Indirect Absorption Edge Research Articles

Two-phonon resonant Raman scattering at the indirect exciton in silver chloride

Resonance Raman scattering in AgCl is reported for excitation in the indirect absorption edge at 1.8K. The observed scattering involves pairs of momentum-conserving TA(L) and LA(L) phonons with energies of 8.2 and 12.9 meV, respectively. The qualitative analysis of the scattered intensity on excitation energy suggests that, besides self-trapping as the main relaxation mechanism, intravalley and intervalley scattering by various acoustic and/or optical phonons are important in free exciton relaxation.

Pressure dependence of the optical properties and the band structure of the copper and silver halides

The absorption edge of CuCl, CuBr, CuI, and AgI is investigated with a diamond anvil cell as a function of pressure up to 16 GPa. The measurements, which reflect the various phase transitions undergone by these materials, yield the pressure coefficients of the lowest gaps. Particular attention is paid to the high-pressure rocksalt modifications, which are shown to have an indirect absorption edge in contrast to the direct edge of the sphalerite phases. This fact results from the influence of the different lattice symmetries on the halogen-$p$---metal-$d$ hybridization in the valence bands. In order to interpret the data quantitatively, we have performed self-consistent local-density calculations with the linear combination of muffin-tin-orbitals---atomic-sphere approximation method and non-self-consistent Korringa-Kohn-Rostoker calculations with the standard muffin-tin potential. The pressure coefficients so obtained agree reasonably with the experimental ones. The gaps obtained by the self-consistent potential (with no adjustable parameter) are about 2 eV smaller than the experimental ones, thus reflecting shortcomings of the local-density method for excitation properties.

Two-phonon resonant Raman scattering at the indirect exciton in silver chloride

Resonant Raman scattering in AgCl is reported for the first time. With excitation in the indirect absorption edge at 1.8K the observed scattering processes involve pairs of momentum-conserving TA(L) and LA(L) phonons with energies of 8.2 meV and 12.9 meV, respectively. The dependence of the scattered intensity on excitation energy suggests that, in contrast to AgBr, intravalley scattering by long wavelength acoustic phonons and intervalley scattering are negligibly small, the main relaxation mechanism of the free exciton being self-trapping. Some enhancement in the 2LO scattering intensity observed is probably due to resonance with the lowest direct exciton.

Stacking disorder effects on resonance Raman scattering in BiI 3

Resonant Raman scattering (RRS) in BiI 3 has been studied at liquid helium temperature. The two-phonon Raman modes show resonance enhancement for excitation above the indirect absorption edge and their cross sections have similar dispersions to those of Cu 2O by Yu and Shen. When tuning the excitation photon energy at four sharp absorption lines, which were assigned to the bound excitons at stacking faults in a previous work, the different behaviors are observed in the RRS spectra; three of them show rather broad one-phonon Raman lines, while for the other one, a new additional one-phonon line appears. On the basis of these experimental results the electronic states and phonon modes involved are discussed and a probable model of exciton structure responsible for the sharp absorption line at the indirect exciton energy is presented.

IR absorption in p-type pb 0.97Sn 0.03Se

IR absorption in p-type melt grown Pb 0.97Sn 0.03Se crystals is reported. The results for the room temperature absorption coefficient (α) in the wavelength region 2–15 μm are analysed. The indirect absorption edge is found to be at 0.26 eV for this ternary alloy. In the longwavelength region α is found to be proportional to λ 2, in agreement with the classical free carrier absorption expression. The conductivity effective mass of holes is found to be 0.067 m 0 at 300°K.

Momentum Dependence of Electronic Excitations in Polyacetylene

Inelastic-electron-scattering experiments indicate that electronic excitations in polyacetylene, ${(\mathrm{CH})}_{x}$, are similar to those of a semiconductor with wide energy bands and an excitonic or indirect absorption edge. However, the measured bulk-plasmon energy increases linearly with momentum unlike that of known inorganic solids. Heavy doping with As${\mathrm{F}}_{5}$ or iodine is found to result in an inhomogeneous mixture of metallic and insulating regions.

