Springer Series in
materials science
Springer Series in
materials science
Editors: R. Hull R. M. Osgood, Jr. J. Parisi H. Warlimont
The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design. Recogniz- ing the increasing importance of materials science in future device technologies, the book titles in this series reflect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials.
Self-Organized Morphology in Nanostructured Materials Editors: K. Al-Shamery and J. Parisi
Self Healing Materials An Alternative Approach
to Centuries of Materials Science Editor: S. van der Zwaag
New Organic Nanostructures for Next Generation Devices Editors: K. Al-Shamery, H.-G. Rubahn, and H. Sitter
Photonic Crystal Fibers Properties and Applications By F. Poli, A. Cucinotta, and S. Selleri
Polarons in Advanced Materials Editor: A.S. Alexandrov
Transparent Conductive Zinc Oxide Basics and Applications
in Thin Film Solar Cells
Editors: K. Ellmer, A. Klein, and B. Rech
Dilute III-V Nitride Semiconductors and Material Systems
Physics and Technology Editor: A. Erol
Into The Nano Era
Moore’s Law Beyond Planar Silicon CMOS Editor: H.R. Huff
Organic Semiconductors in Sensor Applications
Editors: D.A. Bernards, R.M. Ownes, and G.G. Malliaras
Evolution of Thin-Film Morphology Modeling and Simulations
By M. Pelliccione and T.-M. Lu
Reactive Sputter Deposition Editors: D. Depla amd S. Mahieu
The Physics of Organic Superconductors and Conductors
Editor: A. Lebed
Volumes – are listed at the end of the book.
Rüdiger Quay
Gallium Nitride Electronics
123
Dr. Rüdiger Quay
Fraunhofer Institut für Angewandte Festkörperphysik (IAF) Tullastr. , , Freiburg, Germany
Series Editors:
Professor Robert Hull University of Virginia
Dept. of Materials Science and Engineering Thornton Hall
Charlottesville, VA -, USA Professor R. M. Osgood, Jr.
Microelectronics Science Laboratory Department of Electrical Engineering Columbia University
Seeley W. Mudd Building New York, NY , USA
Professor Jürgen Parisi
Universität Oldenburg, Fachbereich Physik Abt. Energie- und Halbleiterforschung Carl-von-Ossietzky-Strasse –
Oldenburg, Germany Professor Hans Warlimont Institut für Festkörper- und Werkstofforschung, Helmholtzstrasse
Dresden, Germany
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To our son, Jonathan Benedikt
In memoriam, Oliver Winterer (1970–2006)
Preface
Electronic RF-communication and sensing systems have dramatically changed our daily lives since the invention of the first electronic transistor in 1947.
Advanced semiconductor devices are key components within electronic sys- tems and ultimately determine their performance. In this never ending chal- lenge, wide-bandgap nitride semiconductors and heterostructure devices are unique contenders for future leading-edge electronic systems due to their out- standing material properties with respect to speed, power, efficiency, linearity, and robustness. At the same time, their material properties are challenging compared with any other material system due to high growth temperatures and many other intrinsic properties.
Wide bandgap semiconductors have attracted a lot of attention in the last ten years due to their use in optoelectronic and electronic applications.
The field is developing rapidly due to the high investments in US, Japanese, and increasing European research and development activities. Some of the knowledge acquired may not be available to the general public because of military or civil restrictions. However, this work compiles and systemizes the available knowledge and evaluates remaining issues. This book is of interest to graduate students of electrical engineering, communication engineering, and physics; to material, device, and circuit engineers in research and industry;
and to scientists with general interest in advanced electronics.
The author specially thanks those people, without whom and without whose individual contributions such a challenging work would have been impossible. He owes special thanks to:
Prof. Dr. G¨unter Weimann, director of the Fraunhofer Institute of Applied Solid-State Physics (IAF), for his encouragement, his advice, and continuous support.
Prof. Dr. Joachim Wagner for the encouragement to start this project.
Prof. Dr. Siegfried Selberherr, Insitut f¨ur Mikroelektronik, TU Wien, for con- tinuous encouragement and support.
VIII Preface
Dr. Michael Schlechtweg, head of the RF-device and circuits department at Fraunhofer IAF, and Dr. Michael Mikulla, head of the technology department at Fraunhofer IAF, for their generous support.
Dr. Rudolf Kiefer for his outstanding contributions and careful advise on the technology chapter, for his kind understanding, and for valuable discussions.
Dipl.Phys. Stefan M¨uller and Dr. Klaus K¨ohler for their valuable contribu- tions of the epitaxy chapter and for proof reading.
Dr. Friedbert van Raay for his proof reading, contributions to large-signal modeling and circuit design and for countless discussions on modeling, large- signal measurements, layout, and circuit design.
