Physica 134B (1985) 169-173 North-Holland,Amsterdam 169 MONTE CARLO ANALYSIS OF HOT-PHONONEFFECTS ON NON-POLARSEMICONDUCTOR TRANSPORTPROPERTIES Paolo BORDONE, Carlo JACOBONI, Paolo LUGLI, Lino REGGIANI Dipartimento di Fisica e Centro Interuniversitario di Struttura della Materia dell'UniversitA di Modena, Vie Campi 213/A, 41100 Modena, Italy Peter KOCEVAR Institut fur Theoretische Physik, Universitat Graz, Universitatsplatz 5, A-8010 Graz, Austria An iterative procedure to include phonon disturbances into a Monte Carlo algorithm is presented. Low temperature transport in p-Ge is considered. Calculations show that carrier drift velocity and mean energy increase as a result of the phonon amplification. I . INTRODUCTION The inclusion of phonon disturbances into calculations of the electrical or optical response of a semiconductor represents a still widely unexplored area of nonlinear transport theory. When an electric field E is applied to a crystal, it feeds energy and momentum into the free carrier system. In contrast with the thermal equilibrium case of equal phonon emission and absorption rates per carrier, a field induced emission sets in and the phonons, which are stronply coupled to the carriers, become amplified. Noticeable effects of such phonon disturbances on transport coefficients can be expected under the following two conditions: (i) the carrier system has to be far from equilibrium; (ii) the lifetimes of the electronically-active phonons must be comparable or longer than the characteristic times for their field-induced built up. Accordingly, we consider only disturbances of the first phonon generation created directly by * Partially supported by Ministero Pubblica Istruzione the carriers. We neglect the amplification of the second and later generations, resulting from the decay cascade of the initally excited phonons, as they do not couple effectively to the carriers. Because of the computational complexity in the evaluation of a coupled nonequi~ibrium carrier-phonon system, almost all hitherto published attempts used a heated Maxwellian in a diffusion approximation or assumed a ileated and displaced Maxwel I i an (or Fermi ) I-5 distribution of the carriers some predi cti ve power, carri er-temperat ure model s have known limits. Since the Monte technique solutions of this step, in inclusion An iterative self-consistent procedure that combines a MC calculation for the electronic and Centro di Calcolo dell'Universit~ di Modena Although of these their well Carlo (MC) provides a more general approach to of nonlinear transport 6, the purpose contribution is to establish a first a long term project, toward the of phonon disturbances into MC codes. 0378-4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)