Large-signal characterization of DDR silicon IMPATTs operating in millimeter-wave and terahertz regime

Abstract: Large-signal (L-S) characterization of double-drift region (DDR) impact avalanche transit time (IMPATT) devices based on silicon designed to operate at different millimeter-wave (mm-wave) and terahertz (THz) frequencies up to 0.5 THz is carried out in this paper using an L-S simulation method developed by the authors based on non-sinusoidal voltage excitation (NSVE) model. L-S simulation results show that the device is capable of delivering peak RF power of 657.64 mW with 8.25% conversion efficiency at 94 GHz for 50% voltage modulation; whereas RF power output and efficiency reduce to 89.61 mW and 2.22% respectively at 0.5 THz for same voltage modulation. Effect of parasitic series resistance on the L-S properties of DDR Si IMPATTs is also investigated, which shows that the decrease in RF power output and conversion efficiency of the device due to series resistance is more pronounced at higher frequencies especially at the THz regime. The NSVE L-S simulation results are compared with well established double-iterative field maximum (DEFM) small-signal (S-S) simulation results and finally both are compared with the experimental results. The comparative study shows that the proposed NSVE L-S simulation results are in closer agreement with experimental results as compared to those of DEFM S-S simulation.

Abstract: The authors have developed a quantum corrected drift-diffusion model for impact avalanche transit time (IMPATT) devices by coupling the density gradient model with the classical drift-diffusion model. A large-signal simulation technique has been developed by incorporating the quantum potentials in the current density equations for the analysis of double-drift region IMPATT devices based on different semiconductors such as Wurtzite---GaN, InP, type-IIb diamond (C), 4H---SiC and Si deigned to operate at different millimeter-wave (mm-wave) and terahertz (THz) frequencies. It is observed that, the RF power output and DC to RF conversion efficiency of the devices operating at higher mm-wave ($$>$$>140 GHz) and THz frequencies reduce due to the incorporation of quantum corrections in the model; but the effect of quantum corrections are negligible for the devices operating at lower mm-wave frequencies ($$\le $$≤140 GHz).

Abstract: Quantum correction is necessary on the classical drift-diffusion (CLDD) model to predict the accurate behavior of high frequency performance of ATT devices at frequencies greater than 200 GHz when the active layer of the device shrinks in the range of 150---350 nm. In the present work, a quantum drift-diffusion model for impact avalanche transit time (IMPATT) devices has been developed by incorporating appropriate quantum mechanical corrections based on density-gradient theory which macroscopically takes into account important quantum mechanical effects such as quantum confinement, quantum tunneling, etc. into the CLDD model. Quantum potentials (synonymous as Bohm potentials) have been incorporated in the current density equations as necessary quantum mechanical corrections for the analysis of millimeter-wave (mm-wave) and Terahertz (THz) IMPATT devices. It is observed that the large-signal (L-S) performance of the device is degraded due to the incorporation of quantum corrections into the model when the frequency of operation increases above 200 GHz; while the effect of quantum corrections are negligible for the devices operating at lower mm-wave frequencies.

Abstract: An attempt is made in this paper to explore the potentiality of semiconducting type-IIb diamond as the base material of double-drift region (DDR) impact avalanche transit time (IMPATT) devices operating at both millimetre-wave (mm-wave) and terahertz (THz) frequencies. A rigorous large-signal (L-S) simulation based on the non-sinusoidal voltage excitation (NSVE) model developed earlier by the authors is used in this study. At first, a simulation study based on avalanche response time reveals that the upper cut-off frequency for DDR diamond IMPATTs is 1.5 THz, while the same for conventional DDR Si IMPATTs is much smaller, i.e. 0.5 THz. The L-S simulation results show that the DDR diamond IMPATT device delivers a peak RF power of 7.79 W with an 18.17% conversion efficiency at 94 GHz; while at 1.5 THz, the peak power output and conversion efficiency decrease to 6.19 mW and 8.17% respectively, taking 50% voltage modulation. A comparative study of DDR IMPATTs based on diamond and Si shows that the former excels over the later as regards high frequency and high power performance at both mm-wave and THz frequency bands. The effect of band to band tunneling on the L-S properties of DDR diamond and Si IMPATTs has also been studied at different mm-wave and THz frequencies.

