Lead chalcogenides have long been used for space-based and thermoelectric remote power generation applications, but recent discoveries have revealed a much greater potential for these materials. This renaissance of interest combined with the need for increased energy efficiency has led to active consideration of thermoelectrics for practical waste heat recovery systems—such as the conversion of car exhaust heat into electricity. The simple high symmetry NaCl-type cubic structure, leads to several properties desirable for thermoelectricity, such as high valley degeneracy for high electrical conductivity and phonon anharmonicity for low thermal conductivity. The rich capabilities for both band structure and microstructure engineering enable a variety of approaches for achieving high thermoelectric performance in lead chalcogenides. This Review focuses on manipulation of the electronic and atomic structural features which makes up the thermoelectric quality factor. While these strategies are well demonstrated in lead chalcogenides, the principles used are equally applicable to most good thermoelectric materials that could enable improvement of thermoelectric devices from niche applications into the mainstream of energy technologies.

Band Engineering of Thermoelectric Materials

Piezoresistive sensors are among the earliest micromachined silicon devices. The need for smaller, less expensive, higher performance sensors helped drive early micromachining technology, a precursor to microsystems or microelectromechanical systems (MEMS). The effect of stress on doped silicon and germanium has been known since the work of Smith at Bell Laboratories in 1954. Since then, researchers have extensively reported on microscale, piezoresistive strain gauges, pressure sensors, accelerometers, and cantilever force/displacement sensors, including many commercially successful devices. In this paper, we review the history of piezoresistance, its physics and related fabrication techniques. We also discuss electrical noise in piezoresistors, device examples and design considerations, and alternative materials. This paper provides a comprehensive overview of integrated piezoresistor technology with an introduction to the physics of piezoresistivity, process and material selection and design guidance useful to researchers and device engineers.

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Review: Semiconductor Piezoresistance for Microsystems

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

Expressions for the temperature dependence of the carrier mean free path for optical phonon scattering and the mean energy loss per collision are presented which predict avalanche multiplication as a function of electric field for any operating temperature once the appropriate parameters have been determined at a single temperature. This has been verified for electrons in Si by the correlation of measurements at 300°K, 213°K, and 100°K. The temperature dependence of the breakdown voltages of a variety of abrupt and linear‐graded Si and Ge p‐n junctions has also been predicted. The fractional change in breakdown voltage with increasing temperature is predicted to decrease with increased doping concentration and, for the same breakdown voltage, to be less for linear‐graded junctions than for abrupt junctions.

Temperature dependence of avalanche multiplication in semiconductors

Shock compression of solids

The simple model of a semiconductor, based on a single effective mass for the charge carriers and a spherical shape for the surfaces of constant energy, is now known to be inadequate for most of the semiconductors which have been extensively studied experimentally. However, some of these do correspond to what may be called the “many-valley” model, a model for which the band edge occurs at a number of equivalent points K(i) in wave number space, and for which the surfaces of constant energy are multiple ellipsoids, one centered on each of these points. This paper develops, for models of this type, the theory for: mobility (Section 2) and its temperature dependence (Section 3); thermoelectric power (Section 4); piezoresistance (Section 5); Hall effect (Sections 6 and 9); high-frequency dielectric constant (Section 7); and magnetoresistance (Sections 8 and 9). These phenomena are treated, for cases to which Maxwellian statistics apply, on the assumption that the scattering of the charge carriers is describable by a relaxation time which depends on energy only, but is otherwise unrestricted. This assumption can be shown to be justified in a large class of cases, although for some cases it fails, notably when ionized impurity scattering predominates and at the same time the effective mass is very anisotropic. Special attention is given to the role of inter-valley lattice scattering, i.e., to processes whereby a charge carrier is scattered from the neighborhood of one of the band edge points

Transport properties of a many-valley semiconductor

An analysis is given of the transient behavior of the density of holes n h in an excess semiconductor as a function of lime t and of position x with respect to the electrode from which they are being injected. When the geometry is one-dimensional, an exact solution for the function n h (x, t) can he constructed, provided certain simplifying assumptions are fulfilled, of which the most important are that there be no appreciate trapping of holes or electrons and that diffusion be negligible. An attempt is made to estimate the range of conditions over which the neglect of diffusion will be justified. A few applications of the theory to possible experiments are discussed.

Conyers Herring

Papers

Transport properties of a many-valley semiconductor

Theory of transient phenomena in the transport of holes in an excess semiconductor