Enhanced bulk heterojunction devices prepared by thermal and solvent vapor annealing processes
09768402 · 2017-09-19
Assignee
- University Of Southern California (Los Angeles, CA)
- The Regents Of The University Of Michigan (Ann Arbor, MI)
Inventors
- Stephen R. Forrest (Ann Arbor, MI)
- Mark E. Thompson (Anaheim, CA)
- Guodan Wei (San Jose, CA, US)
- Siyi Wang (Los Angeles, CA, US)
Cpc classification
H10K71/441
ELECTRICITY
H10K30/353
ELECTRICITY
H10K30/30
ELECTRICITY
International classification
Abstract
A method of preparing a bulk heterojunction organic photovoltaic cell through combinations of thermal and solvent vapor annealing are described. Bulk heterojunction films may prepared by known methods such as spin coating, and then exposed to one or more vaporized solvents and thermally annealed in an effort to enhance the crystalline nature of the photoactive materials.
Claims
1. A method of preparing a photosensitive device, comprising: providing a structure having at least one first electrode and a bulk heterojunction, wherein said bulk heterojunction comprises at least one first organic photoactive material and at least one second organic photoactive material, wherein said first and second organic photoactive materials are small-molecule materials, and at least one of the first and second organic photoactive materials is a squaraine; providing at least one solvent; vaporizing at least a portion of the solvent; and exposing at least a portion of the bulk heterojunction to the vaporized solvent, wherein said exposure to the vaporized solvent increases the crystallinity of at least one of the first and second organic photoactive materials.
2. The method of claim 1, further comprising thermally annealing said structure.
3. The method of claim 2, wherein the thermal annealing takes place after exposing the bulk heterojunction to the vaporized solvent.
4. The method of claim 2, wherein the thermal annealing takes place at a temperature of about 50° C. or greater.
5. The method of claim 1, wherein the structure is prepared by depositing the at least one first and the at least one second small molecule organic photoactive materials over the at least one first electrode.
6. The method of claim 5, wherein the deposition is performed by spin-casting.
7. The method of claim 6, wherein the at least one first and the at least one second small molecule organic photoactive materials are cast from a casting solvent having a boiling point no greater than about 70° C. at 1 atm.
8. The method of claim 7, wherein the casting solvent is chloroform.
9. The method of claim 6, wherein the at least one first and the at least one second small molecule organic photoactive materials are cast from a casting solvent having a boiling point greater than about 175° C. at 1 atm.
10. The method of claim 9, wherein the casting solvent is 1,2-dichlorobenzene.
11. The method of claim 5, further comprising positioning an interfacial layer between the at least one first electrode and the bulk heterojunction.
12. The method of claim 1, further comprising patterning at least one second electrode over the bulk heterojunction.
13. The method of claim 12, further comprising positioning at least one blocking layer between the bulk heterojunction and the at least one second electrode.
14. The method of claim 1, wherein the at least one blocking layer comprises BCP.
15. The method of claim 1, wherein the bulk heterojunction is exposed to the vaporized solvent in a closed container.
16. The method of claim 1, wherein the bulk heterojunction is exposed to the vaporized solvent for a period of about 5 minutes to about 30 minutes.
17. The method of claim 1, wherein the at least one solvent is dichloromethane.
18. The method of claim 1, wherein the squaraine is 2,4-bis[4-(N,N-diisobutylamino)-2,6-dihydroxyphenyl] squaraine.
19. The method of claim 1, wherein one of the first and second organic photoactive materials is PC.sub.70BM.
20. A method of enhancing the crystallinity of a bulk heterojunction in a photosensitive device, said bulk heterojunction comprising at least one first organic photoactive material and at least one second organic photoactive material, wherein said first and second organic photoactive materials are small-molecule materials, and at least one of the first and second organic photoactive materials is a squaraine, comprising: exposing at least a portion of the bulk heterojunction to a vaporized solvent, wherein the photosensitive device exhibits one or more of the following characteristics when compared to said device before exposure to the vaporized solvent: increased fill factor (FF); increased external quantum efficiency (EQE); and increased current density versus voltage (J-V).
21. The method of claim 20, further comprising thermally annealing the bulk heterojunction.
22. The method of claim 21, wherein the thermal annealing takes place after exposing the bulk heterojunction to the vaporized solvent.
