Electron Transport In Semiconductors Research Articles

A WENO-Solver for the 1D Non-Stationary Boltzmann–Poisson System for Semiconductor Devices

In this work we present preliminary results of a high order WENO scheme applied to a new formulation of the Boltzmann equation (BTE) describing electron transport in semiconductor devices with a spherical coordinate system for the phase velocity space. The problem is two dimensional in the phase velocity space and one dimensional in the physical space, plus the time variable driving to steady states. The new formulation avoids the singularity due to the spherical coordinate system.

Negative Differential Conductivity in Gases: The “True Origin”

In a recent article [Yamamoto and Ikuta: J. Phys. Soc. Jpn. 68 (1999) 2602] state that the true origin of negative differential conductivity (NDC) has never been shown, in apparent contradiction of claims made in earlier papers [Z. Lj et al. .: Aust. J. Phys. 37 (1984) 23; R. E. Robson: ibid. 37 (1984) 35]. In the present paper, we argue that the true origin of NDC has indeed been explained satisfactorily, and present a comprehensive range of calculations for a number of cases, demonstrating the effectiveness of momentum transfer theory [ Hot electron transport in semiconductors (Springer, Berlin, 1985) p. 82] for understanding NDC from both a qualitative and quantitative perspective.

Wigner-function approach to multiband transport in semiconductors

In this work we present a one-dimensional, multi-band model for electron transport in semiconductors that makes use of the Wigner-function formalism and that allows for energy bands of any shape. A simplified two-band model is then derived from the general equations, by using the parabolic band approximation.

Field effect on the impact ionization rate in semiconductors

Impact ionization plays a crucial role for electron transport in semiconductors at high electric fields. We derive appropriate quantum kinetic equations for electron transport in semiconductors within linear response theory. The field-dependent collision integral is evaluated for the process of impact ionization. A known, essentially analytical result is reproduced within the parabolic band approximation [W. Quade et al., Phys. Rev. B 50, 7398 (1994)]. Based on the numerical results for zero field strengths but realistic band structures, a fit formula is proposed for the respective field-dependent impact ionization rate. Explicit results are given for GaAs, Si, GaN, ZnS, and SrS.

ELASTIC AND DRIFT–DIFFUSION LIMITS OF ELECTRON–PHONON INTERACTION IN SEMICONDUCTORS

This paper deals with electron transport in semiconductors when electron–phonon interaction is considered. Smallness of the mean free path compared to a characteristic length scale and of the phonon energy compared to the thermal energy of the crystal are assumed. The corresponding limits in the transport problem are carried out and shown not to commute. An intermediate limit leads to a new macroscopic model.

A Lattice Boltzmann Scheme for Semiconductor Dynamics

We discuss an extension of the Lattice Boltzmann method which may prove useful for the numerical study of electron transport in semiconductors.

Performance of silicon drift detectors in a magnetic field

A study of the properties of silicon drift detectors in a magnetic field was carried out. A silicon drift detector with 41 anodes, providing unambiguous x and y position information, was used for measurements. Studies were done in three principal orientations of the detector relative to the direction of the magnetic field. The magnetic field was varied between 0 and 0.7 T and the drift field between 300 and 600 V/cm. Basic agreement with the theory of electron transport in semiconductors in a magnetic field was found. The transport properties of electrons in a magnetic field can be described by a mobility matrix. The components of the matrix depend on the electron mobility, Hall mobility and on the vector of the magnetic field. The precision of measurement was better than 0.2% for most of the parameters. For the electric field of a silicon drift detector, there is a first-order effect of the magnetic field only in one out of three principal directions. In this direction, the plane of the detector is perpendicular to the magnetic field and electrons drift at an angle α relative to the direction of the drift field. In two other principal directions, which are more important for tracking of the particles with drift detectors, there are no first-order magnetic effects.

A precise new method to evaluate Monte Carlo simulations of electron transport in semiconductors

Monte Carlo simulations of the electron drift response to an ac-electric field are used to calculate the power dependent third harmonic generation efficiency for far-infrared radiation. The results are compared with far-infrared frequency tripling experiments. It is shown that the nonlinear optical properties are much more sensitive to parameter changes in the Monte Carlo simulation than conventional drift velocity results. Hence, this is a sensitive method to test Monte Carlo transport simulations.

