solstate.htm (Ó R. Egerton)

Figure references are to the second edition of Modern Physics by Serway, Moses and Moyer

(Saunders Publishing, 1997)


Aspects of Solid-State Physics


Solid-state physics deals with the properties of solids, from the atomic level upwards. It is closely linked to materials science (which also explores the chemical and engineering aspects of materials) and to electronic device technology, which has had a profound influence on our way of life. Here we discuss some of the technological revoltions which have relied on solid-state physics for the basic discoveries and inventions.


The Semiconductor Revolution


The transistor was invented by scientists at Bell Laboratories in 1948 (they shared the 1956 Nobel prize for this discovery). It is a signal-amplification device which by 1960 had largely replaced vacuum tubes in radios, television receivers and other electronic equipment. The transistor is constructed from semiconducting material (originally the element germanium, now usually silicon) in single-crystal form, where the atoms regularly arranged on a crystal lattice. This regular arrangement acts like a diffraction grating to electrons; wave mechanics predicts that the electron energies must lie within certain regions (energy bands) separated by other regions (energy gaps) where the electrons are forbidden.


The electrical conductivity of pure (intrinsic) silicon or germanium is rather low at room temperature because there are just enough outer-shell atomic electrons (four per atom, each forming chemical bonds with the neighbouring atoms) to completely fill the valence band of energies. A full energy band means that the electrons cannot change their momentum in response to an electric field applied to the material. But if the temperature is raised, a few of the valence electrons will acquire enough energy to appear in a conduction band above the energy gap. Since the conduction band is nearly empty, these electrons can each contribute to current flow. Moreover, the spaces left in the valence band (known as holes) are also mobile; they behave like positively charged particles and give rise to hole conduction. As a result of the increasing electron and hole concentrations, the electrical conductivity of a pure semiconductor increases rapidly as its temperature is raised; see Fig. 11.22.


Another way of increasing the conductivity of a semiconductor is to add certain types of impurities (called dopants). If an atom with five electrons in its outer shell (such as arsenic) replaces a silicon atom in the crystal lattice, the fifth electron

does not form a chemical bond but remains free to wander about the crystal, giving rise to n-type conductivity. In terms of the energy-band picture, this electron appears in the conduction band because the arsenic atom creates an energy level (donor level) just below the bottom of the conduction band.

If however we add in trivalent impurity atoms such as indium, which has only three outer-shell electrons per atom, acceptor energy levels are created (just above the top of the valence band) which can capture an electron from the valence band, creating a hole which can contribute to electrical conduction. We then have a p-type semiconductor containing positive holes as the current carriers.


By diffusing in trivalent and pentavalent impurities into different regions, the conductivity of the semiconductor and the type of current carrier can be changed, in order to produce useful devices. For example a p-n structure forms a semiconductor diode which has rectifying properties: current can flow in one direction only, allowing an ac voltage or current to be converted to dc. A p-n-p or n-p-n structure can be used as an amplifying device (called a bipolar transistor because both electrons and holes are involved), as required in many analogue electronics applications.


A later invention was the field effect transistor, whose structure resembles a parallel-plate capacitor (containing an insulating dielectric) with one plate made of metal (the gate electrode) and the other a slab of semiconductor, along which a dc current is passed between source and drain electrodes. Applying a voltage to the gate induces an electric field in the dielectric which penetrates the semiconductor and changes its conductivity, leading to a change in the source-drain current. In this way, a relatively large amount of electrical power can be controlled by means of a small applied voltage (and negligible current).


Silicon wafers are made by slicing and polishing cylindrical-shaped single crystals (6 or 8 inches in diameter). By diffusing dopants into different regions of the wafer, integrated circuits (containing transistors, resistors and capacitors) can be made. Since field-effect and bipolar transistors may also be used as switches, such IC's form the microprocessors which control many modern electrical and electronic devices, including microwave ovens, video recorders, CD players and computers.


The Intel Pentium microprocessor contains several million transistors and can operate at high speed because the components have been made very small. The number of transistors on a single "silicon chip" is expected to reach 10^9 by the year 2000. Computer memory chips use field-effect transistors (as switches set to the "on" or "off" state) to store information, with high density if the individual transistors are made small. The patterns needed to control the various processing steps are generated by ultraviolet light, and the image resolution is therefore limited to about 0.3 micrometers. Beams of electrons and x-rays are being investigated for future patterning techniques, capable of yielding devices with even smaller dimensions.


