US 20060189155 A1
A process of forming a compound film includes formulating a nano-powder material with a controlled overall composition and including particles of one solid solution The nano-powder material is deposited on a substrate to form a layer on the substrate, and the layer is reacted in at least one suitable atmosphere to form the compound film. The compound film may be used in fabrication of a radiation detector or solar cell.
1. A powder material for use in preparing a compound film on a substrate comprising particles of a copper-gallium solid solution which are submicronic in size.
2. The powder material of
3. The powder material of
4. The powder material of
5. The powder material of
6. The powder material of
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8. The powder material of
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10. The powder material of
11. The powder material of
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13. The powder material of
14. The powder material of
15. The powder material of
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17. The powder material of
18. The powder material of
19. The powder material of
20. The powder material of
21. The powder material of any one of claims 2, 5-7, 9-10, 13, 15-17, 19-20 and additionally including particles of a CuGaIn solid solution.
22. The powder material of any one of claims 1-20, and further including particles of at least one of selenium, sulfur, and tellurium.
23. The powder material of
24. The powder material of
25. The powder material of
26. The powder material of
This application is a division of and claims the benefit of priority to U.S. patent application Ser. No. 10/474,259 filed under 35 USC 371 on May 19, 2004 from PCT International Application Serial No. US02/11047 filed Apr. 11, 2002, which claims the benefit of priority to U.S. Provisional Application Ser. No. 60/283,630 filed Apr. 16, 2001, the entire disclosures of which are fully incorporated herein by reference for all purposes.
The present invention relates to methods of preparing polycrystalline thin films of semiconductors for active or passive electronic component and device applications especially for the fabrication of radiation detectors and solar cells.
Solar cells convert sunlight directly into electricity. These electronic devices are commonly fabricated on silicon (Si) wafers. However, the cost of electricity generated using silicon-based solar cells is rather high, compared to electricity generated by the traditional methods, such as fossil-fuel-burning power plants. To make solar cells more economically viable, low-cost, thin-film growth techniques that can deposit high-quality light-absorbing semiconductor materials need to be developed. These techniques need to employ cost-effective approaches to grow solar cell absorbers on large-area substrates with high throughput and high materials utilization. Therefore, low-cost and high-efficiency thin film solar cell fabrication requires: i) a solar cell absorber material that fundamentally has the capability to yield high-efficiency devices, ii) a low-cost deposition technique that can deposit this absorber material in the form of a high-quality thin film on a low-cost substrate. Both of these ingredients are necessary for manufacturing high-efficiency, low-cost solar cell structures. When solar cells formed on large-area substrates are interconnected, modules with higher voltage and power output are obtained.
Copper-indium-sulfo-selenide, Cu(In,Ga)(S,Se)2, compounds are excellent absorber materials for thin-film solar cell structures provided that their structural and electronic properties are good. An important compositional parameter of Cu(In,Ga)(S,Se)2 thin films is the metals molar ratio of Cu/(In+Ga). The typically acceptable range of this molar ratio for high-efficiency solar cell absorbers is about 0.70-1.0, although in some cases when the compound is doped with a dopant such as sodium (Na), potassium (K) or lithium (Li), this ratio can go even lower. If the Cu/(In+Ga) molar ratio exceeds 1.0, however, a low-resistivity copper selenide, sulfide or sulfo-selenide phase precipitates and deteriorates the performance of the device due to electrical shorting paths it creates through the absorber. Therefore, control of the Cu/(In+Ga) ratio is important for any technique that is used for the preparation of Cu(In,Ga)(S,Se)2 films for radiation detector or solar cell applications. The Ga/(In+Ga) ratio is also important to control since this ratio determines the bandgap of the absorber, which can be varied from about 1 eV (for CuInSe2) to 2.43 eV (for CuGaS2). In principal the Ga/(In+Ga) ratio may vary from zero in CuIn(S,Se)2 to 1.0 in CuGa(S,Se)2. However, laboratory experience to date has shown that best device efficiencies are obtained for Ga/(In+Ga) ratios in the range of 0.1-0.3.
