulated dependence of EAlGaN versus VG at the center of the gate is

compared to the 1D model with experimentally determined parameters (Figure 4-8). In

the simulation, σint was matched to the experimentally obtained value of 1.25 x 10-6

C/cm2. The trend of the 2D simulated EAlGaN is similar to the 1D calculation. Above

threshold, |EAlGaN| increases until threshold with decreasing reverse gate bias. Below

threshold, |EAlGaN| tends to saturate. Although σint is matched, the saturation value of

EAlGaN 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

μm), it is important to analyze the edges of the gate for a comprehensive understanding

of the EAlGaN versus VG relationship.

Vertical cross-section plots of EAlGaN through the middle of the gate and drain edge

of the gate are shown in Figure 4-9. The AlGaN/GaN interface is referenced at y = 0

μm and the AlGaN surface is at y = -0.018 μm. In the middle of the gate, EAlGaN remains

essentially constant throughout the depth of the AlGaN layer for VG = -2 to -10 V. As

shown in Figure 4-5, the magnitude of EAlGaN increases more above VT than below VT as

a function of VG, demonstrating the saturation of EAlGaN below VT. However, at the gate

edge, EAlGaN varies with depth in the AlGaN barrier, and EAlGaN continues increasing with

increasing reverse gate bias.

68
 A horizontal cross section 1 nm below the gate contact in the AlGaN barrier shows

a large increase in EAlGaN at the gate edges (Figure 4-10). At VG = 0 V, |EAlGaN| 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 explain the large increase in EAlGaN 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

near the gate edges. This potential drop results in a large horizontal electric field at the

gate edge. The 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 EAlGaN increasing at the gate

edges.

Summary

The relationship between EAlGaN and VG was calculated for an ideal 1D device. It

was experimentally matched to the actual device, and a 2D simulation was performed.

A 1D model was used to investigate the dependence of EAlGaN with VG. Adjusting σint

and ns based on experimental measurements provides an accurate relationship above

threshold. The 1D model fails to capture the edge physics of a realistic device. 2D

Sentaurus device simulation showed the 1D model is accurate above threshold, but

below threshold, EAlGaN at the gate edges continues increasing. Above threshold,

|EAlGaN| increases linearly with increasing reverse gate bias and the field is

approximately constant throughout the depth of the AlGaN layer. Below threshold, VG <

69
VT, 2D effects change the field profile. In the middle of the gate, EAlGaN saturates, but at

the gate edges, EAlGaN increases. With the relationship between EAlGaN and VG

understood, this relationship can be used to explain the gate leakage transport

mechanism in the AlGaN/GaN HEMT.

70
Table 4-1. List of parameters used in 1D EAlGaN calculation
Parameter Symbol Value Units
Temperature T 300 K
Intrinsic carrier concentration ni 10-10 cm-3
AlGaN thickness tAlGaN 18 nm
Permittivity of GaN 9.5 -
Permittivity of AlN 8.5 -
Bandgap of GaN EG,GaN 3.4 eV
Bandgap of AlN EG,AlN 6.13 eV
Electron affinity of GaN 4.1 eV
Ni work function 5.27 eV
Mass of GaN m*GaN 0.2*m0 -
Mass of AlN m*AlN 0.48*m0 -
Fixed charge at AlGaN/GaN interface σint 2.2 x 10-6 C/cm2

71
 Ni AlGaN GaN

E AlGaN

b VAlGaN

EC
VG = 0 EF
EC EF 0

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

72
 12
x 10
12

Electron Density (cm-2) 10

ns0

2 VT

0
-10 -8 -6 -4 -2 0
VG (V)
Figure 4-2. Dependence of the 2DEG density (ns) with gate bias for the 1D case, with
no interface trapped charge. Threshold is defined when ns is entirely
depleted (ns = 0).

73
 3.0
|EAlGaN| (MV/cm)
2.5

2.0 VT

1.5

1.0

0.5

0.0
-10 -8 -6 -4 -2 0

VG (V)
Figure 4-3. Idealistic 1D calculation of EAlGaN, assuming no interface trapped charge.
EAlGaN increases linearly until the threshold voltage, then saturates.

74
 Charge Density (C/cm2)
-6
x 10

σint
1
σint

0
Qit = 0 σPZ

Qit
-1

Ideal Actual
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.

