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Photon upconversion (UC) using trivalent erbium (Er+3) doped crystals is a promising concept to harness near-infrared photons of the solar spectrum which cannot be directly absorbed by silicon solar cells. However, their UC efficiency at low-intensity 1 sun illumination is not relevant on device level so far. Exploiting giant near-field enhancement effects on metasurfaces is an appealing approach to enable efficient UC at low irradiance conditions. Here, we report on more than 1000-fold enhanced photon UC of NaYF 4 :Er+3 nanoparticles interacting with the near-fields supported by a silicon metasurface under 1550 nm excitation.

Light emitting diodes (LEDs) in the deep ultra-violet (DUV) offer new perspectives for multiple applications ranging from 3D printing to sterilization. However, insufficient light extraction severely limits their efficiency. Nanostructured sapphire substrates in aluminum nitride based LED devices have recently shown to improve crystal growth properties, while their impact on light extraction has not been fully verified. We present a model for understanding the impact of nanostructures on the light extraction capability of DUV-LEDs. The model assumes an isotropic light source in the semiconductor layer stack and combines rigorously computed scattering matrices with a multilayer solver. We find that the optical benefit of using a nanopatterned as opposed to a planar sapphire substrate to be negligible, if parasitic absorption in the p-side of the LED is dominant. If losses in the p-side are reduced to 20%, then for a wavelength of 265 nm an increase of light extraction efficiency from 7.8% to 25.0% is possible due to nanostructuring. We introduce a concept using a diffuse ('Lambertian') reflector as p-contact, further increasing the light extraction efficiency to 34.2%. The results underline that transparent p-sides and reflective p-contacts in DUV-LEDs are indispensable for enhanced light extraction regardless of the interface texture between semiconductor and sapphire substrate. The optical design guidelines presented in this study will accelerate the development of high-efficiency DUV-LEDs, but the model is also readily applicable to other multilayer opto-electronic nanostructured devices such as photovoltaics or photodetectors., Comment: 16 Pages, 8 Figures

Dimensional microscopy is an essential tool for non-destructive and fast inspection of manufacturing processes. Standard approaches process only the measured images. By modelling the imaged structure and solving an inverse problem, the uncertainty on dimensional estimates can be reduced by orders of magnitude. At the same time, the inverse problem needs to be solved in a timely manner. Here we present a method of accelerating the inverse problem by reducing images to their elementary features, thereby extracting the relevant information and distinguishing it from noise. The resulting reduction in complexity allows the inverse problem to be solved more efficiently by utilize cutting edge machine learning based optimization techniques. By employing the techniques presented here, we are able to perform for highly accurate and fast dimensional microscopy.

We present a concept for an ultra-thin solar fuel device with a nanostructured back contact. Using rigorous simulations we show that the nanostructuring significantly increases the absorption in the semiconductor, CuBi$_2$O$_4$ in this case, by 47\% (5.2~mAcm$^{-2}$) through the excitation of plasmonic modes. We are able to attribute the resonances in the device to metal-insulator-metal plasmons coupled to either localised surface plasmon resonances or surface plasmon polaritons. Rounding applied to the metallic corners leads to a blueshift in the resonance wavelength while maintaining absorption enhancement, thus supporting the possibility for a successful realization of the device. For a 2D array, the tolerance of the polarization-dependent absorption enhancement is investigated and compared to a planar structure. The device maintains an absorption enhancement up to incident angles of 75$^{\circ}$. The study highlights the high potential for plasmonics in ultra-thin opto-electronic devices such as in solar fuel generation., 4 Figures 18 Pages. Supporting Information Included (7 Figures 11 pages)

