AlGaN/GaN HEMT DC Simulation
by
Ruocan Wang
A thesis submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Auburn, Alabama
May 3, 2014
Keywords: GaN HEMT, TCAD simulation, high power devices
Copyright 2014 by Ruocan Wang
Approved by
Guofu Niu, Professor of Electrical and Computer Engineering
Fa Dai, Professor of Electrical and Computer Engineering
Bogdan Wilamowski, Professor of Electrical and Computer Engineering
Minseo Park, Professor of Physics
Abstract
Increasing demand in high power and high frequency semiconductor devices has pro-
moted the rapid development of microwave power devices using GaN and SiC. Character-
istics like high breakdown voltage and high electron mobility enable AlGaN/GaN HEMT
the possibility to be utilized as high power RF devices. However, obstacles prevent the
widely utilization of AlGaN/GaN transistor in this field. It has been generally recognized
the superabundant trap density in GaN and AlGaN material limits the performance of the
devices by bringing in reliability issues like current collapse and gate-lag. Lattice mismatch
in GaN and AlGaN and abrupt heterojunction interface of AlGaN/GaN contribute to the
unstable performance while high voltage is applied to drain contact which will cause high
field between thin layer of AlGaN/GaN interface.
An overall introduction to HEMT physics will be presented in chapter 2 of this work.
Attention will be paid to the performance degradation analysis caused by issues such as trap-
ping effect, self-heating, displacement damage and high voltage induced lattice mismatch.
The chapter 3 of this work presents a process to use TCAD simulation tool to match
the simulation results with measurements from real devices starting from building device
structure. Adjustments of parameters including gate barrier height, electron mobility, po-
larization coefficients and parasitic resistance will be made to fit the measurements.
ii
Acknowledgments
I would like to express thanks to my professor Dr. Guofu Niu for giving me the opportu-
nity to finish my master?s thesis. I would like to thank Dr. Niu for the continuous patience,
encouragement and academic support he offers during my master?s program study.
I am grateful for my group members for all the help they provide, and kindly accompany
through the long, tough but meaningful years of study in Auburn. I would like to express
thanks to Dr. Park and his students Fei and Henry for their support in device measurement.
Last but not the least, I would like to express my gratefulness to my parents for their
love, patience, encouragement and support since I was born. Without them, I will not be
able to get so far.
iii
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Brief introduction of wide band gap (WBG) material . . . . . . . . . . . . . 2
2.2 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 GaN(gallium nitride) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 AlN (aluminum nitride) and AlGaN (aluminum gallium nitride) . . . 6
2.3 Polar material and polarization effect . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Mechanism of GaN HEMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Traps in GaN HEMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 GaN bulk traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2 AlGaN barrier traps . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.3 Surface traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Effects of traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6.1 Current collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6.2 Gate-lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 AlGaN/GaN HEMT simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Device Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Device structure building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
iv
3.2.2 Charge calculation and placement . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Conversion from cylindrical coordinate to rectangular coordinate . . . 37
3.2.4 Leakage current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.5 Convergence control . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.6 Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 Simulation result matching measurement . . . . . . . . . . . . . . . . . . . . 52
3.4 Gate scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
v
List of Figures
2.1 Intrinsic electron concentration of Si, Ge, GaN and GaAs respect to temperature
[1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Crystal structure of Ga face GaN [1]. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Polarization effect in Ga-face and N-face GaN [9]. . . . . . . . . . . . . . . . . 9
2.4 2DEG sheet charge density as a function of AlGaN barrier thickness at room tem-
perature from an AlGaN/GaN diode structure with Schottky contact on AlGaN
and Ti Ohmic contact on GaN[4]. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 2DEG sheet charge density as a function of AlGaN Al composition [4]. . . . . . 12
2.6 Band diagram of heterojunction interface and charge distribution [1]. . . . . . . 13
2.7 Traps in crystal, Left: traps caused by dislocation, Right: traps caused by missing
row of atoms [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.8 Left: point defect traps, Right: volumetric dislocation. . . . . . . . . . . . . . . 16
2.9 Current collapse in GaN HEMTs. Id ?Vd before (i) and after (ii) a drain bias of
20 V is applied [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.10 Current collapse in GaN HEMTs, with (solid) and without (dash) light illumi-
nation [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.11 Current recovery dependence of wavelength of light illumination. . . . . . . . . 20
vi
2.12 Pulsed Id ?Vd characteristics for an unpassivated GaN HEMT [25]. . . . . . . . 20
2.13 Pulsed Id ?Vd characteristics of a passivated GaN HEMT [25]. . . . . . . . . . 21
3.1 HEMT device die photo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Schematic diagram of AlGaN/GaN HEMT studied in this work. . . . . . . . . . 24
3.3 Refined mesh at heterojunction interface. . . . . . . . . . . . . . . . . . . . . . 25
3.4 SumofspontaneousandpiezoelectricpolarizationinAlGaNwithAlmolefraction
is 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Comparison of Id?Vd simulation results from manual charge placement and built
in model in rectangular coordinate. . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.6 Cross-sectional view of cylindrical HEMT along vertical direction (half structure). 37
3.7 Top view of drain and channel region of cylindrical HEMT. . . . . . . . . . . . 38
3.8 Comparison of cylindrical and rectangular HEMT Id ?Vd with donor trap and
n-type doped buffer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.9 HEMT structure with n-type doped buffer. . . . . . . . . . . . . . . . . . . . . 41
3.10 Id ?Vg curve of n-type doping buffer in linear scale (Vd = 5V). . . . . . . . . . 42
3.11 Id ?Vg curve of n-type doping buffer in logarithmic scale (Vd = 5V). . . . . . . 42
3.12 Id ?Vg measurement in linear scale (Vd = 5V). . . . . . . . . . . . . . . . . . . 43
3.13 Id ?Vg measurement in logarithmic scale (Vd = 5V). . . . . . . . . . . . . . . . 44
3.14 Leakage current in buffer region and substrate (n-type doped buffer). . . . . . 44
vii
3.15 Layer structure of HEMT with p-type doped buffer. . . . . . . . . . . . . . . . 45
3.16 Id ?Vg curves of p-type doped buffer and n-type doped buffer HEMT in linear
scale (Vd = 5V). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.17 Id ? Vg curves of p-type doped buffer and n-type doped buffer HEMT in loga-
rithmic scale (Vd = 5V). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.18 Current density of a HEMT with p-type doped buffer. . . . . . . . . . . . . . . 47
3.19 Comparison of Id ?Vd simulation results with and without donor trap. . . . . . 51
3.20 Comparison of Id ?Vd simulation results with trap of various energy levels. . . . 51
3.21 Comparison of Id ?Vg measurement from sample A and simulation results with
various barrier heights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.22 Id ?Vg measurement of sample A compared with simulation. . . . . . . . . . . . 53
3.23 Transconductance gm measurement of sample A compared with simulation. . . . 54
3.24 Comparison of Id ?Vd measurement and simulation in tunneling contact model
mt = 0.01 m0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.25 Comparison of Id ?Vd measurement and simulation in tunneling contact model
mt = 0.1 m0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.26 Id ?Vd simulations with gate length equaling 40 um. . . . . . . . . . . . . . . . 57
3.27 Id ?Vd simulations with gate length equaling 10 um. . . . . . . . . . . . . . . . 58
3.28 Id ?Vd simulations with gate length equaling 1 um. . . . . . . . . . . . . . . . . 59
3.29 Schematic of HEMT with gate length being shrunk to 10 um. . . . . . . . . . . 59
viii
3.30 Schematic of HEMT with gate length being shrunk to 1 um. . . . . . . . . . . . 60
3.31 Comparison of Id ?Vg from HEMTs with gate length being shrunk down from
40 um to 1 um. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.32 Comparison of normalized Id ?Vg from HEMTs with gate length being shrunk
down from 40 um to 1 um. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.33 Off state drain current density as gate length shrunk from 40 um to 1 um. . . . 61
3.34 Transconductance as gate length shrunk from 40 um to 0.1 um. . . . . . . . . . 62
ix
List of Tables
2.1 Properties of various semiconductors [1]. . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Thermal conductivity of various semiconductors. . . . . . . . . . . . . . . . . . 5
3.1 Dimension of HEMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Spontaneous polarization in AlGaN and GaN. . . . . . . . . . . . . . . . . . . . 31
3.3 Piezoelectric polarization coefficients and stiffness constants in AlGaN. . . . . . 31
3.4 Strain parameters and relaxation parameter. . . . . . . . . . . . . . . . . . . . . 31
3.5 Piezoelectric polarization and spontaneous polarization in AlGaN. . . . . . . . . 34
3.6 Piezoelectric polarization and spontaneous polarization charge densities in AlGaN. 34
x
Chapter 1
Introduction
Recent progress in research of wide band gap material has been successful in attracting
attention in application of wide band gap material in device fabrication during the last 10
years. Compared to the most popular semiconductor materials, the majority of the WBG
(wide band gap) material utilizations are in optoelectronics such as shortwave light emitting
diode and high power electronic devices. Another application of WBG material is RF device
that requires rapid carrier transport which results from the formation of two dimensional
electron gas due to polarization effect [1].
