Phonon Replicas Research Articles

Multiphonon resonant Raman scattering and the second-order Raman processes in the excitonic luminescence of ZnO

Multiphonon assisted optical emission processes of ZnO in the vicinity of excitonic luminescence were investigated using the excitation-emission maps and the photoluminescence (PL) excitation spectra recorded at different emission photon energies. Multiphonon resonant Raman scattering (RRS) was found to have the temperature dependence similar to the excitonic luminescence, but not to be influenced by the surface conditions and annealing process. The multiphonon RRS and the longitudinal optical (LO) phonon replicas of PL lines were substantiated to originate from the cascade scattering of exciton polaritons with successively emitting LO phonons. The second-order Raman processes were observed to take part in the capture of exciton polaritons by the defects, forming the neutral donor bound excitons.

The hunt for the third acceptor in CuInSe2 and Cu(In,Ga)Se2 absorber layers

The model for intrinsic defects in Cu(In,Ga)Se2 semiconductor layers is still under debate for the full range between CuInSe2 and CuGaSe2. It is commonly agreed by theory and experiment, that there are at least one shallow donor and two shallow acceptors. Spatially resolved photoluminescence on CuGaSe2 previously revealed a third acceptor. In this study we show with the same method that the photoluminescence peak at 0.94 eV in CuInSe2, previously attributed to a third acceptor, is a phonon replica. However another pronounced peak at 0.9 eV is detected on polycrystalline CuInSe2 samples grown with high copper and selenium excess. Intensity and temperature dependent photoluminescence measurements reveal that this peak originates from a DA-transition from a shallow donor (<8 meV) into a shallow acceptor A3 (135 10) meV. The DA3 transition has three distinct phonon replicas with 28 meV spectral spacing and a Huang Rhys factor of 0.75. Complementary admittance measurements are dominated by one main step with an activation energy of 125 meV which corresponds well with the found A3 defect. The same defect is also observed in Cu(In,Ga)Se2 samples with low gallium content. For [Ga]/([Ga] + [In])-ratios of up to 0.15 both methods show a concordant increase of the activation energy with increasing gallium content shifting the defect deeper into the bandgap. The indium vacancy is discussed as a possible origin of the third acceptor level in CuInSe2 and in Cu(In,Ga)Se2.

Emerging photoluminescence from the dark-exciton phonon replica in monolayer WSe2

Tungsten-based monolayer transition metal dichalcogenides host a long-lived “dark” exciton, an electron-hole pair in a spin-triplet configuration. The long lifetime and unique spin properties of the dark exciton provide exciting opportunities to explore light-matter interactions beyond electric dipole transitions. Here we demonstrate that the coupling of the dark exciton and an optically silent chiral phonon enables the intrinsic photoluminescence of the dark-exciton replica in monolayer WSe2. Gate and magnetic-field dependent PL measurements unveil a circularly-polarized replica peak located below the dark exciton by 21.6 meV, equal to E″ phonon energy from Se vibrations. First-principles calculations show that the exciton-phonon interaction selectively couples the spin-forbidden dark exciton to the intravalley spin-allowed bright exciton, permitting the simultaneous emission of a chiral phonon and a circularly-polarized photon. Our discovery and understanding of the phonon replica reveals a chirality dictated emission channel of the phonons and photons, unveiling a new route of manipulating valley-spin.

Tunable bandgap and blue emission of ZnS nanoparticles induced by controlled S vacancies

Poly(vinylpyrrolidone) capped ZnS semiconductor nanoparticles with a controlled amount of S vacancies have been synthesized through the one step hydrothermal method at low temperatures by varying the concentration of thiourea, the sulfur reagent. The hexagonal wurtzite structure of ZnS with particle like morphology has been identified from powder X-ray diffraction, field emission scanning electron microscopy, and transmission electron microscopy. The formation of compound ZnS and elemental purity has been studied from energy dispersive spectra. The role of S vacancy, the influence of lattice strain and surface defect on the emission, as well as the variation of emission intensity with different excitation wavelengths have been studied using a photoluminescence spectrometer. With an increase in the excitation wavelength, a variation intensity and a red shift in the peak position due to different contributions of free excitonic emissions and its phonon replicas have been noticed and discussed in detail. Raman spectroscopy confirms the formation of ZnS nanoparticles; the shift and broadening in Raman spectra have been studied in detail. The spectral shift and the tunable bandgap of ZnS with S vacancy have been explained on the basis of crystallinity, crystallite size, particle size, lattice strain, and defects on the surface.

