Semiempirical determination of avalanche breakdown temperature parameters in p-n junctions

A method is proposed which permits the determination of the electric field dependence of the ionization coefficient at any temperature. Relative simple semiempirical expressions for the ionization coefficients α_n and α_p for electrons and holes as a function of electric field and temperature are derived. This is applied to express the avalanche breakdown voltage (U_B) and its temperature coefficient (β) as a function of impurity density or concentration gradient for abrupt and linearly graded p-n junctions, and of temperature. The results for U_B and β obtained from these expressions compare satisfactorily with exact numerical results. It is confirmed (both theoretically and experimentally) that β(T) exhibits a maximum at a definite temperature and that U_B (T) deviates significantly from a linear temperature dependence.