This thesis consists of four chapters. The first chapter presents the motivation and
outline of this work. A brief background introduction is presented in Chapter 2 including
wide band gap material properties, polar material, polarization effect and mechanism of GaN
HEMT. Simulation is illustrated in Chapter 3 consisting of building structure, specifying
parameters, fitting measurement and gate scaling. Fitting of measurement and gate scaling
are applied to Id ?Vd and Id ?Vg curves.
1
Chapter 2
Background
In this chapter, a brief introduction of WBG material characteristics is presented in the
first and second sections for the goal of further discussion of HEMT models mentioned in
Chapter 3. Most of the attention is drawn on GaN and AlGaN, which are the predominant
materials used to fabricate HEMT this thesis concerns.
2.1 Brief introduction of wide band gap (WBG) material
The predominant advantage of wide band gap materials over other semiconductors is
large band gap energy Eg which enables their application in high power devices where high
electric breakdown field is required. Table 2.1 reports material properties of AlN, SiC,
GaN, GaAs and Si including band gap, electric breakdown field, saturated electron velocity,
electron mobility, lattice constant and so on.
Intrinsic carrier concentration increases along with temperature. When the intrinsic
carrier concentration increases above 1015cm?3, the material is unsuitable for electronic
devices [1]. Compared with other semiconductors like Si, intrinsic concentration of wide band
gap material is lower under same temperature which offers WBG material the potential to
operate under high temperature. Figure 2.1 shows intrinsic carrier concentrations of several
semiconductors respect to temperature. GaN intrinsic carrier concentration at 300K is below
104cm?3 which is several orders of magnitude smaller than that of Si.
2
Figure 2.1: Intrinsic electron concentration of Si, Ge, GaN and GaAs respect to temperature
[1].
3
Property GaN AlN InN SiC Si GaAs
Band Gap (Eg) [eV] 3.44 6.2 1 3.26 1.12 1.43
Electric breakdown field
(Ec) [MV/cm]
3.0 1.4-1.8 3.0 3.0 0.4 0.5
Saturated electron velocity
(vsat)[107cm/s]
2.5 1.7 4.5 2.0 1.0 1.0
Electron mobility
(?n)[cm2/V ?s?1]
2000 135 3200 700 1500 8500
Electron effective mass
(mc)[m0 ]
0.22 0.44 0.11 0.2 1.18 0.63
Electron effective mass
(mv)[m0 ]
0.8 3.53 0.27 1.0 0.55 0.52
Lattice constant 3.175 3.11 3.533 3.073 5.431 5.653
Table 2.1: Properties of various semiconductors [1].
2.2 Material properties
2.2.1 GaN(gallium nitride)
In the HEMT studied in this thesis , GaN is used to construct the bulk region and
channel region considering its electric properties. It is also a dominant material compositing
HEMT channel and buffer in commercial HEMT fabrication where fast carrier transport and
high breakdown voltage are desired. Moreover, WBG materials have large saturation velocity
which allows them to operate under high electric field. Although reported outstanding
characteristics make WBG materials suitable for working under high electric field, WBG
materials still have disadvantages that cannot be ignored. Compared with conventional
semiconductor material for example GaAs, relatively low electron mobility in bulk GaN is
the main shortage in fabricating HEMT. The bulk GaN electron mobility is about 800 - 900
cm2/V ?s?1 which is one order lower in magnitude than GaAs which has mobility of 8500
cm2/V ?s?1.
Though low in intrinsic material electron mobility, the electron mobility in heterojunc-
tion interface of AlGaN/GaN is high enough to achieve good performance. At the hetero-
junction interface between GaN and AlGaN, a relatively high electron concentration can
4
Property GaN AlN InN SiC Si GaAs
Thermal conductivity(?)[W/cm?K] 1.3-2.1 2.85 0.45 3.7-4.5 1.5 0.5
Table 2.2: Thermal conductivity of various semiconductors.
be achieved as a result of polarization effect even without intentional doping. The high
concentration electron at the interface due to polarization effect is called two-dimensional-
electron-gas (2DEG). This sheet of electron locates at the top of GaN layer which is channel
of HEMT provides path for current flowing from drain to source. Electron mobility in chan-
nel region is reported to be between 1200 cm2/V ?s?1 to 2000 cm2/V ?s?1 which is higher
than that in the bulk region of which electron mobility is reported to be 800 cm2/V ?s?1 [1].
Another advantage of WBG materials over conventional semiconductors is their large
thermal conductivity (?). High thermal conductivity is essential to the high temperature
performance of a device. Thermal conductivity reveals the ability of a material to extract
dissipated power away from the device which further enables device operation under high
temperature. Table 2.2 shows thermal conductivities of several semiconductors at 300K in-
cluding WBG materials and conventional semiconductors such as Si and GaAs. Conventional
semiconductors, particularly GaAs has poor thermal conductivity of 0.5 W/cm?K. On the
contrary, WBG materials, for instance, SiC and AlN are excellent in power extracting with
high thermal conductivities of 3.7-4.5 W/cm?K and 2.85 W/cm?K respectively.
Thermal conductivity of GaN is reported to be 1.7W/cm?K by Slack [2]. However, in
reality, the measured thermal conductivity of GaN reveals a peak value of 1.3 W/cm?K which
is slight lower than that reported by Slack. Research in this field indicates that the effects of
impurities and dislocations are responsible for the decrement of thermal conductivity. The
lattice constant of SiC and GaN are quite similar, therefore SiC can be used as substrate for
Si to grow on since utilizing of high thermal conductivity of SiC will enable device cooling
off effectively.
5
2.2.2 AlN (aluminum nitride) and AlGaN (aluminum gallium nitride)
Being one of the most important binary material in III-V material family, AlN is an
insulator with a band gap of 6.2eV which is difficult for electron in valence band to be
excited. AlN can be used as nucleation layer between SiC or sapphire substrates and bulk
GaN since intrinsic AlN has high thermal conductivity which will help dissipated heat to be
removed from device [3]. Additionally, nucleation layer can modify the breakdown voltage of
GaN buffer layer. Young Chul Choi?s paper [3] shows the thickness of AlN nucleation layer
has dominant influence on the breakdown voltage of devices.
Ternary compound of AlN such as AlGaN is widely used in heterojunction of HEMT.
Highly doped AlGaN is source of electron in GaN channel in devices where AlGaN is used
as barrier layer on top of GaN. Equation (2.1) shows the calculation of model parameters of
ternary compound AlGaN using corresponding parameters of AlN and GaN.
PAxB1?xN = x?PAN +(1?x)?PBN (2.1)
In Equation (2.1), PAxB1?xN stands for a certain parameter of AxB1?xN that needs to be
calculated from the corresponding ones of binary compound AN and BN. Parameters of AlN
and GaN include spontaneous polarization, elastic constants, piezoelectric coefficients which
will determine the calculation of polarization charge density and 2DEG density. Calculation
of charge densities will be illustrated in the next subsection.
2.3 Polar material and polarization effect
Three crystal structures exist in Nitride compounds: wurtzite, rock-salt and zinc-blende.
In electronic devices, Wurtzite crystal material is prevalently used. Its crystal structure is
called the wurtzite crystal structure which is a member of the hexagonal crystal system
6
Figure 2.2: Crystal structure of Ga face GaN [1].
and consisting of tetrahedrally coordinated zinc and sulfur atoms that are stacked in an
ABBABBABB pattern.
Figure 2.2 shows the crystal structure of Ga-face GaN. In GaN material, as shown in
Figure 2.2, each Ga atom is bonded by the other four adjacent N atoms while each N atom
is bonded by other four adjacent Ga atoms as well. The solid line represents the chemical
bond between atoms and dash line is used to indicate that atoms are in the same plane. The
wurtzite crystal structure then can be departed into identical segments that periodically
repeat in space domain. The horizontal direction is parallel to the plane of GaN growth.
The vertical direction is along the direction that GaN grows.
It can be observed that the wurtzite crystal structure is not central symmetric along
the vertical direction which is called c-axis [0001]. Net volume dipole moment is nonzero
in the nitride crystal even when no external electric field is applied to the structure. The
polarization effect caused by non-central-symmetric structure in GaN is called spontaneous
7
polarization effect. Spontaneous polarization effect also exists in AlGaN, which is different in
magnitude from that of GaN. The difference of spontaneous polarization of GaN and AlGaN
is one source of 2DEG.
