Two-photon interband transitions in crossed electric and magnetic fields in semiconductors. Non-local effects

Summary It is shown that in the presence of a crossed electric and magnetic field the electronic states of a semiconductor in the effective-mass approximation are described by a Hamiltonian containing a non-local potential. In order to preserve the gauge invariance of the two-photon interband transition rate, the interaction Hamiltonian between the electrons and the incident radiation has to be generalized. For GaAs, the transition rate between two particular levels is evaluated in both length and velocity gauges demonstrating the correctness of our approach. Work partially supported by the European Community Programme ESPRIT, Basic research, action n. 6878, EASI.     

Electronic interband Raman scattering in semiconductors in a static magnetic field. Non-local effects

Since the Hamiltonian describing the electronic states in the effective mass approximation contains non-local potentials, the interaction with the electromagnetic field has to be modified in order to preserve the gauge independence of physical quantities. The interband Raman efficiency using the modified interaction is evaluated and the difference with previous calculations is discussed.     

Nonlinear index of refraction in semiconductors

Summary Experimental work on light refraction in semiconductors suggests that there are two separate mechanisms by which the index of refraction becomes nonlinear: direct saturation, on the one hand, and the Burstein-Moss effect, on the other hand. We show that this picture is incorrect, since it was based on the usage of the Bloch equation. Electron systems are not Boltzmann systems and the appropriate Fermi-Dirac master equation leads to a saturation that differs from the saturation of the Bloch equation. We show, using a simple two-level system, that this result may look like the spin result in one extreme (phonon bottleneck saturation), while it shows the features of the Burnstein-Moss effect in the limit of small degeneracy of the upper level (Fermi saturation).

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Riassunto I lavori sperimentali sulla rifrazione della luce nei semiconduttori suggeriscono la presenza di due meccanismi separati grazie ai quali l'indice di rifrazione diventa non lineare: la saturazione diretta, da un lato, e l'effetto Burstein-Moss, dall'altro. Noi mostriamo che questo quadro non è corretto, in quanto basato sull'equazione di Bloch. I sistemi di elettroni non sono sistemi di Boltzmann e l'appropriata ?master equation? produce una saturazione differente da quella dell'equazione di Bloch. Si mostra, usando un semplice sistema a due livelli, che questo risultato assomiglia a quello di un sistema di ?spin? ad un limite estremo (saturazione fononica a collo di bottiglia), mentre mostra le caratteristiche dell'effetto Burstein-Moss nel limite di piccola degenerazione del livello superiore (saturazione di Fermi).

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Резюме Экспериментальная работа по преломлению света в полупроводниках предполагает, что существуют два различных механизма, благодаря которым преломление становится нелинейным: с одной стороны прямое насыщение, а с дуугой стороны эффект ъурштейна-Мосса. Мы показываем, что эта картина не является корректной, т.к.основана на использовании уравнения ълоха. Электронные системы не являются больцмановскими системами и соответствующее управляющее уравнение Ферми-Дирака приводит к насыщению, котрое отличается от насыщения уравнения Блоха. Мы показываем, используя простую двухуровневую систему, что этот результат похож на результат для спина в случае одного максимума, тогда как этот результат обнаруживает особенности эффекта Бурштейна-Мосса в пределе малой вырожденности верхнего уровня.

     

Dark and photomagnetoresistance in semi-magnetic semiconductors

Summary Magnetic-field dependence of electron mobility and photoconductivity in semi-magnetic semiconductors are studied both theoretically and experimentally. The electron relaxation times due to various scattering mechanisms are calculated paying special attention to spin disorder and alloy scatterings. The calculated mobility in Cd_1−c Mn _c Te is compared with experimental photomagnetoresistance (PMR) results. It is concluded that the magnetic-field-dependent mobility may contribute significantly to PMR at high Mn concentrations and low temperatures. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Direct and indirect two-photon processes in semiconductors

Summary The expressions describing direct and indirect two-photon absorption in crystals are given. They are valid both near and far from the energy gap. A perturbative approach through two different band models is adopted. The effects of the nonparabolicity and the degeneracy of the energy bands are considered. The numerical results are compared with the other theories and with recent experimental data in ZnO and AgCl. It is shown that the dominant transition mechanisms are of the allowed-allowed type near and far from the gap for both direct and indirect processes. Permanent address: Physics and Mathematics Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt.     

