Excitonic energy transfer to increase inorganic solar cell efficiency
11088338 · 2021-08-10
Assignee
- The Regents Of The University Of Michigan (Ann Arbor, MI)
- University Of Southern California (Los Angeles, CA)
Inventors
Cpc classification
H01L31/055
ELECTRICITY
H01L31/02322
ELECTRICITY
Y02E10/52
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H10K30/10
ELECTRICITY
H10K85/626
ELECTRICITY
H10K85/621
ELECTRICITY
Y02E10/549
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
International classification
H01L31/055
ELECTRICITY
Abstract
The present disclosure relates to a photosensitive optoelectronic device comprising two electrodes, an inorganic subcell positioned between the two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a band gap energy (E.sub.G), and an organic sensitizing window layer disposed on the inorganic subcell. In one aspect, the organic sensitizing window layer comprises a singlet fission material. In another aspect, the organic sensitizing window layer comprises a singlet fission host and a phosphorescent emitter dopant, where the singlet fission host exhibits an excitation triplet energy (E.sub.T-SF) greater than or equal to an excitation triplet energy (E.sub.T-PE) exhibited by the phosphorescent emitter dopant.
Claims
1. A photosensitive optoelectronic device comprising: two electrodes; an inorganic subcell positioned between the two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a band gap energy (E.sub.G); and an organic sensitizing window layer disposed on the inorganic subcell and in physical contact with the at least one inorganic semiconductor material, wherein the organic sensitizing window layer comprises a singlet fission material and a phosphorescent emitter dopant, wherein the organic sensitizing window layer has a thickness in the range of 0.1 to 2 μm such that the thickness does not exceed a triplet diffusion length of the singlet fission material, and wherein the phosphorescent emitter dopant emits radiation at an energy greater than or equal to the band gap energy (E.sub.G) of the at least one inorganic semiconductor material such that photons emitted from the phosphorescent emitter dopant are absorbed by the inorganic subcell.
2. The device of claim 1, wherein the singlet fission material exhibits an absorptivity of light of at least 10.sup.3 cm.sup.−1 at one or more wavelengths ranging from 300 to 700 nm.
3. The device of claim 1, wherein the singlet fission material exhibits an excitation triplet energy (E.sub.T-SF) substantially matching the band gap energy (E.sub.G).
4. The device of claim 1, wherein the inorganic subcell comprises at least one p-n junction.
5. The device of claim 4, wherein the at least one p-n junction comprises at least one semiconducting material chosen from Ge, Si, GaAs, InP, GaN, AlN, CdTe, ZnTe, copper indium gallium (di)selenide (CIGS), and combinations thereof.
6. The device of claim 1, wherein the at least one inorganic semiconductor material comprises a material chosen from III-V materials, Si, Ge, CdTe, ZnTe, and copper indium gallium (di)selenide (CIGS).
7. The device of claim 6, wherein the at least one inorganic semiconductor material is chosen from GaAs, InP, GaN, AlN, and InGaAs.
8. The device of claim 1, wherein the inorganic subcell comprises at least one p-n junction and an inorganic energy matching layer positioned between the at least one p-n junction and the organic sensitizing window layer, wherein the inorganic energy matching layer comprises the at least one inorganic semiconductor material, and wherein the band gap energy (E.sub.G) of the at least one semiconductor material substantially matches an excitation triplet energy (E.sub.T-SF) of the singlet fission material.
9. The device of claim 8, wherein the at least one inorganic semiconductor material comprises a III-V material.
10. The device of claim 9, wherein the III-V material is In.sub.xGa.sub.1-xAs, wherein x is chosen such that the band gap energy E.sub.G substantially matches the excitation triplet energy (E.sub.T-SF) of the singlet fission material.
11. The device of claim 1, wherein the singlet fission material is chosen from polyacenes, rylenes, rubrenes, and biradicaloids.
12. The device of claim 11, wherein the polyacenes are anthracene, tetracene, pentacene, and derivatives thereof, and the biradicaloids are benzofurans.
