# Floating gate potential of a MOSFET

1. Feb 10, 2010

### divB

Hi,

First of all, I posted a similar question in [1] but I think it is the wrong forum and wrong question (maybe the reason why I get no answer...).

I have to solve this (I think easy?) exercise:

http://img705.imageshack.us/img705/8241/floatingmosfet.png [Broken]

I think (3.1) is easy and I solved it. I also solved (3.2) but my solution is so primitive that I think it is wrong.

In (3.2) I should express $$\phi_F$$ as a function of $$t$$ if I apply a ramp function (i.e. switch on with a high voltage $$V_{pp}$$).

If I look at it, the one parameter dependent on the gate voltage is $$V_g$$ (which is just replaced by $$V_{pp}$$) and $$Q_F$$.

The current which flows from/to the floating gate is given by the formula in the problem statement but I think it is NOT dependent on time ... What do you think?!

If this is the case I just integrate $$I$$ from $$0$$ to $$t$$ in order to get the total charge but of course this is only linear behavior which also grows without stopping!

So my total solution would be:

$$\phi_F(t) = \frac{C_1 V_{pp} + t \cdot A \cdot E^2 \cdot e^{-\frac{B}{E}}}{C_1 + C_2}$$

Do you think this is true or am I on the wrong way?

Best regards,
divB