High-field Transport In Semiconductors Research Articles

New Solution to High-Field Transport in Semiconductors: II. Velocity Saturation and Ballistic Transmission

High-field transport in semiconductor diodes at room temperature is analyzed in the reflection–transmission regime. The pseudo-one-dimensional Boltzmann equation with a constant electric field is transformed into a pair of carrier flux equations. They are analytically solved neither with the relaxation time approximation nor with the perturbation expansion. The carrier energy relaxation due to optical phonon emission is essential in high-field transport. The current- and velocity-field characteristics are closely related to flux transmission through a specific layer, in which the elastic scattering is dominant and the optical phonon emission is absent. If the transmission coefficient is much less than unity, the proportionality of the current to the field results as the Ohm's law in high-field range. The current and velocity tend to saturate when the coefficient approaches unity (ballistic transmission). This result provides simple insight into transport in nanoscale devices.

New Solution to High-Field Transport in Semiconductors: I. Elastic Scattering without Energy Relaxation

High-field transport in a semiconductor diode structure at room temperature is newly analyzed in a reflection–transmission regime. The Boltzmann equation with a constant electric field E is applied to a semiconductor channel of length L, and a pair of flux equations is analytically solved. For applied fields larger than ∼500 V/cm for silicon, the energy relaxation by the acoustic phonon scattering hardly catches up with the energy gain from the field, and the kinetic energy accumulates generating hot carriers. As a limiting case, in this paper we analyze carrier transport with elastic scattering and without energy relaxation. Current density proportional to √E/L is derived for a wide electric field range. At much higher fields, the ballistic transmission of carriers through the channel occurs, and current density tends to saturate. The result will find its application in sufficiently small systems, where energy relaxation by optical phonon scattering is not dominant.

Maximum-entropy principle for static and dynamic high-field transport in semiconductors

Within the maximum entropy principle we present a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport under electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. The theoretical approach is applied to $n\text{\ensuremath{-}}\mathrm{Si}$ at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with experimental data.

Gauge-invariant formulation of high-field transport in semiconductors

Gauge-invariant formulation of high-field transport in semiconductors

Intracollisional field effect: a gauge-invariant formulation in semiconductors

A gauge-invariant formulation of high-field transport in semiconductors is proposed. We revisit the conventional description of carrier–phonon scattering within the Fermi golden rule scheme by means of a gauge-invariant generalization of the scattering rates. With a density-matrix approach, we show that the so-called intracollisional field effect, as usually accounted for, has always been overestimated due to the neglect of the time variation of the basis states, which in turn leads to a ill-defined Markov limit in the carrier–phonon interaction process. This is confirmed by a fully three-dimensional simulation of charge transport in state-of-the-art semiconductor superlattices.

Gauge-Invariant Formulation of Fermi's Golden Rule and Its Application to High-Field Transport in Semiconductors

A gauge-invariant formulation of Fermi's Golden rule is proposed. We shall revisit the conventional description of carrier-phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. We show that the so called intracollisional field effect, as usually accounted for, has been always overestimated due to the neglect of the time variation of the basis states, which in turn leads to a ill-defined Markov limit in the carrier-phonon interaction process. This is confirmed by our fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices.

Gauge-invariant formulation of high-field transport in semiconductors

A gauge-invariant formulation of Fermi's Golden rule is proposed. We shall rivisit conventional description of carrier–phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. We show that the so-called intracollisional field effect—usually accounted for—is ill-defined: it is simply an artifact due to the neglect of the time variation of the basis states which, in turn, leads to a ill-defined Markov limit in the carrier–phonon interaction process. This may account for the surprisingly good agreement between semiclassical and rigorous quantum-transport calculations.

Ultrafast high-field transport in semiconductors

Non-equilibrium transport in GaAs and InP is investigated at electric fields up to 130 kV/cm and with a time resolution of 20 fs. The experiment is based upon ultrabroadband detection of the THz transient emitted by accelerating carriers photo-excitated with 12 fs laser pulses. The strong dependence of the ultrafast dynamics on material and electric field provides new insights into the microscopic mechanisms governing ultrafast electronic conduction. Overshoot velocities as high as 6×10 7 and 8×10 7 cm/s are obtained in GaAs and InP, respectively. Depending on the experimental conditions, the drift distances during the non-thermal regime can exceed 100 nm even at room temperature. In addition, the measurements lead to a detailed understanding of the interplay between free carrier displacement and dielectric response of the polar semiconductors.