23. The method of claim 21, wherein the thermal annealing takes place at a temperature of about 50° C. or greater.
24. The method of claim 20, wherein the bulk heterojunction is exposed to the vaporized solvent in a closed container.
25. The method of claim 24, wherein the bulk heterojunction is exposed to the vaporized solvent for a period of about 5 minutes to about 30 minutes.
26. The method of claim 20, wherein the at least one solvent is dichloromethane.
27. The method of claim 20, wherein the squaraine is 2,4-bis[4-(N,N-diisobutylamino)-2,6-dihydroxyphenyl] squaraine.
28. The method of claim 20, wherein one of the first and second organic photoactive materials is PC.sub.70BM.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate several embodiments described herein and, together with the description, serve to explain the principles of this application. The figures are not necessarily drawn to scale.
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DETAILED DESCRIPTION OF THE INVENTION
Definitions
(35) As used herein, the term “organic” includes polymeric materials as well as small molecule organic materials that may be used to fabricate organic optoelectronic devices. “Small molecule” refers to any organic material that is not a polymer, and “small molecules” may actually be quite large. Small molecules may include repeat units in some circumstances. For example, using a long chain alkyl group as a substituent does not remove a molecule from the “small molecule” class. Small molecules may also be incorporated into polymers, for example as a pendent group on a polymer backbone or as a part of the backbone. Small molecules may also serve as the core moiety of a dendrimer, which consists of a series of chemical shells built on the core moiety. The core moiety of a dendrimer may be a fluorescent or phosphorescent small molecule emitter. A dendrimer may be a “small molecule.” In general, a small molecule has a defined chemical formula with a molecular weight that is the same from molecule to molecule, whereas a polymer has a defined chemical formula with a molecular weight that may vary from molecule to molecule. As used herein, “organic” includes, but is not limited to, metal complexes of hydrocarbyl and heteroatom-substituted hydrocarbyl ligands.
(36) Methods and processes are described herein for using solvent annealing, and specifically solvent vapor annealing, and thermal annealing during the preparation bulk heterojunction organic photovoltaic cells. The morphology and phase separation of the organic materials may be important in that they enable both charge separation and collection. The solvent vapor annealing process described herein may be useful in having a templating effect on one or more of the organic photoactive materials comprising the bulk heterojunction, which results in the self-assembling of the organic material to form ordered aggregates. Nanomorphology and crystallinity of the organic materials may be dependent on solvent type and duration. In some embodiments, the solvent vapor annealing and/or thermal annealing processes described herein may be capable of increasing the crystalline features of one or more of the organic materials comprising a bulk heterojunction blend that is largely amorphous in nature as cast.
(37) In one embodiment, there is described a method of preparing a photosensitive device which comprises:
(38) providing a structure comprising at least one electrode and a bulk heterojunction, wherein the bulk heterojunction comprises at least one first organic photoactive material and at least one second organic photoactive material;
(39) providing at least one solvent;
(40) vaporizing at least a portion of the solvent; and
(41) exposing at least a portion of the structure to the vaporized solvent, wherein the exposure increases the crystallinity of at least one of the first or second organic photoactive materials.
(42) In some embodiments, the method further comprises thermally annealing the structure. In some embodiments, the thermal annealing step takes place after exposing at least a portion of the structure to the vaporized solvent.
(43) In some embodiments, the structure may be prepared by depositing the at least one first and the at least one second organic photoactive materials over the first electrode. After the annealing process is complete, a second electrode may be patterned over the bulk heterojunction.
(44) Electrodes, such as anodes and cathodes, may be composed of metals or “metal substitutes.” Herein the term “metal” is used to embrace both materials composed of an elementally pure metal, and also metal alloys which are materials composed of two or more elementally pure metals. The term “metal substitute” refers to a material that is not a metal within the normal definition, but which has the metal-like properties such as conductivity. Metal substitutes include, for example, doped wide-bandgap semiconductors, degenerate semiconductors, conducting oxides, and conductive polymers.
