Luminescent solar concentrators and related methods of manufacturing

Abstract

Luminescent solar concentrators in accordance with various embodiments of the invention can be designed to minimize photon thermalization losses and incomplete light trapping using various components and techniques. Cadmium selenide core, cadmium sulfide shell (CdSe/CdS) quantum dot (“QD”) technology can be implemented in such devices to allow for near-unity QDs and sufficiently large Stokes shifts. Many embodiments of the invention include a luminescent solar concentrator that incorporates CdSe/CdS quantum dot luminophores. In further embodiments, anisotropic luminophore emission can be implemented through metasurface/plasmonic antenna coupling. In several embodiments, red-shifted luminophores are implemented. Additionally, top and bottom spectrally-selective filters, such as but not limited to selectively-reflective metasurface mirrors and polymeric stack filters, can be implemented to enhance the photon collection efficiency. In some embodiments, luminescent solar concentrator component is optically connected in tandem with a planar Si subcell, forming a micro-optical tandem luminescent solar concentrator.

Claims

1. A luminescent solar concentrator comprising: a waveguide configured to trap light incident on a first surface via total internal reflection, the waveguide comprising: embedded luminophores configured to absorb at least a portion of trapped light and emit photoluminesced light; and at least one embedded planar cell disposed on a second surface opposite the first surface, the at least one embedded planar cell configured to absorb and convert at least a portion of the photoluminesced light to an electric signal; a subcell configured to absorb and convert the at least the portion of the trapped light and the at least the portion of the photoluminesced light to the electric signal; and a first selectively-reflective mirror and a second selectively-reflective mirror configured to filter light of specific wavelengths, wherein: the first selectively-reflective mirror is configured to filter light before such that passed light is incident on the waveguide; and the second selectively-reflective mirror is disposed between the waveguide and the subcell.

2. The luminescent solar concentrator of claim 1, wherein the subcell comprises a silicon subcell.

3. The luminescent solar concentrator of claim 1, further comprising a plurality of glass slides.

4. The luminescent solar concentrator of claim 3, wherein the luminescent solar concentrator is constructed with an air gap between the waveguide and the first selectively-reflective mirror.

5. The luminescent solar concentrator of claim 4, wherein the luminescent solar concentrator is constructed with an air gap between the waveguide and the second selectively-reflective mirror.

6. The luminescent solar concentrator of claim 1, wherein at least one of the first selectively-reflective mirror and the second selectively-reflective mirror comprises a structure selected from the group consisting of a metasurface mirror, a polymeric stack filter, a Bragg grating, and a dielectric stack.

7. The luminescent solar concentrator of claim 1, wherein at least one of the first selectively-reflective mirror and the second selectively-reflective mirror comprises a high contrast grating metasurface mirror.

8. The luminescent solar concentrator of claim 7, wherein the high contrast grating metasurface mirror comprises a hexagonal array of AlSb cylindrical pillars patterned on a glass substrate.

9. The luminescent solar concentrator of claim 8, wherein the hexagonal array of AlSb cylindrical pillars has a pitch of about 475-515 nm and the AlSb cylindrical pillars have thicknesses of about 85-125 nm and radii of about 80-120 nm.

10. The luminescent solar concentrator of claim 1, wherein the first selectively-reflective mirror comprises a high contrast grating metasurface mirror and the second selectively-reflective mirror comprises a dielectric stack.

11. The luminescent solar concentrator of claim 1, wherein the at least one embedded planar cell comprises a cell selected from the group consisting of an InGaP cell and a GaAs cell.

12. The luminescent solar concentrator of claim 11, wherein the at least one embedded planar cell comprises an array of embedded planar cells.

13. The luminescent solar concentrator of claim 11, wherein the at least one embedded planar cell comprises a bifacial cell.

14. The luminescent solar concentrator of claim 1, wherein the waveguide comprises a polylaurylmethacrylate.

15. The luminescent solar concentrator of claim 1, wherein the waveguide comprises a material selected from the group consisting of polymethyl methacrylate, polydimethylsiloxane, and ethylene-vinyl acetate.

16. The luminescent solar concentrator of claim 1, wherein the embedded luminophores comprise CdSe/CdS quantum dots.

17. The luminescent solar concentrator of claim 1, wherein the embedded luminophores comprise luminophores selected from the group consisting of InP quantum dots, Si quantum dots, and nanorods.

18. The luminescent solar concentrator of claim 1, wherein the emitted photoluminesced light is of a longer wavelength than the trapped light absorbed by the embedded luminophores.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A conceptually illustrates an exploded isometric view of a micro-optical tandem luminescent solar concentrator in accordance with an embodiment of the invention.

