Task-4 Determine the doping density of the silicon substrate

Doping density I associated with the work function which is links the capacitance. One equation can be used to synthesise the donor’s concentration.

The interpretation for the physical quantities are listed underneath:

Capacitor area – 2.37589444e(-7)/m^2

Charge carried by an electron – 1.602e-(19) C

Boltzmann’s constant – 

Room temperature – 300 K

Permittivity in free space - 8.85e(-12) F/m

Relative permittivity for silicon – 11.2

Silicon intrinsic carrier concentration –  10e15/m^3 

Minimum capacitance (read from the given txt file) – 53.4 pF

Maximum capacitance (read from the given txt file) - 2.919e3 pF

Simplify the equation, we have

The result is a transcendental function of , and MATLAB was utilized to obtain the value of . Two methods were used.

-       Method 1: Adopting the build-in function

The answer is clearly wrong because it indicate there is no doping on the semiconductor.

-       Method 2: Adopting the image method

Separate the equation with the right hand side as

 , and left hand side as

After running the above program, a graph containing two curves was displayed on screen.

The linear line represents for the equation 

and the curve represents for the right hand side equation 

Clearly, the intersection is the desired value for 

Because of the intersection is between 4e21 and 5e21, the domain of the doping concentration could be reduce to an interval between 3.5e21 and 5e21. The result is shown in figure 2.

In order to acquire a more accurate value of doping concentration,  ‘Data cursor’ under the tool bar was utilized and the final approximation value is shown below:

Therefore, the doping concentration is approximately equal to 4.088e21/m^3