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Mathematical Analysis  

Calculation of threshold voltage

Threshold will be defined as when the carrier concentration in the channel is equal to the bulk doping. This is equivalent, approximately, to saying that

Ec - Ef at Si surface= Ef - Ev in bulk.

The following figure illustrates this condition.

Figure

Question: Find the threshold voltage for n-channel MOS when

Solution:

VT = Vi + Vox + Vms, ----- (1)

Vi = potential drop in bulk Si at threshold,
Vox = potential drop over oxide layer due to charges in oxide and in semiconductor (space charge), and
Vms = potential needed to compensate for the work function difference between M and Si.


Let us now calculate the bias voltage needed to go from one condition to another. This will help you understand the physical reasons for tht threshold voltage, etc.

1. From Equilibrium (Vgb = 0 V) to Flat-Band (Vgb = VFB).

2. From Flat-Band (Vgb = VFB) to Threshold (Vgb = VT).

3. Beyond Threshold.