(2) FIG. 1B conceptually illustrates various views of a waveguide structure with an embedded array of solar cells in accordance with an embodiment of the invention.

(3) FIG. 2A conceptually illustrates a side view schematic of an exemplary MOTLSC construction along with a diagram of optical losses in accordance with an embodiment of the invention.

(4) FIG. 2B conceptually illustrates the escape cone of luminophores embedded in a waveguide in accordance with an embodiment of the invention.

(5) FIGS. 3A and 3B show measured Si and InGaP EQE curves with respect to wavelength and the absorption and photoluminescence spectra for synthesized and measured CdSe/CdS QDs in accordance with various embodiments of the invention.

(6) FIG. 3C shows reflectance of an exemplary spectrum dielectric stack filter with respect to wavelength for a given angle of incidence in accordance with an embodiment of the invention.

(7) FIG. 4 conceptually illustrates the absorption and PL spectra for varying red-shifted luminophores in accordance with an embodiment of the invention.

(8) FIGS. 5A-5D show tandem LSC-Si module efficiency in the case without mirrors in accordance with various embodiments of the invention.

(9) FIG. 6A shows tandem LSC-Si module efficiency for varying rejection-band widths in accordance with an embodiment of the invention.

(10) FIG. 6B shows tandem LSC-Si module efficiency for varying rejection-band left edge and right edge locations in accordance with an embodiment of the invention.

(11) FIG. 6C shows tandem LSC-Si module efficiency for varying R.sub.rejection vs. R.sub.pass across all angles at ideal rejection-band widths in accordance with an embodiment of the invention.

(12) FIG. 6D shows tandem LSC-Si module efficiency for varying R.sub.short-pass of the bottom mirror in accordance with an embodiment of the invention.

(13) FIGS. 7A-7D show tandem LSC-Si module efficiency in the perfect-mirrors case in accordance with various embodiments of the invention.

(14) FIG. 8A shows tandem LSC-Si module efficiency with varying fractions of light that is normally incident upon the structure in accordance with an embodiment of the invention.

(15) FIGS. 8B-8D show performance analysis of best-case scenarios from both the no-mirror and perfect-mirror cases in accordance with various embodiments of the invention.

DETAILED DESCRIPTION

(16) Luminescent solar concentrators offer a unique solution to capture sunlight and to reduce the overall Levelized Cost of Electricity. LSC module efficiency can suffer from two key loss mechanisms. First, embedded luminophores can require near-unity photoluminescence quantum yield (“PLQY”) in order to achieve desired optical efficiencies. To prevent further luminophore parasitic absorption, separation between absorbed and emitted photon energies (i.e., the Stokes shift) should be maximized. Historically, luminophores have not been able to maintain high enough PLQY and large Stokes shifts. Thus, many incident photons are usually parasitically absorbed by the luminophores in traditional devices. Second, the index of refraction contrast between the optical waveguide and the surrounding medium can limit complete photon trapping. Polymer waveguides experience significant escape cone losses for photons radiated at angles that lie between normal incidence and the critical angle of the waveguide.

(17) Luminescent solar concentrators in accordance with various embodiments of the invention can incorporate various novel components and techniques to minimize photon thermalization losses and incomplete light trapping. Such components and techniques can include but are not limited to efficient quantum dot (“QD”) luminophores, planar and micro-scale InGaP solar cells, selectively-reflective metasurface mirrors and polymeric stack filters for further light trapping, LSC-Si tandem architecture, novel waveguide materials (e.g., EVA, PMMA, PLMA), anisotropic luminophore emission through metasurface/plasmonic antenna coupling, red-shifted luminophores and GaAs microcells, and a hybridization of an LSC and traditional Si solar cell technology.

(18) In many embodiments, the LSC includes a waveguide, an absorber material, and at least one solar cell. During operation, light incident on the surface of the waveguide can be redirected through refraction and TIR to travel within the waveguide structure. In some embodiments, at least a portion of the trapped light is redirected to the absorber material. The absorber material can be designed to selectively absorb a subsection of the trapped light. Depending on the type of absorber material, different ranges of wavelengths of light may be absorbed. In several embodiments, the absorber material is a luminescent material capable of emitting light under an external application of energy. In such embodiments, the absorbed light can be re-emitted. In some embodiments, the absorbed light can be re-emitted at a different wavelength. In a number of embodiments, the waveguide structure traps and redirects the photoluminesced light toward the solar cell(s) for energy conversion.

