Patent Publication Number: US-2017352771-A1

Title: Systems, Methods, and Apparatus for Concentrating Photovoltaic Cells

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation application of International Application No. PCT/US2016/021182, filed Mar. 7, 2016, entitled “Systems, Methods, and Apparatus for Concentrating Photovoltaic Cells,” which claims priority to U.S. Application No. 62/128,699, filed Mar. 5, 2015, entitled “WAFER-LEVEL MICRO-OPTICAL SENSING AND METHODS FOR MAKING THE SAME.” Each of these applications is hereby incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Concentrating photovoltaics (CPV) systems use refractive and/or reflective optical components to concentrate sunlight onto high performance solar cells (e.g., multijunction cells), thereby reducing material and processing costs of solar cells and improving the conversion efficiency. Since CPV modules typically provide high efficiency output, area-related costs can also be reduced due to the decreased usage of total area, such as balance-of-system and land usage, among others. 
     Several issues may hinder the development of CPV technologies. One issue originates from limited concentration and acceptance angle and the challenge to collect diffuse light. Another issue relates to practical difficulties, including, but are not limited to, complexity of fabrication, integration and installation of the CPV systems, complexity and size of optical systems, tight misalignment tolerance, use of high-precision trackers, and thermal management. 
     Micro-concentrating PV (MCPV) scales down the dimensions of conventional concentrated PV cells (e.g., on the order of 100 microns in diameter) and the concentrating optics from millimeters to microns. Compared to conventional flat panel silicon PV, MCPV have the potential to integrate arrays of PV cells and concentrating optics more closely within a single module, thereby providing higher conversion efficiency given the same form factor. Additional benefits of MCPV include reduced semiconductor and optic materials costs, enhanced solar cell performance, improved thermal management, improved interconnect flexibility, and more compact physical profiles. 
     Low-cost molded concentrator optical elements are typically utilized for conventional concentrated PV modules. In current practices, MPCV technologies simply miniaturize conventional CPV approaches. However, low-cost molding tools are generally not suitable for making optical components with a size of a few hundred microns or smaller. The feature size, shape, surface quality, and aspect ratio of a micro-optical component is limited by the machining tool size, geometry, and tip rounding effects. In addition, the position accuracy of optical elements during the molding process is usually on the order of 10 μm. Therefore, the tolerance to fabrication deviations can also become tight, with dimensional accuracy of about a few microns or less. 
     These fabrication challenges can limit the employment of efficient non-imaging optical concentrators with performance close to the thermodynamic limit in a micro-scale PV system. In terms of integration and assembly of MCPV cells, the position accuracy of the optics layer on the PV cell layer is approximately ±25 μm. Since the solar cells are usually very small (˜100 μm) and errors from desired positions can grow as a function of the number of layers, this accuracy can limit the use of multi-stage optical concentrators to improve the collection efficiency and/or illumination uniformity. The conversion efficiency of existing MCPV cells can be further reduced by diffuse light, which is usually difficult to concentrate due to its low directionality. 
     SUMMARY 
     Embodiments of the present invention include apparatus, systems, and methods of working and using concentrating photovoltaic technologies. In one example, an apparatus includes a substrate having a first substrate surface and a second substrate surface. The substrate defines at least one cavity extending from the first substrate surface toward the second substrate surface. The at least one cavity defines a first end to receive incident light, a second end opposite the first end, and a side surface, extending from the first end to the second end, to concentrate or direct the incident light, received by the first end, toward the second end. A photovoltaic (PV) cell is in optical communication with the second end of the at least one cavity to convert the incident light into electricity. An optical adhesive layer may be positioned between the PV cell and the second end of the at least one cavity. 
     In another example, a method of making a photovoltaic (PV) device includes etching a substrate to form at least one cavity extending from a first substrate surface of the substrate toward a second substrate surface of the substrate. The at least one cavity defines a first end to receive incident light, a second end opposite the first end, and a side surface, extending from the first end to the second end, to concentrate or direct the incident light received by the first end toward the second end. The method also includes coupling a PV cell to the second end of the at least one cavity. 
     In yet another example, a photovoltaic (PV) device includes a silicon substrate having a first substrate surface and a second substrate surface. A micro-lens array is disposed on the first substrate surface to focus incident light toward the first substrate surface. The silicon substrate defines an array of cavities having a pitch of about 0.1 mm to about 10 mm. Each cavity in the array of cavities extends from the first substrate surface toward the second substrate surface. Each cavity also defines a first end to receive the incident light from the micro-lens array, a second end opposite the first end, and a side surface to concentrate or direct the incident light received by the first end toward the second end. The PV device also includes an array of PV cells (such as multi junction PV cells), disposed in optical communication with the second end of a respective cavity in the array of cavities, to convert the incident light into electricity. 
     It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. It should also be appreciated that terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements). 
         FIG. 1  shows a schematic of a photovoltaic (PV) apparatus using a wafer-level concentrating element. 
         FIG. 2  shows a schematic of a PV apparatus using a concentrator defined by a cavity fabricated within a substrate and a PV cell disposed on the bottom surface of the cavity. 
         FIG. 3  shows a schematic of a PV apparatus using a concentrator fabricated on a substrate. 
         FIG. 4  shows a perspective view of a PV apparatus using a pyramid-shape concentrator defined by a cavity fabricated in a substrate. 
         FIGS. 5A-5B  illustrate a PV apparatus including a wafer-level concentrator and an additional concentrator that can be molded or pre-fabricated. 
         FIGS. 6A-6B  illustrate a PV apparatus including an array of PV elements, each of which includes a wafer-level concentrator and an additional concentrator that can be molded or pre-fabricated. 
         FIG. 7  shows a perspective view of a flexible PV apparatus including wafer-level concentrators. 
         FIGS. 8A-8D  illustrate a PV apparatus including a first substrate for fabricating wafer-level concentrators and a second substrate for mechanical support or electrical coupling. 
         FIGS. 9A-9D  show a PV apparatus including a silicon substrate for fabricating wafer-level concentrators and a Polydimethylsiloxane (PDMS) layer including additional concentrators. 
         FIGS. 10A-10D  show a PV apparatus including wafer-level concentrators disposed on one side of a glass layer and a PDMS layer including additional concentrators disposed on the other side of the glass layer. 
         FIGS. 11A-11D  show a PV apparatus including wafer-level concentrators fabricated in a silicon layer, a PDMS layer, and a poly(methyl methacrylate) (PMMA) layer including additional concentrators. 
         FIGS. 12A-12B  show a PV apparatus including wafer-level concentrators fabricated in a substrate and an optical layer including both refractive and reflective concentrators. 
         FIGS. 13A-13B  show a PV apparatus including PV cells to collect diffuse light. 
         FIGS. 14A-14B  show a PV apparatus including a cascade of PV cells. 
         FIGS. 15A-15B  show a PV apparatus including a ball lens (or a cylinder lens) that acts as an additional concentrator and an alignment element. 
         FIGS. 16A-16B  show a PV apparatus including an array of PV element, each of which includes a ball lens (or a cylinder lens) that acts as an additional concentrator and alignment element. 
         FIG. 17  shows a cross sectional view of a PV apparatus including multiple layers of concentrating elements. 
         FIGS. 18A-18B  show an apparatus using cavities and balls (or cylinders) as alignment elements. 
         FIGS. 19A-19B  show an apparatus including an additional concentrating element with integrated alignment elements. 
         FIGS. 20A-20B  show an apparatus including wafer-level concentrating elements and alignment elements. 
         FIGS. 21A-21C  illustrate a method of fabricating a PV apparatus including wafer-level concentrating elements. 
         FIGS. 22A-22B  illustrate a method of fabricating cavities in silicon substrates as wafer-level concentrating elements. 
         FIGS. 23A-23C  illustrate a method of fabricating a PV apparatus including throughout cavities as wafer-level concentrating elements. 
         FIGS. 24A-24F  illustrate a method of fabricating a PV apparatus including wafer-level concentrating elements and a back substrate. 
         FIGS. 25A-25G  illustrate a method of fabricating a PV apparatus including wafer-level concentrating elements and alignment elements. 
         FIGS. 26A-26C  are simulation results of ray traces in an apparatus including wafer-level concentrating elements. 
         FIGS. 27A-27B  are simulation results of ray traces in an apparatus including two stages of light concentrating elements. 
         FIGS. 28A-28B  are simulation results of ray traces in an apparatus including two stages of light concentrating elements and an additional reflective concentrator. 
         FIG. 29  shows comparisons of baseline systems including wafer-level concentrating elements with state-of-the-art micro-/mini-CPV technologies. 
         FIGS. 30A-30C  show simulations of PV systems with and without wafer-level concentrating elements. 
         FIGS. 31A-31C  show simulation results of a PV system with respect to direct/global irradiation ratios. 
         FIG. 32  show simulation results of optical losses in a PV system including wafer-level concentrating elements. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     To address, at least partially, challenges in conventional concentrating photovoltaic (PV) technologies, systems, apparatus, and methods described herein employ an approach that integrates wafer-level micro-optical concentrating elements with micro-scale solar cells to enhance conversion efficiency, reduce material and fabrication costs, and significantly reduce system form factors. In this approach, a multi-functional platform is constructed by fabricating wafer-level micro-concentrating elements in or on a substrate. The concentrating element can include, for example, cavities etched in a silicon substrate, wedge- or pyramid-shaped silicon pieces, and micro-lenses, among others. Semiconductor etching techniques can fabricate features with high precision on the order to nanometers, much greater than the precision achieved in conventional techniques used for manufacturing micro-concentrating PV cells. 
