Impurity and Temperature Dependence of Saturated Drift Velocity in Silicon

Abstract

The drift velocity of electrons in silicon in the hot electron range approaches a constant value which varies with the temperature of the lattice (1). It has been shown theoretically that the temperature dependence of drift velocity comes about from the momentum loss due to acoustic phonons (2, 3 ) . The theoretical drift velocity agrees well with the experimental results above room temperature. However, the agreement i s poor and the departure is rignificant below room temperature. T o see the explicit effect of impurity scattering we devide the c a r r i e r energy in two regions. The lower energy range extends from zero to W , where W is the limiting value of energy upto which the losses due to ionized impurity scattering a r e upto 10% of that due to acoustic phonon scattering. ToderiveW, we performed momentum loss rate calculations due to impurity scattering and compared them with those due to acoustic phonon scattering. It turns out that the value of W is < .fiw for the im-16 3 purity concentrations of the order of 10In the range 0 to W the losses due to optical phonons a r e negligible a s optical phonons a r e not excited at these low energies (W < ?iw ). In this range we shall solve the Boltzmann transport equation for acoustic phonons and ionized impurity scattering only, above this limit we shall neglect the impurity scattering (N S 10 /cm ) and adopt the solution of Reik and Riskin (4). Following Reik and Riskin and Conwell (5), we find the symmetric and assymmetric part of the distribution function as follows: 0 /cm ; 60 being the optical phonon energy.