Use of model depth resolution functions for the deconvolution of depth profiling data

The problem of deconvolution of SIMS depth profiles with model depth resolution function, which may differ from the true resolution function, is considered. The concept of residual depth resolution function is introduced to describe mathematically the result of the deconvolution. The consequences of using a model depth resolution function of double exponential form are explored and the range of exponents over which a deconvolution might give useful information is derived analytically. It is shown how a depth resolution function of double exponential form distorts the initial profiles of different types. The analytical expressions are obtained for rectangular and exponential initial profiles. It is shown that the convolution of the initial exponential profile with a double exponential resolution function leads to a linear combination of exponential functions containing separately either exponential parameters of the resolution function or that of the initial profile. The resultant inverse of the exponential slope cannot be calculated by direct summation of the characteristic lengths of the initial profile and those of the resolution function. The asymptotic behaviour of the convolution of the initial Gaussian profile with a double exponential resolution function is explored analytically.