     This multi-functional platform can seamlessly integrate hybrid photovoltaics, optical micro-concentration, and mechanical micro-assembly in one substrate, particularly designed for high-performance, low-cost micro-scale concentrating photovoltaics. For example, a multi-functional platform can be fabricated from active silicon (e.g., ˜160 μm thick standard crystalline Silicon wafers used in the solar industry). Micro-PV cells (e.g., high-efficiency multi junction micro-PV cells on the order of  100  microns in diameter) can be bonded to the multi-function platform to receive concentrated direct sunlight, while the multi-function platform itself collects diffuse sunlight or light not collected by the micro-PV cell, thereby increasing conversion efficiency and allowing all-weather operation of the resulting PV devices. 
     In addition, efficient non-imaging micro-optical concentrating elements (e.g., two-dimensional reflective cavity arrays) can be directly fabricated in the silicon substrate using standard PV fabrication processes to reduce the usage of multi junction cells while providing sufficient angular and spatial tolerances. Such elements can also be used as precise alignment features for micro-assembly of the Si substrate to molded micro-concentrator arrays (in addition to the wafer-level concentrating elements) and other opto-mechanical components. Therefore, multiple layers of concentrating optics can be integrated into the resulting PV device to further increase the concentration ratio, which can reduce the use of expensive multi junction PV cells. 
     The approach described herein can address several dilemmas in current PV industry. For example, it is usually desirable to increase the geometric concentration ratio of PV cells to reduce materials costs, but normally at the price of reducing the acceptance angle of concentrating PV devices, resulting in tight tolerance to angular misalignment and increased module- and system-level costs (e.g., requirements for high-precision manufacturing/integration processes and high-accuracy but expensive solar trackers). This compromise can be addressed by using multi-stage non-imaging optics to improve the overall concentration ratio×acceptance angle product. In another example, increasing the size and complexity of concentrator systems usually leads to increased efficiency but also quickly induces costs. Due to its high position accuracy, a wafer-level etched concentrator can be easily integrated with multiple layers of simple molded plastic optics, thereby effectively controlling the total cost. In yet another example, hot spots can arise when the concentration ratio is high. These hot spots may be eliminated by advanced lens surfaces and non-imaging optic design that redistribute focused light while maintaining a good acceptance angle. 
     Based on the wafer-level micro-concentrating elements fabricated directly within a substrate, a fully-integrated hybrid micro-CPV device can be constructed to offer the high performance of CPV and the flat profile of conventional flat panel PV. Some advantages of these devices include: i) integration of electrical, micro-optical, and micro-mechanical functionalities on a single low-cost thin platform; ii) higher concentration-acceptance angle products; iii) collecting and converting diffuse light under a hybrid micro-CPV architecture; and iv) low-cost in fabrication and assembly. 
     PV Apparatus Including Wafer-Level Concentrating Elements 
       FIG. 1  shows an apparatus  100  including a wafer-level concentrating element for photovoltaic conversion. The apparatus  100  includes a substrate  110  which has a front surface  112  and a back surface  114 . A cavity  120  is fabricated in the substrate  110  to function as an example of concentrating elements to concentrate or direct incident light. The cavity  120  has an entrance end  124  on one end, an exit end  126  on the other, and side surfaces  122   a  and  122   b  (collectively referred to as side surface  122 ) that connect the entrance end  124  with the exit end  126 . Incident light for photovoltaic conversion is received by the entrance end  124  and reflected by the side surfaces  122  toward the exit end  126 , where a PV cell  130  is disposed to convert the incident light into electricity. Since the entrance end  124  is larger than the exit end  126 , incident light is concentrated by the side surfaces  122  such that the PV cell  130  can have a smaller size and lower cost. From another perspective, the side surfaces  122  can also reflect or direct obliquely incident light towards the PV cell  130  and thus improve acceptance angle or field-of-view of the PV system. 
     Various materials can be used for the substrate  110  to form the cavity  120 . In general, it is beneficial to use semiconductor material in order to take advantage of existing etching technologies. In one example, the substrate  110  includes silicon, such as single crystalline silicon, poly-crystalline silicon, or amorphous silicon. In another example, the substrate  110  includes germanium. In yet another example, the substrate  110  includes a compound semiconductor material such as a III-V semiconductor (e.g., GaAs and InP, among others). 
     The substrate  110  can be inactive (no p-n junction) and provide mechanical support for the cavity  120  or any other component in prospective PV devices. In another example, the substrate  110  can include p-n junctions or additional PV cells.  FIG. 1  shows one p-n junction  150  (not to scale) formed in the substrate. In practice, the substrate  110  can include multiple p-n junctions. In this case, the substrate  110  can include low cost materials (e.g., silicon) and the PV cell  130  can use more efficient and more costly materials (e.g., III-V semiconductor). As a result, the PV cell  130  can receive concentrated light, and the substrate  110 , which functions as another PV cell (because of the p-n junctions) to collect and convert diffuse light or light not collected by the PV cell  130 . This hybrid architecture can improve performance of the apparatus  100  without incurring significantly higher cost (at least because the substrate material is less expensive than the PV cell  130 ). Based on U.S. solar radiation data from “National Solar Radiation Data Base”, the hybrid approach can produce 40-60% and 20-40% more energy per unit area than Si flat panel PV and CPV, respectively. 
     The cavity  120  functions as a concentrating element that reflects incident light received by the entrance end  124  toward the exit end  126  and the PV cell. The incident light can arrive at the PV cell  130  after one or more reflections so the cavity  120  can be non-imaging optics suitable for solar energy concentration. To this end, the cavity  120  can have various shapes. In one example, the cavity  120  can be one-dimensional (1D), such as a V-shaped groove. In another example, the cavity  120  can be two-dimensional (2D). For example, the cavity  120  can have a pyramid shape with four side surfaces  122  (two sides surfaces  122   a  and  122   b  are shown in  FIG. 1 ). In another example, the cavity  120  can have a cone shape with one continuous side surface  122  (in this case the side surfaces  122   a  and  122   b  shown in  FIG. 1  merge into one surface). In yet another example, the cavity  120  can have a spherical or paraboloidal shape. In these cases, the side surfaces  122  can focus or direct the incident light. The focal point can be re-distributed over the PV cell  130  so that the entire area of the PV cell  130  is illuminated. In yet another example, the cavity  120  can be formed by the [111] crystal plane of the substrate  110  when silicon is used as the substrate  110 . 
     The side surfaces  122  can be coated with a reflective layer (not shown in  FIG. 1 ) to increase the reflectivity and therefore the optical efficiency of the cavity  120 . The reflective coating can include, for example, aluminum, silver, gold, or any other reflective material known in the art. In another example, the PV cells  130  can be disposed or formed on the side surfaces of the cavity  120 , to collect and convert at least a portion of the light incident on the side surfaces. 
     In one example, the cavity  120  can be filled with air or vacuum. In another example, the cavity  120  can be filled with one or more other dielectric materials, such as Ethylene vinyl acetate (EVA), Epoxy, poly(methyl methacrylate) (PMMA), Polydimethylsiloxane (PDMS), water, or oil. The filling material that immerses the PV cell  130  can increase the concentration ratio and acceptance angle of the apparatus  100  to, compared to CPV systems with PV cells immersed in air or vacuum. The acceptance angle of the PV apparatus  100  can be defined as the maximum angle at which incoming sunlight can be captured by the PV cell  130 . Filling a dielectric material into the cavity  120  can decrease the index refractive difference between the cavity  120  and other components in the apparatus including additional concentrators disposed above the cavity  120  (e.g., see  FIGS. 5A-5B ). The filling material can also improve the mechanical stability of the apparatus  100  by providing mechanical support to other components of the apparatus (e.g., the PV cell  130 ). 
     The PV cell  130  in the apparatus  100  is bonded to the back surface  114  of the substrate  110 . When filling material is used, the PV cell  130  can also be bonded to the filling material in the cavity  120 . Since the PV cell  130  usually has a small size (e.g., on the order of 50 μm, 100 μm, or 200 μm), material costs of expensive but efficient materials, such as III-V semiconductors, can be reduced. The typical thickness of the PV cell  130  can range from a few microns to hundreds of micron. 
     The cavity  120  shown in  FIG. 1  extends through the substrate  110  (i.e., extending from the front surface  112  all the way to the back surface  114 ). In practice, various etch depths can be used. 
       FIG. 2  shows an apparatus  200  in which a cavity  220  is etched only partially through a substrate  210 . In this case, the exit end of the cavity  220  includes a bottom surface that receives a PV cell  230 . Similar to the apparatus  100  shown in  FIG. 1 , the apparatus  200  concentrates the incident light onto the PV cell  230  via reflection from side surfaces  222   a  and  222   b  (collectively referred to as side surfaces  222 ). The depth (i.e., distance from the entrance end to the exit end of the cavity  220 ) can depend on, for example, the desired concentration ratio and the total cost of the apparatus  200  (the total cost depends on the area of the PV cell  230 ). 
     The apparatus  100  and  200  use cavities  120  and  220  as concentrating elements to concentrate light. Alternatively, the remaining portion of the substrate (the solid part), in which cavities  120  and  220  are fabricated, can also be used as the concentrating element to concentrate or redirect incident light via total internal reflection (TIR). 
       FIG. 3  shows a schematic of an apparatus  300  including a concentrating element  320  that includes the remaining portion of an etched substrate. In this case, the concentrating element  320  can considered the “complement” of the cavities  120  and  220  shown in  FIGS. 1 and 2 . The concentrating element  320  can have shapes such as pyramid, paraboloid, cone, hemisphere, or any other shape applicable here. Incident light received by the concentrating element  320  are reflected by side surfaces  322   a  and  322   b  via internal reflection. A front substrate  310  is included in the apparatus  300  to, for example, provide mechanical support for the concentrating element  320 . A PV cell  330  is disposed at the smaller end of the concentrating element  320  to receive concentrated incident light for electricity conversion. 