Study of high-field electron transport in semiconductors using balance equations for nonparabolic multivalley systems

Balance equations for high-field electron transport in nonparabolic multiband (multivalley) semiconductors are proposed based on the Heisenberg equations of motion for the total physical momentum, the total energy and the population of carriers in each energy band (each valley), and the statistical average with respect to an initial density matrix having a lattice wave-vector shift, an electron temperature, and a chemical potential for each energy band (each valley) as parameters. As an example, these equations are applied to the discussion of hot-electron transport in bulk Si, assuming Kane-type energy dispersion for six elliptical valleys. The theoretical results are in good agreement with experiments and with Monte Carlo simulations, over the entire range of the electric field up to 140 kV/cm.

On a hierarchy of macroscopic models for semiconductors

This paper shows that various models of electron transport in semiconductors that have been previously proposed in the literature can be connected one with each other by the diffusion approximation methodology. We first investigate the diffusion limit of the semiconductor Boltzmann equation towards the so-called ‘‘spherical harmonic expansion model,’’ under the assumption of dominant elastic scattering. Then, this model is again connected, either to the energy-transport model or to a ‘‘periodic spherical harmonic expansion model’’ through a diffusion approximation, respectively making electron–electron or phonon scattering large. We provide the mathematical background which makes the Hilbert expansions associated with these various diffusion limits rigorous.

The Child-Langmuir law as a model for electron transport in semiconductors

A model for space-charge limited electron transport in an N +- N- N + device and a Schottky diode is proposed. It is based on the smallness of the lattice temperature with respect to the applied voltage. This model, derived from the stationary Boltzmann equation of semiconductors, has a much lower computational cost and leads to a good prediction for the I- V curve as well as for the built-in potential.

Distribution functions and balance equations of drifting Bloch electrons in an electric field.

The Lei-Ting balance-equation method for high-field electron transport in semiconductors has recently been extended to general energy bands by several authors with different results. We present a test of these extensions, especially those proposed by Lei [Phys. Status Solidi B 170, 519 (1992)] and by Huang and Wu [Phys. Rev. B 49, 2223 (1994)], by applying them to superlattice miniband transport. It is shown that except for Lei's nonparabolic method, none of them is able to produce the well-established negative differential mobility of the Esaki-Tsu type in the vertical conduction of a semiconductor superlattice. Some confusions concerning the nature of the distribution functions in the balance-equation theory are discussed.

Three-dimensional simulation of semiconductor devices: state of the art and prospects

In this paper we present a generalized model for electron transport in semiconductors accounting for three separate energy balance equations. Such a model generalizes the hydrodynamic and the electrothermal models, and comprises six partial differential equations, to be solved within the device domain with suitable boundary conditions. Next, we present simulation results obtained with a 3D code implementing a partial set of the above equations, which leads to a modified electrothermal model, and discuss the current status and future trends in multidimensional device simulation.

Weighted Monte Carlo approach to electron transport in semiconductors

The theory of electron transport in semiconductors is traditionally formulated in terms of the semiclassical Boltzmann equation. In nonlinear transport such an equation must be solved without linearization with respect to the external driving fields. This task is practically impossible by analytical means, but for many years a Monte Carlo numerical technique has been successfully applied to all sorts of problems in semiconductor electron transport. In this paper a new approach to Monte Carlo simulation of electron transport in semiconductors, which has recently appeared in the literature, is reviewed. In the traditional Monte Carlo approach a direct simulation of the electron motion is realized, where all possible events (scattering processes) occur with the same probability as in the 'real' world. On the contrary, in the new approach, called the weighted Monte Carlo technique, events occur with arbitrary probabilities, and the weight of the particle in the simulation is accordingly modified in such a way as to maintain an unbiased result. In this way it is possible to emphasize, during the simulation, the analysis of the effect of rare events that in standard simulations would occur too rarely. The traditional Monte Carlo approach is recovered as a special case of this new more general technique. Applications of the weighted Monte Carlo technique to the evaluation of high-energy tails of the distribution function and of the electron current through a potential barrier are presented. A generalization of the method to quantum electron transport is also reviewed.