Depending on the kind of atom of the basal layer, GaN can be divided into Ga-face and
N-face. In Ga-face GaN, Ga atoms consist the top layer along the direction of the growth and
Ga-face GaN corresponds to [1000] polarity. Ga-face GaN and N-face GaN are different in
chemical, physical and electrical properties. The spontaneous polarization for GaN and AlN
is negative for layers grown in the [0001] direction and increases in magnitude by going from
GaN to AlN [4]. Direction of polarization affects the sign and amount of polarization charge
at heterojunction interface, which will further influence the sign and density of polarization
induced charge and 2DEG. In this work, Ga-face GaN is used for simulation since most GaN
is Ga-face by nature.
Piezoelectric polarization is a result of the strain or stress of the crystal lattice due to
physical distortion while layers are connected at the heterojunction interface. Due to the
differences in the lattice constants of AlN, GaN and AlGaN, growing AlGaN on GaN leads
to compressive strain in AlGaN [14]. A few other papers reports in detail the direction of
polarization in different combination of materials [9], [10].
At an abrupt interface, the polarization sheet charge density is defined as the difference
in charge densities between the upper and lower layers. Equation (2.2) shows the way of
calculation of charge density at the heterojunction interface due to spontaneous polarization
and piezoelectric polarization.
? = P(AlGaN)?P(GaN) = PSP(AlGaN)+PPE(AlGaN)?PSP(GaN) C/cm2 [1]
(2.2)
8
Figure 2.3: Polarization effect in Ga-face and N-face GaN [9].
9
PPE = 2a?a0a
0
(e31 ?e33C13C
33
) C/cm2 [1] (2.3)
PSP(x) = ?0.052x?0.029 C/cm2 [1] (2.4)
PSP(0) = ?0.029 C/cm2 [1] (2.5)
?(x) = (2a?a0a
0
(e31 ?e33C13C
33
)+PSP(x)+PSP(0))? 1e /cm2 [1] (2.6)
Equation (2.3) shows the calculation of piezoelectric polarization using piezoelectric
coefficients and elastic constants. In Equation (2.3), e33 and e31 are piezoelectric coefficients,
C33 and C13 are elastic constants. Piezoelectric coefficient e33 and e31 are related to lattice
constanta0 and ax. Equation (2.4) and (2.5) show the calculation of spontaneous polarization
in AlGaN and GaN respectively which are dependent of Al mole composition x. Unit of
piezoelectric coefficient and spontaneous coefficient is C/cm2 while unit of elastic constants
is Pa. Values of piezoelectric coefficient, elastic constants and spontaneous polarization
are presented in comparison of charge placement methods in Chapter 3. The density of
polarization induced charge is equal in amount to the sum of piezoelectric polarization charge
and spontaneous polarization charge but negative in sign in order to maintain the charge
neutrality in whole structure. Equation (2.6) shows the calculation of amount of polarization
induced charge density. The first term in Equation (2.6) is equal to Equation (2.3) which
10
indicates the amount of piezoelectric polarization in AlGaN. The second term PSP(x) and
third term PSP(0) indicate spontaneous polarization in AlGaN and GaN respectively. Values
of piezoelectric coefficients, spontaneous coefficients and elastic constants used for simulation
are provided in Chapter 3.
Figure 2.3 shows signs and locations of polarization induced charges in different hetero-
junction structures. In the case of Ga-face AlGaN/GaN heterojunction with AlGaN on the
top, sum of polarization induced charge is positive which is shown in Figure 2.3 b). Free
electrons will accumulate at the GaN top to compensate polarization induced charge to hold
neutrality. These electrons will form a 2DEG with a sheet carrier concentration ns by as-
suming that the AlGaN/GaN band offset is reasonably high and that the interface roughness
is low.
Figure 2.4: 2DEG sheet charge density as a function of AlGaN barrier thickness at room
temperature from an AlGaN/GaN diode structure with Schottky contact on AlGaN and Ti
Ohmic contact on GaN[4].
.
11
Figure 2.5: 2DEG sheet charge density as a function of AlGaN Al composition [4].
Several researchers have made progress in exploring the mechanism of 2DEG formation.
These conjectures indicate that the source of 2DEG includes piezoelectric doping [7], polar-
ization effects coupled with thermal generation [9], unintentional impurities in the AlGaN
[11] and donor like traps or states in AlGaN barrier [5]. Though no conclusion about source
of 2DEG has been made, properties of AlGaN barrier layer has significant influence on 2DEG
density. Figure 2.4 shows measurement of 2DEG as a function of AlGaN barrier thickness
from an AlGaN/GaN diode structure with Schottky contact on AlGaN and Ti Ohmic con-
tact on GaN [4]. Measurement of 2DEG density is obtained by C-V measurement. From
Figure 2.4 it can be observed that 2DEG forms only when AlGaN barrier thickness is above
certain threshold which is about 3nm. Figure 2.5 indicates 2DEG density as a function of
Al composition in linear scale under 13K. Despite that physics of formation of 2DEG is not
fully understood, it can be observed that 2DEG is strongly controlled by AlGaN barrier
thickness and Al composition.
12
2.4 Mechanism of GaN HEMT
Figure 2.6: Band diagram of heterojunction interface and charge distribution [1].
Figure 2.6 shows the band diagram of AlGaN/GaN heterojunction interface. In Figure
2.6, negative charge ?pol in the upper layer of AlGaN is the sum of piezoelectric and sponta-
neous polarization charge. The positive charge ?surf represents the donor like surface state
which will compensate negative polarization charge of AlGaN. Positive charge ?int represents
the net polarization charge at the AlGaN/GaN heterointerface. Since polarization charge is
positive in AlGaN lower layer and is larger in magnitude than negative polarization charge in
GaN, the sign of ?int is positive. In Figure 2.6, at AlGaN/GaN interface, conduction band
is below Fermi level of AlGaN which indicates accumulation of large amount of electrons
13
at interface. Negative charge ?2DEG represents the two dimensional electron gas which is
induced by the excess positive charge in AlGaN/GaN heterointerface. This high density of
electron with high electron mobility plays the role of conducting current.
Density of 2DEG can be controlled by applying voltage to gate contact which is located
at the top of the structure. While no voltage applied, Fermi level Ef lies at 0 voltage as
shown in Figure 2.6. If the gate contact is negatively biased, Ef will go down to negative
value which will decrease electron density. As higher negative bias applied to gate contact,
eventually Ef will be below conduction band energy level Ec which will result in depletion of
2DEG. The negative voltage which leads to device pinch-off is called threshold voltage VT.
2.5 Traps in GaN HEMT
Researches show that traps in GaN are one of the essential factors that cause the current
degradation in GaN HEMTs. Studies indicate that trapping and de-trapping effect are
responsible for the increment of formation of quasi-static charge distribution that makes
the current-voltage characteristics at microwave frequencies lower than under direct current
condition [12]. In this section, a detail discussion in trap definition, types of traps, spatial and
energy locations of traps and their effects in GaN I-V characteristics will be demonstrated.
Figure 2.7 and Figure 2.8 show various traps in crystal structure [1]. One of the origin of
traps is the limitation of hetero epitaxy growth technology. Traps in the bulk could be result
of dislocation, missing rows of atoms, atom vacancy, self interstitial and impurity interstitial.
At heterointerface, traps are generated with high possibility due to lattice constrain occurring
between different layers. Other possible trap locations inside the AlGaN/GaN layer are first
reported by Khan et al [12], [1] including:
? the semi-insulating substrate(in the case of growth on SiC)
? at the interface between GaN and the substrate (either sapphire or SiC)
? in the non-intentional-doped high-resistivity GaN buffer (deep traps result from good
insulation)
14
Figure 2.7: Traps in crystal, Left: traps caused by dislocation, Right: traps caused by
missing row of atoms [1].
? at the AlGaN/GaN interface
? in the AlGaN barrier layer (bulk trap)
Although sources of traps, trap properties and their effects are not fully understood,
controlling of traps is essential to the performance of devices. The following subsections will
demonstrate the main kinds of traps in HEMT and degradation involved by those traps.
2.5.1 GaN bulk traps
Bulk traps are also called deep level traps. Typically, GaN buffer region has a back-
ground electron concentration due to the presence of oxygen and nitrogen vacancies [13].
SourceofoxygenisimpuritiespresenceinNH3 andmetal-organicprecursorsusedinMOCVD
growth and residual water vapor in MBE or MOCVD chamber [14]. Those presence of elec-
trons in bulk GaN region provide path for current flowing in substrate and furthermore cause
buffer or substrate leakage which will result in degradation in pinch-off characteristics.
