11.4.3. Current Flow Beyond Pinch Off

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 . V and V of course, they are applied here.

In this segment, the lecturer introduces the topic of current flow in MOSFETs, emphasizing the relationship between current and the dimensions of the device (W and L) as well as the gate-source and drain-source voltages (Vgs and Vds). The goal is to derive expressions that describe how these factors influence current flow.

Think of a water pipe where the width (W) affects the amount of water that can flow through it and how long the pipe (L) is affects the resistance to flow. More pressure (Vgs and Vds) makes more water flow, just like a higher voltage allows more current to flow in a MOSFET.

So, you may say directly that I it is proportional to W or you can say that aspect ratio of the channel.

Here, the lecturer explains that the current (I) flowing through the MOSFET is directly proportional to the width (W) of the channel. If the width is increased, while keeping the length constant, the resistance decreases and thus the current increases. Conversely, if the length (L) increases, resistance increases and current decreases.

Consider a highway: more lanes (greater W) allow for more cars (current) to travel simultaneously. If the highway narrows (greater L), fewer cars can fit, reducing the overall flow.

So, this will be proportional to the conductivity in the channel regions which is controlled by this V ‒ V.

The discussion highlights that the conductivity of the channel, and hence the current, is influenced by the excess voltage (Vgs - Vth). The more the excess voltage above the threshold, the better the conductivity and hence more current can flow through the device.

Imagine needing to push a ball up a hill. The more force you apply (the excess voltage), the easier it is to roll the ball (create current). If you don't push hard enough, it won't move at all (no 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.

The current (I) can be expressed as proportional to the product of the term (Vgs - Vth) and Vds, encapsulated by a constant 'K'. This constant includes device-specific parameters such as electron mobility and capacitance.

Think of baking a cake: the ingredients (like flour and sugar) are your parameters; the recipe (the formula combining these ingredients) is your expression for the cake (or current). The cake’s taste (current output) is determined by how well you mix those ingredients together.

So, this equation it assumes that the V is very small compared to V ‒ V.

The lecturer explains that the assumptions made in the earlier equations hold true only when Vds is much smaller compared to the difference (Vgs - Vth). If Vds becomes significant and comparable to this difference, corrections must be made to accurately express the current.

A thermostat is set to maintain a specific temperature (Vgs - Vth). If the room temperature (Vds) gets too close to this setting, the thermostat might need adjustments to keep things balanced.

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...

As voltage increases, there comes a point where the voltage at the drain (Vgd) equals the threshold voltage (Vth), and the current expression is derived under these conditions. This state is known as pinch off, where the channel near the drain effectively disappears, affecting how current can flow through the device.

Imagine a water faucet that you slowly close. Initially, water (current) flows freely; as you close it (increase V), the water flow decreases. At some point, water trickles just a bit, and when fully closed, it stops—the 'pinch off' point.

If I take the V higher than (V ‒ V), so, if I consider equal... however, we do have the lateral field V.

Once Vds exceeds Vgs - Vth, the channel does not fully conduct current as expected. Instead, the current behaves differently—it is mostly limited by a shorter effective channel length due to pinch off, creating a condition where adjustments are necessary.

Consider a river where the flow is varied by dams (voltage). If too much water is sent through (increased V), it could cause a backup or create obstacles, leading to diminished flow downriver (current).

So, in summary what you can say that this expression of this I it is × × (V ‒ V ) × V.

In conclusion, the current through the MOSFET is influenced by various parameters like channel dimensions, voltages, and material properties. Different operating regions, such as saturation and linear regions, influence how we use these expressions for practical applications.

Like adjusting gears in a car depending on speed (current expression), the different voltages and dimensions allow users to control the flow of electricity through the circuit just as gears control a car's speed effectively.

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