Wavelength-modulated Reflectivity Research Articles

Chemical vapor transport of chalcopyrite semiconductors: CuGaS2 and AgGaS2

Crystals of CuGaS2 and AgGaS2 with different isotopic compositions have been grown by chemical vapor transport (CVT) using iodine as the transport agent. Before performing the CVT growth, sulfur and copper were purified by sublimation and etching, respectively. 109Ag and the etched 71Ga isotopes were purified from oxides by vacuum annealing. Transparent yellow orange crystals of CuGaS2 and greenish yellow crystals of AgGaS2 were obtained in the shape of platelets, chunks, rods and needles in sizes of up to 8mm (CuGaS2) and 30mm (AgGaS2).These crystals were used to study their electronic, vibrational and thermodynamic properties. Higher excitonic states (n=2,3) were observed at low temperatures with wavelength-modulated reflectivity spectroscopy, thus proving an excellent surface and crystal quality. In addition, the experimentally determined non-monotonic temperature dependence of the excitonic energies can be well fitted by using two Bose–Einstein oscillators and their statistical factors, corresponding to characteristic acoustic and optical phonon frequencies. Isotopic shift of excitonic energies has also been successfully observed in these crystals.

Isotopic-mass dependence of the A, B, and C excitonic band gaps inZnOat low temperatures

Low temperature wavelength-modulated reflectivity measurements of isotopically engineered $\mathrm{ZnO}$ samples have yielded the dependence of their A, B, and C excitonic band gaps on the isotopic masses of Zn and O. The observed dependence is analyzed in terms of the band gap renormalization by zero-point vibrations via electron-phonon interaction and the volume dependence on isotopic mass. A simplified, two-oscillator model, employed in the analysis, yields zero-point renormalizations of the band gaps, $\ensuremath{-}154\ifmmode\pm\else\textpm\fi{}14\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ (A), $\ensuremath{-}145\ifmmode\pm\else\textpm\fi{}12\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ (B), and $\ensuremath{-}169\ifmmode\pm\else\textpm\fi{}14\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ (C), for $\mathrm{ZnO}$ with natural isotopic composition.

Magnetic susceptibility and compositionaldependence of the energy gap in Cd1-xCoxTe

Single crystals of the diluted magnetic semiconductorCd1-xCoxTe grown by the vertical Bridgman technique arecharacterized by wavelength-modulated reflectivity andmagnetization measurements. Low-temperature magnetization andhigh-temperature magnetic susceptibility analysis were used toextract the exchange integrals for up to third-neighbourCo2+ pairs in the CdTe host: J1/kB = -25pm7 K,J2/kB = -3.0pm1.5 K, and J3/kB = -1.3pm0.3 K. Thesevalues correspond well to the values obtained for other Co-basedII-VI diluted magnetic semiconductors and are a clearmanifestation of the unusually large Co2+-Co2+ antiferromagnetic interaction. The excitonic energy gapEg(x) of Cd1-xCoxTe in the wavelength-modulated reflectivityshows a linearmonotonic increase with increasing x in the composition rangestudied.

Spatial dispersion in polariton spectra of CuGaS2 crystals

The unmodulated and wavelength-modulated reflectivity spectra of CuGaS2 crystals for the polarization E ‖ c, k ⊥ c at 77 and 8 K have been studied. The states n=1, 2, and 3 of A excitons and n=1 and 2 of B and C excitons are established. The luminescence spectra from the surface at k ‖ c and k ⊥ c are obtained. The fine structure of the reflectivity spectra of excitons are analyzed with due regard for the normal and oblique incidence of light onto the crystal surface. The main parameters of the A, B, and C excitonic series are determined such as the energies of the longitudinal and transverse excitons Γ4 (E ‖ c) for states n=1 and 2, the longitudinal and the transverse mass of excitons in CuGaS 2, and the effective masses of electrons (m c1*) and holes (m v1*, m v2*, m v3*). It is shown that the mass m v1* in the upper valence band at k ‖ c equals (0.7–0.8)m 0 and at k ⊥ c, 1.87m 0.

