Contactless Microwave Characterization of Encapsulated Graphene $p\text{−}n$ Junctions

Accessing intrinsic properties of a graphene device can be hindered by the influence of contact electrodes. Here, we capacitively couple graphene devices to superconducting resonant circuits and observe clear changes in the resonance frequency and widths originating from the internal charge dynamics of graphene. This allows us to extract the density of states and charge relaxation resistance in graphene $p\text{−}n$ junctions without the need for electrical contacts. The presented characterization paves a fast, sensitive, and noninvasive measurement of graphene nanocircuits.

Figure 1

Sample layout. (a) An optical picture of the stub tuner with arm lengths $l$ and $d$. Central conductor and gap widths of the transmission lines are 15 and $6\mu \mathrm{m}$, respectively. Light areas show the Nb film and darker areas are exposed ${\mathrm{SiO}}_2$ substrate after Nb is etched away. (b) An SEM image near the $l$ end showing a narrow slit between the signal line and the ground plane. (c) An SEM image of a $h\text{−}\mathrm{BN}/\mathrm{graphene}/h\text{−}\mathrm{BN}$ stack for device $B$ placed over the slit. Areas $A_1$ and $A_2$ correspond to two parts of graphene lying on the signal line and the ground plane. (d) A cross section schematic of the device near the slit. (e) An equivalent circuit with lumped capacitance and resistance elements.

Figure 2

Reflectance response of the stub tuner. (a) A color map of the measured reflectance power near the resonance frequency versus different gate voltages. Arrows denote the charge neutrality points (CNP) corresponding to respective graphene parts. Its asymmetric separation around the zero voltage is due to inhomogeneous distribution of an average offset doping $\sim 3\times 10^{11}{\mathrm{cm}}^{-2}$ in the system. (b) Main panel: Cuts of the reflectance curves at two different gate voltages with fits to Eq. (3). Inset: The reflectance response of the same device without graphene. The input rf power is $-110\mathrm{dBm}$, which corresponds to an ac excitation amplitude of $0.7\mu \mathrm{V}$.

Figure 3

Quantum capacitance of graphene. (a) The extracted capacitance from the fitting of the reflectance response to Eq. (3) for device $B$ and (b) for device $A$. Error bars are smaller than the symbol size. Solid lines are the best fits to Eq. (1) showing good agreement with the graphene density of states. Insets: schematics of relative dimensions of graphene flake across the slit. In device $B$, areas lying on the signal plane (SP) and on the ground plane (GP) are similar, $A_2\approx A_1$. In contrast for device $A$, areas $A_2\approx 2A_1$.

Figure 4

Dissipation in graphene. (a) The extracted charge relaxation resistance for two devices fabricated on the same $h\text{−}\mathrm{BN}/\mathrm{graphene}/h\text{−}\mathrm{BN}$ stack. The same loss constant is used in fitting the reflectance map. (b) Inverse quantum capacitance, obtained by subtracting geometric capacitance from the total extracted capacitance, as a function of the simultaneously extracted charge relaxation resistance.