Theory of Electronic States and Transport in Graded Mixed Semiconductors

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Abstract
Semiconductors which are slowly graded in composition can be shown to have position-dependent band gaps and position-dependent effective masses, describable in terms of an effective Hamiltonian in an effective-mass equation. The effective Hamiltonian previously obtained is, in the present work, rendered Hermitian. Electronic minority-carrier transport for graded systems is described in terms of an effective field which includes the electrostatic field plus a term in the gradient of the band edge and another in the gradient of the effective mass. The local radiative-recombination lifetime and local density of states for inhomogeneous semiconductors are discussed. The equation for the excess minority-carrier concentration in an inhomogeneous semiconductor is deduced and is found to differ from that in an homogeneous system, by the effective field replacing the electric field, by the position dependences of lifetime and mobility, and by terms in the mobility gradient. Some phenomena specific to graded mixed semiconductors are considered on the basis of the theoretical analysis.