Chapter 10: Q49E (page 469)
In Figure 10.24, the n=1 band ends at , while in Figure 10.27 it ends at
It is proved that two ends are compatible.
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Assuming an interatomic spacing of 0.15 nm, obtain a rough value for the width (in eV) of the band in a one-dimensional crystal.
Question:In Chapter 4. we learned that the uncertainty principle is a powerful tool. Here we use it to estimate the size of a Cooper pair from its binding energy. Due to their phonon-borne attraction, each electron in a pair (if not the pair's center of mass) has changing momentum and kinetic energy. Simple differentiation will relate uncertainty in kinetic energy to uncertainty in momentum, and a rough numerical measure of the uncertainty in the kinetic energy is the Cooper-pair binding energy. Obtain a rough estimate of the physical extent of the electron's (unknown!) wave function. In addition to the binding energy, you will need to know the Fermi energy. (As noted in Section 10.9, each electron in the pair has an energy of about EF.) Use 10-3 eV and 9.4 eV, respectively, values appropriate for indium.
Question: The photons emitted by an LED arise from the energy given up in electron-hole recombinations across the energy gap. How large should the energy gap be to give photons at the red end of the visible spectrum (700nm) ?
Question: The diagram shows the energy bands of a tunnel diode as the potential difference is increased. In this device high impurity atom density causes the occupied donor and unoccupied acceptor levels to spread into impurity bands which overlap respectively the n-type conduction- and the p-type valence bands. In all unbiased diodes, the depletion zone between the n-type and p-type bands constitutes a potential barrier (see Section 6.2) but in the tunnel diode it is so thin that significant tunnelling occurs. The current versus voltage plot shows that unlike a normal diode significant current begins to flow as soon as there is an applied voltage—before the bias voltage is Egap /e. It then decreases (so called negative resistance) before again increasing in the normal way. Explain this behavior.
Exercise 29 outlines how energy may be extracted by transferring an electron from an atom that easily loses an electron from an atom that easily loses an electron to one with a large appetite for electrons , then allowing the two to approach , forming an ionic bond.
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