One problem which gets worse as device sizes shrink is that of soft errors, caused by faulty operation of a transistor when a charged particle passes through it. These particles include cosmic rays and alpha-particles generated by radioactive decay of uranium and other unstable elements which may be present in trace amounts in the device packaging.




The phenomenon of superconductivity was discovered by Onnes in 1911, when he reduced the temperature of solid mercury below 4.3 K and found that its resistance vanished; see Fig.12.8. Since then, about half of the common chemical elements have been found to exhibit superconductivity, if cooled below a critical temperature Tc. The values of Tc vary from 0.0003K (for rhodium) to 9.5 K (for niobium).


Careful measurements show that the resistivity of a superconductor really is zero. For example, a persistent current, circulating in a superconducting loop of wire, showed no decrease after several years. If the resistance were non-zero, Joule heating would dissipate electrical power as heat and reduce the current flow. Quantum mechanics provides an explanation for this remarkable behaviour: below Tc, the electrons in a superconductor form Cooper pairs (with opposite spin) which are not scattered by atoms within a solid. In fact, the motion of all Cooper pairs is correlated; they form a single quantum-mechanical state. If the superconductor is warmed to a temperature exceeding Tc, the thermal energy of the solid disrupts each Cooper pair and normal conduction (with resistance) resumes.


Superconductors are useful because the persistent current can generate a constant magnetic field without consuming electrical power. Unfortunately, the magnetic field tends to destroy the superconductivity; there is a critical field Bc above which the superconductivity vanishes. The value of Bc depends on the temperature T (see Fig.12.9); it is a maximum at T=0K and decreases to zero at T=Tc. Therefore the windings of superconducting magnets must be cooled to temperature considerably below Tc in order to generate a usefully large magnetic field. Alloys containing niobium have been developed which have Tc as high as 23K and which support a magnetic fields of more than 20 Tesla at T = 4.2 K, the boiling point of liquid helium. Helium is used as the refrigerant in large magnets, such as those used for medical-resonance imaging (MRI scanning).


However, liquid helium is expensive (about $10/litre), whereas liquid nitrogen (boiling point 77k) is cheap and easier to handle. This situation created an incentive to develop superconductors with higher Tc. The first major progress in this direction came in 1986, when two scientists at the IBM Zurich laboratories created a superconductor containing lanthanum, barium, copper and oxygen with Tc > 30 K. The following year, scientists at the University of Texas replaced lanthanum by the element yttrium to give a superconductor (Y Ba2 Cu3 O7, generally known as YBCO) with Tc = 93 K. That same year, a superconducting compound containing bismuth, strontium, calcium, copper and oxygen (known as BSCCO) was found to form a phase having Tc = 110 K. Related compounds have been discovered with Tc up to 133 K. Collectively, these materials are known as high-temperature superconductors.


These discoveries have generated intense interest among physicists, partly out of a desire to understand the basic mechanism of high-temperature superconductivity. It is known that the current carriers are Cooper pais of holes and that conduction takes place along the copper-oxygen planes in these materials, but the mechanism which provides the attractive force within the Cooper pairs remains undecided.


The more general reason for interest in high-temperature superconductors is their possible applications. These include powerful magnets (for MRI, particle accelerators etc.), lossless transmission lines for electrical power, highly efficient motors and generators (where the resistive "copper losses" would be absent). However, all of the high-temperature superconductors are brittle ceramics; forming wires and coils from them has proved a formidable task.


Another remarkable property of superconductors is magnetic levitation: a magnet placed over a superconductor remains supended above its surface because any vertical fall oif the magnet induces circulating currents in the superconductor which oppose the motion. This has inspired designs for high-speed magnetically-levitated trains, which are currently being tested.


High-temperature superconductors are currently being used to construct resonant cavities used in microwave communication equipment. Other possible applications rely on the Josephson effect: if two pieces of superconductor are separated by a thin (<2nm) oxide layer, Cooper pairs can tunnel through the oxide gap, even in the absence of an applied voltage. If a dc voltage V is applied across the junction, an alternating current flows, whose frequency is f = (2e/h)V = 483.6 MHz for V = 1 microvolt. This allows small voltages to be measured reliably, since frequency can be measured with very high accuracy. A loop of superconductor which contains two Josephson junctions forms a superconducting quantum-interference device (SQUID) which is sensitive to small magnetic fields, such as those produced in the heart or brain.


