Exciton Effective Mass Research Articles

Picosecond Time of Flight Measurements of Excitonic Polariton in CuCl

The group velocity of excitonic polariton in CuCl has been measured at 4.2 K using picosecond light pulses. It is derived by measuring both the time delay of light pulses and the thickness of samples. Experimental results are well explained by the dispersion relation of excitonic polariton including spatial dispersion. In addition, the translational effective mass of exciton in CuCl is directly derived, i.e. M =(2.0 ±0.1) m 0 .

The exciton dispersion in polar semiconductors

AbstractThe influence of optical phonons on the exciton dispersion is studied for various coupling strengths as a function of the exciton radius aex. The variational method yields an effective exciton mass which for not too large radii aex (smaller than the polaron‐radii) is reasonably approximated by the bare mass. Only for very large aex, the exciton mass is that of two independent polarons. Corrections to the quadratic dispersion in higher order of the centre of mass momentum are found to be negligible small. The dispersion curves for the materials TlCl and PbI2 are calculated.

Resonant Brillouin scattering via free and bound excitons in CdSe

We report resonant Brillouin scattering results in CdSe. Enhancements in Brillouin scattering have been observed at both the I 2 bound exciton and the free exciton. As a result of the spatial dispersion of the exciton-polariton, the Brillouin frequencies vary with the polariton energy. From this variation of the Brillouin frequencies, we deduced the following parameters in CdSe: transverse exciton frequency =14713 cm −1, splitting between longitudinal and transverse exciton frequencies = 4cm −1 and exciton effective mass (perpendicular to the c-axis) =0.40 times free electron mass. The Brillouin linewidths were found to vary with polariton energies in qualitative agreement with the theory of Brenig, Zeyher and Birman.

Comparison of Additional Boundary Conditions Based on Thermoreflectance Spectra of the An=1‐Exciton in CdS Crystals at Oblique Incidence

AbstractThermoreflectance spectra of the An=1‐exciton in CdS are measured at 8 K for angles of incidence of the light ranging from 5° to 85°, using three different spatial arrangements between the c‐axis, the E‐ and k‐vector of light. Additional boundary conditions of Pekar, Ting et al. and Agarwal et al. are discussed for the first time in terms of optical constants. The refractive indices for these additional boundary conditions are derived, considering special features of CdS, such as optical anisotropy, exciton symmetry, and effective exciton mass anisotropy. Fitting calculations based on the experimental data show that Pekar's additional boundary condition gives the best agreement between theory and experiment.

Coherent pairing of excitons in insulators and semiconductors

A microscopic theory is developed concerning the coherent pairing of Wannier-Mott type excitons in insulators and semiconductors. The coherent pairing of excitons occurs in the presence of a resonant electromagnetic field and the resulting energy gap is in competition with that induced by the electromagnetic field. Due to the electrical neutrality of the electron-hole pairs, the excitation spectrum is of the excitonic insulator type and the presence of the electromagnetic field results in the splitting of the energies of excitation. The expression for the coherent gap function depends on the exciton density, the effective exciton mass, the exciton-exciton interaction, and the effective energy band gap, which is equal to the difference between the transition frequency and the frequency of the field and the binding energy of the exciton. Under resonance conditions and at temperatures below some valueT c , the biexciton state can exist provided that the dielectric gap is less than that for the biexciton state. The ground-state energy resulting from the coherent pairing of excitons is calculated and is found to be lower in energy than the normal exciton state. This indicates the existence of a bound biexciton state as long as there is a net attractive exciton-exciton interaction.

Excitons in 2H-WSe2and 3R-WS2

The A exciton series in the liquid-nitrogen-temperature epsilon 2 spectra of 2H-WSe2 and 3R-WS2, derived from Kramers-Kronig analyses of normal-incidence, basal-plane reflectivity spectra, have been fitted to a Lorentzian oscillator model. It has been found that the energy levels and oscillator strengths of the excitons obey a three-dimensional theoretical model for 2H-WSe2 and a two-dimensional model for 3R-WS2. The experimental observations are consistent with Toyozawa's (1958) theory for weak exciton-phonon interactions and small exciton effective mass.