In order to achieve good insulation in bulk region, Fermi-level of GaN in bulk region is
required to be located at the intrinsic Fermi-level of GaN. Although GaN of high purity has
Fermi-levelthatisjustlocatedattheintrinsicFermi-level, itisimpossibletoobtainextremely
15
Figure 2.8: Left: point defect traps, Right: volumetric dislocation.
pure GaN in real fabrication process. The idea here is to minimize electron concentration
of bulk region, which in another way is to pin the Fermi-level of bulk GaN close to the
intrinsic Fermi-level. That is the main reason to introduce acceptor impurity into GaN
bulk to compensate with residual electron, and furthermore maintain good insulation. From
fabrication point of view, compensation process will be introduced by adding acceptor-like
impurities which is the dominant source of deep traps in GaN bulk region. The accurate
properties of deep traps are still unclear. Various papers on photo ionization report that
GaN buffer layer that grown for GaN MESFET and HEMT have deep traps are 1.8 eV and
2.8 eV below the conduction band as the two main trap centers [15], [16], [17], [18].
2.5.2 AlGaN barrier traps
Recent studies do not indicate much detail and progress in AlGaN barrier traps. Re-
searches report the existence of AlGaN barrier trap with an activation energy of 0.57 eV
from the conduction band and is responsible for the performance degradations in [1] and
[18]. Those traps provide path between gate and channel that will further deplete channel
current carriers which finally leads to degradation of drain current.
16
2.5.3 Surface traps
Another influential trap in AlGaN/GaN HEMT is the surface trap or surface donor
like state which is considered to be the main contributing cause of degradations including
gate-lag and DC to RF dispersion. Although evidence of existence of surface trap in Al-
GaN/GaN HEMT is demonstrated in various papers; the exact type, accurate energy level
and mechanism remain unclear [19].
Cause of surface traps on the top layer of AlGaN is the strong strain between GaN cap
layer and AlGaN barrier layer. Also, under high voltage beneath gate region traps are gen-
erated since large stress is induced by high field [23], [24]. Moreover, crystallographic defects
are formed when elastic energy exceeds critical value, large amount of defects will be gen-
erated at the heterojunction interface due to lattice mismatch. Those traps are responsible
for performance degradation.
Surface traps can be classified into two sorts: intrinsic traps and defects related states
[1]. The term intrinsic means that these states will exist even on an ideally perfect surface
without defects. They correspond to solutions of Schrodinger?s equations with energy levels
within the forbidden gap or imaginary values of the wave vector k: the wave functions
are evanescent waves that decay exponentially with distance and exist only at the surface.
Extrinsic trap, on the contrary is related to the surface defects and impurities occur during
crystal growth. The type of surface trap is reported to be donor type in [20], [21] and [22].
2.6 Effects of traps
2.6.1 Current collapse
Current collapse in AlGaN/GaN HEMTs is first discovered by comparison of DC current
voltage characteristics before and after high drain voltage is applied. Degradation in current
is reported after high drain to source voltage stress is applied. Device is kept under high
17
drain to source voltage for instance 20 V and zero gate bias for long time. Current recovery
could be observed while illuminated by the light with wavelength around 600 nm [14].
Figure 2.9: Current collapse in GaN HEMTs. Id?Vd before (i) and after (ii) a drain bias of
20 V is applied [26].
Figure 2.9 shows the current collapse effect due to the deep bulk traps in GaN obtained
by measuring HEMT DC characteristics before and after voltage stress of 20V being applied
todraincontact. Asdiscussedintheprevioussubsectionofbulktraps, iftheconclusionabout
bulk traps is true, device will present a resistive characteristic due to high trap concentration.
In Figure 2.9, after applying voltage stress to HEMT, strong resistive property is observed
from curve (ii) which proves the existence of deep bulk traps in GaN. Figure 2.10 and Figure
2.11 show the DC characteristics of voltage stressed HEMT before and after exposing to light
illumination. From figure 2.10 and 2.11, evidence show that deep bulk traps are responsible
for the current collapse under high drain voltage stress.
18
Figure 2.10: Current collapse in GaN HEMTs, with (solid) and without (dash) light illumi-
nation [20].
2.6.2 Gate-lag
Gate-lag is defined as the reduction in the drain current observed in the pulsed Id ?Vd
characteristics relative to DC measurements made at the same bias point[14].Pulsed-gate
Id ?Vd measurements are made by keeping the drain voltage constant and pulsing the gate
from the off to on state. Several papers report the surface traps are responsible for gate-lag
and gate-lag can be reduced by annealing and inclusion of passivation layer. Figure 2.12 and
2.13 show the pulsed Id ? Vd measurement of HEMTs with and without passivation layer
respectively. Device with passivation layer performs better in pulsed Id ?Vd measurement
which provides evidence for the improvement trap density by Nitride passivation layer [22].
19
Figure 2.11: Current recovery dependence of wavelength of light illumination.
Figure 2.12: Pulsed Id ?Vd characteristics for an unpassivated GaN HEMT [25].
20
Figure 2.13: Pulsed Id ?Vd characteristics of a passivated GaN HEMT [25].
21
Chapter 3
AlGaN/GaN HEMT simulation
Simulation is performed in Sentaurus version 2012.09 [27]. Svisual is used to visualize
simulation results. The first step is to create a 2D HEMTs structure with proper mesh in
Sentaurus Structure Editor. Physics models are applied to the structure in Sdevice. Gener-
ally the simulation result should consist of DC output simulation which is often known as
Id ?Vd and Id ?Vg, AC simulation for high frequency characteristics and transient simula-
tion of which trap is a key influential factor. Only DC simulation will be presented in this
work. Later, attempts to achieve gate length scaling are examined in this work in DC output
simulation. There are two approach for polarization charge placement in simulation. One
approach is to use built-in model provided by simulator, the other approach is to add TCL
code calculating polarization charge density for each material and place charge manually in
each layer. Manual charge placement approach is used for matching measurements since real
device is cylindrical and built-in model does not support cylindrical coordinate simulation
with anisotropic axis.
3.1 Device Structure
The HEMTs in this work are all cylindrical. Figure 3.1 is a photograph of HEMTs in
various sizes. The dark brown small circle located at center of each device is drain contact,
the outer circle is the source contact, bright yellow part is metal contact of gate.
Table 3.1 shows the geometries of fabricated cylindrical HEMT. In Table 3.1, Lgd refers
to the distance between gate and drain, and Lsg refers to the distance between source and
gate. Lg refers to the length of gate.
22
Figure 3.1: HEMT device die photo.
Device Number Lgd (um) Lsg (um) Lg (um)
1 and 6 10 10 220
2 and 7 10 10 170
3 and 8 10 10 120
4 and 9 10 10 70
5 and 10 10 10 40
Table 3.1: Dimension of HEMT.
23
Figure 3.2: Schematic diagram of AlGaN/GaN HEMT studied in this work.
Figure 3.2 shows the schematic diagram of the HEMT studied. The substrate of the
structure is specified as oxide,buffer layer is GaN which has a lower mobility compared with
channel region GaN. The top of GaN buffer layer is channel which directly connects to
AlGaN barrier layer. The heterojunction interface between GaN channel and AlGaN barrier
is essential part of the device which requires refined mesh which will be illustrated in the
Meshing subsection in order to properly simulate the characteristics of the device. A 2 nm
GaN cap layer is placed on the top of AlGaN barrier. Some commercial GaN HEMTs contain
an additional layer that called passivation layer that consists of nitride. It is reported that
lower trap density can be achieved by growing passivation layer on top of GaN cap layer. To
simplify the process of adding trap to GaN cap layer, Ni passivation layer is constructed in
simulation.
To match measurements, some adjustments are introduced during the simulation. Ad-
justments include electron mobility of channel GaN, barrier height of gate metal, dopant type
and doping concentration in GaN. Furthermore, in obtaining polarization charge density
and 2DEG density, two different approaches of charge placement are presented in this work.
24
Figure 3.3: Refined mesh at heterojunction interface.
Sentaurus simulator itself contains an adjustable built-in model of polarization charge cal-
culation consisting of spontaneous polarization charge and piezoelectric polarization charge.
The second approach of obtaining polarization charge is through Sentaurus Workbench by
adding TCL script that calculates polarization at the beginning of sdevice command file,
then placing each portion of calculated polarization charge density to respective region in
the device. The calculation of polarization charge is based on Equation (2.3), Equation (2.4)
and Equation (2.5).
