Question 7. Calculate the mid-gap voltage

When gate voltage of this p-type gate is continuously increased to be positive(decreased to be negative for n type), majority carriers (holes in this case) are forced away from the surface of the semiconductor and form a depletion region, which is called depletion or mid-gap. 

Similarly to the flat-band c=voltage, the mid-gap voltage can be calculated indirectly by matching the capacitance at that moment with the datum given in 'HFCV_70%Hf.txt'. The total capacitance will be the oxide capacitance in series with the depletion capacitance.

    (1)

(2)

Therefore,

 (3)

To improve the accuracy, the slop k at the matched point can be calculated, and the mid-gap voltage will be:

  (4)

Finally, the value of flat-band voltage is found to be 1.366 V.