13. A photosensitive optoelectronic device comprising: two electrodes; an inorganic subcell positioned between the two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a band gap energy (E.sub.G); and an organic sensitizing window layer disposed on the inorganic subcell and in physical contact with the at least one inorganic semiconductor material, wherein the organic sensitizing window layer comprises a singlet fission material and a phosphorescent emitter dopant, wherein the singlet fission material exhibits an excitation triplet energy (E.sub.T-SF) substantially matching the band gap energy (E.sub.G), and wherein the phosphorescent emitter dopant emits radiation at an energy greater than or equal to the band gap energy (E.sub.G) of the at least one inorganic semiconductor material such that photons emitted from the phosphorescent emitter dopant are absorbed by the inorganic subcell.
14. The device of claim 13, wherein the inorganic subcell comprises at least one p-n junction and an inorganic energy matching layer positioned between the at least one p-n junction and the organic sensitizing window layer, wherein the inorganic energy matching layer comprises the at least one inorganic semiconductor material, and wherein the band gap energy (E.sub.G) of the at least one semiconductor material substantially matches an excitation triplet energy (E.sub.T-SF) of the singlet fission material.
15. The device of claim 13, wherein the at least one inorganic semiconductor material comprises a III-V material.
16. The device of claim 14, wherein the III-V material is In.sub.xGa.sub.1-xAs, wherein x is chosen such that the band gap energy E.sub.G substantially matches the excitation triplet energy (E.sub.T-SF) of the singlet fission material.
17. The device of claim 13, wherein the excitation triplet energy is tuned by donor/acceptor substitution.
18. The device of claim 13, wherein the excitation triplet energy is tuned by nitrogen substitution.
Description
(1) The foregoing and other features of the present disclosure will be more readily apparent from the following detailed description of exemplary embodiments, taken in conjunction with the attached drawings. It will be noted that for convenience all illustrations of devices show the height dimension exaggerated in relation to the width.
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(15) As used herein, the term “singlet fission material” or “singlet fission host” means a material that exhibits an excitation singlet energy (E.sub.S-SF) and an excitation triplet energy (E.sub.T-SF) satisfying the following condition: E.sub.S-SF≥2E.sub.T-SF. For purposes of satisfying the condition under the present disclosure, an E.sub.S-sF within 0.2 eV of 2E.sub.T-SF is considered “equal to” 2E.sub.T-SF, and thus satisfies the condition.
(16) As used herein, the term “layer” refers to a member or component of a photosensitive device whose primary dimension is X-Y, i.e., along its length and width. It should be understood that the term layer is not necessarily limited to single layers or sheets of materials. In addition, it should be understood that the surfaces of certain layers, including the interface(s) of such layers with other material(s) or layers(s), may be imperfect, wherein the surfaces represent an interpenetrating, entangled or convoluted network with other material(s) or layer(s). Similarly, it should also be understood that a layer may be discontinuous, such that the continuity of the layer along the X-Y dimension may be disturbed or otherwise interrupted by other layer(s) or material(s).
(17) The terms “electrode” and “contact” are used herein to refer to a layer that provides a medium for delivering photo-generated current to an external circuit or providing a bias current or voltage to the device. That is, an electrode, or contact, provides the interface between the active regions of a photosensitive optoelectronic device and a wire, lead, trace or other means for transporting the charge carriers to or from the external circuit. Anodes and cathodes are examples.
(18) As used herein, the term “III-V material” may be used to refer to compound crystals containing elements from group IIIA and group VA of the periodic table. More specifically, the term III-V material may be used herein to refer to compounds which are combinations of the group of Gallium (Ga), Indium (In) and Aluminum (Al), and the group of Arsenic (As), Phosphorous (P), Nitrogen (N), and Antimony (Sb). Representative materials may include GaAs, InP, InGaAs, AlAs, AlGaAs, InGaAsP, InGaAsPN, GaN, InGaN, InGaP, GaSb, GaAlSh, InGaTeP, and InSb and all related compounds.
(19) As described herein, the inorganic subcell is “positioned between” or “deposited between” the two electrodes if it is physically positioned in a manner such that the inorganic subcell is electrically between the two electrodes in that holes flow from the inorganic subcell to one electrode and electrons flow from the inorganic subcell to the opposing electrode.