3.2 Device structure building
3.2.1 Meshing
Meshing needs to be extreme intense at the interface of GaN buffer and AlGaN barrier
where the 2DEG locates. At the gate contact edge deep below the channel region, meshing is
also required to be refined. In those regions, changes of parameters such as electron density,
electric field and current density are huge. To simulate the properties of those regions,
mesh need to be intense enough. Figure 3.3 illustrates a refined mesh at the heterojunction
interface and contacts. In Figure 3.3, thin layers of intense mesh are presented at the
25
AlGaN/GaN heterojunction interface and gate contact edge. Besides those regions, mesh is
not so dense for the goal of reducing calculation in simulation. Good mesh should on one
hand be dense in the region where fast changes of parameters occur, on the other hand, be
minimum to reduce simulation time. For example, the mesh of HEMT structure in this thesis
is homogeneous intense at beginning. The amount of elements in mesh is roughly 100,000.
It consumes over 1 hour for simulating a complete Id ?Vg curve when Vd is ramped to 5 V
and Vg is swept from -5 V to 5 V. Then, meshing in regions where parameters change slowly
is gradually reduced. Time consumption is expected to decrease with less elements in mesh.
The final refined mesh of HEMT contains nearly 20,000 elements. Simulation will fail due
to convergence issue with mesh that contains elements less than the final refined mesh. The
error in Poisson equation and carrier density can be observed using error print. The largest
error locates at the interface of passivation layer and GaN cap where mesh is reduced. Time
consumption for final refined mesh to finish the same Id ?Vg simulation is roughly 25 min.
3.2.2 Charge calculation and placement
Spontaneous polarization effect exists in the whole region of both AlGaN and GaN. It
is mole fraction dependent and varies with the composition of each element in the mate-
rial. Piezoelectric polarization effect is generated from the heterojunction interface lattice
mismatch between two layers. Two approaches of charge calculations and placements are
presented in this subsection. The first approach is applying built-in polarization model in
the simulator. Parameters in polarization charge equation such as piezoelectric coefficients
are modified in a separate parameter file. Once built-in model is activated, simulator will au-
tomatically calculate charge densities in each layer and place them respectively. The charge
equation used to calculate polarization charge is marked as Formula 2 in simulator which is
defined in separate parameter file as well. The second approach is to use the same charge
equation to calculate sum polarization charge density at each interface and place charge as
fixed trap into corresponding interface. Parameters used in manual charge placement in
26
charge calculation are set to be identical to the built-in model. TCL command that used for
charge calculation is shown below:
# Calculation of polarization charge
set q = 1.602e-19 ;
set x = @x@;
set strainRelax = @relax@;
# Mole fraction dependent spontaneous polarization
set Psp_AlN = -8.1E-6/q;
set Psp_GaN = -2.9E-6/q;
set Psp_AlGaN = x*Psp_AlN + (1 - x)*Psp_GaN ;
set DPsp = Psp_GaN - Psp_AlGaN;
# Mole fraction dependent piezo electric polarization
#AlN
# e31 = -5.0e-5
# e33 = 1.79e-4
# c13 = 1.08e11 = 108 GPa
# c33 = 3.73e11 = 373 GPa
# GaN
# e31 = -3.5e-5
# e33 = 1.27e-4
# c13 = 1.06e11 = 106 GPa
# c33 = 3.98e11 = 398 GPa
set e31i =(x * (-0.50E-4) + (1 - x) * (-0.35E-4))/ q ;
27
set e33i = (x * 1.79E-4 + (1 - x) * 1.27E-4) / q ;
set c13i = x * 108 + (1 - x) * 106 ;
set c33i = x * 373 + (1 - x) * 398 ;
set straini = (1- strainRelax) * (x * (3.189 - 3.112) / (x * 3.112 + (1- x) * 3.189 ) ) ;
set Ppz_AlGaN = 2* straini * ( e31i - c13i / c33i * e33i ) ;
set DPpz = -Ppz_AlGaN ;
set intCharge = DPsp + DPpz ;
set AlGaN_Spontaneous = Psp_AlGaN
set AlGaN_Piezoelectirc = Ppz_AlGaN
set GaN_Spontaneous = Psp_GaN
set Total_AlGaN = Psp_AlGaN + Ppz_AlGaN
set AlGaN_GaN_Interface = intCharge
set AlGaN_Nitride_Interface = Total_AlGaN
One important thing should be noticed if using built-in model for simulation. Polariza-
tion charge at bottom layer of GaN almost has no influence on 2DEG density since thickness
of bulk GaN is 1 micron which is relatively large compared with the heterojunction structure
which is less than 100 nm. In other words, particularly in this structure, there is no polar-
ization charge at the bottom layer of GaN. In Sentaurus device, if the key word piezoelectric
28
written in the scripts, the simulator will automatically turn on all the piezoelectric polar-
ization effect at all region interface even there should not be any polarization effect between
certain interfaces. To solve this problem, one line of command is inserted to the script to
eliminate the incorrect interface simulation:
Physics (MaterialInterface = "GaN/Oxide")
{Piezoelectric polarization (activation = 0)}
For both built-in model and manual charge placement, lattice axis, simulation axis
and anisotropic direction need to be defined. Lattice axis is defined in separate parameter
file, simulation axis and anisotropic direction are modified in Sdevice command file. The
command used to modify those parameters is shown as below:
# Define lattice parameters for all materials outside of any material or region
LatticeParameters {
X = (1, 0, 0)
Y = (0, 0,-1)
}
# Also define Piezoelectric polarization Formula=2 outside of any material
# it is used for all regions in the simulation
Piezoelectric_Polarization {
Formula= 2
}
# Define anisotropic epsilon for GaN and AlN
Material= "GaN" {
29
Epsilon
{ * Ratio of the permittivities of material and vacuum
* epsilon() = epsilon
epsilon = 9.5 # [1]
}
Epsilon_Aniso
{ * Ratio of the permittivities of material and vacuum
* epsilon() = epsilon
epsilon = 10.4 # [1]
}
}
Material= "AlN" {
Epsilon
{ * Ratio of the permittivities of material and vacuum
* epsilon() = epsilon
epsilon = 9.0 # [1]
}
Epsilon_Aniso
{ * Ratio of the permittivities of material and vacuum
* epsilon() = epsilon
epsilon = 10.7 # [1]
}
30
Psp[C/cm2] in AlGaN ?0.042
Psp[C/cm2] in GaN ?0.029
Table 3.2: Spontaneous polarization in AlGaN and GaN.
C11 [GPa] 391.5
C12 [GPa] 143.0
C13 [GPa] 106.5
C33 [GPa] 391.6
e31 [C/cm2] ?3.189?10?5
e33 [C/cm2] 1.4?10?4
Table 3.3: Piezoelectric polarization coefficients and stiffness constants in AlGaN.
}
Aniso (Poisson direction (0, 0, 1))
Table 3.5 shows the spontaneous polarization of AlGaN and GaN that are used in built-
in model and manual charge density calculation. Table 3.6 shows piezoelectric polarization
coefficients and stiffness constants in AlGaN barrier that used during simulation. Modifying
parameters in built-in model is achieved by editing a separate parameter file. In built-in
model, polarization model can be active by using the commands shown below. Relaxation
factor is modified from default value 0.1 to 0 in the separate parameter file to achieve the
maximum piezoelectric polarization charge due to stain.
Piezoelectric_Polarization (strain)
# Modified in separate parameter file inside material parameter modification
a0 3.189
a 3.16975
Relax 0.0
Table 3.4: Strain parameters and relaxation parameter.
31
Material= "GaN" {
Piezoelectric_Polarization
relax = 0.0
}
Material= "AlN" {
Piezoelectric_Polarization
relax = 0.0
}
To validate manual charge placement, dummy structures including single layer of Al-
GaN, AlGaN/GaN heterojunction layer and GaN/AlGaN/GaN triple layer structure are
constructed to explore the relation between polarization charge density obtained using built-
in model and manual charge placement. Currentplot section in TCAD can be used to attract
additional data in a specified region. To detect the polarization charge in each layer, the
following command is included in sdevice file. In the command shown below,
PE_polarization
total polarization in a specified material consisting of spontaneous polarization and piezopo-
larization. The word Integrate will enable simulator to output the integral of polarization
charge over the specify the region. In the command shown below, integration window is
specified at the middle of the x dimension in each layer.
CurrentPlot {
PE_polarization(
Integrate(Name = "PE_GaN_cap" Window[(0.4 0.49 0) (0.6 0.5 0)]) )
}
Dividing the integral by the integration range in x dimension, polarization charge in
sheet charge density format can be obtained. The default integration unit is um which will
32
give the integral an unit of um2 / cm3 which is 10?8/cm. By changing the integration unit
to cm, the final result will have the unit of /cm. The command used to change integration
unit is modified in Math section shown as below:
Math {
CurrentPlot (IntegrationUnit = cm )
}
To manually place charge at interface, commands shown below are applied:
Physics {
(MaterialInterface = "AlGaN/GaN")
{Traps ( FixedCharge Conc = !(puts Conc )! ) }
}
The sheet charge of concentration Conc is obtained from the manual calculation based
on Al mole fraction. Assumption that there is no relaxation between AlGaN and GaN
interface has been made during calculation. In other words, it is the maximum polarization
charge that can exist at the heterojunction interface.