In this work, light trapping effects based on dielectric nanoparticles (NPs) are numerically evaluated in ultrathin CuIn1-xGaxSe2 (CIGSe) solar cells for different locations of NPs, cell architectures and illumination directions, with relevant implications and optimized NP parameters being specified. The severe absorption in Mo is the main constraining factor for the effective implementation of light trapping NPs in ultrathin CIGSe cells. For a significant light absorption enhancement, it is favoured to integrate dielectric NPs at the rear interface of CIGSe/back contact and employ transparent conductive oxide (TCO) back contacts rather than the conventional Mo. It is demonstrated, that under front illumination, the low-index (n = 1.5) hemispherical NPs at the CIGSe/TCO interface cause significant light trapping effects. The NP-patterned ultrathin cells achieve a maximum short circuit current density (Jsc) of 36.4 mA/cm2 at an upper limit of 500 nm CIGSe thickness, which is as high as 94% Jsc of their thick flat counterparts with a CIGSe thickness of 2000 nm. In contrast, under back illumination, the patterned ultrathin cells realize comparable absorption to the corresponding thick counterpart at a CIGSe thickness of only 300 nm and the maximum Jsc (35.2 mA/cm2) saturates at a CIGSe thickness of 425 nm. Further, Jsc is less attenuated by the parasitic absorption in Al:ZnO (AZO) under back illumination than under front illumination in module configuration, where a much thicker AZO is required. This suggests that patterned ultrathin CIGSe solar cells under back illumination will be a promising cell architecture simultaneously for high efficiencies and less material usage in industrial module production.

Photon upconversion upon 1550 nm excitation is of high relevance for applications in the third biological excitation window, for photovoltaics beyond current limitations, and enables appealing options in the field of glass fiber telecommunications. Trivalent doped erbium ions Er3 are the material of choice for 1550 nm excited upconversion, however, they suffer from a low absorption cross section and a low brightness. Therefore, the ability of silicon metasurfaces to provide greatly enhanced electrical near fields is employed to enable efficient photon upconversion even at low external illumination conditions. Hexagonally shaped beta NaYF4 Er3 nanoparticles are placed on large area silicon metasurfaces designed to convert near infrared 1550 nm to visible light. More than 2400 fold enhanced photon upconversion luminescence is achieved by using this metasurface instead of a planar substrate. With the aid of optical simulations based on the finite element method, this result is attributed to the coupling of the excitation source with metasurface resonances at appropriate incident angles. Analysis of the excitation power density dependence of upconversion luminescence and red to green emission ratios enables the estimation of nanoscale near field enhancement on the metasurface. The findings permit the significant reduction of required external excitation intensities for photon upconversion of 1550 nm light, opening perspectives in biophotonics, telecommunication, and photovoltaics

Perovskite/silicon tandem solar cells are the most promising concept for a future photovoltaic technology. We report on recent progress from an optical viewpoint and disucss how we achieved more than 25% device efficiency.

We evaluate the potential of inserting metallic, metal-dielectric core-shell, and fully dielectric nanoparticles in ultrathin chalcopyrite solar cells to enhance absorption which experiences a significant drop for absorber thicknesses below 500 nm. For different integration positions at the front or at the rear of the solar cell structure theoretical expectations and potential benefits originating from light scattering, near-field enhancement and coupling into waveguide modes by the nanoparticles are presented. These benefits are always balanced against experimental challenges arising for particular geometries due to the very specific fabrication processes of chalcopyrite solar cells. In particular high absorber deposition temperatures as well as contact layers that are relatively thick compared to other devices need to be considered. Based on this, we will need to go beyond some geometries that have proven beneficial for other types of solar cells and identify the most promising configurations for chalcopyrite-based devices.

We present large-area (25 cm2) dielectric metasurfaces based on silicon photonic crystal slabs. Adjustment of the slab thickness allows to systematically shift the metasurface resonances over several hundreds of nanometers. We compute the three-dimensional field energy density near the surface and determine optimum slab thicknesses for selected near-infrared excitation wavelengths applied in biophotonics. Our simulations reveal up to 17-fold enhanced near-field energy densities at normal incidence, but over 500-fold enhancement at 4° incident excitation. We explain this behaviour via the coupling of external radiation with symmetry-protected bound states in the continuum. These results enable metasurface-enhanced spectroscopy on large areas and underline the benefit of slight oblique incidence excitation conditions.

BMBF, 03ZZ0134B, Zwanzig20 - Advanced UV for Life - Verbundvorhaben: UV Power; TP2: Entwicklung von high-power UVB-LEDs um 300 nm

We present optical simulations for a tandem solar cell consisting of a nanostructured thin-film perovskite top cell and a silicon heterojunction (SHJ) wafer bottom cell. The absorption and related current density are calculated using the rigorous simulations in the form of the finite element method for the nanostructured perovskite cell and a semi-empirical method for the SHJ cell. In order to reach the optimal value for the perovskite layer thickness we employ Newton’s method using derivatives obtained directly from the rigorous simulation. Using this we obtain an optimal layer thickness using typically one iteration step and eliminate the need for a parameter scan. We compare the results for different sinusoidal nanotextures applied to different layers in the multilayer thin-film perovskite top cell. The nanotextures lead to a gain in absorption and power conversion efficiency in comparison to an optimized planar reference. We also present experimental results towards a realisation of the proposed structure. These results give valuable insight for the emerging field of high efficiency perovskite/SHJ tandem solar cells.

