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5.5: Simplified models of FET switching

  • Page ID
    51616
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    To further simplify the problem, we define two quantities, \(N_{S}\) and \(N_{D}\), the charges injected into the channel from the source and drain contacts, respectively. Next, we assume that \(\tau=\tau_{S}+\tau_{D}\), where \(\tau_{S}=\tau_{D}\) and \(C_{G}\ggC_{S},\ C_{D}\), Equations (5.3.4), (5.3.5) and (5.3.6) become

    \[ U=-qV_{GS}+\frac{q^{2}}{C_{G}}(N-N_{0}) \nonumber \]

    \[ N = \frac{N_{S}+N_{D}}{2} \nonumber \]

    \[ I = \frac{q}{\tau}(N_{S}-N_{D}) \nonumber \]

    where

    \[ N_{S} = \int^{\infty}_{-\infty}g(E-U)f(E,\mu_{S})dE \nonumber \]

    \[ N_{D} = \int^{+\infty}_{-\infty}g(E-U)f(E,\mu_{D})dE \nonumber \]

    Conduction in the FET is controlled by the number of electron states available to charges injected from the source. For switching applications, transistors must have an OFF state where \(I_{DS}\) is ideally forced to zero. The OFF state is realized by minimizing the number of empty states in the channel accessible to electrons from the source. In the limit that there are no available states, the channel is a perfect insulator.

    Switching between ON and OFF states is achieved by using the gate to push empty channel states towards the source chemical potential. The transition between ON and OFF states is known as the threshold. Although the transition is not sharp in every channel material, it is convenient to define a gate bias known as the threshold voltage, \(V_{T}\), where the density of states at the source chemical potential \(g(E_{F})\) undergoes a transition


    This page titled 5.5: Simplified models of FET switching is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Marc Baldo (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.