(20) The present disclosure relates to a photosensitive optoelectronic device comprising two electrodes, an inorganic subcell positioned between the two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a band gap energy (E.sub.G), and an organic sensitizing window layer disposed on the inorganic subcell. A non-limiting example of this device is shown in
(21) The inorganic subcell referred to and depicted herein may comprise a p-n junction, e.g., any p-n junction known in the art for a conventional, high-efficiency inorganic solar cell. This is shown in
(22) The organic sensitizing window layer as described herein is designed to increase the efficiency of the underlying inorganic subcell.
(23) In one aspect, the organic sensitizing window layer comprises a singlet fission material. The singlet fission material may exhibit an absorptivity of light of at least 10.sup.3 cm.sup.−1 at one or more wavelengths ranging from 300 to 700 nm.
(24) In this aspect, upon absorption of light by the singlet fission material, energy transfer to the underlying inorganic subcell occurs by direct Dexter (i.e. non-radiative) transfer of energy from the triplet state of the singlet fission material upon diffusion to the interface of the organic layer and the inorganic subcell. Thus, in some embodiments, the singlet fission material exhibits an excitation triplet energy (E.sub.T-SF) substantially matching the band gap energy E.sub.G of the at least one inorganic semiconductor material. “Substantially matching” as used throughout this disclosure means an energy difference ≤0.3 eV. In some embodiments, the energy difference is ≤0.2 eV, ≤0.1 eV, or ≤0.05 eV. The singlet/triplet energies of the singlet fission material may be fine-tuned by donor/acceptor and/or nitrogen substitution. In this way, the excitation triplet energy (E.sub.T-SF) of the singlet fission material may be tuned to substantially match the band gap energy E.sub.G of the at least one inorganic semiconductor layer.
(25) Another approach for substantially matching the excitation triplet energy (E.sub.T-SF) of the singlet fission material with the band gap energy E.sub.G of the at least one inorganic semiconductor material is through the use of an inorganic energy matching layer. Thus, in some embodiments, the inorganic subcell comprises at least one p-n junction and an inorganic energy matching layer positioned between the at least one p-n junction and the organic sensitizing window layer, wherein the inorganic energy matching layer comprises the at least one inorganic semiconductor material. In this embodiment, the band gap energy (E.sub.G) of the at least one inorganic semiconductor material can substantially match the excitation triplet energy (E.sub.T-SF) of the singlet fission material. For example, the inorganic energy matching layer can be chosen to provide a band gap energy E.sub.G that substantially matches the excitation triplet energy (E.sub.T-SF) of the singlet fission material. The at least one inorganic semiconductor layer may comprise a III-V material. As shown in the non-limiting example in
(26) The Dexter energy transfer referenced above is shown in
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k.sub.Dex=KJ.sub.i-f exp(−2z/L) (1)
where K is a constant, J.sub.i-f is the integral of the overlap between the emission of the triplet state and the absorption of the semiconductor medium (i.e. it is a measure of the orbital energy resonance between the initial and final states of the excited species), z is the distance between the molecule and the semiconductor, and L is the characteristic tunneling distance. In sum, this process involves the coherent and simultaneous transfer of an electron and hole from the initial (organic) to the final (inorganic semiconductor) state over a distance z.
(28) In accordance with equation (1), the free charge generation within the inorganic subcell should occur within a diffusion length, L.sub.D, of the inorganic subcell base region. Thus, the emitter layer, e.g., as shown in
(29) In some embodiments, the thickness of the organic sensitizing window layer is chosen so as not to exceed the triplet diffusion length of the singlet fission material. In certain embodiments, the thickness of the organic sensitizing window layer is in a range of 0.01 to 2 μm, 0.1 to 2 μm, or 0.1 to 1 μm. While the thickness of the organic sensitizing window layer should be chosen so as not to exceed the exciton diffusion length of the singlet fission material to prevent triplet loss to nonradiative decay, this is balanced by the desire to achieve high optical density in the window layer. Thus, in some embodiments, the singlet fission material exhibits long-range crystalline order. In some embodiments, the singlet fission material is a single crystal film. Such crystalline organic materials exhibit long diffusion lengths allowing for thicker organic sensitizing window layers resulting in higher optical densities. Organic materials of long range crystalline order and organic single crystal films may be grown using organic vapor phase deposition (OVPD) techniques known in the art.