(19) Waveguides in accordance with various embodiments of the invention can be made of any of a variety of materials, such as but not limited to polymethyl methacrylate (“PMMA”), polydimethylsiloxane (“PDMS”), ethylene-vinyl acetate (“EVA”), polylaurylmethacrylate (“PLMA”), and other suitable polymers. In some embodiments, photovoltaic cells can be embedded within the waveguide to efficiently capture the trapped light. In several embodiments, microcells and/or planar cells can be embedded within a waveguide. Various PV materials can be utilized, such as but not limited to InGaP and GaAs. In many embodiments, bifacial solar cells, including but not limited to InGaP bifacial cells and GaAs bifacial cells, can be embedded within a waveguide. In further embodiments, an array of such solar cells, including bifacial cells, can be embedded within a waveguide. Suitable LSC optical designs typically trap light emitted by the luminescent material in all directions and redirect it such that the minimal amount escapes the photovoltaic converters. Redirection techniques can include internal reflection, refractive index gradients, and diffraction. In a number of embodiments, an LSC top cell working in tandem with a subcell is implemented to allow for greater energy conversion efficiency. For example, an LSC top cell can work in tandem with a traditional single-junction silicon photovoltaic cell to allow for greater energy conversion efficiency compared to a Si-only module. In further embodiments, wavelength-selective mirrors are applied as cladding to the LSC to increase the concentration factor and overall module efficiency.

(20) Many types of absorber materials can be utilized in accordance with various embodiments of the invention. In several embodiments, luminophores are utilized as the absorber materials. In further embodiments, the LSC incorporates luminophores that allow for near-unity QDs and sufficiently large Stokes shifts. One such type of luminophore includes cadmium sulfide shell (CdSe/CdS) quantum dots. Luminophores utilized in various embodiments of the invention can also include but are not limited to InP quantum dots, Si quantum dots, and nanorods. Both organic and inorganic luminophores can be implemented in an LSC. In a number of embodiments, the luminophores are configured to absorb short wavelength, high energy light and re-emit a longer wavelength, lower energy light. In a number of embodiments, luminophores are dispersed and embedded within a waveguide structure. Inorganic QD luminophores can span a wide wavelength range of absorption and PL features. For instance, CdSe/CdS core/shell QDs typically exhibit absorption bands near 500 nm in wavelength and PL peaks centered near 650 nm, whereas Cd.sub.1-xCu.sub.xSe QDs absorb farther into the red (around 700 nm) and emit around 900 nm. LSC devices incorporating embedded luminophores and the characterization of such devices are described in the sections below in further detail.

(21) Micro-Optical Tandem Luminescent Solar Concentrators

(22) LSC devices in accordance with various embodiments of the invention can be designed to minimize photon thermalization losses and incomplete light trapping using various components and techniques. In many embodiments, the LSC includes a waveguide with embedded luminophores and at least one solar cell. During operation, light incident on the waveguide can be redirected throughout the waveguide through refraction and TIR. The trapped light can be absorbed by the embedded luminophores and re-emitted. The type of luminophores used can be selected such that a specific range of wavelengths is absorbed. In some embodiments, the luminophores are chosen to absorb short wavelength, high energy light and re-emit a longer wavelength, lower energy light. The re-emitted light can be redirected towards the solar cell(s) for energy conversion.

(23) In many embodiments, an LSC component is optically connected in tandem with a planar solar cell, forming a micro-optical tandem luminescent solar concentrator (“MOTLSC”). In further embodiments, the planar solar cell is a Si cell. Si—PV typically does not exhibit strong external quantum efficiency (“EQE”) in the short wavelength regime as a result of front surface absorption and non-radiative recombination. However, an LSC-Si tandem module can allow for greater spectral efficiency across the solar spectrum. For example, in several embodiments, planar InGaP microcells are embedded in the LSC device. The EQE of InGaP can be tuned to the photoluminescence (“PL”) emission wavelength. Planar InGaP cell geometry can allow for more rigorous control of the GG, resulting in further optimization of the overall power conversion efficiency. In a number of embodiments, GaAs microcells are implemented, and the MOTLSC can be designed accordingly.

