Abstract:
Techniques for combining nanotechnology with photovoltaics are provided. In one aspect, a method of forming a photovoltaic device is provided comprising the following steps. A plurality of nanowires are formed on a substrate, wherein the plurality of nanowires attached to the substrate comprises a nanowire forest. In the presence of a first doping agent and a first volatile precursor, a first doped semiconductor layer is conformally deposited over the nanowire forest. In the presence of a second doping agent and a second volatile precursor, a second doped semiconductor layer is conformally deposited over the first doped layer. The first doping agent comprises one of an n-type doping agent and a p-type doping agent and the second doping agent comprises a different one of the n-type doping agent and the p-type doping agent from the first doping agent. A transparent electrode layer is deposited over the second doped semiconductor layer.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a divisional of U.S. application Ser. No. 11/494,195 filed on Jul. 27, 2006 the disclosure of which is incorporated by reference herein. 
    
    
     STATEMENT OF GOVERNMENT RIGHTS 
     This invention was made with Government support under N66001-05-C-8043 awarded by Defense Advanced Research Projects Agency (DARPA). The Government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to use of nanotechnology in photovoltaics, and more particularly, to nanostructure-based photovoltaic devices. 
     BACKGROUND OF THE INVENTION 
     Photovoltaic devices, such as photocells, are an important energy source that has thus far remained underutilized for widespread energy production due to undesirable efficiency and/or production cost factors. For example, conventional photocells comprise a silicon-based substrate that includes a large-area p-n junction. Crystalline semiconductor substrates, such as silicon, are expensive, making production of photocells cost prohibitive for many applications. Further, photocells generate electrical energy by converting photons from a light source into electricity (e.g., by freeing electron-hole pairs). Conventional photocells typically provide a light-to-electricity conversion efficiency of only up to about 25%. This low conversion efficiency similarly makes photocells an undesirable option for many applications. 
     Attempts have been made to increase photocell energy conversion efficiency. Some of the attempts have employed nanotechnology as a tool. See, for example, U.S. Patent Application No. 2005/0009224 filed by Yang et al., entitled “Nanowire Array and Nanowire Solar Cells and Methods for Forming the Same” (wherein nanowire oxides are used in conjunction with a charge transport medium in optoelectronic devices); U.S. Patent Application No. 2005/0214967 filed by Scher et al., entitled “Nanostructure and Nanocomposite Based Compositions and Photovoltaic Devices” (wherein nanostructures, such as core-shell nanocrystals, are used in photovoltaic devices oriented horizontally along the plane of the electrodes); and Kayes et al.,  Comparison of the Device Physics Principles of Planar and Radial p - n Junction Nanorod Solar Cells,  97 J. A PPL . P HYS.  114302 (2005) (wherein radial p-n junction nanorod solar cells are described). 
     As these references show, nanotechnology can be employed in photovoltaics. However, improved techniques for combining these technologies to cost-effectively produce more efficient photovoltaic devices are needed. 
     SUMMARY OF THE INVENTION 
     The present invention provides techniques for combining nanotechnology with photovoltaics. In one aspect of the invention, a method of forming a photovoltaic device is provided comprising the following steps. A plurality of nanowires are formed on a substrate, wherein the plurality of nanowires attached to the substrate comprises a nanowire forest. In the presence of a first doping agent and a first volatile precursor, a first doped semiconductor layer is conformally deposited over at least a portion of the nanowire forest. In the presence of a second doping agent and a second volatile precursor, a second doped semiconductor layer is conformally deposited over at least a portion of the first doped layer. The first doping agent comprises one of an n-type doping agent and a p-type doping agent and the second doping agent comprises a different one of the n-type doping agent and the p-type doping agent from the first doping agent. A transparent electrode layer is deposited over at least a portion of the second doped semiconductor layer. 
     In another aspect of the invention, a method of forming a photovoltaic device is provided comprising the following steps. In the presence of a first doping agent and a first volatile precursor, a plurality of nanowires are formed on a substrate, wherein the plurality of nanowires attached to the substrate comprises a nanowire forest. In the presence of a second doping agent and a second volatile precursor, a doped semiconductor layer is conformally deposited over at least a portion of the nanowire forest. The first doping agent comprises one of an n-type doping agent and a p-type doping agent and the second doping agent comprises a different one of the n-type doping agent and the p-type doping agent from the first doping agent. A transparent electrode layer is deposited over at least a portion of the doped semiconductor layer. 
