AbstractThe solution is given for long persisting controversial problems in the theory of non‐radiative multiphonon capture of free carriers. Taking the adiabatic wave functions as basic states for the perturbational treatment of the transition probability particular attention is focused on the correct determination of the transition matrix elements. In this framework it is shown that to first order in the non‐diagonal matrix element of the electron‐lattice interaction all approaches developed so far (Condon approximation, non‐Condon approximation, static approximation, etc.) lead to the same result, in contradiction to statements in the literature. In particular, the reason is found why earlier results for the transition rate within the adiabatic and Condon approximation are much too small. The static approximation is shown to be the lowest approximation to the adiabatic approach.

AbstractThe off‐diagonal matrix element of the non‐adiabaticity operator, on which usually the theory of non‐radiative multiphonon transitions is based, is recast into a form much more convenient for the calculation of the transition probability W in non‐Condon approximation. This is demonstrated first for a two‐level system coupled to a single vibrational mode and then extended to the more general case of a complete set of non‐degenerate electronic states coupled linearly to N normal modes. The strong anharmonicity of the adiabatic potentials due to the mixture of states caused by the electron–phonon interaction operator is stressed, which limits the applicability of the theory to situations where only transitions well below “level crossing” are important, and, consequently, imposes serious restrictions on the parameters of the system and the temperature. Keeping to these restraints and to two electronic levels, the transformed matrix element of the non‐adiabaticity operator is identical with that of the perturbation operator used in the static coupling scheme of Haug and Pässler, which turns out in this way to be equivalent to a closed‐form of non‐Condon approximation based on a well defined set of adiabatic wave functions. Explicit expressions for W are also given, and some aspects of the theory in general are discussed.

A critical survey is given on the theory of NRMPT for the standard case in which the transition probability W is calculated in first order perturbation theory. A transformation of the transition-inducing matrix element of the adiabatic approximation is reported, leading to a form essentially equivalent to that of the static approximation, which allows to present a closed-form non-Condon approximation for arbitrary temperature under well defined conditions. Limitations arising from anharmonicity and some other relevant aspects are briefly discussed.

The spectrum of secondary radiation emitted from excitonic molecules under resonant two-photon excitation is investigated theoretically. Taking into account the optical orientation for the final exciton states of the emission process, we derive polarization and angular features of the radiation, reflecting directly the relaxation stage of the molecules.

AbstractThe absorption coefficient of CdS is measured over the whole region of the fundamental absorption edge, between liquid helium and room temperature. The experimental results are analysed and discussed in the framework of known theoretical work on exciton‐phonon interaction. In this connection the excitonic self‐energy in dependence on energy and temperature is derived from the experimental data on the one hand and from theory on the other. It is shown that the absorption behaviour is determined by different mechanisms of interaction, namely i) scattering of excitons optically generated at k ≈ 0 and ii) many‐phonon proceeses and phonon‐assisted transitions. Each mechanism is subjected to a special temperature dependence, reflecting the share of the interaction with acoustic and longitudinal optical phonons, respectively.

The present state of investigation of the phonon-assisted broad-band edge emission in II-VI-semiconductors is analysed critically. Experimental results on band shape, polarisation and related phenomena are presented and discussed. Strong evidence is supplied that both series of the edge emission are due to bound-to-bound transitions between closely associated donor-acceptor pairs under the condition of strong electron-phonon interaction.

A strong magnetic field applied along the growth direction of a quantum cascade laser (QCL) active region gives rise to a spectrum of discrete energy states, the Landau levels. By combining quantum engineering of a QCL with a static magnetic field, we can selectively inhibit/enhance non-radiative electron relaxation process between the relevant Landau levels of a triple quantum well and realize a tunable surface emitting device. An efficient numerical algorithm implementation is presented of optimization of GaAs/AlGaAs QCL region parameters and calculation of output properties in the magnetic field. Both theoretical analysis and MATLAB implementation are given for LO-phonon and interface roughness scattering mechanisms on the operation of QCL. At elevated temperatures, electrons in the relevant laser states absorb/emit more LO-phonons which results in reduction of the optical gain. The decrease in the optical gain is moderated by the occurrence of interface roughness scattering, which remains unchanged with increasing temperature. Using the calculated scattering rates as input data, rate equations can be solved and population inversion and the optical gain obtained. Incorporation of the interface roughness scattering mechanism into the model did not create new resonant peaks of the optical gain. However, it resulted in shifting the existing peaks positions and overall reduction of the optical gain.Program title: QCLCatalogue identifier: AERL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 37763No. of bytes in distributed program, including test data, etc.: 2757956Distribution format: tar.gzProgramming language: MATLAB.Computer: Any capable of running MATLAB version R2010a or higher.Operating system: Any platform supporting MATLAB version R2010a or higher.RAM: Minimum required is 1 GB. Memory usage increases for less intense magnetic fields.Classification: 15.Nature of problem:The nature of the problem is to provide an efficient numerical algorithm implementation for optimization of GaAs/AlGaAs QCL active region parameters and calculation of output properties in the magnetic field.Solution method:The optimization of the QCL laser performance at selected wavelength is performed at entire free-parameters space using simulated annealing algorithm. The scattering rates are calculated in the presence and without magnetic field and used as coefficients in rate equations. The standard MATLAB procedures were used to solve iteratively this system of equations and obtain distribution of electron densities over electronic states.Restrictions:The machine must provide the necessary main memory which decreases roughly quadratically with the increase of the magnetic field intensity.Running time:Optimization time on Intel 3 GHz processor is about 2×104 s. The calculation time of laser output properties for values set automatically in GUI is 5×104 s.