Equations used for polarization charge calculation are shown as below:
? = P(AlGaN)?P(GaN) = PSP(AlGaN)+PPE(AlGaN)?PSP(GaN)C/cm2 (3.1)
PPE = 2a?a0a
0
(e31 ?e33C13C
33
)C/cm2 (3.2)
33
Mole fraction of Al (x) Psp (C/ cm2) Ppz (C/ cm2) Sum (C/ cm2)
0 -2.9? 10?6 0? 10?6 -2.9? 10?6
0.2 -3.9? 10?6 -0.73? 10?6 -4.67? 10?6
0.4 -4.98? 10?6 -1.593? 10?6 -6.57? 10?6
0.6 -6.02? 10?6 -2.592? 10?6 -8.62? 10?6
0.8 -7.06? 10?6 -3.742? 10?6 -10.8? 10?6
1.0 -8.1? 10?6 -5.039? 10?6 -13.14? 10?6
Table 3.5: Piezoelectric polarization and spontaneous polarization in AlGaN.
Mole fraction of Al (x) Psp charge density (/cm2) Ppz charge density (/cm2) Sum (/cm2)
0 -1.8102? 1013 0? 1013 -1.8102? 1013
0.2 -2.4594? 1013 -0.4556? 1013 -2.9150? 1013
0.4 -3.1086? 1013 -0.9945? 1013 -4.1031? 1013
0.6 -3.7578? 1013 -1.6201? 1013 -5.3779? 1013
0.8 -4.4070? 1013 -2.3359? 1013 -6.7429? 1013
1.0 -5.0562? 1013 -3.1455? 1013 -8.2017? 1013
Table 3.6: Piezoelectric polarization and spontaneous polarization charge densities in AlGaN.
PSP(x) = ?0.052x?0.029C/cm2 (3.3)
PSP(0) = ?0.029C/cm2 (3.4)
?(x) = 2a?a0a
0
(e31 ?e33C13C
33
)+PSP(x)+PSP(0) (3.5)
Based on Al mole fraction, spontaneous polarization, piezoelectric polarization, sponta-
neous polarization charge density and piezoelectric polarization charge density are calculated
and shown in Table 3.5 and Table 3.6.
34
Compared with the corresponding results from built-in model, a perfect match can be
achieved. The simulation results of built-in model polarization of Al mole fraction of 0.4 are
shown in Figure 3.4.
Figure3.4: SumofspontaneousandpiezoelectricpolarizationinAlGaNwithAlmolefraction
is 0.4.
Figure 3.4 shows the polarization in AlGaN. In AlGaN, spontaneous polarization is
pointing from upper edge to lower edge which causes the spontaneous polarization induced
charge being negative in upper edge while being positive at the lower edge. Since in single
layer of AlGaN, the whole region has the same lattice constant. There is no strain or
stress effect in the material which leads to the zero piezoelectric polarization in the material.
From Figure 3.4, it can be observed that the sum of polarization is equal to spontaneous
polarization in single layer structure. The sum of polarization is -4.98 C/cm2 which is
identical to the value obtained from manual charge placement in Table 3.5.
35
Figure 3.5: Comparison of Id ? Vd simulation results from manual charge placement and
built in model in rectangular coordinate.
Simulation results using built-in model and manual charge placement in rectangular
coordinate are compared in Figure 3.5. In Figure 3.5, the magenta curve presents the sim-
ulation result from built-in model and the green curve is the corresponding result for using
manual charge placement method. From Figure 3.5 it can be observed that simulation re-
sults from built-in model matches with that from manual charge placement. This observation
proves manual charge placement method producing correct polarization charge density.
In this subsection, a comparison between manual charge calculation and built-in model
charge is presented. In triple layer of GaN/AlGaN/GaN, polarization charge density ob-
tained from the built-in model in each layer is identical to the charge density calculated us-
ing piezoelectric polarization charge equation. This conclusion justifies using manual charge
placement instead of built-in model in further simulation when built-in model fails in cylin-
drical coordinate.
36
Figure 3.6: Cross-sectional view ofcylindrical HEMT along verticaldirection (half structure).
3.2.3 Conversion from cylindrical coordinate to rectangular coordinate
The cross-sectional view of cylindrical HEMT (half structure) is shown in Figure 3.6. In
Figure 3.6, rd is the distance from center of cylindrical HEMT to the edge of drain contact
which is also the radius of circular drain contact. rs is the distance from center of cylindrical
HEMT to inner edge of source contact.
Equation (3.6) and Equation (3.7) show simplified equations for rectangular MOSFET
channel current calculation. A HEMT is similar in Equation (3.6) and Equation (3.7), IDS
is the current in the channel of a rectangular MOSFET or HEMT. ? is the electron mobility
in the channel, W is the channel width, L is the channel length and Cox is capacitance per
unit area of channel. VGS represents the gate to source voltage, VT is the threshold voltage
to turn on the device and VDS is drain voltage.
IDS = WL ???Cox ?(VGS ?VT ? 12VDS)?VDS if VDS ? (VGS - VT) (3.6)
37
Figure 3.7: Top view of drain and channel region of cylindrical HEMT.
IDS = WL ???Cox ? 12(VGS ?VT)2 if VDS ? (VGS - VT) (3.7)
To make the form of current calculation in cylindrical coordinate similar to the rectan-
gular current calculation, some assumptions and simplifications can be made. Firstly, the
capacitance per unit area of the channel is a constant. HEMT can be divided into infinite
numbers of ring like structures with different radii r as shown in Figure 3.7. Considering
the symmetry in cylindrical structure, current will flow from center of circular drain to the
circular source. The cross-sectional view cut along direction of current flowing of cylindrical
HEMT is shown in Figure 3.6 that is similar to a cross-section of rectangular HEMT. The
equation for cylindrical coordinate current calculation is shown in Equation.(3.8) and Equa-
tion (3.9). In Equation.(3.8) and Equation (3.9), IDScylin is the channel current in cylindrical
coordinate.
38
IDScylin = ???Cox ?(VGS ?VT ? 12VDS)?VDS ?
Z 2pir
dr if VDS ? (VGS - VT) (3.8)
IDScylin = ???Cox ? 12(VGS ?VT)2 ?
Z 2pir
dr if VDS ? (VGS - VT) (3.9)
Moving the integration related to r to the left side of equation, a relation between r and
channellengthandwidthcanbeachieved. ThesimplifiedrelationisshowninEquation(3.10)
and Equation (3.11). In Equation (3.10) and Equation (3.11), rs represents the distance from
the origin (symmetry axis) to the channel outer edge, while rd represents the distance from
symmetry axis to channel inner edge.
L
W =
1
2pi
Z rd
rs
dr
r (3.10)
L
W =
1
2pi ln
rs
rd (3.11)
Weff = WL ?Lg = 2?pi ? Lgln rs
rd
(3.12)
For the device that needs to be simulated, rd equals to 40 um, rs is 100 um while
gate length Lg is 40 um. Plugging in rs and rd values into Equation.3.12, Weff equals to
427.35 which is the effective channel width. In simulation, channel width can be defined as
area factor in the Physics section for rectangular HFET simulation. By default, area factor
39
Figure 3.8: Comparison of cylindrical and rectangular HEMT Id ?Vd with donor trap and
n-type doped buffer.
is 1 um in simulation if no specification is made in command file. To make comparison
between the effective rectangular HFET simulation model with cylindrical model, area factor
in rectangular model simulation is modified to be the value of Weff. Simulation result of
comparison of manual charge placement HEMT in cylindrical and rectangular coordinate is
shown in Figure 3.8.
In Figure 3.8, the magenta curve represents the Id ?Vd simulation result for cylindrical
coordinate while the green curve is the corresponding result for rectangular coordinate.
From Figure 3.8, it can be observed that two curve fit each other well in the linear region
but have some variation in saturation region. When drain voltage is relative low, electrons in
channel are distributed as a function that only relates to location. In another words, electron
distribution is only a function respected to r which is the distance from certain point to the
symmetry axis. Thus the approximation in Equation (3.12) is valid. When drain voltage
is increasing until saturation region, charge distribution in channel is influenced by drain
voltage. As a result, certain phenomena begin to occur such as pinch-off which furthermore
leads to the charge distribution change. Thus approximation in Equation (3.12) fails which
is the main reason of the difference in Id ?Vd curve in saturation region between cylindrical
40
Figure 3.9: HEMT structure with n-type doped buffer.
and rectangular HEMTs. The approximation is less valid under high voltage or for short
channel device.