Co-solvent medium volume ratio effect on the properties of refluxed sol-gel synthesized ZnO nanopowder

Nanocrystalline ZnO were synthesized using refluxed sol-gel method by varying the co-solvent volume ratio of methanol to water (MeOH:Water) from 0:1 to 1:0 with step of 0.2, respectively. It is known that solvent type and ratio significantly affect the morphology, structural and luminescence properties of ZnO. All the produced ZnO samples have nanoneedle, rod, sheet, spherical and nanoplate like mixed morphology and pure highly crystalline hexagonal wurtzite structure. The crystallite size varies from 22.2 to 26.7 nm with an increase in the amount of methanol in a co-solvent from 0:1 to 1:0 and the average lattice parameters are calculated as a = b = 3.246 Å and c = 5.202 Å. The room temperature PL measurement results showed that both near band gap emission (NBE) at around 380 nm and deep level emission (DLE) in the yellow-green region centered at 530 nm are displayed with an excitation NeCu laser source of wavelength 248.6 nm. The ratio of the intensity of NBE to DLE decreases as the amount of the methanol increases in the solvent. The NBE emission band of the prepared ZnO samples were blue shifted and the emission energy center increased from 3.237 to 3.263 eV as methanol amount increased in the co-solvent. The free and donor-bound excitonic emissions were also studied using low temperature PL measurements and quantum the quenching effects are observed from the results. Primary and secondary longitudinal (LO) phonon replica of the bound excitons also observed during low temperature PL measurements. The optical band gaps of the produced samples determined from UV–Vis reflectance measurements decreased as methanol volume increased in the co-solvent.

Phonon-induced multicolor correlations in hBN single-photon emitters

Color centers in hexagonal boron nitride have shown enormous promise as single-photon sources, but a clear understanding of electron-phonon interaction dynamics is critical to their development for quantum communications or quantum simulations. We demonstrate photon antibunching in the filtered auto- and cross-correlations $g^{(2)}_{lm}(\tau)$ between zero-, one- and two-phonon replicas of defect luminescence. Moreover, we combine autocorrelation measurements with a violation of the Cauchy-Schwarz inequality in the filtered cross-correlation measurements to distinguish a low quantum-efficiency defect from phonon replicas of a bright defect. With no background correction, we observe single photon purity of $g^{(2)}(0)=0.20$ in a phonon replica and cross-spectral correlations of $g^{(2)}_{lm}(0)=0.18$ between a phonon replica and the zero phonon line. These results illustrate a coherent interface between visible photons and mid-infrared phonons and provide a clear path toward control of photon-phonon entanglement in 2D materials.

Near room temperature atomic layer deposition of ZnO thin films on poly (methyl methacrylate) (PMMA) templates: A study of structure, morphology and photoluminescence of ZnO as an effect of template confinement

ZnO thin films were grown on confined Poly (methyl methacrylate) (PMMA) templates, with high coverage and sharp interface, by atomic layer deposition (ALD) at near room temperature (at 35 °C). Crystalline ZnO films, with c-axis orientation along surface normal, were formed on PMMA templates. With decreasing PMMA template thickness, from 80 nm (5Rg, Rg ∼ 16 nm, the radius of gyration of PMMA) to 32 nm (2Rg) and below (5 nm, 0.3Rg), the photoluminescence (PL) of ALD grown ZnO films changes significantly. Pronounced deep level emission (DLE), corresponding to the oxygen vacancy related defect level (VO++) of ZnO grown on 5Rg PMMA, reduced noticeably for ZnO on 2Rg PMMA and below. Furthermore, in the near-band-edge emission (NBE) of ZnO, the contribution of free-exciton (FX) with respect to its phonon replica (FX-2LO) increased with reduction of PMMA template thickness from 5Rg to 2Rg or below. The observed trend of the photoluminescence spectra indicates significant reduction of surface induced defects in the ZnO nanostructures, formed on the thinner PMMA templates (2Rg and 0.3Rg) and can be ascribed to the formation of smaller ZnO nanoparticles on 5Rg PMMA, which is consistent with the results obtained from structure and surface morphology study.