Although important to control, the Cu/(In+Ga) and Ga/(In+Ga) ratios are not the only factors that influence the electronic properties of Cu(In,Ga)(S,Se)2 compound thin films. The compositional ratios of a compound film may be within the acceptable ranges, but solar cells fabricated on this film may still have poor light-to-electricity conversion efficiencies. Cu(In,Ga)(S,Se)2 compound thin films used in high-efficiency solar cell structures, besides having the right composition, also need to have good morphology and large-grain structure. For example, a typical high-quality Cu(In,Ga)(S,Se)2 thin film is 1.0-3.0 μm thick; it is dense and it has columnar grains with widths of at least 0.5 μm.
One approach that yielded high-quality Cu(In,Ga)Se2 films for solar cell applications is co-evaporation of Cu, In, Ga and Se onto heated substrates in a vacuum chamber [see for example, Bloss et al., “Thin Film Solar Cells”, Progress in Photovoltaics, 1995, vol. 3, page 3]. Absorbers grown by this technique are typically dense and they have large columnar grains. The Cu/(In+Ga) ratio and the Ga/(In+Ga) ratio are closely controlled during deposition by monitoring and controlling the individual evaporation rates of Cu, In and Ga. Consequently, Cu(In,Ga)Se2 solar cells fabricated on co-evaporated absorbers yielded small, laboratory-size solar cells with close to 19% conversion efficiency. Although there are now concentrated efforts to apply this technique to the fabrication of large-area Cu(In,Ga)Se2 modules, the method is not readily adaptable to low-cost production of large-area films, mainly because control of Cu/(In+Ga) and Ga/(In+Ga) ratios by evaporation over large-area substrates is difficult, materials utilization is low and the cost of vacuum equipment is high.
Another technique for growing Cu(In,Ga)(S,Se)2 type compound thin films for solar cell applications is the two-stage processes where at least two components of the compound are first deposited onto a substrate, and then reacted with each other and/or with a reactive atmosphere in a high-temperature annealing process. U.S. Pat. No. 4,798,660 issued to J. Ermer et al. teaches a method for fabricating a CuInSe2 film comprising sequentially depositing a film of Cu on a substrate by DC magnetron sputtering and depositing In on said film of Cu and heating the composite film in the presence of Se to form the compound. This approach is schematically depicted in
Karg et al. in U.S. Pat. No. 5,578,503 teach an alternate two-stage technique where a Cu film, an In or Ga film and a S or Se film are deposited on a substrate to form a stacked layer and then this stacked layer is heated rapidly to form the compound. The stacked structure of this prior art approach is depicted in
Yet another two-stage processing approach is taught in European Patent application No EP0838864A2 by K. Kushiya et al. In that method a stacked precursor comprising a Cu—Ga sub-layer and an In sub-layer was employed. This method is schematically shown in
All of the prior art two-stage techniques reviewed above yielded high-quality compound films in terms of their structural and electronic properties. Large-scale manufacturing, however, also requires strict control of the material composition over large-area substrates. This means that in the two-stage processes that utilize a stack of various sub-layers, the uniformity and thickness of each sub-layer have to be individually controlled over large-area substrates. This is very difficult. DC magnetron sputtering techniques which are commonly used to deposit the sub-layers of
Since compositional control, especially the control of the Cu/(In+Ga) ratio is important for Cu(In,Ga)(S,Se)2 compounds, attempts have been made to fix this ratio in an initial material, before the deposition process, and then transfer this fixed composition into a thin film formed using this initial material. T. Arita et al. in their 1988 publication [20th IEEE PV Specialists Conference, 1988, page 1650] described a screen printing technique that involved mixing and milling pure Cu. In and Se powders in the compositional ratio of 1:1:2 and forming a screen printable paste, screen printing the paste on a substrate, and sintering this film to form the compound layer. They reported that although they had started with elemental Cu, In and Se powders, after the milling step the paste contained the CuInSe2 phase. Solar cells fabricated on the sintered layers had very low efficiencies because the structural and electronic quality of these absorbers were poor.
Thin layers of CuInSe2 deposited by a screen printing method were also reported by A. Vervaet et al. [9th European Communities PV Solar Energy Conference, 1989, page 480]. In that work a CuInSe2 powder was used along with Se powder to prepare a screen printable paste. Layers formed by screen printing were sintered at high temperature. A difficulty in this approach was finding a suitable fluxing agent for dense CuInSe2 film formation. Therefore, solar cells fabricated on the resulting layers had poor conversion efficiencies.
