Measurement of the Quantum Capacitance Between Two Metallic Electrodes

Abstract

Two factors contribute to the electrical capacitance between two electrodes: a classical contribution, stemming from the electric field, and a quantum contribution, governed by the Pauli exclusion principle, which increases the difficulty of adding charge to the electrodes. In metals, the high electronic Density of States (DOS) at the Fermi energy allows the quantum contribution to be neglected, and a classical description of the electrical capacitance between two metallic electrodes is normally used. Here, we study the evolution of the capacitance as two metallic electrodes (Pt or Au) are approached to the limit when quantum corrections are needed, before contact formation. At small distances, we observe that the classical increase in capacitance turns into saturation as the electrodes are approached, reaching the quantum capacitance limit. Finally, a capacitance leakage due to quantum tunneling is observed. Since the quantum capacitance depends on the electronic DOS on the surface of the electrodes, we use it to probe the DOS change induced by molecular adsorption (Toluene) on the metallic surface.

Figures (3)

• Figure 1: (a) Schematic illustration of the measurement of conductance and capacitance between two crossed metallic wires as a function of their separation distance. The equivalent circuit consists of a resistance and a capacitor connected in parallel between both electrodes. Panels (b) and (c) show an example of a frequency sweep for measuring the real and imaginary part of the admittance of the junction. Panels (d) and (e) display the experimental measurements of Pt wires conductance and capacitance at 77 K. In panel (e), we also label the three observed regions as tunneling, quantum, and classical domains.
• Figure 2: Fitting of the capacitance curve for two gold electrodes in cryogenic vacuum at 4.2 K. For the blue curve, we neglect the quantum capacitance contribution. The fitting for large distances gives the actual radius of our wire samples $R_{\rm geo}$ = 0.25 mm and a stray capacitance parameter $C_0~=~0.94$ pF. When we include the quantum capacitance term, the red-orange curve is obtained, which fits perfectly our experimental data for the case of an electronic DOS per unit area, $\rho_A$ = $1.15\cdot10^{18}$ eV$^{-1}$m$^{-2}$.
• Figure 3: The upper panel shows the capacitance curves for clean Au electrodes and the same but Toluene-covered, measured at 4 K. In the lower panel, the difference in quantum capacitance is numerically extracted, showing a reduction of about 10%. In panel (b), the results for 77 K are also shown in light red. Notice that for long distances, the dominant geometrical capacitance makes it difficult to appreciate changes in the quantum contribution.