2D Metal-insulator transition behavior in a high mobility strained Si quantum well

The apparent metal-insulator transition is observed in a high quality two-dimensional electron system (2DES) in the strained Si quantum well of a Si/Si$_{1-x}$Ge$_{x}$ heterostructure with mobility $\mu$=1.9$\times$10$^{5}$cm$^{2}$/Vs at $n$=1.45 $\times$10$^{11}$cm$^{-2}$. The critical density $n_c$, where the thermal coefficient of low T resistivity changes sign, is 0.32$\times$10$^{11}$cm$^{-2}$, much smaller than the $n_c$ of $\sim$0.8$\times10^{11}$cm$^{-2}$ seen in clean Si-MOSFET's (usually with a peak $\mu$$\sim$4$\times$10$^{4}$cm$^{2}$/Vs). This result is consistent with previous observations in the GaAs systems that $n_c$ decreases with increasing 2DES quality. Moreover, in low $n$ range, for 0.27$\times$10$^{11}$cm$^{-2} $$<$$n$$<$0.35$\times$10$^{11}$cm$^{-2}$, close to the transition region, the conductivity increases roughly linearly with $T$ around the Fermi temperature and, surprisingly, all the curves of different densities are parallel to each other for $T>1.2K$. In the higher density range where the 2DES shows metallic-like behavior, the in-plane magnetoresistance $\rho$(B) first increases $\sim$B$^{2}$ and then saturates to a finite value $\rho$(B$_C$) for B$>$B$_C$. The full spin-polarization field B$_C$ decreases monotonically with $n$ but appears to saturate to a finite value as $n$$\rightarrow$0. We find $\rho (B_C)/\rho(0)$$\sim$1.8 for all the densities ranging from 0.35 to 1.45$\times10^{11}$cm$^{-2}$ and, when plotted versus B/B$_C$, collapse onto a single curve.