Introduction N THE FACE OF IT, "SOLID-STATE PLASMA" is a O contradiction in terms. How can one have a plasma (a word derived from the Greek, meaning "plastic" or "fluid" and used to describe a collec­ CYCLOTRON RESONANCE IN tion of mobile charged particles) and simultane­ SOLID-STATE PLASMA ously a solid, manifestly a crystalline collection of atoms rigidly fixed in a uniform lattice? The answer T.O. Poehler and J.R. Ape! is to be found in the collective behavior of electrons in the material. Crystals (except for insulators) contain a number of electrons free to wander about between lattice sites. These electrons are largely responsible for the current-carrying properties of the solid; they also contribute to the infrared and optical characteris­ prototype controlled thermonuclear reactors under tics of the material in a way that depends, among study by gas plasma physicists the world over. other things, upon their concentration nco The pro­ In most of these applications, an externally­ gression from a nearly insulating, optically trans­ imposed magnetic field B plays an important role­ parent crystal such as diamond, through the silver­ it establishes in the solid a second characteristic sheened semiconductors like silicon or germanium, frequency, the electron cyclotron frequency We = to the highly conducting metals is best typified by eB/ mc, where B is the magnetic field in gauss and a monotonic increasing electron concentration. At c is the velocity of light. Recall that this frequency any concentration, there exists a characteristic fre­ is the angular rate at which an electron gyrates in quency W p , the plasma frequency, equal to (47rnce2 / a magnetic field; it also causes a striking aniso­ mEL) !, for which the crystal becomes transparent to tropy in the propagation features of any electro­ electromagnetic radiation of angular frequency magnetic wave traversing the sample. It may serve w> Wp. Here e and m are the carrier charge and to control and channel the plasma in somewhat effective mass respectively, and El is the lattice or the same fashion as occurs in a magnetically con­ background dielectric constant. In impure diamond fined gas plasma. It is this magnetic field that lends at room temperature, Wp may be in the radiofre­ much of the interest to the subject, allowing not quency range; in semiconductors, it is in the infra­ only variety and flexibility in the devices that utilize red, while in the alkali metals (Na, K, etc.), it lies it, but introducing, as it does, significant changes in in the near-ultraviolet. The existence of this ubiqui­ the quantum states of a conduction electron and in tous cutoff frequency at which reflection of electro­ its interaction with the other fundamental excita­ magnetic waves occurs is due to a cooperative, tions of the solid-photons, phonons, plasmons, fluid-like motion of the conduction electrons and and the like. It is to the investigation of such inter­ holes in response to the waves; it is this collective actions that the solid-state plasma activity at the response, virtually identical to that existing in Applied Physics Laboratory is addressed. ionized gas plasma, that leads to the name "solid­ state plasma" for mobile carriers. Semiconductor Properties Why is one interested in solid-state plasmas? The majority of the experiments described here Aside from the usual scientific reasons falling under have been conducted in those materials called com­ the heading of Natural Philosophy, there are com­ pound semiconductors.l These materials are gener­ pelling practical motivations well known to tech­ ally binary compounds between elements of groups nologists: Devices. By properly utilizing the plasma II and VI, or groups III and V of the periodic table, characteristics of certain semiconductors, one such as GaAs and InSb. These semiconductors might hope to construct miniaturized microwave crystallize in the zinc-blende or wurtzite structures and infrared sources, magnetically-tuned lasers which are similar to the diamond structure of the and band-pass filters, sensitive infrared and optical detectors and, to a limited extent, small-sized solid­ 1 Physics of III-VI Compounds, Willardson and Beer, Ed., Academic state analogs to the very large (and hence expensive) Press, New York, 1966. 