Currently, perovskite silicon tandem solar cells are one of the most investigated concepts for overcoming the theoretical limit for the power conversion efficiency of silicon solar cells. For monolithic tandem solar cells, the available light must be distributed equally between the two subcells, which is known as current matching. For a planar device design, a global optimization of the layer thicknesses in the perovskite top cell allows current matching to be reached and reflective losses of the solar cell to be minimized at the same time. However, even after this optimization, the reflection and parasitic absorption losses add up to 7 amp; 8201; amp; 8201;mA amp; 8201; amp; 8201; amp; 8201; amp; 8201;cm2. In this contribution, we use numerical simulations to study how well hexagonal sinusoidal nanotextures in the perovskite top cell can reduce the reflective losses of the combined tandem device. We investigate three configurations. The current density utilization can be increased from 91 for the optimized planar reference to 98 for the best nanotextured device period 500 nm and peak to valley height 500 nm , where 100 refers to the Tiedje Yablonovitch limit. In a first attempt to experimentally realize such nanophotonically structured perovskite solar cells for monolithic tandems, we investigate the morphology of perovskite layers deposited onto sinusoidally structured substrates

All-inorganic CsPbBr3 perovskite colloidal quantum dots have recently emerged as promising material for a variety of optoelectronic applications, among others for multi-photon-pumped lasing. Nevertheless, high irradiance levels are generally required for such multi-photon processes. One strategy to enhance the multi-photon absorption is taking advantage of high local light intensities using photonic nanostructures. Here, we investigate two-photon-excited photoluminescence of CsPbBr3 perovskite quantum dots on a silicon photonic crystal slab. By systematic excitation of optical resonances using a pulsed near-infrared laser beam, we observe an enhancement of two-photon-pumped photoluminescence by more than one order of magnitude when comparing to using a bulk silicon film. Experimental and numerical analyses allow relating these findings to near-field enhancement effects on the nanostructured silicon surface. The results reveal a promising approach for significant decreasing the required irradiance levels for multi-photon processes being of advantage in applications like low-threshold lasing, biomedical imaging, lighting and solar energy.

We provide a computational method for quickly determining the correct distribution of optically active nanoparticles for a desired response. This is achieved by simulating the optical response of single nanoparticles and performing a statistical averaging over different sizes. We find good agreement between experiment and theory for the transmission, reflectance and absorption of both an ordered and disordered array. By repeating the simulation for different particle distributions, we show that the method is capable of accurately predicting the correct nanoparticle distribution for a desired optical response. We provide a referential graph for predicting the optical response of different Ag nanoparticle distributions on a glass substrate, which can be extended to other substrate and particle materials, and particle shapes and sizes., Comment: 6 figures

Recently, we studied the effect of hexagonal sinusoidal textures on the reflective properties of perovskite-silicon tandem solar cells using the finite element method (FEM). We saw that such nanotextures, applied to the perovskite top cell, can strongly increase the current density utilization from 91% for the optimized planar reference to 98% for the best nanotextured device (period 500 nm and peak-to-valley height 500~nm), where 100% refers to the Tiedje-Yablonovitch limit. In this manuscript we elaborate on some numerical details of that work: we validate an assumption based on the Tiedje-Yablonovitch limit, we present a convergence study for simulations with the finite-element method, and we compare different configurations for sinusoidal nanotextures., Proceedings article, SPIE conference "Photonics for Solar Energy Systems VII," edited by Ralf B. Wehrspohn, Alexander N. Sprafke (Strasbourg, France, April 2018). This article is based on earlier work: D.Chen et. al, J. Photonics Energy 8}, 022601 (2018, arXiv:1801.07252 [physics.app-ph])

Nanoimprint lithography can be used to fabricate sinusoidal nanotextures on a large scale. We present optical and numerical results for sinusoidal nanotextures in two types of solar cells: thin film c-Si and perovskite-silicon tandem solar cells.