(24) An exploded isometric view of a micro-optical tandem luminescent solar concentrator in accordance with an embodiment of the invention is conceptually illustrated in FIG. 1A. As shown, the MOTLSC 100 includes a first mirror 102, a polymer waveguide 104, a second mirror 106, and a subcell 108. In many embodiments, the first and second mirrors 102, 106 function as wavelength-selective filters for the aid in the confinement of light. The mirrors 102, 106 can also be referred to as top and bottom mirrors, relative to the subcell 108. Such filters can be implemented in various ways, including but not limited to using alternative dielectric materials in an aperiodic fashion, extruding polymers into a stack of low/high index of refraction materials, and applying various materials (e.g., AlSb, ZnO, TiO2, etc.) in a sub-wavelength periodic structure (e.g., a metasurface or conventional Bragg gratings) to reflect certain wavelengths of incident light. In a number of embodiments, high contrast grating metasurfaces are implemented as wavelength-selective filters due to their tunable reflectance spectrum and potentially lower fabrication costs. Suitable materials for the polymer waveguide 104 can include but are not limited to EVA, PMMA, PLMA, and PDMS. In the illustrative embodiment, the polymer waveguide 104 includes embedded luminophores 110 for the absorption and reemission of light. Examples of luminophores can include but are not limited to CdSe/CdS QDs, InP QDs, Si QDs, and nanorods. The polymer waveguide 104 further includes an array of embedded solar cells 112. Various PV materials can be utilized, such as but not limited to InGaP and GaAs. In many embodiments, bifacial cells can be utilized. FIG. 1B conceptually illustrates various views of a waveguide structure with an embedded array of solar cells in accordance with an embodiment of the invention. As shown, the waveguide includes 114 an array of interconnected microcells 116 and array busbars 118 configured for energy extraction.

(25) Although FIGS. 1A and 1B illustrates a specific MOTLSC construction, various configurations can be implemented. FIG. 2A conceptually illustrates a side view schematic of an exemplary MOTLSC construction along with a diagram of optical losses in accordance with an embodiment of the invention. In the illustrative embodiment, the constructed MOTLSC 200 includes a first mirror 202, a second mirror 204, a polymer waveguide 206 incorporating luminophores 208 and an InGaP cell 210, and a subcell 212. The constructed MOTLSC also includes multiple glass slides 214 and two air gaps 216, 218, which can serve various purposes, such as providing a desired refractive index interface to aid in the confinement of light. As shown, there are various sources of optical losses from light that are not ultimately converted to energy. Such losses can include mirror reflection losses 220, escape cone angle losses 222, and non-unity QD losses 224. Escape cone losses can result from light re-emitted by the luminophores at an angle below the critical angle, allowing light to refract out of the waveguide. FIG. 2B conceptually illustrates the escape cone of luminophores embedded in a waveguide in accordance with an embodiment of the invention. As shown, the waveguide 220 includes embedded luminophores 222. Incident rays 224 on the waveguide 220 can be trapped and absorbed by the luminophores 222. Once the light is absorbed, the luminophores 222 can re-emit the light at various angles. A range of angles, termed the escape cone 226, is shown and describes the angles of emission at which the light can refract out of the waveguide is shown.

(26) As shown in FIGS. 1A-1B and 2A-2B, MOTLSCs in accordance with various embodiments of the invention can be constructed with certain materials and components so as to allow for a greater spectral efficiency across the solar spectrum. In many embodiments, the MOTSLC is constructed with a silicon subcell and a polymer waveguide having embedded CdSe/CdS QDs and an array of embedded planar InGaP cells. FIGS. 3A and 3B show measured Si and InGaP EQE curves with respect to wavelength and the absorption and photoluminescence spectra for synthesized and measured CdSe/CdS QDs in accordance with an embodiment of the invention. MOTLSCs can also include filters designed to filter for a specific range of wavelengths. FIG. 3C shows reflectance of an exemplary spectrum dielectric stack filter with respect to wavelength for a given angle of incidence in accordance with an embodiment of the invention. In the illustrative filter, there is high reflectivity in the rejection band (R.sub.rejection) and low reflectivity in the out of band (R.sub.short-pass, R.sub.long-pass). In the illustrative embodiment, R.sub.short-pass, R.sub.rejection, and R.sub.long-pass correspond to the short-wavelength (300 to 585 nm), mid-wavelength (585 to 665 nm), and long-wavelength (665 to 1100 nm) reflection regimes, respectively.

(27) Performance Modeling of MOTLSCs

(28) A tandem LSC-Si module design in accordance with various embodiments of the invention can be characterized through the use of a Monte Carlo ray tracing model. The algorithm traces photons throughout the module architecture. Photon trajectories can be determined via scattering, reflection, transmission, and absorption probabilities for each component in the device. Photon reflection probabilities can be calculated by Fresnel laws for the transverse-electric (“TE”) and transverse-magnetic (“TM”) polarizations, and refraction angles can be calculated via Snell's law. The algorithm assumes either complete transmission or reflection at a given interface, thereby stochastically treating photon paths. To achieve sufficient statistical averaging, approximately 1×10.sup.6 photons were initialized for a given Monte Carlo simulation. To simulate low DNI environments, 40% of incident photons are assumed to normally strike the tandem module and 60% are assumed to approach with angles uniformly distributed throughout the incident photon hemisphere. Cosine factor intensity losses apply to all initialized photons, and the net incident power were determined.