(45) The term “cathode” is used in the following manner. In a non-stacked PV device or a single unit of a stacked PV device under ambient irradiation and connected with a resistive load and with no externally applied voltage, e.g., a PV device, electrons move to the cathode from the photo-conducting material. Similarly, the term “anode” is used herein such that in a PV device under illumination, holes move to the anode from the photoconducting material, which is equivalent to electrons moving in the opposite manner. It will be noted that as the terms are used herein, anodes and cathodes may be electrodes or charge transfer layers.
(46) Electrodes may comprise a single layer or multiple layers (a “compound” electrode), and may be transparent, semi-transparent, or opaque. Examples of electrodes and electrode materials include, but are not limited to, those disclosed in U.S. Pat. No. 6,352,777 to Bulovic et al., and U.S. Pat. No. 6,420,031, to Parthasarathy, et al., each incorporated herein by reference for disclosure of these respective features. As used herein, a layer is said to be “transparent” if it transmits at least 50% of the ambient electromagnetic radiation in a relevant wavelength.
(47) In one embodiment, the first electrode may comprise an interfacial layer comprising molybdenum oxide (MoOx). MoOx is an exemplary interfacial layer in organic PV cells, which is believed to serve to reduce dark current and increase open circuit voltage (Li, N. et al., Open circuit voltage enhancement due to reduced dark current in small molecule photovoltaic cells, Appl. Phys. Lett., 94, 023307, January 2009).
(48) In some embodiments, the first organic photoactive material may comprise a donor-type material. Non-limiting examples of the first organic photoactive material that may be used herein include subphthalocyanine (SubPc), copper pthalocyanine (CuPc), chloroaluminium phthalocyanine (CIAIPc), tin phthalocyanine (SnPc), pentacene, tetracene, diindenoperylene (DIP), and squaraine (SQ).
(49) In some embodiments, the second organic photoactive material may comprise an acceptor-type material. Non-limiting examples of second organic photoactive materials that may be used herein include C.sub.60, C.sub.70, [6,6]-phenyl C.sub.70 butyric acid methyl ester (PC.sub.70BM), 3,4,9,10-perylenetetracarboxylicbis-benzimidazole (PTCBI), and hexadecafluorophthalocyanine (F.sub.16CuPc).
(50) In another embodiment, a blocking layer may be included, such as between the bulk heterojunction and the second electrode. Examples of exciton blocking layers (EBLs) are described in U.S. Pat. Nos. 6,451,415 and 7,230,269 to Forrest et al., which are incorporated herein by reference for their disclosures related to EBLs. Additional background explanation of EBLs may also be found in Peumans et al., “Efficient photon harvesting at high optical intensities in ultrathin organic double-heterostructure photovoltaic diodes,” Applied Physics Letters 76, 2650-52 (2000), which is also incorporated herein by reference. EBLs are believed to reduce quenching by preventing excitons from migrating out of the donor and/or acceptor materials. Non-limiting examples of the exciton blocking layer that may be used herein include bathocuproine (BCP), bathophenanthroline (BPhen), 3,4,9,10-perylenetetracarboxylicbis-benzimidazole (PTCBI), 1,3,5-tris(N-phenylbenzimidazol-2-yl)benzene (TPBi), tris(acetylacetonato) ruthenium(III) (RuAcaca3), and aluminum(III)phenolate (Alq.sub.2 OPH).
(51) Examples of the second electrode that may be used herein include a metal substitute, a non-metallic material or a metallic material chosen from, for example, Ag, Au, and Al.
(52) It is appreciated that the first electrode may comprise a conducting oxide, such as one chosen from indium tin oxide (ITO), tin oxide (TO), gallium indium tin oxide (GITO), zinc oxide (ZO), and zinc indium tin oxide (ZITO), and the transparent conductive polymers comprises polyanaline (PANI). In one embodiment, the bulk heterojunction organic photovoltaic cell comprises:
ITO/MoO.sub.3/SQ:PC.sub.70BM/LiF/Al; and
ITO/MoO.sub.3/SQ:PC.sub.70BM/C.sub.60/BCP/LiF/Al.
(53) The organic layers described herein may have thicknesses ranging from 25-1200 Å, such as 50-950 Å, or even 100-700 Å.
