Role of the charge state of interface defects in electronic inhomogeneity evolution with gate voltage in graphene

Evolution of electronic inhomogeneities with back-gate voltage in graphene on ${\mathrm{SiO}}_2$ was studied using room temperature scanning tunneling microscopy and spectroscopy. Reversal of contrast in some places in the conductance maps and sharp changes in cross correlations between topographic and conductance maps, when graphene Fermi energy approaches its Dirac point, are attributed to the change in charge state of interface defects. The spatial correlations in the conductance maps, described by two length scales, and their growth during approach to Dirac point, show a qualitative agreement with the predictions of the screening theory of graphene. Thus a sharp change in the two length scales close to the Dirac point, seen in our experiments, is interpreted in terms of the change in charge state of some of the interface defects. A systematic understanding and control of the charge state of defects can help in memory applications of graphene.

Figure 1

(a) An STM image $(11.2\times 11.2{\mathrm{nm}}^2$, 0.3 V/0.1 nA) of sample 1 showing the atomically resolved honeycomb lattice of graphene. (b) shows the local tunneling conductance spectra (0.8 V/0.1 nA) at different $V_g$ values taken at a fixed location on graphene. The black arrow in each spectrum marks the minimum location while the purple arrow indicates the second shoulderlike feature. The inset in (b) shows the studied graphene sample surrounded by gold film on top. In (c) the continuous lines show the calculated dependence of conductance on $V_g$ (see text for details) while the discrete points (diamonds) show the average conductance found from STS maps with the bars depicting the standard deviation of the maps.

Figure 2

(a) to (k) show the conductance maps depicting electron inhomogeneities with $\left({\mathrm{a}}^{\prime }\right)$ to $\left({\mathrm{k}}^{\prime }\right)$ showing corresponding topographic maps over an area of $120\times 120{\mathrm{nm}}^2$ at different $V_g$ values. Imaging parameter for all the maps are bias voltage $V_b=0.25$ V and current set point 0.1 nA. (l) shows the cross-correlation coefficient between the conductance and topographic maps as a function of $V_g$.

Figure 3

(a) shows the product image of the conductance maps (after average subtraction and division by standard deviation of respective maps) of $V_g=+50$ and $-50$ V. (b) shows a 3D rendering of cross-correlation coefficients between different $V_g$ conductance maps as a function of gate voltage.

Figure 4

(a) and (b) show the autocorrelation maps, calculated using Eq. (2), of conductance images at $V_g=-50$ and +50 V, respectively. (c) shows angular average of the line cut passing through the center of (a) and (b) with its single and double Gaussian fits.

Figure 5

(a) Single and two Gaussian fits of theoretically calculated A(r) at $d=1.0$ nm and $n_{\mathrm{imp}}=5\times {10}^{11}{\mathrm{cm}}^{-2}$ for low $n_g(\xi =7.2$ nm, $\sigma =0.32,{\xi }_1=17.2$ nm, ${\xi }_2=4.4$ nm) and high $n_g(\xi =3.1$ nm, $\sigma =0.24,{\xi }_1=7.9$ nm, ${\xi }_2=2.2$ nm). (b) shows the evolution of ${\xi }_1$ and ${\xi }_2$ as a function of $n_{\mathrm{imp}}$ at $d=1.0$ nm; inset shows $\sigma$ as a function of $n_{\mathrm{imp}}$. (c) shows the evolution of $\sigma ,{\xi }_1$, and ${\xi }_2$ as a function $d$ at $n_{\mathrm{imp}}=5\times {10}^{11}{\mathrm{cm}}^{-2}$.

Figure 6

Evolution of $\sigma ,{\xi }_1,{\xi }_2$, and $\xi$ as a function of gate voltage $V_g$ extracted from conductance maps of (a) sample 1 and (b) sample 2. The gray shaded region can be accessed by choosing appropriate $n_{\mathrm{imp}}$ and $d$ values in a range defined by these parameters for the blue and red limiting lines that have been calculated using the screening theory. The error bars in these fitted parameters were found from the extreme values of these parameters with respect to azimuthal angle $\varphi$.