75
 0.005 12
4x10

0.004
12
3x10

0.003

ns (cm )
2

-2
C F/m

12
2x10
0.002

12
1x10
0.001

0.000 0
-2.0 -1.5 -1.0 -0.5 0.0

VG (V)
Figure 4-5. Capacitance-Voltage measurement, which is integrated in order to
determine ns(V).

76
 3.0

2.5
Experiment
|EAlGaN| (MV/cm)

2.0
1D Idealistic
Calculation
1.5

1.0

0.5

0.0
-6 -4 -2 0

VG (V)
Figure 4-6. 1D ideal (no interface trapped charge) calculation and the experimental
result from experimental parameters obtained by adjusting σint and obtaining
ns from C-V

77
 -0.04

-0.03 Passivation
Gate
-0.02
y (μm)

-0.01 AlGaN Barrier

0.01
GaN
0.02

-0.04 -0.02 0 0.02 0.04

x (μm)
Figure 4-7. Optimized grid for Sentaurus simulation of the AlGaN/GaN HEMT device.

78
 2.0

Experiment
1.5
|EAlGaN| (MV/cm)

1.0 2D Simulation
(center of gate)

0.5

0.0
-6 -4 -2 0

VG (V)
Figure 4-8. Experimental calculation of EAlGaN versus VG compared to 2D simulation
results.

79
 a. 7
Center of Gate
Ni AlGaN GaN
6

|EAlGaN| (MV/cm)
5 VG = -10 V
4 VG = -4 V
VG = -2 V
3 VG = 0 V
2
1
0
-0.02 -0.01 0.00
y (m)
b. 7
Edge of Gate
Ni AlGaN GaN
6 VG = -10 V
|EAlGaN| (MV/cm)

5 VG = -4 V
VG = -2 V
4 VG = 0 V
3
2
1
0
-0.02 -0.01 0.00
y (m)
Figure 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
 6 Source Gate Drain

VG = -10 V
5 VG = -4 V
|EAlGaN| (MV/cm)

VG = -2 V
VG = 0 V
4

0
-4 -3 -2 -1 0 1 2 3 4

x (m)
Figure 4-10. Horizontal cross-section of EAlGaN taken near the top surface of the AlGaN
barrier 1 nm below the gate contact.

81
 Electrostatic Potential (V) 2

0 VG = -10 V
VG = -4 V
VG = -2 V
VG = 0 V
-2

-4

-6

Source Gate Drain

-8
-4 -3 -2 -1 0 1 2 3 4

x (m)
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.

82
 a. 1.0
Center of Gate
Ni AlGaN GaN
0.5

Ex (MV/cm)
0.0

-0.5 VG = -10 V
VG = -4 V
-1.0 VG = -2 V
VG = 0 V
-1.5

-2.0
-0.02 -0.01 0.00
y (m)
b. Edge of Gate
1.0
Ni AlGaN GaN
0.5
EX (MV/cm)

0.0

-0.5
VG = -10 V
-1.0 VG = -4 V

-1.5 VG = -2 V
VG = 0 V
-2.0
-0.02 -0.01 0.00
y (m)
Figure 4-12. Horizontal component of EAlGaN at the (a) center and (b) edge of the gate.

83
 CHAPTER 5
FIELD DEPENDENT MECHANICAL STRESS SENSITIVITY OF ALGAN/GAN HEMT
GATE LEAKAGE CURRENT

Introduction

AlGaN/GaN HEMTs provide benefits over Si, SiGe, SiC and GaAs material

systems for high frequency and high power applications. Unique advantages include a

built-in polarization 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 shown to increase the gate leakage current density (JG), 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 physical breakdown of the AlGaN barrier has been shown to occur at voltages

beyond the critical voltage (Vcrit), creating an irreversible increase in JG [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 VG step

electrical stress on JG at the VDS = 0 V state, showing a sudden increase in JG at Vcrit.

This type of degradation has been hypothesized to be related to the generation of

crystallographic defects via the inverse piezoelectric effect [11]. At large VG, as seen

from the Sentaurus 2D simulations in Chapter 4, increased vertical field occurs at the

gate edges. This creates additional tensile stress in the AlGaN barrier through the

inverse 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 in

84
order to relax the internal elastic energy [11]. These defects cause a low resistance

leakage path through the AlGaN barrier resulting in a sudden increase in JG. A

mechanical wafer bending experiment in literature showed a reduction of Vcrit with

applied mechanical stress, however, only five pairs of devices were investigated in this

study and a more comprehensive study is required [101].

