Approximate Theory of Emitter-Push Effect

Abstract

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

$$D_b{\mathrm{/D}}_b^{*}{\mathrm{=(C}}_v{\mathrm{/C}}_v^{*}{\mathrm{)x}}_{\mathrm{jb}}{\text{≈16π}}^{\text{−1/2}}{a}^{\text{−3}}\text{β{1−√π}\mathrm{ierfc}{\mathrm{[x}}_r{\text{/2(Dt)}}^{\text{1/2}}{\mathrm{]\}\; C}}_0{\mathrm{D(C}}_s{D}_s^{*}{)}^{\text{−1}}\text{+1}$$

, where D_b is the base diffusivity, C_v 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, x_r is the dislocation penetration depth, D is the emitter diffusivity, C₀ the emitter surface concentration, C_s the concentration of lattice sites, and D_s the self‐diffusivity. It is also shown that the amount of enhanced collector junction movement δ is given by

$${\text{δ≈2D}}_b{\mathrm{t\lambda }}^{\text{−2}}{x}_j^{\text{−1}}\ln {\mathrm{(C}}_{\text{b0}}{\mathrm{/C}}_B{\mathrm{)[(D}}_b{\mathrm{/D}}_b^{*}\text{)−1]}$$

, where λ is a constant (=0 73), x_j is the collector junction depth, C_b0 is the base surface concentration, and C_B is the bulk concentration.