Electroabsorption spectra in the exciton region were measured on very thin CdS and CdSe single crystals at 77 °K in the field range 1 × 10 3 to 2.4 × 10 4 V/cm for both polarizations of incident light with respect to the c ‐axis. The electroabsorption spectra exhibit much more details than electroreflection spectra know so far. The variation of peak positions and peak heights with electric field strength is different for different parts of the spectrum. Some of the peaks shift to lower and others o higher energies with increasing field strength. The spectra can be interpreted in terms of a second order Stark shift, field induced line broadening and Franz‐Keldysh type interband oscillations.

AbstractThe valence band structure of wurtzite type materials is investigated using a k · p approximation. The E(k) dependence for the bands A, B, and C is completely determined by six parameters: two for k ∥ c, three for k⟂c and one additional parameter for a general direction. Relationships between the effective masses at k = 0 are given for the three bands. Even near k = 0 the sub‐bands are strongly non‐parabolic. The constant‐energy surfaces retain their rotational symmetry. Numerically calculated E(k) curves are presented for k ∥ c and k ⟂ c for CdS and CdSe.

AbstractA 12×12 representation is given of the valence band Hamiltonian at k = 0 which includes the spin‐orbit interaction. Expressions are derived for the energies and the linear combinations of the wave functions for the Γ7, Γ8, and Γ9 subbands. The whole valence band is completely determined by eight parameters: three energies, two parameters coupling states of equal spin, and three parameters coupling states of opposite spin. In principle, all parameters can be obtained experimentally from the energy separations and oscillator strengths for interband transitions for polarization ⟂ c and ∥ c. Anisotropic spin‐orbit interaction and mixing of states originating from the two anions per unit cell are discussed.

AbstractMeasurements are presented of the electroreflectance spectra of CdS and CdSe single crystals. Comparison with the photon energies of the interband edges and exciton peaks demonstrates that the low‐energy peak of the spectra is dominated by exciton quenching. At higher energies field‐influenced interband transitions are also important at room temperature.

AbstractThe short‐wavelength series of the edge emission of CdS single crystals is studied in the temperature range 18 to 150 °K with respect to (i) band shape, (ii) dependence of the half‐width of the components on temperature and excitation intensity, (iii) temperature dependence of the peak position of the zero‐phonon component, (iv) of the polarization ratio, and (v) of the luminescent intensity. It is concluded that this emission is due to an internal electronic transition occurring in nearest‐neighbour donor‐acceptor associates. The half‐width of the components is ascribed to 5 meV‐phonon and centre‐centre interaction. The polarization ratio IE⊥c/IE∥︁c is interpreted as due to a temperature dependent distribution of the associates over the possible directions of orientation in the crystal.

physica status solidi (b)Volume 13, Issue 2 p. K131-K133 Short Note Temperature Dependence of the Field-Induced Shift of the Absorption Edge in CdS and CdSe Single Crystals E. Gutsche, E. Gutsche Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, und IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorH. Lange, H. Lange Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, und IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this author E. Gutsche, E. Gutsche Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, und IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorH. Lange, H. Lange Physikalisch-Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, und IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this author First published: 1966 https://doi.org/10.1002/pssb.19660130246Citations: 4AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 W. Franz, Z. Naturf. 13a, 484 (1958). 2 D. Dutton, Phys. Rev. 112, 785 (1958). 3 R. B. Parsons, W. Wardzynski, and A. D. Yoffe, Proc. Roy. Soc. A262, 120 (1961). 4 E. Gutsche and H. Lange, Phys. stat. sol. 4, K21 (1964). 5 E. Gutsche and H. Lange, Proc. Intern. Conf. Semicond. Phys., Paris 1964 (p. 129). Citing Literature Volume13, Issue21966Pages K131-K133 ReferencesRelatedInformation