(29) For the cases with and without a selective mirror, photons impinge upon either the top filter or the LSC waveguide, respectively. For this model, a PLMA polymer waveguide (refractive index n=1.44) with uniformly distributed QDs was used for simulations. Given a certain optical loading of QDs within the PLMA, QD absorption within the polymer can be determined using the Beer-Lambert law. Experimentally synthesized CdSe/CdS QDs' absorption and PL characteristics can be entered as a baseline for Monte Carlo optimization. As can readily be appreciated, while this analysis assumes PLMA and the CdSe/CdS as the respective materials for the polymer waveguide and the embedded luminophores, other suitable materials for the waveguide (e.g., PMMA, PDMS, and EVA) and the luminophores (e.g., InP QDs, Si QDs, and nanorods) can be used in practical applications. For instance, the effects of red-shifted absorption and PL bands on the overall module efficiencies of the tandem LSC/Si device can be modeled. FIG. 4 conceptually illustrates the absorption and PL spectra for varying red-shifted luminophores, assuming a constant PL distribution and absorption feature. Furthermore, possible luminophore features such as non-isotropic emission of the radiated light (either by direct QD manipulation and non-uniformity or by metasurface/photonic crystal/plasmonic antenna resonator coupling to the isotropic luminophore radiation) can be included. This can engender an anisotropic distribution of radiated light from the embedded luminophores.

(30) The heterojunction structure of the CdSe/CdS core/shell QDs can allow for fine-tuning of the absorption and photoluminescence spectra. Luminophores exhibiting large Stokes shifts at high PLQY can minimize both the number of photons parasitically absorbed by the QDs as well as the amount of light transmitted through the escape cone of the waveguide. Steady-state absorption spectra can be collected using a Shimadzu UV-3600 double beam spectrometer, and steady state PL spectra can be collected via a Horiba Jobin-Yvon FluoroLog 2 spectrofluorometer. For the Monte Carlo simulation, the PLQY can be defined as the probability of photon re-emission directly after absorption by a QD.

(31) In order to account for secondary effects, such as polymer non-radiative absorption and photon scattering, PLMA waveguides of corresponding thicknesses can be engineered for direct measurement and use in the Monte Carlo. Luminescent waveguides can be fabricated via the UV polymerization method. The monomer lauryl methacrylate (Sigma Aldrich) and the cross-linker ethylene glycol dimethacrylate (Sigma Aldrich) can be mixed at a 10:1 volume ratio, and the CdSe/CdS quantum dots can be dispersed in hexane solution. To control film thickness, 0.05 vol % photo-initiator Darocur 1173 (Sigma Aldrich) can be introduced into solution, where the photo-initiator can be filled through capillary action between two quartz plates with soda lime glass spacers at the corners. Finally, the assembled device can polymerize under UV illumination and inert atmosphere for approximately 30 minutes. The top quartz plate can then be removed. Waveguide absorption can be measured using a Varian Cary 5G spectrophotometer.

(32) Once a photon strikes either the embedded InGaP microcell or the Si subcell, the measured EQE can determine the photon to electron conversion. Upright InGaP solar cells with a thin emitter can be grown by metal organic vapor phase epitaxy. Microcells can be processed and placed on glass using transfer printing techniques. An angle-averaged EQE can be calculated for the InGaP device when embedded in PLMA with a ZnS anti-reflective coating (“ARC”). An EQE curve from measurements (and fitting) of larger InGaP devices in air can be calculated without an ARC.

(33) For the Si subcell, an advanced design suitable for reaching high efficiencies, specifically an interdigitated back passivated contact cell, can be utilized. This back contacted architecture can free the cell of optical shading losses. Passivated contacts can enable high open circuit voltages. The cell can be fabricated from 180 μm thick n-type Cz wafer with a resistivity of 3 Ω-cm. Wafer saw damage can be removed by etching and KOH. The wafers can be RCA cleaned, and a rear tunneling oxide can be formed at 700° C. with O.sub.2 flow. Approximately 100 nm of intrinsic amorphous Si can be deposited on the rear side by plasma-enhanced chemical vapor deposition. Beamline ion implantation at 5 kV can be used to implant 4×10.sup.15 cm.sup.−2 B for the rear emitter regions using photolithographic masking to define the area of the device that is implanted. Similarly, beamline ion implantation can be used to implant 7×10.sup.15 cm.sup.−2 P for the rear BSF regions. The sample can be annealed at 850° C. to crystallize the amorphous Si and activate the implanted dopants. Approximately 15 nm of Al.sub.2O.sub.3 can be deposited on the entire surface of the device by atomic layer deposition (“ALD”), and approximately 75 nm SiNx can be deposited on the front side as an anti-reflection coating. The sample can be annealed at 400° C. in forming gas to activate hydrogen passivation of its surfaces. The Al.sub.2O.sub.3 can be etched from the rear of the sample, and an interdigitated pattern can be defined photolithographically and then metalized by evaporating 1 μm Al. The cell EQE can be measured using an Oriel QE system.