Dr. Michael Dammann, Dipl.Ing. Helmer Konstanzer, and Andreas Michalov for their contributions and their work on device reliability.
Dr. Wolfgang Bronner for his contributions to the development of technology and the SiC back-end process.
Dr. Wilfried Pletschen for his thorough proof reading and his kind advise on etching.
Dr. Matthias Seelmann-Eggebert for his inspired work on thermal simulations and large-signal modeling.
Dr. Patrick Waltereit for numerous fruitful discussions on epitaxial and pro- cess development.
Dipl.Ing. Daniel Krausse for his work on low-noise amplifiers.
Dr. Vassil Palankovski and Dipl.Ing. Stanislav Vitanov, TU Vienna, for proof reading and their valuable support on physical device simulation.
Dr. Axel Tessmann for his continuous good mood and valuable motivation for the development of mm-wave technology.
Markus Riesle and Dr. Herbert Walcher for their contributions to the MMIC module and device packaging.
Martin Zink and Ronny Kolbe for the patient dicing and picking of a numer- ous MMICs.
Dipl.Ing. Christoph Schw¨orer for valuable discussions on circuit design and for his contribution on the broadband amplifiers.
Dr. Lutz Kirste for his help on crystal structures.
Dipl.Ing. Michael Kuri , Dipl.Ing. Hermann Massler and the members of the RF-devices and circuits characterization group at Fraunhofer IAF for their support.
Dr. Arnulf Leuther for wise hints and good cooperation on process develop- ment.
Fouad Benkhelifa for his creative and careful development of processing tech- nology and for active discussions.
Further, I would like to thank the technical staff in the Fraunhofer RF-devices- and-circuit and technology-departments, especially Dr. Gundrun Kauffel and W. Fehrenbach.
Preface IX Dr. Hardy Sledzik, Dr. Patrick Schuh, Dr. Ralf Leberer, and Dr. Martin Oppermann at EADS DE in Ulm for good cooperation and for valuable dis- cussions.
Dipl.Ing. Dirk Wiegner, Dr. Wolfgang Templ, and Ulrich Seyfried at the Research Center at Alcatel-Lucent/Stuttgart for outstanding cooperation on highly-linear power amplifiers.
Dr. Thomas R¨odle and his team at NXP research center, Nimwegen, for good cooperation on power amplifier technology.
The Team at United Monolithic Semiconductors (UMS), Ulm for good coop- eration on device technology.
Mark van Heijningen and Dr. Frank van Vliet at TNO Safety and Security, the Hague, Netherlands, for the good cooperation on high-power amplifiers at Ka-band.
Joyce Visne, Wien, for her patient and thorough language corrections and her kind support.
The Springer team, especially, Adelheid Duhm and Dr. Claus Ascheron for their great support and kind understanding.
The le-tex team, especially Steffi Hohensee, for their kind support.
I thank my wife Christine and my son Jonathan, to whom this book is dedi- cated, for their endless patience.
Freiburg i.Br. R¨udiger Quay
Januar 2008
Contents
List of Symbols . . . XVII List of Acronyms . . . XXV
1 Introduction . . . . 1
2 III-N Materials, and the State-of-the-Art of Devices and Circuits . . . . 3
2.1 State-of-the-Art of Materials Research . . . 3
2.1.1 Binary Materials . . . 4
2.1.2 Material Limitations . . . 20
2.1.3 Thermal Properties and Limitations . . . 21
2.1.4 Ternary and Quaternary III-N Materials . . . 23
2.2 Polar Semiconductors for Electronics . . . 28
2.2.1 Spontaneous Polarization . . . 28
2.2.2 Piezoelectric Polarization . . . 30
2.2.3 Device Design Using Polarization-Induced Charges . . 32
2.2.4 Analytical Calculation of Channel Charge Concentrations . . . 38
2.2.5 Doping Issues . . . 38
2.2.6 Surfaces and Interfaces . . . 40
2.2.7 Transport Properties in Polarized Semiconductors . . . 46
2.2.8 Polarization-Based Devices and Their Specific Properties . . . 48
2.3 Electrical and Thermal Limitations of Materials and Devices 48 2.3.1 Physical Modeling of Devices . . . 49
2.3.2 Devices: Figures-of-Merit . . . 51
