11.4.2. Channel Disappearance

So, what happens when we increase V such that it approaches VGS − Vth? This leads to a condition where the channel conductivity starts to diminish. When V becomes significant compared to VGS − Vth, the channel conductivity must be adjusted.

When we raise the drain-source voltage (V_DS) while keeping the gate-source voltage (V_GS) constant, the channel that allows current to flow through the MOSFET begins to shrink. This is because the excess voltage applied to the drain (V_DS) diminishes the channel area available for current flow as it approaches a critical threshold where the channel disappears altogether.

Think of the channel like a narrow pathway in a park. If you keep adding height (voltage) to a fence on one side of the path, at some point, the height of the fence may block the pathway entirely, making it harder for people (electrons) to pass through. Initially, the walkway is clear, but as you increase the fence (V_DS), fewer and fewer people can pass through until it’s closed off completely.

Toward the source side, we have VGS − Vth, while toward the drain side, we have V_DS = VGS − Vth − VGD. The average conductivity will need to take both of these factors into account.

As we approach the point where V_DS becomes significant, the effective channel voltage drops, affecting how well the channel can conduct. Near the source, the channel remains strong, but near the drain, it weakens. This means we must consider both ends of the channel, as the difference in voltage across the channel leads to varying levels of conductivity along its length.

Imagine a water pipe: if one end of the pipe is well-pressurized (like the source), but the other end has a blockage (like the drain), the water flow (current) decreases significantly as the blockage approaches the pipe's end. The varying pressure from source to drain resembles the changes in conductivity across the channel.

When we make V_D = V_th, it leads us to a situation known as pinch-off. The current expression changes as the channel starts to disappear completely.

In MOSFET operation, when we reach a condition where the drain voltage equals the threshold voltage, known as pinch-off, the current behavior shifts. The current ceases to rely on the voltage differences as it used to; instead, it is limited by this pinch-off condition, and the remaining current flows through a reduced channel length.

Picture a narrow river flowing between two banks. If the river is pinched at one end due to a dam, the flow of water decreases drastically. The current still flows, but through a smaller section of the river, similar to how current continues to flow in a MOSFET even when pinch-off occurs, but through a reduced channel area.

Even after pinch-off, current continues to flow, albeit in a different manner since the channel now is not continuous. The effective channel length shortens.

After the pinch-off point, while it may seem current would stop flowing, it doesn't. Instead, current flows through a shortened channel length, which alters how we calculate it. The remaining voltage still drives current flow, but the current now behaves as if it is passing through a smaller device.

Think of a hosepipe delivering water. If you cover a portion of the opening, water will still flow, but at a reduced rate. The pinch-off in the MOSFET functions similarly, as it still allows current to flow through a minimized channel.

In saturation, the current becomes less dependent on the voltage due to the channel length modulation effect, which indicates that the channel length effectively shrinks more with increased voltage.

When the device is in the saturation region, the current is less responsive to changes in the drain-source voltage. Instead, the length of the channel that effectively conducts diminishes due to channel length modulation, causing a nonlinear response to the applied voltage.

Imagine a car moving down a road that narrows toward the end. Initially, the car can speed up (current increases), but as the road narrows (saturation) the car can only go so fast regardless of how much more you press the accelerator (increase voltage). The car’s speed stabilizes, analogous to how the MOSFET current settles in saturation.

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