On exciton absorption, band structure, and phase transformation of GaSe under pressure

AbstractThe spectra of the absorption coefficient (α) of GaSe at the photon energy range 1.94 to 2.64eV and at pressures between 1 bar and 12 kbar are investigated at 295°K. Data at 1 to 4360 bar confirm that the edge exciton of GaSe is the direct allowed one. The pressure coefficient of the band gap (dEg/dP = −6.2 × 10−6eV bar−1), one of the Rydberg exciton constant (dR/dP = −0.6 × 10−6eV bar−1), and one of the exciton effective mass [(1/μ) (dμ/dP) = −2.4 × 10−5 bar−1] are approximately determined. It is supposed that two interband exciton transitions at 2.001 and 3.25eV give the contribution into the α spectrum above 2.1eV. The assignment of these transitions is discussed in connection with the band structure calculation of Schlüter. At 5280 bar a discontinuous jump of the absorption edge shape is observed for GaSe, with a change of the sign and a value for dEg/dP of +2.0 × 10−6eV bar−1 within the range of 5280 to 11780 bar. This effect is interpreted as the transformation of one GaSe polytype into another, i.e. as a possible phase transformation close to that of second kind.

Temperature Genesis of the Curves of Absorption and Dispersion of Light by Ionic Crystals in the Exciton Region

AbstractThe temperature dependence of the curves of absorption and dispersion of light of ionic crystals in the exciton region is investigated taking into account the interaction of excitons with acoustic and optical phonons. It is shown that the shape of the curves depends on the sign of an effective exciton mass m. In the approximation linear in the phonon operators the maxima of the curves shift with increasing temperature towards lower energies when m > 0, and towards higher energies when m < 0.

Lifetimes and Diffusion of Singlet Excitons in Naphthalene Crystals

Fluorescence decay times of naphthalene crystals were observed pulsively and their temperature dependence was analyzed with a mechanism of violated forbidden transition by molecular vibration. Fluorescence decay times of anthracene and naphthacene doped crystals were also observed by a pulsive method and the probabilities of energy transfer from singlet excitons to doped acceptors were observed. The probabilities of energy transfer were analyzed with a model that diffusing excitons transfer their energy to acceptors by dipole-dipole interactions. From the temperature dependence of the probabilities the diffusion coefficient D of an exciton was determined as 1/D=1/α'T -1/2 +1/βT 1/2 exp(hν/kT)-1, where ν is the frequency of the longitudinal optical phonon. This result means that the transport effective mass of exciton is constant in the exciton band of a naphthalene crystal. Above 250 K, the temperature dependence of energy transfer was analyzed with a thermal activation process of the excited acceptor by ...

Polariton Theory of Raman Scattering. III. Effect of Exciton and Band Properties on the Frequency Dependence of the Cross Section

In the present work, a polariton approach is employed to derive cross sections for resonant Raman scattering mediated by dipole-forbidden and quadrupole-allowed excitons. The results are contrasted with those in the dipole-allowed case. We investigate differences in polariton dispersion and in the nature of the discrete-state and continuum contributions in the various cases, and demonstrate how these influence the resonance properties of the cross section. We find that, in general, continuum effects dominate in forbidden scattering, while continuum-discrete interference is strongest in allowed scattering. Considerably sharper onsets to resonance are predicted for the quadrupole case, as compared to the dipole. Resonance properties are shown to depend as well, often strongly, on the values of various crystalline parameters, such as the exciton effective mass and the frequency of the phonons involved in the scattering. The predictions are illustrated via detailed numerical computations for a hydrogenic exciton model, and parameters appropriate to insulators such as CdS.

Polarization Investigations of Localized Exciton States of Doped Benzene Crystals

AbstractThe absorption spectra of localized exciton states of benzene crystals doped with heterocyclic compounds are studied at T = 4.2 °K using polarized light. When the localized level approaches the exciton A‐band edge, the intensity of the localized absorption is shown to increase anomalously in the a‐component and to decrease in the c‐component of the absorption spectrum. Simultaneously the A‐band is partly depolarized and shifts towards the violet side. The experimental results obtained favour certain conclusions about the exciton band structure and the exciton effective mass and are qualitatively interpreted on the basis of current theories of localized states.