physica status solidi (b)Volume 17, Issue 1 p. K11-K14 Short Note Transient Photoconductivity Quenching in CdS Single Crystals due to Surface Trapping E. Gutsche, E. Gutsche Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorF. Spiegelberg, F. Spiegelberg Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorJ. Voigt, J. Voigt Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this author E. Gutsche, E. Gutsche Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorF. Spiegelberg, F. Spiegelberg Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this authorJ. Voigt, J. Voigt Physikalisch—Technisches Institut der Deutschen Akademie der Wissenschaften zu Berlin, Bereich elektrischer Durchschlag, and IV. Physikalisches Institut der Humboldt-Universität zu BerlinSearch for more papers by this author First published: 1966 https://doi.org/10.1002/pssb.19660170152AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 See for instance E. H. Taft and M. H. Hebb, J. Opt. Soc. Am. 42, 249 (1952); R. H. Bube, Phys. Rev. 99, 1105 (1955); S. H. Liebson, J. Electrochem. Soc. 102, 529 (1955); J. Auth, E. A. Niekisch, and H. Puff, Z. phys. Chem. (Leipzig) 212, 175 (1959); R. H. Bube, Photoconductivity of Solids, Wiley, New York 1960; V. E. Lashkarev, A. V. Lubtschenko, and M. K. Sheinkman, Dokl. Akad. Nauk SSSR 161, 1310 (1965); L. Grabner, Phys. Rev. Letters 14, 551 (1965). Volume17, Issue11966Pages K11-K14 ReferencesRelatedInformation

AbstractEs wurden Oberflächenabdrucke von unbehandelten sowie von verschiedenen Behandlungen unterworfenen CdS‐ und CdSe‐Aufdampfschichten elektronenmikroskopisch untersucht. Als Behandlungsverfahren wurden Temperungen im Hochvakuum, in Argon, in Stickstoff und an Luft durchgeführt. Es zeigte sich eine Zunahme der mittleren Kristallitgröße mit wachsender Kondensationstemperatur. Bei den Temperungen wurde eine Rekristallisation in inerter Atmosphäre bei Temperaturen oberhalb 500 °C, an Luft auch bereits unterhalb 500 °C, beobachtet.

AbstractEs wurde die spektrale Verteilung der Intensität der blauen Lumineszenzbande von CdS‐Einkristallen bei Anregung mit ultraviolettem Licht für die beiden Polarisationsrichtungen 𝔈 senkrecht und 𝔈 parallel zur c‐Achse zwischen 77 °K und 295 °K untersucht. Die Temperaturabhängigkeit der energetischen Lage der beiden Hauptmaxima und das Verhältnis χ der Maximalintensitäten für die beiden Polarisationsrichtungen wurden im angegebenen Temperaturbereich bestimmt. Ferner wurde die Winkelverteilung der Polarisation bei 90 °K gemessen. Es wird dargelegt, daß beide Banden der direkten strahlenden Annihilation von Eigen‐Exzitonen zuzuschreiben sind. Auf der Basis dieser Vorstellung werden die Meßergebnisse im einzelnen diskutiert.

AbstractThe influence of hydrostatic pressure up to 12000 atm on the semiconductivity, and the spectral distribution of photoconductivity and photoquenching is measured. The pressure coefficient of the semiconductivity of high‐conductivity CdS is found to be caused by the pressure coefficient of the mobility only, and indicates ionized impurity and optical phonon scattering at room temperature. For low‐conductivity CdS the pressure coefficient is about two orders of magnitude higher, and can be explained by the pressure shift of the ionization energy of the levels controlling the conductivity. The shifts, with pressure, of the maximum of the spectral distribution of the photocurrent and the absorption edge are about equal. The decrease of photocurrent is interpreted as due to the influence of pressure on the recombination mechanism. A comparable small additional shift of the photocurrent maximum can be explained by the differing influence of pressure on recombination in the intrinsic and extrinsic ranges.

AbstractOberflächenabdrucke von unbehandelten sowie von verschiedenen Behandlungen unterworfenen CdS‐Einkristallen wurden elektronenmikroskopisch bei 12000‐facher Vergrößerung untersucht. An Behandlungsverfahren wurden Temperungen im Hochvakuum, Bestrahlungen mit hohen Lichtintensitäten und Beschuß mit Ionen einer H2‐Gas‐entladung angewendet. Die Oberflächen der unbehandelten Kristalle zeigten in der Regel eine Belegung mit Teilchen, die eine Größe von maximal 1 μm besaßen. Eine Temperung der Kristalle im Hochvakuum führte im allgemeinen zu einer Abnahme der Teilchendichte, während bei intensiver Belichtung stets eine Zunahme der Teilchendichte beobachtet wurde. Bei Ionenbeschuß bildete sich eine polykristalline Kadmiumschicht aus. Die beobachteten Teilchen werden als Kadmiumabscheidungen gedeutet.