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CHAPTER 11 Semiconductor Theory and Devices. 11.1 Band Theory of Solids 11.2 Semiconductor Theory 11.3 Semiconductor Devices 11.4 Nanotechnology.
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It is evident that many years of research by a great many people, both before and after the discovery of the transistor effect, has been required to bring our knowledge of semiconductors to its present development. We were fortunate to be involved at a particularly opportune time and to add another small step in the control of Nature for the benefit of mankind.
- John Bardeen, 1956 Nobel lecture
In this chapter we concentrate on electrical conduction.
There is a different conduction mechanism for semiconductors than for normal conductors.
Figure 11.1: (a) Resistivity versus temperature for a typical conductor. Notice the linear rise in resistivity with increasing temperature at all but very low temperatures. (b) Resistivity versus temperature for a typical conductor at very low temperatures. Notice that the curve flattens and approaches a nonzero resistance as T→ 0. (c) Resistivity versus temperature for a typical semiconductor. The resistivity increases dramatically as T → 0.
An atom in the symmetric state has a nonzero probability of being halfway between the two atoms, while an electron in the antisymmetric state has a zero probability of being at that location.Band Theory of Solids
Thus there is a splitting of all possible energy levels (1s, 2s, and so on).
When more atoms are added (as in a real solid), there is a further splitting of energy levels. With a large number of atoms, the levels are split into nearly continuous energy bands, with each band consisting of a number of closely spaced energy levels.Band Theory of Solids
Each potential well models attraction to an atom in the lattice, so the size of the wells must correspond roughly to the lattice spacing.Kronig-Penney Model
where the wave number k is given by the usual relation:Kronig-Penney Model
Here K is another wave number.Kronig-Penney Model
Plotting this it is observed there exist restricted (shaded) forbidden zones for solutions.Kronig-Penney Model
Figure 11.5 (a) Plot of the left side of Equation (11.3) versus ka for κ2ba / 2 = 3π / 2. Allowed energy values must correspond to the values of k for
for which the plotted function lies between -1 and +1. Forbidden values are shaded in light blue. (b) The corresponding plot of energy versus ka for κ2ba / 2 = 3π / 2, showing the forbidden energy zones (gaps).
The result is a semiconductor.
β = (kT)−1 and EF is the Fermi energy.
Only those electrons that have jumped from the valence band to the conduction band are available to participate in the conduction process in a semiconductor. More and more electrons are found in the conduction band as the temperature is increased, and the resistivity of the semiconductor therefore decreases.
where A, B, and K are constants.
Figure 11.7: (a) An experimental test of the Clement-Quinnell equation, using resistance versus temperature data for four standard carbon resistors. The fit is quite good up to 1 / T≈ 0.6, corresponding to T ≈ 1.6 K. (b) Resistance versus temperature curves for some thermometers used in research. A-B is an Allen-Bradley carbon resistor of the type used to produce the curves in (a). Speer is a carbon resistor, and CG is a carbon-glass resistor. Ge 100 and 1000 are germanium resistors. From G. White, Experimental Techniques in Low Temperature Physics, Oxford: Oxford University Press (1979).
Examples of intrinsic semiconductors include pure carbon and germanium.
Thus while four of arsenic’s outer-shell electrons participate in covalent bonding with its nearest neighbors (just as another silicon atom would), the fifth electron is very weakly bound.
It takes only about 0.05 eV to move this extra electron into the conduction band.
The new arsenic energy levels just below the conduction band are called donor levels because an electron there is easily donated to the conduction band.
where Q is called the thermoelectric power.
This is the Thomson Effect.
Here heat is generated if current flows toward the higher temperature and absorbed if toward the lower.
This difference makes possible the operation of a thermocouple.
We call these situations forward bias and reverse bias, respectively.
Figure 11.12: The operation of a pn-junction diode. (a) This is the no-bias case. The small thermal electron current (It) is offset by the electron recombination current (Ir). The net positive current (Inet) is zero. (b) With a DC voltage applied as shown, the diode is in reverse bias. Now Ir is slightly less than It. Thus there is a small net flow of electrons from p to n and positive current from n to p. (c) Here the diode is in forward bias. Because current can readily flow from p to n, Ir can be much greater than It. [Note: In each case, It and Ir are electron (negative) currents, but Inet indicates positive current.]
Figure 11.14: Circuit diagram for a diode bridge rectifier.
Figure 11.16: A Zener diode reference circuit.
Figure 11.15: A typical I-V curve for a Zener diode.
Figure 11.17: Schematic of an LED. A photon is released as an electron falls from the conduction band to the valence band. The band gap may be large enough that the photon will be in the visible portion of the spectrum.
Figure 11.18: (a) Schematic of a photovoltaic cell. Note the similarity to Figure 11.17. (b) A schematic showing more of the working parts of a real photovoltaic cell. From H. M. Hubbard, Science 244, 297-303 (21 April 1989).
Figure 11.22: (a) In the npn transistor, the base is a p-type material, and the emitter and collector are n-type. (b) The two-diode model of the npn transistor. (c) The npn transistor symbol used in circuit diagrams. (d) The pnp transistor symbol used in circuit diagrams.
Figure 11.23: (a) The npn transistor in a voltage amplifier circuit. (b) The circuit has been modified to put the input between base and ground, thus making a current amplifier. (c) The same circuit as in (b) using the transistor circuit symbol.
Figure 11.25: (a) A schematic of a FET. The two gate regions are connected internally. (b) The circuit symbol for the FET, assuming the source-to-drain channel is of n-type material and the gate is p-type. If the channel is p-type and the gate n-type, then the arrow is reversed. (c) An amplifier circuit containing a FET.
This will happen as long as the work function of the metal is higher (or lower, in the case of a p-type semiconductor) than that of the semiconductor.
Figure 11.26: (a) Schematic drawing of a typical Schottky-barrier FET. (b) Gain versus frequency for two different substrate materials, Si and GaAs. From D. A. Fraser, Physics of Semiconductor Devices, Oxford: Clarendon Press (1979).
A photon is emitted when an electron falls back to the valence band to recombine with the hole.
One advantage of using semiconductor lasers in this application is their small size with dimensions typically on the order of 10−4 m.
Being solid-state devices, they are more robust than gas-filled tubes.Semiconductor Lasers
Figure 11.29: Moore’s law, showing the progress in computing power over a 30-year span, illustrated here with Intel chip names. The Pentium 4 contains over 50 million transistors. Courtesy of Intel Corporation. Graph from http://www.intel.com/research/silicon/mooreslaw.htm.
Figure 11.30: Model of a carbon nanotube, illustrating the hexagonal carbon pattern superimposed on a tubelike structure. There is virtually no limit to the length of the tube. Fromhttp://www.hpc.susx.ac.uk/~ewels/img/science/nanotubes/.
In a multi-walled nanotube, multiple layers are nested like the rings in a tree trunk.
Single-walled nanotubes tend to have fewer defects, and they are therefore stronger structurally but they are also more expensive and difficult to make.Carbon Nanotubes
These are referred to as nanotransistors.Nanoscale Electronics
Examples of unusual materials designed for specific purposes include the molecules that make up claws, feathers, and even tooth enamel.