Conservation of the Lateral Electron Momentum at a Metal-Semiconductor Interface Studied by Ballistic Electron Emission Microscopy

We report on ballistic electron emission microscopy and spectroscopy studies on epitaxial (3–5 nm thick) Bi(111) films, grown on $n$-type Si substrates. The effective barrier heights of the Schottky barrier observed are 0.58 eV for the $\mathrm{Bi}/\mathrm{Si}(100)\mathrm{\text{−}}(2\times 1)$ and 0.68 eV for the $\mathrm{Bi}/\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$. At the step edges of the epitaxial films a strong increase of the ballistic electron emission microscopy current is observed for $\mathrm{Bi}/\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$, while no increase occurs for $\mathrm{Bi}/\mathrm{Si}(100)\mathrm{\text{−}}(2\times 1)$. These observations can be explained by the conservation of the lateral momentum of the electron at the metal-semiconductor interface.

Figure 1

(a) BEES spectrum for $\mathrm{Bi}(111)\mathrm{\text{−}}\mathrm{Si}(100)\mathrm{\text{−}}(2\times 1)$, measured at $I_{\mathrm{tunnel}}=40\mathrm{pA}$. The numerical fit yields a local Schottky barrier height of 0.58 eV. (b) Distribution of Schottky barrier heights for 60 spectra. (c) BEES spectrum, measured on $\mathrm{Bi}(111)\mathrm{\text{−}}\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ at $I_{\mathrm{tunnel}}=82\mathrm{pA}$. The fit yields a local Schottky barrier height of 0.68 eV. (d) Distribution of Schottky barrier heights for 48 spectra.

Figure 2

$\mathrm{Bi}/\mathrm{Si}(100)\mathrm{\text{−}}(2\times 1)$. (a) Topography of $\mathrm{Bi}/\mathrm{Si}(100)\mathrm{\text{−}}(2\times 1)$ measured at $I_{\mathrm{tunnel}}=50\mathrm{pA}$, $U_{\mathrm{tip}}=-1.8\mathrm{V}$ ($300\times 300{\mathrm{nm}}^2$). (b) Simultaneously measured BEEM image, the gray scale varies from 7% to 12% of the tunneling current. (c) Topography of a triangular shaped hole ($29\times 29{\mathrm{nm}}^2$). (d) BEEM image measured simultaneously with (c) in forward (left to right) scan direction. The gray scale varies from 8% to 15%. (e) BEEM image corresponding to (c) for the reversed scan direction. (f) Tunneling current measured simultaneously with (c) and (d). The gray scale varies from 35 to 55 pA.

Figure 3

$\mathrm{Bi}/\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$. (a) Topography of $\mathrm{Bi}/\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ measured at $I_{\mathrm{tunnel}}=82\mathrm{pA}$, $U_{\mathrm{tip}}=-1.8\mathrm{V}$ ($300\times 300{\mathrm{nm}}^2$). (b) Simultaneously measured BEEM image. The gray scale varies from 0% to 10% of the tunneling current. (c) Topography of a triangular shaped hole ($24\times 24{\mathrm{nm}}^2$). (d) BEEM image measured simultaneously with (c) in forward direction. The gray scale varies from 7% to 12%. (e) BEEM image corresponding to (c) for the reversed scan direction. (f) Tunneling current measured simultaneously with (c) and (d). The gray scale varies from 70 to 90 pA.

Figure 4

(a) Electronic band structure of a (freestanding) Bi film with a thickness of 5 bilayers. (b),(d) Show the projection of the electronic states of Si as well as Bi on the Si(111) surface. The Bi states are drawn for an energy of 0.58 eV (red line) and 0.68 eV (blue line), the Si states are pockets which are limited by the dashed line for 0.2 eV. (c),(e) Show the projection of the electronic states of Si as well as Bi on the Si(100) surface.