Scanning tunneling microscopy and spectroscopy of reconstructed $\mathrm{Si}\left(100\right)$ surfaces

We combine theory and experiments to study bias-dependent scanning tunneling microscopy (STM) images of the different reconstructions of $\mathrm{Si}\left(100\right)$ surfaces. Coupling with the analysis of scanning tunneling spectroscopy (STS) data, we show that STM images result from a subtle interplay between topographic effects and the energy dependence of probed electronic states. We confirm that the second STS peak at positive sample bias arises from the injection of electrons into surface electronic states mainly localized on the dimer's backbonds but also containing ${\pi }^{*}$ and $\sigma$ components. The comparison between theory and experiments strongly suggests an important role played by tip-sample interactions, through a local modification of the dimer buckling and by the surface band bending induced by the applied bias.

Figure 1

Energy dispersion of the $\pi$ and ${\pi }^{*}$ surface bands for the $c(4\times 2)$ reconstruction along the $\Gamma -J^{\prime }$ direction of the Brillouin zone. Inset: a quarter part of the Brillouin zones of the $p(2\times 2)$ and $p(2\times 1)$ structures denoted by solid and dashed lines, respectively. Crosses: energy dispersion calculated in Ref. 3. Other symbols: experimental data obtained by Yokoyama et al. (Refs. 25, 43, 44).

Figure 2

Calculated band structure of $\mathrm{Si}$ slabs for the $p(2\times 1)s$ (a), $p(2\times 2)$ (b), and $c(4\times 2)$ (c) reconstructions plotted in the Brillouin zone associated with the $p(2\times 2)$ lattice. The zero of energy corresponds to the top of the bulk valence band.

Figure 3

Simulated STM images obtained on the $c(4\times 2)$ phase for sample voltages of $-1.0$ (a), $+0.7$ (b), $+1.6$ (c), and $+2.1\mathrm{V}$ (d).

Figure 4

Experimental STM images obtained on the $c(4\times 2)$ phase of an $n$-type $\mathrm{Si}\left(100\right)$ surface for sample voltages of $-1.5$ (a), $+0.7$ (b), $+0.7$ (c), and $+1.5\mathrm{V}$ (d) at a temperature of $77\mathrm{K}$. Images (b) and (c) differ by the setpoint currents, which are $500$ and $160\mathrm{pA}$, respectively.

Figure 5

Simulated STM images obtained on $c(4\times 2)$ (a) and $p(2\times 2)$ (b) phases when up and down atoms of the dimer have been shifted $0.2\mathrm{\AA }$ downward and upward, respectively, to reduce the buckling ($\text{sample voltage}=+0.7\mathrm{V}$).

Figure 6

Simulated STM images obtained on the $p(2\times 2)$ phase for sample voltages of $-0.7$ (a), $+0.7$ (b), $+1.6$ (c), and $+2.1\mathrm{V}$ (d).

Figure 7

Simulated STM images obtained on the $p(2\times 1)a$ phase for sample voltages of $-0.7$ (a) and $+0.7\mathrm{V}$ (b).

Figure 8

STS spectra calculated for the $c(4\times 2)$ reconstruction at different positions of the tip indicated by crosses in the inset ($\text{large circles}=\text{upper surface atoms}$; $\text{small circles}=\text{lower atoms}$). The zero of the voltage is determined by the Fermi level of the sample which is close to the midgap of the electronic structure. The spectra do not go to zero at $V_{\mathrm{s}}=0$ because of the broadening of the Green’s functions.

Figure 9

STS spectra for the $c(4\times 2)$ reconstruction: (a) theoretical tunneling spectrum; (b) experimental tunneling spectrum obtained on a $p$-type sample at $5\mathrm{K}$; (c) experimental tunneling spectrum obtained on an $n$-type sample at $77\mathrm{K}$. The positions of the filled surface states, tip induced states, empty states, and backbond states are indicated by the symbols $\pi$, TIS, ${\pi }^{*}$, and BB, respectively.

Figure 10

STS spectra for the $p(2\times 2)$ reconstruction (continuous line: theory; dashed line: experiment achieved on $p$-type $\mathrm{Si}$ at $5\mathrm{K}$). The experimental curve has been shifted slightly to align the $\pi$ peaks. The positions of the filled surface states, tip-induced states, empty states, and backbond states are indicated by the symbols $\pi$, TIS, ${\pi }^{*}$, and BB, respectively.

Figure 11

Band profile showing the influence of the band bending at low positive sample voltage on the transmission of electrons from the tip to the surface for $p$-type $\mathrm{Si}$.