The theory for a new form of transistor is presented. This transistor is of the "field-effect" type in which the conductivity of a layer of semiconductor is modulated by a transverse electric field. Since the amplifying action involves currents carried pre-dominantly by one kind of carrier, the name "unipolar" is proposed to distinguish these transistors from point-contact and junction types, which are "bipolar" in this sense. Regarded as an analog for a vacuum-tube triode, the unipolar field-effect transistor may have a m? of 10 or more, high output resistance, and a frequency response higher than bipolar transistors of comparable dimensions.

A Unipolar "Field-Effect" Transistor

This paper reviews the experimental studies of displacive phase transitions in solids. Primary emphasis is upon inelastic light scattering and neutron scattering; related infrared reflectivity measurements, as well as x-ray and EPR analyses are also summarized. Several prototype structures are considered in detail: (1) the rocksalt IV-VI semiconductors PbTe, SnTe, and GeTe; (2) the ferroelectric perovskites exemplified by PbTi${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$; (3) perovskites which exhibit cell-doubling transitions, such as LaAl${\mathrm{O}}_{3}$, SrTi${\mathrm{O}}_{3}$, and KMn${\mathrm{F}}_{3}$; (4) crystals having the $\ensuremath{\alpha}$-quartz structure, including Ge${\mathrm{O}}_{2}$, Si${\mathrm{O}}_{2}$, and AlP${\mathrm{O}}_{4}$; (5) the "improper ferroelectrics" ${\mathrm{Gd}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$ and ${\mathrm{Tb}}_{2}$${(\mathrm{M}\mathrm{o}{\mathrm{O}}_{4})}_{3}$; (6) the V-VI-VII semiconductors typified by SbSI; (7) the hydrogen-bonded ferroelectrics of the K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ family; (8) Jahn-Teller systems such as DyV${\mathrm{O}}_{4}$ and RbCo${\mathrm{F}}_{3}$, in which structural distortions occur as secondary effects; (9) order-disorder systems such as NaN${\mathrm{O}}_{2}$ and the ammonium halides (N${\mathrm{H}}_{4}$Cl, N${\mathrm{H}}_{4}$Br), in which no "soft mode" occurs in the spectral region ($\ensuremath{\omega}g{10}^{11}$ Hz) probed by ir, Raman, and neutron spectroscopy; (10) $\ensuremath{\beta}$-tungsten ($A\ensuremath{-}15$) structures such as ${\mathrm{V}}_{3}$Si and ${\mathrm{Nb}}_{3}$Sn, which exhibit high-temperature superconductivity. These crystal categories are used to illustrate several phenomena of current physical interest: Specifically, we discuss harmonic and anharmonic mode coupling; "critical exponents" $\ensuremath{\beta}$ differing from one-half in the temperature dependences of the order parameter $\ensuremath{\phi}(T)={\ensuremath{\phi}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$ and of the soft-mode frequency $\ensuremath{\omega}(T)={\ensuremath{\omega}}_{0}{(T\ensuremath{-}{T}_{0})}^{\ensuremath{\beta}}$; and the recently discovered "central" modes centered at zero frequency, which grow in intensity as the transition temperature ${T}_{0}$ is approached from above or below. The review covers the period 1940-1972. A few 1973 works are mentioned for which the author had preprints in 1972 or very early 1973. This review is in no sense a comprehensive survey of ferroelectricity. Readers are referred to the following earlier reviews on that subject: Silverman (1966, 1969), Cochran and Cowley (1967), Blinc (1968), Murzin et al. (1968), Nettleton (1970), and Blinc and Zaks (1972).

Soft-mode spectroscopy: Experimental studies of structural phase transitions

It is shown that the observed falloff in the f T of a transistor at high currents is due to the spreading of the neutral base layer into the collector region of the device at high current densities. The base layer spreading mechanism derives from an analysis of the effect of the current-dependent buildup of the mobile-carrier space-charge density in the collector transition layer. Calculations show that at sufficiently high collector current levels, the mobile space-charge density in the collector transition layer cannot be considered negligible in comparison to the fixed charge density of that region. The over-all effect of taking the mobile space charge into account in analyzing the collector transition region is that, at high current densities, the transition region boundary adjacent to the neutral base layer is displaced toward the collector metal contact with increasing collector current. The attendant widening of the neutral base layer results in the observed, high-current falloff in f T . The application of this theory to transistor structures of both the alloy and mesa variety yields, in each case, calculated curves of f T vs I c which are in reasonably good agreement with experiment.

