Task 4: Determine the Doping Density of the Silicon Subtract

These formulas have been used:


and CMAX has been calculated in task 2, which is 2.92Nf.

assuming that it is a uniformly doped semiconductor, then

and,

so that,


 It is not a simple function and cannot be calculate directly, in this case, we use MATLAB to calculate the NA, and NA=4.2*1021m-3



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Task7. Calculate the Mid-gap Voltage.

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 To calculate the mid-gap voltage, we need to obtain the depletion capacitor value at mid-gap.                                           Figure5. The a.c. equivalent circuit at mid-gap Assuming a uniformly doped semiconductor, we can calculate the depletion capacitor value by the formula: Then, the value of C dep   is 3.28E-4 F/m 2 Using the formula: we can calculate the value of 1/C midgap . And we know the relationship between C Dep and C dep . With the values of C Dep and C OX , we can calculate the value of C midgap is 7.587*10 -11 F, and V midgap equals 1.35V.
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Task5. Work Function Difference (Calculate the work function difference assuming a gold (Au) gate.）

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  The work function Ф M is defined as the minimum energy required for an electron with an energy equal to Fermi level to escape from the metal into vacuum. It is shown in figure 2. For metals, the work function Ф M = Ф VA - Ф FM is constant. Thus,  Ф M (Au)=5.1eV. For semiconductors, the work function is: which is shown in figure 2. According to known conditions, the electron affinity of Si is and the Bandgap energy of silicon is The Fermi potential Ф F is equal to and is about 25mV at 300k. Thus, Fermi potential: and the work function of semiconductors: The definition of Mental-Semiconductors work function difference is: Thus, the work function difference: Figure 2: Energy band diagram explaining work function
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