U.S. Pat. No. 5,985,691 issued to B. M. Basol et al describes another particle-based method to form a Group IB-IIIA-VIA compound film, where IB=Cu, Ag, Au, IIIA=In, Ga, Al, TI, and VIA=S, Se, Te. The described method includes the steps of preparing a source material, depositing the source material on a base to form a precursor, and heating the precursor to form a film. In that invention the source material includes Group IB-IIIA alloy-containing particles having at least one Group IB-IIIA alloy phase, with Group IB-IIIA alloys constituting greater than about 50 molar percent of the Group IB elements and greater than about 50 molar percent of the Group IIIA elements in the source material. The powder is milled to reduce its particle size and then used in the preparation of an ink which is deposited on the substrate in the form of a precursor layer. The precursor layer is then exposed to an atmosphere containing Group VIA vapors at elevated temperatures to convert the film into the compound. The precursor films deposited using this technique were porous and they yielded porous CuInSe2 layers with small-grain regions as reported by G. Norsworthy et al. [Solar Energy Materials and Solar Cells, 2000, vol. 60, page 127]. Porous solar cell absorbers yield unstable devices because of the large internal surface area within the device. Also small grains limit the conversion efficiency of solar cells.
PCT application No. WO 99/17889 (Apr. 15, 1999) by C. Eberspacher et al. describes methods for forming solar cell materials from particulates where various approaches of making the particulates of various chemical compositions and depositing them on substrates are discussed.
As the above brief review of prior art demonstrates, there have been attempts to use Cu(In,Ga)Se2 compound powders, oxide containing particles, and Cu—(In,Ga) alloy powders with (In,Ga)-rich compositions, to form precursor layers which were then treated at high temperatures to form Cu(In,Ga)Se2 compound films. These techniques were successful in demonstrating compositional control. In other words the overall composition of the powder was directly transferred into the precursor layer and then into the compound layer. As discussed previously however, composition is only one of the important parameters of high-quality solar cell absorbers. The other important parameters are the morphology and the grain size, which directly influence the electronic properties of these films. Solar cell absorbers need to be dense layers with large grain size. This requires precursor layers that are dense and compositionally uniform both in micro-scale and macro-scale. Repeatability and the overall yield of the process further requires the quality of the source material or the initial powder material to be repeatable. This means that the chemical composition and the phase content of the individual particles comprising the powder need to be well controlled and repeatable.
To this end, there is a need for a low-cost method that has the capability to form Cu(In,Ga)(S,Se)2 thin films over large-area substrates with controlled compositional uniformity, good structural and electronic properties in a repeatable manner with high yield.
In accordance with the invention, a method of forming a Cu(In,Ga)(S,Se)2 semiconductor compound film includes the steps of formulating a nano-powder material with controlled phase content and overall composition, depositing the nano-powder on a substrate to form a micro-layer and heating and reacting the micro-layer in suitable atmosphere(s) to form a Cu(In,Ga)(S,Se)2 semiconductor compound film. The nano-powder material may contain nano-size particles of only solid solutions or elemental forms of Cu, In, and Ga. Additionally particles of at least one of Se, S and Te may be included in the nano-powder. The nano-powder material may also contain a dopant to enhance p-typeness of the semiconductor compound film. The Cu(In,Ga)(S,Se)2 semiconductor compound film of the present invention may be used in electronic device structures including solar cells.
More generally, according to the invention, a process of forming a compound film includes formulating a nano-powder material with a controlled overall composition and having particles of one solid solution. The nano-powder material is deposited on a substrate to form a layer on the substrate, and this layer is reacted in at least one suitable atmosphere to form the compound film. The invention also concerns a semiconductor compound film for use in fabrication of a radiation detector or solar cell made by such a process, as well as a powder material, for use in preparing such a compound film on a substrate, comprising particles of a copper-gallium solid solution which are sub-micronic in size. According to one preferred embodiment, the compound film has a Cu/(In+Ga) compositional range of 0.7-1.0 and a Ga/(In+Ga) compositional range of 0.05-0.3.
The foregoing and additional features and advantages of this invention will become further apparent from the detailed description and accompanying drawings that follow. In the figures and written description, numerals indicate the various features of the invention, like numerals referring to like features.