Since stress is inherent in AlGaN/GaN HEMTs, understanding the role of stress on

JG is essential 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 JG such as trap-assisted

tunneling [34], [78-81], direct or 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 PF emission

[89-94]. We 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 uniaxial

stress up to 360 MPa was applied longitudinal to the channel direction. The stress

dependence of the AlGaN/GaN HEMT JG was characterized at the VDS = 0 state,

isolating the effect of electric field induced by the gate. Various reverse biases (-0.1 V

to -4 V) were applied to the gate and held constant until JG reached steady-state to

eliminate transient trapping effects before each measurement. At each bias,

mechanical stress was incrementally applied then released, while simultaneously

85
measuring JG. High-temperature measurements were taken on a temperature-

controlled probe station using sample stage heaters.

Results and Discussion

Wafer Bending Results

Longitudinal stress, up to 360 MPa, was incrementally applied to the AlGaN/GaN

HEMT device while JG was simultaneously measured over a period of 1800 seconds.

Averaging JG over 1800 seconds was done to account for random fluctuations in the

measured current. It was found that a time duration of 1800 seconds while the stress

was held constant was adequate to obtain a reasonable statistical confidence in the

measured JG. The normalized change in JG due to applied stress (ΔJG(σ)/JG(0)) was

measured for several constant applied gate biases (VG = -0.1, -0.25, -0.5, -1, -2, and -4

V) using the above mentioned procedure. Figure 5-2 shows results of ΔJG(σ)/JG(0) for

VG = -0.25 V and -4 V. The stress dependence of JG was weaker at VG = -4 V than at

VG = -0.25 V. Tensile (compressive) stress increased (decreased) JG for all applied

gate biases. At each bias, after the compressive or tensile stress was applied to its

maximum magnitude of 360 MPa, then the stress was incrementally released. Upon

releasing the stress to zero, JG returned to its initial, unstressed value. This

demonstrates that the measured change in JG is purely a reversible consequence of the

applied stress, and not a transient effect. Also, 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 gate current density,

ΔJG(σ)/JG(0), for each applied gate bias and stress level, JG is averaged over the

duration of time the stress was held constant. Figure 5-3 shows ΔJG(σ)/JG(0) averaged

for all levels of compressive and tensile stress at VG = -0.25 V and -4 V. Error bars

86
representing the uncertainty in the measurement of ΔJG(σ)/JG(0) are three times the

standard deviation of the JG measurements over the duration when the stress was held

constant.

The sensitivity of JG to stress defined as the normalized change in JG per stress,

[ΔJG(σ)/JG(0)]/σ, is calculated from the slope of the weighted total least squares linear fit

of ΔJG(σ)/JG(0) versus stress, including uncertainty in JG at each stress increment. The

stress sensitivity of JG is plotted as a function of reverse gate bias in Figure 5-4.

Increasing the reverse gate bias is observed to decrease the sensitivity of JG to stress.

The sensitivity of JG to stress decreased from 1.7 ±0.3 %/100MPa at VG = -0.25 V to 0.6

±0.1 %/100MPa at VG = -4 V as shown in Figure 5-4. To interpret the 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 JG with increasing reverse

gate bias and compare the measurements to gate leakage transport models, the

experimentally determined 1D EAlGaN values discussed in Chapter 4 are used. Since the

2D edge effects complicate the EAlGaN profile under the gate for gate biases below VT,

the simple 1D model cannot be used. Therefore, we analyze the gate leakage

mechanism only for VG above VT. Simulations performed indicate that thermionic

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.

87
 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 compensation is [103-105]:

√
* + (5-1)

where,

√ (5-2)

C is a constant related to mobility and density of states, EA 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 concentration and position of the Fermi energy with respect to EA [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, the

concentration of acceptor levels is small compared to the number of donor levels and

excited electrons. The EA extracted 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 EA only represents the traps participating in emitting electrons to the

conduction band via the PF effect. Also, the trap levels are assumed to be located

88
physically close to the top surface of the AlGaN layer, under the gate, therefore the

traps are assumed to be filled, and only the emission is considered.