Abstract: In this paper, we study the effect of energy loss of charge carriers due to carrier-carrier interactions prior to impact ionization on the static and large-signal characteristics of double-drift region impact avalanche transit time (IMPATT) diodes based on Si designed to operate at millimeter-wave (mm-wave) atmospheric window frequencies such as 94, 140, and 220 GHz. The above mentioned effect has been incorporated in the simulation by taking into account a recently reported generalized analytical model of impact ionization rate of charge carriers based on multistage scattering phenomena in the base semiconductor. Results are compared with static and large-signal signal simulation results of the same diodes that we have reported earlier by taking into account the empirical relation of ionization rates fitted from the experimental data (experiment was carried out on IMPATT structures suitable for operating near 100 GHz). It is observed that both the large-signal RF power output and DC to RF conversion efficiency of the diodes are deteriorated significantly due to reduced ionization rates as a consequence of carrier-carrier collision events prior to the impact ionization. This effect is found to be more pronounced in 140 and 220 GHz diodes due to the enhanced carrier-carrier collisions within those diodes having greater background doping densities as compared to 94 GHz diode. The simulation results presented in this paper found to be in closer agreement with the experimental results as compared to the results that we have reported earlier.

Abstract: This paper presents theoretical calculations of the large-signal admittance and efficiency achievable in a silicon p-n-v-ns Read IMPATT diode. A simplified theory is employed to obtain a starting design. This design is then modified to achieve higher efficiency operation as specific device limitations are reached in large-signal (computer) operation. Self-consistent numerical solutions are obtained for equations describing carrier transport, carrier generation, and space-charge balance. The solutions describe the evolution in time of the diode and its associated resonant circuit. Detailed solutions are presented of the hole and electron concentrations, electric field, and terminal current and voltage at various points in time during a cycle of oscillation. Large-signal values of the diode's negative conductance, susceptance, average voltage, and power-generating efficiency are presented as a function of oscillation amplitude for a fixed average current density. For the structure studied, the largest microwave power-generating efficiency (18 percent at 9.6 GHz) has been obtained at a current density of 200 A/cm2, but efficiencies near 10 percent were obtained over a range of current density from 100 to 1000 A/cm2.

Abstract: The theory of ``direct'' and ``phonon‐assisted'' tunneling is reviewed. Theoretical I–V characteristics are calculated using the constant field model. Generalizations to nonconstant field and more complicated band structure models are discussed briefly.

Abstract: This paper discusses the behavior of oscillators with multiple-resonant circuits. It discusses the condition for free-running stable oscillations, the injection locking phenomena, the stable locking range, the noise of free-running and injection-locked oscillators, and a condition for parasitic oscillations in detail, and presents a graphical interpretation of this study for clarity. Finally, this paper shows how broadbanding of oscillators can be achieved with a double-resonant circuit. This provides a systematic guide for the design of broadband frequency deviators and broadband injection-locked oscillators for numerous applications.

