WEEK 2 TASK 4, determine the doping density of the silicon substrate

The minimum capacitance Cmin is given as the series contribution of oxide and semiconductor:

Where Cox is equal to Cmax which has been calculated in task2.

Cdep can be calculated as follow:
The equivalent circuit for depletion can be measured two capacitors in series.

and assuming a uniformly doped semiconductor, we have

where W is the depletion width. Width increases with gate voltage so the capacitance Cdep decreases and so does the measured capacitance.

can be calculated as follow:

This is the energy band diagram explaining work function.

Where ni = 1 * 10^10 cm^-3 and Vt = 25 mV at a temperature of 300K.

While Cmin can also be read in the C-V curve which in task 1.

The extraction of doping density is given by:

where A is calculated in task 2, k is Boltzmann's constant, T is temperature of 300K. q, epsilon o, epsilon s and ni are given in the project specification

So that the doping density is

the answer NA cannot be calculated directly, while we can applying the method of Newton ralphson to plot two curves using matlab and then find the value of interconnection point which is the answer.