To determine the dominate gate leakage mechanism of the experimentally

measured devices, the JG versus VG curves (Figure 5-5) were measured from 300 K to

400K. Since PF emission is a thermal assisted process whose efficiency increases at

higher temperatures, the gate current was measured at temperatures larger room

temperature. The temperature and field dependence of JG were plotted in a PF plot

(plot of the natural logarithm of the gate current divided by the electric field versus

square root of the electric field) as shown in Figure 5-6. When plotted in this manner,

the linear region of the PF plot signifies that PF emission dominates the gate leakage

for that range of EAlGaN.

By taking the natural log of Equation 5-1, the 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. Then, 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

89
reverse tunneling current is included into the overall expression to satisfy the equilibrium

condition, JG(VG = 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 temperatures (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 (m’), is

√ (5-6)

Then, the permittivity is calculated from

(5-7)

giving a value of 5.88. Including the uncertainty in the measured JG of 3.3% from a

control measurement of 1200 simultaneous measurements, the uncertainty in the

extracted value of is determined by including the error in the linear fit when

calculating m’. The resulting uncertainty in is approximately ±0.16. So, for r = 1,

= 5.88 ±0.16.

Then, the trap activation energy 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 EA is calculated from the slope (m’’), and ln(C) is the y-intercept of the

linear fit to the plot in Figure 5-8, where

(5-9)

90
Hence,

(5-10)

EA was determined to be 0.37 eV and ln(C) = -14.23. The uncertainty in EA and ln(C) is

estimated by including the uncertainty of the linear fit when obtaining m’’. This gives an

estimate for the error of ±0.05 eV for EA and ±1.55 for ln(C).

The stress dependence of the PF current can be derived by first defining the

unstressed PF current for r = 1 as:

√
( ) ( ) (5-11)

In the PF expression, only EA 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, EAlGaN will not be affected by the externally

applied stress. Under these assumptions, the PF current under stress is given by

( ) √ ( )
( ) ( ) ( ) ( ) (5-12)

91
 where ΔEA(σ) is the change in trap energy level due to the applied mechanical

stress. The normalized change in PF current with stress is:

( ) ( ) ( ) ( )
( ) (5-13)
( ) ( )

Based on Equation 5-13, the expected normalized change in PF current for a

given amount of stress is constant independent of EAlGaN or VG. However, the

experimentally measured [ΔJG(σ)/JG(0)]/σ from wafer bending experiments decreases

with increasing reverse gate bias. Therefore, the simplistic model (r = 1 independent of

stress) fails to capture the correct trend observed experimentally.

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. The high

frequency permittivity of AlGaN is = 5.1 ±0.5, based on the high frequency

permittivities of AlN (4.6) and GaN (5.3) [108]. However, the 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 the 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 = 1.07 ±0.02 is extracted in order to provide

a more physical fit to the PF model. This value of r still signifies very high

compensation. Since the r value is adjusted to match the high frequency permittivity of

AlGaN, the EA value is also adjusted. Based on Equation 5-5 including r = 1.07 ±0.02,

the value of EA becomes 0.40 ±0.05 eV and ln(C) is -13.55 ±1.55.

Since r is no longer fixed at the limit of maximum compensation, when EA changes

with stress, r also will change with stress. Figure 5-9 shows a schematic of the trap

92
level change with stress, and how compensation affects PF emission. When EA

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 EA (tensile

stress), the opposite is true. Including the change in EA and change in r with stress (Δr)

the PF current under stress is written as

( ) √
( ) ( ) (5-14)
( )

The normalized change in JPF with stress is

( ) ( ( )) ( ) ( )√
( ) (5-15)
( ) ( )

Both ΔEA and Δr 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 EA

and r gives ΔEA = -0.26 ±0.07 meV/100 MPa and Δr = 0.0017 ±0.0001 /100 MPa.

Tensile stress decreases EA and compressive stress increases EA.

This result is unlike the Si/HfSiON system, where both tensile and compressive

stress decreased the trap energy level, increasing JG [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 EA. 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 EA, and compressive stress will tend to return the bond angles and lengths

back to equilibrium increasing EA.

