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Chapter 5: Problem 24

At a certain temperature, the electron and hole mobilities in intrinsic germanium are given as \(0.43\) and \(0.21 \mathrm{~m}^{2} / \mathrm{V} \cdot \mathrm{s}\), respectively. If the electron and hole concentrations are both \(2.3 \times 10^{19} \mathrm{~m}^{-3}\), find the conductivity at this temperature.

Short Answer

Expert verified
Answer: The conductivity at this temperature is \(15.84 ~ S / m\).

Step by step solution

01

Identify given values

First, we need to identify the given values in the problem: - Electron mobility, \(\mu_e = 0.43 ~ m^2 / (V \cdot s)\) - Hole mobility, \(\mu_h = 0.21 ~ m^2 / (V \cdot s)\) - Electron concentration, \(n_e = 2.3 \times 10^{19} ~ m^{-3}\) - Hole concentration, \(n_h = 2.3 \times 10^{19} ~ m^{-3}\) - Elementary charge, \(e = 1.6 \times 10^{-19} ~ C\)
02

Write the formula for conductivity

Next, we write the formula for conductivity: $$ \sigma = e(n_{e}\mu_{e} + n_{h}\mu_{h}) $$
03

Substitute given values into the formula

Now, we substitute the given values into the formula: $$ \sigma = (1.6 \times 10^{-19})(2.3 \times 10^{19} \times 0.43 + 2.3 \times 10^{19} \times 0.21) $$
04

Calculate the conductivity

Finally, we calculate the conductivity: $$ \sigma = (1.6 \times 10^{-19})(9.9 \times 10^{19}) $$ $$ \sigma = 15.84 \times 10^{0} ~ S / m $$ $$ \sigma = 15.84 ~ S / m $$ The conductivity at this temperature is \(15.84 ~ S / m\).

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Most popular questions from this chapter

Two equal but opposite-sign point charges of \(3 \mu \mathrm{C}\) are held \(x\) meters apart by a spring that provides a repulsive force given by \(F_{s p}=12(0.5-x) \mathrm{N}\). Without any force of attraction, the spring would be fully extended to \(0.5 \mathrm{~m}\). (a) Determine the charge separation. (b) What is the dipole moment?

Let the surface \(y=0\) be a perfect conductor in free space. Two uniform infinite line charges of \(30 \mathrm{nC} / \mathrm{m}\) each are located at \(x=0, y=1\), and \(x=0, y=2 \cdot(a)\) Let \(V=0\) at the plane \(y=0\), and find \(V\) at \(P(1,2,0)\). (b) Find \(\mathbf{E}\) at \(P\).

A coaxial conductor has radii \(a=0.8 \mathrm{~mm}\) and \(b=3 \mathrm{~mm}\) and a polystyrene dielectric for which \(\epsilon_{r}=2.56 .\) If \(\mathbf{P}=(2 / \rho) \mathbf{a}_{\rho} \mathrm{nC} / \mathrm{m}^{2}\) in the dielectric, find (a) \(\mathbf{D}\) and \(\mathbf{E}\) as functions of \(\rho ;(b) V_{a b}\) and \(\chi_{e} \cdot(c)\) If there are \(4 \times 10^{19}\) molecules per cubic meter in the dielectric, find \(\mathbf{p}(\rho)\)

A coaxial transmission line has inner and outer conductor radii \(a\) and \(b\). Between conductors \((a<\rho

Two perfectly conducting cylindrical surfaces of length \(\ell\) are located at \(\rho=3\) and \(\rho=5 \mathrm{~cm}\). The total current passing radially outward through the medium between the cylinders is 3 A dc. (a) Find the voltage and resistance between the cylinders, and \(\mathbf{E}\) in the region between the cylinders, if a conducting material having \(\sigma=0.05 \mathrm{~S} / \mathrm{m}\) is present for \(3<\rho<5 \mathrm{~cm}\). (b) Show that integrating the power dissipated per unit volume over the volume gives the total dissipated power.
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