Simultaneous heat capacity and thermal-diffusivity photoacoustic measurement at liquid-crystal phase transitions

Summary The photoacoustic-technique application to the simultaneous characterization of the thermal diffusivity, specific-heat capacity and thermal conductivity of a liquid crystal at a phase transition is presented for the first time. The first two parameters show a critical decrease and increase, respectively, while the third one does not exhibit any critical behaviour. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Nonlocal potential and optical properties of solids

Summary The theory of the RPA optical response of a solid has been generalized in order to take into account also the possible presence of spatially nonlocal potentials in the Hamiltonian. Explicit expressions for first- and second-order susceptibilities are given in the new framework. The expressions obtained depend on the matrix elements of operators of the form of a commutator of a component of the position operatorr and an operator that commutes with the lattice translations. The problem of the evaluation of these matrix elements is solved in a simple manner by introducing an auxiliary, periodic position operator,XXXr. In such a way a general formulation is obtained that preserves the gauge invariance. As an application of the new theory, the second harmonic generation (SHG) from a semiconductor in a simple two-band model has been studied. The differences between our correct gauge-invariant results and those obtained in the usual local approximation is an indication of a slow convergence of the expressions obtained in the local approximation.     

Two-photon transitions to exciton states in semiconductors

We consider the gauge invariance of the two-photon transition rate from the crystal ground state to exciton states in semiconductors in the framework of the Wannier model. We show that the non-locality correction in the velocity gauge is essential to preserve the gauge invariance. As a numerical example, we calculate in the length and in the velocity gauge the transition rates for the two-photon direct creation of 2p excitons in a two-band semiconductor.     

Linear and nonlinear optical properties in a disk-shaped quantum dot with a parabolic potential plus a hyperbolic potential in a static magnetic field

Linear and nonlinear optical properties in a disk-shaped quantum dot (DSQD) with a parabolic potential plus a hyperbolic potential in a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron are obtained by three kinds of approximation methods. It is found that optical absorption coefficients and refractive index changes are not only by the characteristic parameters of the hyperbolic potential and the confinement frequency, but also by the magnetic field.     

Combined effects of magnetic and electric fields on the interband optical transitions in InAs/InP quantum wire

Combined effects of magnetic and electric fields on the confined exciton in an InAs_1−xP_x/InP (x=0.2) quantum well wire are investigated taking into account the geometrical confinement effect. Variational formulism, within the frame work of effective mass approximation, is applied to obtain the exciton binding energy. The second order harmonic generation and the optical gain are carried out using compact density method. The strain effects are included with the confinement potential in the Hamiltonian. The energy difference of the ground and the first excited state is found in the presence of magnetic and electric fields taking into the consideration of spatial confinement effect. The result shows that the optical properties are more influenced taking into account the effects of geometrical confinement, magnetic field and electric field. It is shown that the telecommunication wavelength can be achieved with the suitable doping barrier material with the wire material and the external perturbations.     

The influence of multiphonon transitions on interband optical absorption in semiconductors with a Coulomb-type random field

The temperature dependence of the optical absorption coefficient in the tail region is studied in semiconductors with a random Coulomb-type field. The results of numerical calculation are compared with data for chalcogenide glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 63–67, September, 1981.The author is grateful to V. L. Bonch-Bruevich for his attention to the work.     

