Polarity-dependent pinning of a surface state

We illustrate a polarity-dependent Fermi level pinning at semiconductor surfaces with chargeable surface states within the fundamental band gap. Scanning tunneling spectroscopy of the $\mathrm{GaN}\left(10\overline{1}0\right)$ surface shows that the intrinsic surface state within the band gap pins the Fermi energy only at positive voltages, but not at negative ones. This polarity dependence is attributed to arise from limited electron transfer from the conduction band to the surface state due to quantum mechanically prohibited direct transitions. Thus, a chargeable intrinsic surface state in the band gap may not pin the Fermi level or only at one polarity, depending on the band to surface state transition rates.

Figure 1

Scanning tunneling spectroscopy of the $n$-type $\mathrm{GaN}(10\overline{1}0$) surface at 290 K. The squares show the experimental data measured at a tip-sample separation fixed by a set voltage of $-3.6$ V and a set current of 150 pA. The lines represent calculations of the tunnel current with no intrinsic surface state in the band gap (red solid and dashed lines) and with an empty surface state at $E_{\mathrm{C}}-0.7$ eV (blue solid and dashed lines), pinning the Fermi energy. Inset: STM image of the $\mathrm{GaN}\left(10\overline{1}0\right)$ surface, on which the spectrum was measured.

Figure 2

Calculated valence ($E_{\mathrm{V}}$) and conduction ($E_{\mathrm{C}}$) band edge positions for unpinned GaN surfaces with no surface states in the band gap for (a) negative ($-3.5$ V) and (b) positive ($+1.0$ V) voltages applied to the semiconductor sample. The sample is on the right side at positive distance values. The Fermi energy $E_{\mathrm{F}}$ is close to the conduction band in the bulk. The tip with its Fermi energy at $E_{\mathrm{F}}+eV$ is shown on the left-hand side. The dark blue (light blue) areas represent filled (empty) states. The band gap and the vacuum gap (tunnel barrier) between the surface at zero position (0 nm) and the tip position (at $-1.06$ nm) are shown in white. At negative voltages (a) the downward band bending induces an accumulation of electrons in the conduction band. These accumulated electrons tunnel into the tip resulting in an accumulation current $I_{\mathrm{acc}}$. At positive voltages (b) the electrons tunnel from the tip into the conduction band states ($I_{\mathrm{C}}$).

Figure 3

Calculated valence ($E_{\mathrm{V}}$) and conduction ($E_{\mathrm{C}}$) band edge positions for a GaN surface with a filled and an empty intrinsic surface state. Their density of states is modeled as Gaussian distributions and given on the top axis. Following band-structure calculations [23] the upper (empty) intrinsic surface state is assumed to be 0.7 eV below the conduction-band minimum, whereas the lower one is below the valence-band edge. The same color and labeling conventions as in Fig. 2 are used. Four different configurations are shown: (a) Surface without tip and no applied voltage in equilibrium. The intrinsic surface state is partially occupied (see the tiny red area in the enlarged inset), fully pinning the surface and hence inducing an upward band bending. (b) Surface in the presence of the metallic tip with a negative sample voltage of $-3.5$ V. The system reaches equilibrium by partially occupying the surface state (see inset). This induces an upward band bending and fully pins the Fermi level. Hence, no electron accumulation in the conduction band exists and only electrons from the valence band tunnel ($I_{\mathrm{V}}$). (c) Surface biased at $+1.0$ V with the tip present. The system is again in equilibrium by partially filling the surface state and thus pinning the Fermi level. The band edge positions are presented by solid lines. For comparison, the band edge positions without surface state taken from Fig. 2 are shown as dashed lines. The bands are shifted by $\mathrm{\Delta }E$, resulting in an offset of the onset voltage of the conduction-band tunnel current $I_{\mathrm{C}}$ as experimentally observed. (d) Nonequilibrium case of the tip-vacuum-semiconductor system with the semiconductor surface biased at $-3.5$ V. Under tunneling conditions the surface state does not reach its equilibrium filling, since the optical electron transition between the conduction band and the surface state is prohibited. Hence, there is no Fermi level pinning. This situation is observed experimentally.