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If two semiconductor materials have exactly the same properties except that, material A has a band gap of 1.0 eV and material B has a band gap of 5.0 eV then, the ratio of the intrinsic concentration of material A to that of B will be ___ × 1033
(Answer up to two decimal places)
Correct answer is '2.55'. Can you explain this answer?
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If two semiconductor materials have exactly the same properties excep...
**Explanation:**
Intrinsic concentration (ni) is the concentration of charge carriers (electrons and holes) in a pure semiconductor at thermal equilibrium. The value of ni depends on the bandgap of the semiconductor material and the temperature.
**Formula:**
ni² = (Nc * Nv) * exp(-Eg/2kT)
Where,
Nc = Effective density of states in the conduction band
Nv = Effective density of states in the valence band
Eg = Bandgap energy
k = Boltzmann's constant
T = Temperature
**Calculation:**
Given, Eg(A) = 1.0 eV and Eg(B) = 5.0 eV
Let's assume the values of Nc and Nv are the same for both materials.
Taking natural log on both sides of the formula and dividing the two equations, we get:
ln(ni,A) - ln(ni,B) = (Eg,B - Eg,A) / 2kT
ln(ni,A / ni,B) = (5.0 - 1.0) / (2kT) = 2.0 / (2kT)
ni,A / ni,B = exp[2.0 / (2kT)]
At room temperature (T = 300 K), kT is approximately 0.026 eV.
ni,A / ni,B = exp(2.0 / 0.052) ≈ 2.55 × 10³
Therefore, the ratio of the intrinsic concentration of material A to that of material B is 2.55 × 10³.
Intrinsic concentration (ni) is the concentration of charge carriers (electrons and holes) in a pure semiconductor at thermal equilibrium. The value of ni depends on the bandgap of the semiconductor material and the temperature.
**Formula:**
ni² = (Nc * Nv) * exp(-Eg/2kT)
Where,
Nc = Effective density of states in the conduction band
Nv = Effective density of states in the valence band
Eg = Bandgap energy
k = Boltzmann's constant
T = Temperature
**Calculation:**
Given, Eg(A) = 1.0 eV and Eg(B) = 5.0 eV
Let's assume the values of Nc and Nv are the same for both materials.
Taking natural log on both sides of the formula and dividing the two equations, we get:
ln(ni,A) - ln(ni,B) = (Eg,B - Eg,A) / 2kT
ln(ni,A / ni,B) = (5.0 - 1.0) / (2kT) = 2.0 / (2kT)
ni,A / ni,B = exp[2.0 / (2kT)]
At room temperature (T = 300 K), kT is approximately 0.026 eV.
ni,A / ni,B = exp(2.0 / 0.052) ≈ 2.55 × 10³
Therefore, the ratio of the intrinsic concentration of material A to that of material B is 2.55 × 10³.
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If two semiconductor materials have exactly the same properties excep...
ni(A)/ni(B) = 2.55 x 1033
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If two semiconductor materials have exactly the same properties except that, material A has a band gap of 1.0 eV and material B has a band gap of 5.0 eV then, the ratio of the intrinsic concentration of material A to that of B will be ___ × 1033(Answer up to two decimal places)Correct answer is '2.55'. Can you explain this answer?
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