       FIG. 4  shows a perspective view of a PV apparatus  400  including a wafer-level concentrating element. The apparatus  400  includes a substrate  400 , in which a cavity  420  is fabricated as the concentrating element. A PV cell  430  is disposed at the smaller end of the cavity  420  (e.g., either on the bottom surface if the cavity  420  is partially through the substrate  410  or on the back surface of the substrate  410  if cavity  420  goes through the substrate  420 ). The cavity  420  has an inverted pyramid shape for illustrating and non-limiting purposes only. In practice, various other shapes, such as cone, sphere, and paraboloid can also be used. 
     PV Apparatus Including Multi-Stage Concentrating Elements 
     To further increase the concentrating ratio, which can be defined as the ratio of the area of incident light over the area of the concentrated light received by the PV cell, additional concentrating elements can be included in the apparatus shown in  FIGS. 1-3 . Since the cavity micro-concentrating element embedded at the wafer level can improve concentration ratio and acceptance angle, it can accordingly facilitate the fabrication and assembly of additional optical components to be integrated with the wafer-level concentrators to form robust multi-stage optical concentrating systems. As introduced before, the high precision of semiconductor etching techniques employed for fabricating the wafer-level concentrating elements also help precise alignment with other components such as additional concentrating optics. 
       FIGS. 5A-5B  show a cross sectional view and a perspective view, respectively, of an apparatus  500  including two levels of concentrating elements. The apparatus  500  includes a substrate  510  in which a cavity  520  is fabricated as a wafer-level concentrating element. A PV cell  530  is disposed at the exit of the cavity  530 . An additional concentrating element  540 , which may include a coating layer  545  (e.g., anti-reflection coating or structures), is disposed on the substrate  510  to concentrate incident light toward the entrance of the cavity  520 . The aperture (e.g., the area of the receive surface) of the additional concentrating element  540  is larger than the entrance of the cavity  520 , which is further larger than the PV cell  530 . Therefore, the incident light across a wide range of incident angles can be directed or concentrated twice in a cascade manner from the additional concentrating element  540  toward the PV cell  530 , where the received light is converted into electricity. Note that  FIGS. 5A-5B  are not to scale. In practice, the additional concentrating element  540  can be more than 50 times wider than the PV cell  530  (e.g., 100 times larger, 500 larger, 1000 times larger, 1500 times larger, 3000 times larger, or even greater). 
     The additional concentrating element  540  is usually much larger than the wafer-level concentrating element (i.e., cavity  520 ) and the PV cell  530 , for example, about 0.5 mm to about 100 mm in diameter or other lateral dimension. On this size scale, various techniques can be used to manufacture the additional concentrating elements  540  such as molding, polishing, lithography, etching, or any other techniques known in the art. 
     The additional concentrating element  540  can include either imaging optics or non-imaging optics. In one example, the additional concentrating element  540  includes a lens that can concentrate or direct the incident light toward the entrance of the cavity  520 . Since the incident light focused by micro-lens is usually directional, the cavity  520  can concentrate the received incident light with good efficiency. In another example, the additional concentrating element  540  includes at least one curved reflective mirror (such as a parabolic mirror) that concentrates or directs the incident light toward the entrance of the cavity  520 . 
     In another example, the additional concentrating element  540  can be non-imaging (e.g., another cavity-like structure as shown in  FIGS. 12A-12B ). In this case, the additional element  540  may cause some incident to become not directional and difficult to be concentrated by the cavity  520 . However, this issue can be addressed by at least two approaches. In one approach, the substrate  510  can include active silicon or other solar cell material such that the substrate  510  can function as another PV cell to collect and convert diffuse light or light not directed towards the PV cell  530 . In another approach, additional PV cells can be disposed on the interface between the substrate  510  and the additional concentrating element to collect diffuse light or light not directed towards the PV cell  530  (see, e.g.,  FIGS. 13A-13B ). In yet another example, additional PV cells can be disposed on the side surfaces of the cavity. In yet another example, a combination of imaging and non-imaging optical components can be used. 
       FIGS. 6A-6B  show a cross sectional view and a perspective view, respectively, of a PV apparatus  600  including an array of PV elements, each of which is substantially similar to the structure as shown in  FIGS. 5A-5B . The apparatus  600  includes a substrate layer  610  in which a plurality of cavities  620  are fabricated. On the exit end of each cavity  620  is disposed a PV cell  630 . An additional concentrating layer  640  is disposed on the substrate layer  610  to receive incident light. The additional concentrating layer  640  can optionally include a coating layer  645 . 
     In one example, the additional concentrating layer  640  includes a molded micro-lens array, which is precisely aligned and assembled on the top of the cavities  620 . The resulting apparatus  600  can be compact and have a flat physical profile. Integrated with PV cells  630 , the wafer-embedded micro-concentrator structure, including the cavities  620  and the additional concentrating layer  640 , can act as an efficient two-stage non-imaging concentrator with a simple optical architecture. 
     The cavities  620  and the corresponding PV cells  630  in the apparatus  600  can be substantially periodic. The period (also referred to as pitch) of the cavities  620  and the PV cells  630  can be about 0.1 mm to about 100 mm (e.g., about 0.1 mm, 0.5 mm, 1 mm, 5 mm, 10 mm, 20 mm, 50 mm, and 100 mm). The aperture (diameter or other lateral dimension) of each element (e.g., micro-lens) in the additional concentrating layer  640  can be substantially equal to the period of the cavities  620 . The PV cells  630  are smaller than the aperture of additional concentrating element and can be about 10 μm to about 2 mm (e.g., about 10 μm, 20 μm, 50 μm, 100 μm, 200 μm, 500 μm, 1 mm, and 2 mm). 
     The overall size of the apparatus  600  can depend on the application of the apparatus  600 . For example, the apparatus  600  can be used for consumer electronics, such as a cellphone or watch, in which case the size of the apparatus  600  can be on the order to  1  inch. In another example, the apparatus  600  can be used to generate electricity for a utility. In this case, the apparatus  600  can be on the order of several feet to tens of feet. 
       FIG. 7  shows an apparatus  700  including an array of silicon substrates  710 . A cavity  720  is fabricated in each silicon substrate  710  as the wafer-level concentrating element. An additional concentrating layer  740  is disposed on the array of silicon substrates  710  to receive incident light. The additional concentrating layer  740  also includes an array of concentrating elements, each of which corresponds to one silicon substrate  710  (and one cavity  720 ). In  FIG. 7 , each cavity  720  is fabricated in its respective silicon substrate  710 . In another example, an array of cavities can be fabricated in one substrate which is subsequently singulated to form an array of substrates  710  each containing a cavity  720 . The substrate array  710  can be assembled on a substrate or a superstrate. The substrate or superstrate may be rigid or flexible. For one example, the additional concentrating layer  740  can be made of flexible material such as PDMS or PMMA and act as a superstrate for the silicon substrate array  710 . The resulting apparatus  700  is therefore also flexible and can be used in more applications. For example, the apparatus  700  can be conformally disposed on a non-flat surface to fit the shape of electronics to be powered. In another example, the apparatus  700  can be used in wearable technologies (e.g., wearable devices). Alternatively, when the flexibility of the apparatus  700  is of less concern, a monolithic substrate can be used to fabricate the array of cavities  720 . 
     PV Apparatus Including a Back Substrate 
     As described above, a PV apparatus can include an array of wafer-level concentrating elements such as cavities, each of which is coupled to a PV cell. These wafer-level concentrating elements can be either fabricated out of a monolithic semiconductor substrate or fabricated on different individual substrates (i.e., an array of substrates is used to match the array of PV cells). In this case, it can be helpful to employ a back substrate to hold together the array of wafer-level concentrating elements. In addition, this back substrate can also provide physical protection, moisture protection, and electrical connection among internal devices and to external devices. Alternative, electrical components (such as interconnects) can be formed directly on the silicon substrate itself. 
       FIGS. 8A-8D  illustrate an apparatus  800  including a back substrate  850 .  FIG. 8A  shows a cross sectional view of one cell  801  in an array of PV cells  800 .  FIG. 8B  shows the cross sectional view of the apparatus  800 .  FIG. 8C  and  FIG. 8D  show a perspective view of one individual cell  801  and the entire apparatus  800 , respectively. The apparatus  800  (and the individual cell  801 ) includes a primary substrate  810  in which a cavity  820  is fabricated. A PV cell  830  is disposed at the exit end of the cavity  820 . For convenience, one combination of these three elements  810 ,  820 , and  830  is collectively referred to as one integrated PV element. The integrated PV element is sandwiched between an additional concentrating element  840  and a back substrate  850 .  FIG. 8B  and  FIG. 8D  show that the apparatus  800  includes an array of integrated PV elements, each of which includes a respective primary substrate  810 , a cavity  820 , and a PV cell  830 . Both the additional concentrating element  840  and the back substrate  850  are monolithic, extending across the array of integrated PV elements. 
     In one example, the back substrate  850  includes a glass plate to provide mechanical support to other components in the apparatus  800 . Electrical components (such as interconnects) can be positioned on the glass plate. In another example, the back substrate  850  includes a printed circuit board to electrically couple the plurality of PV cells  830  with external devices that the PV cells  830  can power. In yet another example, the back substrate  850  includes a backsheet, which can protect and connect the apparatus  800  to other electronic components as readily understood in the art. One benefit of using micro-scale PV cells is that as the cell size reduces below about 1 mm, the ratio between the cell total surface area and its aperture area increases dramatically, which can improves thermal dissipation, thereby allowing the utilization of a much wider range of substrate materials compared to conventional CPV approaches. 
       FIGS. 9A-9D  show a PV apparatus  900  including a back substrate  950  on which wafer-level concentrating elements and an additional concentrating layer are disposed.  FIG. 9A  shows a cross sectional view of the apparatus  900  including a silicon substrate  910  in which a plurality of cavities  920  are fabricated. For each cavity  920 , a PV cell is disposed at the narrower end of the cavity  920 . The combination of silicon substrate  910 , the cavities  920 , and the PV cells  930  is sandwiched between an additional concentrating layer  940  and a back substrate  950 . The additional concentrating layer  940  includes a micro-lens array made of optical materials such as PDMS, PMMA, BK7, etc. A diffractive optic (e.g., a Fresnel lens) can be utilized as well. Each micro-lens in the micro-lens array is aligned with a respective cavity  920  and a PV cell  930 . The back substrate  950  shown in  FIG. 9A  includes a backsheet. A front glass  970  is disposed above the additional concentrating layer  940  to protect all the components below the front glass  970 . The front glass  970  may have anti-reflection coatings to improve its optical transmission. The substrate  910  can be a PV cell. 
