Evidence for multiple impurity bands in sodium-doped silicon MOSFETs

We report measurements of the temperature-dependent conductivity in a silicon metal-oxide-semiconductor field-effect transistor that contains sodium impurities in the oxide layer. We explain the variation of conductivity in terms of Coulomb interactions that are partially screened by the proximity of the metal gate. The study of the conductivity exponential prefactor and the localization length as a function of gate voltage have allowed us to determine the electronic density of states and has provided arguments for the presence of two distinct bands and a soft gap at low temperature.

Figure 1

The source drain conductivity vs gate voltage at $300\mathrm{mK}$ following a $+4\mathrm{V}$ drift and a $-4\mathrm{V}$ drift (dotted line).

Figure 2

(a) Temperature dependence of the conductivity for $V_g=0.1$ (엯), $-0.24$ (●), $-1.48\mathrm{V}$ (⋆), and $-2.26$ (◁). (b) Variation of the reduced ${\chi }^2$ with $s$ for $\gamma =2$ for the gate voltages listed showing minima at $s=0.412$, 0.406, 0.394, and 0.385, respectively. (c) Variation of the reduced ${\chi }^2$ with $\gamma$ for $s$ equal to the optimum value found in (b), for the appropriate gate voltages, displaying consistency with a minimum at $\gamma =2$ (dotted line). Lines in (b) represent the exponent for the Mott hopping regime (left) and Efros and Schklovskii regime (right).

Figure 3

Temperature dependence of the conductivity for $V_g=0.1$ (엯), $-0.24$ (●), $-1.48\mathrm{V}$ (∗), and $-2.26$ (◁) for the optimum values of $\gamma$ and $s$ defined in Eq. (1). For clarity, curves are shifted downward, respectively, by 0, 1, 2, and 3 from their original values.

Figure 4

Variation of the DOS at $E_F$ with gate voltage. The dashed and dotted lines represent, respectively, the background density due to the conduction band tail and the upper band tail. The inset is the relative variation of the DOS to the background in the same units.

Figure 5

Variation of the localization length (●) and the transmission coefficient at $1\mathrm{K}$ (엯) with gate voltage.