(30) In some embodiments, the organic sensitizing window later comprising the singlet fission material is in physical contact with the at least one inorganic semiconductor material of the inorganic subcell. In some embodiments, the organic sensitizing window layer comprising the singlet fission material is within a distance ≤2 nm from the at least one inorganic semiconductor material of the inorganic subcell.
(31) In some embodiments, the singlet fission material can be deposited on the surface of a templating layer, such as a 1 nm thick film of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA), to forma continuous film. For example, deposition of diphenylisobenzofuran on the surface of PTCDA can result in a continuous film. Absorbance measurements of the deposited diphenylisobenzofuran film confirms that the film has the same morphology as required for 200% singlet fission efficiency, as shown in
(32) The singlet fission material may be chosen from materials that satisfy the condition E.sub.S-SF≥2E.sub.T-SF as defined above. Examples of suitable singlet fission materials include polyacenes, rylenes, rubrenes, and biradicaloids. In certain embodiments, the singlet fission material is chosen from anthracene, tetracene (E.sub.S-SF=2.3 eV. E.sub.T-SF=1.25 eV), pentacene, rubrene, and derivatives thereof. In certain embodiments, the singlet fission material is chosen from benzofurans and related compounds. Dimer molecules of these exemplary materials can also be appropriate for the singlet fission material. For example, a slipped stack arrangement can be formed by preparing acene dimers, such as tetracene dimers, around a cyclophane core as shown in
(33) In certain embodiments, the singlet fission materials may be chosen from materials that also satisfy the condition E.sub.(T-SF)2<2E.sub.T-SF, where E.sub.(T-SF)2 is the next highest triplet state.
(34) The at least one inorganic semiconductor material as described herein may comprise a material chosen from III-V materials, Si, Ge, CdTe, ZnTe, and copper indium gallium (di)selenide (GIGS). In certain embodiments, the at least one inorganic semiconductor material is chosen from GaAs, InP, GaN, AlN, and InGeAs.
(35) In another aspect, the organic sensitizing window layer comprises a singlet fission host and a phosphorescent emitter dopant, wherein the singlet fission host exhibits an excitation triplet energy (E.sub.T-SF) greater than or equal to an excitation triplet energy (E.sub.T-PE) exhibited by the phosphorescent emitter dopant. Under the present disclosure, an E.sub.T-SF within 0.2 eV of E.sub.T-PE is considered “equal to” E.sub.T-PE. The singlet fission host may exhibit an absorptivity of h of at least 10.sup.3 cm.sup.−1 at one or more wavelengths ranging from 300 to 700 nm.
(36) In this aspect, a singlet produced upon the absorption of a high energy photon by the singlet fission host undergoes fission into two triplets, which are transferred to the phosphorescent emitter dopant. This energy process is shown in
(37) To transfer the triplets of the singlet fission host to the phosphorescent emitter dopant, the excitation triplet energy (E.sub.T-SF) of the singlet fission host should be greater than or equal to the excitation triplet energy (E.sub.T-PE) of the emitter dopant. In some embodiments, the excitation triplet energy of the singlet fission host substantially matches the excitation triplet energy of the emitter dopant. In addition, the rate of triplet transfer from the singlet fission host to the phosphorescent emitter dopant should be faster than the rate of deactivation of the singlet or triplet excited states of the singlet fission host. The photons emitted from the phosphorescent emitter dopant should be of sufficiently high energy to be absorbed in the active region of the underlying inorganic subcell. Thus, in some embodiments, the phosphorescent emitter emits radiation at an energy greater than or equal to the band gap energy (E.sub.G) of the at least one inorganic semiconductor material.
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(39) The maximum power conversion efficiency (PCE) can be modeled for a system based on singlet fission-sensitized phosphorescence coupled to an inorganic subcell of bandgap E.sub.G. The upper limit to total system efficiency is defined by assuming that 100% of photons with energy >E.sub.S-SF are absorbed by the singlet fission host and subsequently emitted at E.sub.T-PE with 200% quantum efficiency.
