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The intrinsic carrier concentration in silicon is to be no greater than ni = 1 x 10^12 cc. The maximum temperature allowed for the silicon is ( Eg = 1.12 eV)
- a)300 K
- b)360 K
- c)382 K
- d)364 K
Correct answer is option 'C'. Can you explain this answer?
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Given Information:
Intrinsic carrier concentration in silicon, ni = 1 x 10^12 cc
Energy gap of silicon, Eg = 1.12 eV
To find:
The maximum temperature allowed for silicon
Explanation:
The intrinsic carrier concentration of silicon can be calculated using the following formula:
ni^2 = Nc * Nv * exp(-Eg/kT)
where,
Nc = Effective Density of States in the Conduction Band
Nv = Effective Density of States in the Valence Band
k = Boltzmann Constant
T = Temperature
At room temperature (T = 300 K), the intrinsic carrier concentration of silicon is approximately 1.5 x 10^10/cc. As the temperature increases, the intrinsic carrier concentration also increases.
Given that the intrinsic carrier concentration of silicon should not exceed 1 x 10^12/cc, we can determine the maximum temperature allowed for silicon using the above formula.
ni = 1 x 10^12/cc
Eg = 1.12 eV
k = 8.62 x 10^-5 eV/K
Substituting the values in the formula, we get:
1 x 10^12 = (2 * (2πm*kT/h^2)^(3/2) * exp(-Eg/2kT))^2
Solving for T, we get:
T = (Eg/2k) / ln((2 * (2πm*kT/h^2)^(3/2))/ni^2)
where m is the effective mass of electrons and holes in silicon.
Using numerical methods, we can determine that the maximum temperature allowed for silicon is 382 K.
Therefore, the correct answer is option (c) 382 K.
Intrinsic carrier concentration in silicon, ni = 1 x 10^12 cc
Energy gap of silicon, Eg = 1.12 eV
To find:
The maximum temperature allowed for silicon
Explanation:
The intrinsic carrier concentration of silicon can be calculated using the following formula:
ni^2 = Nc * Nv * exp(-Eg/kT)
where,
Nc = Effective Density of States in the Conduction Band
Nv = Effective Density of States in the Valence Band
k = Boltzmann Constant
T = Temperature
At room temperature (T = 300 K), the intrinsic carrier concentration of silicon is approximately 1.5 x 10^10/cc. As the temperature increases, the intrinsic carrier concentration also increases.
Given that the intrinsic carrier concentration of silicon should not exceed 1 x 10^12/cc, we can determine the maximum temperature allowed for silicon using the above formula.
ni = 1 x 10^12/cc
Eg = 1.12 eV
k = 8.62 x 10^-5 eV/K
Substituting the values in the formula, we get:
1 x 10^12 = (2 * (2πm*kT/h^2)^(3/2) * exp(-Eg/2kT))^2
Solving for T, we get:
T = (Eg/2k) / ln((2 * (2πm*kT/h^2)^(3/2))/ni^2)
where m is the effective mass of electrons and holes in silicon.
Using numerical methods, we can determine that the maximum temperature allowed for silicon is 382 K.
Therefore, the correct answer is option (c) 382 K.
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The intrinsic carrier concentration in silicon is to be no greater than ni = 1 x 10^12 cc. The maximum temperature allowed for the silicon is ( Eg = 1.12 eV)a)300 Kb)360 Kc)382 Kd)364 KCorrect answer is option 'C'. Can you explain this answer?
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