Question 6. Calculate the flat-band voltage

When gate voltage of this p-type gate is increased (decreased for n type), the accumulation capacitor is decreased which will in turn reduce the measured capacitance. When the gate voltage is zero for ideal case, the condition is thus called flat-band. However, in real cases, because of the exist of oxide charges, the gate voltage will be a complex function of oxide charges instead of zero.

Fortunately, the flat-band 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 Debye capacitance.

    (1)

        (2)

    (3)

According to the calculation, the result of C_FB is equal to 345.27pF. 

However, it is obviously inaccurate to just find the nearest capacitance point in datum and use its voltage as the flat-band voltage. To improve the accuracy, the slop k at the matched point can be calculated, and the flat-band voltage will be:

  (4)

Finally, the value of flat-band voltage is found to be 0.932 V.