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Optical excitation of intrinsic Germanium creates an average density of 1018 conduction electrons per m3 in the material at liquid nitrogen temperature. At this temperature electrons and holes mobilities are equal.
μ = 0.5 x 104cm2 /volts sec and Germanium dielectric constant is 20. The diffusion coefficient for electron is
  • a)
    3.3 x 10-3 m2/s
  • b)
    3.6 x 10-3 m2/s
  • c)
    4.4x 10-3 m2/3
  • d)
    2.8 x 10-3 m2 /s
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Optical excitation of intrinsic Germanium creates an average density o...
The diffusion coefficient D is given by Einstein relation

∵ liquid nitrogen temperature TD = 77K . μ = 0.5 x 10-4 x 104 m2 /V.s = 0.5 m2/V.s
e = 1.6 x 10-19
kB =1.38 x 10-23
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Optical excitation of intrinsic Germanium creates an average density o...
The fact that electrons and holes mobilities are equal at liquid nitrogen temperature means that the mobility of both electrons and holes is the same. Let's denote this common mobility value as μ.

Given that the average density of conduction electrons is 1018 per m³, we can use this information to find the carrier concentration (n), which is the number of conduction electrons per unit volume. The carrier concentration (n) is related to the average density (N) by the equation:

n = N / 2,

since for every conduction electron, there is also a hole.

Thus, the carrier concentration is:

n = 1018 / 2 = 5 x 10^17 electrons/m³.

Now, let's consider the relationship between carrier concentration (n), mobility (μ), and electrical conductivity (σ). The electrical conductivity is given by:

σ = n * e * μ,

where e is the elementary charge.

Since electrons and holes have the same mobility, we can represent the electrical conductivity as:

σ = (n + p) * e * μ,

where p is the hole concentration, which is equal to the electron concentration (n) since the mobility of electrons and holes is equal.

Therefore, the electrical conductivity is:

σ = (n + n) * e * μ = 2n * e * μ.

Given that the carrier concentration (n) is 5 x 10^17 electrons/m³ and the mobility (μ) is equal for both electrons and holes, we can calculate the electrical conductivity (σ).

σ = 2 * (5 x 10^17) * e * μ.

The value of the elementary charge (e) is approximately 1.602 x 10^-19 C.

Let's assume a value for the mobility (μ), for example, μ = 1000 cm²/Vs = 1000 x 10^-4 m²/Vs.

Substituting the values into the equation, we get:

σ = 2 * (5 x 10^17) * (1.602 x 10^-19 C) * (1000 x 10^-4 m²/Vs).

Simplifying the expression, we find:

σ = 1.602 x 10^-3 S/m.

Therefore, the electrical conductivity of intrinsic Germanium at liquid nitrogen temperature with an average density of 1018 conduction electrons per m³ is approximately 1.602 x 10^-3 S/m.
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Optical excitation of intrinsic Germanium creates an average density of 1018 conduction electrons per m3 in the material at liquid nitrogen temperature. At this temperature electrons and holes mobilities are equal.μ = 0.5 x 104cm2/volts sec and Germanium dielectric constant is 20. The diffusion coefficient for electron isa)3.3 x 10-3m2/sb)3.6 x 10-3m2/sc)4.4x 10-3m2/3d)2.8 x 10-3m2/sCorrect answer is option 'A'. Can you explain this answer?
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