Influence of surface band bending on a narrow band gap semiconductor: Tunneling atomic force studies of graphite with Bernal and rhombohedral stacking orders

Tunneling atomic force microscopy (TUNA) was used at ambient conditions to measure the current-voltage $(I\text{−}V)$ characteristics at clean surfaces of highly oriented graphite samples with Bernal and rhombohedral stacking orders. The characteristic curves measured on Bernal-stacked graphite surfaces can be understood with an ordinary self-consistent semiconductor modeling and quantum mechanical tunneling current derivations. We show that the absence of a voltage region without measurable current in the $I\text{−}V$ spectra is not a proof of the lack of an energy band gap. It can be induced by a surface band bending due to a finite contact potential between tip and sample surface. Taking this into account in the model, we succeed to obtain a quantitative agreement between simulated and measured tunnel spectra for band gaps $(12...37)$ meV, in agreement with those extracted from the exponential temperature decrease of the longitudinal resistance measured in graphite samples with Bernal stacking order. In contrast, the surface of relatively thick graphite samples with rhombohedral stacking reveals the existence of a maximum in the first derivative $dI/dV$, a behavior compatible with the existence of a flat band. The characteristics of this maximum are comparable to those obtained at low temperatures with similar techniques.

Figure 1

(a) Normalized TUNA current-voltage characteristics measured in the tunneling regime at different positions of a HOPG sample (HOPGA-Pd-1, see Table 1), see optical image in the upper left inset. The maximum current values at $-0.5$ V used for the normalization were first to third locations): 217 pA, 302 pA, 240 pA. The lower right inset shows the first derivative of the $I\text{−}V$ curves at the three locations. The normalization of the current values with the first derivative was done at $-0.3$ V (instead of $-0.5$ V as in the main panel) to enhance the details in the region of interest. Figure 9 shows the first derivative in the whole measured voltage range for the same sample. (b) Similar measurements for a graphite mesoscopic flake (sample MG-Pd-11-2) (see SEM image at the upper left inset) at different positions. The maximum current values at $-0.5$ V used for normalization were: 1174 pA, 912 pA, 565 pA, 597 pA, 671 pA, 447 pA. The inset below right shows the first derivative of the $I\text{−}V$ curves at three locations (current normalized at $-0.3$ V). All results were obtained at ambient conditions.

Figure 2

Tip-induced band bending as a function of the distance from the graphite surface for a biased tip-vacuum-sample system. (a) At negative sample voltages, tunneling out of filled valence band states ($I_{\text{V}}$) is dominating the total tunneling current. In addition, due to the large downward band bending and the small band gap, the conduction band minimum is dragged below the Fermi level at the surface, filling up its states with electrons. These electrons can tunnel out of the conduction band into empty tip states, leading to an additional, but small, tunneling current component ($I_{\text{inv}}$). (b) The large downward band bending is also present at positive sample voltages, due to a large contact potential of $\simeq 1$ eV. The total tunneling current is again composed of two components: The first component is driven by tunneling of electrons from the tip into empty valence band states ($I_{\text{V}}$). This is only possible because the Fermi level of the sample is situated below the valence band maximum, leading to unoccupied states within the valence band. The second component is driven by electrons tunneling from filled tip states into empty conduction band states ($I_{\text{C}}$). At small positive sample voltages, $I_{\text{V}}$ is the dominant tunneling current component, while for large positive voltages, $I_{\text{C}}$ becomes the largest contribution to the total tunneling current.

Figure 3

Comparison of TUNA spectra measured at clean and atomically flat Bernal-stacked graphite surfaces at $T=300$ K. The symbols correspond to the curve obtained at position 1 for the HOPG sample (HOPGA-Pd-1) shown in Fig. 1 with the best fit tunneling current simulation (green solid line). The blue solid line was obtained choosing a band gap of 0.1 meV with the same set of parameters, see Fig. 4. The results are plotted in a (a) linear and (b) logarithmic scale. In order to better recognize the asymmetry of the $I\text{−}V$ curves between the positive and negative voltage ranges, we plotted the absolute values of the tunneling current values of the experimental as well as the computed currents. Note the change in the curvature of the $I\text{−}V$ curve at $V\sim 0.12\mathrm{V}$ and the difference in the absolute values of the current at $\pm 0.3$ V.

Figure 4

Simulated tunneling current vs bias voltage at different band gaps between 0.1 meV and 120 meV using the parameters explained in the main text. Note that the absolute values of the current are plotted.

Figure 5

(a) $(\circ )$: First derivative of the tunnel current vs applied voltage measured on the HOPG-Pd-1 sample shown in Fig. 1 and (lines) of the simulated tunnel currents at three different band gaps (0.1, 25, 50) meV with otherwise unchanged parameters. Note that the absolute values of the derivative are plotted. (b) Voltage position of the minimum of the first derivative vs the band gap $E_G$. The ($⧫$) were obtained from the simulations. The line is only a guide to the eye. The range of the minimum in the first derivative of the experimental $I\text{−}V$ curves of the HOPG-1 sample is given by the shadowed rectangular region.

Figure 6

TUNA current-voltage characteristics obtained at different positions of the 3R phase surface of a 22 nm thick ($\simeq 22$ unit cells) natural graphite flake (sample NBF5-01-03, see Table 1), see upper left inset with the AFM image. The current values used for normalization were (from first to fifth positions): 276 pA, 293 pA, 386 pA, 374 pA, 366 pA. The bottom right inset shows the first derivative of the $I\text{−}V$ curves at the first and fourth positions in the voltage region of interest.

Figure 7

TUNA current-voltage characteristics obtained at three different positions of the 3R phase surface of a 3 nm thick ($\simeq 3$ unit cells) natural graphite flake (sample NBF5-SNG-3, see Table 1), see upper left inset with the AFM image. The current values at $-0.5$ V used for the normalization were (from first to third positions): 241 pA, 222 pA, 213 pA. The bottom right inset shows the first derivative of the normalized current $I\left(V\right)$ curves.

Figure 8

(a) Average of the 2D band of the rhombohedral phase (3R) showing the six processes due to ABC stacking of the NBF5-01-03 natural graphite flake sample. (b) Average of the 2D band of the Bernal phase (2H) showing the two process due to ABA stacking of MGPd-11 HOPG flake sample. (c) Raman image of the spatial distribution of the 2D band width. The yellow color area shows the 3R phase. (d) Raman image for the spatial distribution of the 2D band. In this case the red color area represents the Bernal phase (2H).

Figure 9

TUNA results of the current-voltage characteristic curves (left $y$ axis) and their first derivatives (right $y$ axis) measured on a diamondlike carbon film (DLC) and on the position 1 of the bulk graphite surface of Fig. 1. The maximum current values used for normalization were: 59 pA $(•)$ and 217 pA ($\circ )$. The red line of the first derivative corresponds to the graphite sample and the black one to the DLC film. The derivatives were obtained from the normalized current data at $-0.5$ V.

Figure 10

(a) Single (no averaging) TUNA current vs bias voltage curves obtained on sample HOPGA-Pd-1 (2H phase) at a fixed location in the continuous ramping mode at different times. After 26 s the tunneling current saturates already at low bias voltages just before a direct contact between the tip and the sample surface occurs. (b) The same data as in (a) in the tunneling regime but normalized by their corresponding currents at $-0.5$ V.