Transition Probability for Photoelectric Emission from Semiconductors

Abstract

An adaptation of Makinson's theory of photoelectric emission from metals is used to treat simple one- and three-dimensional semiconductor models. The probability of excitation from a state of initial energy $\ensuremath{\epsilon}$ lying near ${\ensuremath{\epsilon}}_{0}$, the top of an occupied band, is found proportional to ${\ensuremath{\epsilon}}_{0}\ensuremath{-}\ensuremath{\epsilon}$. Thus, the transition probability vanishes at the top of the band. For a density of states having the normal form, $n\ensuremath{\sim}{({\ensuremath{\epsilon}}_{0}\ensuremath{-}\ensuremath{\epsilon})}^{\frac{1}{2}}$, the energy distribution of the emitted electrons contains a factor ${({\ensuremath{\epsilon}}_{0}\ensuremath{-}\ensuremath{\epsilon})}^{\frac{3}{2}}$ and is thus concave upward near the band edge.For certain simple surfaces, the photoelectric threshold may be high because transitions requiring low energy are forbidden. It is pointed out that this feature is an idealization probably not found for real surfaces having the usual inevitable irregularities. In a qualitative discussion, more realistic cases are mentioned. It is suggested that the results retain the form derived above, although the high threshold energy disappears.An energy distribution proportional to ${({\ensuremath{\epsilon}}_{0}\ensuremath{-}\ensuremath{\epsilon})}^{\frac{3}{2}}$ near the band edge is in good agreement with previous experimental results on Te and other monatomic semiconductors. With the graphical methods of analysis previously applied to data on these materials, the point of view taken above permits more definite location of the edges of occupied bands. Improved estimates of upper limits to the density of occupied surface levels are then possible.