Calculation of Electron Mobility in High Fields by Path Integral Method

Abstract

The mobility of elemental semiconductor is calculated for all fields up to breakdown by means of the path integral method. A self-consistent solution of the Boltzmann transport equation is obtained and analytic expressions for thr drift velocity,mobility and the relationship between electron temperature and the electric field is obtained. The validity of this calculation is limited to elemental semiconductors, such as Ge and Si at lattice temperatures high enough so that inter-valley scattering may be neglected, and the scattering is dominated by electron- phonon scattering. A comparison between theory and the experimental results for n-type and p-type Ge is made. It is found that agreement between theory and experiment is good for both n- and p-type Ge. A saturation velocity of 6.10*10^3 cm/sec between 2.1*10^3 v/cm and 5.1*10^3 v/cmis predicted for n-type Ge.