Valence Surface Electronic States on Ge(001)

The optical, electrical, and chemical properties of semiconductor surfaces are largely determined by their electronic states close to the Fermi level ($E_F$). We use scanning tunneling microscopy and density functional theory to clarify the fundamental nature of the ground state Ge(001) electronic structure near $E_F$, and resolve previously contradictory photoemission and tunneling spectroscopy data. The highest energy occupied surface states were found to be exclusively back bond states, in contrast to the Si(001) surface, where dangling bond states also lie at the top of the valence band.

Figure 1

Schematics of the bonding structures of (a) symmetric and (b) buckled dimers of the dimerized Ge(001) and Si(001) surfaces. The labels BBd and BBu denote the back bonds associated with the down and up dimer atoms, respectively.

Figure 2

Filled-state STM images of clean Ge(001) at sample biases of (a) $-1.0\mathrm{V}$, (b) $-0.6\mathrm{V}$, (c) $-0.4\mathrm{V}$, (d) $-0.2\mathrm{V}$, (e) $-0.1\mathrm{V}$. The images in (b)–(e) are for the area of $\sim 2.3\times 3.7{\mathrm{nm}}^2$ indicated by the white rectangle in (a). All images were acquired at $\sim 0.8\mathrm{nA}$ tunneling current. Simulated filled-state STM images for $\mathrm{Ge}(001)c(4\times 2)$ corresponding to an integration range of (f) $-0.6\mathrm{eV}$, (g) $-0.4\mathrm{eV}$, (h) $-0.3\mathrm{eV}$, and (i) $-0.2\mathrm{eV}$. All of these ILDOS plots are for an isosurface value of $1.8\times {10}^{-4}\mathrm{e}/{\AA }^3$.

Figure 3

The electronic structure of the clean $\mathrm{Ge}(001)c(4\times 2)$ surface close to $E_F$ (dashed horizontal line) calculated using a ($4\times 4$) surface unit cell. The filled squares denote the surface back bonds, and the filled circles indicate the $\pi$ dangling bond surface states. The unoccupied (${\pi }^{*}$) dangling bond surface states are indicated by the double-headed arrow above $E_F$.

Figure 4

Charge density plots for the highest occupied state at the $\mathbf{k}$-point one quarter of the distance along the $\Gamma –K$ symmetry direction (see Fig. 3); (a) top, and (c) side views (isosurface value $6.5\times {10}^{-3}\mathrm{e}/{\AA }^3$); (b) plane above the $\mathrm{Ge}(001)c(4\times 2)$ surface (isosurface value $3.8\times {10}^{-4}\mathrm{e}/{\AA }^3$). The plot in (c) is along the dashed line in (a).