Abstract: PART I INTRODUCTION TO SEMICONDUCTORS 1 lNTRODUCTION TO CRYSTALS AND CURRENT CARRIERS IN SEMICONDUCTORS, THE ATOMIC-BOND MODEL 1.1 INTRODUCTION TO CRYSTALS 1.1.1 Atomic Bonds 1.1.2 Three-Dimensional Crystals 1.1.3 Two-Dimensional Crystals: Graphene and Carbon Nanotubes 1.2 CURRENT CARRIERS 1.2.1 Two Types of Current Carriers in Semiconductors 1.2.2 N*Type and P-Type Doping 1.2.3 Electroneutrality Equation 1.2.4 Electron and Hole Generation and Recombination in Thermal Equilibrium 1.3 BASICS OF CRYSTAL GROWTH AND DOPING TECHNIQUES 1.3.1 Crystal-Growth Techniques 1.3.2 Doping Techniques Summary Problems Review Questions 2 THE ENERGY-BAND MODEL 12.1 ELECTRONS AS WAVES 2.1.1 De Broglie Relationship Between Particle and Wave Properties 2.1.2 Wave Function and Wave Packet 2.1.3 Schrodinger Equation 2.2 ENERGY LEVELS IN ATOMS AND ENERGY BANDS IN CRYSTALS 2.2.1 Atomic Structure 2.2.2 Energy Bands in Metals 2.2.3 Energy Gap and Energy Bands in Semiconductors and Insulators 12.3 ELECTRONS AND HOLES AS PARTICLES 2.3.1 Effective Mass and Real E-k Diagrams 2.3.2 The Question of Electron Size: The Uncertainty Principle 2.3.3 Density of Electron States 2.4 POPULATION OF ELECTRON STATES, CONCENTRATIONS OF ELECTRONS A:"D HOLES 2.4.1 Fermi-Dirac Distribution 2.4.2 Maxwell-Boltzmann Approximation and Effective Density of States 2.4.3 Fermi Potential and Doping 2.4.4 Nonequilibrium Carrier Concentrations and Quasi-Fermi Levels Summary Problems Review Questions 3 DRIFT 3.1 ENERGY BANDS WITH APPLIED ELECTRIC FIELD 3.1.1 Energy-Band Presentation of Drift Current 3.1.2 Resistance and Power Dissipation due to Carrier Scattering 3.2 OHM'S LAW, SHEET RESISTANCE, AND CONDUCTIVITY 3.2.1 Designing Integrated-Circuit Resistors 3.2.2 Differential Form of Ohm's Law 3.2.3 Conductivity Ingredients 3.3 CARRIER MOBILITY 3.3.1 Thermal and Drift Velocities 3.3.2 Mobility Definition 3.3.3 Scattering Time and Scattering Cross Section 3.3.4 Mathieson's Rule 3.3.5 Hall Effect Summary Problems Review Questions 4 DlFFUSION 4.1 DIFFUSION-CURRENT EQUATION 4.2 DIFFUSION COEFFICIENT 4.2.1 Einstein Relationship L4.2.2 Haynes-Shockley Experiment 4.2.3 Arrhenius Equation 4.3 BASIC CONTINUITY EQUATION Summary Problems Review Questions 5 GENERATION AND RECOMBINATION 5.1 GENERATION AND RECOMBINATION MECHANISMS 5.2 GENERAL FORM OF THE CONTINUITY EQUATION 5.2.1 Recombination and Generation Rates 5.2.2 Minority-Carrier Lifetime 5.2.3 Diffusion Length 5.3 GENERATION AND RECOMBINATION PHYSICS AND SHOCKLEYREAD- HALL (SRH) THEORY 5.3.1 Capture and Emission Rates in Thermal Equilibrium 5.3.2 Steady-State Equation for the Effective Thermal Generation/Recombination Rate 5.3.3 Special Cases 5.3.4 Surface Generation and Recombination Summary Problems Review Questions PART II FUNDAMENTAL DEVICE STRUCTURES 6 JUNCTIONS 6.1 P-N JUNCTION PRINCIPLES 6.1.1 p-~ Junction in Thermal Equilibrium 6.1.2 Reverse-Biased P-N Junction 6.1.3 Forward-Biased P-K Junction 6.1.4 Breakdown Phenomena 6.2 DC MODEL 6.2.1 Basic Current-Voltage (I-V) Equation 6.2.2 Important Second-Order Effects 6.2.3 Temperature Effects 6.3 CAPACITA CE OF REVERSE-BIASED P-:-I JUNCTION 6.3.1 C-V Dependence 6.3.2 Depletion-Layer Width: Solving the Poisson Equation 6.3.3 SPICE Model for the Depletion-Layer Capacitance 6.4 STORED-CHARGE EFFECTS 6.4.1 Stored Charge and Transit Time 6.4.2 Relationship Between the Transit Time and the Minority-Carrier Lifetime 6.4.3 Switching Characteristics: Reverse-Recovery Time 6.5 METAL-SEMICONDUCTOR CONTACT 6.5.1 Schottky Diode: Rectifying Metal-Semiconductor Contact 6.5.2 Ohmic Metal-Semiconductor Contacts Summary Problems Review Questions 7 MOSFET 7.1 MOS CAPACITOR 7.1.1 Properties of the Gate Oxide and the Oxide-Semiconductor Interface 7.1.2 C-V Curve and the Surface-Potential Dependence on Gate Voltage 7.1.3 Energy-Band Diagrams 7.1.4 Flat4Band Capacitance and Debye Length 7.2 MOSFET PRINCIPLES B.1.1 MOSFET Structure 7.2.2 MOSFET as a Voltage-Controlled Switch B.1.3 The Threshold Voltage and the Body Effect B.1.4 MOSFET as a Voltage-Controlled Current Source: Mechanisms of Current Saturation 7.3 PRINCIPAL CURRENT-VOLTAGE CHARACTERISTICS AND EQUATIONS 7.3.1 SPICE LEVEL 1 Model 7.3.2 SPICE LEVEL 2 Model 7.3.3 SPICE LEVEL 3 Model: Principal Effects 7.4 SECO:\D-OROER EFFECTS 7.4.1 Mobility Reduction with Gate Voltage 7.4.2 Velocity Saturation (Mobility