(40) It has been shown that triplet transfer from the singlet fission host to the phosphorescent emitter dopant can be highly efficient even if the process is endothermic with an energy difference as large as 0.1 eV. Also, singlet fission can be endothermic by as much as 0.2 eV and still proceed with high efficiency. Thus, the overall process considers both endothermic processes such that the total endothermic energy barrier is defined as A=E.sub.T-PE−½ E.sub.S-SF. The result is shown in
(41) The presence of endothermic transfer shifts the optimum band gap of the underlying inorganic subcell to commensurately higher voltages. For example, at A=0.3 eV, the maximum efficiency is achieved for E.sub.G=1.3 eV. This is only slightly lower than that of GaAs (where E.sub.G=1.42 eV). Thus, in some embodiments, the inorganic subcell comprises at least one p-n junction and an inorganic energy matching layer positioned between the at least one p-n junction and the organic sensitizing window layer, wherein the inorganic energy matching layer comprises the at least one inorganic semiconductor material. In this embodiment, the band gap energy (E.sub.G) of the inorganic energy matching layer can be tuned to optimize the PCE for a given single fission host/phosphorescent emitter dopant pair. The at least one inorganic semiconductor material may comprise a III-V material. As shown in the non-limiting example in
(42) One significant potential loss mechanism s the outcoupling process from the window layer. The loss is due to outcoupling from triplet remission into 4n solid angle from the phosphorescent emitter dopant as shown in
(43) In some embodiments, the organic sensitizing window layer comprising the singlet fission host and the phosphorescent emitter dopant is in physical contact with the at least one inorganic semiconductor material of the inorganic subcell. In some embodiments, the organic sensitizing window layer comprising the singlet fission host and the phosphorescent emitter dopant is within a distance several microns, e.g., 5 microns, from the at least one inorganic semiconductor material of the inorganic subcell. The organic sensitizing window layer comprising the singlet fission host and the phosphorescent emitter dopant may have a thickness in the range of 0.1 to 2 μm.
(44) The singlet fission host may be chosen from materials that satisfy the condition E.sub.S-SF≤2E.sub.T-SF as defined above. Examples of suitable singlet fission materials include polyacenes, rylenes, rubrenes, and biradicalocis. In some embodiments, the polyacenes are anthracene, tetracene, pentacene, and derivatives thereof, and the biradicaloids are benzofurans and related compounds. Dimer molecules of these exemplary materials can also be appropriate for the singlet fission host. For example, a slipped stack arrangement can be formed by preparing acene dimers, such as tetracene dimers, around a cyclophane core as shown in
(45) In certain embodiments, the singlet fission host comprises 5,12-diphenyltetracene (DPT) or derivatives thereof. In other embodiments, the singlet fission host comprises diphenylisobenzofuran or derivatives thereof. In some embodiments, the singlet fission host exhibits an excitation singlet energy E.sub.S-SF greater than 2.0 eV. In certain embodiments, the singlet fission host may be chosen from materials that also satisfy the condition E.sub.(T-SF)2>2E.sub.T-SF, where E.sub.(T-SF)2 is the next highest triplet state of the singlet fission host.
(46) The phosphorescent emitter dopant may be chosen to emit radiation in the red/NIR spectral region. In some embodiments, the phosphorescent emitter dopant exhibits highest phosphorescence efficiencies in the red/NIR spectral region. The phosphorescent emitter dopant may comprise, for example, an organometallic material. In some embodiments, the phosphorescent emitter dopant comprises a material chosen from metal porphyrins and phthalocyanines. The metal porphyrins may be chosen from, for example, platinum porphyrins. In certain embodiments, the platinum porphyrins are platinum-tetraphenyl-tetrabenzo-porphyrin (PtTPBP), tetraphenyltetranaptho platinum porphyrin (PtTPNP), tetraphenyltetraanthro platinum porphyrin (PtANP), platinum-diphenyltetranaptho-porphyrin (PtDPNP), and derivatives thereof.