Normal- and oblique-incidence reflection of semi-infinite crystals: Adiabatic approach with excitonic effects

Summary Excitonic reflection spectra of semi-infinite crystals are calculated within Stahl's coherent wave approach to band gap dynamics. Stahl's constitutive equations are solved by an adiabatic approximation in a surface region of the thickness z₀ and exactly in the bulk. The depth z₀ determines a region where the repulsive surface potential plays a decisive part for the motion of electrons and holes. The method yields simple analytical expressions for the reflectivity and for the bulk polariton amplitudes both for the normal and for the oblique incidence. Calculated reflectivity curves are compared with experimental data for various semiconductors and various angles of incidence showing a fairly good agreement.

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Riassunto Si calcolano gli spettri di riflessione eccitonica di cristalli semi infiniti entro l'approccio d'onda coerente di Stahl alla dinamica dell'intervallo di banda. Le equazioni costitutive di Stahl si risolvono con un'approssimazione adiabatica in una regione di superficie di spessore z₀ ed esattamente nel volume. La profondità z₀ determina una regione in cui il potenziale di superficie repulsivo ha un ruolo decisivo per il moto degli electtroni e delle lacune. Il metodo rende semplici espressioni analitiche per la riflettività e per le ampiezze del polaritone di volume sia per l'incidenza normale che per quella obliqua. Si confrontano le curve di riflettività calcolate con i dati sperimentali per vari semiconduttori e vari angoli d'incidenza mostrando un accordo abbastanza buono.

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Резюме Вычисляются экситонные спектры отражения для полубесконечных кристаллов в рамках подхода когерентных волн Сталя к динамике ширины запрещенной зоны. Решаются конститутивные уравнения Сталя с помощью адиаватического приближения в поверхностной области для толщины z₀ и точно в объеме. Глубина z₀ определяет область, где поверхностный потенциал отталкивания играет суцественную роль для движения злектронов и дырок. Предложенный метод дает простые аналитические выражения для овоих случаев нормального и наклонного падения. Вычисленные кривые отражательной срособности сравниваются с экспериментальми данными для раэличных полупроводников и различнях углов падения. Обнаружено довольно хорошее соответствие.

     

Oscillator strengths of optical transitions of a cylindrical shell: Crossed static electric and magnetic fields

The single-electron eigenstates of a cylindrical shell are determined as functions of the applied crossed electric and magnetic fields in the effective-mass approximation. The system considered consists of donor charges taken to be uniformly distributed within an inner core of infinitely long length. The core is concentrically enveloped by a semiconducting material of finite thickness; which is essentially the host material. This configuration of the donor charges sets up a spatially varying electric field nonetheless with only the radial component. In addition, a uniform magnetic field is applied parallel to the axis of symmetry of the inner core. As is well known, the axial applied magnetic field lifts the double degeneracies of the electron’s subbands characterized by the same azimuthal quantum numbers which differ only in sign. The main effect of increasing the external electric field is to elevate the various energy subbands, more or less to the same extent, to higher values. Further, evaluations of the oscillator strengths of optical transitions of the cylindrical shell are carried out within the dipole approximation. The radiation field is taken to be that of circularly polarized light incident along the axis of the core. The oscillator strengths of optical transitions are found to increase with an increase of the applied magnetic field, particularly in the regime of small magnetic fields. In contrast, the oscillator strengths of these optical interactions become suppressed as the donor charge density is increased.     

Reflectancevs. Electroreflectance measurements on arsenic-doped silicon crystal

Summary Reflectance and electroreflectance measurements from 2.5 to 5.5 eV, performed on arsenic heavily doped silicon samples, are reported and discussed. Silicon crystals implanted with arsenic up to a fluence of 10¹⁷ cm⁻² were laser irradiated and a free-carrier concentration of the order of 10²¹cm⁻³ was reached. The reordering of the system is studied in detail at different initial conditions. A comparison between reflectance and electro-reflectance appears to be quite useful to determine the behaviour of the heavily doped semiconductor. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