Fundamental optical absorption and photo-conduction in PbI 2 single crystals

This paper describes measurements of the optical absorption of gel-grown PbI 2 in the region from 0.5–15 μ and photoconductive measurements in the region of the absorption edge at about 0.525 μ. The edge is dichromatic, with a splitting of 0.048 eV which is explained in terms of a split valence band. The absorption edge of PbI 2 for E ⊥ c is found to obey Urbach's rule for α = 50 cm −1 to 10 4 cm −1 in the temperature range 144–361°K and has a temperature dependence which may be represented by (ΔE/ΔT)α = (9.95-0.60 ln α) × 10 −4 e V °K . A well defined absorption band at 4.2 μ and an activation energy of 0.26 eV evaluated from the measurements of dark current vs. 1 T are attributed to a deviation from stoichiometry. The exciton effective mass in PbI 2 is estimated to be M = 0.094 m 0.

Exciton spectra in thin crystals: the diamagnetic effect

The optical absorption spectrum of MoS2 shows two series of exciton absorption bands associated with direct optical transitions from a split valence band. The diamagnetic shifts of the exciton absorption bands (H[parallel]c, H[perpendicular]c) have been measured and values obtained for the exciton effective mass and anisotropy parameter (ellipsoidal model). In thin crystals the exciton absorption bands occur to the high-energy side of their positions in thick crystals and there is an associated diminution in the diamagnetic shifts.

Structure of Exciton Bands in Crystalline Anthracene

AbstractAn investigation is made of the dependence of the exciton energy, in an anthracene crystal, on the magnitude and direction of the quasi‐momentum in the two energy bands which correspond to the first electron excitation of the molecule. It is shown that the exciton band width, the exciton effective mass, and the magnitude of the “resonance splitting”, depend only on the direction of the quasi‐momentum but also on the dimension of the region where the interaction between the molecules occurs. The theory predicts a polarization of the exciton doublets and gives their position for the various directions of the exciton wave‐vector. From a comparison of theoretical and experimental values for the resonance splitting the radius of the effective molecular resonance interaction in the anthracene crystal is established to be of the order of 0.05 μm.

Exciton states in crystalline argon∗†

The formalism of the preceding paper is applied numerically to exciton states in crystalline argon arising from the atomic 3 p 54 s configuration. Under the assumptions that higher configurations do not perturb the energies and transition probabilities and that the L öwdin symmetrical orthogonalization process converges at terms of order S 2, the F renkel model predicts two exciton absorption lines at 9 eV (±1 eV) separated by 0.2 eV and having a combined integrated absorption coefficient of the order of 10 6 cm −1 eV. The estimated computational error in excitation energy arises not from the neglect of any important interactions but from difficulties in evaluating two- and three-center integrals and from the natural inaccuracy of the atomic H artree-F ock functions. Exciton effective masses are relatively insensitive to the direction of exciton momentum, are of the order of +5 electron masses, and are found to depend primarily on exchange and overlap interactions rather than the H eller-M arcus long-rangp interaction. It is suggested that closely related overlap and exchange terms may be of considerable importance in the attractive part of crystal binding energies, particularly in the rare gases.

Theory of Line-Shapes of the Exciton Absorption Bands

A general theory of line-shapes of the exciton absorption bands is developed with the help of generating function method. When the exciton-lattice coupling is weak, and the exciton effective mass is small, the absorption band is of a Lorentzian shape, provided that the temperature T is not too high. The half-value width H is given by the level broadening of the optically produced K = 0 exciton due to lattice scattering, so that it is proportional to T except at low temperatures. If the coupling is strong, or the exciton effective mass is large, or the temperature is very high, the absorption band is expected to be of a Gaussian shape, and H is proportional to √T. The mutual influence of adjacent absorption bands is also discussed; it causes the asymmetry and repulsion of the components as temperature rises. If we replace T by the density of lattice imperfections, the above statements are valid, without substantial modifications, as regards the dependence on the degree of imperfections. These conclusions are in qualitative agreement with experimental data. The comparison further provides us with information on the strength of the exciton-lattice coupling and the energy band structure of the exciton.