(54) In some embodiments, a bulk heterojunction may be made, for example, by vacuum thermal evaporation (VTE), spin coating, or organic vapor phase deposition (OVPD). OVPD is different from vacuum thermal evaporation (VTE) in that OVPD uses a carrier gas to transport vapors into a deposition chamber. Spatially separating the functions of evaporation and transport leads to precise control over the deposition process, and enabling control over the organic surface morphology, e.g., flat with smooth surface or layers with protrusions.
(55) In one embodiment, the bulk heterojunction is prepared by spin coating. The use of different solvent systems when preparing bulk heterojunctions via spin coating may have an effect on the ultimate efficiency of the photosensitive device upon completion. For example, devices may be made with solvents having a lower boiling point temperature, or those with a higher boiling point. Because low boiling-point solvents evaporate quickly, it may be desirable to use higher boiling-point solvents to further control morphology. In some embodiments, the use of solvents like 1,2-dichlorobenzene (DCB) in the initial preparation of the bulk heterojunction may ultimately result in PV devices exhibiting improved performance properties after solvent vapor annealing when compared to those prepared with lower boiling-point solvents.
(56) In some embodiments, the at least one first and the at least one second organic photoactive materials are cast from a casting solvent having a boiling point no greater than about 70° C. at 1 atm. Exemplary solvents may include chloroform. In another embodiment, the at least one first and the at least one second organic photoactive materials are cast from a casting solvent having a boiling point greater than about 130° C. at 1 atm. In another embodiment, the at least one first and the at least one second organic photoactive materials are cast from a casting solvent having a boiling point greater than about 175° C. at 1 atm. Exemplary solvents may include DCB.
(57) To improve the characteristics of bulk heterojunction PV cells, the film morphology of the deposited organic layers may be further optimized by exposing one or more of the organic photoactive materials to solvent vapor annealing. In some embodiments, one or more solvents may be employed to achieve optimal annealing. Exposure times may also affect the ultimate morphology of the organic materials.
(58) An exemplary vaporizing solvent includes dichloromethane. In some embodiments, it may be desirable to expose the structure to the vaporized solvent in a closed container. In some embodiments, the structure may be exposed to the vaporized solvent for a period of about 5 minutes to about 30 minutes or more, such as from 6 minutes to about 15 minutes, or even about 10 minutes to about 12 minutes.
(59) In some embodiments, it may also be desirable to further expose the heterojunction to thermal annealing. A thermal annealing step may help to further control the morphology, crystallinity, and/or enhanced performance of the prepared devices. For example, it may be desirable to thermally anneal the structure after the as-cast device has been exposed to solvent vapor annealing. Thermal annealing may take place at a temperature that is sufficient to drive off any remaining solvent from the vapor annealing step. For example, after exposing a structure to solvent vapor annealing with dichloromethane, it may be desirable to thermally anneal the device by applying heat directly to the structure. This may be accomplished by placing the structure on a hotplate heated to 50° C. under a N.sub.2 atmosphere.
(60) Also described herein are methods of enhancing the crystallinity of a bulk heterojunction in a photosensitive device, wherein the bulk heterojunction comprising at least one first and at least one second organic photoactive materials. In this embodiment, the method comprises:
(61) exposing at least a portion of the bulk heterojunction to a vaporized solvent, wherein the photosensitive device exhibits one or more of the following characteristics when compared to the device without exposure to the vaporized solvent:
(62) increased fill factor (FF);
(63) increased external quantum efficiency (EQE); and
(64) increased current density versus voltage (J-V).
(65) In some embodiments, the method further comprises thermally annealing the structure. In some embodiments, the thermal annealing step takes place after exposing at least a portion of the structure to the vaporized solvent.
(66) Suitable methods and materials include, but are not limited to, those discussed in detail below.
EXAMPLES
(67) The present disclosure may be understood more readily by reference to the following detailed description of exemplary embodiments and the working examples. It is understood that other embodiments will become apparent to those skilled in the art in view of the description and examples disclosed in this specification.
