Dependence of hole velocity upon electric field and hole density for p-type silicon

The hole velocities in p-type Si have been determined for fields E to 1.1 × 10⁵V/cm at 300°K for hole densities in the range 10¹⁴ – 10¹⁶/cm³. Results significantly different from Prior's (which shows a large dependence of v upon doping) have been obtained. Our specimens were p⁺pp⁺ structures made from uncompensated, low dislocation density silicon; the p⁺ regions being diffused. Current density measurements were made as a function of applied voltage using pulse techniques. The E field was oriented in the (111) crystal direction. The measured low field Hall mobility and its established relation with drift mobility were employed to obtain the low field velocities. Steady state solutions for the injected space charge and the electric fields throughout the specimen were calculated. The injected space charge density (majority carriers) is not greatly in excess of the equilibrium hole density. Several thicknesses of the p region are studied. An analysis of the current voltage data gives a curve for the high field velocity relation v(E) which is independent of the hole concentration to within 10 per cent. At E = 10⁵° V/cm, we obtain v = 8.6 × 10⁶cm/sec.