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Showing papers on "Exciton published in 1970"


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01 Jan 1970

3,789 citations


Journal ArticleDOI
TL;DR: In this article, the experimental evidence concerning the density of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c and a.c. conductivity, drift mobility and optical absorption.
Abstract: The experimental evidence concerning the density of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c. and a.c. conductivity, drift mobility and optical absorption. There is evidence that for some chalcogenide semiconductors the model proposed by Cohen, Fritzsche and Ovshinsky (1969) should be modified by introducing a band of localized states, near the centre of the gap. The values of C, when the d.c. conductivity is expressed as C exp (- E/kT), are considered. The behaviour of the optical absorption coefficient near the absorption edge and its relation to exciton formation are discussed. Finally, an interpretation of some results on photoconductivity is offered.

3,465 citations


Journal ArticleDOI
TL;DR: In this paper, a model for determining the density of states of pure stoichiometric NiO is proposed, taking into account the free-ion energy levels, and taking the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects.
Abstract: The electrical and optical properties of materials which are characterized by narrow bands in the vicinity of the Fermi energy are discussed. For such materials, electronic correlations and the electron-phonon coupling must be considered explicitly. Correlations in $f$ bands and in extremely narrow $d$ bands can be handled in the ionic limit of the Hubbard Hamiltonian. It is shown that free carriers in such bands form small polarons which contribute to conduction only by means of thermally activated hopping. Wider bands may also exist near the Fermi energy. Carriers in these bands may form large polarons and give a bandlike contribution to conductivity. A model is proposed for determining the density of states of pure stoichiometric crystals, beginning with the free-ion energy levels, and taking into account the Madelung potential, screening and covalency effects, crystalline-field stabilizations, and overlap effects. Exciton states are considered explicitly. The Franck-Condon principle necessitates the construction of different densities of states for electrical conductivity and optical absorption. Because of the bulk of experimental data presently available, the model is applied primarily to NiO. The many-particle density of states of pure stoichiometric NiO is calculated and is shown to be in agreement with the available experimental data. When impurities are present or nonstoichiometry exists, additional transitions must be discussed from first principles. The case of Li-doped NiO is discussed in detail. The calculations are consistent with the large mass of experimental information on this material. It is concluded that the predominant mechanism for conduction between 200 and 1000 \ifmmode^\circ\else\textdegree\fi{}K is the transport of hole-like large polarons in the oxygen $2p$ band. A method for representing the many-particle density of states on an effective one-electron diagram is discussed. It is shown that if correlations are important, donor or acceptor levels cannot be drawn as localized levels in the energy gap when multiple conduction or valence bands are present. This result comes about because extrinsic ionization energies of two correlated bands differ by an energy which bears no simple relation to the difference in energies of the intrinsic excitations, which are conventionally used to determine the relative positions of the bands.

738 citations


Journal ArticleDOI
A. Suna1
TL;DR: In this article, a theory for calculating the kinematic part of the exciton-exciton annihilation rate in molecular crystals is developed for calculating their spatial and spin motion, as well as the annihilation process itself.
Abstract: A theory is developed for calculating the kinematic part of the exciton-exciton annihilation rate in molecular crystals. The spatial and spin motion of the excitons, as well as the annihilation process itself, is treated phenomenologically. Exciton propagation is assumed to take place as in the hopping model. The importance of the dimensionality of the exciton motion is pointed out; in nearly one- or two-dimensional cases, certain lifetime processes control the exciton collision rate, in contrast to the three-dimensional case. These lifetime processes include motion out of the one- or two-dimensional subspace and, for excitons with spin, spin relaxation. The theory leads to a description of magnetic field effects on the annihilation rate of triplet excitons at room temperature. When applied to triplet excitons in anthracene, this description gives a satsfactory fit to the observed effects and leads to the determination of the nearest-neighbor exciton annihilation rate, the singlet-channel annihilation rate constant, and the exciton diffusion constant for motion perpendicular to the $\mathrm{ab}$ plane of anthracene.

307 citations


Journal ArticleDOI
TL;DR: In this paper, a comprehensive study of electric field effects on optical absorption by Wannier excitons is presented, showing that the electron-hole interaction enhances these oscillations near an ${M}_{0}$-type edge (positive effective masses) and quenches them near an${M}{3}$)-type edge(negative effective masses).
Abstract: A comprehensive study of electric field effects on optical absorption by Wannier excitons is presented, showing field effects on both bound and continuum states. The calculations and results have been simplified by defining appropriate dimensionless parameters such that the eigenvalues are independent of field when expressed in terms of these parameters. A general normalization procedure for wave functions with continuous eigenvalues is outlined. The effect of the electron-hole interaction on the electric-field-induced oscillations is demonstrated, with the result that the electron-hole interaction enhances these oscillations near an ${M}_{0}$-type edge (positive effective masses) and quenches these oscillations near an ${M}_{3}$-type edge (negative effective masses). This effect would inhibit the observation of ${M}_{3}$-type edges in electroreflectance.

