How do Quantum Effects Influence the Capacitance and Carrier Density of Monolayer MoS$_2$ Transistors?

When transistor gate insulators have nanometer-scale equivalent oxide thickness (EOT), the gate capacitance ($C_\textrm{G}$) becomes smaller than the oxide capacitance ($C_\textrm{ox}$) due to the quantum capacitance and charge centroid capacitance of the channel. Here, we study the capacitance of monolayer MoS$_\textrm{2}$ as a prototypical two-dimensional (2D) channel while considering spatial variations in the potential, charge density, and density of states. At 0.5 nm EOT, the monolayer MoS$_\textrm{2}$ capacitance is smaller than its quantum capacitance, limiting the single-gated $C_\textrm{G}$ of an n-type channel to between 63% and 78% of $C_\textrm{ox}$ for gate overdrive voltages between 0.5 and 1 V. Despite these limitations, for dual-gated devices, the on-state $C_\textrm{G}$ of monolayer MoS$_\textrm{2}$ is 50% greater than that of silicon at 0.5 nm EOT and more than three times that of InGaAs at 1 nm EOT, indicating that 2D semiconductors are promising for nanoscale devices at future technology nodes.