This work elaborates on the high scattering which dielectric nanorods exhibit and how it can be exploited to control light propagation across material interfaces. A detailed overview of how dielectric nanorods interact with light through a combination of dipolar scattering and leaky modes is performed via outward power flux calculations. We establish and account for design parameters that best result in light magnification owing to resonant behavior of nanorods. Impact of material parameters on scattering and their dispersion have been calculated to establish that low loss dielectric oxides like ZnO when nanostructured show excellent antenna like resonances which can be used to control light coupling and propagation. Interfacial scattering calculations demonstrate the high forward directivity of nanorods for various dielectric interfaces. A systematic analysis for different configurations of single and periodic nanorods on air dielectric interface emphasizes the light coupling tendencies exhibited by nanorods to and from a dielectric. Spatial characteristics of the localized field enhancement of the nanorod array on an air dielectric interface show focusing attributes of the nanorod array. We give a detailed account to tailor and selectively increase light propagation across an interface with good spectral and spatial control.

Ag nanoparticles have attracted interest for plasmonic absorption enhancement of solar cells. For this purpose, well-defined particle sizes and densities as well as very low deposition temperatures are required. Thus, we report here a new spray chemical vapour deposition method for producing Ag NP films with independent size and density control at substrate temperatures even below 100 °C, which is much lower than for many other techniques. This method can be used on different substrates to deposit Ag NP films. It is a reproducible, low-cost process which uses trimethylphosphine (hexafluoroacetylacetonato) silver as a precursor in alcoholic solution. By systematic variation of deposition parameters and classic experiments, mechanisms of particle growth and of deposition processes as well as the low decomposition temperature of the precursor could be explained. Using the 3D finite element method, absorption spectra of selected samples were simulated, which fitted well with the measured results. Hence, further applications of such Ag NP films for generating plasmonic near field can be predicted by the simulation.

We demonstrate the fabrication and characterization of nanostructured transparent conductive oxides and via numerical simulation observe the parametric optical transmission trend. These structures can be used for customized light coupling to and from optoelectronic devices.

Publisher’s Note: This paper, originally published on 23 September 2016, was replaced with a corrected/revised version on 21 December 2016. If you downloaded the original PDF but are unable to access the revision, please contact SPIE Digital Library Customer Service for assistance. Light concentration has proven beneficial for solar cells, most notably for highly efficient but expensive absorber materials using high concentrations and large scale optics. Here we investigate light concentration for cost efficient thinfilm solar cells which show nano- or microtextured absorbers. Our absorber material of choice is Cu(In,Ga)Se2 (CIGSe) which has a proven stabilized record efficiency of 22.6% and which - despite being a polycrystalline thin-film material - is very tolerant to environmental influences. Taking a nanoscale approach, we concentrate light in the CIGSe absorber layer by integrating photonic nanostructures made from dielectric materials. The dielectric nanostructures give rise to resonant modes and field localization in their vicinity. Thus when inserted inside or adjacent to the absorber layer, absorption and efficiency enhancement are observed. In contrast to this internal absorption enhancement, external enhancement is exploited in the microscale approach: mm-sized lenses can be used to concentrate light onto CIGSe solar cells with lateral dimensions reduced down to the micrometer range. These micro solar cells come with the benefit of improved heat dissipation compared to the large scale concentrators and promise compact high efficiency devices. Both approaches of light concentration allow for reduction in material consumption by restricting the absorber dimension either vertically (ultra-thin absorbers for dielectric nanostructures) or horizontally (micro absorbers for concentrating lenses) and have significant potential for efficiency enhancement.

We demonstrate the optical near field and light directing properties of ZnO nanorod structures using rigorous methods. Our focus is on evaluating scattering from nanorods on different substrates and observing the associated near field enhancement.

