ANALYTIC CALCULATION FOR SOME USEFUL DEPTH PROFILES OF THE LINEAR EXPANSION COEFFICIENTS USED IN SPACES

One of the strengths of the stochastic theory for the energy loss of charged particles in matter, applied to narrow-resonance depth profiling, is that, once the autoconvolutions of the primary energy loss function have been performed, the calculation of either straggling or excitation curves reduces to the calculation of a weighted linear combination of these autoconvolutions. This paper presents the calculation of these weights in the cases of some analytic profiles such as those of the finite ascending or descending linear, polynomial or exponential type. In the case of the half-Gaussian related to diffusion processes, the weights are given by an iteration formula which is stable only when calculated in descending order. We also show that if a concentration profile can be expressed as a convolution of two functions, then the weights corresponding to that profile are the discrete convolutions of the respective weights of those two functions. As an example we calculate the weights for error-function profiles, which are the convolution of a Heaviside step function and a half-Gaussian. © 1990.