Phonon-assisted Indirect Transitions Research Articles

Effect of Bi 2O 3 content on the optical band gap, density and electrical conductivity of MO·Bi 2O 3·B 2O 3 (M = Ba, Sr) glasses

Glasses with compositions 20MO· xBi 2O 3·(80− x)B 2O 3 (M = Ba, Sr) with 10 ≤ x ≤ 60 (in mol%) have been prepared using the normal melt-quench technique. The optical absorption spectra of the glasses have been recorded in the wavelength range 400–700 nm. The fundamental absorption edge has been identified from the optical absorption spectra. The values of optical band gap for indirect allowed and indirect forbidden transitions have been determined using available theories. The origin of the Urbach energy is associated with the phonon-assisted indirect transitions. The density and molar volume studies indicate that Bi 2O 3 in these glasses is acting partly as network modifier and partly as network former. Values of the direct-current electrical conductivity have been measured from 373 to 623 K and the activation energy has been calculated. The variations in optical band gap, density and electrical conductivity with Bi 2O 3 content have been discussed in terms of changes in the glass structure. Values of the theoretical optical basicity are also reported.

Electron-phonon renormalization of electronic band gaps of semiconductors: Isotopically enriched silicon

Photoluminescence and wavelength-modulated transmission spectra displaying phonon-assisted indirect excitonic transitions in isotopically enriched $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, as well as in natural $\mathrm{Si}$, have yielded the isotopic mass $(M)$ dependence of the indirect excitonic gap $({E}_{gx})$ and the relevant phonon frequencies. Interpreting these measurements on the basis of a phenomenological theory for $(\ensuremath{\partial}{E}_{gx}∕\ensuremath{\partial}M)$, we deduce ${E}_{gx}(M=\ensuremath{\infty})=(1213.8\ifmmode\pm\else\textpm\fi{}1.2)$ meV, the purely electronic value in the absence of electron-phonon interaction and volume changes associated with anharmonicity.

A photoacoustic spectroscopic investigation of the optical energy gap in Zn–Mn–Se type dilute magnetic semiconductors

Using photoacoustic spectroscopy (PAS) we have measured the composition dependent optical absorption coefficient and band gap of the Zn l− x Mn x Se (0≤ x≤0.5) diluted magnetic semiconductors at room temperature. The band gap E 0 estimated from the PAS spectra varies nonlinearly, showing a downwards bowing with the Mn-concentration. The exchange interaction of electrons in conduction and valence bands with the d-electrons of Mn ion interactions, effects of polytypes, micro-structures and mixed crystallization (zinc-blende and wurtzite structures) are considered for the analysis of the data. The observed exponential edge (Urbach's edge) can be considered as an internal Franz–Keldish effect arising from the charged impurity-generated and “frozen-in” optical phonon-generated fields. This can be described in the framework of the Tauc and Dow–Redfield model. The phonon-assisted indirect transition at the band tail regions for some samples are also observed from the present studies.

Observation of direct and phonon-assisted indirect transitions inGaAs/GaxAl1−xAsmultiquantum wells under hydrostatic pressure

Using photomodulated transmission spectroscopy we investigated the interband transitions in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ multiquantum wells as a function of hydrostatic pressure up to 50 kilobar. A number of spectral structures, associated with the \ensuremath{\Gamma}, $L,$ and $X$ critical points in GaAs wells and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ barriers were observed, and calculations were performed to help understanding their origins. The pressure coefficients of the direct transitions in the quantum wells fall between those of GaAs and ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ bulk. The observation of phonon-assisted indirect transitions is made easy by photomodulated transmission technique, and by the band folding effect in the multiple-quantum-well systems. The indirect transitions derived from the $L$ conduction subbands and \ensuremath{\Gamma} valence subbands have been observed in wide pressure ranges.

Investigation of L-related indirect transitions in GaAs/GaAlAs multiquantum wells under hydrostatic pressure

Intersubband transitions in GaAs/GaAlAs multiquantum wells (QW) under hydrostatic pressure have been investigated with photomodulated transmission spectroscopy and free-standing QW samples. In addition to the direct transitions associated with the Γ critical points, several L-related transitions between the L conduction band and the Γ valence band of the GaAlAs barriers and between the L conduction subbands and the Γ valence subbands inside the GaAs quantum wells are observed. The distinct L-related spectral features are a clear indication that photomodulated transmission is particularly useful for enhancement of the weak phonon-assisted indirect transitions.