2.3.3 III-N Devices: Frequency Dispersion . . . 52
2.4 Substrates for Electronic Devices . . . 55
2.4.1 Criteria for Substrate Choice . . . 55
2.4.2 Silicon Carbide Substrates . . . 56
XII Contents
2.4.3 Sapphire Substrates . . . 61
2.4.4 Silicon Substrates . . . 62
2.4.5 GaN and AlN Substrates . . . 62
2.5 State-of-the-Art of Devices and Circuits . . . 65
2.5.1 Nitride-Based Diodes . . . 65
2.5.2 Power Electronics . . . 66
2.5.3 RF-Metal Semiconductor Field-Effect Transistors (MESFETs) . . . 68
2.5.4 Metal Insulator Semiconductor Field-Effect Transistors (MISFETs) . . . 70
2.5.5 High-Electron Mobility Transistors (HEMTs) . . . 71
2.5.6 Heterojunction Bipolar Transistors (HBTs) . . . 84
2.5.7 MMIC HEMT Technology . . . 86
2.6 Applications Issues . . . 87
2.6.1 Broadband Communication . . . 88
2.6.2 Radar Components . . . 88
2.6.3 Electronics in Harsh Environments . . . 89
2.7 Problems . . . 90
3 Epitaxy for III-N-Based Electronic Devices . . . . 91
3.1 The AlGaN/GaN Material System . . . 92
3.1.1 Metal Organic Chemical Vapor Deposition (MOCVD) . . . 92
3.1.2 Molecular Beam Epitaxy (MBE) . . . 112
3.1.3 MOCVD and MBE Growth on Alternative Substrates . . . 121
3.1.4 Epitaxial Lateral Overgrowth (ELO) . . . 122
3.1.5 Hydride Vapor Phase Epitaxy (HVPE) . . . 122
3.2 Indium-Based Compounds and Heterostructures . . . 123
3.2.1 MOCVD Growth of Indium-Based Layers . . . 124
3.2.2 MBE Growth of Indium-Based Layers . . . 125
3.2.3 Indium-Based Heterostructure Growth . . . 126
3.3 Doping and Defects . . . 127
3.3.1 MOCVD Growth . . . 128
3.3.2 MBE Growth . . . 130
3.4 Epitaxial Device Design . . . 131
3.4.1 Geometrical Considerations . . . 131
3.4.2 Growth of Cap Layers . . . 133
3.4.3 Doping . . . 134
3.4.4 AlN Interlayer . . . 135
3.4.5 Channel Concepts . . . 137
3.4.6 Epitaxial In-Situ Device Passivation . . . 137
3.5 Problems . . . 138
Contents XIII
4 Device Processing Technology . . . . 139
4.1 Processing Issues . . . 139
4.2 Device Isolation . . . 142
4.2.1 Mesa Structures . . . 143
4.2.2 Ion Implantation for Isolation . . . 143
4.3 Contact Formation . . . 144
4.3.1 Ohmic Contacts . . . 144
4.3.2 Schottky Contacts . . . 151
4.4 Lithography . . . 157
4.4.1 Optical Lithography . . . 157
4.4.2 Electron Beam Lithography . . . 158
4.4.3 Field Plates and Gate Extensions . . . 160
4.5 Etching and Recess Processes . . . 165
4.5.1 Dry Etching . . . 166
4.5.2 Wet Etching . . . 169
4.5.3 Recess Processes . . . 170
4.6 Surface Engineering and Device Passivation . . . 174
4.6.1 Passivation of the Ungated Device Region . . . 174
4.6.2 Physical Trapping Mechanisms . . . 177
4.6.3 Trap Characterization . . . 178
4.6.4 Technological Measures: Surface Preparation and Dielectrics . . . 182
4.6.5 Epitaxial Measures: Surface Preparation and Dielectrics . . . 188
4.7 Gate Dielectrics . . . 189
4.8 Processing for High-Temperature Operation . . . 191
4.9 Backside Processing . . . 192
4.9.1 Thinning Technologies . . . 192
4.9.2 Viahole Etching and Drilling Technologies . . . 193
4.9.3 Viahole Metallization . . . 195
4.10 Problems . . . 196
5 Device Characterization and Modeling . . . . 197
5.1 Device Characteristics . . . 197
5.1.1 Compact FET Analysis . . . 197
5.1.2 Compact Bipolar Analysis . . . 209
5.2 Frequency Dispersion . . . 211
5.2.1 Dispersion Effects and Characterization . . . 211
5.2.2 Dispersion Characterization and Analysis . . . 214
5.2.3 Models for Frequency Dispersion in Devices . . . 217
5.2.4 Suppression of Frequency Dispersion . . . 220
5.3 Small-Signal Characterization, Analysis, and Modeling . . . 220
5.3.1 RF-Characterization and Invariants . . . 220
5.3.2 Common-Source HEMTs . . . 222
5.3.3 Dual-Gate HEMTs . . . 227
XIV Contents
5.3.4 Pulsed-DC- and RF-Characteristics . . . 227
5.3.5 Small-Signal Modeling . . . 230
5.4 Large-Signal Analysis and Modeling . . . 235