(34) To simulate photon reflection via front contact shading, a finite probability can be assigned to the InGaP cell. In one embodiment, the Monte Carlo simulation for a fabricated Si cell EQE yielded an overall PCE of η.sub.Si≈21.8% for the stand-alone Si subcell under direct illumination.

(35) Photon loss mechanisms in MOTLSCs in accordance with various embodiments of the invention can occur from either initial reflection off the top mirror of the module, parasitic absorption via the QDs, or transmission through the top surface of the device. A count of the photons and their incident wavelength accepted by either the InGaP or Si cell can be integrated with respect to the standard AM1.5G spectrum. The model can then use a detailed balance calculation of the open circuit voltage (V.sub.oc) and fill factor (FF) to give an overall tandem LSC-Si module efficiency. An ideality factor of n=1 is assumed for both the InGaP and Si cell cases, and the ideal diode equation can be applied to determine the V.sub.oc and FF, given as:

(36) $V_{\mathrm{OC}}=\frac{{\mathrm{nk}}_{B}T}{q}\ln \left(\frac{I_L}{I_0}\right)+\frac{{\mathrm{nk}}_{B}T}{q}\ln \left(Q_{\mathrm{ERE}}\right)$
where q is the electron charge, k.sub.B is the Boltzmann constant, T is the cell operating temperature (assumed to be T=300K), I.sub.L is the simulated illumination current, and I.sub.0 is the dark saturation current. I.sub.0 is approximated based on the radiative limit of the cell, which can be determined from the measured energy bandgaps (E.sub.g) of the fabricated InGaP and Si cells:

(37) $I_0=\frac{q}{k_B}\frac{q15\sigma }{{\pi }^4}{A}_{\mathrm{wg}}{T}^3{\int }_{E_g/k_{B}T}^{\infty }\frac{x^2}{e^x-1}\mathrm{dx}$
where σ is the Stefan-Boltzmann constant and A.sub.wg is the waveguide area. This simulation assumes a GG of 100, where the fabricated InGaP micro-cell dimensions were measured to be 1.5×10.sup.−3 m by 1×10.sup.−4 m, yielding an InGaP cell area of 0.15 mm.sup.2 and therefore a waveguide area of 15 mm.sup.2.

(38) Tandem LSC-Si devices in accordance with various embodiments of the invention can include a large number of module components. Given this large parameter space, an extensive multi-parameter sweep can be performed while assuming no top or bottom mirrors in the device architecture. As a first step, the QD PL peak location, the QD PL full width at half maximum (“FWHM”), the optical density (“OD”) of QDs within the PLMA waveguide, and the QD PLQY can be varied. FIG. 5A-5D show the results of these parametric variations.

(39) As shown in FIG. 5A, in the case without mirrors, the ideal PL peak location obtains a maximum module performance slightly above 650 nm across all PLQY values. This results from a Stokes shift increase, minimizing re-absorption loss at wavelengths with high InGaP EQE. An optimum FWHM for the QD PL was observed, at approximately 80 nm, as shown in FIG. 5B. With a larger FWHM of the QD PL, increased photon spread yields more frequent opportunities for radiated photons to be absorbed by either the more efficient InGaP micro-cell or the higher EQE Si subcell. In contrast, when the FWHM spreads too far, non-radiative recombination via QDs' re-absorption can decrease the overall module efficiency.

(40) Across all PLQY values, maximum PCE occurs at an OD of 0.30 at 450 nm, as shown in FIG. 5C. For OD values less than 0.30, QDs do not absorb and re-direct enough photons to the InGaP micro-cells. However, for OD values greater than 0.30, photons are either parasitically absorbed by the QDs or re-radiated at angles within the escape cone at a greater frequency. With unity PLQY, optimized PL peak location, ideal FWHM, and intermediate waveguide OD, a maximum PCE of η=26.6% can be achieved.

