An automatic smoothing algorithm for the calculation of impurity concentration from sheet resistivity and sheet hall coefficient data

Abstract

A new processing algorithm is described for the conversion of incremental sheet resistance and sheet Hall coefficient data to impurity concentration, for the case of smooth unimodal carrier profiles. The method is based on two improvements to existing techniques. The first involves the application of an inverse error function complement transformation which attempts to linearize the experimental data. The second refinement, concerning the numerical differentiation of the data, includes the use of a cubic spline function and also a simple editing facility, so that the results obtained are not influenced by occasional poor data values. As an example of the power of these new techniques, results are given of an application to the sheet resistance data published by Plunkett et al. Full details of the extension of the algorithm to incorporate the use of sheet Hall data are described, and it is noted that the differentiation of the Hall and sheet resistance data are accomplished independently. Finally an application of the complete algorithm is described on new experimental sheet resistance and sheet Hall coefficient data.