Yutaka Toyozawa

Dynamical Jahn-Teller Effect in Alkali Halide Phosphors Containing Heavy Metal Ions

Possible patterns of vibration-induced splitting in the absorption band of localized electrons in solid are investigated within the Condon approximation. The modes of lattice vibrations around the imperfection which give rise to the level splitting of degenerate excited states are classified into active and potentially active modes according as they cause the absorption band to split or not. The result is applied to the analysis of the absorption bands of Tl + - like ions in alkali halides. One can explain the triplet structure of the C band and the doublet structure of the A band with its temperature sensitive asymmetry, by introducing the coupling constant c between the p -electron and the trigonal lattice vibrations as a single adjustable parameter. The dependences of c upon the host alkali halide and on the charge of the impurity ion are explained by a point-charge plus point-dipole model for the neighboring halide ions.

Urbach-Martienseen Rule and Exciton Trapped Momentarily by Lattice Vibrations

Theory for the Urbach-Martienssen (U-M) rule on the low energy tail of the fundamental absorption edge of insulators is proposed. The exciton propagator solved for an adiabatic lattice is averaged for lattice vibrations at finite temperature, and the self-energy of exciton is obtained. It describes two characters of exciton in the lattice; the one is the mobile nature of exciton in the undeformed lattice, and the other is the localized nature of exciton trapped momentarily by the lattice deformation due to thermal vibrations. The interplay of the two natures results in the U-M tail below the exciton absorption peak. The result can be interpreted in terms of the Franck-Condon principle where the mobile nature is incorporated in the giant oscillator strength of the momentarily trapped exciton. Emission from this trapped state is discussed in connection with the U-M rule.

Self-Trapping of an Electron by the Acoustical Mode of Lattice Vibration. I

The importance of the acoustical mode of lattice vibration for self- trapping of an electron is shown. It is shown that when the coupling constant between the electron and the acoustical mode vibration exceeds a certain critical value, the effective mass of the electron changes discontinuously to such an enormous value that the electron is practically allowed to take a localized self- trapping state as an eigenstate. This model is in contrast with the case of the pelaron, in which the effective mass changes continuously with coupling constant. This difference is attributed to the different force range of electron-lattice interaction in the two cases. (auth)

Excitons in Alkali Halides

Exciton states in alkali halides are analyzed on the basis of the energy band picture. First the excitons at the point \(\varGamma\) are discussed. A simple treatment in which the spin-orbit and the electron-hole exchange interactions are taken into account indicates that the intensity ratio of the halogen doublet is fairly sensitive to the exchange energy, while the doublet splitting is not very sensitive. It is shown that a pure triplet exciton state exists below the first allowed exciton state. Although such a state has not yet been detected, lifetime broadening of the first peak due to the existence of such a hidden state is conceived to make the magnitude of the width of the first peak comparable with that of the second peak. The pronounced structure observed in K and Rb halides in the spectral region just above the step is ascribed to d e exciton formed at the point X . Multiplicities of the observed absorption peaks are explained in terms of this model. Semiquantitative analysis of the triplet stru...

Photoelectron Spectra of Core Electrons in Metals with an Incomplete Shell

Analytic investigations of the photoelectron spectra of core electrons and numerical calculations of their overall line shapes are made with the model proposed in our previous paper. In the final state of the photoemission, an electronic level of the incomplete shell of the excited atom, initially located well above the Fermi energy e F , is assumed to be lowered down to e d due to the core hole left behind. When e d e F , a singular photoemission edge appears at \(\tilde{\varepsilon}_{\text{F}}\), with a weak spectral hump around \(\tilde{\varepsilon}_{d}\). The results are compared qualitatively with experimental data. Finally, some remarks are made on the relationship between the analytic features of the photoelectron and optical absorption spectra.

Theory of Localized Spins and Negative Magnetoresistance in the Metallic Impurity Conduction

The co-operative effect of electron correlation and random lattice in the impurity conduction of semiconductors is investigated in terms of the Greens function with in the frame-work of Hartree-Fock approximation. There appear magnetic states embedded in the metallic impurity band, being located at those impurity sites which are relatively isolated from other sites. The fraction of these magnetic sites is estimated to be of the order of ten percents, being a decreasing function of impurity concentration. The magnetic moment of the localized spin is calculated with a method which is different from the conventional one. Treating the localized spins as collective modes which act upon the individual electrons of the impurity band as potential fluctuation (in space and in time), we have calculated the effect of magnetic field or spin ordering on the electrical resistivity.

Numerical Experiments on the Absorption Lineshape of the Exciton under Lattice Vibrations. I. The Overall Lineshape.

A standardized formulation is introduced for the lineshape problem–the effect of lattice vibrations on the exciton absorption, and used in a Monte-Carlo calculation of the density of exciton states and the absorption spectra in the regime of weak scattering. For the direct edge, we obtain the asymmetric lineshape with a strongly decaying low-energy side while the high-energy side can be approximated by a life-time broadened Lorentzian. The linewidth is found to depend on temperature as T 2/3 , T 1 and T 3/2 for one-, two-, and three-dimensional lattices in agreement with renormalized perturbation theory in one and two dimensions. The discrepancy of the perturbational result ( T 2 ) in three dimensions is ascribed to the density of states which is most sensitive to disorder in this case. The shift of the absorption peak is found to be linear in T for low T , the origin of its sublinear behaviour for higher T is clarified.

Two-Photon Absorption and Energy Band Structure

A new method of investigating energy band structure is proposed which makes use of the angular dependence of two-photon absorption coefficient of polarized beams. The angular dependences of the allowed transitions are calculated and tabulated for 32 crystal point groups. The exciton as well as interband transitions are discussed, and the method will be explained for the cases of NaCl–, CsCl–, ZnS– and diamond-type crystals how to determine the points of extremum vertical energy separation in the Brillouin zone with the help of associated tables and figures.

Numerical Experiments on the Absorption Lineshape of the Exciton under Lattice Vibrations. III. The Urbach Rule

We analyze the low-energy tail of the exciton absorption spectra calculated numerically on the standard model of exciton-phonon interaction. The empirical Urbach rule is established in its exponential decay for several orders of magnitude with a decay constant proportional to inverse temperature T -1 in two and three dimesnions and to T -2/3 in one dimension. A posteriori, the exponential tail is unambiguously ascribed to the “momentarily localized” excitons by considering the behaviour of the average oscillator strength per state. We introduce the steepness index s which relates the steepness coefficient σ and the exciton-phonon coupling constant g through σ= s / g . Our calculated values of 1.24 for square and 1.50 for simple cubic lattices enable us to correlate experimental observations on Urbach behaviour and self-trapping consistently.

Interband Absorption Spectra of Disordered Semiconductors in the Coherent Potential Approximation

The interband absorption spectra of a system with Gaussian site diagonal disorder are calculated in the coherent potential approximation. The electron-hole vertex part due to interband stochastic correlation is taken into account. The relaxation of the k -selection rule and the effect of localization are studied through the calculation of the optical transition matrix elements. It is clarified that the band tail states contribute to an exponential absorption tail (the so-called Urbach tail) as a result of interplay between transfer energy and Gaussian-distributed site energies. Introduction of a negative interband correlation leads to a red shift of the absorption edge. This effect is discussed in connection with the photo-structural change observed in chalcogenide glasses.