Expressions for the "quantum capacitance" are derived, and regimes are discussed in which this concept may be useful in modeling electronic devices. The degree of quantization is discussed for one-and two-dimensional systems, and it is found that two-dimensional (2D) metals, and onedimensional (1D) metallic carbon nanotubes have a truly quantized capacitance over a restricted bias range. For both 1D and 2D semiconductors, a continuous description of the capacitance is necessary. The particular case of carbon nanotube field-effect transistors (CNFETs) is discussed in the context of one-dimensional systems. The bias regime in which the quantum capacitance may be neglected when computing the energy band diagram, in order to assist in the development of compact CNFET models, is found to correspond only to the trivial case where there is essentially no charge, and a solution to Laplace's equation is sufficient for determining a CNFET's energy band diagram. For fully turned-on devices, then, models must include this capacitance in order to properly capture the device behaviour. Finally, the relationship between the transconductance of a CNFET and this capacitance is revealed.

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