Assume a temperature of 293 K and fi nd the value Vof the bias voltage in Equation

Why is the free-electron model not applicable to semiconductors and insulators?

How does a semimetal differ from a normal conductor?

Compare the resistivities of conductors, semiconductors, and insulators at room temperature.

Why does the addition of impurities to a conductor increase its resistivity, whereas the addition of impurities to a semiconductor generally decreases its resistivity?

Would you expect carbon resistors to be useful as thermometers at room temperature and above? Explain.

Why are semiconductors referred to as non-ohmic?

Use the size of the energy gap to decide whether the following should tend to be transparent to visible light: conductors, semiconductors, and insulators.

Repeat Question 7 considering near-infrared light with  1 m.

A semiconductor has an energy gap Eg. Explain what happens when the semiconductor is bombarded with electromagnetic radiation with wavelength l  hc/Eg. Repeat for l hc/Eg.

Describe the effect of high temperatures on a semiconductor diode.

What role do capacitors play in the conversion of alternating current to direct current?

Why is it appropriate to think of a photovoltaic cell as an LED operating in reverse?

What are some possible applications of carbon nanotubes?

Why are quantum effects important in electronic circuits that are nanometers in size but not in those circuits microns in size?

Explain why the size of the band gap in a quantum dot decreases as the size of the dot increases.

A single-walled carbon nanotube has 2.3 1019 carbon atoms per m2 along its surface. The nanotube diameter is 1.4 nm. (a) Find the mass density of the nanotube in kg/m3. (b) Compare your answer to (a) with the density of steel, about 7800 kg/m3.

Using the data in the preceding problem, fi nd the density of a nanotube peapod that also contains one buckyball (C60) for each nm of its length.

The Fermi-Dirac factor is expressed in Equation (9.34) as FFD  1 exp3b1E EF 2 4  1 In a semiconductor or insulator, with an energy gap Eg between the valence and conduction bands, we can take EF to be halfway between the bands, so that EF  Eg/2. (a) Show that for a typical semiconductor or insulator at room temperature the Fermi-Dirac factor is approximately equal to exp (Eg/2kT). (b) Use the result in (a) to compute the Fermi-Dirac factor for a typical insulator, with Eg  8.0 eV at T  300 K. (c) Repeat for a semiconductor, silicon, with Eg  1.11 eV at T  293 K. (d) Your result in (c) is still small, but suffi ciently large to explain why there will be conduction. Explain.

Consider what happens when silicon is doped with arsenic. Suppose that the extra, weakly bound electron from arsenic moves in the fi rst Bohr orbit in a silicon atom. The fi rst Bohr orbit has a radius of a0  4pP0U2 me 2 Because of the effects of screening, it is necessary to replace 0 with the electric permittivity  0, where  is the dielectric constant (  11.7 for silicon). (a) Compute the effective Bohr radius for this electron. (b) Compare your result with the lattice spacing in silicon, about 0.235 nm, and comment on the result.

Follow the same procedure as in Problem 19 to fi nd the binding energy E0 for the fi rst Bohr orbit of the extra electron in silicon. Comment on the result.

(a) Use the thermocouple data in Table 11.3 and a computer to perform a linear least-squares fi t of voltage versus temperature for the range 0C to 50C and for the range 50C to 100C. Over which range is the fi t better? (b) Repeat your analysis of (a), this time using a second-order least-squares fi t (voltage will be a function of T and T 2). Compare your results with those you obtained in (a).

A certain diode has a reverse bias current of 1.05 A. Now this diode is connected in forward bias in the circuit shown below, in series with a resistor and with a constant voltage source of 6.0 volts. (a) Find the value of resistance R such that a current of 140 mA will fl ow at room temperature (293 K). (b) Under the condition described in (a), fi nd the voltage drop across the resistor.

Assume a temperature of 293 K and fi nd the value V of the bias voltage in Equation (11.9) where (a) I  7I0 and (b) I  0.7I0.

A light-emitting diode made of the semiconductor GaAsP gives off red light (  650 nm). Determine the energy gap for this semiconductor.

How large an energy gap is required for a GaN laser used in a Blu-ray DVD player?

(a) Find the length of each side of a square computer chip with 580 million transistors, if each transistor occupies a square of side 45 nm. (b) Find the number of transistors on a chip of the same size you found in (a) if the transistor size can be reduced to 32 nm on a side.

Early research on semiconductor materials focused on silicon and germanium, which have band gaps of 1.11 eV and 0.67 eV, respectively. (a) Use the result of Problem 18a to compute the Fermi-Dirac factor for silicon and germanium at T  0C and T  75C. (This represents a fair temperature range for semiconductors in use.) On the basis of your computed value for FFD for germanium at the higher temperature, explain why silicon is preferred in most applications.

Suppose the average solar fl ux reaching the United States is 200 W/m2 . This average is taken over a whole year, and takes into account seasonal effects and weather (clouds), and assumes fi xed solar cells. (a) Find the total energy produced in one year by a 1-m2 cell producing energy with an effi ciency of 15%. (b) How much area would have to be covered with these solar cells to supply the United States with all its electricity, if the yearly electrical energy consumption in the United States is about 4.0 1012 kW # h? (c) Real solar arrays require about 2.5 times as much area as you found in (b) in order to keep one array of cells from shading another. What fraction of the land area of the United States (about 9 106 km2 ) would have to be covered with solar cells to meet the nations energy requirements?

In this problem you will examine the temperature dependence of the forward/reverse bias modes of a diode. (a) For a pn-junction diode compute the ratio of forward bias current to reverse bias current with an applied voltage of 1.50 volts at each of the following temperatures: 77 K, 273 K, 350 K, 600 K. (b) Comment on the results with respect to possible applications.

Pure silicon is used as a photon detector. An incoming photon can strike the surface and excite electrons from the valence band to the conduction band, where they can be counted. (a) Compute the number of electrons you would expect to count if a silicon detector is struck with a 1.04-MeV gamma ray produced in the decay of a 136Cs nucleus. (b) Explain why the counting of electrons should be more precise if the detector is cooled well below room temperature.

Suppose you apply the same voltage, 250 mV, to a pn-junction diode, fi rst in forward bias and then in reverse bias, at room temperature (293 K). What is the ratio of currents in forward and reverse bias?

A carbon nanotube has a diameter of 1.6 nm. Youngs modulus for the nanotube is 1050 GPa. With one end of the tube fi xed, how large a force must be applied to the other end to increase the tubes length by 1%?

A DVD has an effective inner radius of 2.3 cm and outer radius of 5.8 cm. The disks capacity is 4.7 gigabytes, where 1 byte  8 bits. Find the number of bits stored per square meter, and compare with the density on a magnetic device, 1 1013 bits/m2.

A Blu-ray DVD has the same dimensions as the DVD described in the preceding problem, but it can store 25 gigabytes of information. If the width of each track of the Blu-ray DVD is 320 nm, what is the average bit length?

The Nevada Solar One solar thermal power plant covers a land area of 140 hectares and has an estimated peak output of 64 MW. If the peak solar fl ux reaching the surface of that part of Nevada is about 630 W/m2, what is the net effi ciency of the power plant? Compare your answer with some of the higher effi ciencies of semiconductor solar cells described in the text.

A quantum dot is composed of CdS, with a density of 4820 kg/m3. (a) Find the number of atoms in a spherical quantum dot of radius 2.50 nm. (b) Model the energy levels of a quantum dot as a one-dimensional infi - nite potential well of 2.0-nm width. What is the lowest energy level in this well? (c) What is the band gap between the n  5 and n  6 levels?