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A semiconductor having electron mobility μn = 7500 cm2/V-sec, hole mobility μp=300 cm2/V-sec, intrinsic carrier concentration as 13.6×1011/cm3 is kept at 300°K. The maximum value of resistivity is _________ Ω-m.
- a)12.212
- b)15.318
- c)18.214
- d)20.502
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A semiconductor having electron mobility μn = 7500 cm2/V-sec, hole mo...
The resistivity of a semiconductor can be calculated using the formula:
ρ = 1 / (q * μ * n)
where ρ is the resistivity, q is the charge of an electron, μ is the mobility of the charge carriers (electrons or holes), and n is the carrier concentration.
In this case, we are given the electron mobility (μn = 7500 cm2/V-sec), the hole mobility (μp = 300 cm2/V-sec), and the intrinsic carrier concentration (ni = 13.6×1011/cm3). We need to find the maximum value of resistivity at 300°K.
1. Calculate the resistivity for electrons (ρn):
ρn = 1 / (q * μn * ni)
2. Calculate the resistivity for holes (ρp):
ρp = 1 / (q * μp * ni)
3. Compare the two resistivities and choose the maximum value as the maximum resistivity.
Detailed calculations:
1. Calculate the resistivity for electrons (ρn):
The charge of an electron, q, is 1.6 × 10^-19 C.
ρn = 1 / (1.6 × 10^-19 C * 7500 cm2/V-sec * 13.6 × 10^11/cm3)
Converting cm2 to m2 and cm3 to m3:
ρn = 1 / (1.6 × 10^-19 C * 7500 * 10^-4 m2/V-sec * 13.6 × 10^17/m3)
Simplifying the expression:
ρn = 1 / (1.6 × 7500 × 13.6 × 10^-2 × 10^-19 × 10^17)
ρn = 1 / (17472 × 10^-4 × 10^-19 × 10^17)
ρn = 1 / (17472 × 10^-6 × 10^-2)
ρn = 1 / (174.72 × 10^-8)
ρn = 5.718 × 10^6 Ω-m
2. Calculate the resistivity for holes (ρp):
The charge of an electron, q, is 1.6 × 10^-19 C.
ρp = 1 / (1.6 × 10^-19 C * 300 cm2/V-sec * 13.6 × 10^11/cm3)
Converting cm2 to m2 and cm3 to m3:
ρp = 1 / (1.6 × 10^-19 C * 300 * 10^-4 m2/V-sec * 13.6 × 10^17/m3)
Simplifying the expression:
ρp = 1 / (1.6 × 300 × 13.6 × 10^-2 × 10^-19 × 10^17)
ρp = 1 / (65280 × 10^-4 × 10^-19 × 10^17)
ρp = 1 / (6528 × 10^-6 × 10^-2)
ρp = 1 / (65.28 × 10^-8)
ρp = 1.53 × 10^7 Ω-m
3. Compare the two resist
ρ = 1 / (q * μ * n)
where ρ is the resistivity, q is the charge of an electron, μ is the mobility of the charge carriers (electrons or holes), and n is the carrier concentration.
In this case, we are given the electron mobility (μn = 7500 cm2/V-sec), the hole mobility (μp = 300 cm2/V-sec), and the intrinsic carrier concentration (ni = 13.6×1011/cm3). We need to find the maximum value of resistivity at 300°K.
1. Calculate the resistivity for electrons (ρn):
ρn = 1 / (q * μn * ni)
2. Calculate the resistivity for holes (ρp):
ρp = 1 / (q * μp * ni)
3. Compare the two resistivities and choose the maximum value as the maximum resistivity.
Detailed calculations:
1. Calculate the resistivity for electrons (ρn):
The charge of an electron, q, is 1.6 × 10^-19 C.
ρn = 1 / (1.6 × 10^-19 C * 7500 cm2/V-sec * 13.6 × 10^11/cm3)
Converting cm2 to m2 and cm3 to m3:
ρn = 1 / (1.6 × 10^-19 C * 7500 * 10^-4 m2/V-sec * 13.6 × 10^17/m3)
Simplifying the expression:
ρn = 1 / (1.6 × 7500 × 13.6 × 10^-2 × 10^-19 × 10^17)
ρn = 1 / (17472 × 10^-4 × 10^-19 × 10^17)
ρn = 1 / (17472 × 10^-6 × 10^-2)
ρn = 1 / (174.72 × 10^-8)
ρn = 5.718 × 10^6 Ω-m
2. Calculate the resistivity for holes (ρp):
The charge of an electron, q, is 1.6 × 10^-19 C.
ρp = 1 / (1.6 × 10^-19 C * 300 cm2/V-sec * 13.6 × 10^11/cm3)
Converting cm2 to m2 and cm3 to m3:
ρp = 1 / (1.6 × 10^-19 C * 300 * 10^-4 m2/V-sec * 13.6 × 10^17/m3)
Simplifying the expression:
ρp = 1 / (1.6 × 300 × 13.6 × 10^-2 × 10^-19 × 10^17)
ρp = 1 / (65280 × 10^-4 × 10^-19 × 10^17)
ρp = 1 / (6528 × 10^-6 × 10^-2)
ρp = 1 / (65.28 × 10^-8)
ρp = 1.53 × 10^7 Ω-m
3. Compare the two resist
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Community Answer
A semiconductor having electron mobility μn = 7500 cm2/V-sec, hole mo...
n = ni2/ρ
σ = qμnn + qμρρ = qμnni2/ρ2 + qμρρ
For non conductivity dσ/dρ = 0 = -qμnni2/ρ2 + qμρ
= 68 x 1011/cm3
σmin = 6.528 x 10-4 V/cm
Σmin = 1/σmax = 1/6.528 x 10-4
= 15.318 Ω-m
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A semiconductor having electron mobility μn = 7500 cm2/V-sec, hole mobility μp=300 cm2/V-sec, intrinsic carrier concentration as 13.6×1011/cm3 is kept at 300°K. The maximum value of resistivity is _________ Ω-m.a)12.212b)15.318c)18.214d)20.502Correct answer is option 'B'. Can you explain this answer?
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