THEORY OF SURFACE PHOTOVOLTAGE IN A SEMICONDUCTOR WITH DEEP IMPURITIES

A recent theory of the surface photovoltage is extended to a semiconductor with deep impurities, whose concentration N(T) less-than-or-equal-to 0.1\N(I)\, where N(I) is the net concentration of shallow impurities. Numerical solutions, which have been obtained for both n-type and p-type Si with gold as an example of a deep impurity, are used to guide the development of the theory, By approximating the gold acceptor and donor levels as two independent levels, expressions are derived for the relationships between the surface photovoltage and the splitting of the quasi-Fermi potentials nu(SC) in the surface space charge region, and between nu(SC) and the photon flux density in terms of recombination in the space charge region and at surface states, as well as carrier diffusion in the bulk. From these expressions, a complete theory is built up which is capable of predicting the photon flux density required to yield a specified photovoltage for a given wavelength of light. The theory is shown to agree well with the numerical solutions. In particular, it explains the unexpectedly large surface photovoltage observed from the numerical solutions for n-type gold-doped Si with N(T) = 0.1\N(I)\. As an application of the theory, it is shown that Goodman's surface photovoltage method will yield the appropriate minority carrier diffusion lengths in the bulk regions of n-type and p-type gold-doped Si material.