QUANTUM CAPACITANCE IN NANOSCALE TRANSISTORS

This paper aims to introduce the third terminal of the transistor to the two terminals' device with two big contacts and a channel, to control the conductance of the channel by moving the electrochemical potential, up or down according to how much gate voltage (????????) is needed. The gate voltage (????????) terminals separated from the channel by an insulating material, to let no current to flow through the gate terminal, although the insulating layer is very thin no doubt there will be an undesirable leakage current to flow. The gate voltage (????????) changes the potential inside the channel. The negative gate voltage (????????) adds extra electrons in the channel to increase the channel energy, therefore, the entire energy levels float up. If the electrochemical potential is kept where was before applying the negative gate potential (????????), the density of states in the channel become smaller and the channel will not conduct as well any more as before, till it reaches a point of pinch off, where the current stops due to the lack of any available states for conduction. Note that the electrochemical potential might get to the point where the channel starts to conduct through the valance band, if the gate voltage (????????) kept increasing, but that is usually outside the voltage limit of interest. The channel stands for one plate of a capacitor, and the gate terminal is the other plate, between them there is an insulator for the potential to form a capacitor. Therefore, another aim of this paper is to study this capacitor for low bias in the nanoscale limit to see how it looks like. The quantum capacitance (????????) depends on the density of the states, so it requires the wave nature of the electron. The electrostatic capacitor in origin is basically just repulsion between electrons to account for interaction between them.