11.5.1. Modification of Length

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 introduction, we are establishing the conditions under which we examine the current in a MOSFET. The assumptions made are critical: V_GS needs to be greater than the threshold voltage V_th so that a conducting channel forms in the device. The vertical field created by V_GS and the lateral field from V_DS are essential for current flow. This sets the foundation for understanding how voltage influences the current.

Imagine you are planning to water a garden. You need a certain pressure (analogous to V_GS) to push the water through the hose (the channel). If the pressure isn’t enough, nothing flows. Once you have that threshold pressure, you can adjust the flow (akin to V_DS) to control how water reaches different parts of the garden.

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.

The discussion highlights how the physical dimensions of the MOSFET, specifically its length (L) and width (W), affect its electrical characteristics. Increasing the length L of the channel increases resistance, which in turn decreases current (I_DS). In contrast, increasing the width W reduces resistance and allows more current to flow. This relationship demonstrates the importance of the aspect ratio (W/L) in the device’s function.

Think of a water pipe: if you make it longer (increasing L), it will be harder for the water to flow through (more resistance), just as it is harder to move through long traffic. Conversely, if you make the pipe wider (increasing W), the water can flow more freely, just like adding more lanes to a busy road.

This will be proportional to the conductivity in the channel regions which is controlled by this V ‒ V which means that whatever the excess voltage you do have beyond the threshold voltage that is effectively contributing to the conductivity or it is helping to increase the conductivity in the channel.

The discussion focuses on how the difference between gate-source voltage (V_GS) and the threshold voltage (V_th) influences the conductivity in the channel. The greater the excess voltage (V_GS - V_th), the more conductive the channel becomes, allowing more current to flow through the transistor. This concept is crucial for optimizing the performance of a MOSFET in circuits.

Imagine a classroom where students (carriers) need a certain level of interest (voltage) to engage in a discussion. If the interest level (excess voltage) exceeds the threshold, more students will participate actively, leading to a vibrant discussion (more current flow).

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.

Combining the relationships established earlier leads us to a key formula that expresses the drain-source current (I_DS) as a function of voltages and device parameters. The current is proportional to (V_GS - V_th) multiplied by V_DS. This expression encapsulates how current through the MOSFET is affected by voltages and dimensions.

Think of baking a cake: the ingredients (voltages and parameters) must be mixed in the right proportions (the equation) to get the cake (current) to rise correctly. Too little flour or sugar will affect the cake – just as not having the right voltages will affect the current flow in a MOSFET.

However, we need to emphasize that if the V is higher than V and whatever the excess amount we have it is contributing for the conductivity of the channel, but this is valid probably in this portion.

At this point, we discuss the assumptions made regarding the voltages applied across the MOSFET. The initial equations derived only hold true under specific conditions where V_DS is minimal compared to the difference (V_GS - V_th). If V_DS approaches significant values, the channel conductivity changes, and adjustments to the formulas are required for accurate predictions of current flow.

Think of adjusting the volume on a speaker system. If you raise the volume too high (significant V_DS), the sound quality may distort, just as current equations may become inaccurate if certain voltage conditions aren't met.

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