     The plurality of cavities  920  can be either fabricated out of a single piece of silicon substrate  910  or formed in multiple pieces of silicon substrates as described above, depending on, for example, the desired flexibility of the resulting apparatus  900 . As shown in the  FIG. 9A , the cavities  920  are filled with optical materials such as PDMS, which constitutes the additional concentrating layer  940  as well. This filling can improve optical performance (e.g., concentration and acceptance angle), provide mechanical support to the PV cells  930 , and improve the overall integration (e.g., mechanical stability) of the apparatus  900 . 
       FIG. 9B  and  FIG. 9C  show an assembled view and an exploded view, respectively, of the apparatus  900 . For illustrating purposes only, a monolithic silicon substrate is used to fabricate the array of cavities  920 . The additional concentrating elements  940  also form a monolithic layer, which can be made of optical materials (such as PDMS, PMMA, BK7) via, for example, molding techniques. In this case, the two layers can be conveniently bonded together to form the apparatus  900 . 
       FIG. 9D  shows an individual PV cell in the apparatus  900  including an array of such PV cells. The individual PV cell has a hexagonal contour for illustrating purposes. In practices, various other shapes can also be used, such rectangular, square, round, trapezoid, or any other shape applicable. 
       FIGS. 10A-10D  show a PV apparatus  1000  including a middle sheet  1060 .  FIG. 10A  shows a cross sectional view of the apparatus  1000 , which includes a middle sheet  1060  sandwiched between an additional concentrating layer  1040  and a filling layer  1025  disposed in cavities  1020  that are fabricated in a primary substrate  1010 . The middle sheet can be a piece of glass or a plastic sheet. Each cavity  1020  is also coupled to a PV cell  1030 . The primary substrate  1010  is disposed on a back substrate  1050 . A front glass piece  1070  is disposed on the top for protection or to act as a substrate or superstrate for other optical components. 
       FIG. 10B  and  FIG. 10C  show an assembled view and an exploded view, respectively, of the apparatus  1000 . As can be seen from  FIGS. 10B-10C , using glass or plastic as a middle layer may facilitate the manufacturing of the apparatus  1000 . More specifically, the additional concentrating layer  1040  and the primary substrate layer  1010 , which may further including the PV cells, can be separately bonded to the middle sheet to form the apparatus  1000 . Since the additional concentrating layer  1040  and the primary substrate layer can be soft (e.g., made of PDMS) and delicate, direct bonding between them may be challenging. Using the middle glass piece  1060  as mechanical support can therefore improve the manufacturing efficiency and reliability.  FIG. 10D  shows a perspective view of an individual PV cell in the apparatus  1000  including an array of such PV cells. 
       FIGS. 11A-11D  shows a PV apparatus  1100  including an intermediate optical layer  1125 .  FIG. 11A  shows a cross sectional view of the apparatus  1100 , which includes an intermediate optical layer  1125  (e.g., made of PDMS) disposed in cavities  1120  that are fabricated in a primary substrate  1110 . An additional concentrating layer  1140 , which can be made of PMMA, is bonded to the intermediate optical layer  1125 . The intermediate optical layer  1125  can provide mechanical cushion between the additional concentrating layer  1140  and the primary substrate  1110  to reduce any deformation effect. As a result, the selection of optical materials for  1140  (e.g., high refractive index molded plastic components) can be free from restriction by the material of substrate  1110 . For example, by using relatively soft PDMS as the intermediate optical layer  1125 , high refractive index plastic materials (e.g., PMMA) can be used as the micro-lens material to improve concentration and acceptance angle. Each cavity  1120  is also coupled to a PV cell  1130 . The primary substrate  1110  is disposed on a back substrate  1150 . A front glass  1170  is disposed on the top for protection purposes.  FIG. 11B  and  FIG. 11C  show the assembled view and the exploded view, respectively, of the apparatus  1100 . In these views, the intermediate optical layer  1125  can be regarded as the middle layer sandwiched by the additional concentrating layer  1140  and the primary substrate  1110 .  FIG. 11D  shows the perspective view of an individual PV cell in the apparatus  1100  including an array of such PV cells. 
       FIGS. 12A and 12B  show a PV apparatus  1200  with a faceted optical concentrating element  1240  on a wafer-level concentrating element  1220 . As shown in  FIG. 12A , the apparatus  1200  includes a primary substrate  1210  and a cavity  1220  fabricated therein. A PV cell  1230  is disposed at the exit end of the cavity  1220 . The combination of the primary substrate  1210 , the cavity  1220 , and the PV cell  1230  is sandwiched between an additional concentrating layer  1240  on the top and a back substrate  1250  on the bottom. The additional concentrating layer  1240  includes a top surface  1245  that can concentrate incident light toward the cavity  1220  either refraction (e.g., a micro-lens) or reflection (e.g., a curved mirror). The additional concentrating layer  1240  also has a side surface  1242  that can reflect incident light (e.g., via internal reflection) toward the bottom, thereby further concentrating the incident light. The side surface  1242  or facet can have various shapes such as pyramid, cone, paraboloid, or sphere, or free-form, among others. 
     PV Apparatus Including a Cascade of PV Cells 
     In practice, one layer of PV cells may not collect all the incident light because of diffuse light or finite transmission of the PV cells (i.e. part of the incident light transmits through the PV cells without being converted into electricity). Therefore, it can be beneficial to use more than one layer of PV cells in a cascade, tile, or lateral architecture to increase the conversion efficiency. 
       FIG. 13A  shows a cross sectional view of an apparatus  1300  including a substrate  1310 , in which a cavity  1320  is fabricated as a wafer-level concentrating element, and secondary PV cells  1335  to collect diffuse light so as to increase conversion efficiency. A PV cell  1330  is disposed at the exit end of the cavity  1320 . An additional concentrating element  1340  is disposed on the substrate  1310  to focus, concentrate, or direct incident light toward the entrance of the cavity  1320 . In addition to the PV cell  1330 , the apparatus  1300  further includes the secondary PV cell(s)  1335  disposed on the front surface (the surface toward incident light) of the substrate  1310  to collect light that is received by the additional concentrating element  1340  but ends up on the substrate  1310 .  FIG. 13B  shows the same apparatus  1300  but with illustration of ray traces. The solid lines represent rays  1301  that are directly focused onto the PV cell  1330 . The dashed lines represent rays  1302  that are incident at an oblique angle and are redirected by the cavity  1320  and then received by the PV cell  1330 . Rays that are not collected by the PV cell  1330  may be collected by the secondary PV cell  1335 . 
     In one example, the secondary PV cell  1335  is disposed on the front surface of the substrate  1310  (e.g., as shown in  FIG. 13A ). The PV cell  1335  may also be disposed at the bottom of the substrate  1310 , or be sandwiched between two substrates. In another example, the secondary PV cell  1335  can be directly fabricated in the substrate  1310 . For example, the substrate  1310  can use active silicon material with p-n junctions and therefore can function as the secondary PV cell. The p-n junctions can be disposed at any position with the secondary PV cell  1335 . Since the secondary PV cell  1335  generally has no concentration or low concentration, less expensive material such as silicon can be used, without significantly incurring the cost of the resulting apparatus  1300 . 
       FIG. 14A  shows a cross sectional view of an apparatus  1400  with a cavity  1420  fabricated in a substrate  1410 . An additional concentrating element  1440  is disposed on the substrate  1410  to receive incident ray  1401  (normal incidence rays, see  FIG. 14B ) and  1402  (oblique incidence rays, see  FIG. 14B ) and focus or direct the incident rays  1401  and  1402  toward the entrance of the cavity  1420 . Three layers of PV cells are disposed at the exit of the cavity  1420  to receive the focused/concentrated/directed incident light  1401  and  1402 . On the first layer is a primary PV cell  1430 , which can be a high efficiency PV cell such as a III-V type semiconductor solar cell. The second layer includes a non-concentrating PV cell  1434 , which can be directly fabricated inside the substrate  1410  by, for example, creating p-n junctions. This non-concentrating PV cell  1434  can extend across the entire substrate  1410 , collecting not only incident light transmitted through the primary PV cell  1430  but also diffuse light that arrives at the non-concentrating PV cell  1434 . The third layer of PV cells includes a secondary PV cell  1436  that can also use high efficiency materials.  FIG. 14B  shows the same apparatus  1400  but illustrates ray traces of incident light. Solid lines indicate rays  1401  that are directly focused or directed onto the PV cell  1430  and dashed lines indicate rays  1402  incident at oblique angles that are redirected by the cavity  1420  and received by the PV cell  1430 . 
     The primary PV cell  1430  and the secondary PV cell  1436  can have different bandgaps for converting to incident light at different wavelengths. For example, the primary PV cell  1430  can convert incident lights with shorter wavelengths (e.g., visible light) while the secondary PV cell  1436  can convert incident lights with longer wavelengths (e.g., infrared and near infrared light) that is not absorbed by the primary PV cell  1430 . The primary PV cell  1430  and the secondary PV cell  1436  can also have different thickness so as to reduce recombination losses within the PV cells. For example, at the optimal thickness of the primary PV cell  1430 , where recombination loss is low, the primary PV cell  1430  may not be able to absorb and convert the incident light efficiently or completely. In this case, the secondary PV cell  1436  can collect any light that is transmitted through the primary PV cell  1430  and increase the overall conversion efficiency of the apparatus  1400 . 
     PV Apparatus Including Alignment Elements 
     As introduced above, a substrate fabricated with an array of cavities is a multifunctional platform that can integrate hybrid photovoltaics, optical micro-concentration, and mechanical micro-assembly in one substrate. Other than light concentration, this multi-functional platform can also allow self-alignment of micro-optical systems, including micro-photovoltaic systems. 
