Carlo Jacoboni

The Monte Carlo method for semiconductor device simulation

1 Introduction.- References.- 2 Charge Transport in Semiconductors.- 2.1 Electron Dynamics.- 2.2 Energy Bands.- 2.2.1 Relationship of Energy to Wavevector.- 2.2.2 Effective Masses.- 2.2.3 Nonparabolicity.- 2.2.4 Herring and Vogt Transformation.- 2.2.5 Actual Bands of Real Semiconductors.- 2.3 Scattering Mechanisms.- 2.3.1 Classification and Physical Discussion.- 2.3.2 Fundamentals of Scattering.- 2.4 Scattering Probabilities.- 2.4.1 Phonon Scattering, Deformation-Potential Interaction.- 2.4.2 Phonon Scattering, Electrostatic Interaction.- 2.4.3 Ionized Impurity Scattering.- 2.4.4 Carrier-Carrier Scattering.- 2.5 Transport Equation.- 2.6 Linear Response and the Relaxation Time Approximation.- 2.6.1 Relaxation Times for the Various Scattering Mechanisms.- 2.6.2 Carrier Mobilities in Various Materials.- 2.7 Diffusion, Noise, and Velocity Autocorrelation Function.- 2.7.1 Basic Macroscopic Equations of Diffusion.- 2.7.2 Diffusion, Autocorrelation Function, and Noise.- 2.7.3 Electron Lifetime and Diffusion Length.- 2.8 Hot Electrons.- 2.9 Transient Transport.- 2.10 The Two-dimensional Electron Gas.- 2.10.1 Subband Levels and Wavefunctions.- 2.10.2 Scattering Rates.- References.- 3 The Monte Carlo Simulation.- 3.1 Fundamentals.- 3.2 Definition of the Physical System.- 3.3 Initial Conditions.- 3.4 The Free Flight, Self Scattering.- 3.5 The Scattering Process.- 3.6 The Choice of the State After Scattering.- 3.6.1 Phonon Scattering, Deformation-Potential Interaction.- 3.6.2 Phonon Scattering, Electrostatic Interaction.- 3.6.3 Ionized Impurity Scattering.- 3.6.4 Carrier-Carrier Scattering.- 3.7 Collection of Results for Steady-State Phenomena.- 3.7.1 Time Averages.- 3.7.2 Synchronous Ensemble.- 3.7.3 Statistical Uncertainty.- 3.8 The Ensemble Monte Carlo (EMC).- 3.9 Many Particle Effects.- 3.9.1 Carrier-Carrier Scattering.- 3.9.2 Molecular Dynamics and Monte Carlo Method.- 3.9.3 Degeneracy in Monte Carlo Calculations.- 3.10 Monte Carlo Simulation of the 2DEG.- 3.11 Special Topics.- 3.11.1 Periodic Fields.- 3.11.2 Diffusion, Autocorrelation Function, and Noise.- 3.11.3 Ohmic Mobility.- 3.11.4 Impact Ionization.- 3.11.5 Magnetic Fields.- 3.11.6 Optical Excitation.- 3.11.7 Quantum Mechanical Corrections.- 3.12 Variance-reducing Techniques.- 3.12.1 Variance Due to Thermal Fluctuations.- 3.12.2 Variance Due to Valley Repopulation.- 3.12.3 Variance Related to Improbable Electron States.- 3.13 Comparison with Other Techniques.- 3.13.1 Analytical Techniques.- 3.13.2 The Iterative Technique.