Structural and Optical Properties of GaN Thin Films Grown on Si (111) by Pulsed Laser Deposition

In this work we present results and analysis concerning the processing and characterization of Gallium Nitride (GaN) thin films (TF) grown on Si (111) substrates by pulsed laser deposition technique (PLD), which were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM), photoluminescence (PL) and Raman spectroscopy (RS). The GaN films showed the hexagonal phase with a preferential orientation in the (100) direction, SEM pictures showed a cauliflower-like morphology. Room temperature PL studies showed the so called GaN-yellow band, at 2.29 eV, as well as the donor-acceptor (DA) pair luminescent transition around 3.0 eV. At 10 K, phonon replicas, separated by 69 meV, were observed. By RS, the optical mode on 710 cm-1 was observed, corresponding to the longitudinal optical phonon, A1(LO), as reported for this material.

Electron-phonon interactions in subband excited photoluminescence of hexagonal boron nitride

The h-BN microcrystalline powder with carbon and oxygen impurities have been studied at 83 and 296 K using Raman and photoluminescence (PL) spectroscopies. The observed blue shift of Raman peaks with temperature decreasing have been discussed. Two series of phonon replicas in PL emission spectra with a zero-phonon line at 4.08 eV have been registered under 4.28 eV excitation. The energy levels model of the impurity (CN-ON)-complex responsible for observe luminescence was proposed. It was shown that the optically active center retains its electroneutrality in the processes of radiative recombination under subband (in 4.28 eV) or band-to-band excitation. Possible mechanisms of electron-phonon scattering and phonon replicas forming under subband excitation of (CN-ON)-complex were analyzed. It was substantiated that at 83 K the longitudinal optical (ℏωLO = 174 meV) and transverse acoustic (ℏωTA = 60 meV) phonons at the middle points of high symmetry in the first Brillouin zone participate in the processes of intravalley (M- and Κ-scattering) and intervalley (Κ → Μ)-scattering, respectively.

Luminescent Defects in a Few-Layer h -BN Film Grown by Molecular Beam Epitaxy

We report on luminescent centers contained in a few-layer-thick hexagonal boron nitride (h-BN) film grown on Ni by molecular beam epitaxy. After transfer to a SiO$_2$/Si substrate, sharp lines are observed in photo- and cathodoluminescence spectra in both the ultraviolet and the visible range. Spatially resolved measurements reveal that the luminescent centers responsible for these lines are localized within microscopic multi-layer islands that form at the nucleation centers of the h-BN film. The comparison of their energy, polarization and phonon replica emission with previous theoretical predictions suggest that the N$_\mathrm{B}$V$_\mathrm{N}$ anti-site could be one of the light emitters present in our sample. Moreover, we have also observed evidences of other kinds of centers that could be associated to defects containing carbon or oxygen. The characterized luminescent defects could have potential applications as quantum light sources.

Enhanced Photoluminescence and Stimulated Emission in CsPbCl3 Nanocrystals at Low Temperature

CsPbCl3 nanocrystals (NCs) are known to show low photoluminescence (PL) quantum efficiency compared to CsPbBr3 NCs. In the present work, at 20 K, stimulated emission is observed from CsPbCl3 NCs at low excitation intensity. Efforts are made to understand the optical behavior and structural properties of chemically grown, 5.3 ± 1.1 nm sized CsPbCl3 NCs. Bulk CsPbCl3 is known to become cubic at 320 K, while, NCs are cubic or tetragonal at room temperature. Temperature dependent PL studies on CsPbCl3 NCs are carried out in a wide temperature range. The primary experimental finding is, about 90 times rise in PL emission intensity and existence of multiple sharp features at low temperature attributable to free exciton, bound excitons, phonon replica along with the defect related emission and stimulated emission. The optical phonon energy is about 26 meV with coupling constant of 54 meV in ∼5.3 nm sized CsPbCl3 NCs. Structural phase transition in CsPbCl3 NCs at about 200 K is also observed.

Phonon replicas of type-II GaSb/GaAs quantum dot structure grown by liquid phase epitaxy

Type-II GaSb/GaAs quantum dot (QD) structures have attracted a great deal of attention owing to their unique optical and electrical properties associated with type-II band alignment. In this study, GaSb QDs were grown on GaAs substrates using liquid phase epitaxy (LPE) technique. The morphology of the obtained QDs was studied by scanning electron microscope and atom force microscope. The optical properties of the QDs were investigated by photoluminescence (PL) spectra. Strong first- and second-order longitudinal optical-phonon replicas were observed on the low-energy side of the wetting layer peak in the PL spectra.