       FIGS. 15A-15B  shows a cross sectional view and a perspective view of an apparatus  1500  including a ball lens  1560  for both light concentration and alignment. The apparatus  1500  includes a substrate  1510  in which a cavity  1520  is fabricated for both light concentration and alignment. The entrance end of the cavity  1520  is coupled to the ball lens  1560  and the exit end of the cavity  1520  is coupled to a PV cell  1530 . A secondary PV cell  1535  is sandwiched between the substrate  1510  and an additional concentrating element  1540 . In another example, the secondary PV cell  1535  can be directly fabricated in the substrate  1510 . For example, the substrate  1510  can use active silicon material with p-n junctions and therefore can function as the secondary PV cell. The p-n junctions can be disposed at any locations of the secondary PV cell  1535 . 
     The additional concentrating element  1540  is configured to receive incident light, including normal incidence light  1501 , oblique incidence light  1502 , and diffuse light (collectively referred to as incident light). Most of the incident light concentrated by the additional concentrating element  1540  is received by the ball lens  1560 . Light not received by the ball lens  1560  can be collected and converted into electricity by the secondary PV cell  1535 . The ball lens  1560  further focuses the incident light into the cavity  1520 . In general, the normal incidence light  1501  can be directly focused or directed onto the PV cell  1530 , while the oblique incidence light  1502  can reach the PV cell  1530  after some reflection by the cavity  1520 . 
     The additional concentrating element  1540  can be formed by plastic molding and can be either directly molded on the substrate  1510  or pre-fabricated and then assembled onto the substrate  1510 . The ball lens  1560  can have a higher refractive index than the material of additional concentrating element  1540  to provide further concentration. In another example, the ball lens  1560  and the additional concentrating element  1540  can be separated by an air gap. The ball lens  1560  can be made of plastic or glass. 
     The ball lens  1560 , in addition to concentrating light, also aligns the substrate  1510  and other optical or mechanical elements, such as the additional concentrating element  1540 . For example, the additional concentrating element  1540  can be pre-fabricated and then coupled to the substrate  1510  (e.g., see  FIG. 9C, 10C, and 11C ). In this case, an array of holes can be made at the bottom of the additional concentrating element  1540  to fit the shape of the ball lens  1540 . When coupling these layers together, the ball lens  1560  can hold the additional concentrating element  1540  in position, in a similar manner as mortise and tenon. 
       FIGS. 15A-15B  show a ball lens  1560  (3D lens). The entrance of the cavity  1520  can have various shapes such as square, hexagon, and round, among other. In practice, the ball lens  1560  can be replaced by a cylindrical lens and accordingly the cavity  1520  can be replaced by a V-shape grove to achieve similar optical and mechanical functions. 
       FIGS. 16A-16B  show an apparatus  1600  including an array of the apparatus  1500  shown in  FIGS. 15A-15B . The apparatus  1600  includes a substrate  1610  in which a plurality of cavities are fabricated. A plurality of ball lenses  1660  is disposed on or partially into the cavities. An additional concentrating layer  1640  is disposed on the ball lenses  1660 . 
       FIGS. 16A-16B  show that the ball lenses  1660  are separated from each other. In this case, the ball lenses  1660  can be disposed individually onto the substrate  1610  after the cavities are fabricated, after which the additional concentrating layer  1640  can be disposed. Alternatively, the ball lenses  1660  can be connected together by, for example, disposing the ball lenses  1660  onto a film or sandwiching the ball lenses by two films. Therefore, the ball lenses  1660  can collectively form a ball lens layer. In this case, each layer, including the substrate  1610  including the cavities, the ball lens layer, and the additional concentrating layer  1640 , can be pre-fabricated and then bonded layer by layer to improve manufacturing efficiency. 
       FIG. 17  shows an apparatus  1700  using the multi-functional platform for optical micro-concentration and mechanical micro-assembly to assembly multiple concentrating layers. The apparatus  1700  includes a plurality of primary substrates  1710 , each of which has a cavity  1720  fabricated therein and a PV cell  1730  disposed at the bottom end of the cavity  1720 . Each cavity  1720  is also coupled to a ball lens  1760 , which can be self-aligned due to the matching of shapes between the cavity  1720  and the ball lens  1760 . The primary substrates  1710  can be PV cells (e.g., silicon cells). 
     A diffuse collector  1740  is disposed on the primary substrate  1710  to direct diffuse light towards the primary substrate  1710  for electricity conversion when the primary substrate  1710  is a PV cell itself. The diffuse collector  1740  includes a first portion  1742  having a wedge shape and a second portion  1744  that is complementary to the first portion. In one example, the first portion  1742  can be filled with air and the second portion  1744  is solid. In this case, the diffuse collector  1740  can collect diffuse light by reflecting the diffuse light via the inner surface of the first portion  1742 , in a manner similar to the wafer-level concentrating element described above. In another example, the first portion  1742  can also be filled with solid material, such as Ethylene-vinyl acetate (EVA) or PDMS, to enhance the mechanical stability of the apparatus  1700 . In yet another example, the first portion is solid and the second portion is filled with air, in which case the diffuse collector  1740  can be substantially similar to the additional concentrating element  1240  shown in  FIG. 12A . Incident light can be concentrated by total internal reflection of the first portion  1742 . 
     A primary optical layer  1780  is disposed above the diffuse collector  1740  to focus or direct incident light toward the ball lens  1760 . The primary optical layer  1780  includes a plurality of focusing surfaces, each of which corresponds to a ball lens  1760  and a cavity  1720 . All the above mentioned components are sandwiched between a front substrate  1770  and a back substrate  1750  that can provide physical protection, electrical connection, and mechanical support, among other things. The primary optical layer  1780  can be directly molded on the front substrate  1770  before integration with other components, such as the diffuse collector  1740 . Similarly, the diffuse collector  1740  can also be directly molded on the back substrate  1750  to facilitate manufacturing. The primary optical layer  1780  and the diffuse collector  1740  can also be pre-fabricated and subsequently assembled with other components. The front substrate  1770  can be a glass sheet. Both the front substrate  1770  and the back substrate  1750  can be flexible to allow broader applications such as in wearable technologies. 
       FIGS. 18A-18B  show an assembled view and an exploded view of an apparatus  1800  using the multi-functional platform for alignment. The apparatus  1800  includes a substrate  1810  in which two lower alignment cavities  1812  (or grooves) are fabricated. A PV cell  1830  is disposed on the substrate  1810  to receive incident light concentrated by a concentrator  1840 , which includes two upper alignment cavities  1842  at the bottom. Two ball alignment elements  1860  are disposed between the substrate  1810  and the concentrator  1840 . When assembled, the top hemispheres of the two ball alignment elements  1860  are received by the upper alignment cavities  1842  and the bottom hemispheres of the two ball alignment elements  1860  are received by the lower alignment cavities  1812  in the substrate  1810 . The two ball alignment elements function as a connector coupling the substrate  1810  with the concentrator  1840 . Various materials can be used to make the ball alignment elements  1860 , including plastic, glass, and metal. In addition, a layer of epoxy or index matching material (not shown in  FIGS. 18A-18B ) can be applied between the concentrator  1840  and the PV cell  1830  and/or the substrate  1810 . 
       FIGS. 19A-19B  show an assembled view and an exploded view of an apparatus  1900  in which alignment elements are integrated into or formed monolithically on optical components in the apparatus. More specifically, the apparatus  1900  includes a substrate  1910  in which two cavities  1912  (or grooves) are fabricated. A PV cell  1930  is disposed on the substrate  1910  to receive incident light concentrated by a concentrator  1940 , which includes two alignment elements  1942  at the bottom. The two alignment elements  1942  can have a hemisphere shape and can be received by the cavities  1912  when assembled. In this case, the concentrator  1940  and the substrate  1910  can be directly aligned without the use of additional connectors. 
       FIGS. 20A-20B  show the assembled view and the exploded view of a micro-concentrating PV apparatus  2000  in which alignment elements are integrated into or formed monolithically on optical concentrators. The apparatus  2000  includes a substrate  2010 , in which two lower alignment cavities  2012  and one concentrating cavity  2020  are fabricated. A PV cell  2030  is disposed at the bottom of the concentrating cavity  2020  to receive concentrated or directed incident light for electricity generation. A concentrator  2040  is disposed on the substrate  2010  to receive incident light and focus or direct the incident light toward the concentrating cavity  2020 . The concentrator  2040  includes two alignment elements  2042  at the bottom, which can have a hemisphere shape and can be received by the alignment cavities  2012  when assembled. 
     Other Applications of Wafer-Level Multi-Functional Platform 
     The photovoltaic apparatus described above are examples of wafer-level multi-functional micro-platforms fabricated from semiconductor substrates. Other than photovoltaic applications, the multi-function platform can also benefit several other technologies. 
     In one example, the wafer-level multi-function platform can be used for optical imaging or sensing, in which the PV cells as used in apparatus shown in  FIGS. 1-20B  can be replaced by an imager, such as a charge-coupled-device (CCD), a complementary metal-oxide semiconductor (CMOS) device, or a photodiode (e.g., avalanche photodiode). The cavities fabricated in the substrate can concentrate light and therefore increase sensitivity of the resulting imaging/sensing apparatus. 
     In one example, the wafer-level multi-function platform can be used for illumination. In this case, the PV cells as used in apparatus shown in  FIGS. 1-20B  can be replaced by a light source (e.g., a light emitting diode (LED), lasers, or vertical-cavity surface-emitting lasers (VCSELs)). Instead of concentrating light, cavities in the substrate can manipulate (e.g., diverge or direct) light from the light source (reverse process of concentration) toward areas to be illuminated. Alternatively, the cavities can also collimate the emitted light and direct the illumination towards desired directions. 
     In another example, the wafer-level multi-function platform can be used for optical communication. Optical beams containing optical signals are manipulated (e.g., diverged, collimated, focused, or steered) by the cavities and other optical element described towards at least one receiver that detects the optical signals. In another example, photodetectors and light source can be integrated on the same multi-function wafer for applications such as active imaging, optical communication, sensing, etc., based on the methods and systems described above. For optical sensing, the light source emits a probing beam towards an interested region; the reflected beam is collected by the concentrated photodetector. The substrate containing the cavities can be a larger-area photodetector, which can be used to detect ambient light level. 
     Methods of Making Apparatus Including Wafer-Level Concentrating Elements 
