Screening Breakdown on the Route toward the Metal-Insulator Transition in Modulation Doped Si $/$SiGe Quantum Wells

Exploiting the spin resonance of a two-dimensional (2D) electron in SiGe/Si quantum wells, we determine the carrier density dependence of the magnetic susceptibility. Assuming weak interaction, we evaluate the density of states at the Fermi level, $D\left(E_F\right)$, and the screening wave vector, $q_{\mathrm{TF}}$. Instead of the constant values of an ideal 2D system, we observe a gradual decrease towards the band edge. Calculating the mobility from $q_{\mathrm{TF}}$ yields good agreement with experimental values justifying the approach. The decrease in $D\left(E_F\right)$ is explained by potential fluctuations which lead to tail states that make screening less efficient and, in a positive feedback, cause an increase of the potential fluctuations.