Closed analytical expressions for the real part ϵ1(q, ω) and the imaginary part ϵ2(q, ω) of the frequency- and wave-vector-dependent dielectric function are obtained including a gap Eg in an appropriate manner in the spirit of the nearly-free electron approximation, and requiring that these functions will exactly satisfy the Kramers-Kronig relations and the f-sum rule. In the long wavelength limit the classical Lorentz oscillator result comes out, whereas for ω = 0 the static screening function is decisively improved with regard to earlier model calculations. The results also yield the plasmon dispersion relations ωL(q) and ωT(q) for Si, Ge, GaAs, and ZnSe in good agreement with previous detailed computations. With the average gap width Eg going to zero the expressions obtained transform into the well-known RPA (Lindhard) formulae for a free electron gas.

Frequency- and wave-vector-dependent dielectric function of a model semiconductor

We start with a short look at the problem of low-capacitance Josephson junctions, its history, and actual state-of-the-art It is argued that such devices are important for applications requiring nonhysteretic current-voltage characteristics since reduction of capacitance by several times makes it possible to increase the device resistance by the same amount while keeping the McCumber-Stewart damping parameter unaltered Moreover, at very high frequencies the capacitance in the RCSJ circuit with a parallel connection starts to shunt the superconducting current component due to reduction of the corresponding reactance inversely proportional to C Hence, to extend the operating frequency range of a Josephson junction its capacitance should be as small as possible As a solution of a new type of the Josephson device, less resistive and with smaller capacitance, we propose and realize a submicron-sized trilayer with tens nm-thick Si interlayer doped by metallic ultra-small inclusions and superconducting Mo-Re alloy electrodes

Submicron-sized MoRe-doped Si-MoRe Josephson junctions with a low specific capacitance

A modified calculation of the small wave vector q and frequency ω dependent longitudinal di-electric function for Milchev's model semiconductor is presented. To evaluate the matrix elements, two-band wave functions are used instead of plane waves (as used by Milchev). The energy difference between the valence and conduction bands is taken to be the same as Milchev's. It is found that the general behaviour of the real and imaginary parts of the dielectric function ϵ1(q, ω) and ϵ2(q, ω) are similar to that found by Milchev and by Walter and Cohen using a realistic band structure. The static dielectric function ϵ1(q, 0) agrees well with the exact calculation of Walter and Cohen. ϵ(0,ω) accounts properly for the Kramers-Kronig relation and up to a reasonable extent for the f-sum rule. It is also in good agreement with optical data. For small q the plasmon dispersion is given by Ep(q) = Ep(0) + Aq2 where A is an analytical function of Δ = Eg/4EF where Eg is the energy gap parameter and EF the Fermi energy.



Es wird eine modifizierte Berechnung der vom kleinen Wellenvektor q und der Frequenz ω abhangigen, longitudinalen dielektrischen Funktion fur den Milchevschen Modell-Halbleiter vorgelegt. Um die Matrixelemente zu berechnen, werden zwei Band-Wellenfunktionen an Stelle der ebenen Wellen (wie von Milchev benutzt) verwendet. Fur die Energiedifferenz zwischen Valenz- und Leitungsband wird der Wert von Milchev angenommen. Es wird gefunden, das das allgemeine Verhalten des Real- und Imaginarteils der dielektrischen Funktion ϵ1(q, ω)und ϵ2(q, ω) dem von Milchev und Walter und Cohen gefundenen ahnlich ist, die eine realistische Bandstruktur ansnehmen. Die statische dielektrische Funktion ϵ1(q, ω) stimmt gut mit den exakten Berechnungen von Walter und Cohen uberein ϵ(0,ω) erklart exakt die Kramers-Kronig-Beziehung und zu einem vernunftigen Ausmas die f-Summenregel. Sie befindet sich such in guter Ubereinstimmung mit optischen Daten. Es wird gefunden, das fur kleine q die Plasmondispersion durch Ep(q) = EP(0) + Aq2 gegeben wird, wobei A eine analytische Funktion von Δ = Eg/4EF ist, wo Eg die Energielucke und EF die Permienergie ist.

Small Wave Vector q and Frequency ω Dependent Longitudinal Dielectric Funtion for a Model Semiconductor

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Low-Capacitance Josephson Junctions

In the random phase approximation the dielectric permittivity is evaluated for a semiconductor with a band structure described by Kane's energy band scheme (spin-orbit interaction is neglected and the effect of higher bands is included in a very simplified form). It is demonstrated that the fact that several hole bands have been taken into account, when the operator of the kinetic energy ceased to be the Dirac one plays the principal role in the calculation of the static dielectric permittivity σ(q 0). The analytical dependence of σ(q 0) on the parameters of the semiconductor, width of the forbidden band Eg, effective mass, and the lattice constant, is obtained. The spatial dispersion of the dielectric permittivity for zero-gap semiconductors is considered in the long-wave limit.



[Russian Text Ignored].

D. I. Sheka

Papers

Dielectric Permittivity of Semiconductors with Narrow Forbidden Gap in the Long‐Wave Limit