Convolution and deconvolution in Auger electron spectroscopy with application to silicon

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Abstract
Auger electrons emitted from the valence band in solids carry information on the local density of states in this band in the surface region. The emitted Auger electron intensity distribution is a convolution product of the transition densities of the two valence-band electrons involved in the Auger process in the ionized solid, multiplied with the probability of escape of the outgoing electron. In a first-order approximation the transition density is proportional to the density of states. A comparison between a theoretical, or a directly measured, density of states and Auger spectra must rely on mathematical convolution/deconvolution techniques. Here it is proposed to use spline functions to represent the densities of states to be convolved. This method is unconstrained with respect to form of the density of states. The same representation is used to deconvolve experimental kinetic energy distributions of Auger electrons, in a nonlinear least-squares fitting of a convolution square of a trial density-of-states function. As an example, the Auger spectrum of Si is considered and compared with a calculated density of states.

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