Scaling limits for the two-dimensional metal-insulator transition at B = 0 in Si-MOSFET’s

We have examined data on the density-driven conductivity transition at $B=0$ in Si-MOSFET's. Data from this transition can be arranged such that it appears to collapse into certain one-parameter scaling forms. This fact has been used to support the idea that a quantum phase transition to a two-dimensional metallic phase is occurring in these systems. Here we present a quantitative analysis on the compatibility of the data with such a quantum phase transition. For this purpose, we developed a self-consistent nonlinear regression method, which extracts all scaling parameters with statistical error estimates in single unbiased fits. By carefully tracking sources of error and statistical uncertainties in the experimental data, we are able to determine the normalized mean-square deviation, ${\ensuremath{\chi}}^{2},$ of such fits. Using ${\ensuremath{\chi}}^{2}$ as a quantitative measure of goodness of fit, we analyzed E-field scaling in three different samples. We also investigated the variation of the fitted parameters and ${\ensuremath{\chi}}^{2}$ as automated truncations are imposed on the data. We determined that individual fits can show quantitative agreement with scaling. However, this agreement is sensitive to truncation. For example, we found larger variation in fitted parameters, even within a single sample, than our statistical error estimates suggest.