Modelling of small-signal response and electronic noise in semiconductor high-field transport

Abstract

We present a survey on the theoretical modelling of the small-signal response and noise associated with velocity fluctuations in semiconductor high-field transport. Because of the high values of the applied electric field, current-voltage characteristics and electrical noise are found to deviate strongly from Ohm's law and Nyquist's relation respectively. Accordingly, in the case of homogeneous (bulk) structures the field and frequency dependence of the differential mobility, diffusivity and electronic noise temperature are investigated within a rigorous microscopic approach which solves exactly the appropriate kinetic equations through analytical and Monte Carlo techniques. Spectral functions in the frequency domain are obtained from their correspondent response and correlation functions in the time domain. The subject is also analysed within a balance-equation approach which enables us to obtain simple analytical expressions which can provide a direct microscopic interpretation and can be applied to device modelling. For validation purposes calculations are applied to the relevant case of holes in Si and electrons in GaAs. In the latter material the presence of negative differential conductivity (Gunn effect) leads to interesting behaviour of the small-signal response and noise spectra which are also investigated for the simplest prototype of non-homogeneous structures, that is the n + nn + diode. The comparison between the different approaches so developed and between calculations and experiments is found to be quite good, thus providing a quantitative microscopic interpretation of the main features associated with small-signal response and fluctuations in semiconductors under high-field conditions. Nomenclaturea.c. alternating current (dynamic state) BE balance equations d.c. constant current (static state) HD hydrodynamics MC Monte Carlo NDM negative differential mobility

Electronic noise of warm electrons in semiconductors from first principles

“…As computational resources became increasingly available, numerical implementations of the methods described above permitted computations of electronic noise for both warm (∆T /T 0 1) and hot (∆T /T 0 ∼ 1) electrons, where ∆T is the steady-state temperature rise of the electrons and T 0 is the lattice temperature. Due to the lack of knowledge of the precise transition rates between electronic states, these studies employed simplified band structures and parameterized models for scattering such as deformation potential theory for acoustic phonon scattering [38,39]. For example, Stanton and Wilkins obtained the Green's function of the Boltzmann equation under the single-mode relaxation time approximation, demonstrating qualitative agreement with experiment in GaAs for one [40] and two [41] valleys.…”

Theory of the Monte Carlo method for semiconductor device simulation

“…The derivation begins with a transformation of (13) into the standard form (1) by augmenting the kernel. 14(15) (16) denotes the unit step function and the initial distribution. The integral form (13) is immediately recovered from (14) by performing the integration and replacing the upper bound of the time integral by , thus eliminating the unit step function.…”

A Monte Carlo method for small signal analysis of the Boltzmann equation

“…The steady-state algorithms are based on the theory of correlation functions. 2 The linear response to an impulse in the electric field is directly simulated. The particle trajectories evolve under the action of a stationary electric field.…”