Theory of the photovoltage at semiconductor surfaces and its application to diffusion length measurements

Abstract

This paper presents an analytical theory of the steady-state surface photovoltage, which takes into account recombination in the surface space charge region and at surface states, as well as bulk diffusion in the semiconductor. For a given wavelength of light used in the photo-excitation, the theory is able to predict the photon flux required to yield a specified surface photovoltage. The validity of the theory has been established by means of detailed comparison with exact numerical solutions. It is shown that for an Si specimen space charge recombination plays an important role in determining the surface photovoltage, particularly at photovoltages of the order 0.1 times the thermal voltage or less. The theory is applied to a rigorous examination of the validity of two standard test methods of the American Society for Testing and Materials for measuring the minority carrier diffusion length, which are based on the surface photovoltage. It is found that while the method due to Goodman works well in general and even in the presence of large surface recombination, the method due to Quilliet and Gosar does not always give the correct value of diffusion length, because of the importance of recombination in the space charge region and at the surface states—it does so only under certain restrictive conditions, i.e. the material must have a doping concentration greater than 10 15 cm −3 and a long minority carrier lifetime (> 10 μs), with a surface in depletion (but not in inversion) at equilibrium and a very low surface recombination velocity.