11.1.4. Lecture – 11

So, what will be the expression of this I_DS? So, we do have, so this is the big question. First of all, let me quickly put the biases. For vertical field, we do have V_GS here, so that creates vertical field. And let me assume that this V_GS is higher than V_th. So, the first assumption is that this is higher than V_th; that means, the channel is existing. And then we apply the other potential, so we do have the V_DS which is providing the lateral field.

In this chunk, we start with the formulation of the expression for the drain current (I_DS) in a MOSFET. First, we note that the vertical field is created by the gate-source voltage (V_GS), and the assumption is made that V_GS is greater than the threshold voltage (V_th). This assumption is vital as it indicates that the channel for current flow exists, which is necessary for the MOSFET to operate correctly. Furthermore, the drain-source voltage (V_DS) is applied to create a lateral field that influences current flow.

Think of V_GS as the 'key' that unlocks a door (the channel) in a building (the MOSFET). If the key (V_GS) is effective and meets a certain level (greater than V_th), the door opens, allowing people (electrons) to flow through the corridor (the channel). If the key is not sufficient (less than V_th), then the door stays shut, blocking any movement.

So, we can say V_GS - V_th is directly increasing this current. And also we do have the lateral field which is getting produced by V_DS, so we can also say that this is proportional to V_DS. So, if I combine all of them, so what we can say here it is I_DS is say proportionality constant say × (V_GS - V_th) × V_DS.

Here, we discuss how the drain current (I_DS) is related to two specific parameters: the gate-source voltage exceeding the threshold voltage (V_GS - V_th) and the drain-source voltage (V_DS). The idea is that the higher the effective gate voltage and the lateral field from the drain, the more current can flow. Mathematically, this is represented as I_DS being proportional to the product of these two parameters, encapsulated by a proportionality constant (K) that includes other device characteristics like electron mobility and dielectric properties.

Imagine you are pumping water through a hose. The pressure of the water (analogous to V_GS - V_th) and the diameter of the hose (analogous to V_DS) both affect how much water flows through. If you increase either the pressure or the hose diameter, more water flows out, just as increasing V_GS or V_DS allows more current to flow electronically.

However, this equation assumes that the V_DS is very small compared to V_GS - V_th. If the V_DS is going to be higher and higher or it is significant we need some correction in this equation.

In this part, it is emphasized that the derived expression for I_DS is based on certain assumptions. It assumes that V_DS (the voltage applied across the drain and source) is quite small in comparison to V_GS - V_th. If this condition is not satisfied, meaning V_DS becomes substantial, then the initial equation will not accurately describe the current flow. This leads to the need for a corrected version of the equation that can account for higher values of V_DS.

Consider the water hose analogy again: if you suddenly crank up the pressure (akin to increasing V_DS), the flow rate could exceed the hose's capacity and cause issues. In a practical scenario, an operator would need to adjust their approach to prevent water spilling out or causing bursts.

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

This segment touches on the behavior of the MOSFET when the drain-source voltage (V_DS) approaches a condition known as pinch-off. Here, as V_DS increases significantly, the effective channel width at the drain end becomes very slim, leading to a condition where current flow essentially stops. Yet, there's still current due to a phenomenon where carriers jump across the constricted channel region, flowing to the drain. This is a crucial concept in understanding how the MOSFET operates under saturation conditions.

Imagine a narrow river (the channel) flowing into a wider lake (the drain). If sections of the river are closed off (increasing V_DS), fewer fish (electrons) can travel freely towards the lake, but if they jump over the barriers, some can still reach the lake, albeit with much more effort.

If the current is not flowing then, of course, from here to here there is no potential drop. So, then what happens? The channel will completely break...

In this portion, it is outlined that when the MOSFET enters the saturation region and the channel effectively shrinks, the current flow becomes dependent on the effective length of the channel (L - ΔL). This shortening occurs due to the pinch-off condition, where the total length that influences current flow is reduced. There’s a further mention of channel length modulation, which explains how even in saturation, the effective channel length changes slightly with varying V_DS, affecting the current minimally.

Think of squeezing a tube where water flows through; as you push down (increasing V_DS), the water can still flow, but if you squeeze too much (approaching pinch-off), the flow reduces dramatically. The water’s journey through the tube is like electrons traveling through the MOSFET channel.

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