It is shown by experiment that the small-signal microwave conductivity of n-type InSb at 77 °K and 35 GHz decreases considerably, when an electric de field in excess of 10 V/cm is applied simultaneously. Further, a marked anisotropy with respect to the direction of the applied de field is observed. A sample with higher electron mobility shows a stronger anisotropy than a sample with lower mobility. It is possible to measure the momentum relaxation time because of the occurrence of strong relaxation effects. The microwave conductivity, which is dominated by these effects, can be calculated by assuming mean momentum and energy relaxation times according to Kopetz and Potzl. The applicability of these relaxation times to the hot-electron region of InSb is proved by the good agreement between experimental and theoretical results.



Experimente zeigen, das bei 77 °K und 35 GHz die Kleinsignal-Mikrowellenleitfahigkeit von n-InSb stark absinkt, wenn gleichzeitig ein elektrisches Gleichfeld > 10 V/cm angelegt wird. Weiter zeigt sich eine ausgepragte Anisotropie in bezug auf die Richtung des angelegten Gleichfeldes. Bei einer Probe mit hoherer Elektronenbeweglichkeit ist die Anisotropie starker ausgepragt als bei einer Probe niedrigerer Beweglichkeit. Auftretende Relaxationseffekte erlauben die Messung der Impulsrelaxationszeit in Abhangigkeit von der Gleichfeldstarke. Diese Effekte bestimmen auch den Verlauf der Mikrowellenleitfahigkeit, der durch Annahme einer mittleren Impuls- und einer mittleren Energierelaxationszeit berechnet werden kann. Durch die gute Ubereinstimmung zwischen Experiment und Theorie wird die Anwendbarkeit mittlerer Relaxationszeiten nach einem Vorschlag von Kopetz und Potzl auf den polaren Halbleiter InSb auch bei hohen Gleichfeldstarken gerechtfertigt.

On the Anisotropic Microwave Conductivity in the Hot‐Electron Region of n‐InSb

Anisotropy of Small‐Signal Microwave Conductivity due to Hot Electrons in InSb

The small‐signal microwave conductivity of n‐type single‐crystal InSb, GaSb, InAs, and epitaxial GaAs under the influence of a heating dc field was studied experimentally at 4‐mm waves. Contrary to low‐frequency results, the millimeter‐wave conductivity of InSb at 78 K increases with increasing dc field as a consequence of relaxation effects. The anisotropy with respect to the direction of this field is reversed so that the conductivity for parallel dc and ac fields exceeds the conductivity for perpendicular fields. Mean momentum and energy relaxation times τm and τe, respectively, are evaluated from the conductivity data: τe, almost constant, is about 2×10−12sec, τm drops from 6.1×10−12 sec and 2.6×10−12 sec, depending upon sample mobility, to some 2×10−12 sec when the electric field is increased from zero to 170 V/cm. Agreement of microwave τm with dc measured values is satisfactory. In GaSb at 300 K and 85 GHz, relaxation effects show up in a pronounced deviation of the parallel microwave conductivity ...

Millimeter-wave investigation of electronic conduction in semiconducting III-V compounds

Using the equilibrium distribution function obtained from the Boltzmann transport equation, and the collision term given by Matz [D. Matz, Solid State Commun. 4, 491 (1966); J. Phys. Chem. Solids 28, 373 (1967)], expressions have been derived for microwave conductivity (in parallel and perpendicular orientations to an externally applied, high‐dc electric field) in III‐V semiconductors with nonparabolic energy bands. Electron scattering with phonons, via the polar optical mode and with ionized impurities, has been considered to be the dominant scattering mechanism. Numerical evaluation of the results for a typical case of n InSb shows that, for the same dc field, the perpendicular microwave conductivity is always greater than the parallel one. An interesting reduction to the case of parabolic‐band semiconductors has also been made for the sake of comparison; it reveals that the band nonparabolicity has the effect of reducing the magnitude of conductivity anisotropy.

Hot‐Electron Anisotropy of Microwave Conductivity in Nonparabolic Semiconductors

A method is presented for determining transfer functions of sharp cut-off low-pass and band-pass filters having small pass-band magnitude and group delay distortion. It is similar to the conventional approach in the sense that the minimum phase shift filter section and the all-pass phase equalizer section are designed separately and then connected in cascade. Unlike the latter, however, the present technique does not use the smallest possible order of function to realize the minimum phase-shift part of the network, but some redundant elements are permitted in order to simplify the design of phase-equalizer section. To this end, the prescribed magnitude rosponse is approximated by use of a recently introduced class of monotonic pass-band filters, referred to as LSM filters. It is shown that this leads to a reduction in the overall complexity of the network when compared with conventional Cauer filter and phase-equalizer combination. Also, the relative sensitivity of the resulting network taken with respect...

Transfer functions for sharp cut-off filters with an equalized phase response

Theoretical results are presented for the small-signal microwave conductivity of nInSb at TL = 77°K in the presence of a high d.c. field directed parallel or perpendicular to the microwave field. Reasonable agreement with experiments by Richter and Bonek is demonstrated. At frequencies below 50GHz, the parallel microwave conductivity is smaller than the perpendicular one, whereas the opposite is true at 70GHz.

H.W. Pötzl

Papers

Microwave conductivity of polar semiconductors in the presence of a high electric field