5.4.1 Large-Signal Characterization and Loadpull Results . 235 5.4.2 Large-Signal Modeling . . . 241
5.5 Linearity Analysis and Modeling . . . 255
5.5.1 Basic Understanding . . . 256
5.5.2 Nitride-Specific Linearity Analysis . . . 259
5.6 Noise Analysis . . . 262
5.6.1 Low-Frequency Noise . . . 262
5.6.2 RF-Noise Analysis and Characterization . . . 265
5.7 Problems . . . 270
6 Circuit Considerations and III-N Examples . . . . 271
6.1 Passive Circuit Modeling . . . 271
6.1.1 Coplanar-Waveguide Transmission-Line Elements . . . . 271
6.1.2 Microstrip-Transmission-Line Elements . . . 273
6.2 High-Voltage High-Power Amplifiers . . . 274
6.2.1 Basic Principles of High-Voltage High-Power Operation . . . 274
6.2.2 General Design Considerations of III-N Amplifiers . . . 278
6.2.3 Mobile Communication Amplifiers Between 500 MHz and 6 GHz . . . 279
6.2.4 C-Frequency Band High-Power Amplifiers . . . 285
6.2.5 X-Band High-Power Amplifiers . . . 287
6.2.6 Design, Impedance Levels, and Matching Networks . . 294
6.2.7 Broadband GaN Highly Linear Amplifiers . . . 297
6.2.8 GaN Mm-wave Power Amplifiers . . . 298
6.3 Robust GaN Low-Noise Amplifiers . . . 300
6.3.1 State-of-the-Art of GaN Low-Noise Amplifiers . . . 300
6.3.2 Examples of GaN MMIC LNAs . . . 301
6.4 Oscillators, Mixers, and Attenuators . . . 304
6.4.1 Oscillators . . . 307
6.4.2 GaN HEMT Mixer Circuits . . . 307
6.4.3 Attenuators and Switches . . . 308
6.5 Problems . . . 309
7 Reliability Aspects and High-Temperature Operation . . . . 311
7.1 An Overview of Device Testing and of Failure Mechanisms . . . 311
7.1.1 Description of Device Degradation . . . 311
7.1.2 Degradation Mechanisms in III-N FETs . . . 314
7.1.3 III-V HBT Device Degradation . . . 316
7.2 Analysis of Nitride-Specific Degradation Mechanisms . . . 317
7.2.1 DC-Degradation . . . 318
7.2.2 RF-Degradation . . . 322
Contents XV
7.3 Failure Analysis . . . 324
7.3.1 Failure Mechanisms . . . 325
7.3.2 Reliability Case Studies . . . 327
7.4 Radiation Effects . . . 331
7.5 High-Temperature Operation . . . 332
7.6 Problems . . . 336
8 Integration, Thermal Management, and Packaging . . . . 337
8.1 Passive MMIC Technologies . . . 337
8.1.1 Passive Element Technologies . . . 337
8.1.2 Microstrip Backend Technology . . . 340
8.2 Integration Issues . . . 341
8.3 Thermal Management . . . 343
8.3.1 Thermal Analysis . . . 343
8.3.2 Thermal Material Selection and Modeling . . . 345
8.3.3 Basic Thermal Findings, Heat Sources, and Thermal Resistances . . . 349
8.3.4 Backside Cooling . . . 352
8.3.5 Flip-Chip Integration . . . 355
8.3.6 Dynamic Thermal Effects . . . 357
8.4 Device and MMIC Packaging . . . 358
8.4.1 Dicing . . . 358
8.4.2 Die-Attach . . . 359
8.4.3 Package Technology Selection . . . 361
8.4.4 Thermal Management for Linear Applications . . . 363
8.4.5 Active Cooling . . . 365
8.5 Problems . . . 366
9 Outlook . . . . 367
Appendix . . . . 369
References of Chapter 2 . . . . 371
References of Chapter 3 . . . . 395
References of Chapter 4 . . . . 405
References of Chapter 5 . . . . 419
References of Chapter 6 . . . . 429
References of Chapter 7 . . . . 439
References of Chapter 8 . . . . 447
Index . . . . 455
List of Symbols
Δ Step, difference, change
ΔEV, ΔEC Discontinuity of the valence/conduction band at a heterointerface
ΔEg Total difference of the bandgaps at
a heterointerface
Δf Frequency interval
ΔV Voltage drop over the depletion zone
Θ(T0) Temperature-dependent thermal
resistance
α, β, γ General exponent
α General temperature coefficient
α Common base current gain
αa, αc Coefficients of thermal expansion along a- and c-axis
αAB Temperature exponent of the ternary
AxB1−x
αH Hooge parameter
αn, αp Impact ionization parameter for elec- trons and holes
αn Fitting parameter in the LS-model
αT Base transmission factor
αS Fitting parameter in the LS-model
β Common emitter current gain in bipolar
devices
γi Emitter injection efficiency
