On the limit of the injection ability of silicon $p^{+}$–$n$ junctions as a result of fundamental physical effects

Analytical expressions describing the dependences of the $p^{+}$–$n$–junction leakage current on the doping level of the $p^{+}$-type region are derived by taking into account a whole set of nonlinear physical effects: electron–hole scattering, Auger recombination, band-gap narrowing, and nonlinear dependences of the charge-carrier lifetime and mobility on the doping level. It is shown that the dependence for the leakage current has a minimum at which the injection ability of the $p^{+}$-type emitter is at a maximum. The dependence of the extremum position on the main parameters of the heavily doped $p^{+}$ layer is analyzed. The data obtained make it possible to optimize the structure of high-power silicon devices and to facilitate the adequacy of numerical calculations.