NONLINEAR TRANSPORT OF ELECTRONS UNDER A STRONG HIGH FREQUENCY ELECTRIC FIELD IN SEMICONDUCTORS

The nonlinear transport of electrons in semiconductors is studied when a strong high frequency (HF) electric field is applied together with a direct current (dc) electric field. A set of equations is developed, from which the amplitude and phase of each harmonic component of the electron drift velocity and the electron temperature can be computed. In the weak HF field limit our approach reduces to the well-known memory function method. The DC conductivity decreases and definitely becomes negative with increase of the first and second harmonic components of the applied HF field. Comparison is made with experiment.

Ballistic electron emission testing of semiconductor heterostructures

In ballistic electron emission microscopy (BEEM) and spectroscopy, ballistic electrons are injected into a sample using a scanning tunneling microscope to probe the electrical properties of buried interfaces. In this communication, a method is proposed that uses the BEEM technique to observe the electron wave optical properties of semiconductor heterostructures. This method provides a three-terminal configuration for characterizing electron wave devices that overcomes many of the limitations encountered in other two- and three-terminal measurement techniques. Specifically, the method provides an injector, which is well isolated from the heterostructure, that injects a collimated beam of ballistic carriers with a precisely controlled energy distribution. These carriers accurately probe the quantum transmittance of a voltage-tunable electron wave interference structure, which can be designed with a light doping to minimize impurity and electron-electron scattering. A general procedure is presented for analyzing this experimental configuration based on a combination of the models used to describe BEEM and ballistic electron transport in semiconductors. Using this procedure, BEEM testing of an electron wave energy filter is modeled and clear quantum interference effects are predicted. This BEEM configuration should allow for the precise characterization of a wide range of ballastic electron transport effects such as quantum reflections from interfaces and electron wave interference effects, phenomena that are presently of wide interest.

Electronic transport in semiconductors at high energy

We briefly review the hot-electron effects which have necessitated the development of accurate solutions of the Boltzmann transport equation. The Monte Carlo particle method of simulating electronic transport in semiconductors is described, with emphasis on the importance of the bandstructure and scattering rates. Three active areas of research then reviewed: (1) simulation of femtosecond spectroscopy experiments, (2) precise calculation of the band-to-band impact ionization rates, and (3) calculation of the electron-phonon interaction based on pseudopotentials. With these three examples we indicate the direction Monte Carlo simulation of electronic transport in semiconductors is taking, i.e., the inclusion of more precise physics and the elimination of phenomenological, adjustable parameters.

Lattice-gas approach to semiconductor device simulation

A new approach to semiconductor device simulation is presented which is based on a lattice-gas or cellular-automata model and is quite similar to methods recently explored in fluid dynamics. The approach obtains a stochastic solution to the diffusion-drift partial differential equations describing electron transport in semiconductors. The lattice-gas method appears to be fairly well-suited to electron transport simulation with its ability to handle complex geometry, its ease of programming and its stability being some key advantages. In addition, we show that the structure of the model itself—its Boolean character—leads to a partial inclusion of electron degeneracy effects. Finally, we make a preliminary assessment of the performance of the diffusion-drift lattice-gas model, finding it to be competitive with conventional approaches when its inherent parallelism is fully exploited.

Analytical Description of the Electric Field Effect on the Electron Transport in Semiconductors and Insulators

A l'aide d'un modele developpe precedemment par l'auteur, on obtient une equation de diffusion des electrons excites, en tenant compte de la structure electronique du solide et de l'effet du champ electrique

Novel photoemission approach to hot-electron transport in semiconductors.

We have performed high-resolution energy analysis of the near-band-gap photoemission of a p-type InP/Ag Schottky diode under electrical bias. This original technique brings direct information on high-electric-field electron transport in semiconductors. From our experimental data, using simple models, we estimate characteristic phonon emission times in an energy range which spans the whole first conduction band, and we evidence an efficient ${\mathrm{\ensuremath{\Gamma}}}_{6}$-${\mathit{X}}_{6}$ intervalley transfer.