2.1.2. Threshold Voltage and Body Effect
The threshold voltage Vth for a nMOS transistor is the minimum amount of the gate-to-source voltage VGS necessary to cause surface inversion so as to create the conducting channel between the source and the drain. For VGS< Vth , no current can flow between the source and the drain. For VGS> Vth , a larger number of minority carriers (electrons in case of an nMOS transistor) are drawn to the surface, increasing the channel current. However, the surface potential and the depletion region width remain almost unchanged as VGS is increased beyond the threshold voltage.
The physical components determining the threshold voltage are the following.
- work function difference between the gate and the substrate.
- gate voltage portion spent to change the surface potential.
- gate voltage part accounting for the depletion region charge.
- gate voltage component to offset the fixed charges in the gate oxide and the silicon-oxide boundary.
Although the following analysis pertains to an nMOS device, it can be simply modified to reason for a p-channel device.
The work function difference 
between the doped polysilicon gate and the p-type substrate, which depends on the substrate doping, makes up the first component of the threshold voltage. The externally applied gate voltage must also account for the strong inversion at the surface, expressed in the form of surface potential 2
, where denotes the distance between the intrinsic energy level EI and the Fermi level EF of the p-type semiconductor substrate.