δ The base recombination factor
ε Permittivity
ij Dielectric tensor components
0 Dielectric constant
εr Relative permittivity
XVIII List of Symbols
εeffr Effective permittivity
εinfr Relative permittivity for ω→ ∞
ηd Drain efficiency
κL Lattice thermal conductivity
κL(T ) Thermal conductivity as a function of
temperature
κA300 Thermal conductivity at 300 K
of material A
λn Fitting parameter in the LS-model
μν Mobility of carrier type ν
μAB Mobility of the ternary semiconductor
AxB1−xN
τ Phase term of the transconductance gm
τthermal Thermal time constant
φB Schottky barrier potential
ψ Electrostatic potential
ψi Polynomials of the potential
ρs Semiconductor resistivity
ρc Metal resistivity
σB Total interface charge at the boundary
σB,SP Interface charge due to spontaneous
polarization
σB,PZ Interface charge due to piezoelectric polarization
σA Electric drift-region-conductance per
unit area in the semiconductor
τD The delay due to the extension of the
depletion zone to the drain
τ Small-signal phase constant
τRC Channel-charge RC-delay
τT Total delay
τe, τb, τc Emitter, base, collector delay
τTR Transistor delay
τthermal Thermal time constant
ω Oscillation frequency
A Area
AR Richardson constant
A1, . . . , An General coefficient
Aν Coefficient for impact ionization for
carrier ν = n,p
B Direct radiative recombination parame-
ter
B0 Bulk modulus
BVCE0 Open collector–emitter breakdown
voltage
List of Symbols XIX
BVDS Drain–source breakdown voltage
BVDS RF RF drain–source breakdown voltage
BVGD Gate–drain diode breakdown voltage
BVGS Gate–source diode breakdown voltage
C Correlation parameter
C Capacitance in the passive model
Cij Elastic constants index i, j
Cth Thermal capacitance
Cds Drain–source capacitance
Cg Gate capacitance
Cgd Gate–drain capacitance
Cgs Gate–source capacitance
Cjc Collector junction capacitance
Cje Emitter junction capacitance
Cpds, Cpgs, Cpgd Parasitic drain–source, gate–source, and gate–drain capacitances
Cgs,0,Cgd,0 Large-signal charge modeling coefficients
C0 Static capacitance
Css Parasitic capacitance in the dispersion
model
Cth Thermal capacitance
DnB,DpE Diffusivity of electrons in the base, holes in the emitter
E Local electric field
EA Acceptor energy
Ea Activation energy
Ebreak Breakdown field
Ecrit Critical field
EC Conduction band energy
EF(x) Fermi energy at position x
Ef1 Fermi-level correction energy
Eg Bandgap energy
Eg,Γ Bandgap energy in the Γ -valley
Eg,Γ1, Eg,Γ3 Bandgap energy in the Γ1, Γ3-valley
Eg,G−A Bandgap energy in the G–A valley
Eg,L Bandgap energy in the L-valley
Eg,L−M Bandgap energy in the L–M valley
Eg,X Bandgap energy in the X-valley
Eg,0 Bandgap energy at TL= 0 K
EV Valence band energy
G Conductance in the passive model
Gass Associated gain
Gp Power gain
Gm,2, Gm,d, Gm,2,d Current parameters in Volterra approach
H Hardness
XX List of Symbols
I0 Current parameter in the diode equation
I0 Current at time t= 0
IB, IC, IE Base, collector, and emitter currents
ID Drain current
IDmax,IDmin Maximum, minimum drain current IDmax,RF, IDmin,RF Maximum/minimum RF-drain current
IDS Drain–source current
IDpp Peak-to-peak drain current
IDsat saturated drain current
IDSn,IDSp Drain–source current in the LS-modeling
IDq Quiescent drain current
IDSS Saturated drain current, typically at
VGS= 0 V
IG Gate current
II3 Ratio of input intermodulation 3rd order
IM3 Intermodulation distortion ratio
3rd order
IM D3 Intermodulation distortion 3rd order
Iij Current at port with index i,j
Iopt Drain current optimized for noise figure
Ipk, Ipk0 Peak current parameter in LS-model
Kbg Dispersion parameter in the LS-model
Ktrg Soft-breakdown pinch-off parameter
KC Fracture toughness
L Channel length
L Line inductance in the passive model
Le Emitter length
LD, LG, LS Drain, gate, and source inductances
LD Length of the depletion zone
Lsb Soft breakdown function
Lsb0 LS-parameter for the soft-breakdown
