Plotting MOS I-V 2.13 2000/08/04 2007/08/14 11:51:32.540 GMT-5 Bill Wilson wlw@madriver.net Bill Wilson wlw@madriver.net Liqun Wang liqun@rice.edu Elizabeth Gregory elizabeth.gregory@gmail.com Jeffrey M Silverman JSilverman@astro.berkeley.edu Gerard Wysocki gerardw@rice.edu Plotting MOS I-V Plotting MOS I-V, and sketching the I-V behavior. Now we use two of the equations ( and ) that we found in the discussion about MOS Regimes to calculate a set of Vdsat and Idsat values for various value of Vgs . (Note that Vgs must be greater than VT 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 Idsat , Vdsat points have been determined, it is easy to sketch in the I-V behavior. You just draw a curve from the origin up to any given point, having it "peak out" just at the dot, and then draw a straight line at Idsat 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 of applications.

V gs V dsat V V dsat mA 3 1 0.44 4 2 1.76 5 3 3.96 6 4 7.04 7 5 11 Results of calculating Vdsat and Idsat .

Plotting Idsat and Vdsat .

Sketching in one of the I-V curves.

The complete set of curves.

There is a particularly easy way to measure by k and VT 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 .

Schematic symbol for a MOSFET

Circuit for finding VT and k

Since the gate of this transistor is connected to the drain, there is no doubt that V gs V ds is less than VT . In fact, since V gs V ds , their difference, is zero. Thus, for any value of Vds , this transistor is operating in its saturated condition. Since V gs V ds , we can rewrite a previous equation derived equation from the section on MOS transistor as I d k 2 V ds V T 2 Now let's take the square root of both sides: I d k 2 V ds V T So if we make a plot of I d as a function of Vds , we should get a straight line, with a slope of k 2 and an x-intercept of VT .

Obtaining VT and k

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