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Homework Help: Finding MOSFET threshold voltage

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data

    I have a MOSFET with a [tex]Si/SiO_{2}[/tex] interface. I need to find the threshold voltage. I'd also like to know whether this puts the transistor in the "on" state or "off" state (I know this is simple; I'd just like a little verification).
    I know the values for [tex]\Phi_{ms}[/tex], [tex]Q_{i}[/tex] (the interface charge density), and [tex]N_{A}[/tex] (the acceptor density).
    I also know [tex]d[/tex], the thickness of the [tex]SiO_{2}[/tex].

    2. Relevant equations

    [tex]V_{T} = \Phi_{ms} - \frac{Q_{i} + Q_{d}}{C_{i}} + 2\phi_{F}[/tex]
    where [tex]\phi_{F}[/tex] is the surface potential required to bend the bands down to the intrinsic condition at the surface.
    [tex]C_{i} = \frac{\epsilon_{i}}{d}[/tex]
    [tex]Q_{d} = -qN_{a}W_{m}}[/tex]
    [tex]W_{m} = 2\sqrt{\frac{\epsilon_{s}kT\ln{N_{A}/n_{i}}}{q^{2}N_{A}}}[/tex]
    [tex]\phi_{F} = \frac{kT}{q}\ln{\frac{N_{A}}{n_{i}}}[/tex]

    3. The attempt at a solution

    I'm given [tex]\Phi_{ms}[/tex]. I can find [tex]C_{i}[/tex], and I know [tex]N_{A}[/tex].
    So if I find [tex]W_{m}[/tex], the maximum depletion region, then I can find [tex]\phi_{F}[/tex] and [tex]Q_{d}[/tex] quite easily. But it seems that I'm missing an equation. Also, I don't quite understand what [tex]n_{i}[/tex] represents, or at least I think it's only going to convolute the problem if I try to substitute for it, so there must be an easier way. What am I missing?

    Thank you.
  2. jcsd
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