Reduction with Drain Voltage) 7.4.3 Finite Output Resistance 7.4.4 Threshold-Voltage-Related Short-Channel Effects 7.4.5 Threshold Voltage Related Narrow-Channel Effects 7.4.6 Subthreshold Current 7.5 Nanoscale MOSFETs 7.5.1 Down-Scaling Benefits and Rules 7.5.2 Leakage Currents 7.5.3 Advanced MOSFETs 7.6 MOS-BASED MEMORY DEVICES 7.6.1 1C1T DRAM Cell 7.6.2 Flash-Memory Cell Summary Problems Review Questions 8 BJT 8.1 B.JT PRINCIPLES 8.1.1 BJT as a Voltage-Controlled Current Source 8.1.2 BJT Currents and Gain Definitions 8.1.3 Dependence of ? and ? Current Gains on Technological Parameters 8.1.4 The Four Modes of Operation: BJT as a Switch 8.1.5 Complementary BJT 8.1.6 BJT Versus MOSFET 8.2 PRINCIPAL CURRENT-VOLTAGE CHARACTERISTICS, EBERE-MOLL MODEL IN SPICE 8.2.1 Injection Version 8.2.2 Transport Version 8.2.3 SPICE Version 8.3 SECOND*ORDER EFFECTS 8.3.1 Early Effect: Finite Dynamic Output Resistance 8.3.2 Parasitic Resistances 8.3.3 Dependence of Common-Emitter Current Gain on Transistor Current: Low-Current Effects 8.3.4 Dependence of Common-Emitter Current Gain on Transistor Current: Gummel-Poon Model for High-Current Effects 8.4 HETEROJUNCTION BIPOLAR TRANSISTOR Summary Problems Review Questions PART III SUPPLEMENTARY TOPICS 9 PHYSICS OF NANOSCALE DEVICES 9.1 SINGLE-CARRIER EVENTS 9.1.1 Beyond the Classical Principle of Continuity 9.1.2 Current-Time Form of Uncertainty Principle 9.1.3 Carrier-Supply Limit to Diffusion Current 9.1.4 Spatial Uncertainty 9.1.5 Direct Nonequilibrium Modeling of Single-Carrier Events 9.2 TWO-DIMENSIONAL TRANSPORT IN MOSFETs AND HEMTs 9.2.1 Quantum Confinement 9.2.2 HEMT Structure and Characteristics 9.2.3 Application of Classical MOSFET Equations to Two-Dimensional Transport in MOSFETs and HEMTs 9.3 ONE-DIMENSUIONAL TRANSPORT IN NANOWIRES AND CARBON NANOTUBES 9.3.1 Ohmic Transport in Nanowire and Carbon-Nanotube FETs 9.3.2 One-Dimensional Ballistic Transport and the Quantum Conductance Limit Summary Problems Review Questions 10 DEVICE ELECTRONICS, EQUIVALENT CIRCUITS A D SPICE PARAMETERS 10.l DIODES 10.1.1 Static Model and Parameters in SPICE 10.1.2 Large-Signal Equivalent Circuit in SPICE 10.1.3 Parameter Measurement 10.1.4 Small-Signal Equivalent Circuit 10.2 MOSFET 10.2.1 Static Model and Parameters LEVEL 3 in SPICE 10.2.2 Parameter Measurement 10.2.3 Large-Signal Equivalent Circuit and Dynamic Parameters in SPICE 10.2.4 Simple Digital ~1od.el 10.2.5 Small-Signal Equivalent Circuit 10.3 BJT 10.3.1 Static Model and Parameters: Ebers-Moll and Gummel-Poon Levels in SPICE 10.3.2 Parameter Measurement 10.3.3 Large-Signal Equivalent Circuit and Dynamic Parameters in SPICE 10.3.4 Small-Signal Equivalent Circuit Summary Problems Review Questions 11 PHOTONIC DEVICES 11.1 LIGHT EMITTING DIODES (LED) 11.2 PHOTODETECTORS AND SOLAR CELLS 11.2.1 Biasing for Photodetector and Solar-Cell Applications 11.2.2 Carrier Generation in Photodetectors and Solar Cells 11.2.3 Photocurrent Equation 11.3 LASERS 11.3.1 Stimulated Emission, Inversion Population, and Other Fundamental Concepts 11.3.2 A Typical Heterojunction Laser Summary Problems Review Questions 12 JFET AND MESFET 12.1 JFET 12.1.1 JFET Structure 12.1.2 JFET Characteristics 12.1.3 SPICE Model and Parameters 12.2 MESFET 12.2.1 MESFET Structure 12.2.2 MESFET Characteristics 12.2.3 SPICE Model and Parameters Summary Problems Review Questions 13 POWER DEVICES 13.1 POWER DIODES 13.1.1 Drift Region in Power Devices 13.1.2 Switching Characteristics 13.1.3 Schottky Diode 13.2 POWER MOSFET 13.3 IGBT 13.4 THYRISTOR Summary Problems Review Questions

Abstract: Ionization rates for electrons and holes are extracted from photomultiplication measurements on silicon p+n mesa diodes for electric fields of 2·0 × 105−7·7 × 105 V/cm at temperatures of 22, 50, 100 and 150°C. These results are particularly pertinent to the analysis of high-frequency (∼ 100 GHz) silicon IMPATT diodes. The rates obtained here are in reasonable agreement with previously published data of van Overstraeten and DeMan, although slightly larger in magnitude. Calculated curves of breakdown voltage vs background doping level are presented using the room temperature ionization rates. Also a comparison is made to previously reported rates. The new rates provide a closer agreement between predicted and measured breakdown voltages for breakdown voltages less than 70 V.