Hole initiated impact ionization in wide band gap semiconductors

Band-to-band impact ionization by hot electrons and holes is an important process in high-field transport in semiconductors, leading to carrier multiplication and avalanche breakdown. Here we perform first principles calculations for the respective microscopic scattering rates of both electrons and holes in various wide band gap semiconductors. The impact ionization rates themselves are calculated directly from the electronic band structure derived from empirical pseudopotential calculations for cubic GaN, ZnS, and SrS. In comparison with the electron rates, a cutoff in the hole rate is found due to the relatively narrow valence bandwidths in these wide band gap semiconductors, which correspondingly reduces hole initiated carrier multiplication.

Spectral Functions for Ultra-Fast Phenomena and High Field Transport in Semiconductors

Spectral Functions for Ultra-Fast Phenomena and High Field Transport in Semiconductors

Kinetic theory of high-field transport in semiconductors

The paper deals with electron transport in a semiconductor of arbitrary band structure and electron-phonon interaction, subjected to a high, but not necessarily homogeneous, electric field. The Boltzmann transport equation is simplified under the assumption that the occupation of momentum space is almost isotropic, as is the case for a drifting, not ballistic, electron. A closed-form equation for the electron energy distribution ensues: the equation is of the multivariate Fokker-Planck type in four-dimensional energy-position space. The typical relative departure between the Boltzmann and Fokker-Planck transport equations is the ratio of the hard-phonon energy to the average electron energy. Previous electron-transport equations in solids and gases are recovered as instantiations of ours. The hierarchies of scales underlying the derivation of the Fokker-Planck equation are those used in the lucky-drift model.

Statistical mechanics of high-field transport in semiconductors.

The paper is devoted to the statistical-mechanical description of high-field transport in semiconductors within the semiclassical picture, assuming the band structure and electron-phonon interaction to be known. Our goal is to obtain a physical understanding in simple, universal terms without resorting to specific, simplified models for the band structure and/or the electron-phonon interaction. We first examine the lucky-drift model against an exact (analytical and numerical) solution of the Boltzmann transport equation in the simple parabolic case, and two discrepancies are found. The first stems from an incorrect expression for the drift velocity of a hot electron, while the second is associated with the approximate nature of the statistical device yielding the energy distribution. With the aim of retaining the features of simplicity of the lucky-drift description, another approach to the statistics of transport in the high-field regime is developed, based upon a nonlinear Fokker-Planck equation in energy space. While it gives the exact solution in the parabolic case, it has the ability to take up transport in an arbitrary band structure as well, and accounts for the success of the generalized lucky-drift model. The carrier energy distribution is expressed in terms of integrals over constant-energy surfaces in the Brillouin zone; the integrals involve the electron-phonon interaction and have direct physical meaning. The momentum-space distribution is derived approximately from the energy distribution. A simple comprehensive picture of transport statistics emerges that is not linked to a particular material or to specific assumptions regarding the electron-phonon interaction.

Cellular automata simulation of stationary and transient high-field transport in submicron Si and GaAs devices

The authors present a detailed discussion, critical tests and applications of a new lattice gas simulation technique for high-field transport in semiconductors. This method may be viewed as a variant of the ensemble Monte Carlo technique but can easily handle ensembles with more than 105 particles, can efficiently deal with complex geometries and achieve accelerations on multiprocessor computers that scale linearly with the number of processors. The stationary and transient transport properties of Si and GaAs that have been calculated with this new technique compare very favourably with the standard Monte Carlo results.