- 3.13.3 Comparison of the Different Techniques.- References.- 4 Review of Semiconductor Devices.- 4.1 Introduction.- 4.2 Historical Evolution of Semiconductor Devices.- 4.2.1 Evolution of Si Devices.- 4.2.2 Evolution of GaAs Devices.- 4.2.3 Technological Features.- 4.2.4 Scaling and Miniaturization.- 4.3 Physical Basis of Semiconductor Devices.- 4.3.1 p-n Junction.- 4.3.2 Bipolar Transistors.- 4.3.3 Heterojunction Bipolar Transistor.- 4.3.4 Metal-Semiconductor Contacts.- 4.3.5 Metal-Semiconductor Field-Effect Transistor.- 4.3.6 Metal-Oxide-Semiconductor Field-Effect Transistor.- 4.3.7 High Electron Mobility Transistor.- 4.3.8 Hot Electron Transistors.- 4.3.9 Permeable Base Transistor.- 4.4 Comparison of Semiconductor Devices.- 4.4.1 Device Parameters.- 4.4.2 Comparison of Semiconductor Devices.- References.- 5 Monte Carlo Simulation of Semiconductor Devices.- 5.1 Introduction.- 5.2 Geometry of the System.- 5.2.1 Boundary Conditions.- 5.2.2 Grid Definition.- 5.2.3 Superparticles.- 5.3 Particle-Mesh Force Calculation.- 5.3.1 Particle-Mesh Calculation in One Dimension.- 5.3.2 Charge Assignment Schemes in Two Dimensions.- 5.4 Poisson Solver and Field Distribution.- 5.4.1 Finite Difference Scheme.- 5.4.2 Matrix Methods.- 5.4.3 Rapid Elliptic Solvers (RES).- 5.4.4 Iterative Methods.- 5.4.5 Calculation of the Electric Field.- 5.4.6 The Collocation Method.- 5.5 The Monte Carlo Simulation of Semiconductor Devices.- 5.5.1 Initial Conditions.- 5.5.2 Time Cycles.- 5.5.3 Free Flight.- 5.5.4 Scattering.- 5.5.5 Carrier-Carrier Scattering.- 5.5.6 Degenerate Statistics.- 5.5.7 Statistics.- 5.5.8 Static Characteristics.- 5.5.9 A.C. Characteristics.- 5.5.10 Noise.- References.- 6 Applications.- 6.1 Introduction.- 6.2 Diodes.- 6.2.1 n+-n-n+ Diodes.- 6.2.2 Schottky Diode.- 6.3 MESFET.- 6.3.1 Short Channel Effects.- 6.3.2 Geometry Effects.- 6.3.3 Space-Charge Injection FET.- 6.3.4 Conclusions.- 6.4 HEMT and Heterojunction Real Space Transfer Devices.- 6.4.1 HEMT.- 6.4.2 Real-Space Transfer Devices.- 6.4.3 Velocity-Modulation Field Effect Transistor.- 6.5 Bipolar Transistor.- 6.6 HBT.- 6.7 MOSFET and MISFET.- 6.7.1 MOSFET.- 6.7.2 GaAs Injection-modulated MISFET.- 6.7.3 Conclusions.- 6.8 Hot Electron Transistors.- 6.8.1 The THETA Device.- 6.8.2 GaAs FET with Hot-Electron Injection Structure.- 6.8.3 Planar-doped-Barrier Transistors.- 6.9 Permeable Base Transistor.- 6.10 Comparison with Traditional Simulators.- References.- Appendix A. Numerical Evaluation of Some Integrals of Interest.- References.- Appendix B. Generation of Random Numbers.- References.

