In this video, we will continue the discussion on the Short-Channel MOSFET. So, in the last video, we saw that the short-channel theory predicts a finite maximum value that can be achieved for the drain current in the limit of zero channel length, and that maximum drain current was given by this equation. Now, we have the maximum value, maximum achievable value, we can predict how much improvement you can expect by further reducing the channel length. So, that can be done by this ideality factor K sub I, and K sub I is defined as your drain current divided by the maximum value. This can be easily derived, this last equation here can be easily derived by plugging in the equations that we derived for these ID saturation in the previous video. It is obvious that KI is always less than unity, and KI is also dependent on the MOSFET device parameters. So, if you plug in these numbers oxide thickness of 40 nanometers and the channel length of one micron, then the ideality factor coming out to be about 0.72. What does that mean? That means that the maximum improvement that you can expect by reducing the channel length is roughly about 40 percent at best, right? So, this KI is unuseful parameter with which you can expect the anticipated improvement. KI parameter varies more slowly when the MOSFET has larger oxide thickness. So, reducing the channel length affects the drain current more favorably when the oxide layer is thin. So, thinning the oxide layer has been one of the main drive in the technological development in the semiconductor device fabrication industry, and you can see from these two figures here, the effect of the two different oxide thickness as a functional channel lengths, your KI is much steeper when the oxide layer is thinner. But if you thin your oxide too much but at some point, your device becomes not reliable, so there could be a pinholes and other defects that may be present in your fabrication that could create a problem in your device performance. So, there's a certain limit obviously in how thin you can be with your oxide thickness. Now, the last topic I want to talk about is the speed of your MOSFET, and the speed is an important parameter, and from the small signal model, your speed is related to the capacitance of your device and also the transconductance. Now, capacitance is a device parameters, so the capacitance is typically given by this in the case of MOSFET in saturation, and so really what's different for the long-channel versus short-channel devices, the transconductance, and in the long-channel device, you're transconductance is given by this equation here. Once again, transconductance is linearly proportional to your gate voltage. So, the cut-off frequency for the MOSFET, long-channel MOSFET, is given by this equation here, and from the cutoff frequency, you can calculate your transit time which is given by this equation here. The transit time is related to the inverse of your cutoff frequency. For the short-channel MOSFET however, now you use the equation for the transconductance that we derived for short channel in the previous video, then the cutoff frequency is given by this equation here, and in the short-channel limit where the E-saturation, the saturated field times the channel length is small compared to your VG minus VT, then you can simplify this equation into this. So, your cutoff frequency essentially is determined by the saturation velocity. So, what's the difference between the short and long-channel device, the scaling with respect to L, the channel length is different. In the case of the long-channel device, your cutoff frequency goes as one over L squared as shown here, but in the short-channel device, your cutoff frequency goes as one over L. So, your cutoff frequency as a function of your channel length in the long channel case, it scales as one over L squared, in the short channel, it goes as one over L. So, once again, in the short-channel device because of this velocity saturation effect, the improvement in speed slows down as you reduce the channel length in your MOSFET device.