No-Phonon and Phonon-Assisted Indirect Transitions in Si1−xGex Single Crystals

ABSTRACTThe absorption properties of high quality bulk Si1−xGex single crystals (0 ≤ × ≤ 0.16) are studied. Transmission measurements were performed at the indirect absorption edge. The shape of the absorption edge is characterized by structures attributed to the onset of no-phonon and phonon-assisted indirect optical transitions. Threshold energies have been determined using a differential method. A corrected calibration function for the dependence of the excitonic energy gap on composition is presented for the compositions, where x ranges from 0 to 0.16. The presented calibration function can be used for the composition analysis by an optical method. The analysis is independent of absolute transmission values.A simulation of the absorption spectra by calculations based on second order perturbation theory was used to fit the experimental data This procedure allows to estimate the oscillator strength of the no-phonon transition in dependence on x.

Electronic band structure of isotopically pure germanium: Modulated transmission and reflectivity study.

The piezomodulated and photomodulated reflectivity spectra of monoisotopic Ge ${(}^{70}$Ge, $^{73}\mathrm{Ge}$, $^{74}\mathrm{Ge}$, $^{76}\mathrm{Ge}$) and natural Ge measured at T=6 K show clear signatures of the ${\mathit{E}}_{0}$ and the ${\mathit{E}}_{0}$+${\mathrm{\ensuremath{\Delta}}}_{0}$ transitions; their energies increase with increasing isotopic mass. From a comparison of the phonon-assisted indirect transition energies obtained from electromodulated and wavelength-modulated transmission and photoluminescence, the isotopic mass dependence of both the indirect gap and the relevant zone-boundary phonons are deduced. The isotopic-mass dependence of the energy gaps is interpreted in the context of the electron-phonon interaction and the volume expansion of the crystal lattice.

Observation of coherent optical phonons inBiI3

Resonant coherent lattice vibrations in the vicinity of the indirect absorption edge in a ${\mathrm{BiI}}_{3}$ layered crystal are observed in a femtosecond pump-probe experiment. Coherent optical phonons that are impulsively excited by femtosecond pump pulses modulate the phase of probe pulses, causing oscillation of the probe spectrum in time. This oscillation, which has a period given by the period of the oscillation, continues for more than 100 cycles. We speculate that the coherent phonon-assisted indirect exciton transitions also contribute to the data.

Reply to "Comment on 'Radiative and nonradiative recombination of bound excitons in GaP:N. I. Temperature behavior of zero-phonon line and phonon sidebands of bound excitons' and 'Radiative and nonradiative recombination of bound excitons in GaP:N. IV. Formation of phonon sidebands of bound excitons' "

For excitons trapped at deep centers such as N in GaP, the phonon sidebands are composed of a phonon-assisted momentum-conserving indirect transition and a multiphonon transition. As a result, the temperature dependence of phonon sidebands can be different from that of the corresponding zero-phonon lines. We suggest distinguishing the term ``replica'' due only to multiphonon processes from the term ``sideband.'' A full-kinetic-analysis method is suggested for use in unraveling the complicated temperature dependence of the luminescence of bound excitons in GaP:N.

Neutron-irradiation effect on the absorption edge of NaBrO3 single crystals

Single crystals of sodium bromate are prepared from an aqueous solution of pure material. The effect of neutron irradiation on the absorption edge and indirect band-gap energy, as well as phonon-assisted indirect transitions, are studied in the low-absorption region.

Optical absorption coefficient of silicon at 1.152 μ at elevated temperatures

The optical absorption coefficient of silicon has been measured at the HeNe near-infrared line (λ = 1.152 μm) from room temperature to 1140 K. The results are compared with the previous less extensive data in the literature, and with the formulation given by Macfarlane et al. [Phys. Rev. 111, 1245 (1958)]. It is found that the absorption is described very well by phonon-assisted indirect transitions across an energy gap having the temperature dependence described by Thurmond.

Calculation of theΓ−ΔElectron-Phonon and Hole-Phonon Scattering Matrix Elements in Silicon

With use of the "rigid-pseudoion" model, the first calculation of the electron-phonon and hole-phonon scattering matrix elements for the TO, LO, TA, and LA phonon-assisted indirect transitions ($\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Delta}$) in Si has been performed. Excellent agreement with experimental values for the TO phonon is found. Based on the present results, the intensities of the entire $\ensuremath{\Gamma}\ensuremath{-}\ensuremath{\Delta}$ indirect spectrum of this material can be accurately described, thereby rigorously testing the model.

