Monte Carlo determination of electron transport properties in gallium arsenide

Royal Radar Establishment, Malvern, Worcestershire, England
Journal of Physics and Chemistry of Solids 09/1970; DOI: 10.1016/0022-3697(70)90001-6

ABSTRACT A Monte Carlo technique has been used to calculate the electron distribution functions in the (000) and (100) valleys of gallium arsenide. This method avoids having to make any of the conventional approximations used to solve the Boltzmann transport equation, but instead evaluates the distribution function exactly once the scattering rates have been specified. Polar, acoustic and relevant intervalley scattering processes have been included, together with the non-parabolicity and wavevector dependence of the cell-periodic part of the Bloch functions in the (000) valley. The structure found in the distribution function in the (000) valley is interpreted in terms of the energy dependence of the scattering processes, particular reference being made to the prediction of a population inversion for fields in excess of about 10 . The mobility, mean energy, and electron population in each valley and the mean velocity are calculated as functions of the electric field strength, and comparison is made with previous theoretical results and the experimental data.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Control of material composition at the nanometer and atomic scale dramatically increases electronic device design space due, in part, to quantum effects. New engineering tools are needed to explore this space and ensure that the best, technologically significant device designs are discovered in a most efficient manner. Using a few prototype examples, this paper describes how a methodology for synthesis might be implemented to advance quantum engineering for electronics.
    Proceedings of the IEEE 03/2008; · 6.91 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Electronic band structure is incorporated into a versatile energy transport model that treats heat flow between mobile electron ensembles with the thermodynamic identity for ideal gases instead of an electron thermal conductivity. This alleviates the closure issue common to thermal conductivity models and is amenable to different forms of charge gas transport. This flexibility allows the model to accommodate band dispersions typical of semiconductors. A simulation scheme and the device equations for a generalized band structure are presented. The model is then implemented for GaAs using a band structure calculated with the empirical pseudopotential method. Comparisons to Monte Carlo for certain bulk GaAs test cases indicate that the model may capture hot electron effects with sufficient accuracy and reduced computational cost suitable for larger scale device simulation and design. KeywordsCharge transport model–Ideal Fermi gas–Boltzmann equation
    Journal of Computational Electronics 01/2011; 10(3):271-290. · 1.01 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We analyzed the steady-state electron transport for bulk GaN in frame of two opposite approaches: the electron temperature approach that assumes a high-density electron gas and numerical single-particle Monte-Carlo method that assumes a low-density electron gas and does not take into account electron-electron (e-e) scattering. We have also presented an analytical solution of the Boltzmann transport equation based on diffusion approximation. The transport characteristics such as the drift velocity electric field,   E V d , and mean electron energy electric field,   E  , have been calculated at nitrogen and room temperatures in the wide range of applied electric fields from zero fields up to runaway ones (~100 kV/cm) for both approaches. Our calculations were performed for doped semiconductor with equal impurity and electron concentrations, 3 16 cm 10    n N i . The electron distribution functions in various ranges of applied fields have been also demonstrated. Within the range of heating applied fields 0– 300 V/cm, we found a strong difference between the transport characteristics obtained by means of the balance equations (electron temperature approach) and Monte-Carlo procedure. However, the Monte-Carlo calculations and diffusion approximation show a good agreement at 77 K. Within the range of moderate fields 1–10 kV/cm at 77 K, we established that the streaming effect can occur for low-density electron gas. In spite of significant dissimilarity of a streaming-like and a shifted Maxwellian distribution functions, the calculated values of   E V d and   E  show similar sub-linear behavior as the functions of the applied field E. In the high-field range 20–80 kV/cm, the streaming effect is broken down, and we observe practically linear behavior of both   E V d and   E  for both approaches. At higher fields, we point out the initiation of the runaway effect.
    01/2009; 20202335(73):328-338.