Fixing the Energy Scale in Scanning Tunneling Microscopy on Semiconductor Surfaces

In scanning tunneling experiments on semiconductor surfaces, the energy scale within the tunneling junction is usually unknown due to tip-induced band bending. Here, we experimentally recover the zero point of the energy scale by combining scanning tunneling microscopy with Kelvin probe force spectroscopy. With this technique, we revisit shallow acceptors buried in GaAs. Enhanced acceptor-related conductance is observed in negative, zero, and positive band-bending regimes. An Anderson-Hubbard model is used to rationalize our findings, capturing the crossover between the acceptor state being part of an impurity band for zero band bending and the acceptor state being split off and localized for strong negative or positive band bending, respectively.

Figure 1

Contact potential difference and acceptor-induced conductance for different tip apices. (a) Frequency shifts measured as a function of sample bias $\Delta f(V)$ (black lines), parabolic fits, and the corresponding flat-band voltages $V_{\mathrm{CPD}}$ are indicated (colored lines). (b) Calculated tip-induced band bending. For any sample bias below (above) $V_{\mathrm{CPD}}$, the band bending is negative (positive). (c),(d) $I(V)$ and $dI/dV(V)$ spectra away from (dashed lines) and atop (solid lines) subsurface acceptors; positions are indicated in the constant-current STM images (inset: $V=1.5\mathrm{V}$, $I=20\mathrm{pA}$). For all tip apices, acceptor-induced enhanced current and conductance are observed in negative, zero, and positive band-bending regimes.

Figure 2

$dI/dV$ maps of subsurface acceptors acquired with tip apices #1 (inset: constant-current topography, $V=1.5\mathrm{V}$, $I=20\mathrm{pA}$) to #3. For each apex, maps are acquired at voltages below, at, and above the corresponding flat-band voltage (sample biases as indicated; the gray scale is identical for each apex). For all apices, within all band-bending regimes, a similar triangular feature of enhanced conductance is observed.

Figure 3

Simulated electron transport within the junction. (a) Calculated $I(V)$ (dashed lines) and $dI/dV(V)$ (solid lines) spectra for vanishing ($U=0$) and nonvanishing on-site Coulomb energy ($U=2|t|$). The simulation yields nonzero current and conductance in a broad voltage range including negative, zero, and positive band bending. The inset sketches the relevant energies of the single-particle levels used as input for the many-body calculations. (b) Calculated average population $⟨n_5⟩$ of the foremost acceptor.