The conduction process in semiconductors exhibits effects associated with inertia of the carriers when the observation frequency is comparable to the reciprocal of the relaxation time for randomization of momenta. These effects can cause significant changes in the conductivity and permittivity of germanium and silicon measured at ordinary microwave frequencies and should become increasingly important as semiconductor devices are developed for ultra-microwave applications. The present paper derives equivalent circuits which illustrate inertial effects and discusses their temperature dependence. A highly accurate reflection bridge technique for measuring microwave conductivity and permittivity is then described. Finally, measurements of conductivity and permittivity of n-type silicon and p-type germanium at 24 Gc and at temperatures between 77° and 300° Kelvin are presented and compared with theory. At 77°, the inertial effects are found to be largest for the p-type germanium and cause the microwave conductivity to be less than the dc conductivity by a factor of one-half.

Charge carrier inertia in semiconductors

Electric Conductivity of Hot Carriers in Si and Ge

Electron energy relaxation time in Si and Ge

Galvanomagnetic effects of hot electrons in n-type silicon

Shockley's hot electron picture for semiconductors in high electric fields is extended to include arbitrary (though “non-quantizing”) magnetic fields. The effects are then more diversified and offer wider experimental possibilities. While preserving the original simplicity of Shockley's model, its scope can be extended by including a reduction of the power input due to the deflection caused by the Lorentz force. Explicit calculations are carried out for an idealized isotropic model which Conwell [15] used to interpret the experimental data for n-Ge in zero magnetic field. This involves interactions of electrons with acoustic and covalent optical modes. This model calculation is designed to illustrate the main physical features of an extended Shockley picture. The results here derived are discussed from the point of view of the planning and analysis of experimental investigations which may bear on the subject.



Shockleys Modell der heisen Elektronen in Halbleitern in starken elektrischen Feldern wird erweitert, um beliebig grose (nicht quantisierte) magnetische Felder behandeln zu konnen. Es ist dann moglich, eine grosere Anzahl von Effekten, die durch heise Elektronen verursacht werden, zu beschreiben und neue Experimente anzuregen. Ohne die ursprungliche Einfachheit, die Shockleys Modell auszeichnet, zu verlieren, ist es moglich, dieses Modell so zu verallgemeinern, das es die durch die Lorentzkraft-Ablenkung verursachte Abnahme der zugefuhrten Leistung beschreibt. Es werden an einem idealisierten, isotropen Modell, das Conwell [15] benutzt hat, um experimentelle Ergebnisse uber n-Ge im magnetfeldfreien Fall zu erklaren, explizite Rechnungen durchgefuhrt. Diese Rechnungen berucksichtigen die Wechselwirkungen der Elektronen mit den akustischen und kovalenten optischen Phononen. Die an diesem Modell durchgefuhrten Rechnungen verfolgen als Hauptzweck, den physikalischen Gehalt des Shockleyschen Modells zu illustrieren. Die gewonnenen Resultate werden im Hinblick auf zukunftige Experimente diskutiert.

Non‐Ohmic Transport in Semiconductors in a Magnetic Field

The distribution function of carriers in a semiconductor when subjected to a small microwave field and a high steady electric field is derived, considering both the acoustic and optical phonon scattering. Expressions for microwave conductivity and change in apparent dielectric constant are obtained from the distribution function. It is shown by numerical calculations that the conductivity evaluated from these expressions agree closely with the experimental value. The calculated value of the change in apparent dielectric constant, however, is found to be of the same order as the experimental value, but the agreement is poorer than that for the conductivity.

Microwave Conductivity of Semiconductors in the Presence of High Steady Electric Fields

The velocity distribution function of hot carriers in a semiconductor in high magnetic fields is obtained correct up to the second approximation. The Hall mobility and magnetoresistance are calculated from this distribution function. It is found that the Hall mobility is not very dependent on the magnetic field and that the hot-carrier magnetoresistance would be larger than the small field magnetoresistance.

https://iopscience.iop.org/article/10.1088/0370-1328/81/4/315/pdf

Hall Mobility and Magnetoresistance of Semiconductors due to Hot Carriers in High Magnetic Fields

The Hall mobility of electrons in n-type germanium at high electric fields is studied, taking into consideration the ellipsoidal many-valley band structure. The distribution function of carriers in a many-valley semiconductor is first obtained assuming acoustic phonon, optical phonon and intervalley scattering. Expressions for Hall mobility are then derived using this distribution function and numerical computations made with the parameter values of n-type germanium. It is found that (i) the Hall mobility is anisotropic, (ii) its value is a maximum when the electric field is applied in the direction, and (iii) its value is a minimum when the electric field is in the direction. It is also found that the anisotropy factor is independent of the value of the electric field for predominant acoustic phonon scattering, but depends on the field for predominant optical and intervalley scattering.

https://iopscience.iop.org/article/10.1088/0370-1328/82/6/311/pdf

Hot Electron Hall Mobility of n-type Germanium

The distribution function of carriers in a high electric and a simultaneous magnetic field is derived taking into consideration the effect of both acoustic and optical phonon scattering Using this distribution function, expressions for the Hall mobility are obtained These expressions indicate, and the numerical results calculated with the parameter values of n-type germanium also verify, that if optical phonon scattering occurs in addition to acoustic phonon scattering the value of the Hall mobility is increased The Hall mobility is also found to increase with magnetic field

http://iopscience.iop.org/article/10.1088/0370-1328/82/5/310/pdf

Effect of optical phonon scattering on hot electron hall mobility of semiconductors

Expressions are derived for the propagation function of a microwave signal inside a waveguide filled with a semiconductor with carrier density varying in time. The bearing of these expressions on the performance of semiconductor microwave modulators and on microwave methods for the measurement of lifetime in semiconductors is discussed.

P. Das

Papers

Microwave Conductivity of Semiconductors in the Presence of High Steady Electric Fields

Hall Mobility and Magnetoresistance of Semiconductors due to Hot Carriers in High Magnetic Fields

Hot Electron Hall Mobility of n-type Germanium

Effect of optical phonon scattering on hot electron hall mobility of semiconductors

Microwave Propagation in Semiconductors with Carrier Density Varying in Time