Connection of anisotropic conductivity to tip-induced space-charge layers in scanning tunneling spectroscopy of $p$-doped GaAs

The electronic properties of shallow acceptors in $p$-doped GaAs{110} are investigated with scanning tunneling microscopy (STM) at low temperature. Shallow acceptors are known to exhibit distinct triangular contrasts in STM images for certain bias voltages. Spatially resolved $I\left(V\right)$ spectroscopy is performed to identify their energetic origin and behavior. A crucial parameter—the scanning tunneling microscope tip’s work function—is determined experimentally. The voltage dependent potential configuration and band bending situation are derived. Ways to validate the calculations with the experiment are discussed. Differential conductivity maps reveal that the triangular contrasts are only observed with a depletion layer present under the STM tip. The tunnel process leading to the anisotropic contrasts calls for electrons to tunnel through vacuum gap and a finite region in the semiconductor.

Figure 1

(Color online) $(40\times 40{\mathrm{nm}}^2)$ STM constant current topography of the atomically flat GaAs $\left(1\overline{1}0\right)$ cleavage surface. The corrugation of the surface states is clearly visible. At the selected sample bias, $+1.6\mathrm{V}$ zinc acceptors superimpose triangular shaped protrusions on the otherwise atomically flat surface. The triangles’ heights vary depending on the depth of the dopant under the surface. The image shows acceptors buried up to eight monolayers.

Figure 2

(Color online) Spatially resolved $I\left(V\right)$ spectroscopy. The spectroscopy is measured above a part of the clean GaAs cleavage surface. The setpoint sample bias is $+1.85\mathrm{V}$, and the tunnel current is set to $1\mathrm{nA}$. Two subsurface Zn acceptors are visible in the topography. They appear as faint circular depressions. No $z$ shift was applied. The red curve labeled (1) is evaluated in the small rectangle above the contrast of the lower acceptor and shows the energetic distribution of the acceptor induced conductivity. The blue curve labeled (2) is evaluated above the undisturbed region of the image (large rectangle). The open circles are raw data and the solid lines are the Gauss-weighted average. The lower part shows the differential conductivity $dI∕dV$ of the upper two curves. Two intervals of negative differential conductivity are observed (NDC). The tunnel current above the acceptor rises up to 10% of the setpoint current.

Figure 3

Numerically derived dependence of the tip-induced band bending on the applied sample bias $\mathrm{TIBB}\left(V\right)$. The solid curve is evaluated for the measured value of the $4.0\mathrm{eV}$ tip work function, whereas the dotted curve corresponds to the $4.5\mathrm{eV}$ work function. The main difference is the sample bias where the band bending vanishes (flatband condition).

Figure 4

The tunneling barrier height is recorded for every pixel during the STS measurement via the $dI∕dz$ modulation technique. The map shows the lateral variations of the barrier height that correspond to the corrugation of the surface states. Histogram analysis shows two peaks: $4.2\mathrm{eV}$ above the corrugation maxima and $3.8\mathrm{eV}$ for the corrugation minima. The weighted mean value is $4.05\mathrm{eV}$.

Figure 5

Histogram of the mean work functions of 25 STS measurements on the sample system. The average value for all measurements is $3.96\mathrm{eV}$ work function, assuming a Gaussian distribution of the data points.

Figure 6

Some representative $dI∕dV$ maps extracted from the STS measurement shown in Fig. 2. The differential conductivity is shown in gray scale: reduced (black) and enhanced (white) conductivities with respect to the mean conductivity in each map. The black triangles in the maps for $+1525\text{to}1547\mathrm{mV}$ are negative differential conductivity. The STS measurement covers four different tunneling situations. The potential configuration for each column of this figure is the same. The respective band alignment is sketched for each column by a rigid-band diagram (the band alignment scheme labels sc, d, $E_F$, etc., are described in Sec. 6): (a) depletion layer under the surface and electrons tunneling from the bulk of the sample through the depletion layer and the vacuum gap to the tip, (b) depletion layer and electrons tunneling from the tip through vacuum and depletion layer into the bulk sample, (c) flatband condition and electrons tunneling into the acceptor band and the conduction band, and (d) accumulation of free holes under the surface and tunneling into the conduction band and the accumulation layer.

Figure 7

Current map derived from the $dI∕dV$ maps representing the amount of tunnel current originating from the sample bias interval $(+1547\text{to}+1668\mathrm{mV})$. The hole charge density oscillations are observed. The cross section directly through the center of the oscillatory pattern allows us to estimate that the amount of tunnel current flowing into the hole accumulation layer is about $\eta =27\mathrm{pA}$.

Figure 8

(Color online) Identification of deeply buried acceptors. (a) Setpoint topography of the STS measurement in Fig. 2 recorded $1.85\mathrm{V}$ sample bias. Only two acceptors are identified as faint circular depressions. The area inside the dashed rectangle is the same region as shown in the $dI∕dV$ maps of Fig. 6. (b) Integral current map of the same area. The color coded image shows the tunnel current integrated over the voltage interval from $0\text{to}1.5\mathrm{V}$. This map identifies all subsurface acceptors by their triangular contrast, even those not visible in constant current topographies. (c) The upper $I\left(V\right)$ curve is reproduced from Fig. 2. The lower one is an averaged curve above the undisturbed region marked in (b) with the white rectangle. The ordinate axis is magnified by a factor of $\sim 20$ with respect to the upper plot.