稳态磁场抑制肿瘤细胞生长机制

近年来人们在稳态磁场抑制肿瘤生长的基础科学研究方面取得了多项进展。文章主要总结和分析了目前国内外学者在分子、细胞、动物以及人体各个层面取得的相关研究进展。尽管稳态磁场在治疗肿瘤方面还处于实验探索阶段,但是其研究结果却显示了稳态磁场的安全性和良好的治疗前景。因此,系统性研究稳态磁场和肿瘤之间的关系,进行一系列符合国际规范的临床实验,并深入探索磁场作用于机体的分子机制至关重要。     

Single-photon interference experiment using a mechanical frequency shifter

Summary A variation of the interference experiment on the single photon has been performed. By means of a mechanical effect, we change the frequency of the photon only on one arm of a Mach-Zender interferometer. We observe the beat signals even when the intensity is so small that only one photon at a time passes through the interferometer. Our experiment gives a further proof of the classical behaviour of the electromagnetic radiation at arbitrarily small intensity, in agreement with the probabilistic interpretation of quantum mechanics.

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Riassunto è stata realizzata una variante dell'esperimento d'interferenza del singolo fotone. Variando, mediante un effetto meccanico, la frequenza del fotone soltanto in uno dei due bracci di un interferometro di Mach-Zender, si osservano segnali di battimento anche quando l'intensità è così bassa che solo un fotone per volta attraversa l'interferometro. Questo esperimento dà un'ulteriore dimostrazione del comportamento classico della radiazione elettromagnetica ad intensità arbitrariamente ppicole, in accordo con l'interpretazione probabilistica della meccanica quantistica.

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Резюме Осуществлен вариант интерференционного эксперимента с одним фотоном. С помощью механического эффекта мы изменяем частоту фотона в одном из плеч интерферометра Маха-Цендера. Мы наблюдаем сигналы биения даже в том случае, когда интенсивность настолько мала, что только один фотонодновременно проходит через интерферометр. Наш эксперимент указывает на классическое поведение электромагнитного излучения при произвольномалых интенсивностях, что согласуегся с вероятностной интерпретацией квантовой механики.

     

Decay from photo-excited doubly degenerate electronic levels. A simple interpretative approach

Summary A simple physical model for interpreting decay processes from excited doubly degenerate electronic levels is described. It considers different de-excitation channels on the potential energy surfaces in the two-dimensional space of the ε-type coordinates. The obtained results are then discussed and their relevance for photophysics and photochemistry is stressed.

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Riassunto Si descrive un semplice modello fisico per l'interpretazione dei processi di decadimento da livelli elettronici eccitati doppiamente degeneri. Esso prende in considerazione differenti canali di diseccitazione sulle superfici di energia potenziale nello spazio bidimensionale delle coordinate di tipo ε. I risultati ottenuti sono poi discussi e si sottolinea la loro importanza per la fotofisica e la fotochimica.

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Резюме Описывается простая физическая модель для интерпретации процессов распада из возбужденных двукратно вырожденных электронных уровней. Рассматриваются различные каналы девозбуждения на поверхностях потенциальной энергии в двумерном пространстве координат ε-типа. Обсуждаются полученные результаты и отмечается их значимость для фотофизики и фотохимии.

     

Effect of a random deformation-potential field on interband optical transitions

We have calculated the correlation function for the random field caused by the deformation potential due to spherical clusters randomly distributed throughout the sample. We evaluate the characteristic energy which determines the rate at which the interband optical absorption coefficient decreases as the frequency decreases in the neighborhood of the optical tail.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 3–6, February, 1984.     

Anisotropic effects induced by magnetic field in zero-gap semiconductors

The magnetic sub-band structure in zero-gap semiconductors α—Sn and HgTe is calculated and shown to depend strongly on the field orientation. This effect is discussed in connection with high-field transport and optical phenomena. It is demonstrated that a transverse electric field acts to increase the magnetically induced gap in α—Sn and to decrease it in HgTe.