258 IEEE ELECTRON DEVICE LETTERS, VOL. 18, NO. 6, JUNE 1997 Monte Carlo Simulation of Electron Velocity in Degenerate GaAs Jose Miguel Miranda Pantoja, Member, IEEE, and Jose Luis Sebastian Franco Abstract— A calculation of the electron velocity in heavily doped GaAs has been performed. A model to account for the LO phonon–plasmon coupling effects is proposed in a full Monte Carlo simulator; we believe this is the first time this fact has been tried out. Nonequilibrium screening effects are considered in the simulation. The Pauli exclusion principle is extended to the hot electron regime by the use of the electron temperature, which is calculated self consistently from the mean energy. A direct comparison with experimental velocities is made to show the accuracy of the simulation at both 77 and 300 K. Comparisons with simpler Monte Carlo models are also presented to illustrate the influence of the different effects considered in this letter. I. INTRODUCTION R ECENT works show that GaAs device simulation still finds a pressing problem in the modeling of the ohmic parts of the semiconductor [1]–[4]. This problem has not been solved satisfactorily as yet. A long standing discrepancy persists among Monte Carlo researchers about the relevance of plasmon effects on the carrier velocity in degenerate III–V semiconductors. Classical plasmon scattering models have been criticized because plasmon damping effects have not been considered. However, neglecting the plasmon scatttering implies neglecting the well known coupling effects between LO phonons and plasmons. Therefore, the classical expres- sions for the LO phonon scattering rates are not consistent with the physics of the material, and one may expect to find inaccuracies in the calculated velocities if these rates are used in a simulation. However, how important are these inaccuracies? A satisfactory answer to this question has not been found in the bibliography, and a suggestion will be offered in this paper. In addition, a full Monte Carlo simulator is presented. This simulator is able to accurately calculate the mean velocity in GaAs at doping concentrations close to those usually encountered in ohmic contacts. The main features of this letter may be summarized as follows: 1) the coupled plasmon-LO phonon scattering is included in the simulation; 2) hot electron screening effects are considered in the scattering of the hybrid modes and in the Pauli exclusion principle; and 3) direct comparison is performed with experimental velocities in samples which have been prepared and characterized with modern technologies. Manuscript received December 3, 1996; revised February 6, 1997. The authors are with the Departamento de Fisica Aplicada III, Facultad de Fisicas, Universidad Complutense de Madrid, 28040 Madrid, Spain. Publisher Item Identifier S 0741-3106(97)04299-7. II. THE MONTE CARLO MODEL The core of the simulator is an isotropic, three-valley Monte Carlo model with the well known scattering mechanisms that operate in GaAs. Nonparabolic valleys are assumed in the simulation. The electron temperature is calculated in a self consistent way from the mean energy at each valley. First, we assume a Fermi-like distribution with an effective Fermi level for the Gamma valley, and nondegenerate distributions for the satellite valleys. Then we impose the energy at each valley to the corresponding distribution function, and finally the total electron temperature is calculated by promediating the three temperatures, which are weighted by the carrier population of each valley. The Pauli exclusion principle has been applied to the Gamma valley by the rejection technique suggested in [5], but using directly the Fermi distribution with the electron temperature at the Gamma valley. Plasmon and polar optical phonon collisions are substituted by two hybrid modes. Analytical expressions have recently been suggested for their corresponding scattering rates without any experimental validation [6]. We have adopted these rates, but in the calculation of the cuttoff wave vectors of each mode we have substituted the lattice temperature for the electron one. The optical permittivity was considered instead of the static permittivity in the simulation of the hybrid-mode screening effects [7], [8]. It must be pointed out that the plasmon–phonon damping processes are not considered in our work. This issue still demands further research. The dispersion angle after an scattering event with an hybrid mode is obtained by assuming that, in a collision, the electron only scatters either with the electronic or with the ionic part of the mode. The choice is made by comparing the normalized phonon content of the mode with a random number generated between 0 and 1. If the electron scatters with the plasmonic part of the mode, the momentum exchanged in the collision is checked. If it is higher than the corresponding cuttoff wave vector, the scattering event is turned into a self-scattering event. This scheme enables us to account for the cuttoff properties of the hybrid modes in a simple way. Accurate values for the intervalley effective deformation potentials have recently been suggested [9]–[11]. However, these values are not fully compatible with the Conwell model of intervalley scattering commonly used in Monte Carlo simu- lations. Therefore, we have adopted the effective deformation potentials and intervalley phonon energies as reported in [12]. Fig. 1(a)–(d) shows the results of our simulations compared to velocities calculated by making some widely used approx- imations [13]. The measured velocities were taken from the 0741–3106/97$10.00  1997 IEEE