212 citations


Journal ArticleDOI
TL;DR: In this article, the effect of the spin exchange interaction between electron and hole is investigated for the case of excitons originating from one of the valence bands and an $s$-like conduction band, as is the case for IIb-VIb compounds.
Abstract: The effect of the spin-exchange interaction between electron and hole is investigated for the case of excitons originating from one of the $p$-like valence bands and an $s$-like conduction band, as is the case for IIb-VIb compounds. A general exciton matrix is constructed, starting from the work of Pikus. It includes spin-orbit, crystal-field, spin-exchange, and deformation-potential interactions. Use of this matrix then allows a theoretical fit to our experimental data which describes the shift of exciton levels under uniaxial pressure in ZnO, CdS, and CdSe. This fit results in the determination of six deformation potentials, two spin-orbit parameters, the crystal-field parameter, and the exchange parameter. The general theory, when adapted to the zinc-blende structure, allows us to fit our data on cubic ZnS and ZnSe, resulting in a determination of two deformation potentials and the spin-exchange parameter for each compound.

178 citations


Journal ArticleDOI
TL;DR: In this paper, the interaction of Frankel excitons with optical phonons in molecular crystals is studied by means of a Green's function method in which the use of a canonical transformation allows most of the exciton-phonon interaction to be treated nonperturbatively.
Abstract: The interaction of Frankel excitons with optical phonons in molecular crystals is studied by means of a Green's function method in which the use of a canonical transformation allows most of the exciton–phonon interaction to be treated nonperturbatively. The self‐energy of the Green's function is then expanded in terms of the intermolecular potential. An expression is obtained for the absorptive part of the dielectric function of the exciton–phonon system. Comparison is made with experiment and also with earlier theories, some of the limitations of which are pointed out.

136 citations


Journal ArticleDOI
K. L. Shaklee1, R.E. Nahory1
TL;DR: In this article, it was shown that there is no valley-orbit splitting of the excitons, contrary to previous suggestions, and it is shown theoretically that such splitting of free exciton cannot exist, and also that previous determinations of the energies of higher exciton states were in error.
Abstract: Measurements of the wavelength derivative of the indirect absorption edge in Si show features associated with the creation of free excitons in states $n=1 \mathrm{and} 2$ as well as in the exciton continuum. The spectrum shows no valley-orbit splitting of the excitons, contrary to previous suggestions, and it is shown theoretically that such splitting of free excitons cannot exist. It is found also that previous determinations of the energies of higher exciton states ($ng1$) were in error. Finally, LO phonon participation has been identified for the first time in the indirect edge of Si.

136 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear integral equation for the high density excitons is derived and it is solved in two ways: 1) by the perturbational method and 2) exactly for a simple model of the Coulomb interaction in the random phase approximation and the effective mass approximation for the two band model of a conduction band and a valence band.
Abstract: The boson creation and annihilation operators of excitons are introduced and the fermion Hamiltonian of high density electrons and holes is expanded in terms of these boson operators. Then a nonlinear integral equation for the high density excitons is derived and it is solved in two ways: 1) by the perturbational method and 2) exactly for a simple model of the Coulomb interaction in the random phase approximation and the effective mass approximation for the two band model of a conduction band and a valence band. As a result, the cutting down effects of both the band edges due to formation of high density excitons are shown to overcome the exchange self-energy of the electrons and the holes composing the high density excitons.

113 citations


Journal ArticleDOI
TL;DR: In this paper, the Davydov splittings of the 3800-A transition are found to be substantially different from those observed for the (001) face, which is interpreted as strong evidence for the dependence of dipole sums on the relative orientation of the wave vector k to the transition moment d.
Abstract: The reflection spectra of three faces of crystalline anthracene in the region 5000–1820 A have been observed at room temperature, and the corresponding absorption spectra have been derived by a Kramers–Kronig analysis. The results for face (001) agree with previous direct absorption work. For faces (201) and (110) the Davydov splittings of the 3800‐A transition are found to be substantially different from those observed for the (001) face. The strong 2500‐A transition gives rise to reflection bands which are 1.5–2.0 eV wide. These bands are examples of metallic reflectivity which had previously been observed only for some organic dye crystals. For radiation incident upon the (201) and (110) faces the splittings of the strong transition are smaller by nearly an order of magnitude relative to that observed in the case of the (001) face. These results are interpreted as strong evidence for the dependence of dipole sums on the relative orientation of the wave vector k to the transition moment d. The experimental observations are compared with the dipole theory of exciton states in molecular crystals. Qualitative agreement between dipole calculations and experiment is good, and quantitative differences are attributed to the presence of higher multipole and electron exchange effects. It is estimated that these nondipolar interactions contribute approximately − 1600 cm−1 to the total Davydov splitting of the intense 2500‐A transition.