Physics of nonlinear transport in semiconductors

The Lectures.- 1. Phenomenological Physics of Hot Carriers in Semiconductors.- The Carrier Temperature Model.- Drift, Diffusion, and Generation-Recombination of Hot Electrons.- The Influence of Classical Magnetic Fields on Hot Electrons.- Hot Electrons in Semiconductor Devices and Layered Structures.- Appendices,.- 2. Electronic Structure of Semiconductors.- The Single Particle Description: Bonds and Bands.- Many-Body Effects on the Electronic Structure of Semiconductors.- 3 The Electron-Phonon Interaction in Semiconductors.- The Adiabatic Approximation.- The Deformation Potential Interaction.- Non-polar Optical Phonon Scattering.- Polar-Optical Interaction.- Piezoelectric Interaction.- A Microscopic Approach.- Applications.- The Electron-Phonon Interaction in Nonperfect Semiconductors.- 4. Semi-Classical Boltzmann Transport Theory in Semiconductors.- Displaced Maxwellian.- Numerical Techniques.- 5. Quantum Transport Theory.- Concepts.- Structure of High Field Quantum Kinetic Theory.- Many-Body Formulation and the Screening Problem.- 6. Carrier-Carrier Interactions and Screening.- The Intercarrier Interaction.- The Critical Concentrations.- Distribution Functions.- 7. Multiphonon Scattering.- Electron-multiphonon Processes.- Electron-Two phonon Processes.- Results.- Summary.- 8. Experimental Studies of Nonlinear Transport in Semiconductors.- Transport Parameters.- Electron Temperature.- Hot Electron Distribution Functions.- Conclusions.- 8a. Time-of-Flight Techniques..- Description of ToF Techniques.- Types of Information Available from ToF Techniques.- Alternative Techniques.- Summary of ToF Most Significant Applications.- 9. Hot-Electron Transport in Quantizing Magnetic Fields.- The Shubnikov-de Haas Effect.- The Magnetophonon Effect.- Magneto-Impurity Resonance.- 10. Hot Electron Distribution Function in Quantizing Magnetic Fields.- Quantitative Estimates of Electron Temperature.- Study of the Electron Distribution Function in Crossed Fields.- Conclusions.- 11. Hot Electron Effects in Semiconductor Devices.- Transient Hot Electron Effects in Semiconductor Devices.- Conclusions.- 12. Optical Excitation of Hot Carriers.- Optical Excitation of Electron-Hole Pairs.- Carrier Heating by Optical Injection.- Band Filling by Optical Excitation.- Oscillatory Photoconductivity and Photoluminescence.- Conclusions.- 13. Theoretical Concepts of Photoexcited Hot Carriers.- The Barker-Hearn Model.- Solution of the Integral Equation.- Photoexcited Holes in Cu-Doped Germanium.- Effects of Optical Phonons, 360 Further Physical Effects.- 14. The Physics of Nonlinear Absorption and Ultrafast Carrier Relaxation in Semiconductors.- Review of the Germanium Band Structure.- Physical Processes.- Initial Models.- Conclusion.- 15. Nonequilibrium Phonon Processes.- Phonon Instabilities.- Phonon Lifetimes.- Steady-State Effects of Nonthermal Phonons.- Some Further Aspects of PH-Disturbances in Solids.- 16. Noise and Diffusion of Hot Carriers.- Fluctuations and Noise: General Considerations.- Noise Temperatures of Hot Carriers.- Diffusion of Hot Carriers.- Experimental Techniques.- Theoretical Determinations.- Noise Sources.- Noise of Hot Carriers in Devices.- Some Quantum Effects.- Conclusion.- The Seminars.- 1. High-Field Transport of Holes in Elemental Semiconductors.- Theoretical Model.- Results and Discussion.- Conclusions.- 2. Nonlinear Transport in Quasi-One-Dimensional Conductors.- Nonlinear Transport in Organic Charge Transfer Salts: TTF-TCNQ and Related Compounds.- Non-Ohmic Effects in KCP.- Non-Ohmic Conductivity of Quasi-ID Trichalcogenides: NbSe3.- Nonlinear Transport in Highly Conducting Polymers.- Summary.- 3. Optical Absorption of Solids Under Laser Irradiation.- Band Structure Effects.- Optical Properties.- Conclusions.- 4. High Intensity Picosecond Photoexcitation of Semiconductors.- Dynamic Saturation of the Optical Absorption.- High Photogenerated-Carrier Densities.- Hot Phonons,.- The Relaxation-Diffusion-Recombination Model.- Summary.- 5. Hot Electron Contributions in Two and Three Terminal Semiconductor Devices.- Two-Terminal Devices.- Three-Terminal Devices.- 6. Modeling of Carrier Transport in the Finite Collision Duration Regime: Effects in Submicron Semiconductor Devices.- The Intracollisional Field Effect.- The Retarded Equations.- Discussion.- 7. On the Physics of Sub-Micron Semiconductor Devices..- Physical Scales and Phenomena.- On Medium Small Devices.- Very Small Scale Devices.- Synergetic Effects and New Device Concepts.- Formal Theory of Coupled Device Arrays.- List of Participants.

A many-band silicon model for hot-electron transport at high energies

Abstract A new silicon model for electron transport at high electric fields is presented. The model features an original conduction-band structure consisting of three isotropic bands together with the lowest non-parabolic band in a finite spherical Brillouin zone. The bands are given by analytic expressions whose parameters are fixed by best fitting the density of states taken from band-structure calculations. Such a model is consistently used in electron dynamics and in the evaluation of the scattering probabilities. The coupling constants to the scattering agents are determined by best fitting the available experimental data on transport properties. The effect of the new model on the results is discussed for a bulk system with particular attention to the features (e.g. the detailed shape of the electron distribution function) which are important for device applications.

An improved impact‐ionization model for high‐energy electron transport in Si with Monte Carlo simulation

A new model for impact ionization in Si is presented, which goes beyond the limitations of the Keldysh formula and is based on a more realistic scheme developed starting from a first‐order perturbation theory. This scattering mechanism is modeled by an extended band structure which includes many bands for electrons and one band for holes in a finite Brillouin zone. Some processes have been identified to bring the dominant contribution to the scattering probability, in the present approach, for electron energies ranging up to 3 eV. Expressions for the differential and integrated scattering probabilities have been obtained which are consistent with the band model and can be included in a Monte Carlo simulation of the electron gas. Results for transport quantities are shown for a bulk material in presence of homogeneous and static electric fields under physical conditions where impact ionization influences the carrier dynamics. A comparison with theoretical and experimental data from the literature is also g...