       FIGS. 21A-21C  illustrate a method  2100  of fabricating a PV apparatus including wafer-level concentrating elements and the multi-functional platform as used in the apparatus shown in  FIGS. 1-20B . The method  2100  includes disposing a mask  2105  on the front surface of a substrate  2110 , as shown in  FIG. 21A . The mask  2105  has the pattern to be transferred to the substrate  2110 . For example, the mask  2105  can have a square aperture for etching a pyramid cavity or a slit shape for etching a groove. The method  2100  also includes etching the substrate  2110  to form a cavity  2120 , as shown in  FIG. 21B . The lateral size (or aperture) of the cavity  2120  generally decreases as the etching reaches deeper into the substrate  2100 . In one example, the etching can be achieved by anisotropic etching using, for example, KOH. In another example, the etching can be achieved by grey-scale lithography to form a more complex cavity shape such as free-form shapes. A PV cell  2130  is then disposed at the bottom of the cavity  2120 , as shown in  FIG. 21C , to form the PV apparatus. The PV cell  2130  can be placed in position by, for example, pick-and-place procedures, in which a tweezers (or other moving tool) can pick the PV cell  2130  and place it onto the desired locations. If the substrate  2110  is also a PV cell, steps for forming p-n junctions in the substrate  2110  and forming the PV cell can be performed before or after the pyramid cavities or grooves are etched. 
       FIGS. 22A-22B  illustrate fabrication of wafer-level concentrating elements in a silicon substrate using anisotropic etching. The method  2200  includes disposing a mask  2205  on the front surface of a substrate  2210 , as shown in  FIG. 22A . Anisotropic etching (using an etchant such as KOH) of [100] oriented (face-aligned) silicon wafers exposes the [111] crystal plane, as schematically shown in  FIG. 22B , to form a cavity  2220 . The [111] plane naturally makes an angle of 54.7° with respect to the [100] plane. 
       FIGS. 23A-23C  illustrate a method  2300  of fabricating a PV apparatus including throughout cavities as wafer-level concentrating elements. As shown in  FIG. 23A , a mask  2305  is disposed on the front surface of a substrate  2310 . A PV cell  2330  is then disposed on the back surface of the substrate  2310  as shown in  FIG. 23B . Etching the substrate  2310  then forms a cavity  2320  that extends from the front surface of the substrate  2310  all the way to the back surface of the substrate  2310  and reaches the PV cell  2330 , thereby exposing the PV cell  2330  to incident light. 
     The order between integrating (e.g., by bonding) or forming the PV cell  2330  (shown in  FIG. 23B ) and etching the substrate  2310  (shown in  FIG. 23C ) can be reversed. In other words, the substrate  2310  can be etched to form the cavity  2320  before the PV cell  2330  is integrated or formed to the back surface of the substrate  2310 . In one example, the substrate  2310  is also a PV cell, and steps for forming a p-n junction in the substrate  2110  and other PV cell forming steps can be performed before or after the etching process. One example process is to first etch the substrate  2310  to form the cavities, followed by steps for forming p-n junctions in the substrate  2310  and other PV cell forming steps. Then the PV cell  2330  is subsequently integrated onto the active substrate  2310  by, for example, bonding. 
       FIGS. 24A-24F  illustrate a method  2400  of fabricating a PV apparatus including wafer-level concentrating elements and a back substrate.  FIG. 24A  shows that a silicon substrate  2410  is first prepared with an etching mask  2405  positioned to define the size and position of the desired etched facets and/or cavities. The silicon substrate  2410  may be active and/or serve as a mechanical support. Anisotropic etching is employed to create a cavity  2420  in the substrate  2410 , as shown in  FIG. 24B . A reflective metallization layer is subsequently deposited on the inner surfaces of the cavity  2420 , as shown in  FIG. 24C , to increase the reflectivity of the inner surfaces and accordingly the concentration efficiency of the cavity  2420 .  FIG. 24D  illustrates an optional step after the metallization step shown in  FIG. 23C . An epoxy layer  2425  is disposed in the cavity  2420  and planarized so as to provide mechanical support to the PV cell  2430  bonded later as shown in  FIG. 24E . The PV cell  2420  can be a concentrating PV cell (e.g., multi-junction solar cells) to efficiently convert received light into electricity. After the wafer bonding step, the PV cell  1430  with wafer-level concentrators (i.e. cavity  2420 ) is further integrated onto a back substrate  2450  that provides further mechanical support and metal interconnections (a glass substrate, a printed circuit board, etc.), as shown in  FIG. 24F . 
     In an alternative method for making the structure, the silicon substrate  2410  and the PV cell  2430  can be bonded together first ( FIG. 24E ), followed by the anisotropic etching step ( FIG. 24B ). Epoxy layers may be applied to provide mechanical support and/or act as an etch stop. 
     Additional steps can be performed on the manufactured apparatus shown in  FIG. 24F  to make apparatus shown in, for example,  FIGS. 8A-12B . For example, direct molding of a micro-lens array on the substrate or assembly of a pre-fabricated lens array onto the substrate can be carried out to integrate additional concentrating elements (e.g.,  940 ,  1040 , and  1140  shown in  FIGS. 9A, 10A, and 11A , respectively) into the apparatus. In another example, a piece of glass (e.g., about 0.1 mm to about a few mm thick) can be employed to assemble the Si platform on one side of the glass and assemble the micro-lens array on the opposite side of the glass. This approach can reduce the cost of plastic materials and improve overall robustness during the integration and assembly process. 
       FIGS. 25A-25G  illustrate a method  2500  of manufacturing a PV apparatus including alignment elements.  FIG. 25A  shows that a silicon substrate  2510  is first prepared with an etch mask  2505  positioned to define the size, shape, and position of the desired etched facets/cavities array. The silicon substrate  2510  can be active and/or serve as a mechanical support. As shown in  FIG. 25B , an anisotropic etching is performed on the silicon substrate  2510  to create a cavity  2520 . In  FIG. 25C , a reflective metallization layer is deposited on the facet surfaces of the cavity  2520  to increase reflectivity. After the metallization step, an epoxy layer  2525  is flown to fill the cavity  2520  and planarized, as shown in  FIG. 25D . The epoxy layer  2525  can provide mechanical supports to the PV cell  2530  bonded in next step shown in  FIG. 25E . Subsequently, as shown in  FIG. 25F , a ball lens  2560  is disposed in the cavity  2420  by, for example, picking and placing. The cavity  2520  can align and hold the ball lens  2560  in position.  FIG. 25G  shows that after the wafer bonding or the ball lens assembly step, the PV cell  2530  with wafer-level concentrators (i.e., cavity  2520 ) is further integrated onto a back substrate  2550  that provides further mechanical support and conductive interconnections (a glass substrate, a printed circuit board, etc.). In an alternative method, the electrical interconnections can be formed directly on the silicon substrate  2510 . 
     Characterization of Apparatus Including Wafer-Level Concentrating Elements 
     The approaches and concepts described above can be modeled and simulated with optical ray-tracing.  FIGS. 26A-26C  shows simulation results of an exemplary wafer-level concentrating PV system  2600 , including the ray traces of light incident on the system. The PV system includes a substrate  2610  in which a cavity  2620  is etched as the wafer-level concentrating element. The cavity  2620  is a rectangular cavity with 35.3° facets in the x- and y-directions. The cavity  2620  is also filled with silicone and the etched facets are coated with silver. A PV cell  2630  is disposed at the lower end of the cavity  2620  to receive incident light concentrated by the cavity  2620 . An additional concentrating element  2640  is disposed on the substrate  2610  to receive incident light and focuses or directs the incident light toward the entrance of the cavity  2620 . Silicone can be used to form the additional concentrating element  2640  because it is directly moldable and flexible. The geometric concentration between the input aperture of the additional concentrating element  2640  and the PV cell  2630  is about 500 ×. 
     The optical structure can be simulated with a 3D non-sequential Monte Carlo ray-trace, under a light source with AM 1.5 solar spectrum and a half-degree divergence angle, simulating the direct irradiation from the sun. Simulations yield acceptance angles of ±2° and ±2.5° at 90% and 50% (FWHM) of the peak transmission, respectively. At the same acceptance angle, the concentration ratio that can be achieved by similar optical materials and structures without the reflective cavity is about 200×. Therefore, simulation results indicate that the simple optical design with naturally-formed silicon cavity can provide a considerable improvement on the concentration ratio (e.g., more than 2× usage reduction of costly multi junction PV cells) while maintaining a reasonable acceptance angle tolerant to most low-cost trackers (1° ˜1.5° tracking accuracy). The silicon substrate  2610  can be made a PV cell as well to collect and convert diffuse light and light out the concentrator&#39;s field-of-view into electrical power. 
       FIGS. 27A-27C  show simulation results of a two-stage optical system that can further improve the “concentration x acceptance angle” product (see, e.g., equation (1) below) and meanwhile significantly reduce hot spot effects using advanced lens surface design and the reflective cavity structure. The system  2700  includes a substrate  2710 , in which a cavity  2720  is fabricated. A PV cell  2730  is attached to the back surface of the substrate  2710 . The optical concentration of the system  2700  includes a rear lens  2740  and a front lens  2780  bonded to a front glass  2770 . Ray traces shown in  FIGS. 27A-27B  indicate that nearly all the incident light reaches the PV cell  2730  for electricity generation. In another example, toroidal or other free-form shaped front and rear lens surfaces can be utilized to improve illumination uniformity, reduce hot spot, and improve collection efficiency. 
       FIGS. 28A-28B  show simulation results of a PV system including an additional concentrator compared to the system shown in  FIGS. 27A-27C . The system  2800  includes a substrate  2810 , in which a cavity  2820  is fabricated. A PV cell  2830  is attached to the back surface of the substrate  2810 . The system  2800  includes a rear lens  2840  and a front lens  2880  bonded to a front glass  2870 . The system  2800  further includes an additional concentrator  2845  that can concentrate the incident light enough that a low-concentration substrate cell may be used. As shown in  FIG. 28A , the portion of the rear lens  2840  above the substrate  2810  can be configured to be a reflective concentrator  2845  via either reflective coatings or total internal reflection on the concentrator side surface  2846 . Such a configuration can be applied to all the examples described in this application. In this case, the substrate  2810  can have a low concentration (instead of 1×) but still collect most of the light not collected by the concentrated PV cell  2830 , such as diffuse light. 
     The approaches described in this application are projected to at least double the dollars per Watt of state-of-the-art micro-scale CPV. To evaluate concentrator PV systems, an effective merit function is the concentration-acceptance product: 
       CAP=√{square root over (C g )}sinθ in    (1)
 