The general structure of a Cu(In,Ga)(S,Se)2 compound solar cell that may be constructed using the compound absorbers grown by the method of present invention is shown in
Although the present invention is described for the growth of Cu(In,Ga)(S,Se)2 as the p-type compound absorber film 42, tellurium may also be included into the composition to grow Cu(In,Ga)(S, Se, Te)2 compounds. The compound layer may additionally contain dopants such as potassium (K), sodium (Na), lithium (Li), phosphorous (P), arsenic (As), antimony (Sb) and bismuth (Bi) to enhance its electronic properties.
The transparent window layer 43 may have one or more layers made of materials commonly used in solar cell window layer structures. For example the transparent window layer may contain layers of cadmium-sulfide, cadmium-zinc-sulfide, zinc-selenide, zinc-oxide, indium-tin-oxide, indium-zinc-oxide and tin oxide, among many others.
The preferred cell structure of
Precursor used in precursor formulation 50 step comprises a nano-powder, i.e. a powdered material with nano-meter size particles. Compositions of the particles constituting the nano-powder used in precursor formulation 50 step are important for the repeatability of the process and the quality of the compound films grown by the method of the present invention. As schematically shown in
Precursor formulation 50 step of
After precursor formulation 50 step, the precursor, and thus the nano-powder constituents have to be deposited onto a substrate in the form of a micro-layer through the precursor deposition step 51. As indicated before, precursor deposition step may involve dry or wet processes. Dry processes include electrostatic powder deposition approaches where the prepared powder particles may be coated with poorly conducting or insulating materials that can hold charge. Charged powders may then be deposited on substrates that are biased in a way to attract the charged particles. The materials coating the powder particles may be selected from amongst organic materials so that upon heating they substantially burn or evaporate away without leaving any residues that would deleteriously affect the compound films to be grown. Some examples of wet processes are screen printing, ink jet printing, ink deposition by doctor-blading, reverse roll coating etc. In these approaches the nano-powder may be mixed with a carrier which may typically be a water-based or organic solvent. Well-known additives may then be added into the formulation to form either a thick paste (for screen printing) or a thin dispersion (for ink or slurry deposition). Examples of these additives include a large variety of ionic and non-ionic dispersants marketed by companies such as Rohm and Haas, thickening agents, pH-adjustment agents, surfactants, binders etc. It is preferred that the carrier be a volatile material that once evaporated out of the wet micro-layer, leaves substantially no residue behind that would have deleterious effect on the compound film. The same is also valid for all the other chemical agents used in the precursor formulation. Some examples of the commonly used carriers are water, alcohols, ethylene glycol, etc.
Once the carrier and other agents in the precursor formulation are totally or substantially evaporated away, the micro-layer 52 is formed on the substrate 70 as shown in
The nano-size particles of the present invention contain soft, elemental and solid-solution materials such as In and In—Ga solid solutions. Therefore, the preferred method of preparing an ink or a paste include process steps of mixing and dispersing but not milling or grinding. In other words the preferred size of the particles in the present invention is less than about 200 nm. This way no mechanical grinding or milling should be necessary for further size reduction although such processes may also be employed. If milling or mechanical grinding is not used in precursor formulation step 50, mixing, blending, sonicating etc. steps may be carried out to form a uniform mixture or dispersion ready to be deposited on the substrate in the form of a micro-layer. The substrate temperature during the precursor deposition 51 step may be in the 20-400 C range. Preferably it should be in the 20-150 C range so that the deposition process can be carried out in air rather than in an oxygen-free atmosphere.
Once the micro-layer 52 is formed on the selected substrate it has to be reacted to form the compound film. The reaction step involves at least one annealing process. Annealing may involve furnace-annealing, RTP or laser-annealing, microwave annealing, among others. Annealing temperatures may be in 350-600 C and preferably between 400-550 C. If the micro-layer 52 contains Group VIA particles 66, the annealing atmosphere may be inert. In this case the Group VIA particles react with the metallic particles to form the compound. If there is no Group VIA particles in the nano-powder and thus in the micro-layer, or if the amount of Group VIA particles is not adequate then the reaction step should employ an atmosphere with the vapors of at least one of Group VIA elements (Se,S,Te). It should be understood that the reaction step may consists of two or more annealing processes each with different temperature time profiles and different atmospheres, For example, in the case of metallic micro-films there may be three annealing processes. In the first process which may be carried out at temperatures of 100-300 C, the micro-layer is annealed in inert atmosphere or vacuum to dry the film and to get any impurities out or to fuse and alloy the film and reduce the porosity. The second annealing process may employ a Se-containing atmosphere to grow a Cu(In,Ga)Se2 film. There may be a third annealing process where the Cu(In,Ga)Se2 film is heated in a S-containing atmosphere to convert it into a Cu(In,Ga)(S,Se)2 layer. Alternately, the sequence of the second and third heating processes may be changed to form first a S-containing compound and then the Cu(In,Ga)(S,Se)2 compound. The first heating process may altogether be skipped.