Identification of Defect Levels in Copper Indium Diselenide (CuInSe2) Thin Films via Photoluminescence Studies

Photoluminescence (PL) spectroscopy has been used to study the defect levels in thin film copper indium diselenide (CuInSe2, CIS) which we are developing as the absorber layer for the bottom cell of a monolithically grown perovskite/CuInSe2 tandem solar cell. Temperature and laser power dependent PL measurements of thin film CIS for two different Cu/In ratios (0.66 and 0.80) have been performed. The CIS film with Cu/In = 0.80 shows a prominent donor-to-acceptor peak (DAP) involving a shallow acceptor of binding energy ∼22 meV, with phonon replica at ∼32 meV spacing. In contrast, PL measurement of CIS film for Cu/In = 0.66 taken at 20 K exhibited an asymmetric and broad PL spectrum with peaks at 0.845 eV and 0.787 eV. Laser intensity dependent PL revealed that the observed peaks 0.845 eV and 0.787 eV shift towards higher energy (aka j-shift) at ∼11.7 meV/decade and ∼ 8 meV/decade with increase in laser intensity respectively. The asymmetric and broad spectrum together with large j-shift suggests that the observed peaks at 0.845 eV and 0.787 eV were related to band-to-tail (BT) and band-to-impurity (BI) transition, respectively. Such a band-tail-related transition originates from the potential fluctuation of defect states at low temperature. The appearance of band related transition in CIS film with Cu/In = 0.66 is the indicator of the presence of large number of charged defect states.

Room-temperature excitonic emission with a phonon replica from graphene nanosheets deposited on Ni-nanocrystallites/Si-nanoporous pillar array.

Graphene nanosheets (GNSs) were grown on a Si nanoporous pillar array (Si-NPA) via chemical vapour deposition, using a thin layer of pre-deposited Ni nanocrystallites as catalyst. GNSs were determined to be of high quality and good dispersivity, with a typical diameter size of 15 × 8 nm. Light absorption measurements showed that GNSs had an absorption band edge at 3.3 eV. They also showed sharp and regular excitonic emitting peaks in the ultraviolet and visible region (2.06–3.6 eV). Moreover, phonon replicas with long-term stability appeared with the excitonic peaks at room temperature. Temperature-dependent photoluminescence from the GNSs revealed that the excitonic emission derived from free and bound excitonic recombination. A physical model based on band energy theory was constructed to analyse the carrier transport of GNSs. The Ni nanocrystallites on Si-NPA, which acted as a metal-enhanced fluorescence substrate, were supposed to accelerate the excitonic recombination of GNSs and enhanced the measured emission intensity. Results of this study would be valuable in determining the luminescence mechanism of GNSs and could be applied in real-world optoelectronic devices.

Emission of Cu2O Paraexcitons Confined by a Strain Trap: Hints of a Bose–Einstein Condensate?

We monitor the phonon sideband emission from paraexcitons confined in a strain trap in cuprous oxide at T = 1.25 K. On the low energy ank of the optical phonon replicas, both of Γ 5 − and Γ 3 − symmetry (the latter activated by application of a magnetic field), we detect sharp peaks that might represent indications for a paraexciton Bose–Einstein condensate. In contrast, such peaks are absent in the phonon-mediated emission of the orthoexcitons, and they also disappear at elevated temperatures. The results challenge our understanding of the involved physics, e.g., of the Auger recombination of excitons, which has so far been believed to prevent crossing the border to a condensate.

Exciton Fine Structure and Lattice Dynamics in InP/ZnSe Core/Shell Quantum Dots.

