Strongly Metallic Electron and Hole 2D Transport in an Ambipolar Si-Vacuum Field Effect Transistor

We report experiment and theory on an ambipolar gate-controlled Si(111)-vacuum field effect transistor where we study electron and hole (low-temperature 2D) transport in the same device simply by changing the external gate voltage to tune the system from being a 2D electron system at positive gate voltage to a 2D hole system at negative gate voltage. The electron (hole) conductivity manifests strong (moderate) metallic temperature dependence with the conductivity decreasing by a factor of 8 (2) between 0.3 K and 4.2 K with the peak electron mobility ($\sim 18{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$) being roughly 20 times larger than the peak hole mobility (in the same sample). Our theory explains the data well using random phase approximation screening of background Coulomb disorder, establishing that the observed metallicity is a direct consequence of the strong temperature dependence of the effective screened disorder.

Figure 1

Experimental results for an ambipolar Si(111)-vacuum FET. (a) Electron and hole densities vs gate voltage are shown. (b) Mobility and (c) conductivity for both electrons (right panel) and holes (left panel) measured at $T=0.3\mathrm{K}$ (black) and $T=4.2\mathrm{K}$ (red) are shown as a function of density in linear scale. Inset shows the same data in (b) as a log plot, where top (bottom) two lines are for electron (hole). (d) Conductivity vs density relation is shown in semi-log scale. (e) and (f) show conductivity vs density in log-log scale at $T=0.3\mathrm{K}$ and $T=4.2\mathrm{K}$, respectively. The fitting exponents $\alpha$ in the relation of $\sigma \sim n^{\alpha }$ are given in the figures.

Figure 2

(a) Calculated $k_{F}l$ using experimental conductivity with different values of $g_v$. (b) The experimentally measured conductivity as a function of temperature for several electron densities, $n=0.85$, 0.91, 0.99, 1.15, 1.30, 1.46, 1.61, 1.92, 2.39, 3.17, 3.94, 4.72, 5.49, $6.12\times {10}^{11}{\mathrm{cm}}^{-2}$ (bottom to top). (c) Calculated conductivity in the presence of ionized channel impurities and surface roughness for electron densities $n=1.3$, 1.5, 2.0, 3.0, 4.0, 4.5, 5.5, $6.0\times {10}^{11}{\mathrm{cm}}^{-2}$ (bottom to top). Inset in (c) shows the experiment and theory results together for carrier densities ($n=1.3$, 1.46, 1.61, 1.92, 2.39, 3.17, bottom to top) demonstrating reasonable agreement.

Figure 3

(a) Calculated conductivity as a function of carrier density for two different temperatures $T=0.3\mathrm{K}$ (solid lines) and 4.2 K (dashed lines). For the hole system the effective masses $m_h=0.5m_0$ and $g_v=1$ are used, and for the electron system $m_e=0.3m_0$ and $g_v=2$, 6 are used. (b) The high density exponents in the relation of $\sigma \sim n^{\alpha }$ are shown for an electron system with $g_v=6$ (top two lines) and hole system with $g_v=1$ (bottom two lines). The solid (dashed) lines indicate the calculated conductivity at $T=0.3\mathrm{K}$ (4.2 K). The dotted lines are for a guide of exponents $\alpha$ shown in the figure.