Lsd1 Auxiliary function
MAG Maximum available gain
MC Number of equivalent minima at the
conduction band
MSG Maximum stable gain
MTBF Median time before failure
MTTF Median time to failure
NA Acceptor doping concentration
NB Base carrier concetrations
NC Effective density of states of the
conduction band
ND Donor doping concentration
NDC Donor doping concentration in the
collector
List of Symbols XXI
NE Emitter carrier concentration
NF Noise figure
NF,min Minimum noise figure at optimum
impedance
NT Concentration of traps
NV Effective density of states of the valence
band
OIP3 Output intercept point third order
Pi Function in the charge model
PAE Power-added-efficiency
P−1dB Output power at 1 dB compression
PDC DC-power
Pdiss Dissipated power
Pin Input power
Pij Large-signal parameter for the pinch-off
voltage
Pout Output power
PSP Spontaneous polarization
PPZ Piezoelectric polarization
Psat Saturated output power
R Resistance
RCon Contact resistance
RD Drain resistance
RD,semi Semiconductor contribution to RD
RL Load resistance/impedance
RS,met, RD,met Metal contribution to RSand RD RS, RG, RD Parasitic source, gate, and drain
resistances
RS Series resistance of diode
Rband Band edge contribution to the source
resistance RS
Rbb Base resistance
Rchan Channel resistance
Rds Drain–source resistance
Rgap Contribution of the contact gap to Rbb
Rgd,Rgs Gate–drain/–source resistance
Ri Input resistance
Rn Equivalent noise resistance
Ron On-resistance
Ropt Optimum impedance
Rspread Spread contribution to Rbb
Rss Parasitic output resistance in the
dispersion model
Rth Thermal resistance
Sij Scattering (S-) parameter, i, j = 1, 2
XXII List of Symbols
Sν(f ) Spectral noise density
Tchan Channel temperature
TDebye Debye-temperature
TDrain, TGate Drain and gate noise-temperature
T (Ex) Tunneling probability
TL Local lattice temperature
Tsub Substrate temperature
T0 Backside temperature in the LS-model
U Unilateral gain
V1 Variable in the Curtice model
VBE, VCE, VBC Base–emitter, collector–emitter, and collector–base voltages
Vbreakdown Breakdown voltage
VDS, VGD, VGS Drain–source, gate–drain, and gate–source voltages
VDS0, VGS0 Quiescent drain–source/gate–source voltage
VD,max,RF, VD,min,RF Maximum/minimum RF-VDS-voltage VGS,X Dispersion corrected VGS-voltages VGS,3psat, VGS,3plin Linearity parameters
Vbgate Breakdown parameter in the LS-model
Vdgt Gate–drain voltage function
Vkl Voltage at device port k,l
Vknee Knee voltage
Vp Pinch-off voltage
Vp2 Doping correction to the threshold
voltage
Vthr Threshold voltage
W Wafer bow
We, Web Emitter-(base) width
Wg Gate width
XEB,XE Thickness of the emitter, base Yij Y -parameter for i, j = 1, 2
Zds Complex output conductance
Zij Z-parameter for i, j = 1, 2
Z0 Characteristic impedance
a, b, c, d, n General parameters
agate−lag, adrain−lag Dispersion parameters for gate and drain-lag
agate,cw,adrain,cw Dispersion parameters comparing pulsed and cw
a0, c0 Lattice parameters
c300 Heat capacity at 300 K
cL,AB Nonlinear coefficient of the thermal con-
ductivity of the ternary semiconductor
List of Symbols XXIII
d Thickness, length
dAlGaN Thickness of AlGaN
deff Effective gate-to-channel separation
ddoping Channel layer thickness
dsub Substrate diameter
eij Piezoelectric coefficient
fT Current gain cut-off frequency
fT,ext Extrinsic current gain cut-off frequency
f Frequency
fc Frequency for k = 1
fc Lattice mismatch
fmax Maximum frequency of oscillation
f10 dB Maximum frequency which leaves 10 dB
of power gain
f (t,μ, σ)lognorm Log-normal distribution function f (t,μ, σ)norm Normal distribution function
f1,f2 Distribution function
gds Output conductance
gds m gds Derivatives of output conductance
gds,ext Extrinsic output conductance
gds,ext(CW(RF or Pulsed)) Extrinsic output conductance for CW, RF, or pulsed operation
gm (Complex) transconductance
gm , gm Derivatives of transconductance
