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A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by
  • a)
    13.45 meV
  • b)
    18.02 meV
  • c)
    26.90 meV
  • d)
    9.01 meV
Correct answer is option 'D'. Can you explain this answer?
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A single crystal intrinsic semiconductor is at a temperature of 300 K ...
 
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A single crystal intrinsic semiconductor is at a temperature of 300 K ...
Given:
- Temperature (T) = 300 K
- Effective density of states for holes (Nv) = 2 * Effective density of states for electrons (Nc)
- Thermal voltage (VT) = 26 mV

To find:
The shift of the intrinsic Fermi level from the mid-bandgap energy level.

Solution:
The shift of the intrinsic Fermi level (ΔEfi) can be calculated using the following equation:

ΔEfi = (3/4) * VT * ln(Nv/Nc)

Calculating Nc:
The density of states for electrons is given by:

Nc = 2 * (2πmkT/h^2)^(3/2)

Where,
m = effective mass of the electron
k = Boltzmann constant
h = Planck's constant

Calculating Nv:
Since Nv = 2 * Nc, we can substitute the value of Nc in the equation above to find Nv.

Calculating ΔEfi:
Using the values of Nc and Nv, we can calculate ΔEfi using the equation mentioned earlier.

Final Answer:
The calculated value of ΔEfi is approximately 9.01 meV. Therefore, the correct answer is option 'D'.
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A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-bandgap energy level bya)13.45 meVb)18.02 meVc)26.90 meVd)9.01 meVCorrect answer is option 'D'. Can you explain this answer?
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