     where C g  is the concentration ratio and θ in  is the acceptance angle. In general, CAP is nearly invariant for a given optical architecture. State-of-the-art CPV technologies typically have a CAP between 0.4 and 0.6, making such CPV modules either not cost effective due to insufficient concentration or require high-accuracy but costly trackers due to small acceptance angles. In contrast, the single-lens baseline system (e.g., shown in  FIGS. 26A-26C , C g =500×, θ in =±2°) achieves a CAP of 0.78 with an optical system thickness less than 5 mm. The baseline system is fully compatible with low-cost trackers having a tracking accuracy of about 1° to about 1.5° in manufacturing. 
     A second baseline system for high-concentration can achieve an acceptance angle of ±1° at a concentration of 2000×. A third baseline system for high-concentration can achieve an acceptance angle of ±0.75° at a concentration of ˜3300×. In another exemplary system based on the 2-stage optical concentrator concept (e.g., shown in  FIGS. 27A-27B ), a CAP of ˜0.85 can be achieved, yielding concentrations of 600× and 2700×, acceptance angles of ±2° and ±1°, respectively. Compared with existing technologies, the disclosed approach can reduce the cost of multi junction cells and optical components by more than 50% with improved tolerance to angular misalignment and a simplified compact optical architecture that can further reduce assembly costs. In addition, the single-lens baseline design also allows the flexibility to be revised into advanced optical designs with additional optical element(s) at low cost that further increase CAP. Comparisons of baseline systems of the disclosed approach to state-of-the-art micro-/mini-CPV technologies are shown in Table 1 and  FIG. 29 . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Comparison of baseline systems with existing 
               
