Direct measurement of the Hall effect in a free-electron-like surface state

We have succeeded in directly measuring the Hall effect in a single-atomic layer on a Si(111) crystal surface. Our four-point-probe transport measurements under magnetic field showed that the behavior of majority carriers in the surface state changed from electronlike to holelike during the structural conversion from the $\sqrt{3}\times \sqrt{3}\text{−}\mathrm{Ag}$ to $\sqrt{21}\times \sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ surface superstructure. This is due to a change in the Fermi surface caused by band folding. The results are discussed quantitatively and shown to be consistent with the electronic structure obtained by photoemission spectroscopy.

Figure 1

(a,b) The photoemission intensity maps at the Fermi level (Fermi surface) measured for the $\sqrt{3}\text{−}\mathrm{Ag}$ (a) and $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ (b) surfaces. For a comparison, the dotted lines in (b) indicate the double domain $\sqrt{21}\times \sqrt{21}$ SBZ boundaries. (c) Schematic drawing of a free-electron-like Fermi surface of the $\sqrt{3}\text{−}\mathrm{Ag}$. The dotted lines indicate one of the $\sqrt{21}\times \sqrt{21}$ SBZs. (d) The Fermi surface of the $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ in the extended SBZ scheme, and (e) in the second and (f) third SBZs in the reduced SBZ scheme. The shaded area represents electron-filled regions.[9] The arrows on the Fermi surface indicate the motion of Fermi electrons under a magnetic field $\left(B\right)$ out of the paper. (g,h) Schematic drawing of the change of the free-electron-like surface-state band due to the structure transformation from $\sqrt{3}\text{−}\mathrm{Ag}$ (g) to $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ (h).

Figure 2

(a) Schematic drawing of the two-layer model, in the form of two parallel slabs, to mimic a nonuniform sample in the surface-normal direction. These layers, for example, represent two channels through the surface state and surface space-charge layer. (b) Schematic drawing of the experimental setup in the present measurement with the silicon wafer, tantalum(Ta) clamps and tungsten(W) wire-contact electrodes.

Figure 3

(a,b) The longitudinal resistance $(R_{xx}=V_{xx}∕I)$ (a) and the change of the sheet conductivity $\left(\Delta \sigma \right)$ (b) measured as a function of Au coverage on the $\sqrt{3}\text{−}\mathrm{Ag}$ at RT. The $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ surface, indicated by $\sqrt{21}$, is formed around 0.14 ML Au coverage. (c–f): The Hall resistance $(R_{\text{Hall}}=V_{\text{Hall}}∕I)$ (c,e) and the change of longitudinal resistance [$\delta R_{xx}$ in Eq. (18)] (d,f) measured as a function of the magnetic field for the $\sqrt{3}\text{−}\mathrm{Ag}$ (open circles) and $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ surfaces (closed circles). The data were taken with $p$-($B$-doped, $3900–6400\Omega \mathrm{cm}$) (c,d) and $n$-($P$-doped, $1–10\Omega \mathrm{cm}$) type Si(111) wafers (e,f). The insets show the current-voltage $\left(I\text{−}V\right)$ curves at $3\mathrm{T}$ (c,e) and at $0\mathrm{T}$ (d,f), respectively.

Figure 4

The measured values of $R_H{\sigma }^2$ (data points in open circles) for the $\sqrt{21}\text{−}(\mathrm{Ag},\mathrm{Au})$ with respect to that of the $\sqrt{3}\text{−}\mathrm{Ag}$. The curve shows the calculated result $R_{Hsc}{\sigma }_{sc}^2$ for the surface space-charge layer as a function of the surface Fermi level position for $p$-type $(3900\Omega \mathrm{cm}$) (a) and $n$-type $(10\Omega \mathrm{cm}$) (b) Si wafers. $ss\left(sc\right)$ represents the surface-state (space-charge layer) component.