(41) In the case without mirrors, the majority of output power generated by the tandem LSC-Si module comes from the Si subcell. As shown in FIG. 5D, the generated photocurrent of the Si cell was found to be an order of magnitude greater than the InGaP cell photocurrent across all PLQY. Even at unity PLQY, escape cone loss prevents higher concentration of light impinging upon the InGaP cell. Therefore, in order to achieve both higher overall module efficiencies and more significant InGaP cell power generation, additional light-trapping mechanisms should be integrated into the device architecture.

(42) To determine optimal spectral and angular requirements for the top and bottom PL trapping mirrors, the mirror reflection parameters can be varied with a top-hat like profile as shown in FIG. 3C. The top mirror can impose more stringent spectral requirements. The optical filter can require near unity short-pass response as QD absorption typically occurs only in this spectrum. Similarly, the long-pass response should be ideal in order for light to reach the Si subcell. In contrast, the bottom mirror short-passed light is often parasitically absorbed by the Si subcell. Short-pass requirements for the bottom mirror can be relaxed. However, both the top and bottom mirrors can require maximum light reflection in the rejection-band in order to trap photons exiting the optical waveguide through the escape cone.

(43) Synthesized CdSe/CdS QDs in accordance with various embodiments of the invention exhibit FWHM of approximately 30 nm with a PL peak location centered at 625 nm. These measured values were treated as fixed within the mirror optimization simulations. Given this PL spectra, FIG. 6A shows the module PCE for varying rejection-band widths, centered at 625 nm. In the illustrative embodiment, a width of 68 nm yielded maximum device performance. The rejection-band mirror reflection width therefore captures enough of the QDs' radiated photons without preventing incident light to reach either the embedded QDs or the underlying Si cell. Assuming ideal rejection-band top/bottom mirror widths, the effect of R.sub.rejection against R.sub.pass (the short and long pass regimes) can be investigated where angular independent response is assumed. FIG. 6C details the overall module efficiency results, varying these two reflection parameters. While optimal module efficiency can result from unity R.sub.rejection reflection and zero R.sub.pass, increased mirror R.sub.pass is most detrimental to overall device performance. Assuming no top/bottom mirror parity, the overall module efficiency impact due to varying R.sub.short-pass of only the bottom mirror can be determined while assuming unity R.sub.rejection and zero R.sub.pass for the top mirror. FIG. 6D shows that, as predicted, short-wavelength transmission requirements for the bottom mirror are significantly reduced in order to obtain high performance. With optimized top and bottom, angularly-independent mirrors from these results, an overall module efficiency of η=27.75% can be achieved.

(44) As is the case with common spectrally-selective filters (e.g., dielectric stacks), a greater incident photon angle often blueshifts the rejection-band of the mirror while maintaining a relatively constant width. Simulations varying the rejection-band left and right edges' location for normally incident photons can be conducted. A rejection-band center shift of 1 nm per degree off normal incidence can be assumed. FIG. 6B shows the results of this simulation. For rejection-band left edges located near 620 nm and right edges near 700 nm, a global maximum module efficiency can be determined. For rejection-band widths too large, module efficiency decreases as more of the band's reflection fails to overlap with the PL spectra and reflects incident light. However, this global maximum occurs at rejection-band widths that, at normal incidence, are further red-shifted. This result implies that the top and bottom mirrors' fundamental contribution to tandem LSC-Si module efficiency comes from reflecting back photons with large angles of incidence within the waveguide.

(45) Analogous to the optimization of the device without mirrors, the maximum module efficiency possible with ideal top and bottom mirrors can be determined. FIG. 7A shows that ideal PL peak values depend strongly on the PLQY. For lower QD performance, 650 nm yields maximum module efficiency. Parasitic absorption dominates photon recycling events for poor PLQY values. With optimized top/bottom mirrors, photon thermalization odds increase for PL peaks centered in the mirrors' rejection-band. However, as the limit of PLQY approaches unity, the PL peak optimum shifts to 625 nm. Because top/bottom mirror rejection-band reflection is lossless and centered at 625 nm, unity PLQY results in zero instances of non-radiative absorption by the embedded QDs, and therefore allows for unlimited recycling and trapping of short-wavelength photons.

(46) Similarly, a strong dependence on PLQY in the module performance can be seen by varying the FWHM, as shown in FIG. 7B. As expected, high PLQY values favor sharply-peaked PL. High PLQY minimizes non-radiative photon recycling, and therefore narrower FWHM values allow for more photon capture.

