In this video, we will discuss Halo Implants and how to model the resulting sub-straight doping concentration non-uniformity. Here is a device with Halo Implants, which are used, as we have already mentioned, to limit the extent of the depletion region. Under the channel and thus reduce short channel effects. these regions are doped more heavily than the substrate. You can plot on a log scale the net doping concentration versus distance x. Over at the center of the channel, you have the substrate doping you started with. And here we have the increased doping of the halo regions, over here you have the n type doping of the n type regions. And when n and p doping become equal, than net doping goes through zero, and on the log axis this goes to minus infinity. So, these points, define the boundary between n and p. So it is clear now that in the channel we have different regions, one with low doping and two regions with high doping. So this is approximated for the purposes of simple modeling by centered channel regions. And to handle regions that are assumed to be doped heavily, with a constant doping. So if NA is the substrate doping we start with, and NH is the additionally implanted substrate doping, NA plus NH if the doping here and there. The extent of these regions is L sub H, and the center region is the total length of the channel minus 2LH. So now we can approximate this situation as shown here. We have three transistors in series. The center one is in a region of low doping, and this transistor is another sub transistor in a region of high doping, and so is this what, corresponding to this region. The three channels are of course in series, but the gates of the three sub transistors are common and the bodies are common. So this can now be used to model the device, and I will show you how in the next slide. Here is the, figure from the previous slide, repeated. If you block the drain current, for a very small VDS versus VGS, this is a type of curve we have seen before, for a, a uniform substrate device, you get this broken line. The slope decreases as you go to higher VGS, because the mobility depend on some VGS. And, for the device with the Halo Implants, it goes like this. Initially, it has a high slope region, and then it kind of behaves like the un-implanted device. The question is why is there a high slope region over here? It can be explained roughly as follows, first of all, the center device, because it is on a lightly doped substrate, has a lower threshold on the side devices. So, as you raise VGS, the center device turns on first. But initially the side devices are off. As you keep increasing VGS, eventually the side devices also turn on, but by then the center device has turned on strongly. It has a strong, strongly inverted layer. And initially the resistance of layer is much smaller than that of the two side devices. So you can neglect this resistance and consider the entire combination as consisting of two devices in series each of them with length LH. This means that the device behaves as a transistor with total length of 2LH. Now, if you remember the current equation has a W over L, factor in it, so instead of l, we have 2LH, which is much smaller than L. And because of this large factor, W over 2LH. The current versus VGS initially goes up like this, but later on, when for even larger VGS values, all three devices are sufficiently strongly inverted. The whole device behaves essentially as a single strongly inverted device, with length L. And then again, this curve approximates the one of the un-implanted device. Now if you take the slope of these curves, which is the trans conductance versus VGS, you find that it behaves like this, shown by the broken line for the un-implanted device. Now to model the transistor, the concept of average channel doping is used. So what is the average channel doping here? So let's take the center device multiply by NA, and then take it to this region, which has a length LH, and multiply by NA plus LH. Add both of them to NA, LC. And then divide by the total length. This is the average substrate doping, and as you can see now it's a function of L. So, rewriting, we can write it like this. And now we have an effective gamma which is obtained by the classical formula for gamma but replacing the substrate doping by the effective doping which is shown over here. And this can be written like this, where LPE Is this here, but very often it used as a fitting parameter. And then, you can plug this in, into the, threshold voltage equation to get a VTO that depends on L, and takes into account the effect of the halo regions. This is a repeat of the formula that I showed you. You can see that as L becomes small, gamma becomes large and VTO increases. This is why as we decrease the channel length, VTO goes up. We have seen this curve back then when we discussed short channel effects, this is the main cause of the variation of the threshold. of, with channel length today. So we have seen how we can approximate the halo regions, the doping concentration regions, and model the threshold in a simple way. In the next video we will discuss another situation where doping concentration varies horizontally and results in the so called well proximity effect.