93
 Figure 5-10 shows the simulated ( ) ( ) per 100 MPa calculated from

Equation 5-15 compared to experiment. Although we use EAlGaN in simulation, for the

purpose of plotting, the VG values are used to compare to experiment. Considering r

changing with stress provides a reasonable fit to experiment within the range of

experimental uncertainty. The VG range shown is from 0 to -2 V, since the

experimentally obtained 1D EAlGaN values are only valid until ~VT. It can be observed

that there is some small discrepancy in the fit at low VG. 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 EAlGaN (0.75 MV/cm). This

field should produce a significant forward PF current. However, at VG = 0 V, the net

current must be zero. Therefore, to balance the PF current, a reverse current (JR) of

equal and opposite magnitude should be present to balance the PF current at

equilibrium. The exact transport mechanism of the reverse current is not well

understood at this time, however Yan, et al. proposed that in equilibrium JR0
3/2
exp(α /EAlGaN) where α is a constant [94]. Figure 5-11 shows a schematic diagram

showing JPF and JR, assuming JR is assisted by bulk traps. In the PF plot (Figure 5-6),

the experimentally measured JG differs from the ideal linear fit. The difference between

the ideal linear extrapolated PF plot and the measured data is assumed to be the

reverse current. Figure 5-12 shows the ideal PF (JPF) current, reverse current (JR), and

the total measured gate current (JG), where

(5-16)

94
 The derived expression in Equation 5-15 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 current is written as:

( ) ( ) ( )
(5-17)
( ) ( ) ( )

Solving for ΔJG(σ)/JG(0) based on Equation 5-15 for ΔJPF(σ)/JPF(0) gives

( ) ( ) ( ) ( )√ ( ) ( )
* ( ) +
( ) ( ) ( )

( )
( ) (5-18)

Excluding the last term, ΔJR(σ)/JG(0), this expression is straight forward to

calculate. Since the exact mechanism of JR is not well characterized, interpreting the

stress dependence of JR is also not clear. However, making some simple assumptions

about ΔJR(σ)/JG(0) can provide a better fit to the experimental stress results. Figure 5-

13 shows the experimental fit including reverse current for two situations. First, the

ΔJR(σ)/JG(0) is neglected, but the calculation over estimates ΔJG(σ)/JG(0) at low VG.

Then, ΔJR(σ)/JG(0) is set to 1.5% to achieve a very good fit to the experimental data. It

is likely that JR may depend slightly with stress, in particular at very low VG. However,

more measurements at lower reverse gate biases will be needed to make a definitive

conclusion. The inclusion or omission of ΔJR(σ)/JG(0) only affects the fit at low VG.

Once EAlGaN increases enough to cause JPF >> JR, the first part of Equation 5-18

captures the physics of carrier transport.

95
 At voltages below threshold, EAlGaN at the gate edges continues to increase. Also,

the thickness of the AlGaN potential barrier reduces as shown in Figure 5-14. This

results in the probability of FN tunneling increasing. Around 3 MV/cm, the FN tunneling

current becomes significant [102]. The FN tunneling will occur at the gate edges, where

EAlGaN is the largest, in parallel with the PF tunneling in the middle of the gate. At

extremely large EAlGaN values where degradation occurs, the majority of JG will likely be

dominated by FN tunneling. The stress 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 JG, but can cause defect

formation.

Summary

We have developed a model to explain the gate leakage mechanism in an

AlGaN/GaN HEMT. This model explains the experimentally observed decreasing stress

dependence of JG with increasing reverse gate bias at a given stress. Tensile

(compressive) stress increases (decreases) JG for all applied gate biases (VG = -0.1 to -

4 V). We conclude, based on our model, that both PF and a reverse current

mechanism are present for VG > VT . Table 5-1 sumarizes the key parameters extracted

to match the experimentally measured data. Below VT, EAlGaN at the gate edges

increases due to 2D edge effects. FN tunneling current likely dominates for very large

reverse VG, where EAlGaN > 3 MV/cm. At the critical voltage, JG is dominated by FN

tunneling at the edges of the gate, which will have negligible incremental stress

dependence, but defect formation can occur.