Lattice parameters and optical characterization of Cd 1− xMg xSe alloys grown by vertical gradient freezing technique

Single crystals of Cd 1− x Mg x Se ternaries grown by the vertical gradient freezing technique are characterized by X-ray diffraction and electron probe microanalysis as well as wavelength-modulated reflectivity and photoluminescence to establish their basic structural and optical properties. In the composition range 0< x<0.40, the alloys crystallize in the wurtzite structure with lattice parameters decreasing linearly with increasing Mg concentration ( x). X-ray data considered in the context of interatomic distances yield an improved estimate of the tetrahedral covalent radius of Mg. Energy gap as a function of x increases linearly with increasing Mg concentration. The lattice parameters and the energy gap of the end member of the Cd 1− x Mg x Se wurtzite ternaries, i.e., of MgSe with the wurtzite structure, are deduced from those measurements.

Wavelength-modulated reflectivity study of energy-gap grading in AlxGa1−xAs layers

Wavelength-modulated reflectivity study of energy-gap grading in AlxGa1−xAs layers

Influence of the spin-orbit split-off valence band in InxGa1-xAs/AlyGa1-yAs strained-layer quantum wells.

Quantum-well ground and excited states are observed using wavelength-modulated reflectivity in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As single-quantum-well structures. To account for the dependence of their energies on indium and aluminum concentrations, we find that it is necessary to include the coupling between the light-hole ${\mathrm{\ensuremath{\Gamma}}}_{8}$ valence band and the spin-orbit split-off ${\mathrm{\ensuremath{\Gamma}}}_{7}$ valence band. The calculation is performed using a two-band envelope-function approximation, and good agreement with experiment is obtained.

Electroreflectance and wavelength-modulated reflectivity measurements of Zn1−xMnxTe mixed crystals

Electroreflectance and wavelength-modulated reflectivity data near the fundamental absorption edge of Zn1−xMnxTe solid solutions are presented as a function of temperature and Mn content. From these data the dependence of the energy gap on temperature and composition was determined. The broadening of electroreflectance and wavelength-modulated reflectivity structures is found to depend linearly on [x(1−x)]2 at low temperatures. This indicates that the broadening is produced primarily by the random distribution of Mn and Zn atoms in the lattice.

Electroreflectance and wavelength-modulated reflectivity spectra of Zn1−xMnxSe alloys

Low-field electroreflectance (ER) and wavelength-modulated reflectivity (WMR) spectra have been obtained on Zn1−x Mnx Se single crystals in the whole range of composition, 0≤x≤0.57. An analysis of the ER data enabled us to determine the dependence of the fundamental energy gap on temperature (8 K≤T≤300 K) and Mn molar fraction x. In samples with x≥0.35, which crystallize in a wurtzite structure, two or three temperature-dependent features are observed in WMR spectra and in some ER spectra. We identify these peaks with the ground-state excitons for different valence bands in hexagonal Zn1−x Mnx Se. The observed crystal-field splitting is ∼20 meV for x=0.39 and decreases with increasing Mn content.

Visible and ultraviolet reflectivity of Hg1−xCdxTe

The reflectivity and wavelength-modulated reflectivity of Hg1−xCdxTe samples were measured in the 2.0–8.8 eV energy range to determine the dependence of the spectral features E1, E1+Δ1,A, and B on composition and on temperature. Spectral features of mechanically polished surfaces and sputter-etched surfaces were broadened, decreased in magnitude, and shifted to lower energies than those features of Br2-etched surfaces. At low temperatures, the spectral features of chemically etched surfaces narrow appreciably more than polished or sputter-etched surfaces, indicating that at room temperature there is a large thermal contribution to the width of the spectral features of chemically etched surfaces.

Wavelength-modulated reflectivity spectra of MnxCd1−xTe alloys at the Γ and Λ points

MnxCd1−xTe alloys are studied by wavelength modulation reflectivity for the composition range 0&amp;lt;x&amp;lt;0.75. Optical transitions around Γ and Λ critical points are investigated from T=10–300 K. In all the composition ranges the nature of the transitions appears to be the same as in CdTe: E0=Γv8−Γc6, E1=Λc6−(Λ4+Λ5)v, E1+Δ1=Λc6−Λv8. The energy position of these structures changes linearly with x.

