11.2.5. Effect of Increasing Voltage

So, what will be the expression of this I ? 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 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.

This chunk lays the foundation for understanding how voltage affects the current in a MOSFET. It introduces the key parameters: V_GS (gate-to-source voltage) and V_DS (drain-to-source voltage). It emphasizes that V_GS must exceed a certain threshold voltage (V_th) for a conductive channel to form, and V_DS is responsible for the lateral electric field that affects current flow. Hence, understanding these biases is crucial for analyzing device operation in different voltage conditions.

Think of V_GS as the key to a lock (the conductive channel). If the key (V_GS) is not inserted correctly (i.e., it's below the threshold), the lock won't turn (no current flows). Once the key turns, another part of the mechanism (V_DS) controls how much the door can open (the flow of current), impacting the ease with which you can enter a room.

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 discusses how the geometrical parameters of the MOSFET, specifically the width (W) and length (L), affect the current (I_DS). An increase in width means more available pathways for carriers, reducing resistance and increasing current. Conversely, if the length increases while keeping width constant, the resistance increases leading to a decrease in current. Thus, the width-to-length ratio, or aspect ratio, is critical for determining the device's performance.

Imagine a wide river (large W) allows more boats (current) to travel simultaneously than a narrow stream (small W). If you make the river longer (increase L), but keep it narrow, fewer boats can pass through at once (decreased current). The relationship between W and L is similar to managing water flow in different types of channels.

So, we can say V is, V ‒ V it is directly increasing this current. And also we do have the lateral field which is getting produced by V , so we can also say that this is proportional to V .

This chunk elaborates on how the difference between the gate-source voltage (V_GS) and threshold voltage (V_th) contributes to the channel's conductivity. The larger the excess voltage (V_GS - V_th), the greater the current due to higher electron mobility in the channel. Additionally, the V_DS creates a lateral electric field, which also enhances the movement of carriers, therefore increasing the current.

Consider a water tank heated at the base (V_GS - V_th). The hotter the base gets, more steam (electrons) is generated upwards due to greater pressure (increased conductivity). The lateral flow of steam (V_DS) pushes the steam upwards faster. Thus, greater heating (excess voltage) and strong pressure (lateral field) together increase the flow.

In summary what you can say that this expression of this I it is × × (V ‒ V ) × V . But one important thing we are missing here it is that, whenever we say that V is higher than V and whatever the excess amount we have it is contributing for towards the conductivity of the channel.

This chunk summarizes the overall equation derived from the previous discussion, emphasizing its form and conditions under which it's valid. It notes that the equation is contingent on certain voltage relationships and assumes that the V_DS is much smaller than the difference V_GS - V_th. This highlights that the derived expression has limitations when the voltages approach certain critical values, which changes the electron mobility and current due to channel effects.

Think of this equation as a formula for driving a car. It explains how speed (current) increases with more gas (voltage). However, if you approach a speed limit (limitations of the formula), you can’t just keep pressing the gas pedal without changing your driving strategy (current behavior) to remain safe and compliant.

Towards the source side we do have the V ‒ V . Whereas, on the other side on the other end namely towards the drain side we do have the V which is V ‒ V ‒ V .

This chunk analyzes how different voltage conditions at the source and drain affect overall conductivity. It indicates that the voltage seen at the source (V_GS - V_th) leads to a clear definition of conductivity towards the source, while the voltage at the drain can potentially reduce the channel’s conductivity as it approaches its limits. This effect demonstrates the difference in conductivity along the channel and the need for considering both ends of the device in current calculations.

Imagine a gradient of heat on a metal rod. One end is heated (source) while the other is cooler (drain). The warmth (conductivity) decreases along the length of the rod and if the heat is excessive at the drain, it further impacts the overall warmth along the length. Conductivity must be assessed at both ends, just as voltages must be evaluated in both source and drain contexts.

So, then what happens? In fact, till that point also this equation is valid. So, let me use this equation and let me let me put the condition that V = V or you may say that V .

This chunk introduces the concept of pinch-off, which occurs when V_DS equals V_GS - V_th, meaning the channel is on the verge of collapse. It notes that current expression remains valid even at this point, and describes how the channel strength varies along its length, leading to different conductivity at various points. The idea of pinch-off is essential for understanding saturation in MOSFET operation, identifying the threshold where the device transitions from one operational region to another.

Consider a tube where you restrict the flow by pinching it at the end. As you pinch more (increase V_DS), the flow decreases significantly until it nearly stops (pinch-off). The remaining tiny opening pushes the water (current) through just enough to keep it flowing, although the overall flow is constrained under tension. Understanding pinch-off helps in managing fluid dynamics in this scenario as well as electrical constraints in a MOSFET.

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