Defect-state occupation, Fermi-level pinning, and illumination effects on free semiconductor surfaces

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Abstract
A comprehensive physical model for equilibrium and illuminated free semiconductor surfaces interacting with an arbitrary number of monoenergetic surface and bulk defect states is presented. The position of the surface Fermi energy is shown to be determined by the overall balance of surface charge and surface electric field, and is not merely set by alignment to the energy of the highest-density surface state. Boundary conditions are derived for nonequilibrium device analysis, which includes the full electrostatic and recombinative details of the surface states. An approximate analytical solution is given for the semiconductor transport equations with these boundary conditions and this model is used to describe illumination effects on the free surface. The solution can be represented in a graphical form, which allows the most significant contributions to be easily visualized. Fermi-level pinning on free surfaces is then classified according to the primary contributions to the charge balance and also according to the sensitivity of the surface potential to charge perturbations. The occupation factors for the surface states under illumination conditions are derived from the analytic model and are shown to both shift and saturate with increasing illumination intensity. This allows the origin of free-surface photovoltage, depletion-edge contraction, and band flattening to be reinterpreted as arising from a change in surface-state occupation rather than from a quenching of the depletion-region field by free electrons and holes.