Please provide formulae, beginner explanation and derivation for parts c and d.

Question

Please provide formulae, beginner explanation and derivation for parts c and d. As this is a long question I have provided parts a and b for context, however only require answers for part c and d.

Thanks for your help.

2. Consider an undoped silicon bar of length L 1 mm, width W 0.1 mm and thickness H 0.01 mm. At room temperature the bar has a bandgap of 1.12 eV, an intrinsic carrier density of N 1.5 x 10 cm 3, a mobility un 1350 cm2/v.s (for electrons and up 450 cm s (for holes). A voltage V 5 V is applied along the length L of the bar. (a) How big is the current I flowing in the silicon bar? 16 marks

Explanation / Answer

c) The formula to calculate the position of fermi level in n-type doped semiconductor is

ND = niexp [ (Ec- Ef)/ kT]

but we have given, Eg - Ec = 39 meV

so, Ec- Ef = [(1.12/2) - 0.039 ] eV = 0.521 eV

ND = 1.5 * 1010 exp [ 0.521 / 0.026 ] = 7.56 * 1018  cm-3

In the second case, fermi level will be 0.521 eV above the intrinsic fermi level i.e.

Ec- Ef = [(1.12/2) - 0.039 ] eV = 0.521 eV

d)

The mobility depends on the temperature and It decreases as temperature is increased. current is directly proportional to mobility so as temperature increases mobility decreases and at the same time, current will decrease.

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