2 APL T echnical Digest band, or by excitation of free carriers from im­ purity levels in the energy gap between bands. At room temperatures both carrier generation mecha­ nisms contribute to the conductivity, but at low Electrons and holes in a semiconductor form a solid-state temperatures where the thermal excitation of car­ plasma having many unusual features. When cooled to low riers across the band gap becomes negligible, the temperatures and placed in a large magnetic field, such a plasma interacts with far-infrared laser radiation and with free charge carriers are predominantly those excited ionized impurities in a distinctly quantum-mechanical fashion. from impurity levels. Since a given semiconductor material usually has either a large number of donor impurities contributing excess electrons to the con­ duction band, or a large number of acceptor im­ purities leading to holes in the valence band, low temperature conduction is generally controlled predominantly by one type of carrier. The relation between current density and electric elemental semiconductors, germanium and silicon. The energy band structure of these compounds is field, J = nce/J- nE, (for conduction by electrons) is analogous in many respects to that of the elemental not in general a linear one. At high electric fields semiconductors because of the close relationship and low lattice temperatures, electrons may gain of the crystal structures. sufficient energy from the field to ionize previously neutral impurity atoms on collision in the so-called The energy band structure of a semiconductor is impact ionization process. The electrons which have an important factor in determining the movement of charge carriers causing a transport of charge or derived extra energy from the electric field can also energy through the material. Under the influence be considered to be at a higher temperature than the background lattice-these are called hot elec­ of an electric field E, the electrons and holes move trons. Since the mobility is a function of tempera­ in opposite directions along the field leading to a ture, these electrons will have a mobility which current density J, where J = uE = e(nc/J-n + p/J-p)E. depends on the applied field strength. Thus, there Here the conductivity, u, is related to nc and p , the will be increasing deviations from a linear equation concentration of electrons and holes respectively, at high electric fields through variations in both and /J-n and /J-p are the respective mobilities of these carrier concentration and the mobility. charge carriers. The quantity which characterizes charge transport is the mobility, /J-, which is the As a class the III-V compound semiconductors ratio of the average velocity of the carriers to the are typified by a wide range of energy gaps, low electric field strength; further, /J- = eT / m, where m effective electronic masses, high electron mobilities, is the effective mass of the carriers and T the mean and high conductivity. These characteristics are time between collisions. At room temperature the shown quantitatively in Table 1. The number of mobility in relatively pure semiconductors is lim­ charge carriers ni in an intrinsic semiconductor de­ ited owing to scattering of electrons and holes by pends on the energy gap (, y and the temperature T acoustic or optical phonons, the quantized vibra­ in an exponential fashion, that is, ni ex: exp( - (,y / tional excitations of the crystal lattice. In compound 2kBT) where kB is Boltzmann's constant. Most of semiconductors, scattering of carriers by optical the compounds have sufficiently large energy gaps phonons plays the dominant role while at low tem­ that the number of carriers in a pure material peratures the limit on mobility is determined by should be quite small. However, as the temperature scattering by ionized impurities. The mobility at a is reduced the carrier concentration in each of these given temperature and impurity concentration is materials reaches a constant value essentially inde­ then given by pendent of temperature. The cause of this excessive minimum value is the existence of imperfections in 1/ /J- = 1/ /J-impurity 1/ /J-I attice. + the structure of the crystal. The imperfections can The charge carriers contributing to the conduc­ be either in the form of foreign impurity atoms tivity arise either through the creation of an elec­ introduced into the crystal or deviations from tron-hole pair by excitation of an electron from stoichiometry, that is, where the elements in the the uppermost valence band to the conduction compound are present in an improper proportion. May - June 1970 3 TABLE 1 PROPERTIES OF COMPOUND SEMICONDUCTORS Energy Plasma Debye ~ffective - Mobility Conductivity Compound Electron Gap Frequency Length (cm2 I V-sec) (fl-cm)-I Mass * (eV) (sec-I) (cm) InSb 0.014 0.18 78,000 100 1 X 1012 1. 5 X 10-5 InAs 0.022 0.33 33,000 50 8 X 1012 1. 5 X 10-6 InP 0.067 1. 25 4,600 10 4 X 1012 5 X 10-6 GaSb 0.047 0.67 4,000 25 6 X 1012 7 X 10- 6 GaAs 0.068 1.4 8,800 10 1 X 1012 1 X 10-5 HSI_",Cd",Te 0.005 0.13 60,000 100 1. 5 X 1013 1 X 10-6 (x=0.18) * In units of the free electron mass mo. At room temperature, carriers are thermally excited or holes. With these, the neutralizing charges are from these defect or impurity levels into the con­ fixed ions of opposite sign and the plasma proper­ duction or valence bands causing an excess of ~ar­ ties are established by one type of mobile charge riers above the intrinsic concentration.