Angle-resolved photoemission study of the clean Cu (001) surface in the photon energy range40≤ℏω≤120eV: Comparison of experiment and simple direct-transition theory

Angle-resolved photoemission spectra obtained from the clean Cu (001) surface with photon energies in the range 40-120 eV and emission both normal and non-normal to the surface are well predicted by a simple constant-matrix-element model based upon direct ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ conserving) transitions between initial electronic states with full bulk translational symmetry and final states with a free-electron dispersion relation and a correction for refraction at the crystal surface. In addition, the quantitative agreement between theory and experiment improves significantly by including broadening in the final-state wave vector for spectra obtained in the highly-surface-sensitive region around 100 eV. A strong contribution of phonon-assisted indirect transitions to the spectra also appears to be present. The photoemission spectra have been obtained at two different polarization orientations with respect to the electron emission direction and this can be used for assigning contributions from various initial states.

Optical absorption in iron pyrite (FeS2)

Optical absorption studies in thin (\ensuremath{\sim}100 \ensuremath{\mu}m) natural single crystals of iron pyrite (Fe${\mathrm{S}}_{2}$) are reported in the energy range of 0.7-1 eV. The measurements were made at several temperatures between 20 and 297 K in two samples of different impurity level. In the low-resistivity sample, there is a pronounced absorption varying nearly as ${\ensuremath{\lambda}}^{2}$ ($\ensuremath{\lambda}$ is the wavelength) for energies below the absorption edge. This is probably free carrier absorption. In the high-resistivity sample, it is shown that the absorption band results from phonon-assisted indirect transitions between the valence and the conduction band. From this analysis, the energy of the participating phonon and the band-gap energy ${E}_{g}$ are evaluated at different temperatures. It is found that ${E}_{g}=0.835\ensuremath{-}\frac{\ensuremath{\alpha}{T}^{2}}{(1395\ensuremath{-}T)}$ with $\ensuremath{\alpha}=6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ eV/K. At lower temperatures, three sharp peaks are superposed on the absorption curves. These peaks have been tentatively designated as transitions to exciton levels.

Phonon-Assisted Indirect Transitions in Cadmium Sulfate Crystals

The fundamental absorption edge of “suprapur” cadmium sulphate (3CdSO4 · 8H2O) crystal occurs in the region below 200 nm. The power-law dependence of the optical density on photon energy suggests indirect electronic transitions made possible by the emission or absorption of 0.067 eV phonons. The indirect band gap (Eg′) at 300 K is 6.09 eV. The phonon energy of 0.067 eV is found to arise from one of the Raman-active modes (E ) of the sulphate ion. The band edge is found to shift monotonically towards higher energies at a rate of - 2.3 meV per K between 300 and 77 K. The laser Raman spectrum of the 3CdSO4 · 8H2O is also reported.

Study of Absorption Spectra of Excitons in Cu2O by Wavelength Modulation Technique

The wavelength derivative absorption spectra of Cu 2 O have been measured in the energy regions of the yellow and green exciton series over a wide temperature range. Three phonon assisted indirect transition edges are newly found at 4.2 K, and the structures associated with direct transitions to the 1s state and the higher exciton states are observable up to room temperature. By analysing the impurity associated transition and using the Rydberg constants for both the yellow and the green exciton series, we determine the effective mass of the electron in the conduction band and those of the holes in the valence bands to be m e * ≃0.99 m 0 , m l h * ≃0.64 m 0 (light hole) and m h h * ≃1.40 m 0 (heavy hole).

Indirect Exciton Absorption in Germanium

The indirect exciton absorption in germanium has been investigated using a high-sensitive wavelength modulation technique. The spectrum shows that the structures of indirect-allowed and -forbidden transitions have been clearly identified. It has been established experimentally that the L O phonon-assisted indirect transition is attributed to a forbidden transition, as expected by considerations of the selection rule. The T A phonon-assisted indirect exciton absorption spectrum is interpreted as due to a type of indirect transition which has the optical process for vertical direct transitions allowed and the scattering process for electron-phonon interaction forbidden: the intermediate state in the virtual transition is attributed to \(\varLambda_{3}\) state, whereas the allowed L A phonon-assisted transition is related to the lowest \(\varGamma_{2}{'}\) intermediate state.

