Homework Help: Finding MOSFET threshold voltage

1. Feb 28, 2010

cathaychris

1. The problem statement, all variables and given/known data

I have a MOSFET with a $$Si/SiO_{2}$$ 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 $$\Phi_{ms}$$, $$Q_{i}$$ (the interface charge density), and $$N_{A}$$ (the acceptor density).
I also know $$d$$, the thickness of the $$SiO_{2}$$.

2. Relevant equations

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

3. The attempt at a solution

I'm given $$\Phi_{ms}$$. I can find $$C_{i}$$, and I know $$N_{A}$$.
So if I find $$W_{m}$$, the maximum depletion region, then I can find $$\phi_{F}$$ and $$Q_{d}$$ quite easily. But it seems that I'm missing an equation. Also, I don't quite understand what $$n_{i}$$ 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.