Example 1
(68) X-ray-diffraction (XRD) patterns of the SQ:PC.sub.70BM (in weight concentrations of 1:6) thin films that were spin-coated on indium tin oxide (ITO) substrates precoated with 80 Å MoO.sub.3 at a rate of 6000 RPM (revolutions per minute) were obtained using a Rigaku diffractometer in the θ-2θ geometry using a 40 kV Cu K.sub.α radiation source. The thicknesses of the SQ:PC.sub.70BM (1:6) blend cast from 20 mg/ml solutions in chloroform, as determined by using Woolam VASE ellipsometer, were 680 Å. Atomic force microscopy (AFM) images were collected in a Nanoscope III AFM in a tapping mode. For solvent annealing samples, SQ:PC.sub.70BM (1:6) bulk films were post annealed in a closed glass vial filled with 1 ml dichloromethane (DCM) for times varying from 6 min to 30 min. For thermal annealing samples, SQ:PC.sub.70BM (1:6) films were annealed on a hotplate in N.sub.2 glovebox at 50° C., 70° C., 110° C. and 130° C. for 10 min.
(69) Next DCM solvent annealing of as-cast SQ:PC.sub.70BM(1:6) films (from chloroform solvent) was performed on solar cells having the following structure: ITO/MoO.sub.3 (80 Å)/SQ:PC.sub.70BM(1:6 680 Å)/LiF (8A)/AI (1000 Å). Devices were then capped with thermally evaporated C.sub.60 layer have the structure of ITO/MoO.sub.3 (80 Å)/SQ:PC.sub.70BM(1:6 680 Å)/C.sub.60(40 A)/BCP(10 Å)/LiF (8 Å)/AI (1000 Å). MoO.sub.3 was then thermally evaporated onto the ITO surface in a vacuum system with a base pressure of 10.sup.−7 torr. The devices were completed by thermally evaporating a 8 Å LiF and 1000 Å thick Al cathode through a shadow mask resulting in a device area of 7.9×10.sup.−3 cm.sup.2. The current density-voltage (J-V) characteristics and η.sub.p of the devices were measured using an Oriel 150 W solar simulator irradiation from a Xe arc lamp with AM1.5G filters and an NREL calibrated standard Si detector. Measurements and solar spectral correction were made using standard methods. The EQE was measured using monochromated light from a Xe-lamp chopped at 400 Hz and focused to the device active area.
(70) As shown in
(71) The fill factor of the SQ:PC.sub.70BM (1:6) bulk cells as-cast from chloroform solvent was by thermal annealing at temperatures ranging from 50° C. to 130° C. is shown in
(72) External quantum efficiencies (EQE) of the as-cast and solvent annealed SQ:PC.sub.70BM (1:6) bulk cells cast from DCB solvent in
(73) The J-V characteristics of the SQ:PC.sub.70BM (1:6) bulk cells cast from DCB solvent are shown in
Example 2
(74) X-ray-diffraction (XRD) patterns of the SQ:PC.sub.70BM (in relative weight concentrations of 1:6) thin films spin-coated 1000 rpm for 30 sec on indium tin oxide (ITO)-coated glass substrates precoated with 80 {acute over (Å)} MoO.sub.3 at a low rate of 1000 RPM (revolutions per minute) were obtained using a Rigaku diffractometer in the 8-28 geometry using a 40 kV Cu K.sub.α radiation source. The thicknesses of the SQ:PC.sub.70BM (1:6) blend cast from 42 mg/ml solutions in 1,2 dichlorobenzene (DCB) heated on a hotplate for 12 h, as determined by using Woolam VASE ellipsometer, were 780 Å.
(75) Atomic force microscopy (AFM) images were collected in a Nanoscope III AFM in the tapping mode. Solvent annealing of SQ:PC.sub.70BM (1:6) deposited films was done in a closed glass vial filled with 1 ml dichloromethane (DCM) for a time varying from 6 min to 30 min. For transmission electron microscopy (TEM) studies, the SQ:PC.sub.70BM (1:6) films on ITO substrate coated with 80 Å MoO.sub.3 were immersed in deionized (DI) water for 1 hour. Next, the MoO.sub.3 was dissolved in water, and the organic layers were floated on the surface of the DI water. Then the as-cast and solvent annealed SQ:PC.sub.70BM (1:6) films were transferred onto holy carbon film coated Cu grids. The TEM images were taken using a 200 kV JEOL 2010F analytical electron microscope.