96
Table 5-1. Key parameters extracted to match experimental data
Parameter Maximum Compensation Reduced Compensation
r 1 1.07 ±0.04
Δr - 0.0017 ±0.0001 /100 MPa
EA 0.37 ±0.05 eV 0.4 ±0.05 eV
ΔEA - -0.26 ±0.07 meV/100 MPa
εAlGaN 5.88 ±0.16 5.10
ln(C) -14.23 ±1.55 -13.56 ±1.55

97
 -4
10
0 10
|JG(mA/mm)

-5
JG 10
-1
10

|IG(A)
Vcrit
-6
10
-2
10 -7
10

-3 -8
10 10
0 -20 -40 -60 -80
VGS (V)
Figure 5-1. Electrical step stress measurement showing the breakdown of JG at the
critical voltage.

98
 (a)
10.0 400
VG = -0.25 V
7.5 300
5.0 200

Stress (MPa)
ΔJG/JG (%)

2.5 100
Tension
0.0 0
Compression
-2.5 -100
-5.0 -200
-7.5 -300
-10.0 -400
0 500 1000 1500
Time (s)
(b)
9 400
VG = -4 V
300
6
200

Stress (MPa)
ΔJG/JG (%)

3
100
Tension
0 0
Compression
-100
-3
-200
-6
-300
-9 -400
0 500 1000 1500
Time (s)
Figure 5-2. Normalized change in JG for incrementally increasing and decreasing
uniaxial stress for (a) VG = -0.25 V and (b) VG = -4 V.

99
 (a)
9
VG = -0.25 V
6

3
JG/JG (%)

-3

-6

-9
-400 -200 0 200 400
Stress (MPa)
(b)
9
VG = -4 V
6

3
JG/JG (%)

-3

-6

-9
-400 -200 0 200 400
Stress (MPa)
Figure 5-3. ΔJG(σ)/JG(0) averaged for all levels of compressive and tensile stress at VG
= -0.25 V and -4 V. Uncertainty comes from three standard deviation from the
measurement of ΔJG(σ)/JG(0) over the duration stress was held constant.

100
 2.0
[ΔJG/JG]/σ (%/100MPa)

1.5

1.0

0.5

0.0
-4 -3 -2 -1 0
VG (V)
Figure 5-4. Experimentally measured stress sensitivity of JG per 100 MPa of stress, as
a function of reverse gate bias.

101
 0.1
400 K
0.01

1E-3
JG (A/cm)

1E-4
300 K
1E-5

1E-6

1E-7

1E-8

1E-9
-4 -3 -2 -1 0

VG (V)
Figure 5-5. Measured gate leakage current density versus gate voltage from T = 300 K
to 400 K for unstressed AlGaN/GaN HEMT.

102
 VG (V)
0 -0.5 -1 -1.5 -2

-12 400 K

-14

-16
ln(J/|E|)

-18 300 K

-20

-22

-24

-26
9000 10000 11000 12000
1/2 1/2
|E| [(V/m) ]
Figure 5-6. PF plot showing linear fit to the measured data for T = 300 K to 400 K.

103
 0.0010

0.0008 m’

0.0006 R2 = 0.8864
m

0.0004

0.0002

0.0000
0.000 0.001 0.002 0.003

1/T (1/K)
Figure 5-7. The slope of the PF plot (m) plotted versus 1/T. The slope of this plot (m’)
is used to calculate .

104
 0

-5

-10
ln(C)
-15
b

-20
m’’
R2 = 0.9511
-25

-30
0.000 0.001 0.002 0.003

1/T (1/K)
Figure 5-8. The y-intercept of the PF plot versus 1/T. The slope of this plot (m’’) is used
to calculate the trap energy level.

105
 Compression Tension
reduced emission increased emission

EA -ΔEA
EA
EA
EA +ΔEA EC EC

increased compensation reduced compensation

(r decreases) (r increases)
Figure 5-9. Schematic of change in EA with compressive and tensile stress.
Compressive stress increases EA, decreasing r, increasing compensation,
and reducing PF emission. The opposite is true for tensile stress.

106
 2.0
[ΔJG/JG]/σ (%/100MPa)

Simulation

1.5

1.0

Experiment
0.5

0.0
-2.0 -1.5 -1.0 -0.5 0.0

VG (V)
Figure 5-10. Simulated stress sensitivity of JG per 100 MPa of stress, including EA and r
changing with stress, as a function of reverse gate bias.