Although a Cu(In,Ga)(S,Se)2 compound is used as an example, other compounds in the same family (such as compounds containing Al, TI, Ag and/or Te) may also be formed using the present invention. Similarly compounds from other groups such as Group IIB(Cd,Zn)-IVA(Si,Ge,Sn)-VA(P,As,Sb) and Group IB-VA-VIA compounds may also be grown using the present invention provided that solid solutions exist in their respective binary diagrams.
Referring back to
The phase diagram for copper-indium is shown schematically in
The schematic gallium-indium phase diagram of
The phase diagrams of
Based on experimental results to date, the best compositional range for Cu(In,Ga)(S,Se)2 absorbers are Cu/(In+Ga)=0.7−1.0 and Ga/(In+Ga)=0.05−0.3. Consider the case of growing an absorber with Cu/(In+Ga)=1.0 and Ga/(In+Ga)=0.25, i.e. a compound film of CuIn0.75Ga0.25(S,Se)2. If the metallic precursor film of this composition were to be prepared by the prior art technique of U.S. Pat. No 5,985,691, Cu—Ga, Cu—In, or Cu—In—Ga alloy particles would be utilized where the alloy phase(s) would contain over 50 atomic % of the required Cu and over 50 atomic % of the required Ga and In. These alloy particles would have compositions that are outside the solid-solution regions indicated in
Using the present invention the compound layer with a composition close to CuIn0.75Ga0.25(S,Se)2 may be grown in a repeatable manner and with high quality. In this case a copper-gallium solid solution powder is used where the composition is Cu0.78Ga0.22. This powder is mixed with a powder of indium-gallium solid solution of In0.97Ga0.03 composition. The amounts of each powder are selected so that one mole of the first and one mole of the second are intimately mixed. After forming the micro-film the overall composition of the micro-film yields Cu0.78Ga0.22+In0.97Ga0.03=Cu0.78In0.97Ga0.25. Therefore in the compound layer, Cu/(In+Ga)=0.64 and Ga/(In+Ga)=0.20, which are desirable compositional parameters for high quality compound layers when doped.
In the above example if 1.28 mole of Cu0.78Ga0.22 solid solution powder is mixed with 0.77 mole of In0.77Ga0.03 solid solution powder and a micro film of these powders is obtained. After the reaction step the compound would have the composition of 1.28 Cu0.78Ga0.22+0.77 In0.97Ga0.03=CuIn0.75Ga0.3, which means, Cu/(In+Ga)=0.95 and Ga/(Ga+In)=0.29. These are close to perfect compositional parameters required for undoped compound films yielding high efficiency solar cells. This example demonstrates the flexibility and power of the present invention in changing film composition using just solid solutions. It should be appreciated that amounts of the two solid solutions could be changed to obtain various compound composition. Elemental powders of Cu, In or Ga could also be added in the formulation to further adjust these compositions as desired.
If the desired Ga content in the micro-film and thus in the compound film is less than the solid solubility of Ga in Cu, then there is no need to use the indium-gallium solid solution. Pure In powder can be used in this case. For example, to grow a CuIn1-kGak(S,Se)2 compound with k<0.22, the nano-powder may contain Cu1-kGak solid-solution particles and pure In particles where one mole of the copper-gallium solid-solution powder is mixed with (1-k) mole of pure In powder. Using low melting point pure In or In—Ga solid solution particles in formulations containing Cu—Ga solid solution particles is attractive because upon heating the micro-layer, these low melting phases form a liquid fusing region around the high-melting Cu—Ga solid solution particles.
