3.5 Plotting mos i-v

Now we use two of the equations ( and ) that we found in the discussion about MOS Regimes to calculate a set of $V_{\mathrm{dsat}}$ and $I_{\mathrm{dsat}}$ values for various value of $V_{\mathrm{gs}}$ . (Note that $V_{\mathrm{gs}}$ must be greater than $V_T$ for the two equations to be valid.) When we get the numbers, we build a little table.

Once we have the numbers , then we sketch a piece of graph paper with the proper scale, and plot the points on it. Once the $I_{\mathrm{dsat}}$ , $V_{\mathrm{dsat}}$ points have been determined, it is easy to sketch in the I-V behavior. You just draw a curve fromthe origin up to any given point, having it "peak out" just at the dot, and then draw a straight line at $I_{\mathrm{dsat}}$ to finish things off. One such curve is shown in . And then finally in they are all sketched in. Your curves probably wont be exactly right but they will be good enough for a lot ofapplications.

There is a particularly easy way to measure by $k$ and $V_T$ for a MOSFET. Let's first introduce the schematic symbol for the MOSFET, it looks like . Let's take a MOSFET and hook it up as shown in .

Since the gate of this transistor is connected to the drain, there is no doubt that $V_{\mathrm{gs}}-V_{\mathrm{ds}}$ is less than $V_T$ . In fact, since $V_{\mathrm{gs}}=V_{\mathrm{ds}}$ , their difference, is zero. Thus, for any value of $V_{\mathrm{ds}}$ , this transistor is operating in its saturated condition. Since $V_{\mathrm{gs}}=V_{\mathrm{ds}}$ , we can rewrite a previous equation derived equation from the section on MOS transistor as

Now let's take the square root of both sides:

So if we make a plot of $\sqrt{I_d}$ as a function of $V_{\mathrm{ds}}$ , we should get a straight line, with a slope of $\sqrt{\frac{k}{2}}$ and an x-intercept of $V_T$ .

Because of the expected non-ideality, the curve does not go all the way to $V_T$ , but deviates a bit near the bottom. A simple linear extrapolation of the straight part of the plothowever, yields an unambiguous value for the threshold voltage $V_T$ .