Appendix 3: Electron Mobility and Compensation Ratios at 77 K in n‐Type GaAs and InP

Abstract

The principle electrical parameters of a semiconductor are the carrier concentration (n) and the mobility 0. The carrier concentration is the number of free charge carriers per and the mobility is a measure of the ease with which the carriers can move under the influence of an electric field. The electron mobility in a semiconductor is a strong function of temperature and purity. As the temperature increases, thermal oscillations of the semiconductor lattice lower the charge mobility by scattering processes. When ionized donor and acceptor impurities are present, coulombic forces deflect charge carriers causing scattering and a reduction in mobility. Therefore, the electron mobility in n-type GaAs and InP depends on the total concentration of ionized donor (N,) and acceptor (N,) impurities and is thus a function on the compensation ratio, 0 = N,/N,. Electron mobility values at 77 K in GaAs and InP have been calculated for a wide range of compensation ratios using variational procedu-res which have taken into account all major scattering mechanisms [ 1,2]. The computed mobility values are shown in the following figures (pp. 326 and 327) as a function of electron concentration n = (N,-N,) and the compensation ratio NA/Y,. The compensation ratio is a measure of the total number of ionized impurities and so for a given carrier concentration, the mobility decreases as the compensation ratio increases. A low compensation ratio (e.g., 0.1) indicates that ionized donors (e.g., Si, Sn, etc.) are the dominant impurities, and that there are reatively few acceptors, i.e., NA = 0.1 N,. Conversely, a high compensation ratio (e.g., 0.9) indicates that there are nearly equal numbers of ionized donors and acceptors (Zn, Mg, etc.), i.e., NA = 0.9 N,. The plots of mobility vs. carrier concentration and the derived compensation ratios (N'IN,) are courtesy of Mr. Roy Blunt