3.2.4 Leakage current
Figure 3.9 shows the HEMT structure with n-type doped buffer which is the starting
point of the simulation. The goal of adding n-type dopant is to simulate the effect of
impurities in GaN buffer since GaN buffer region is not an intrinsic semiconductor even
without intentional doping. During the fabrication, GaN buffer region typically will exhibit
some degree of n-type conductivity, presumably due to the unintentional doping of residual
impurities such as Si and O [1]. By following structure in De Brida Christian?s dissertation
[1], n-type dopant of concentration 1015/cm3 is applied to GaN buffer region to simulate the
residual impurities introduced during fabrication. In addition, to achieve better convergence,
highly n-type doped contacts of concentration 1020/cm3 are applied to both drain and source
sides. Convergence issue will be discussed later in convergence subsection.
Figure 3.10 shows simulation result of Id?Vg curve of HEMT with n-type doped buffer of
which doping concentration is 1015/cm3. Figure 3.11 shows the same curve under logarithmic
41
Figure 3.10: Id ?Vg curve of n-type doping buffer in linear scale (Vd = 5V).
Figure 3.11: Id ?Vg curve of n-type doping buffer in logarithmic scale (Vd = 5V).
42
Figure 3.12: Id ?Vg measurement in linear scale (Vd = 5V).
scale. There is a noticeable off-state current which indicates that device does not shut-off
effectively.
Figure 3.12 and Figure 3.13 show the measurement of Id ?Vg curve in linear scale and
logarithmic scale respectively. compared simulation result with measurement, it is clear that
off-state current leakage is huge in simulation. Figure 3.14 shows the current density at
off-state which is at Vg = 5V and Vd = 5V. The red color in Figure 3.14 indicates a high
current density which distributes among the whole buffer region. Thus, the source of leakage
current is n-type dopant in GaN buffer.
In device fabrication, the residual donors in an unintentionally n-doped GaN buffer are
compensated by deep acceptor states to obtain high resistivity [1]. To observe influence of
buffer dopant on off-state leakage, a parallel simulation with p-type doped buffer is built.
Figure 3.15 shows the layer structure of p-type doped buffer, geometry of this structure is
identical to the structure in Figure 3.9. Observed from the comparison of simulation results
43
Figure 3.13: Id ?Vg measurement in logarithmic scale (Vd = 5V).
Figure 3.14: Leakage current in buffer region and substrate (n-type doped buffer).
44
Figure 3.15: Layer structure of HEMT with p-type doped buffer.
from n-type buffer HEMT and p-type buffer HEMT, off-state current leakage is effectively
reduced by applying p-type dopant in buffer region.
Figure 3.16 and Figure 3.17 show the comparison of Id?Vd curves from HEMTs with p-
type doped buffer and n-type doped buffer in linear scale and logarithmic scale respectively.
In Figure 3.16 and Figure 3.17, blue curve represents the p-type doped device, red curve
stands for n-type doped device. Figure 3.18 shows the current density of HEMT with p-
typed doped buffer. It can be observed from Figure 3.17, the off-state current of p-type
doped device is 10 orders less in magnitude than that of n-type doped device. Although,
current density shown in Figure 3.18 indicates current leakage density is reduced by 13 orders
in magnitude. Compared simulation result of p-type buffer HEMT with measurement, off-
state leakage is significantly small. Conclusion is buffer region of real HEMT device contains
no impurities of n-type, instead n-type impurities is contained in channel region. Thus, n-
type doping of concentration of 1015 /cm?3 is applied to GaN channel of simulation HEMT
structure.
45
Figure 3.16: Id ?Vg curves of p-type doped buffer and n-type doped buffer HEMT in linear
scale (Vd = 5V).
Figure 3.17: Id ?Vg curves of p-type doped buffer and n-type doped buffer HEMT in loga-
rithmic scale (Vd = 5V).
46
Figure 3.18: Current density of a HEMT with p-type doped buffer.
3.2.5 Convergence control
For wide band-gap material, intrinsic carrier concentration is extremely small compared
with conventional semiconductor material such as Si. For this reason convergence issue is
one of the obstacles in simulation. Several attempts are introduced during the simulation
to solve convergence problem including extended precision digit, tracing maximum update
error using CNormPrint, using different meshing grids, applying highly doped semiconductor
beneath drain and source contacts and using electron barrier tunneling model for source and
drain contacts. Solving convergence problem has been a big issue in this work. The only
solution is to build parallel simulation with different combination of extended precision digits,
meshing grids, highly n-doped electron barrier tunneling contacts.
From the simulation results, rectangular coordinate system tends to have better conver-
gence than cylindrical one. However, cylindrical coordinate system is still used for simulation.
Highly n-type doped contacts with doping concentration equal to 1020/cm3 are placed be-
low the metal contacts to achieve better convergence. Electron barrier tunneling model is
applied to source and drain contact. Better convergence is achieved by changing source and
drain from Ohmic contacts to Schottky contacts with effective masses of AlN and GaN in
47
contact regions being modified to 0.01m0 to reach small resistive contacts. The method is
to apply nonlocal mesh to source and drain contacts with tunneling current from electron
barrier tunneling current. Effective masses of AlN and GaN are modified to small value only
at source and drain contacts in order to modify the tunneling current to reach zero resistive
contacts. This modification does not influence the global parameter of effective mass applied
in the whole structure other than source and drain contacts. Controlling of source and drain
contacts can be achieved by modifying value of effective masses of AlN and GaN in nonlocal
mesh region.
Extended precision is modified in Math section. Effective masses in GaN and AlN
of nonlocal source and drain are modified in separate parameter file. Schottky drain and
source contacts are defined in electrode section. Electron barrier model is activated in
Physics section. Command used for modifying extended precision, electron barrier tunneling,
Schottky drain source contacts and effective masses are shown in below:
Extrapolate
Iterations = 20
ExtendedPrecision
Digit = 8
RHS = 1e-10
CNormPrint
NewtonPlot(
Error MinError
Residual
)
Electrode {
{ Name="gate" Voltage= 0 Schottky barrier = 1.5 }
{ Name="source" Voltage= 0 Schottky Workfunction= 4.3 }
{ Name="drain" Voltage= 0 Schottky Workfunction= 4.3 }
48
}
Physics {
eBarrierTunneling "NLM_Source"
eBarrierTunneling "NLM_Drain"
}
Material= "AlN" {
BarrierTunneling {
mt = 0.01, 0.01 # [1]
g = 1,1 # [1]
}
}
Material= "GaN" {
BarrierTunneling {
mt = 0.01, 0.01 # [1]
g = 1,1 # [1]
}
}
3.2.6 Trap
Donor trap is inserted to the GaN cap layer during the simulation acting as one of
sources of electrons in 2DEG. Except for being one of the sources of electrons in 2DEG,
another reason to adding trap during simulation is to reduce resistance series in un-gate
49
region of the HEMT due to channel shut-off. Donor trap is neutral when occupied by
electron, and is carrying positive charge of a hole when empty. When there is no trap in the
GaN cap layer, the polarization charges in each layer locate at the edge of each layer. The
upper edge of layer is negatively charged and lower edge is positively charged with equal
amount of charge as the upper edge. There is no induced charge in each layer in this case.
When donor trap is applied to the GaN cap layer of the device, the negative charge in
the upper edge of GaN cap layer is trapped by the donor trap inserted to the layer which
will leave excess positive charge at the lower edge of GaN cap. The excess positive charge
will compensate with the negative charge in the AlGaN upper edge which will leave excess
positive charge at the lower edge of AlGaN. The excess positive charge at lower edge of
AlGaN will induce electron at the upper edge of GaN buffer which is the channel of the
device. The increment of electron density in the channel will finally lead to the increment of
current flowing from source to drain. To prove this scenario, simulations with and without
trap are performed. Donor trap of concentration of 5?1013 cm?2 of various energy levels are
applied to the interface of GaN cap and Nitride.
The magenta curve in Figure 3.19 represents the simulation result with donor trap in
GaN cap layer while the green curve represents the corresponding result for the simula-
tion without donor trap. It can be observed that the simulation result with donor trap is
significantly larger than that without donor trap which is consistent with the scenario.
The comparison of Id?Vd simulation results with various trap energy is shown in Figure
3.20. In Figure 3.20, the magenta curve represents the Id?Vd simulation result with trap of
energy level locating at 0.4 eV above the middle of energy band. The green curve in Figure
3.20 represents the corresponding simulation result with trap energy level locating at 0.4 eV
below the middle of energy band. In the simulation matching measurement subsection, trap
density and trap energy level are adjusted to fit the measurement.
50
Figure 3.19: Comparison of Id ?Vd simulation results with and without donor trap.
Figure 3.20: Comparison of Id ?Vd simulation results with trap of various energy levels.