gmi Intrinsic transconductance
gm,max Maximum transconductance
h, ¯h (Reduced) Planck constant
h21 Current–gain
h(t) Thermal response function in the time
domain
ids Intrinsic drain source current
iII Impact ionization current in the LS-
model
id, ig Noise current at drain and gate
kB Boltzmann constant
kf Fukui factor
kn, krel,n Drain-lag dispersion model parameters
k Stability factor
lfps, lfpd Field-plate extension to the source and drain side
lgd, lgs Gate-to-drain/-to-source separation
lgg Gate-to-gate pitch
lg Gate length
mb Doping coefficient
me Free electron mass
XXIV List of Symbols
mn Effective electron mass
mn(Γ -K), mn(Γ -A), mn(Γ -M)
Effective electron mass at the Γ -K/A/M transition
mn(X) Effective electron mass in X-valley
mν,AB Effective carrier mass of the
semi-conductor AxB1−xN
mn,l Longitudinal electron mass
mn,t Transversal electron mass
mp Effective hole mass
mp,h Effective heavy hole mass
mp,l Light hole mass
mp,so Spin–orbit hole mass
m∗ Tunneling mass
n A normal vector
n Electron concentration
n Ideality factor
n Refractive index
nchannel Channel charge density
ni Intrinsic carrier concentration
nsheet Sheet carrier concentration
p Hole concentration
q Elementary charge
qbulk,traps Charge of bulk traps
qchannel Channel charge
qdiel,interface Interface charge
qdoping Doping charge
qinitial Dynamic charge
qsemi,interfaces Charge at the semiconductor interfaces
t Time
t Thickness of the current-supporting layer
tad Thickness of the adhesive
tsem Semiconductor thickness
tsub Substrate thickness
tsubm Submount thickness
¯
vds,¯vgs Static voltage components in dispersion model
vds, vd Intrinsic drain (source) voltage
veff Effective carrier velocity
vgs, vg Intrinsic gate (source) voltage
vpeak Peak carrier velocity
vsat Saturated carrier velocity
x, y Material composition parameter
y Distance
List of Acronyms
2DEG Two-Dimensional Electron Gas
3G 3rd generation (of mobile communication)
4G 4th generation (of mobile communication)
4H, 6H Polytypes of SiC
AC Alternating Current
ACLR Adjacent Channel Leakage Ratio
ACPR Adjacent Channel Power Ratio
ADS Advanced Design System
AFM Atomic Force Microscopy
AlN Aluminum nitride
AESA Active Electronically Scanned Array
ASIC Application Specific Integrated Circuit
BCB Bencocyclobutene
BEEM Ballistic Electron Emission Spectroscopy
BGA Ball-Grid-Array
BJT Bipolar Junction Transistor
BN Boron Nitride
BS Backside Cooling
BV Breakdown Voltage
CAD Computer Aided Design
CAFM Conductive Atomic Force Microscopy
CAIBE Chemically-Assisted Ion Beam Etching
CAT-CVD Catalytic Chemical Vapor Deposition
CAVET Current Aperture Vertical Electron Transistor
CDMA Code Division Multiple Access
CMOS Complementary Metal Oxide Semiconductor
CMP Chemical Mechanical Polishing
CTE Coefficient of Thermal Expansion
CVD Chemical Vapor Deposition
CW Continuous Wave
XXVI List of Acronyms
c cubic
DBF Digital Beam-Forming
DC Direct Current
DD Drift-Diffusion
DLT(F)S Deep Level Transient (Fourier) Spectroscopy
DHBT Double Heterojunction Bipolar Transistor
DHFET Double Heterojunction Field Effect Transistor DHHEMT Double Heterojunction High Electron Mobility
Transistor
DOD U.S. Department of Defense
DPD Digital Predistortion
DRA Driver Amplifier
EBIC Electron-Beam Induced Current
ECR Electron Cyclotron Resonance
ECMP Electrochemical-Mechanical Polishing
EDGE Enhanced Data Rates for GSM Evolution
EDX Electron Diffraction
EER Envelope Elimination and Restoration
ELO, ELOG, LEO Epitaxial Lateral Overgrowth
ESD Electrostatic Discharge
ET Envelope-Tracking
EUV Extreme Ultraviolet
EVM Error Vector Magnitude
FC Flip-Chip
FET Field Effect Transistor
FIB Focussed Ion Beam
FIT Failures in Time
FOM Figure-Of-Merit
GaAs Gallium Arsenide
GaN Gallium Nitride
GCPW Grounded Coplanar-Waveguide
GSM Global System for Mobile Communications
HBT Heterojunction Bipolar Transistor
HCI Hot Carrier Injection
