Noise, resolution and entropy in sputter profiling

Applications of semiconductor sputter profiling in the near future will demand nm or even sub-nm depth resolution, i.e. the ability to distinguish between adjacent features in a concentration profile which are separated by 1 nm or less (not just the ability to achieve a 16-84% width of 1 nm on some edge transient). Recent developments in SIMS indicate that sputter profiling can meet this challenge-provided that instruments with high current microfocus beams less than 1 keV in energy become widely available, and data processing methods are developed to cope with the results. In this paper we discuss the nature of SIMS sputter profile data in detail and explore the consequences of noise, finite sample interval and the destruction of information by processes such as atomic mixing. The use of empirically determined response functions is discussed. We use simple arguments to show that convolution is only a valid model for atomic mixing in the low concentration limit, and contrast the use of Fourier transform and maximum entropy methods for deconvolution in these circumstances. A depth resolution of 1 nm is demonstrated without deconvolution, showing that the technique has real potential for depth resolution on the scale of 1 atomic plane.