2-D closely packed SiO 2 nanosphere arrays serving as the photonic structure for light absorption enhancement on top of ultra-thin Cu(In 1− x Ga x )Se 2 solar cells are investigated both theoretically and experimentally. It is theoretically demonstrated that whispering gallery modes and high order Mie resonances contribute to the light absorption enhancement for the large spheres and an anti-reflection effect is prominent for small ones. The ultra-thin CIGSe solar cells achieve the optimum absorption enhancement for the small sphere array with a diameter of 110 nm, contrary to the larger spheres used in Si solar cells. The reason is attributed to the strong parasitic absorption in the AZO/ZnO/CdS front layers. They absorb mainly in the short wavelength range where the Mie resonances occur. Additionally, it is shown that the 110-nm-diameter sphere array exhibits a better angular tolerance than a conventional planar anti-reflection layer, which shows the potential as a promising anti-reflection structure.

Integration of plasmonic Ag nanoparticles as a back reflector in ultra-thin Cu(In,Ga)Se2 (CIGSe) solar cells is investigated. X-ray photoelectron spectroscopy results show that Ag nanoparticles underneath a Sn:In2O3 back contact could not be thermally passivated even at a low substrate temperature of 440 °C during CIGSe deposition. It is shown that a 50 nm thick Al2O3 film prepared by atomic layer deposition is able to block the diffusion of Ag, clearing the thermal obstacle in utilizing Ag nanoparticles as a back reflector in ultra-thin CIGSe solar cells. Via 3-D finite element optical simulation, it is proved that the Ag nanoparticles show the potential to contribute the effective absorption in CIGSe solar cells.

Efficient light management in optoelectronic devices requires nanosystems where high optical qualities coincide with suitable device integration. The requirement of chemical and electrical passivation for integrating nanostrutures in e.g. thin film solar cells points towards the use of insulating and stable dielectric material, which however has to provide high scattering and near-fields as well. We investigate metal@dielectric core-shell nanoparticles and dielectric nanorods. Whereas core-shell nanoparticles can be simulated using Mie theory, nanorods of finite length are studied with the finite element method. We reveal that a metallic core within a thin dielectric shell can help to enhance scattering and near-field cross sections compared to a bare dielectric nanoparticle of the same radius. A dielectric nanorod has the benefit over a dielectric nanosphere in that it can generate much higher scattering cross sections and also give rise to a high near-field enhancement along its whole length. Electrical benefits of e.g. Ag@oxide nanoparticles in thin-film solar cells and ZnO nanorods in hybrid devices lie in reduction of recombination centers or close contact of the nanorod material with the surrounding organics, respectively. The optical benefit of dielectric shell material and elongated dielectric nanostructures is highlighted in this paper.

We present a method for calculating the plasmonic and photonic enhancement of the absorption in solar cells. The method involves coupling between a transfer matrix method to describe light propagation in the layered stack and Mie theory for calculating the absorption and angular scattered field distribution from the nanoparticles. We also compare the method to rigorous simulations.

For all applications of plasmonics to technology it is required to tailor the resonance to the optical system in question. This chapter gives an understanding of the design considerations for nanoparticles needed to tune the resonance. First the basic concepts of plasmonics are reviewed with a focus on the physics of nanoparticles. An introduction to the finite element method is given with emphasis on the suitability of the method to nanoplasmonic device simulation. The effects of nanoparticle shape on the spectral position and lineshape of the plasmonic resonance are discussed including retardation and surface curvature effects. The most technologically important plasmonic materials are assessed for device applicability and the importance of substrates in light scattering is explained. Finally the application of plasmonic nanoparticles to photovoltaic devices is discussed.

We theoretically compare the scattering and near field of nanoparticles from different types of materials, each characterized by specific optical properties that determine the interaction with light: metals with their free charge carriers giving rise to plasmon resonances, dielectrics showing zero absorption in wide wavelength ranges, and semiconductors combining the two beforehand mentioned properties plus a band gap. Our simulations are based on Mie theory and on full 3D calculations of Maxwell’s equations with the finite element method. Scattering and absorption cross sections, their division into the different order electric and magnetic modes, electromagnetic near field distributions around the nanoparticles at various wavelengths as well as angular distributions of the scattered light were investigated. The combined information from these calculations will give guidelines for choosing adequate nanoparticles when aiming at certain scattering properties. With a special focus on the integration into thin film solar cells, we will evaluate our results.

