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In germanium semiconductor material at T = 400 K the intrinsic concentration is
- a)26.8 x 1014 cm-3
- b)18.4 x 1014 cm-3
- c)8.5 x 1014 cm-3
- d)3.6 x 1014 cm-3
Correct answer is option 'C'. Can you explain this answer?
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Introduction:
The intrinsic concentration of a semiconductor refers to the concentration of charge carriers (electrons and holes) in the material when no external doping is present. It depends on the temperature and the bandgap of the semiconductor. In this case, we are given that the semiconductor material is germanium (Ge) and the temperature is 400 K.
Explanation:
To determine the intrinsic concentration of germanium at 400 K, we can use the equation:
n_i = N_c * N_v * exp(-E_g / (2 * k * T))
where:
n_i is the intrinsic concentration
N_c is the effective density of states in the conduction band
N_v is the effective density of states in the valence band
E_g is the energy bandgap of germanium
k is Boltzmann's constant
T is the temperature in Kelvin
Calculations:
The values for N_c, N_v, and E_g for germanium are known:
N_c = 2.8 x 10^19 cm^-3
N_v = 1.04 x 10^19 cm^-3
E_g = 0.67 eV
Convert the temperature to Kelvin:
T = 400 K
Substitute the values into the equation and calculate:
n_i = (2.8 x 10^19 cm^-3) * (1.04 x 10^19 cm^-3) * exp(-0.67 eV / (2 * (8.617 x 10^-5 eV/K) * 400 K))
Simplifying the expression:
n_i = (2.91 x 10^38 cm^-6) * exp(-1.565)
n_i ≈ 8.5 x 10^14 cm^-3
So, the intrinsic concentration of germanium at 400 K is approximately 8.5 x 10^14 cm^-3, which corresponds to option 'C' in the given options.
Conclusion:
The correct answer is option 'C' - 8.5 x 10^14 cm^-3. At a temperature of 400 K, the intrinsic concentration of germanium is approximately 8.5 x 10^14 cm^-3.
The intrinsic concentration of a semiconductor refers to the concentration of charge carriers (electrons and holes) in the material when no external doping is present. It depends on the temperature and the bandgap of the semiconductor. In this case, we are given that the semiconductor material is germanium (Ge) and the temperature is 400 K.
Explanation:
To determine the intrinsic concentration of germanium at 400 K, we can use the equation:
n_i = N_c * N_v * exp(-E_g / (2 * k * T))
where:
n_i is the intrinsic concentration
N_c is the effective density of states in the conduction band
N_v is the effective density of states in the valence band
E_g is the energy bandgap of germanium
k is Boltzmann's constant
T is the temperature in Kelvin
Calculations:
The values for N_c, N_v, and E_g for germanium are known:
N_c = 2.8 x 10^19 cm^-3
N_v = 1.04 x 10^19 cm^-3
E_g = 0.67 eV
Convert the temperature to Kelvin:
T = 400 K
Substitute the values into the equation and calculate:
n_i = (2.8 x 10^19 cm^-3) * (1.04 x 10^19 cm^-3) * exp(-0.67 eV / (2 * (8.617 x 10^-5 eV/K) * 400 K))
Simplifying the expression:
n_i = (2.91 x 10^38 cm^-6) * exp(-1.565)
n_i ≈ 8.5 x 10^14 cm^-3
So, the intrinsic concentration of germanium at 400 K is approximately 8.5 x 10^14 cm^-3, which corresponds to option 'C' in the given options.
Conclusion:
The correct answer is option 'C' - 8.5 x 10^14 cm^-3. At a temperature of 400 K, the intrinsic concentration of germanium is approximately 8.5 x 10^14 cm^-3.
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In germanium semiconductor material at T = 400 K the intrinsic concentration isa)26.8 x 1014 cm-3b)18.4 x 1014 cm-3c)8.5 x 1014 cm-3d)3.6 x 1014 cm-3Correct answer is option 'C'. Can you explain this answer?
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