Simplified Theory for Stable Gunn Domains Including Diffusion

Abstract

A simplified theory of Gunn domains is presented assuming a nonzero, but field-independent diffusion coefficient. The simplification is achieved by using an approximate, analytic solution to a well-known transcendental equation (the so-called ``area integral'') of Butcher and Fawcett. Any further computer calculations, where necessary, then involve only simple quadratures of known analytic functions. For the piece-wise linear approximation to the V(F) vs F curve the entire program can be carried out analytically with the aid of the Regional Approximation method. The use of dimensionless variables brings out the central role, in Gunn domain theory, of the critical dimensionless parameter α=εFTVT/eN0D, with FT the threshold field, VT the threshold drift velocity, N0 the thermal-equilibrium free-carrier density and D the diffusion coefficient (mks formula). For GaAs, α≈4×1015/N0 with N0 in cm−3. A particularly simple V(F) vs F curve is proposed for the study of phenomena (e.g., impact ionization across the gap) deriving from very high-field Gunn domains. A complete analytic study is made of the Gunn domains associated with this special characteristic.