Drain current equation of nmos transistor at triode region

 

Drain current equation of NMOS transistor at triode region

 

Question: Derive the drain current equation of NMOS transistor at triode region(resistive region)?

 

Solution:

Figure 1: Elemental capacitor between source and drain

 

Here, V_ds<V_gs-V_t. The voltage across the insulator at the source is V_gs at the drain is V_gd (meaningV_g-V_d). The device structure resembles an infinite number of capacitances between the drain and source, each one having a different voltage across it. Consider one of these capacitances of length dx situated at a distance x meters from the drain, as shown in figure 1. 

The channel width and length are W and L meters respectively. Thus the capacitance, C farads, of the structure shown in figure 1 is