107 citations



Journal ArticleDOI
TL;DR: Very high-resolution optical spectra reveal fine structure in the 1B2u and 3B1u electronic transitions of naphthalene isotopic mixed crystals, C10H8 as a guest in a C10D8 host as discussed by the authors.
Abstract: Very high‐resolution optical spectra reveal fine structure in the 1B2u → 1Ag and 3B1u → 1Ag electronic transitions of naphthalene isotopic mixed crystals, C10H8 as a guest in a C10D8 host. Extensive experimental data allow the spectral lines to be characterized and assigned. Some of the structure corresponds to the resonance splitting arising from neighboring pairs of guest molecules in the host lattice. In the Frenkel tight‐binding approximation, this structure gives directly the intermolecular excitation transfer matrix elements responsible for the exciton mobilities and the energy band structures of both pure and mixed molecular crystals. For the 1B2u state the largest interchange equivalent interactions are approximately + 15.3 cm−1 and + 3 cm−1 while the largest translation equivalent interactions are approximately + 3.7, − 5.1, − 7.9, and − 3.3 cm−1. For the 3B1u state the largest interchange equivalent interaction is 1.25 cm−1.

Journal ArticleDOI
TL;DR: The 3B1u→ 1A1g intrinsic absorption spectra of C6H6 and C6D6 at 4.2°K have been obtained for the first time at high resolution using the phosphorescence-photoexcitation method as discussed by the authors.
Abstract: The 3B1u → 1A1g intrinsic absorption spectra of C6H6 and C6D6 at 4.2°K have been obtained for the first time at high resolution using the phosphorescence–photoexcitation method. The spectrum exhibits very clear evidence of a pseudo‐Jahn–Teller distortion of the normally hexagonal benzene molecule upon excitation to the triplet state. Factor‐group splitting of the 0–0 and 0–0 + ν1 exciton bands have also been observed. The position of the mean of the 0–0 exciton band of C6H6 when compared to the phosphorescence origin of a C6H6 guest in a C6D6 crystal, indicates that the “static” intermolecular interactions between guest and host are different for C6H6 and C6D6 hosts. This result has important implications for the applicability of mixed crystal theories to benzene.

Journal ArticleDOI
TL;DR: In this paper, the 1,1′-diethyl-2,2′-cyanine has been resolved at 77°K. H-aggregate transitions are appropriately described by a molecular exciton theory.

Journal ArticleDOI
P.J. Dean1
TL;DR: In this article, the authors compare the properties of conventional deep states due to the O donor and Si acceptor with those of a shallow isoelectronic trap such as N and Bi.

Journal ArticleDOI
TL;DR: In this paper, the fundamental absorption edge of AlAs and AlP was investigated by optical transmission measurements from 2° to 300°K, and the absorption edge structure in AlAs is consistent with the conduction band minima at or near X.

Journal ArticleDOI
TL;DR: In this paper, a model for electron-phononon coupling in molecular crystals and its effect on transport of excitons and charge carriers in aromatic hydrocarbon crystals is presented.
Abstract: A model is presented for electron–phonon coupling in molecular crystals and its effect on transport of excitons and charge carriers in aromatic hydrocarbon crystals The model differs from the usual ones in that the coupling is taken quadratic instead of linear in the vibrational coordinates It is shown that this coupling dominates in aromatic hydrocarbons, leading to large frequency shifts in out‐of‐plane molecular vibrations on electronic excitation or ionization The present study is limited to weak intermolecular electronic coupling, implying quasilocalized excitons (or electrons) There are then two limiting modes of diffusion, governed by the rate either of exciton transfer between molecules or of phonon transfer In either limit, at high temperatures, transport occurs by incoherent jumps between adjacent molecules (hopping) and increases or decreases gently with temperature, while at low temperatures, coherent transport decreasing rapidly with increasing temperature occurs The diffusion coefficie