Nanocrystalline InP quantum dots (QDs) hold promise for heavy-metal-free optoelectronic applications due to their bright and size-tunable emission in the visible range. Photochemical stability and high photoluminescence (PL) quantum yield are obtained by a diversity of epitaxial shells around the InP core. To understand and optimize the emission line shapes, the exciton fine structure of InP core/shell QD systems needs be investigated. Here, we study the exciton fine structure of InP/ZnSe core/shell QDs with core diameters ranging from 2.9 to 3.6 nm (PL peak from 2.3 to 1.95 eV at 4 K). PL decay measurements as a function of temperature in the 10 mK to 300 K range show that the lowest exciton fine structure state is a dark state, from which radiative recombination is assisted by coupling to confined acoustic phonons with energies ranging from 4 to 7 meV, depending on the core diameter. Circularly polarized fluorescence line-narrowing (FLN) spectroscopy at 4 K under high magnetic fields (up to 30 T) demonstrates that radiative recombination from the dark F = ±2 state involves acoustic and optical phonons, from both the InP core and the ZnSe shell. Our data indicate that the highest intensity FLN peak is an acoustic phonon replica rather than a zero-phonon line, implying that the energy separation observed between the F = ±1 state and the highest intensity peak in the FLN spectra (6 to 16 meV, depending on the InP core size) is larger than the splitting between the dark and bright fine structure exciton states.

Suppression of the green emission, texturing, solute-atom diffusion and increased electron-phonon coupling induced by Ni in sol-gel ZnNiO thin films

Zn1−xNixO thin films (nominal x = 0, 0.01, 0.02, 0.04, 0.1 and 0.2) were synthesized on silicon substrates through a sol-gel/dip-coating technique. Samples were studied by X-ray diffraction, scanning electron microscopy, photoluminescence spectroscopy, Rutherford backscattering spectrometry and depth-profiling X-ray photoelectron spectroscopy. The results from X-ray diffraction show growth in the wurtzite crystal structure for all samples, with cubic NiO being detected as a secondary phase for x = 0.2. While for x = 0 (pure ZnO) no texture is present, for 0 ≤ x ≤ 0.1 strong preferential crystallization along the c-axis is observed. A tendency for Ni diffusion towards the film/Si substrate interface was observed. The formation of substitutional ZnxNi1−xO solid solution for 0.01 ≤ x ≤ 0.04 is suggested by the results. Photoluminescence spectra exhibit strong near band edge UV emission and suppression of deep defect-related emission in the visible upon Ni+2 incorporation into the ZnO lattice. As in pure ZnO, the UV emission in ZnNiO at room temperature is dominated by the first two phonon replica of the excitonic emission, however the LO phonon energy (ħωLO) is reduced by up to ∼15 meV in the 0 ≤ x ≤ 0.04 range. Due to this reduction of ħωLO, the exciton-phonon coupling increases, in consistency with a corresponding expected increase of the Fröhlich coupling constant with decreasing ħωLO.

Phonon Interaction and Phase Transition in Single Formamidinium Lead Bromide Quantum Dots.

Formamidinium lead bromide (FAPbBr3) quantum dots (QDs) are promising materials for light emitting applications in the visible spectral region because of their high photoluminescence (PL) quantum yield (QY) and the enhanced chemical stability as compared to, for instance, methylammonium based analogues. Toward practical harnessing of their compelling optical characteristics, the exciton recombination process, and in particular the exciton-phonon interaction and the impact of crystal phase transition, has to be understood in detail. This is addressed in this contribution by PL studies on single colloidal FAPbBr3 QDs. Polarization-resolved PL measurements reveal a fine structure splitting of excitonic transitions due to the Rashba effect. Distinct phonon replica have been observed within energetic distances of 4.3 ± 0.5, 8.6 ± 0.9, and 13.2 ± 1.1 meV from the zero phonon line, which we attribute to vibrational modes of the lead bromide lattice. Additional vibrational modes of 18.6 ± 0.3 and 38.8 ± 1.1 meV are found and related to liberation modes of the formamidinium (FA) cation. Temperature-dependent PL spectra reveal a line broadening of the emission caused by exciton phonon interaction as well an unusual energy shift which is attributed to a crystal phase transition within the single QD.

Electronic structure-dependent magneto-optical Raman effect in atomically thin WS2

Magneto-optical effect, such as Faraday rotation, magneto-optical Kerr and Zeeman effect, plays a fundamental role and has found extensive applications in condensed-matter physics. Two-dimensional transition metal dichalcogenides provide us an unprecedented platform for exploring abundant magneto-optical phenomena. Here we report such experiments that demonstrate the band structure-dependent magneto-optical Raman effect in atomically thin WS2. Our experiments in conjunction with theoretical calculations uncover that the direct to indirect transition leads to distinct magneto-optical Raman effect between monolayer and bilayer/trilayer. We further quantitatively determine the optical mobility of carriers at different critical points of conduction band (K and Q points). In addition, our measurements reveal that not only the particular single-phonon mode A1g(Γ) but also multiple phonon replica and phonons at the edges of Brillouin zone display electronic structure-dependent gigantic magneto-optical Raman effect. Our work establishes a firm basis for benchmarking a new microscopic quantum Raman scattering theory, and paves a way towards novel magneto-optical applications based on 2D semiconductors.