Cold Fusion


Fusion refers to the ability of small atomic nuclei to fuse together to form a larger nucleus. The small decrease D m in mass (due to the increased binding energy pernucleon) gives rise to a large release (E=D m c^2) of energy. Fusion of hydrogen nuclei to form helium is the source of the energy output of the sun (4 x 10^26 W) and other stars. The fusion of tritium (detonated by the fission of uranium) is the basis of the "hydrogen" bomb.


For several decades, physicists have worked on schemes to control the fusion of hydrogen (or its isotopes) in order to generate energy, either as heat or electrical power. The task is not easy, since it involves the generation of very high temperatures. Hydrogen fusion is possible in the sun's core at a temperature of a few million Kelvin because of the large pressure and density, but hot fusion capable of generating electrical power in a fusion reactor requires temperatures of over 100 million Kelvin.


At these temperatures, the thermal energy greatly exceeds the ionization energy of an atom, so all matter exists as a plasma containing positively charged ions and negative electrons. Magnetic fields can be used to contain the plasma (to prevent it cooling by contact with the walls of a containment vessel) in a machine known as a tokomak, but there are numerous modes of instability which have made it difficult to achieve the necessary temperatures for a sufficient period of time to create useful energy from fusion reactions.


An alternative approach to hot fusion is inertial confinement, in which a large number of powerful laser beams converge to bombard a small plastic pellet containing a few milligrams of deuterium and tritium fuel. During the laser flash (lasting a few nanoseconds and containing a power level several times that of the combined electric power plants in the world), the pressure would rise to 10^12 atmospheres, generating a fuel density 10 times higher than that of lead and 10^10 times higher than that of a magnetically confined plasma.


Although both types of machine have generated fusion reactions, none has exceeded the breakeven point at which more power is liberated than used to heat the fuel. Since deuterium is a constituent of seawater, the supply of fuel is almost inexhaustible; a fusion reactor would generate radioactive by-products, but less than a fission reactor. Although many experts believe that power generation by hot fusion will eventually be feasible (and necessary), the required devlopment cost will likely be in the tens of $billion, and each machine is likely cost several $billion to build.


Given these costs and technical difficulties, it is not surprising that intense interest (among scientists and in the public media) was generated by a press conference given by Drs. Martin Fleischmann and Stanley Pons at the University of Utah on 23 March 1989. These researchers claimed to have observed fusion reactions at room temperature in a small electrolytic cell containing heavy water (deuterium oxide, D2O) and connected to a dc source of a few volts. The negative electrode of the cell was made of palladium, a metallic element which can absorb large quantities hydrogen or deuterium (many times its volume at room temperature), and it was suggested that deuterium nuclei within palladium metal get squeezed together close enough to initiate fusion.


The main evidence for fusion was that the heat output of the electrolytic cell (measured by calorimetry) exceeded the resistance heating by a factor between 1.05 and 2.1. However, the researchers claimed also to have detected neutrons coming form the cell (a normal result of fusion reactions), although only at a low level (three times the natural-radiation background). They also claimed to have detected tritium in the cell, in very small amounts but above the natural background.


Within days, many researchers around the world were trying to duplicate the experiments of Fleischmann and Pons. Some initially reported positive results, but major laboratories at Caltech, MIT, Princeton and Harwell (UK Atomic Energy Authority) came up with negative findings.


One of the criticisms concerned the relative lack of neutrons. At the power output claimed by Fleischmann and Pons (up to 26 W/cm^2), the number of fusion events would exceed 10^12 per second and since each fusionion should produce an energetic neutron, the resulting radiation dose should have been lethal. Experiments at Caltech showed the neutron output from an operating palladium electrode to be less than 2 per minute (a factor of 10^5 lower than reported by Fleischmann and Pons).


A more general criticism was the use of a press conference to announce major scientific results before these had been accepted by peer review and published in the scientific press. Fleischmann and Pons did publish an account of their first experiments in Journal of Electroanalytical Chemistry (10 May 1989, vol. 263, pp.187-188) but a paper which they sent to the journal Nature was criticised by the scientific reviewers and subsequently withdrawn.

Research on cold fusion continues, but on a small scale and privately funded. Because of the bad feeling created by the original discoveries, it is impossible to obtain government funding for cold-fusion research.

Further reading:

The Breakthrough: the Race for the Superconductor, by R.M. Hazen (Summit Books, 1988)

Fire from Ice: Searching for the Truth behind the Cold Fusion Furor, by E.F. Mallove (Wiley, 1991).

Cold Fusion: The Scientific Fiasco of the Century, by J.R. Huizenga (Oxford University Press, 1993).