APPROXIMATE THEORY OF EMITTER-PUSH EFFECT

An approximate theory of the emitter-push effect is presented. The rate of vacancy generation during emitter diffusion is formulated using Prussin's model of dislocation distribution. A time and space average rate 〈R〉 is defined, and a quasi-steady state approximation of vacancy distribution is obtained. It is shown that the ratio of the effective to the intrinsic base diffusivities, which is also equal to the local supersaturation of vacancies in the vicinity of the base - collector junction, is given by Db/D b*=(Cv/Cv*) xjb≈16π-1/2a-3β{1-√π ierfc[xr/2(Dt)1/2]} C0D(CsD s*)-1+1, where Db is the base diffusivity, Cv is the vacancy concentration, the asterisk denotes the condition of an intrinsic semiconductor with vacancy at thermal equilibrium, a is the lattice unit cell dimension, β is the coefficient of lattice contraction, xr is the dislocation penetration depth, D is the emitter diffusivity, C0 the emitter surface concentration, C s the concentration of lattice sites, and Ds the self-diffusivity. It is also shown that the amount of enhanced collector junction movement δ is given by δ≈2Dbtλ -2xj-1ln(Cb0/CB)[(D b/Db*)-1], where λ is a constant (=0 73), xj is the collector junction depth, Cb0 is the base surface concentration, and CB is the bulk concentration. © 1969 The American Institute of Physics.