11.1.5. Revisiting MOSFET (Contd.)

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.

In this chunk, the focus is on determining how the current (I) in a MOSFET depends on various parameters. The text explains the importance of the vertical electric field created by the voltage V_GS and the assumption that the gate voltage (V_GS) is greater than the threshold voltage (V_th), which is crucial for the channel to exist. The lateral field established by V_DS is also important.

Think of V_GS like turning on a tap to let water flow. If the tap (V_GS) is not opened enough (i.e., below the threshold), no water will flow. Once it's sufficiently open, the water can start flowing through the pipes (creating the channel), and how much flows depends on the water pressure (V_DS).

It is proportional to W. In fact, it will be proportional to because if you see here this is the L and this is the orthogonal dimension it is the W. 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. So, you may say directly that I it is proportional to or you can say that aspect ratio of the channel.

This chunk explains the relationship between the current (I) and the dimensions of the MOSFET, specifically width (W) and length (L). If the length of the channel increases while keeping other factors constant, the resistance increases and consequently the current decreases. Conversely, increasing the width decreases resistance, thereby increasing current. The current is therefore directly related to the aspect ratio (W/L).

Imagine a garden hose. If you lengthen the hose (increase L), it takes longer for the water to flow out, reducing the flow rate (I). However, if you widen the hose (increase W), water can flow out faster because there’s less resistance.

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.

This part discusses how the excess voltage between the gate-source voltage (V_GS) and threshold voltage (V_th) affects current. The difference (V_GS - V_th) directly impacts the channel conductivity, meaning that the higher this voltage, the more conductive the channel becomes, allowing for more current to flow.

Think of the excess voltage as adding extra pressure to the water flow. If you have a reservoir (V_GS) that is filled above a certain level (threshold V_th), the extra pressure pushes more water (current) through a tap (the MOSFET channel).

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. And this K, this K it encapsulates whatever the device parameter is there in fact, this K if you see, if the mobility of the electrons is flowing in this way.

In this chunk, the current (I) is articulated as being proportional to a constant (K), the difference in gate-source voltage (V_GS - V_th), and the drain-source voltage (V_DS). The constant K includes parameters like the mobility of electrons and device dimensions, capturing how effectively the MOSFET channels conduct current.

Consider K to be a recipe that combines ingredients (mobility, dimensions) to yield a final product (current). Each ingredient affects the final outcome—the more you understand the ingredients, the better your dish will turn out!

So, we are starting with this one with the assumption that V is higher than V and also we assume that V it is much smaller than V ‒ V .

This segment addresses the critical assumptions needed for the validity of the current equation derived earlier. It stresses that V_GS must be significantly higher than the threshold voltage (V_th) and that V_DS should be small compared to V_GS - V_th for the basic model to hold true.

Imagine tuning a musical instrument. If one string is too tight (V_GS), it produces a better sound. However, if you start messing with the tuning of the entire instrument (V_DS being large), the music will sound off-key, making the assumptions invalid.

If I consider we are applying a voltage V which is say +ve, that means, the voltage across this structure it is not same as the V here.

Here, the text discusses what happens when V_DS becomes significant compared to V_GS - V_th. The assumptions made earlier about the uniformity of the channel conditions may no longer apply, requiring adjustments to the current expression. The equations derived previously might need modifications to be accurate in this new scenario.

This is like driving a car. If you only drive on smooth roads (small V_DS), everything is predictable. But if you suddenly hit a bumpy road (large V_DS), you need to adjust your steering (current equations) to maintain control and accuracy.

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 .

In this portion, it specifies the difference in voltages affecting the channel from the source and drain perspectives. This difference must be factored into the calculations for current to ensure accuracy, especially when V_DS is substantial.

Imagine if each end of a water pipe has different water levels (voltages). If one side is higher than the other, it changes how the water flows through. You have to account for both ends to understand the overall flow of water correctly!

So, we can multiply this by V . So, you have here, this 2 it is coming there. DS

This part discusses how to create a new expression for current that incorporates both the source and drain voltage effects. The formula is adjusted to accommodate changes in channel conductivity due to varying voltages and ensures the current expression remains valid under a broader set of conditions.

Think of making a smoothie. If you add more fruit (adding V_DS influences), the consistency (current) changes. To maintain your desired smoothie texture, you have to adjust the liquid ingredients proportionally (update your current equation).

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.

This section outlines what occurs when V_DS increases to the point where channel conductivity approaches zero, a state known as saturation. Under these conditions, the current is primarily defined by the behavior of the device in this saturation regime, and modifications to the current equation may be necessary.

Imagine squeezing a sponge (the channel). As you push harder (increase V_DS), the sponge becomes unable to hold more water, and water flow decreases (current approaches zero). Understanding this threshold helps in analyzing the MOSFET behavior effectively.

So, if we summarize what we said is that the device characteristic it is, it can be said it is having different regions of operation.

This final section emphasizes the overall behavior and characteristics of the MOSFET including its operational regions: cutoff, triode, and saturation. It sums up the relationships described in earlier parts and addresses how changes in voltages impact the overall current flow.

Consider a toy car with different speed settings: off (cutoff), slow (triode), and fast (saturation). Depending on how much you press the remote button (voltage changes), the car will operate in different ways, similarly to how a MOSFET operates under varying voltage conditions.

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