(47) In some embodiments, the triplet excitation energy (E.sub.T-PE) of candidate phosphorescent emitter dopants may be suitably tuned for use with a singlet fission host. As described above, the excitation triplet energy (E.sub.T-SF) of the singlet fission host should be greater than or equal to the excitation triplet energy (E.sub.T-PE) of the phosphorescent emitter dopant, so that the triplet localizes on the phosphorescent emitter dopant and not the singlet fission host. For example, extending conjugation at the benzopyrole rings as shown for the naptho-fused materials in
(48) In some embodiments, deuterium is substituted for hydrogen in the phosphorescent emitter dopant to increase phosphorescence yields. In certain embodiments, deuterium is substituted for hydrogen in the metal porphyrin based dopants.
(49) In a specific embodiment, the singlet fission host is diphenylisobenzofuran (E.sub.S-SF=2.76 eV, E.sub.T-SF=1.4 eV) and the phosphorescent emitter dopant is PtTPNP (E-T-PE=1.38 eV).
(50) In some embodiments, the blend of singlet fission host and phosphorescent emitter dopant can be deposited on the surface of a templating layer, such as a 1 nm thick film of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA), to form a continuous film. The deposition, for example, of diphenylisobenzofuran on the surface of PTCDA is described above and results are shown in
(51) In some embodiments, the ratio of singlet fission host to phosphorescent emitter dopant in the organic sensitizing window layer may range from 10:1 to 1:1.
(52) The two electrodes referenced herein may comprise an anode and a cathode. Electrode materials known in the art may be used. Examples include Al, Ag, Au, Cu, or other common metals and inorganic compounds such as oxides, e.g. indium tin oxide (ITO), fluorine doped tin oxide (FTO) gallium doped zinc oxide, or metal halides, e.g. Cul.
(53) In another aspect of the present disclosure, there is disclosed a method of fabricating a photosensitive optoelectronic device comprising depositing an inorganic subcell between two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a bandgap (E.sub.G), and depositing an organic sensitizing window layer on the inorganic subcell, wherein the organic sensitizing window layer comprises a singlet fission material.
(54) The inorganic subcell may be deposited according to techniques known in the art for fabricating inorganic solar cells. In some embodiments, the inorganic subcell is deposited by gas-source molecular beam epitaxy.
(55) The organic sensitizing window layer may be deposited on the inorganic subcell by vapor phase methods, for example, vacuum thermal evaporation or organic vapor phase deposition. The organic sensitizing window layer may also be deposited by solution based methods, such as spin coating, spray coating, gravure printing, ink-jet printing, and other solution based methods.
(56) In some embodiments, the inorganic subcell comprises at least one p-n junction and an inorganic energy matching layer positioned between the at least one p-n junction and the organic sensitizing window layer, wherein the inorganic energy matching layer comprises the at least one inorganic semiconductor material, wherein the band gap energy (E.sub.G) substantially matches an excitation triplet energy (E.sub.T-SF) of the singlet fission material. In certain embodiments, the at least one inorganic semiconductor material comprises a III-V material. In certain embodiments, the III-V material is In.sub.xGa.sub.1-xAs, wherein x is chosen to tune the band gap energy E.sub.G to substantially match the excitation triplet energy (E.sub.T-SF) of the singlet fission material.
(57) In another aspect of the present disclosure, there is disclosed a method of fabricating a photosensitive optoelectronic device comprising depositing an inorganic subcell between two electrodes, wherein the inorganic subcell comprises at least one inorganic semiconductor material having a bandgap (E.sub.G), and depositing an organic sensitizing window layer on the inorganic subcell, wherein the organic sensitizing window layer comprises a singlet fission host and a phosphorescent emitter dopant, the singlet fission host exhibiting an excitation triplet energy (E.sub.T-SF) greater than or equal to an excitation triplet energy (E.sub.T-PE) exhibited by the phosphorescent emitter dopant.
(58) Unless otherwise indicated, all numbers expressing quantities of ingredients, reaction conditions, and other properties or parameters used in the specification are to be understood as being modified in all instances by the term “about.” Accordingly, unless otherwise indicated, it should be understood that the numerical parameters set forth in the following specification and attached claims are approximations. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, numerical parameters should be read in light of the number of reported significant digits and the application of ordinary rounding techniques.
(59) Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.