11.1.1. Prof. Pradip Mandal

So, welcome back here again the second part of today’s module. What we are looking for it is the expression of the current as function of the W’s and L’s and V and V . And GS DS V and V of course, they are applied here. And also, just to get an idea that how this current is it depends on the device parameter.

In this segment, the introduction to the topic is given, focusing on how the current in MOSFETs is influenced by various parameters such as width (W), length (L), and the applied voltages (VGS and VDS). The key is understanding that the current produced in the device is not solely a function of applied voltage but also critically depends on its dimensions and operational conditions.

Imagine a waterpark slide where the width represents the channel width (W), the height of the platform before the slide represents the applied voltage (VGS), and the length of the slide represents the channel length (L). Just like how wider slides can accommodate more water (or people) at once, a wider MOSFET channel allows more current to flow. A shorter slide (smaller L) lets people reach the bottom faster, similar to how a shorter channel can enhance current flow as well.

Now, how about the other parameters? So, this will be proportional to the conductivity in the channel regions which is controlled by this V ‒ V which means that whatever the GS th excess voltage you do have beyond the threshold voltage that is effectively contributing the to the conductivity or it is helping to increase the conductivity in the channel.

This chunk explains that the conductivity of the MOSFET channel is determined by the voltage difference (VGS - Vth). When VGS is above the threshold voltage (Vth), the excess voltage enhances the channel's conductivity, allowing more current to flow. Thus, this relationship highlights the critical role of proper biasing for ensuring that the MOSFET operates efficiently.

Think of a garden hose. When you apply a certain amount of pressure (voltage), it allows water (current) to flow through more freely. If the pressure is too low (below the threshold), very little water passes through (low conductivity). As the pressure increases above a certain point, water flows swiftly and abundantly, similar to how a MOSFET conducts current more effectively when VGS exceeds Vth.

If you see here this is the L and this is the orthogonal dimension it is the W. So, if you are having higher length for everything is remaining same it is expected that the resistance here it will increase. So, as a result the corresponding current it will decrease. So, on the other hand if the W is increasing the corresponding resistance it will decrease.

This section discusses how the width (W) and length (L) of the channel directly affect resistance and, consequently, the current. When the length increases, resistance increases, reducing the current flow. Conversely, increasing the width reduces resistance and allows more current to pass through.

Picture the difference between a long, thin straw and a short, wide straw. The long, thin straw (higher L) will take more effort to drink through (higher resistance, less current), while the short, wide straw (higher W) allows you to sip faster and easier (lower resistance, more current).

So, if I combine all of them, so what we can say here it is I it is say proportionality constant say × (V ‒ V ) × V , ok. And this K, this K it encapsulates whatever the GS th DS device parameter is there.

Here, the content introduces the overall formula for current (I) in a MOSFET, which combines the effects of the applied voltages and the device dimensions into one equation. The proportionality constant K encapsulates all device parameters, demonstrating that both geometric and electrical characteristics influence the output current.

Think of baking a cake where K is your recipe. The ingredients (V - Vth and VDS) and their quantities determine how well your cake will rise. Just like adjusting the proportions of flour, sugar, and eggs affects the final cake (current), adjusting the voltages and dimensions of the MOSFET alters its performance.

But one important thing we are missing here it is that, whenever we say that V is higher than V and whatever the excess amount we have it is contributing for GS th towards the conductivity of the channel, but this is valid probably in this portion.

This part of the text stresses the importance of the voltage conditions in deriving the previous current expression. Specifically, it emphasizes that the relationships and equations discussed so far only hold true when VDS is much smaller than VGS - Vth. Understanding these limits is crucial for accurately predicting the behavior of the MOSFET.

Imagine driving a car on a highway. You can only maintain a steady speed (function) when there aren’t too many obstacles (voltages complicating the situation). If the speed limit changes dramatically (VDS approaching critical limits), you need to reconsider your driving strategy, similar to reevaluating the conditions under which a MOSFET operates.

Now, what happens in a critical situation when we are just making this voltage higher and higher keeping this V may be constant and such that the conductivity here it is approaching towards 0.

In this chunk, the discussion revolves around what happens when VDS approaches the pinch-off condition, where the channel's conductivity decreases significantly. It's crucial to understand that even if the device is on the brink of pinch-off, current can still flow, albeit through a shorter effective channel length.

Think of a sponge that is close to being wrung dry (pinch-off). Even as it becomes less saturated (conductivity decreasing), if you apply pressure (additional voltage), some water (charge carriers) can still be pushed through the remaining material, illustrating the diminishing yet ongoing flow.

However, we do have the lateral field V . So, if the current is not flowing then of course, from here to here there is no potential drop.

This section explains the transition from saturation to the triode region in MOSFET operation. It highlights how, despite the pinch-off condition, there is a region where current still flows due to the applied lateral field and emphasizes the need for understanding the differences between these operational regions.

Consider a dam holding back water (potential drop), but when the gates (current flow) are partially opened, a trickle finds its way past. Even near the maximum capacity, small amounts can still escape until the gates are fully closed, representing the later behavior of the MOSFET as it shifts from saturation back into linear (triode) operation.

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