Deformation potentials of the fundamental exciton spectrum of InP

Wavelength-modulated reflectivity spectra are performed on the direct exciton spectrum of InP under uniaxialstress conditions. Working at liquid-helium temperature, both the fundamental (${E}_{0}$) and spin-orbit split-off transition (${E}_{0}+{\ensuremath{\Delta}}_{0}$) are investigated. For unstressed crystals, at 5 K the $1s$ excitons are found at 1418.2 \ifmmode\pm\else\textpm\fi{} 0.5 and 1526.3 \ifmmode\pm\else\textpm\fi{} 0.5 meV, respectively. The spin-orbit splitting energy (${\ensuremath{\Delta}}_{0}$) is found to be 108 \ifmmode\pm\else\textpm\fi{} 1 meV. Next the stress dependence in configurations $X$ parallel to the [001], [111], and [110] crystallographic axes are investigated. An inability to apply stress magnitudes larger than 3 kbar necessitates analyzing the data with a simple model of orbital-strain interaction which neglects the stress-dependent spin-orbit interaction. Three deformation potentials are deduced: A fully symmetric, interband, deformation potential ${C}_{1}+{a}_{1}=\ensuremath{-}8.0\ifmmode\pm\else\textpm\fi{}0.4$ eV, which gives hydrostatic pressure coefficient $\frac{d{E}_{0}}{\mathrm{dP}}=11.1\ifmmode\pm\else\textpm\fi{}0.6$ meV/kbar and two shear deformation potentials, $b=\ensuremath{-}2.0\ifmmode\pm\else\textpm\fi{}0.2$ eV and $d=\ensuremath{-}5.0\ifmmode\pm\else\textpm\fi{}0.5$ eV. The first one, associated with pure ${\ensuremath{\Gamma}}_{12}(2{e}_{\mathrm{zz}}\ensuremath{-}{e}_{\mathrm{xx}}\ensuremath{-}{e}_{\mathrm{yy}})$ components of the strain tensor, gives the stress-induced splitting of the valence band under [001] compression while the second, associated with ${\ensuremath{\Gamma}}_{15}$ components, corresponds to pure [111] stress. The ratio of experimental splittings in both configurations is related to the anisotropic behavior of the valence band. For InP it is found to be about 0.7.

Exciton spectra in MoSe 2

Wavelength-modulated reflectivity spectra have been performed on 2H MoSe 2 at temperatures from 3.1 to 300 K. The A exciton series for which the n = 3 state was observed for the first time is shown to be anomalous with a Rydberg of 109 meV and a reduced effective mass of 0.62 m o . Several additional structures are observed and interpreted as well; in particular, the first two excited states of the B exciton, seen here for the first time, allow the determination of the parameters of that exciton series. No shift in any of the spectral structures was observed in magnetic fields of up to 7.0 T.

Excitonic effects in ZnTe atE0andE1gaps studied by wavelength-modulated reflectivity spectroscopy

Excitonic effects in ZnTe at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>gaps studied by wavelength-modulated reflectivity spectroscopy

Optical properties of GaSe andGaSxSe1−xmixed crystals

Reflectivity and wavelength-modulated reflectivity measurements on GaSe and $\mathrm{Ga}{\mathrm{S}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ mixed crystals are presented for energies ranging from 3 to 6 eV. Additional electroreflectance measurements are used to investigate the excitonic character of the structure at 3.4 eV in GaSe. The results are discussed on the basis of a new pseudopotential band-structure calculation for GaSe. The prominent spectral structures of GaSe are identified in terms of location in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space and atomic character of the states involved in the transitions. The main structures in the optical-response function of GaSe are found to result from excitations of the Ga-Ga bond and from atomiclike transitions between nonbonding Se $p$ and $s$ states. These main transitions are located in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space close to symmetry determined "special $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ points." The observed mixed-crystal spectra can be decomposed into three classes of transitions which exhibit zero, intermediate, and strong energy shifts with anion substitution. Theoretically, the three classes of transitions are found to take place between states with zero or little, intermediate, and large charge concentrations on the anion sites. Thus, the characteristic energy shifts, observed experimentally can directly be related to atomic spectral properties of sulphur and selenium.