Electronic energy levels of cinnabar (α-HgS)

We have calculated the electronic energy levels of trigonal mercury sulfide in the semiempirical tight-binding scheme. The atomic levels $3s$, $3p$ of sulfur and $6s$, $6p$ of mercury constitute the starting basis set. The computed two-center overlap integrals are subsequently scaled by a common multiplicative factor to reproduce the experimental optical gap. The effect of the atomic virtual level $4s$ of sulfur on the conduction bands is also taken into account. The calculated valence-band structure agrees well with the ultraviolet-photoelectron-spectroscopy (UPS) data. The complete band structure is consistent with the absorption measurements which indicate an indirect absorption edge immediately followed by the direct one (at the zone center). This picture can also explain the dependence of the absorption coefficient on the polarization of the exciting light in terms of the symmetry of the levels and the selection rules.

Resonant Brillouin scattering in GaP near the indirect absorption edge

Resonant Brillouin scattering in GaP by the transverse acoustic phonons has been studied at room temperature in the region of the indirect absorption edge by making use of an acoustic-domain injection method. The spectral dependences of the Brillouin-scattering cross sections have shown a monotonic decrease (resonant cancellation) as the incident-photon energy extends beyond the indirect-gap energy. The experimental dispersion curves have been well interpreted by a theoretical model of the indirect-gap resonance and an additional dielectric theory of the direct-gap resonance. The spectral dependences of the photoelastic constants, | p 11 - p 12| and | p 44|, have also been determined as a by-product of the Brillouin-scattering data.

Deformation potentials of the direct and indirect absorption edges of GaP

We present uniaxial-stress experiments performed on the direct and indirect exciton spectrum of GaP. Two direct transitions (${E}_{0}$ and ${E}_{0}+{\ensuremath{\Delta}}_{0}$) and three indirect phonon-assisted transitions (LA, TA, and TO phonon modes) have been investigated at 77 and 4.2\ifmmode^\circ\else\textdegree\fi{}K, respectively. Very-high-stress conditions have been achieved in this work ($X=19$kbar) which correspond to an axial deformation $\frac{\ensuremath{\delta}l}{l}=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, reaching the elastic limit of the material. We have been able to determine all linear and nonlinear deformation potentials that describe the stress dependence of the topmost valence bands (${\ensuremath{\Gamma}}_{7}$ and ${\ensuremath{\Gamma}}_{8}$) and of the lowest minima of the conduction band (${\ensuremath{\Gamma}}_{6}$ and ${X}_{6}$). The stress splitting of the valence band is produced by (i) the orbital-strain interaction, which is described by two deformation potentials ${b}_{1}$ and ${d}_{1}$, and (ii) the stress-dependent spin-orbit interaction which is described by two extra parameters ${b}_{2}$ and ${d}_{2}$. We find $b={b}_{1}+2$ ${b}_{2}=\ensuremath{-}(1.5\ifmmode\pm\else\textpm\fi{}0.2)$ eV, ${b}_{2}=+(0.2\ifmmode\pm\else\textpm\fi{}0.2)$ eV, $d={d}_{1}+2$ ${d}_{2}=\ensuremath{-}(4.6\ifmmode\pm\else\textpm\fi{}0.2)$ eV, and ${d}_{2}=+(0.3\ifmmode\pm\else\textpm\fi{}0.2)$ eV. The effect of hydrostatic deformation is again interpreted in terms of two deformation potentials ${a}_{1}$ (orbital-strain interaction) and ${a}_{2}$ (strain-dependent spin-orbit interaction). They combine with two hydrostatic deformation potentials for the conduction band ${C}_{1} (\mathrm{at} k=0)$ and ${E}_{1} [\mathrm{at} k=(\frac{2\ensuremath{\pi}}{a})(0,0,1)]$ to give the net pressure coefficients. We find ${C}_{1}+{a}_{1}+{a}_{2}=\ensuremath{-}(9.9\ifmmode\pm\else\textpm\fi{}0.3)$ eV, ${E}_{1}+{a}_{1}+{a}_{2}=+(2.3\ifmmode\pm\else\textpm\fi{}0.5)$ eV, and ${a}_{2}=\ensuremath{-}(0.4\ifmmode\pm\else\textpm\fi{}0.3)$ eV. The shear deformation potential ${E}_{2}$ of the indirect minimum of the conduction band has been obtained from the same series of measurements. We find ${E}_{2}=+(6.3+0.9)$ eV. Lastly, the stress-induced coupling between the lowest minimum of the conduction band (${X}_{6}$) and the next higher minimum (${X}_{7}$) has been observed, and is described by a single deformation potential ${E}_{3}$. We find $|{E}_{3}|=13\ifmmode\pm\else\textpm\fi{}1.5$ eV.