(Invited) Emission from Strained Germanium Nanocrystals

A silicon-compatible group IV coherent light source remains the missing link in Si-based photonics, despite much effort. Recently lasing and high efficiency photoluminescence (PL) have been shown for germanium (Ge), a material with a relatively small indirect to direct bandgap (BG) difference. We previously had observed a very intense, low temperature PL in dozens of samples for MBE-grown Si1-xGex epitaxial layers with x from 0.05 to 0.53, with quantum efficiencies up to 5%. This PL was neither defect nor dislocation related, but appeared to be strong with a large lifetime due to localization effects. As shown in Fig. 1, the PL consisted of a broad peak with asymmetry to low photon energies. With Ge fraction this peak was constant in shape and tracked the BG variation, but was ~80 meV below the indirect BG for strained SiGe. The width of this peak at ~50 meV was too small to be due to a no phonon (NP) line with its TO phonon replica if the material were Si or SiGe as the NP-TO spacing is about 58 meV for those materials. Fig. 1 shows that for higher Ge fractions the PL is emitted at energies significantly below those for bulk Ge, with its BG of 744 meV. This broad, intense PL peak has been unexplained, although a morphological origin was suggested by TEM. Here we will show from PL data that the peak is due to Ge nanocrystals (NCs) imbedded in SiGe layers (see Fig. 2). Epitaxy requires that the SiGe epilayers and the Ge NCs be lattice matched to Si (001) in the x-y plane, so that both the SiGe and NCs are under compression in that plane. Unconstrained in the vertical (z) direction, the epilayer is under tensile strain, leading to a vertical lattice constant that increases with Ge fraction and is larger than that for unstrained SiGe. Here the volume of the unit cell for the epitaxial SiGe is assumed to be the same as that for unstrained SiGe. The lattice of the Ge NCs is constrained to match the SiGe epilayer vertically. For relatively Si-rich SiGe, the Ge NCs are under compression vertically, but for more Ge-rich SiGe the vertical lattice constant of the strained SiGe exceeds that of bulk Ge. At this point the vertical strain in the Ge NC becomes tensile, which first occurs for a Ge fraction in the SiGe of 0.36 (Fig. 3 - red trace). The BG variation in Ge with uniaxial strain can be computed using deformation potential theory. As the strain becomes more strongly tensile both the direct and indirect gap energies decline, with the direct energy decreasing more rapidly than the indirect one. As shown in the blue traces of Fig. 3, the direct gap crosses the indirect at a tensile uniaxial strain of 4.4%, resulting in a direct gap semiconductor, a highly desirable outcome. Our results with PL point the way to this transition point, but the maximum vertical tensile strain for the present Ge NCs is not much greater than 2.1%. Nonetheless, the fact that we see PL below the indirect BG of bulk Ge is explained by the Ge NCs being under tensile strain vertically, reducing their BG. The broad peak width and shape can be curve resolved with two peaks, each ~30 meV wide, separated by ~35 meV, i.e., very near the momentum conserving TO phonon energy for Ge.The NP peak is wide (25-30 meV) due in part to confinement shift variations from size variability and to alloy disorder broadening in the SiGe. To test our hypothesis further, we have calculated the emission energy in a numerical model that includes the effects of strain on the Ge BG and of the confinement blue shifts on exciton energy for both the SiGe layers and the imbedded NCs, the latter assumed to be of a single vertical size (2.5 nm). The calculated energies for over 45 samples of varying composition are compared with the measured PL energies in Fig. 4, where the slope is somewhat different from the expected value of unity due to possible lower order influences, such as variations in the NC size and deviations from the linear deformation potential model for the strained BG. However, we do have very good general agreement between our computed emission energies and those observed in PL, which provides validation for our theory that imbedded Ge NCs have given rise through carrier localization in three dimensions to the intense, broad PL observed in MBE grown SiGe. Figure 1