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Consider a bar of silicon having carrier concentration n0=1015 cm-3 and ni=1010cm-3. Assume the excess carrier concentrations to be n=1013cm-3, calculate the quasi-fermi energy level at T=300K?
- a)0.2982 eV
- b)0.2984 eV
- c)0.5971 eV
- d)1Ev
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider a bar of silicon having carrier concentration n0=1015cm-3and ...
=1.38*10-23*300*ln(1013+1015/1013)
=0.2984 eV.
Most Upvoted Answer
Consider a bar of silicon having carrier concentration n0=1015cm-3and ...
To calculate the quasi-Fermi energy level at T=300K, we need to consider the carrier concentrations and the intrinsic carrier concentration of a silicon bar.
Given data:
Carrier concentration, n0 = 10^15 cm^-3
Intrinsic carrier concentration, ni = 10^10 cm^-3
Excess carrier concentration, n = 10^13 cm^-3
Temperature, T = 300K
We can use the equation for quasi-Fermi energy level (Ef) in terms of carrier concentrations:
n = ni * exp((Ef - Ei) / kT)
Where:
n is the carrier concentration
ni is the intrinsic carrier concentration
Ef is the quasi-Fermi energy level
Ei is the intrinsic energy level
k is the Boltzmann constant
T is the temperature in Kelvin
Rearranging the equation, we can solve for Ef:
(Ef - Ei) / kT = ln(n / ni)
Ef - Ei = kT * ln(n / ni)
Ef = Ei + kT * ln(n / ni)
Now, let's substitute the given values into the equation to find the value of Ef:
Ei = 0 (since we are considering the intrinsic energy level as the reference)
k = 8.617333262145 x 10^-5 eV/K (Boltzmann constant)
T = 300K
n = n0 + n (total carrier concentration)
Calculating the total carrier concentration:
n = n0 + n
n = 10^15 + 10^13 cm^-3
n = 10^15 + 10^13 cm^-3
n = 10^28 cm^-3
Substituting the values into the equation:
Ef = 0 + (8.617333262145 x 10^-5 eV/K) * ln((10^28 cm^-3) / (10^10 cm^-3))
Ef = 0 + (8.617333262145 x 10^-5 eV/K) * ln(10^18)
Ef ≈ 0.2984 eV
Therefore, the quasi-Fermi energy level at T=300K is approximately 0.2984 eV, which corresponds to option 'B'.
Given data:
Carrier concentration, n0 = 10^15 cm^-3
Intrinsic carrier concentration, ni = 10^10 cm^-3
Excess carrier concentration, n = 10^13 cm^-3
Temperature, T = 300K
We can use the equation for quasi-Fermi energy level (Ef) in terms of carrier concentrations:
n = ni * exp((Ef - Ei) / kT)
Where:
n is the carrier concentration
ni is the intrinsic carrier concentration
Ef is the quasi-Fermi energy level
Ei is the intrinsic energy level
k is the Boltzmann constant
T is the temperature in Kelvin
Rearranging the equation, we can solve for Ef:
(Ef - Ei) / kT = ln(n / ni)
Ef - Ei = kT * ln(n / ni)
Ef = Ei + kT * ln(n / ni)
Now, let's substitute the given values into the equation to find the value of Ef:
Ei = 0 (since we are considering the intrinsic energy level as the reference)
k = 8.617333262145 x 10^-5 eV/K (Boltzmann constant)
T = 300K
n = n0 + n (total carrier concentration)
Calculating the total carrier concentration:
n = n0 + n
n = 10^15 + 10^13 cm^-3
n = 10^15 + 10^13 cm^-3
n = 10^28 cm^-3
Substituting the values into the equation:
Ef = 0 + (8.617333262145 x 10^-5 eV/K) * ln((10^28 cm^-3) / (10^10 cm^-3))
Ef = 0 + (8.617333262145 x 10^-5 eV/K) * ln(10^18)
Ef ≈ 0.2984 eV
Therefore, the quasi-Fermi energy level at T=300K is approximately 0.2984 eV, which corresponds to option 'B'.
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Consider a bar of silicon having carrier concentration n0=1015cm-3and ni=1010cm-3. Assume the excess carrier concentrations to be n=1013cm-3, calculate the quasi-fermi energy level at T=300K?a)0.2982 eVb)0.2984 eVc)0.5971 eVd)1EvCorrect answer is option 'B'. Can you explain this answer?
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