Electronic energy-band structure of α quartz

The electronic energy bands of silicon dioxide in the $\ensuremath{\alpha}$-quartz structure have been calculated at several p\^oints of high symmetry in the Brillouin zone by the mixed-basis method. A tight-binding interpolation scheme has been used to determine complete valence bands and their state densities. The results are compared with experiment and with calculations on the higher-symmetry $\ensuremath{\beta}$-cristobalite. The quartz and cristobalite bands share many properties; for example, in both cases the optical-absorption edge is predicted to be direct but forbidden. These results are in partial agreement with pseudopotential calculations by Chelikowsky and Schluter (CS). The major disagreements are that CS predict an indirect absorption edge, and their conduction bands are much wider than ours. Possible reasons for these disagreements are suggested.

The splitting of the 1s excitons in silicon

A splitting into a doublet of the indirect 1s excitons in Si has been revealed by a detailed analysis of optical derivative spectra of the indirect absorption edge. The observed splitting of 0.35 ± 0.05 meV agrees well with theoretical results based on the effective mass approximation. The half width of the split components is 0.13 meV which is considerably smaller than previously reported.

Magneto‐Optical Investigation of the Ground State of the Indirect Free Exciton in Si and Gap

AbstractMeasurements are made of the magnetic circular dichroism (MCD) at the indirect absorption edge of intrinsic Si and GaP at low temperatures and at magnetic fields up to 5 T. By comparison with wavelength modulated spectra it is concluded that the thresholds of the indirect absorption edge for σ+‐ and σ−‐ light are rigidly shifted against each other by the magnetic field. The direction of this shift is connected with the type of assisting phonons. This effect can be explained by the splitting of the 1s ground state of the indirect exciton using group theoretical arguments and can be used to estimate hole g‐values.

The interband Faraday effect—A comparative analysis of germanium and silicon

Methods of polarization modulation lead to a measurement accuracy of 10 −5 in the rotation double refraction and 10 −10 in the intensity ratio of the axes of elliptically polarised light. The interconnection between Faraday rotation (FR) and dispersion is discussed in the sense of Becquerel's equation. In the case of Ge the absorption, dispersion and Fr show a “decoupling phenomenon” in the region of the indirect and direct absorption edges. The FR is due to the superposition of the susceptibility components of the 2.2 eV - and 0.8 eV-transitions. The analysis leads to a sum- g-factor g 2.2 = 1.5 for the 2.2 eV-transitions. In the case of Si (without a decoupling phenomenon) the analysis of the FR (up to 3.35 eV) leads to allowed direct transitions with ΔE = 3.3 eV at Γ- or Δ- point. The oscillating spectra of the FR and the Faraday ellipticity (FE) of Ge were measured from 0.79 eV to 0.86 eV. A screening effect by free carriers proves the dominant role of direct excitons even at room temperature. The FE of Si was measured up to 2.4 eV. The fine structure of this spectrum is due to indirect transitions.

Модуляционная спектроскопия сверхпроводящих дихалкогенидов групп IV-A и IV-B

We have measured the optical properties of HfS2, SnS2 and SnSe2 at 5 K and 300 K in the range (2÷6) eV. We report a large number of new structures and discuss the main transitions in the light of recent band structure calculations. We have also investigated the indirect-absorption edge of the 3 compounds by means of additional piezotransmission measurements at 80 K.

Magnetic circular dichroism of indirect excitonic transitions in GaP and In1‐xGaxP

AbstractMeasurements of the magnetic circular dichroism (MCD) of the indirect absorption edge of intrinsic GaP and In1‐xGaxP (x ≧ 0.77) at temperatures from 2.5 to 300 K and at magnetic fields up to 52 kOe are reported. The fine structure of the indirect absorption edge is well resolved. The MCD peaks corresponding to LA and TA assisted indirect transitions have the same shape as the corresponding peaks in the wavelength modulated spectra, but the latter have different signs. That means that the thresholds of the indirect absorption edge are rigidly shifted by the magnetic field and the direction of the shift is connected with the type of the phonons. Additionally an MCD peak appears in mixed crystals which corresponds to the no‐phonon transition. It has the same sign as the LA‐MCD peak. An attempt is made to interprete the experimental results by group theory within an exciton model. Further theoretical effort is necessary for a satisfactory explanation.

