The Transport of Added Current Carriers in a Homogeneous Semiconductor

Taking into account the thermal equilibrium minority carrier concentration and employing the formulation which includes, as one of two fundamental differential equations, the continuity equation for added carrier concentration $\Delta p$, this equation is derived in a form which exhibits the ambipolar nature of the diffusion, drift, and recombination mechanisms under electrical neutrality. The general concentration-dependent diffusivity is given. The local drift velocity of $\Delta p$ has the direction of total current density in an $n$-type semiconductor and the reverse in a $p$-type semiconductor, differing in general in both magnitude and direction from the minority-carrier drift velocity. Specifying a model for recombination fixes the dependence of a lifetime function for $\Delta p$ on $\Delta p$ and the electron and hole mean lifetimes. Negative $\Delta p$, or carrier depletion with electrical neutrality, may occur. For known total current density, the continuity equation alone suffices, as for the case of $\left|\Delta p\right|$ small, for which the equation is linear. A condition for this comparatively important case is derived, and theoretical relationships are given, with the aid of a parameter specifying the Fermi level, which determine for germanium the minority carrier-$\Delta p$ drift velocity ratio as well as the ambipolar diffusivity and group mobility in terms of resistivity and temperature.