11.3. Changes to Current Expression

First of all let me quickly put the biases. For vertical field we do have V here, so that creates vertical field. And let me assume that this V it is higher than V. So, the first assumption is that this is higher than V; that means, the channel is existing. And then we apply the other potential, so we do have the V which is providing the lateral field.

In this chunk, we begin by establishing the conditions necessary for the operation of the MOSFET. Specifically, we define the vertical and lateral fields impacting current flow. The vertical field is created by the gate-source voltage (Vgs), which must be higher than the threshold voltage (Vth) to allow the channel to form. This is the basic premise under which we derive the expressions for current in the MOSFET.

Think of the vertical and lateral fields like a road and traffic lights. The vertical field (Vgs) is like an on-off switch that must be activated (higher than Vth) for cars (charge carriers) to move on the road (channel) which is defined by the lateral field (Vds). Without the switch being on, no traffic can flow, similar to how no current will flow if Vgs is not sufficient.

So, on the other hand if the W is increasing the corresponding resistance it will decrease. So, you may say directly that I it is proportional to or you can say that aspect ratio of the channel.

This chunk describes the relationship between the width (W) and length (L) of the MOSFET's channel and the current (Id). As the width (W) increases, the resistance decreases, leading to a corresponding increase in current. This relationship conveys that the current is directly proportional to the aspect ratio (W/L) of the MOSFET. More area means more charge carriers can flow, demonstrating how geometric design impacts electronic performance.

Imagine a water pipe: the wider the pipe (larger W), the more water can flow through it. If the pipe is long (larger L), it will resist water flow, similar to how increasing length reduces current. This illustrates how the dimensions in a MOSFET design affect current flow.

This will be proportional to the conductivity in the channel regions which is controlled by this V - Vth.

This chunk highlights the significance of voltages applied across the MOSFET, specifically the gate voltage (Vgs) and the threshold voltage (Vth). The difference between these voltages (Vgs - Vth) directly impacts the conductivity of the channel. A higher difference means more charge carriers are available, improving conductivity and hence increasing the current.

Think of charge carriers in the MOSFET like students in a classroom. The Vth is the minimum number of students required to make the class lively. If the number of actual students (Vgs) exceeds this threshold, the class becomes interactive, similar to how the current increases once Vgs exceeds Vth.

Now, if we increase this Vds, we need to consider both this part as well as this part and on an average you may say that let me take average of it.

In this chunk, we examine what happens when the drain-source voltage (Vds) is increased significantly. When Vds becomes comparable to Vgs - Vth, the conductivity in the channel starts to vary along the channel length. This adjustment requires taking an average to accurately reflect the conditions on both the source and drain sides for proper current calculations. This gives rise to a modified expression for current that accounts for changing conductivity.

Imagine a long rail track where trains (current) travel from one station (source) to another (drain). If the distance (voltage) between the stations increases significantly, the speed of trains may vary along the track (changing conductivity), and it becomes essential to consider the average speed across the entire track to understand overall train movement.

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 is approaching towards 0.

This chunk discusses the condition known as 'pinch-off,' where as Vds increases, it approaches the threshold where current can no longer flow effectively due to reduced channel conductivity. This is observed when Vds equals Vgs - Vth, indicating that the channel has effectively ceased to exist at the drain end. Beyond this point, the MOSFET enters the saturation region, where the current remains relatively constant despite further increases in Vds.

Consider a sponge losing all its water. Initially, it soaks up a lot (current increases), but at a certain point, it can't absorb more (conductor pinched off) regardless of more water being applied (further increasing Vds). The sponge has reached its limit and now can't hold more moisture—similarly, the MOSFET reaches a situation where it can't conduct more current even with higher voltage applied.

In fact, this equation should have mentioned V - V, but all practical purposes most of the time we write V.

In this final chunk, we summarize how the current behaves in the saturation region of the MOSFET. While the proper expression for current should account for both Vds and Vgs, simplifications are often made in practice where V is predominantly referenced. This leads to a clearer understanding and representation of MOSFET behavior in saturation, emphasizing its importance for circuit designers who usually operate within this region.

It's like cutting through unnecessary details in a recipe. When cooking, you might ignore some minor ingredients (V) to focus on the main ones (Vgs) that matter most for flavor—the essence you want from your dish exemplifies how engineers simplify equations for practical applications in circuit design.

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