Excitonic Theory of Electroabsorption: Phonon-Assisted Indirect Transitions in Si and Ge

The theory of indirect phonon-assisted optical absorption by semiconductors in a uniform electric field is developed with particular attention being paid to the effects of electron-hole correlations (excitons). The Coulombic electron-hole interaction is treated within the Wannierexciton effective-mass approximation. The physics of indirect electroabsorption is discussed, and it is found that exciton theory predicts an indirect absorption spectrum which is dramatically different, both qualitatively and quantitatively, from the spectrum predicted by one-electron theory (neglecting electron-hole correlations). The excitonic correlations are responsible for four qualitative features found in measured differential electroabsorption spectra but omitted by the one-electron theory: (i) The threshold for potical absorption by excitons lies at a lower energy; (ii) excitons cause a sharp drop on the high-energy side of the first differential electroabsorption peak; (iii) the amplitude of the differential absorption is enhanced by excitons; and (iv) excitonic spectra exhibit longer periods of spectral oscillations. These excitonic effects are analogous to effects previously predicted for direct transitions. Numerical calculations of the differential electroabsorption at the indirect edges of Ge and Si are compared with the data of Frova et al. and are found to be in excellent agreement with experiment.

Indirect Optical Absorption of AgCl-AgBr Alloys

High-resolution measurements of the optical absorption edge of pure crystals of AgBr and AgCl are in good agreement with the theory of phonon-assisted indirect transitions. The indirect optical absorption of AgCl-AgBr mixed crystals has been studied between 4.2 and 77\ifmmode^\circ\else\textdegree\fi{}K. At 4.2\ifmmode^\circ\else\textdegree\fi{}K, the addition of AgBr to AgCl causes the absorption edge to shift continuously from the pure AgCl threshold at 3.252 eV to the pure AgBr threshold at 2.691 eV. Above 5.7 mole% AgBr in AgCl, the absorption coefficient increases steeply to values considerably greater than that of pure AgBr at the same wavelength. The effect of the alloying on the pure-crystal absorption spectra is somewhat different for the two extremes of mixing. In AgBr-rich mixed crystals (>90 mole% AgBr in AgCl), a temperature-independent component with a sharp threshold is observed at an energy precisely halfway between the indirect phonon-emission and phonon-absorption thresholds (which still appear with phonon energy 0.0082 eV as in pure AgBr). This suggests that nonvertical transitions can occur in the alloy without the aid of phonons to conserve crystal momentum. The zero-phonon threshold is not so evident for dilute concentrations of AgBr in AgCl, where a weak shoulder and tail extends approximately 0.07 eV to longer wavelengths. Some comparison with theory is given, but present understanding of the band structure of alloys is rather incomplete.

Intrinsic Optical Absorption in Germanium-Silicon Alloys

The intrinsic optical absorption spectrum for the germanium-silicon alloy system has been measured as a function of temperature and composition. Over the entire composition range the absorption near the threshold ($Kl100$ ${\mathrm{cm}}^{\ensuremath{-}1}$) exhibits a temperature dependence which is characteristic of phonon-assisted indirect electronic transitions. There appears to be no temperature-independent component of the absorption attributable to disorder-assisted transitions. When the phonon contribution to the absorption is explicitly taken into account, as in a Macfarlane-Roberts type analysis, the experimental data yield an equivalent phonon temperature which varies from 270\ifmmode\pm\else\textpm\fi{}20\ifmmode^\circ\else\textdegree\fi{}K for pure Ge to 550\ifmmode\pm\else\textpm\fi{}50\ifmmode^\circ\else\textdegree\fi{}K for pure Si, with most of the variation occurring in the middle of the composition range. The composition dependence of the derived energy gap shows an abrupt change in slope at about 15 atomic percent Si. This is due to a switch from a Ge-like ([111]) to a Si-like ([100]) conduction band structure. The onset of direct electronic transitions (${10}^{2} {\mathrm{cm}}^{\ensuremath{-}1}lKl{10}^{4} {\mathrm{cm}}^{\ensuremath{-}1}$) was observed as a function of composition in the Ge-rich alloys. The data show that the [000] conduction band minimum moves more rapidly than the [111] minima as Si is added to Ge. In an attempt to account for the observed variation of the phonon equivalent temperature with composition, certain lattice vibrational modes were computed on the basis of a number of simplified models. The one which gives the most realistic results emphasizes the presence of atoms of different masses and some short-range order in the alloy lattice.