Cu—In and Cu—Ga solid solutions may both be used in the formulation of the nano-powder. For example, a Cu1-xGax+Cu1-yIny+mIn mixture would allow growth of a wide range of compositions of the compound. Since x≦0.22 and y≦0.11, the value of m can be adjusted to yield a range of Ga/(In+Ga) ratios. Of course the Ga amount can be easily reduced in this composition. However, for Cu/(In+Ga)=1.0, maximum amount of Ga that can be included in the film using this formulation can be calculated as follows:
Therefore, similar calculations may be used to formulate nano-powders containing elemental powders and solid-solution powders and yielding compound films with various compositions after the reaction step.
Copper-gallium solid solution particles, Cu particles and In particles may also be used to obtain micro-layers and compound layers of various compositions. In this case
wCu1-xGax+u Cu+n In would be the formulation of the nano-powder and the composition of the micro-layer and the compound would have
Above examples demonstrate the flexibility of the present invention to yield high quality absorber layers with compositional ranges that are most important for high efficiency solar cell fabrication. The present invention uses particles of elements and solid-solutions to mix and formulate nano-powders which are then deposited in thin film form and converted into the desired compound. Mixtures of particles that can be successfully used in this invention include but are not limited to the following mixtures of binary solid solutions and elements (binary solid solutions are solid solutions of two elements):
[CuGa+In] (meaning CuGa solid solution particles mixed with In particles), [CuGa+InGa] (meaning CuGa solid solution particles mixed with InGa solid solution particles), [CuGa+InGa+In] (meaning CuGa solid solution particles mixed with InGa solid solution particles and In particles), [CuGa+InGa+Cu] (meaning CuGa solid solution particles mixed with InGa solid solution particles and Cu particles), [CuGa+InGa+Cu+In] (meaning CuGa solid solution particles mixed with InGa solid solution particles, Cu particles and In particles), [CuGa+Cu+In] (meaning CuGa solid solution particles mixed with Cu particles and In particles), [CuGa+CuIn+In] (meaning CuGa solid solution particles mixed with CuIn solid solution particles and In particles), [CuGa+CuIn+InGa] (meaning CuGa solid solution particles mixed with CuIn solid solution particles and InGa solid solution particles), [CuGa+CuIn+InGa+In] (meaning CuGa solid solution particles mixed with CuIn solid solution particles, InGa solid solution particles and In particles), [CuGa+CuIn+Cu+In] (meaning CuGa solid solution particles mixed with CuIn solid solution particles, Cu particles and In particles), [CuGa+CuIn+InGa+Cu] (meaning CuGa solid solution particles mixed with CuIn solid solution particles, InGa solid solution particles and Cu particles), and [CuGa+CuIn+InGa+Cu+In] (meaning CuGa solid solution particles mixed with CuIn solid solution particles, InGa solid solution particles, Cu particles and In particles). By selecting relative amounts of particles in the mixture a whole range of compositions can be obtained by this approach including the ranges necessary for solar cell fabrication. In certain cases a film may be fabricated with high Cu content (outside the range acceptable for solar cell fabrication) but then another film with composition of low Cu can be deposited over the first film bringing the overall composition into the acceptable range. These approaches are well known in the field. It should be noted that the above example formulations did not include elemental Ga powders. If this is done, the number of possible powder formulations that can be used increases even further. However, since Ga is a low-melting material that can oxidize easily, the preferred method of the present invention is introduction of Ga into the formulation in the form of a CuGa or InGa solid solution. Also there is no data available on ternary solid solution region for the CuGaIn alloy system. The present invention foresees the use of particles of such ternary solid solutions. For example, it may be possible to dissolve some In in CuGa solid solution to obtain one or more CuGaIn solid solutions. In such case a powder of this material can be mixed with the powders of the elements and/or the other binary solid solutions listed above.
If the composition of the nano-powder does not contain a group VIA powder, the micro-layer which contains only metallic phases need to be reacted to form the compound film. This reaction step may be carried out in the vapor of Group VIA element (Se, S, Te) or other sources such as H2-Group VIA-type gases such as H2S, H2Se or their mixtures at elevated temperatures. Once the compound layers are formed solar cells and other electronic devices may be fabricated on these layers using methods well known in the field.
The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to persons skilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.