107
 Ni AlGaN GaN

JPF

JG

JR

EC
Figure 5-11. Schematic of JG, JPF, and JR assuming JR is a bulk-assisted mechanism
driven by the PF emission current for VG = -2 V and other parameters from
Table 4-1.

108
 0.01

1E-3
J (A/cm )

JPF
2

1E-4 JR

JG
1E-5
-1.2 -0.9 -0.6 -0.3 0.0

VG (V)
Figure 5-12. Measured JG, ideal JPF obtained by linear extrapolation of the linear PF fit,
and JR calculated by the difference between JPF and JG.

109
 Experimental Fit
2.0
ΔJR(σ)/JG(0) = 0
[ΔJG/JG]/σ (%/100MPa)

1.5

1.0
Experimental Fit
ΔJR(σ)/JG(0) = 1.5%
0.5

Experiment
0.0
-2.0 -1.5 -1.0 -0.5 0.0

VG (V)
Figure 5-13. Simulated stress sensitivity of JG at 100 MPa of stress, including JR, as a
function of reverse gate bias. JR not changing with stress overestimates the
stress sensitivity. However, ΔJR(σ)/JG(0) = 1.5% closely matches experiment.

110
 a. 15
Center of Gate
Ni AlGaN GaN
12 VG = -10 V

9 VG = -4 V
EC (eV) VG = -2 V
6 VG = 0 V

0
-0.02 -0.01 0.00
y (m)
b. Edge of Gate
15
Ni AlGaN GaN
12
VG = -10 V
VG = -4 V
9
EC (eV)

6 VG = -2 V
VG = 0 V
3

0
-0.02 -0.01 0.00
y (m)
Figure 5-14. Energy band diagrams showing the reduction in the AlGaN barrier
thickness at the gate edges for VG well below VT.

111
 CHAPTER 6
CONCLUSION

Overall Summary

A systematic study of the effect of mechanical stress on AlGaN/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 technique was developed to apply external stress to small

(~1 cm2) wafer samples while simultaneously taking electrical measurements. A four-

point wafer bending setup applied stress to the small sample, which was attached to a

high carbon stainless steel strip 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 measurements (4 to -

40,000) have been reported in literature (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.

This gauge factor indicates a small stress 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 elastic and piezoelectric coefficients of GaN and AlN.

112
 In order to determine the dominant gate leakage mechanism, a thorough

investigation of the relationship between EAlGaN and VG was presented. In a simple

model of an ideal 1D device, EAlGaN has a linear relationship to VG above VT, and

saturates below VT. Experimentally determined parameters were used in the 1D

calculation to model the actual device. Adjusting σint and ns based on experimental

measurements provided an accurate VG versus EAlGaN relationship above threshold.

Also, a comprehensive 2D simulation was performed to provide insight on EAlGaN for

large reverse biases much below VT. The 2D results proved the 1D model accurate for

VG > VT. However, below threshold, although EAlGaN saturates in the middle of the gate,

at the gate edges, EAlGaN continues to increase.

PF conduction was proven to be the dominant gate leakage transport mechanism

above threshold. Bias and stress dependence of JG was measured simultaneously. A

decreasing stress dependence of JG with increasing reverse gate bias was observed.

Tensile (compressive) stress increases (decreases) JG for all applied gate biases (VG =

-0.1 to -4 V). Compressive stress increases EA, and tensile stress decreases EA. Since

stress shifts the trap energy level, the compensation parameter r is also affected by

stress. A reverse tunneling current was included in the model to balance the forward

PF current at equilibrium. However, the reverse tunneling current only is important at

extremely small gate biases. At very large increasing reverse biases, EAlGaN at the gate

edges continues to increase, which decreases the tunneling barrier making FN

tunneling more probable. When degradation occurs, the contribution to JG is dominated

by FN tunneling at the edges of the gate.

113
 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 mechanical 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.

More measurements of ΔJG(σ)/JG(0) data points need to be obtained at low bias (-0.1 V

< VG 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 insight into 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 there is no body contact in the AlGaN/GaN

HEMT devices making other characterization methods invalid. A more direct

114
measurement of the effect of stress on AlGaN/GaN HEMT traps can help to engineer

more reliable, better performing devices.

115
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 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 investigating the stress

dependence of III-V devices. He received his Ph.D. from the University of Florida in the

fall of 2011.

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