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.

Close

PrevNext

View figure in article