THEORY OF SURFACE PHOTOVOLTAGE IN A SEMICONDUCTOR WITH DEEP IMPURITIES

A recent theory of the surface photovoltage is extended to a semicondu ctor 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 impuriti es. 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 guid e the development of the theory, By approximating the gold acceptor an d donor levels as two independent levels, expressions are derived for the relationships between the surface photovoltage and the splitting o f the quasi-Fermi potentials nu(SC) in the surface space charge region , and between nu(SC) and the photon flux density in terms of recombina tion in the space charge region and at surface states, as well as carr ier diffusion in the bulk. From these expressions, a complete theory i s built up which is capable of predicting the photon flux density requ ired to yield a specified photovoltage for a given wavelength of light . The theory is shown to agree well with the numerical solutions. In p articular, it explains the unexpectedly large surface photovoltage obs erved 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 car rier diffusion lengths in the bulk regions of n-type and p-type gold-d oped Si material.