We calculate the complex refractive index of inhomogeneous thin films using the transfer matrix method and reflection/transmission measurements. To this end we have developed a model for both the 3D distribution of inhomogeneities inside thin films and for light propagation through the inhomogeneities. The model involves splitting the light into contributions from the homogeneous section of the film (modelled coherently) and the inhomogeneous sections (modelled incoherently). Measurements of the film implied an isotropic inhomogeneity distribution, which was replicated in the simulation. The model for light propagation inside a film was implemented into a transfer matrix program allowing for the evaluation of the reflection and transmission of the thin film on a substrate. Using this result and experimental data for the reflection and transmission, the complex refractive index, n+ik, of an inhomogeneous CuInSe₂ film was calculated. The resulting n and k were in much closer agreement to the n and k for a homogeneous CuInSe₂ film than those for the standard transfer matrix approach applied to the data of the inhomogeneous sample. The n value at short wavelengths deviates from the homogeneous value suggesting a breakdown of the scalar scattering theory for short wavelengths. © 2014 IOP Publishing Ltd.

Metallic nanoparticles exhibiting plasmonic effects as well as dielectric nanoparticles coupling the light into resonant modes have both shown successful application to photovoltaics. On the larger scale, microconcentrator optics promise to enhance solar cell efficiency and reduce material consumption. Here we want to make the link between concentrators on the nano- and on the microscale. From metallic nanospheres we turn to dielectric ones and then look at increasing radii to approach concentrator optics on the mircoscale. The nano- and microlenses are investigated with respect to their interaction with light using 3D simulations with the finite element method. Resulting maps of local electric field distributions reveal the focusing behavior of the dielectric spheres. For larger lens sizes, ray tracing calculations can be applied which give ray distributions in agreement with areas of high electric field intensities. Calculations of back focal lengths using ray tracing coincide with results from geometrical optics simulations. They give us insight into how the focal length can be tuned as a function of particle size, but also depending on the substrate refractive index and the shape of the microlens. Turning from spherical to segment-shaped lenses allows us to approach the realistic case of microconcentrator optics and to draw conclusions about focus tuning and system design. Despite the similarities of focusing behavior we find for the nano- and the microlenses, the integration into solar cells needs to be carefully adjusted, depending on the ambition of material saving, concentration level, focal distance and lens size, all being closely related. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Both metallic nanoparticles exhibiting plasmonic effects and dielectric nanoparticles coupling the light into resonant modes have shown successful applications to photovoltaics. On a larger scale, microconcentrator optics promise to enhance solar cell efficiency and to reduce material consumption. Here, we want to create a link between the concentrators on the nano- and on the microscale. From metallic nanospheres, we turn to dielectric ones and then look at increasing radii to approach the microscale. The lenses are investigated with respect to their interaction with light using three- dimensional simulations with the finite-element method. Resulting maps of local electric field distributions reveal the focusing behavior of the dielectric spheres. For larger lens sizes, ray tracing calculations, which give ray distributions in agreement with electric field intensities, can be applied. Calculations of back focal lengths in geometrical optics coincide with ray tracing results and allow insight into how the focal length can be tuned as a function of particle size, substrate refractive index, and the shape of the microlens. Despite the similarities we find for the nano- and the microlenses, integration into solar cells needs to be carefully adjusted, depending on the goals of material saving, concentration level, focal distance, and lens size.

We rigorously simulate light scattering via the FEM from core-shell plasmonic particles and plasmonic particles with an isolating overcoat, in order to recommend design principles for maximising plasmonic scattering gains.

We investigate the influence of substrate and its temperature on the optical constants of CuIn1?xGaxSe2 (CIGSe) thin films using the transfer-matrix method. The optical constants of a CIGSe layer on top of a transparent conducting oxide (TCO) layer were calculated considering the realistic optical constants of the TCO layer after CIGSe deposition. It was found that TCO substrates could influence the optical constants of CIGSe layers and that the ITO (Sn doped In2O3) substrate had a greater impact than IMO (Mo doped In2O3) for the CIGSe (x?=?0.4) film when compared to a reference on bare glass substrate. Additionally, the varied substrate temperatures did not impact the optical constants of CGSe (x?=?1). For CIGSe (x?=?0.4), the refractive index n stayed relatively independent although at low temperature the grain size was reduced and the Ga/(Ga+In) profile was altered compared to that at high temperature (610??C). In contrast, the extinction coefficient k at low temperature showed higher absorption at longer wavelengths because of a lower minimum bandgap (Eg,min) originating from reduced inter-diffusion of Ga?Se at a low substrate temperature.