cathaychris
Feb28-10, 10:39 PM
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.
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.