Scaling Limits for the 2D Metal-Insulator Transition at B = 0 in Si-MOSFETs

Abstract

We have reexamined data on the possible two dimensional metal-insulator transition at B=0 in Si-MOSFETs using a nonlinear regression method to extract all scaling parameters in a single fit. By keeping track of the magnitude of errors in the data we can use the normalized mean square deviation χ^2 of the fit as a quantitative measure of how well the data is compatible with scaling. We have used this method to study electric field scaling in three different samples. We find rather good agreement of the data with scaling in individual fits, i.e. χ^2's of about 1, but also rather large variations in the fits depending on how cut-offs are introduced in the data. In particular, we report how fitted parameters vary when we cut away data that are either far from the critical point or at low excitation power, where temperature effects presumably dominate. In this way we find the critical E-field exponent βto vary from about 3.2 to 3.9 with considerably smaller statistical error estimates in each fit.