A theory of transistor cutoff frequency (f T ) falloff at high current densities

The electron current in a semiconductor at uniform lattice temperature ${T}_{0}$, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion. The first two terms involve the mobility and diffusion coefficient which are functions of the electron temperature $T$ or, more generally, depend on certain averages over the nonequilibrium, field-dependent electron energy distribution function. The third term is due to the electron temperature gradient and is analogous to conventional thermal diffusion of a gas in a temperature gradient. In conventional theory, which neglects electron heating or cooling, the mobility and diffusion coefficient are material constants and thermal diffusion is absent. Contrary to the case of uniform fields, $T$ is not a unique function of the local field; it also depends on the current and can only be determined by a simultaneous solution of the equations for current flow and conservation of energy with boundary conditions for a particular structure. As an example, a one carrier metal-semiconductor contact rectifer has been analyzed in detail including a discussion of the Peltier effect. In the barrier region $T$ is greater than ${T}_{0}$ (i.e., hot electrons) for a reverse bias but less than ${T}_{0}$ (i.e., cold electrons) for a forward bias. Computer solutions have been obtained for a Schottky barrier and electron scattering due to acoustic phonons only.

Diffusion of Hot and Cold Electrons in Semiconductor Barriers

Publisher Summary This chapter examines the signal and noise properties of gallium arsenide (GaAs) microwave field-effect transistors (FET) High frequency gallium arsenide field-effect transistors (GaAs FETs) have demonstrated remarkably low noise figures and high power gains at microwave frequencies A practical microwave GaAs FET is usually fabricated by deposition or diffusion of source, gate, and drain contacts on the surface of an appropriately doped thin epitaxial n-type layer This layer, in turn, is grown on a semi-insulating wafer by either a vapor or liquid epitaxial technique The apparent minor role played by the negative resistance region in practical short-gate FETs suggests that radiofrequency instabilities due to this region, if they exist, occur at frequencies far above the normal frequency regime of microwave FETs The small-signal equivalent circuit of the FET, valid up to moderately high frequencies is elaborated It is found that noise in a microwave GaAs FET is produced both by sources intrinsic to the device and by thermal sources associated with the parasitic resistances

Signal and Noise Properties of Gallium Arsenide Microwave Field-Effect-Transistors

The field dependence of mobility has been determined for electrons and holes in both germanium and silicon. The observed critical field at 298\ifmmode^\circ\else\textdegree\fi{}K beyond which $\ensuremath{\mu}$ varies as ${E}^{\ensuremath{-}\frac{1}{2}}$ is 900 volts/cm for $n$-type germanium, 1400 volts/cm for $p$-type germanium, 2500 volts/cm for $n$-type silicon, and 7500 volts/cm for $p$-type silicon. These values of critical field are between two to four times those calculated on the basis of spherical constant energy surfaces in the Brillouin zone. A saturation drift velocity of ${6(10)}^{6}$ cm/sec is observed in germanium which is in good agreement with predictions based on scattering by the optical modes. Data on $n$-type germanium at 20\ifmmode^\circ\else\textdegree\fi{}K show a range over which impurity scattering decreases and the mobility increases with field until lattice scattering dominates as at the higher temperatures.

Mobility of Holes and Electrons in High Electric Fields

Mobilities of Electrons in High Electric Fields

A pronounced decrease of the heat capacity of ${\mathrm{V}}_{3}$Si in the stressed state has been observed at temperatures below ${T}_{c}$. In addition, a large increase of heat capacity in the stressed state is observed above about 25\ifmmode^\circ\else\textdegree\fi{}K. The effect does not appear to be directly related to the structural transformation per se since it was observed both in samples that transform and in samples that do not. The observations are consistent with a decrease in ${T}_{c}$ of about one degree in the most extensively stressed regions of the sample. So far as is known, these are the first observations of such a pronounced effect of stress on heat capacity (e.g., as much as a 20% decrease in the entropy of ${\mathrm{V}}_{3}$Si at 17\ifmmode^\circ\else\textdegree\fi{}K). Although our present understanding of the observations is incomplete, a large decrease in the density of states at the Fermi surface with stress, as proposed by Weger, appears to be involved.

E. J. Ryder

Papers

Mobility of Holes and Electrons in High Electric Fields

Mobilities of Electrons in High Electric Fields

Pronounced Change in the Low-Temperature Heat Capacity of V 3 Si with Stress

Interpretation of Dependence of Resistivity of Germanium on Electric Field