Chapter 18: Problem 43
Briefly describe electron and hole motions in a \(p-n\) junction for forward and reverse biases; then explain how these lead to rectification.
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Chapter 18: Problem 43
Briefly describe electron and hole motions in a \(p-n\) junction for forward and reverse biases; then explain how these lead to rectification.
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Briefly tell what is meant by the drift velocity and mobility of a free electron.
We noted in Section \(12.5\) (Figure \(12.22\) ) that in \(\mathrm{FeO}\) (wüstite), the iron ions can exist in both \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also noted that in order to retain electroneutrality, one \(\mathrm{Fe}^{2+}\) vacancy will be created for every two \(\mathrm{Fe}^{3+}\) ions that are formed; consequently, in order to reflect the existence of these vacancies the formula for wüstite is often represented as \(\mathrm{Fe}_{(1-x)} \mathrm{O}\), where \(x\) is some small fraction less than unity. In this nonstoichiometric \(\mathrm{Fe}_{(1-x)} \mathrm{O}\) material, conduction is electronic, and, in fact, it behaves as a \(p\)-type semiconductor. That is, the \(\mathrm{Fe}^{3+}\) ions act as electron acceptors, and it is relatively easy to excite an electron from the valence band into an \(\mathrm{Fe}^{3+}\) acceptor state, with the formation of a hole. Determine the electrical conductivity of a specimen of wüstite that has a hole mobility of \(1.0 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{V} \cdot \mathrm{s}\) and for which the value of \(x\) is \(0.060\). Assume that the acceptor states are saturated (i.e., one hole exists for every \(\mathrm{Fe}^{3+}\) ion). Wüstite has the sodium chloride crystal structure with a unit cell edge length of \(0.437 \mathrm{~nm}\).
(a) Using the data in Table \(18.1\), compute the resistance of a copper wire \(3 \mathrm{~mm}(0.12\) in.) in diameter and \(2 \mathrm{~m}(78.7 \mathrm{in}\).) long. (b) What would be the current flow if the potential drop across the ends of the wire is \(0.05 \mathrm{~V}\) ? (c) What is the current density? (d) What is the magnitude of the electric field across the ends of the wire?
At room temperature the electrical conductivity of \(\mathrm{PbTe}\) is \(500(\Omega \cdot \mathrm{m})^{-1}\), whereas the electron and hole mobilities are \(0.16\) and \(0.075 \mathrm{~m}^{2} / \mathrm{V} \cdot \mathrm{s}\), respectively. Compute the intrinsic carrier concentration for PbTe at room temperature.
A hypothetical metal is known to have an electrical resistivity of \(4 \times 10^{-8}(\Omega \cdot \mathrm{m})\). Through a specimen of this metal that is \(25 \mathrm{~mm}\) thick is passed a current of \(30 \mathrm{~A}\); when a magnetic field of \(0.75\) tesla is simultaneously imposed in a direction perpendicular to that of the current, a Hall voltage of \(-1.26 \times\) \(10^{-7} \mathrm{~V}\) is measured. Compute (a) the electron mobility for this metal and (b) the number of free electrons per cubic meter.
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