Disentangling Surface, Bulk, and Space-Charge-Layer Conductivity in $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$

A novel approach for extracting genuine surface conductivities is presented and illustrated using the unresolved example of $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$. Its temperature-dependent conductivity was measured with a microscopic four point probe between room temperature and 100 K. At room temperature the measured conductance corresponds to that expected from the bulk doping level. However, as the temperatures is lowered below $\approx 200\mathrm{K}$, the conductance decreases by several orders of magnitude in a small temperature range and it saturates at a low temperature value of $\approx 4\times {10}^{-8}{\Omega }^{-1}$, irrespective of bulk doping. This abrupt transition is interpreted as the switching from bulk to surface conduction, an interpretation which is supported by a numerical model for the measured four point probe conductance. The value of the surface conductance is considerably lower than that of a good metal.

Figure 1

Temperature-dependent 4pp conductance of the three $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ surfaces and of the Ag film. The solid lines are a guide to the eye. The inset shows a typical micro 4pp.

Figure 2

Modeled and measured conductances as a function of temperature for sample $A$, both for the clean ($7\times 7$) surface and the thin Ag layer on that surface. The ($7\times 7$) model includes the bulk and space-charge layer, but the surface-state conductance is excluded.

Figure 3

Maps of current density from the conductivity models for 100 K (left-hand panels) and 300 K (right-hand panels). The upper panels show the transects along the axis of the probes, the middle panels show the top surface, and the lowest panels are transects through the perpendicular bisector of the probe axis. The plots are scaled such that the highest current density in each plot appears brightest.