(47) Varied optical density of the QDs embedded within the polymer waveguide for the perfect top/bottom mirror case additionally shows this strong dependence on PLQY values, as shown in FIG. 7C. However, in all cases of module PCE, a maximum can be obtained at OD of 0.30 at 450 nm. In contrast to the no-mirror case, the module efficiency curves for non-unity PLQY decrease less rapidly for increasing OD. With increased QD absorption and PL, there is more opportunity for escape-cone losses. However, for ideal mirrors, unity rejection-band redirects all such potential escaped photons back into the waveguide. With unity PLQY, optimized QD PL peak location, ideal FWHM, and an OD of 0.30 at 450 nm, a maximum PCE of η=31.1% can be achieved, approximately a 4.5% boost from the no-mirrors case.

(48) In the perfect-mirrors case, the output power generated by this tandem LSC-Si module is much more evenly split between the Si subcell and the embedded InGaP micro-cell. The InGaP contributes approximately 43% of the total output power for unity PLQY. FIG. 7D displays the short circuit current contribution of the InGaP cell. In contrast to FIG. 5D, the InGaP photocurrent has increased by a factor of 4.5.

(49) The fraction of DNI light affecting the overall module PCE can be investigated. FIG. 8A shows the results of this simulation for the perfect-mirror architecture. As expected, the highest module efficiency results from 100% DNI; however, the absolute percent efficiency increase between the completely diffuse case (i.e., 0% DNI) and the fully direct case is 0.389% overall PCE. This suggests that, while DNI light is ideal for maximum module efficiencies, the tandem LSC-Si architecture can perform with greater than 30% PCE even in the completely diffuse limit.

(50) FIGS. 8B-8D show performance analysis of best-case scenarios from both the no-mirror and perfect-mirror cases. For this, non-unity PLQY of 0.98 was chosen to determine how parasitic QD absorption loss compares to escape cone loss. In the no-mirror case, the dominate performance detriment comes from escape cone loss, shown in FIG. 8C. Escape cone loss stems from non-unity Si EQE and incomplete waveguide trapping. For the perfect mirror case, short-wavelength photons are more likely parasitically absorbed as a result of increased photon recycling, shown in FIG. 8D. This can be demonstrated by comparing the average number of PL events for a given photon of a certain wavelength, shown in FIG. 8B. Long-wavelength photons' loss mechanism for the perfect mirror case is primarily a result of the imperfect absorption of the Si subcell, matching the no mirror case. Table 1 shows the comparison between best-case scenarios of the no-mirror and perfect-mirror configuration for unity and 0.98 PLQY. Additionally, Table 1 compares the overall power output with the use of a 25.6% cell efficiency, silicon heterojunction structure with interdigitated back contacts as the subcell. The power output possible with the tandem LSC-Si architecture can be demonstrated by replacing the subcell with a passivated emitter and rear cell (“PERC”).

(51) As shown, significant PCE enhancements to both traditional LSC designs and flat-plate Si cells via a tandem LSC-Si module with spectrally-selective top and bottom mirrors and CdSe/CdS QD luminophores with optimally tuned absorption and PL spectra can be achieved. The application of a Monte Carlo ray-tracing model to fabricated Si and InGaP cells with measured EQEs yielded cell efficiencies of ηSi=21.8% and ηInGaP=24.9% under full DNI. Under low DNI conditions, maximum LSC-Si PCEs reaching 26.6% and 31.1% for the no-mirrors and perfect-mirrors cases can be achieved, respectively. Furthermore, assuming subcell EQEs of a PERC or a HIT Si cell, tandem LSC-SI PCEs can achieve 32.2% and 32.9%, respectively.

(52) Assuming a tandem structure without top and bottom mirrors, an ideal QD PL peak location of 650 nm given the InGaP and Si cell EQEs, optimized QD PL FWHM of 80 nm, and an OD of the embedded QDs within the PLMA waveguide of 0.30 at 450 nm can be shown. For high QD PLQY under these conditions, a maximum PCE of 26.6% can be shown where roughly 20% of this power is generated by the LSC and 80% by the Si subcell.

(53) Optimizing the top and bottom mirrors' spectral reflection and angular dependence for maximum PCE, an ideal QD PL peak location of 625 nm, optimized QD PL FWHM of 10 nm, and an OD of the embedded QDs within the PLMA waveguide of 0.30 at 450 nm can be shown for near-unity PLQY. Under these conditions and optimized mirror design, a maximum PCE of 31.1% can be shown where roughly 45% of the output power is generated by the LSC and 55% by the Si subcell. These modeling results demonstrate the efficiency amplifications possible, even under low DNI conditions, by the tandem architecture in accordance with various embodiments of the invention.

(54) While the above description contains many specific embodiments of the invention, these should not be construed as limitations on the scope of the invention, but rather as an example of one embodiment thereof. It is therefore to be understood that the present invention may be practiced in ways other than specifically described, without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive. Accordingly, the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their equivalents.