Dielectric thickness dependence of quantum capacitance in graphene varactors with local metal back gates

The temperature-dependent C-V characteristics for two samples with target HfO₂ thicknesses of 20 nm (sample A), and 10 nm (sample B) are shown in Figs. 2 and 3. The results show that the capacitance tuning range increases with decreasing HfO₂ thicknesses, as expected. A comparison of the normalized C-V curves for both samples at room temperature is shown in Fig. 4. The capacitance tuning range from V_g - V_Dirac = 0 to +1.5 V is 1.17:1 for sample A and 1.38:1 for sample B. Fig. 5 shows a comparison of the C-V characteristics for the varactors with MIM capacitors fabricated on the same sample. A very consistent trend is observed where the capacitance-per-unit-area for the MIM capacitors is significantly higher than for the varactors. The EOT values extracted from the MIM capacitors are found to be 4.1 nm and 2.7 nm for samples A and B, respectively. In order to understand this behavior in more detail, numerical modeling was performed on the temperature-dependent C-V characteristics where the random potential fluctuations, σ, in the graphene was used as an adjustable fitting parameter [5]. The results are shown in Fig. 6. The fact that the fitted EOT values cannot completely account for the capacitance reduction in Fig. 5 is a strong indicator that the effective device area of the varactors is less than the layout area. However, additional modeling, particularly taking into account the effect of interface traps, and other imperfections between the graphene and HfO₂ [6-7] is needed to fully understand the observed behavior. In the future, further scaling of the EOT needs to be investigated, as well as fabrication of the devices on insulating substrates for eventual use in resonator circuits. As a preliminary demonstration (Fig. 7), we have fabricated a single-finger varactor on a quartz substrate, with EOT (as determined by MIM capacitors) of 1.9 nm and tuning range >;1.5:1 at room temperature.