Photovoltaic effect and interband magneto-optical transitions in InP

A study is made of the oscillatory spectral distribution of the photovoltaic (PV) effect of a gold-indium phosphide Schottky barrier in magnetic fields of up to 70 kG. Spectra are obtained for both the direct and wavelength-modulated PV signals, the latter being compared to the wavelength-modulated reflectivity data. The spectra are taken at 4.2 K in the Faraday configuration for both circular polarizations. The transition energies associated with the spectral oscillations are corrected for exciton-binding effects, and are analyzed as Landau levels in terms of the Pidgeon and Brown coupled-bands theory of interband magnetoabsorption. The fit to the data gives a conduction-band effective mass $\frac{{m}_{c}}{{m}_{0}}=0.079\ifmmode\pm\else\textpm\fi{}0.001$ and Luttinger parameters ${\ensuremath{\gamma}}_{1}^{L}=5.15\ifmmode\pm\else\textpm\fi{}0.05$, ${\ensuremath{\gamma}}_{2}^{L}=0.94\ifmmode\pm\else\textpm\fi{}0.03$, and ${\ensuremath{\gamma}}_{3}^{L}=1.62\ifmmode\pm\else\textpm\fi{}0.03$. The direct observation of the split-off valence-band-to-conduction-band transition gives ${\ensuremath{\Delta}}_{0}=0.108\ifmmode\pm\else\textpm\fi{}0.003$ eV and an approximate effective mass of $\frac{{m}_{\mathrm{so}}}{{m}_{0}}=0.21\ifmmode\pm\else\textpm\fi{}0.02$.

Excitons in molybdenum disulphide

Optical spectra of Mo${\mathrm{S}}_{2}$ in the excitonic region were obtained by photoconductivity, photovoltaic effect and wavelength-modulated reflectivity at temperatures of 300 to 4.2 K and in magnetic fields of up to 70 kG. Cleaved natural crystals and synthetic crystals studied in both the Faraday and Voigt configurations showed nearly the same characteristics. The results indicate the possibility of up to four excitonic series in Mo${\mathrm{S}}_{2}$ as in other Mo dichalcogenides, and support band-structure calculations predicting flat conduction and valence bands originating from Mo orbitals. A ground-state anomaly of the $A$ exciton is explained by a central cell correction of the type used by Harbeke and Tosatti to explain a similiar anomaly in Pb${\mathrm{I}}_{2}$. The reduced mass of the $A$ exciton is found to be ${\ensuremath{\mu}}^{*}\ensuremath{\simeq}0.4{m}_{0}$, both from the study of the series itself, and from its magneto-optical properties, thus removing a large discrepancy found in previous work.

Lineshape of derivative reflectivity near the fundamental edge of GaTe

Wavelength-modulated reflectivity measurements have been made on GaTe single crystals in the exciton absorption region in the neighbourhood of the band gap. Lineshapes of Δϵ 2, the oscillator strength and the exciton binding energy have been evaluated.

Wavelength-modulated spectra of some Fe3+ oxides

The wavelength-modulated reflectivity spectra in the visible and near uv of GdIG, LuFeO3, FeBO3, Fe2O3, Fe[NiFe]O4, and BaFe12O19 are reported. Features of both the exciton sideband and the charge-transfer spectra are observed. Comparison of these spectra allows some site assignments to be made. In particular the octahedrally coordinated Fe3+ ion is found to contribute a characteristic charge-transfer spectrum that occurs at lower energies than the tetrahedral Fe3+ charge-transfer spectrum. A further charge-transfer process between octahedral and tetrahedral Fe3+ sites is suggested to explain the garnet spectra.

Optical spectra of CsI, CsBr, ZuGeP 2, and SbSI

We report here the study of the normal reflectivity spectra R and the corresponding derivative spectra (1/ R) d R/d E of SbSI between 2 and 6 eV. The spectra show very strong anisotropy. We have also tried to use the change of the wavelength modulation spectrum to monitor the change in the band structure of SbSI due to the phase transition at 292 °C (D 2h 16→C 2v 9). Careful examination of the spectra at various temperatures around T c shows no observable change. We report also the wavelength-modulated reflectivity spectra of the chalcopyrite crystal ZnGeP 2 at 5 K between 2 and 6 eV, for E∥ C and E⊥ C. The experimental results are compared with the theoretical band structure calculation by de Alvarez and Cohen. We also present measurements on CsBr, CsI in the vacuum uv (between 5 and 8 eV) at 1.8K, showing noticeable difference with previous reflectivity measurements at 77 K.