               
                 small-form-factor CPV technologies 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Exam- 
                 Exam- 
               
               
                   
                 Suncore 
                 SolFocu 
                 Sempriu 
                 LPI 
                 ple 1 
                 ple 2 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Concentration 
                 1090X 
                 850X 
                 1600X 
                 710X 
                 500X 
                 3300X 
               
               
                 Acceptance 
                 ±0.7° 
                 ±0.85° 
                 ±0.75° 
                 ±1.27° 
                 ±2°      
                 ±0.75° 
               
               
                 Angle 
               
               
                 CAP 
                 0.4 
                 0.43 
                 0.52 
                 0.59 
                 0.78 
                 0.75 
               
               
                 Element Count 
                 2 
                 2 
                 2 
                 2 
                 1   
                 1 
               
               
                   
               
            
           
         
       
     
       FIGS. 30A-30C  show simulation results of a PV system including wafer-level concentrating elements with simulation results of a similar system without any wafer-level concentrating elements. In this system, a single silicone lens is positioned on top of a silicon substrate which contains an inverted-pyramid-shaped rectangular cavity defined by facets with a slanting angle of 35.3°. The cavity is filled with silicone and the etched facets are coated with silver. A PV cell is located at the bottom of the cavity. The optical system is simulated using 3D non-sequential Monte Carlo ray-trace, under a light source with AM 1.5 solar spectrum and a half-degree divergence angle. Ray-trace simulation of a baseline system yields a geometric concentration of 500× with an acceptance angle of ±2° (at 90% of the maximum transmission) and a total thickness of ˜3.5 mm. The modeling results indicate that the simple optical design with anisotropically etched silicon cavity provides a desirable concentration ratio while maintaining a reasonable acceptance angle compatible with low-cost trackers (1° ˜1.5° tracking accuracy). The same lens design without the reflective cavity is also simulated and yields an acceptance angle of ±1° (shown in  FIG. 30C ), indicating that the etched Si cavity increases the field-of-view of a conventional optical concentrator. 
       FIGS. 31A-31C  show the modeling and simulation of an exemplary system under simulated direct and diffuse light with a variety of direct/global irradiation ratios, representing different geological and weather scenarios. Assuming a 4-junction concentrated cell efficiency of 44% and a Si cell efficiency of 24%, the overall conversion efficiency of the hybrid module is projected and compared to a CPV-only case of the same concentrator but without the Si cell (i.e. wafer-level concentrating element). Between 0.75˜0.6 Direct/Global irradiation ratio, the hybrid module provides a conversion efficiency improvement of 17% to 33% from the CPV-only case. Note that even at regions in the U.S. with abundant solar irradiation, approximately 20% of the total annual radiation comes from diffuse light which cannot be collected by conventional CPV technologies. 
     According to the optical simulations, the overall optical transmission of a baseline system  3200  covered by an AR-coated front glass can be about 92%, as shown in  FIG. 32  with a breakdown of the optical losses. The system  3200  includes a substrate  3210  for fabricating the wafer-level concentrating element and attaching PV cells. A lens  3240  is disposed on the substrate  3210  to focus incident light onto the entrance of the wafer-level concentrating element. A front glass piece  3270  is employed for physical protection of the system  3200 . The scattering loss is estimated to be about 0.2% based on previously fabricated parts. With appropriate AR layers, the transmission of such an optical module to the PV cell is estimated to be greater than 94%. The projected component and module efficiencies of the disclosed approach in a full module (assuming a 3× concentration Si cell that further reduces materials costs) is summarized in Table 3. It is clearly indicated that even at regions with high diffuse irradiation (40%), the hybrid architecture with high-concentration multi junction micro-cells and low-concentration Si cells (3×) can still achieve a conversion efficiency of over 30%, enabling expanded utilization of CPV technologies in regions once deemed unsuitable for CPV installation. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Projected component and module efficiencies 
               
            
           
           
               
               
               
               
            
               
                 Parameter 
                 Symbol 
                 Value 
                 Estimated variation 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Fractional DNI 
                 f DNI   
                 60% 
                   
               
               
                 Opt. Eff. (Direct) 
                 η opt     —     DNI   
                 94% 
                 &lt;0.02 
               
               
                 Opt. Eff. (Diffuse) 
                 η opt     —     Diffuse   
                 56% 
                 &lt;0.001 
               
               
                 DNI PV Eff. 
                 η PV     —     DNI   
                 44% 
                 0.02 
               
               
                 Diffuse PV Eff. 
                 η PV     —     Diffuse   
                 24% 
                 0.02 
               
               
                 Solar Harvesting Eff. 
                 η Harvest     —     DC   
                 30.2%     
                 0.04 
               
               
                   
               
            
           
         
       
     
     Conclusion 
     While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure. 
     The above-described embodiments can be implemented in any of numerous ways. For example, embodiments of designing and making the technology disclosed herein may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. 
     Further, it should be appreciated that a computer may be embodied in any of a number of forms, such as a rack-mounted computer, a desktop computer, a laptop computer, or a tablet computer. Additionally, a computer may be embedded in a device not generally regarded as a computer but with suitable processing capabilities, including a Personal Digital Assistant (PDA), a smart phone or any other suitable portable or fixed electronic device. 
     Also, a computer may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computer may receive input information through speech recognition or in other audible format. 
     Such computers may be interconnected by one or more networks in any suitable form, including a local area network or a wide area network, such as an enterprise network, and intelligent network (IN) or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks. 
     The various methods or processes (outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine. 
     In this respect, various inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above. The computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above. 
     The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention. 
     Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments. 
     Also, data structures may be stored in computer-readable media in any suitable form. For simplicity of illustration, data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computer-readable medium that convey relationship between the fields. However, any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationship between data elements. 
     Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. 
     All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms. 
     The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.” 
     The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. 
     As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e., “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law. 
     As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. 
     In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.