Journal ArticleDOI
TL;DR: The single‐crystal absorption spectrum of 1‐methyluracil, polarized along three mutually perpendicular axes, is investigated from 3200 to 2400 A at room temperature and the transition moment for the lowest π → π* transition is found to be almost parallel to the N1–C4 molecular direction.
Abstract: The single‐crystal absorption spectrum of 1‐methyluracil, polarized along three mutually perpendicular axes, is investigated from 3200 to 2400 A at room temperature. The spectral measurements were made with a microspectrophotometer, and crystal extinction coefficients were obtained from Lambert's law plots. The spectrum polarized normal to the molecular planes uncovers an n → π* transition at 2640 A. The longest wavelength π → π* absorption band at 2755 A exhibits well‐resolved vibrational structure which broadens considerably on the high‐energy side of the band. It is suggested that this broadening results from a perturbation by the underlying n, π* state. The transition moment for the lowest π → π* transition is found to be almost parallel to the N1–C4 molecular direction. The difference of about 23° between the transition moment directions for 1‐methyluracil and 1‐methylthymine agrees well with π‐electron calculations. The exciton splitting of the 0, 0 band for the lowest π → π* transition is in qualit...

Journal ArticleDOI
J. E. Rowe1, David E. Aspnes1
TL;DR: In this article, exciton effects on electric field modulation line shapes at general critical points were treated using a Slater-Koster contact interaction to approximate the Coulomb potential, which produced a mixing of one-electron line shapes similar to that calculated for an unperturbed solid.
Abstract: Exciton effects on electric field modulation line shapes at general critical points are treated using a Slater-Koster contact interaction to approximate the Coulomb potential. This interaction produces a mixing of one-electron line shapes similar to that calculated for an unperturbed solid. By comparison with experiment, we show that exciton effects are present in the ${E}_{1}$ structure of low-temperature electroreflectance data of Ge.

Journal ArticleDOI
TL;DR: In this paper, a strong coupling theory is developed and is used to calculate the vibrational structure of the collective excitation in the Frenkel limit, where the frequency dependence of the self-energy of the excitation and dispersion in the optical phonon branch of the vibration spectrum are included in the analysis.
Abstract: This paper is concerned with a study of the interaction between collective electronic excitations and collective vibrational excitations in a molecular crystal. A strong coupling theory is developed and is used to calculate the vibrational structure of the collective excitation in the Frenkel limit. The frequency dependence of the self‐energy of the excitation and dispersion in the optical phonon branch of the vibrational spectrum are included in the analysis. The line shapes in the absorption spectrum of a molecular crystal are considered for the two limiting cases of exciton–phonon coupling—namely weak and strong coupling. One of the topics considered in detail is the damping of the zero phonon transition.

Journal ArticleDOI
Koichi Shindo1
TL;DR: In this article, the Green's function was extended to the case that the interaction is not instantaneous, and the energy corrections to the exciton due to recoil effects, retardation effects, renormalization constants and vertex parts arising from the interactions of an electron and a hole forming an exciton with longitudinal optical phonons were explicitly calculated by using the extended method.
Abstract: The Green's function method developed by Mahan for excitons is extended to the case that the interaction is not instantaneous. Energy corrections to the exciton due to recoil effects, retardation effects, renormalization constants and vertex parts arising from the interactions of an electron and a hole forming an exciton with longitudinal optical (LO) phonons, which were treated by Haken in another simplified manner, are explicitly calculated by using the extended method to first order in electron-phonon coupling constant α and in (\(E/\hbar\omega_{l}\)), where E is the binding energy of the exciton and ω l is the LO phonon frequency. It is shown that in these corrections, the recoil effect and the retardation effect cancel out each other and the renormalization effect and the vertex effect cancel out each other, and a resultant effective interaction between the electron and hole is reduced to Haken's result for large electron-hole separations.

Journal ArticleDOI
TL;DR: In this article, the energy band calculations of the solid rare gases Ne, Ar, Kr, and Xe and the conduction band density of states of Xe were presented based on the relativistic formulation of the Green's function method.
Abstract: Energy band calculations of the solid rare gases Ne, Ar, Kr, and Xe and calculations of the conduction band density of states of Kr and Xe are presented. Except for Ne the calculations are based on the relativistic formulation of the Green's function method. Exciton states of the valence Γ-excitons in Ar, Kr, and Xe have been computed using the pseudopotential formalism of the exciton problem proposed by Hermanson and Phillips and on the basis of the calculated energy bands. The dependence of the exciton binding energies on certain band parameters has been studied. The results are discussed in connection with the optical spectra of the solid rare gases measured by Baldini and the DESY group.

