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Consider a semiconductor having following parameters:
Electron mobility, αn = 7500 cm2/V-s
Hole mobility,αp = 300 cm2/ V-s
Intrinsic concentration ni = 13.6 x 1011/cm3
The conductivity of the semiconductor will be minimum if hole concentration is ___× 1011/cm3
(Answer up to the nearest integer)
Correct answer is '68'. Can you explain this answer?
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Consider a semiconductor having following parameters:Electron mobilit...
Understanding the problem:
We are given the parameters of a semiconductor, such as electron mobility (αn), hole mobility (αp), and intrinsic concentration (ni). We need to determine the minimum hole concentration (p) for which the conductivity of the semiconductor will be minimum.
Solution:
1. Conductivity of a semiconductor:
The conductivity (σ) of a semiconductor is given by the product of the charge (q), the mobility (μ), and the concentration (n) of the charge carriers. Mathematically, it can be expressed as:
σ = q * μ * n
2. Relationship between electron and hole concentrations:
In an intrinsic semiconductor, the electron concentration (n) and the hole concentration (p) are related by the equation:
n * p = ni^2
3. Minimum conductivity condition:
To determine the minimum conductivity, we need to find the minimum value of the product of charge, mobility, and concentration. Since we are given the values of electron and hole mobilities, we can determine the minimum conductivity by finding the minimum value of the product of electron and hole concentrations.
4. Calculation:
Given:
αn = 7500 cm²/V-s
αp = 300 cm²/V-s
ni = 13.6 x 10^11/cm³
Using the relationship between electron and hole concentrations, we can express the electron concentration (n) in terms of hole concentration (p):
n = ni^2 / p
Now, substituting the values of αn, αp, and n in the conductivity equation, we get:
σ = q * αn * n
= q * αn * (ni^2 / p)
Similarly, substituting the values of αp, αn, and p in the conductivity equation for holes, we get:
σ = q * αp * p
To find the minimum conductivity, we need to equate the two expressions for conductivity and solve for p:
q * αn * (ni^2 / p) = q * αp * p
Simplifying the equation, we get:
(αn * ni^2) / p = αp * p
Cross-multiplying and rearranging, we get:
p^2 = (αn * ni^2) / αp
Taking the square root on both sides, we get:
p = √((αn * ni^2) / αp)
Substituting the given values, we have:
p = √((7500 * (13.6 x 10^11)^2) / 300)
p ≈ 68 x 10^11/cm³
Therefore, the minimum hole concentration is approximately 68 x 10^11/cm³, which is the correct answer.
We are given the parameters of a semiconductor, such as electron mobility (αn), hole mobility (αp), and intrinsic concentration (ni). We need to determine the minimum hole concentration (p) for which the conductivity of the semiconductor will be minimum.
Solution:
1. Conductivity of a semiconductor:
The conductivity (σ) of a semiconductor is given by the product of the charge (q), the mobility (μ), and the concentration (n) of the charge carriers. Mathematically, it can be expressed as:
σ = q * μ * n
2. Relationship between electron and hole concentrations:
In an intrinsic semiconductor, the electron concentration (n) and the hole concentration (p) are related by the equation:
n * p = ni^2
3. Minimum conductivity condition:
To determine the minimum conductivity, we need to find the minimum value of the product of charge, mobility, and concentration. Since we are given the values of electron and hole mobilities, we can determine the minimum conductivity by finding the minimum value of the product of electron and hole concentrations.
4. Calculation:
Given:
αn = 7500 cm²/V-s
αp = 300 cm²/V-s
ni = 13.6 x 10^11/cm³
Using the relationship between electron and hole concentrations, we can express the electron concentration (n) in terms of hole concentration (p):
n = ni^2 / p
Now, substituting the values of αn, αp, and n in the conductivity equation, we get:
σ = q * αn * n
= q * αn * (ni^2 / p)
Similarly, substituting the values of αp, αn, and p in the conductivity equation for holes, we get:
σ = q * αp * p
To find the minimum conductivity, we need to equate the two expressions for conductivity and solve for p:
q * αn * (ni^2 / p) = q * αp * p
Simplifying the equation, we get:
(αn * ni^2) / p = αp * p
Cross-multiplying and rearranging, we get:
p^2 = (αn * ni^2) / αp
Taking the square root on both sides, we get:
p = √((αn * ni^2) / αp)
Substituting the given values, we have:
p = √((7500 * (13.6 x 10^11)^2) / 300)
p ≈ 68 x 10^11/cm³
Therefore, the minimum hole concentration is approximately 68 x 10^11/cm³, which is the correct answer.
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Community Answer
Consider a semiconductor having following parameters:Electron mobilit...
For minimum conductivity,
= 68 x 1011/cm3
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Consider a semiconductor having following parameters:Electron mobility, αn = 7500 cm2/V-sHole mobility,αp = 300 cm2/ V-sIntrinsic concentration ni = 13.6 x 1011/cm3The conductivity of the semiconductor will be minimum if hole concentration is ___× 1011/cm3(Answer up to the nearest integer)Correct answer is '68'. Can you explain this answer?
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