Resonant Raman study of trigonal Se

Resonant Raman scattering has been studied in trigonal Se at low temperatures in the region of its indirect and direct excitonic absorption edges. Whereas no enhancement in Raman cross sections was observed at the indirect absorption edge, strong dispersion was found in the region of the direct excitons. In the vicinity of the direct absorption edge Raman cross sections of one-phonon modes decreased monotonically with increase in photon energy in all three scattering configurations studied. This monotonic decrease in Raman cross sections was explained qualitatively by resonant cancellation between a constant background and a dispersive term due to the 2.20-eV peak in the reflectivity spectrum of Se. Resonant enhancements were observed at the direct excitons only in the scattering configuration where the incident and scattered photons are both polarized perpendicular to the $c$ axis. The enhancements are explained quantitatively by a simple model involving two direct excitons of Se as resonant intermediate states. We have also determined directly the longitudinal and transverse mode splitting of the low-energy $E$ mode in trigonal Se as 7 \ifmmode\pm\else\textpm\fi{} 2 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Temperature dependence of the indirect absorption edge in AgCl: Evidence of a new source of nonparabolicity in the indirect exciton dispersion

The temperature dependence of the indirect absorption edge in AgCl has been studied using wavelength modulation over a temperature range from 7 to 80\ifmmode^\circ\else\textdegree\fi{}K. The results show evidence of exciton formation associated with both the valence-band maximum at $L$ and a subsidiary valence-band maximum at $\ensuremath{\Delta}$. In addition, part of the wavelength-modulation spectrum has been interpreted as being due to nonparabolic effects in the dispersion of the $L$ exciton band. We propose that this nonparabolicity in the exciton dispersion is due to a phonon-induced interaction between the $\ensuremath{\Delta}$ and $L$ exciton bands. We have calculated the expected density of states for the $L$ exciton band assuming that a single phonon is exchanged between the $L$ and $\ensuremath{\Delta}$ exciton bands. The calculated results are in good agreement with experiment.

Temperature dependence of the indirect absorption edge in AlxGa1−xAs

Temperature dependence of the indirect absorption edge in AlxGa1−xAs

Free‐Carrier Generation via Exciton‐Phonon and Exciton‐Impurity Interaction in Ge Crystals

AbstractThe dependence of free electron and hole concentrations on the incident photon energy near the indirect absorption edge in Ge crystals has been investigated by cyclotron resonance at T = 1.8 K. It is shown that such measurements give the possibility to determine the dominant mechanisms of free carrier generation via exciton‐phonon and exciton‐impurity interaction. It is found that in pure crystals free carriers are mainly generated as a result of exciton‐long‐wavelength acoustical phonon interaction. In doped crystals the free carriers are generated due to the interaction of excitons with ionized impurities.

Photovoltage spectra of metal–silicon (p-Type) diodes near the indirect absorption edge of silicon

Photovoltage spectra of Al–, Hf– and Yb–Si(p) Schottky barrier diodes are measured at 300 and 100 K in the photon energy range from 0.8 to 1.3 eV. A detailed analysis of the spectra is made where the following processes are considered: photoemission from metal to semiconductor, band-to-band excitations, and excitations from deep impurity levels in semiconductor. Indirect exciton transitions accompanied both by absorption and by emission of one or two TA, TO, and 0 phonons were observed. The phonon energies, the exciton binding energy, and the shape of the spectrum are compared with earlier experimental results and theory. Measurements with different reverse bias voltages and the analysis of the indirect band-to-band transitions essentially facilitate the determination of the barrier height. Es werden Photospannungspektren von Al–, Hf– und Yb–p-Typ Si Schottky-Dioden bei 300 und 100 K im Photonenenergiebereich von 0,8 bis 1,3 eV gemessen. Eine detaillierte Analyse wird durchgefuhrt, in der die Beitrage der Photoemission vom Metall in den Halbleiter, der Interbandubergange und der Ubergange aus tiefen Storstellen im Halbleiter in Betracht gezogen wurden. Indirekte Exziton-Ubergange werden beobachtet, die sowohl von Absorption als auch Emission von ein oder zwei TA-, TO- und 0-Phononen begleitet werden. Die Phononenenergien, die Exzitonenbindungsenergie und die Form des Spektrums werden mit fruheren experimentellen Resultaten und der Theorie verglichen. Messungen bei verschiedenen Spannungen in Sperrichtung und die Analyse der indirekten Interbandubergange erleichtern wesentlich die Bestimmung der Barrierenhohe.