HEMT High Electron Mobility Transistor
HFET Heterostructure Field Effect Transistor
HPA High-Power Amplifier
HPSI High-Purity Semi-Insulating (substrates)
HR High-Resistivity
HTCC High-Temperature Cofired Ceramics
HTCVD High-Temperature Chemical Vapor Deposition
HVPE Hydride Vapor Phase Epitaxy
IC Integrated Circuit
ICP Inductively Coupled Plasma
IDLDMOS Interdigitated-Drain LDMOS
List of Acronyms XXVII
IF Intermediate Frequency
II Impact Ionization
IMPATT IMPact Avalanche Transit Time
InAlN Indium Aluminum Nitride
InAs Indium Arsenide
InGaN Indium Gallium Nitride
InN Indium Nitride
JFET Junction Field-Effect Transistor
LDMOS Laterally diffused MOS
LED Light-emitting Diode
LEEN Low-Energy Electron-Excited Nanoscale
Luminescence Spectroscopy
LNA Low-Noise Amplifier
LO Local Oscillator
LPCVD Low-Pressure Chemical Vapor Deposition
LT Low-Temperature
LTCC Low-Temperature Cofired Ceramics
MAG Maximum Available Gain
MBE Molecular Beam Epitaxy
MC Monte Carlo
MCM Multi-Chip Module
MEMS Micro-Electro-Mechanical Systems
MERFS Micro Electromagnetic Radio Frequency System
MESFET MEtal Semiconductor Field Effect Transistor
MHEMT Metamorphic HEMT
MIC Microwave Integrated Circuit
MIM Metal–Insulator–Metal
MISFET Metal Insulator Field Effect Transistor
MISHEMT Metal Insulator Semiconductor HEMT
MMIC Monolithic Microwave Integrated Circuit
MOCVD Metal Organic Chemical Vapor Deposition
MOD Ministry of Defense
MODFET Modulation-Doped FET
MOMBE Metal Organic Molecular Beam Epitaxy
MOS Metal–Oxide–Semiconductor
MOSFET Metal–Oxide–Semiconductor FET
MOSDHFET Metal–Oxide Double Heterostructure FET
MOVPE Metal Organic Vapor Phase Epitaxy
MSG Maximum Stable Gain
MSL Microstrip Line
MTBF Mean Time Before Failure
MTTF Mean Time to Failure
NBTI Negative Bias Temperature Instability
NID Non-Intentionally Doped
NiCr Nickel Chromium
XXVIII List of Acronyms
OFDM Orthogonal Frequency-Division Multiplexing
ONO Oxide–Nitride–Oxide
PA Power Amplifier
PAE Power-Added Efficiency
PAMBE Plasma-Assisted Molecular Beam Epitaxy
PAR Peak-to-Average Ratio
PAS Positron Annihilation Spectroscopy
PCB Printed Circuit Board
PCDE Peak Code Domain Error
PEC Photo-enhanced Electrochemical Etching
PECVD Plasma-enhanced Chemical Vapor Deposition
PHEMT Pseudomorphic HEMT
PIC Polarization-Induced Charge
PL Photoluminesce
PLM Polarized Light Microscopy
PVT Physical Vapor Deposition
RF Radio Frequency
RIE Reactive Ion Etching
RMS Root-Mean Square
RTA Rapid Thermal Annealing
Rx Receiver
SAR Synthetic Aperture Radar
SAW Surface Acoustic Wave
SEM Scanning Electron Microscopy
SH Self-Heating
SHBT Single Heterojunction Bipolar Transistor SHFET Single Heterojunction Field Effect Transistor SHHEMT Single Heterojunction High Electron Mobility
Transistor
s.i., SI Semi-Insulating
SiC Silicon Carbide
SiCOI Silicon Carbide on Insulator
SiCoSiC Silicon Carbide on polySiC
SIMS Secondary Ion Mass Spectroscopy
SiN Silicon Nitride
SIP System-In-Package
SIT Static Induction Transistor
SKPM Scanning Kelvin Probe Microscopy
SMD Surface Mount Device
SoC System on a Chip
SOI Silicon On Insulator
SopSiC Silicon on poly-crystalline SiC
SPDT Single Pole Double Throw
SRPES Synchrotron Radiation Photoemission
Spectroscopy
List of Acronyms XXIX
SRH Shockley–Read–Hall
SSPA Solid-State Power Amplifier
STEM Scanning Tunneling Electron Microscopy
TaN Tantalum Nitride
TDD Threading-Dislocation Density
TE Thermionic Emission
TEM Transmission Electron Microscopy
TLM Transmission-Line Model
TMGa, TMAl, TMIn TrimethylGallium, TriMethylAluminum, TriMethylIndium
T/R,TRX Transmit/Receive
TWA Traveling Wave Amplifier
TWTA Traveling Wave Tube Amplifier
UWB Ultra-Wide Band
VCO Voltage-Controlled Oscillator
WBG Wide BandGap
WBS Wide Bandgap Semiconductor
WCDMA Wideband Code Division Multiple Access
WiMAX Worldwide interoperability For Microwave Access
Wz Wurtzite
XRD X-Ray Diffraction
Zb Zincblende