Scanning capacitance microscopy of nanostructures

A theory is developed for scanning capacitance microscopy (SCM) of samples containing quantum wells, nanowires, and nanodots. The observed SCM image does not reproduce the geometric characteristics of the system but can be used for extracting some important information. For quantum wells and nanowire arrays, SCM gives an opportunity to determine the doping level of nanostructures. For individual nanowires and dots, the positions and amplitude of SCM maxima give, respectively, the in-plane location and the depth of the objects, and the pattern shape is extremely sensitive to the nanowire orientation.

Figure 1

Schematic illustration of SCM measurements in nanostructures: (a) single quanum well parallel to the surface, (b) array of nanowires on heavily doped substrate, and (c) system of quantum dots. Heavily doped substrate (the back contact) is shown by dark filling, doped nanowires by light filling.

Figure 2

Spatial resolution (a) and maximal electric field (b) at different depths for $\sqrt{d^2+Rd}=0.1a$ (1) and $\sqrt{d^2+Rd}=0.01a$ (2). The characteristic electric field $E_0=2V∕\left\{\epsilon a\ln [(\sqrt{d+R}+\sqrt{d})∕(\sqrt{d+R}-\sqrt{d})]\right\}$.

Figure 3

Side view (a) and view from above (b) of SCM measurements of a single nanowire. The cross in (b) marks the in-plane position of the tip.

Figure 4

Lines of equal $\Delta C$ around a single small nanowire (placed in the origin) with the tilt angle ${\theta }_0=10°$ (curve 1), 30° (curve 2), 50° (curve 3), and 70° (curve 4) for the case $\sqrt{d^2+Rd}=0.01a$, $z_0=-0.1a$. For each case, only one line corresponding to the electric field $E_{\Vert }=V∕a$ is shown.

Figure 5

Spatial dependence of $\Delta C$ (relative units) for the SCM tip with $\sqrt{d^2+Rd}=0.01a$ along the axis of a nanowire with tilt angle: (a) ${\theta }_0=90°$ (horizontal nanowire), (b) ${\theta }_0=80°$, and (c) ${\theta }_0=70°$ and the position of the center $z_0=-0.1a$ (curves 1) and $z_0=-0.2a$ (curves 2). The dark segment shows the nanowire orientation in the vertical plane.