Bulk hot-electron properties of cubic semiconductors

Abstract This paper contains a review of charge transport properties at high electric fields in bulk cubic semiconductors. The microscopic theoretical interpretation follows a semi-classical approach and is based on the knowledge of the band structure and scattering mechanism of the material under investigation. For the solution of the Boltzmann equation, the Monte-Carlo simulation technique is considered, which provides an ‘exact’ numerical solution limited only by the simplifying assumptions inherent in the physical model assumed. Experimental techniques for the measurements of the most important transport quantities are briefly surveyed. Comparison between theory and experiment is reported for both electron and hole transport properties in Si, Ge and GaAs. These substances, besides being the best known materials, can in fact be considered as models for any other cubic semiconductor.

Monte Carlo algorithm for hot phonons in polar semiconductors

We present a novel ensemble Monte Carlo procedure for the study of electron and phonon dynamics during the relaxation of photoexcited hot carriers. For the first time hot‐electron and hot‐phonon effects are included together in the same Monte Carlo simulation. The algorithm is applied to a simplified model of GaAs, consisting of one‐type carriers (electrons) in a two‐valley system (L and Γ valleys). The buildup of the phonon population on a picosecond scale is monitored, in parallel with the cooling of the electron distribution. As expected, the presence of nonequilibrium phonons is found to slow down the electron relaxation.

The Wigner-function approach to non-equilibrium electron transport

The Wigner-function (WF) approach to quantum electron transport in semiconductors is reviewed in this paper. The main definitions and properties related to the WF are presented, with a discussion of the various forms of the dynamical equations that govern its evolution. Monte Carlo solutions of such equations are also discussed. Interactions of electrons with applied fields, potential profiles, and phonons are analysed in detail. Finally, several physical applications are presented. Each topic has been developed from basic principles for the benefit of interested readers who are not experts in the particular subjects discussed in this paper.

Monte Carlo simulations of high energy electrons and holes in Si-n-MOSFET's

Monte Carlo simulations of high-energy electrons and holes in Si n-MOSFETs are presented. Key features of this work include the use of a suitable silicon model for carrier transport at high electric fields, an original impact ionization model, and sophisticated numerical techniques to speed up the calculation. The case of submicrometer Si n-MOSFETs is considered as a relevant application. >

Polarization Analysis of Hot-Carrier Light Emission in Silicon

In this paper a theoretical-evaluation is given of the absolute intensity and polarization of light emission from silicon devices due to conduction-conduction (c-c) and valence-valence (v-v) direct transitions. The matrix elements of the momentum operator between Bloch states have been obtained from a full band-structure calculation performed with the pseudopotential method. Results have been obtained by using both analytical model distribution functions and realistic hot-carrier distributions obtained from Monte Carlo (MC) simulations based on the same band model. They show a polarization degree of a few per cent, which should be observable for these transitions.

The Physics of Submicron Semiconductor Devices

Modelling of Sub-Micron Devices.- Boltzmann Transport Equation.- Transport and Material Considerations for Submicron Devices.- Epitaxial Growth for Sub Micron Structures.- Insulator/Semiconductor Interfaces.- Theory of the Electronic Structure of Semiconductor Surfaces and Interfaces.- Deep Levels at Compound-Semiconductor Interfaces.- Ensemble Monte Carlo Techniques.- Noise and Diffusion in Submicron Structures.- Superlattices.- Submicron Lithography.- Quantum Effects in Device Structures Due to Submicron Confinement in One Dimension.- Physics of Heterostructures and Heterostructure Devices.- Correlation Effects in Short Time, Nonstationary Transport.- Device-Device Interactions.- Quantum Transport and the Wigner Function.- Far Infrared Measurements of Velocity Overshoot and Hot Electron Dynamics in Semiconductor Devices.- The Influence of Contacts on the Behavior of Near and Sub-Micron INP Devices.- Monte Carlo Simulation of Transport in Submicron Structures.- Two Dimensional Electron Gas Fet.- Hot Electron Transfer Amplifiers.- New Graded Band Gap and Superlattice Structures and their Applications to Photodetectors, Bipolar Transistors and High-Speed Devices.- Metal-Semiconductor Interfaces.- Nonequilibrium Phonons in Semiconductors: Power Dissipation of Highly Laser-Excited Electron-Hole Plasmas.- Picosecond Measurements of Device and Circuit Transient Response with Optoelectric Techniques.