(76) The absorption spectra of the as-cast and four DCM annealed films on quartz substrates were measured using a Perkin-Elmer Lambda 1500 UV-NIR spectrometer. Photoluminescence (PL) was measured with an excitation wavelength of λ=600 nm. Solar cell structures employed the following structure: ITO/MoO.sub.3 (80 Å)/SQ:PC.sub.70BM (1:6 780 Å)/C.sub.60 (40 Å)/BCP (10 Å)/AI (1000 Å). Here, MoO.sub.3 is thermally evaporated onto the ITO surface in a vacuum system with a base pressure of 10.sup.−7 torr. Following spin cast deposition at and solvent annealing, devices were completed by thermally evaporating a 8 Å LiF and 1000 Å thick Al cathode through a shadow mask resulting in a device area of 8×10.sup.−3 cm.sup.2. The current density-voltage (J-V) characteristics and power conversion efficiency (η.sub.P) of the devices were measured using an Oriel 150 W solar simulator irradiation from a Xe arc lamp with AM1.5G filters and an NREL-calibrated standard Si detector. Measurements and solar spectral correction were made using standard methods. The EQE was measured using monochromatic light from a Xe-lamp was chopped at 200 Hz and focused to the device active area.
(77) Post annealing of SQ:PC.sub.70BM (1:6) blends entailed the 6 min to 30 min exposure of the films to DCM vapors in a closed glass vial enclosed in an ultrahigh purity nitrogen filled glove box at room temperature. As shown in
(78) The root-mean-square roughness obtained from the AFM images (
(79) The spectra in the visible for the as-cast, and four DCM solvent-annealed SQ:PC.sub.70BM blended films on quartz substrates are shown in
(80) The photoluminescence (PL) intensity of a film is quenched in the presence of charge transfer from photogenerated donor excitons to acceptor molecules (
(81) The EQE of the as-cast and solvent annealed solar cells in
(82) The J-V characteristics in
(83) The optical and electrical changes on annealing appear to lead to an increase in η.sub.p, as shown in
Example 3
(84) SQ/C.sub.60 planar cells were fabricated as control cells to compare the bilayer structure with bulk solar cells. The as-cast SQ thin layers are annealed from 50° C. to 130° C. to investigate the effect of crystallinity to device performance. As shown in
(85) SQ:PC.sub.70BM (1:6) bulk heterojunctions were prepared in a manner similar to the one described in Example 2. There is no XRD peaks for SQ:PC.sub.70BM (1:6) bulk solar cells annealed at 50° C., 70° C., 110° C. and 130° C. for 10 min, indicating amorphous feature. Without being bound to any particular theory, it is believed that PC.sub.70BM disrupts the aggregation of SQ molecules and damages its crystallinity. The roughness of AFM images for the as-cast and four thermally annealed samples are averaged to be about 0.579±0.06 nm and there is no obvious phase separation contrast of SQ and PC.sub.70BM phases, which is consistent with the measurement of XRD results. The component reorganization of SQ and PC.sub.70BM through thermal annealing is also investigated by XPS (
(86) The device performance for the five devices is shown in
(87) To further control the morphology change and crystallinity of SQ and PC.sub.70BM in the as-cast films, combinations solvent and thermal annealing were explored. Solvent annealing time is controlled by keeping films inside a covered glass jar immediately after spin-coating in air. The jar is filled with 1 ml Dichloromethane (DCM). The jar is covered with a lid in order to prevent rapid evaporation of the solvent. Then as-cast and four annealed films were put on a hotplate in N.sub.2 glovebox to anneal at 50° C. to remove remaining DCM solvent. As shown in
(88) The performance of the devices exposed to solvent annealing with DCM for various periods, and then thermally annealed at 50° C., are set forth in
(89) Other than in the examples, or where otherwise indicated, all numbers expressing quantities of ingredients, reaction conditions, analytical measurements, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about.” Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the present disclosure. At the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should be construed in light of the number of significant digits and ordinary rounding approaches.
(90) Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the disclosure are approximations, unless otherwise indicated the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contains certain errors necessarily resulting from the standard deviation found in their respective testing measurements.
(91) As used herein the terms “the,” “a,” or “an” mean “at least one,” and should not be limited to “only one” unless explicitly indicated to the contrary. Thus, for example, “a layer” should be construed to mean “at least one layer.”