Journal ArticleDOI
TL;DR: In this paper, low-temperature optical spectra of AgBr:Cl were studied and two kinds of phonons assisting the indirect transition of free and bound excitons were observed.
Abstract: Low temperature optical spectra are studied on AgBr:Cl - in comparison with AgBr. Contrary to AgBr:I - , no bound excitons at chlorine are formed in AgBr:Cl - . Absorption spectra of AgBr:Cl - are similar to AgBr, except for existence of exciton absorption without phonon assistance. Photoluminescence spectra of AgBr and AgBr:Cl - contain emission band due to decay of free exciton. This observation leads one to conclude that positive holes in AgBr are not self-trapped even at 2°K. Comparison of free exciton transition energies between absorption and emission spectra reveals existence of two kinds of phonons assisting the indirect transition. Various extrinsic emission bands are also observed. One of them corresponds to shallow-bound exciton at Cd 2+ -type impurity and the other to deep-bound exciton at residual iodine. Transition energies of free and bound excitons, except iodine-bound exciton, shift to higher energy in proportion to chlorine concentration. These results can be explained by virtual crystal...

Journal ArticleDOI
TL;DR: In this article, the free exciton emission in CdS crystals is measured at 4.2 and 77°K both for zero-phonon emission lines (n = 1 A, n = 1 B and n = 2 A ) and for line of exciton annihilation with simultaneous creation of LO phonon ( A 1 - LO).

Journal ArticleDOI
TL;DR: In this article, the authors surveyed phonon structures in the optical spectra of localized electrons and intrinsic excitons from a unified view-point, and classified the phonon motion in a deformable lattice into three types, which are closely correlated with features of exciton emission spectra.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the luminescence spectra of condensed inert gases excited by an electron beam and showed that a transfer of excitation energy from atoms of lower atomic number to those of higher atomic number was observed.

Journal ArticleDOI
TL;DR: In this paper, the low temperature reflectivity of Li and Na halides between 5 and 10 eV was investigated and attributed to the exciton-phonon interaction, and the fine structure accompanying the lowest exciton has been detected in some crystals.
Abstract: New results on the low temperature reflectivity of Li and Na halides between 5 and 10 eV are reported and discussed on the basis of recent band structure calculations. Furthermore, fine structure accompanying the lowest exciton has been detected in some crystals. This structure is examined in detail and attributed to the exciton-phonon interaction.

Journal ArticleDOI
TL;DR: The diffusion length of singlet excitons in crystalline tetracene was measured in the temperature range 293 to 160 °K utilizing the quenching effect exerted on the crystal fluorescence by exciton traps located at the crystal surface as mentioned in this paper.
Abstract: The diffusion length ls of singlet excitons in crystalline tetracene was measured in the temperature range 293 to 160 °K utilizing the quenching effect exerted on the crystal fluorescence by exciton traps located at the crystal surface. It is found that ls = 120 ± 10 A at room temperature. It increases exponentially with decreasing temperature until it approaches a constant value of 580 ± 50 A below 190 °K. The temperature dependence of the singlet exciton lifetime determined by exciton fission can fully account for the observed temperature dependence of the diffusion length. Therefore energy localization, like excimer formation, cannot be an effective process. The exciton diffusion coefficient is by a factor of 4 higher than in anthracene crystals. This can be explained in terms of the increase in the Davydovsplitting.

Journal ArticleDOI
TL;DR: In this paper, an anisotropy in the effect of magnetic field on the photo-enhanced bulk conductivity in anthracene and tetracene single crystals was found, which may be explained in terms of a triplet exciton-trapped hole interaction.

Journal ArticleDOI
TL;DR: In this article, the authors measured the optical properties of GaTe single crystals, such as absorption coefficient, photoconductivity and reflectivity, and deduced the energy gap and exciton binding energy from the shape of the absorption curve near the edge.
Abstract: Some optical properties of GaTe single crystals, such as absorption coefficient, photoconductivity and reflectivity, have been measured. The crystal is usually p -type with carrier density 10 16 cm -3 , mobility 15 cm 2 /volt·sec and resistivity 20\(\varOmega\)·cm at room temperature. In the measurement of the photoconductivity, a minimum of the photoresponse corresponding to the strong line structure of absorption is observed and therefore the line structure is interpreted to be due to the formation of excitons. The energy gap and exciton binding energy are deduced from the shape of the absorption curve near the edge. The energy gap is 1.797 eV at 77°K and 1.700 eV at 300°K and the temperature coefficient ∂ E g /∂ T is found to be -4.35×10 -4 eV/°K. The exciton binding energy and the reduced effective mass associated with conduction and valence band are 0.025 eV and 0.089 m 0 , respectively. The reflectivity is found to change rapidly at the photon energy corresponding to the exciton absorption.