51
3.3 Simulation result matching measurement
In the following part, matching and calibration are mostly done between the simulation
results and measurements. Measurement of Id ?Vg curve is from device marked as Sample
A while IdVd measurement is from device marked as Sample B.
To start with, Id?Vg simulation results are calibrated to fit measurement because once
Id?Vg curves are matched, threshold voltage can be determined. The electron mobility used
is 850 cm2/V ? s?1 which is the default value of simulator. The affinity of GaN is 4.1 eV
and workfunction function for the gate contact Ni ranges from 5.04 eV to 5.35 eV. Thus,
the approximate barrier height between GaN cap and Ni gate is 1.0 eV to 1.3 eV. Sentaurus
Workbench is constructed with various barrier heights from 1.0 eV to 3.0 eV increasing with
a step of 0.5 eV. The comparison of measurement of simulation results is shown in Figure
3.21. From Figure 3.21, it can be observed that simulation result from barrier height of 2.0
eV matches with measurement in threshold voltage. Thus for Id ?Vg curve fitting, barrier
height is adjusted to 2.0 eV. Electron mobility is adjusted to 1500 cm2/V ?s?1 to fit with
measurement. Comparison of measurement and simulation result with barrier height being
2.0 eV and electron mobility being 1500 cm2/V ?s?1 is shown in Figure3.22
Figure 3.22 shows a comparison between measurement and simulation of Id?Vg. Figure
3.23 shows comparison between measured transconductance gm and simulated gm. Presented
in Figure 3.22, HEMT is turned on at around Vg = -2.0V.
Figure3.24showsthesimulationresultmatchingwiththemeasurementdatafromdevice
marked as Sample B which shows typical DC characteristics of HEMT. In this calibration
work, barrier height of gate contact is 1.5 eV. As demonstrated in convergence control
subsection, non local mesh is applied to source and drain contacts for the goal of using
Schottky contact with tunneling current to replace Ohmic contact which causes convergence
problem. Effective masses of AlN and GaN at contacts are modified to small value to achieve
zero resistance. To start with, the effective mass is adjusted to 0.01 m0 to reach almost zero
resistance at the drain and source contacts. Electron mobility is adjusted from default value
52
Figure 3.21: Comparison of Id?Vg measurement from sample A and simulation results with
various barrier heights.
Figure 3.22: Id ?Vg measurement of sample A compared with simulation.
53
Figure 3.23: Transconductance gm measurement of sample A compared with simulation.
850 cm2/V?s?1 to 800 cm2/V?s?1 to fit the measurement. Donor trap of concentration
of 3?1013 cm?2 with energy level locating at the middle of energy band. N-type doping of
concentration of 1015 cm?3 is applied to the GaN cap and AlGaN barrier layer as the electron
source of 2DEG. P-type dopant of concentration of 1015 cm?3 is applied to the GaN buffer
region to reduce off-state leakage current.
To match measurement in linear region, resistance needs to be series to source and
drain contacts. One way to add resistance to contact is to directly add resistance to the
source and drain contact. In this work, instead of adding series resistance to contact, the
effective masses of GaN and AlN at nonlocal mesh region at drain and source contacts are
modified from 0.01 m0 to 0.1 m0 to achieve same effect. The simulation result of Id ? Vd
with effective mass being adjusted to 0.1 m0 is illustrated in Figure 3.25. From Figure 3.25,
it can be observed that a better match in linear region is achieved by modifying tunneling
effective masses of GaN and AlN in nonlocal mesh region with tunneling contact model.
54
Figure 3.24: Comparison of Id?Vd measurement and simulation in tunneling contact model
mt = 0.01 m0.
This modification of effective masses only controls tunneling current of tunneling contacts
but has nothing to do with effective masses of GaN and AlN in AlGaN barrier, GaN cap
and GaN bulk which determine values of NC, NV and so on.
3.4 Gate scaling
The main goal of dimensional gate scaling is to integrate more transistors in the same
area without degrading performance of single transistor. Effectively scaling gate length
will lead to an increment of functionality in the same area. Gate scaling is performed in
rectangular and cylindrical coordinates. With gate scaling, the electric field within the
channel layer increases. An increment in current proportional to WL is expected for long
channel device behavior. One of the goal of this work is to simulate the characteristics of
the devices when gates are shrunk down to 10 um and 1 um.
55
Figure 3.25: Comparison of Id?Vd measurement and simulation in tunneling contact model
mt = 0.1 m0.
Simulation results of gate scaling in rectangular coordinate are shown in Figure 3.26,
Figure 3.27 and Figure 3.28. Figure 3.26 shows the comparison of simulation results when
gate length is 40 um. Figure 3.27 shows the comparison of simulation results when gate
length is shrunk from 40 um to 10 um. Figure 3.28 shows the comparison of simulation
results when gate length is shrunk from 40 um to 1 um. When gate length is shrunk, electric
field in channel will be increased since the same voltage bias is applied to the drain contact
which will lead to increment in drain current density. In both Figure 3.27 and Figure 3.28
enormous increments in drain current density are observed compared with Figure 3.26.
Though significance and emphasis are drawn to the importance of gate scaling, obstacles
occur due to the device size reduction. When gate length is scaled, the shrunk gate has
weaker control over 2DEG in channel region. A threshold voltage shift will be observed
as the result of the increasing influence of drain voltage over the shape of channel region.
Threshold voltage will be a function of both gate bias and drain to source voltage. Gate
56
Figure 3.26: Id ?Vd simulations with gate length equaling 40 um.
scaling will as well increase HEMT transconductance and off-state current. To verify the
scenario, structures with gate length being shrunk down to 10 um and 1um are constructed.
Schematics of HEMTs with gate length 10 um and 1 um are shown in Figure 3.29 and Figure
3.30 respectively.
During each individual gate length, drain contact is biased at 5 V and gate bias is swept
from -5 V to 5 V. As gate length is further scaled, the positive drain voltage will be more
influential on the charge in channel which will further lead to threshold voltage shifting to
be a larger negative value. Additionally, off-state current and transconductance will increase
as gate length being shrunk down to smaller value.
Comparison of Id ?Vg curves with HEMT gate length being shrunk down from 40 um
to 1 um is shown in Figure 3.31, while the normalized corresponding curves are shown in
Figure 3.32. As gate length decreasing, drain total current increases due to the increment
of electric field within the channel. When gate length reaches 1 um, short channel effect
57
Figure 3.27: Id ?Vd simulations with gate length equaling 10 um.
starts to occur. Increment in drain current does not follow the ratio of WL strictly due to
velocity saturation. The simulation result of off-state current and transconductance as a
function of gate length are shown in Figure 3.33 and Figure 3.34 respectively. In Figure
3.33 increment in off-state leakage current can be observed as the result of reduction in gate
length. Moreover, Figure 3.34 indicates an obvious increment in transconductance as gate
length is shrunk down from 40 um to 0.1 um.
58
Figure 3.28: Id ?Vd simulations with gate length equaling 1 um.
Figure 3.29: Schematic of HEMT with gate length being shrunk to 10 um.
59
Figure 3.30: Schematic of HEMT with gate length being shrunk to 1 um.
Figure 3.31: Comparison of Id ?Vg from HEMTs with gate length being shrunk down from
40 um to 1 um.
60
Figure 3.32: Comparison of normalized Id ?Vg from HEMTs with gate length being shrunk
down from 40 um to 1 um.
Figure 3.33: Off state drain current density as gate length shrunk from 40 um to 1 um.
61
Figure 3.34: Transconductance as gate length shrunk from 40 um to 0.1 um.
62
Chapter 4
Conclusion and future work
TCAD has been used to simulate and match measured I-V characteristics for a GaN
based HEMT. Many issues are carefully taken into consideration such as: the thickness of
AlGaN barrier, the doping concentration of GaN buffer, the Al mole concentration of barrier
layer, the electron mobility and the model used for polarization charge density calculation.
Moreover, series contact resistance is adjusted through the electron barrier tunneling model
provided by the simulator. Furthermore, for the goal of reducing un-gated region resistance
and achieving charge modulation in 2DEG, donor trap of concentration 5?1013 cm?2, energy
level locating at 0.4 eV below middle of energy band is applied to the un-gate region at
GaN/Nitride interface. Finally, gate scaling is performed on the manual charge placement
HEMT in rectangular coordinate. Improvement of drain current density is observed as gate
length being shrunk down. However, shift in threshold voltage, increment in transconduc-
tance and off-state current also occur as the drawback of gate length scaling.
In the future work, I would like to emphasize the effect of trap on the performance of
GaN HEMT. A more detail simulation includes but not limits DC simulation, RF simulation
and transient simulation will be constructed to explore the influence of trap in affecting
reliability.
63
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66