Experiment and Analysis on High-Electric-Field Transport in Epitaxial YBaCuO Thin Films

Hot carrier transport in epitaxial (001)Y1Ba2Cu3Oy thin films has been closely investigated under application of pulsed high electric field. The current-vs-field curves of the normal conduction for both the semiconducting and superconducting phase films exhibited strong nonlinearity as the field increased. The nonlinearity of the dynamic resistance measured at 50-100 MHz was exaggerated much more. These phenomena were analyzed through analogy to the high-field transport in semiconductors. On the basis of the dominant phonon scattering, the results implied that the Y1Ba2Cu3Oy carrier localizes in a thin layer and has two-dimensional motion, and that the deduced effective mass is heavier than 2m0 but less than 5m0, where m0 is the free electron mass.

High-field transport in semiconductors. II. Collision duration time.

Le temps de duree de la collision τ CD (une echelle de temps courte <10 −14 s) est evalue pour un semiconducteur non degenere a l'equilibre. Pour l'interaction avec les phonons optiques non polaires, on montre qu'il existe une echelle commune τ CD pour les integrales de diffusion vers l'interieur et les integrales de diffusion vers l'exterieur. Ce temps est defini de sorte que, si τ CD <<τ (τ est la duree de vie des quasiparticules), les evenements de diffusion subsequents n'interferant pas. La meilleur estimation de ce temps independant de la temperature, est le critere de Landau propose pour les metaux. Discussion de la validite de l'approximation des collisions completee

High-field transport in semiconductors. III. Wave-function renormalization

The asymptotic form of the single-particle retarded Green function is discussed in the presence of the homogeneous stationary electrical field. It is shown that different definitions of the instantaneous approximation of the self-energy lead to different values of the field effect on the scattering. This inconsistency is removed if the wave-function renormalization is included. Finally, the choice of the instantaneous approximation that removes the linear dependence on the field is discussed.

High-field transport in semiconductors. I. Absence of the intra-collisional-field effect.

We show that the Levinson (Zh. Eksp. Teor. Fiz. 57, 660 (1969) [Sov. Phys.---JETP 30, 362 (1970)]) quantum transport equation reduces to the semiclassical Boltzmann equation in the limit of a strong homogeneous electrostatic field. To arrive at this conclusion we use a saddle-point approximation which has not been used in this field before. This approximation is exact in the high-field limit. We show that even for a relatively moderate field strength of 3\ifmmode\times\else\texttimes\fi{}${10}^{5}$ V/m in GaAs (even before the onset of the Gunn effect, when 90% of the electrons are still in the central valley) the saddle-point approximation can be used for a majority of the scattering events. The results in this paper are supported by numerical calculations based on realistic scattering mechanisms in GaAs.

A quantum kinetic equation for high-field transport in semiconductors

The authors aim is the formulation of a tractable quantum theory capable of dealing properly with the length and time scales relevant to modern submicron devices. The Kadanoff-Baym-Keldysh non-equilibrium Green function method is employed to develop a formalism appropriate for high fields. No perturbation expansion arguments are employed. The equivalence of the two Kadanoff-Baym equations for the correlation function G< for these systems is demonstrated. A relation analogous to the equilibrium case between G<, the spectral function A and the quantum distribution function f is derived at high fields without the loss of the intracollisional field effect.

Correlation functions of hot electrons in semiconductors.

We present a general theory of the correlation functions for a steady state which is valid for arbitrary strengths of an applied electric field, as obtained in high-field transport in semiconductors. When limiting to the first two moments of the distribution function, we find a closed set of equations coupling energy and velocity which are amenable to an analytical solution. Thus, the theory provides an interpolation formula which gives smooth, analytical expressions for the correlation functions. These expressions can be made to fit the computer simulation by using these simulations to estimate the various parameters. The theory is found to be in excellent agreement with numerical calculations for a simple model semiconductor performed with an ensemble Monte Carlo technique.

High-field transport in semiconductors based on eigenvalue solution to Boltzmann equation

The Boltzmann equation is solved by expanding the distribution function in terms of a finite number of basis functions. The zero eigenvalue of the resulting matrix is solved for the hot-electron distribution. This method arrives at the solution at least two orders of magnitude faster than the commonly used Monte Carlo method. Using the scattering rates due to ionized impurities, phonons, alloy disorder, and intervalley scattering calculated from a realistic band structure, we obtain velocity-field curves for various semiconductor alloys and compounds without any adjustable parameters. The results are in good agreement with experiments.