     In yet another aspect of the invention, a photovoltaic device is provided. The photovoltaic device comprises a substrate; a plurality of nanowires on the substrate, wherein the plurality of nanowires attached to the substrate comprises a nanowire forest; a first doped semiconductor layer disposed conformally over at least a portion of the nanowire forest, the first doped semiconductor layer comprising a first doping agent; a second doped semiconductor layer disposed conformally over at least a portion of the first doped semiconductor layer, the second doped semiconductor layer comprising a second doping agent, wherein the first doping agent comprises one of an n-type doping agent and a p-type doping agent and the second doping agent comprises a different one of the n-type doping agent and the p-type doping agent from the first doping agent; and a transparent electrode layer disposed over at least a portion of the second doped semiconductor layer. 
     In still another aspect of the invention, a photovoltaic device is provided. The photovoltaic device comprises a substrate; a plurality of nanowires on the substrate, the nanowires comprising a first doping agent and wherein the plurality of nanowires attached to the substrate comprises a nanowire forest; a doped semiconductor layer disposed conformally over at least a portion of the nanowire forest, the doped semiconductor layer comprising a second doping agent, wherein the first doping agent comprises one of an n-type doping agent and a p-type doping agent and the second doping agent comprises a different one of the n-type doping agent and the p-type doping agent from the first doping agent; and a transparent electrode layer disposed over at least a portion of the doped semiconductor layer. 
     A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating an exemplary methodology for growing a nanowire forest according to an embodiment of the present invention; 
         FIG. 2  is a scanning electron micrograph image of an exemplary nanowire forest according to an embodiment of the present invention; 
         FIG. 3  is a diagram illustrating an exemplary methodology for forming a photovoltaic device according to an embodiment of the present invention; 
         FIG. 4  is a diagram illustrating another exemplary methodology for forming a photovoltaic device according to an embodiment of the present invention; and 
         FIG. 5  is a diagram illustrating an exemplary photocell according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  is a diagram illustrating exemplary methodology  100  for growing a nanowire forest. The term “nanowire forest,” as used herein, refers to a plurality of nanowires attached to a substrate. As will be described in detail below, the growth of the nanowire forest is conducted in a chemical vapor environment. 
     Nanowires are highly-anisotropic, rod-like crystals with diameters d of between about ten nanometers (nm) and about 70 nm and lengths L of between about 0.1 micrometers (μm) and about 100 μm. Due to the nanowires having large L to d ratios, the surface area of the substrate is increased by a factor (4L/d)f, wherein f denotes the fraction of the substrate area covered by nanowires. By way of example only, for a five percent substrate areal coverage, nanowires of diameter d=40 nm and length L=five μm will provide a surface area that is 25 times greater than that of the substrate alone. 
     While the present description is directed to nanowires being a preferred nanostructure for use herein, any other suitable nanostructures may be similarly employed. Other suitable nanostructures include, but are not limited to, nanoparticles, quantum dots and other nanoscale materials. 
     In step  102  of  FIG. 1 , at least a portion of substrate  110  is coated with a catalyst metal to form catalyst layer (film)  112 . Catalyst layer  112  can be deposited on substrate  110  using chemical vapor deposition (CVD) techniques. 
     Substrate  110  can comprise any suitable substrate material, including, but not limited to, one or more of glass, quartz and a semiconductor material, such as silicon (Si) or germanium (Ge). Optionally, when substrate  110  comprises a semiconductor material, substrate  110  can be doped with either an n-type or a p-type doping agent, so as to be conductive. Suitable doping agents include, but are not limited to, diborane (B 2 H 6 ) (a p-type doping agent) and phosphine (PH 3 ) (an n-type doping agent). According to an exemplary embodiment, substrate  110  comprises Si and is doped with an n-type doping agent. 
     Catalyst layer  112  deposited onto substrate  110 , can comprise any suitable catalyst metal, including, but not limited to, one or more of gold (Au), gallium (Ga) and indium (In). According to one exemplary embodiment, catalyst layer  112  comprises Au and is deposited on substrate  110  to a thickness of up to about ten Angstroms (Å). 
     In step  104 , substrate  110  is annealed to cause catalyst layer  112  to form small droplets  114 . According to an exemplary embodiment, substrate  110  is annealed at a temperature of between about 400 degrees Celsius (° C.) and about 500° C. to form droplets  114  having diameters of between about ten nm and about 30 nm. Further, as shown in  FIG. 1 , droplets  114  of varying diameters are typically formed by the annealing process. 
     In step  106 , substrate  110  is exposed to an ambient of one or more volatile precursors  116 . Suitable precursors include, but are not limited to, one or more of silane (SiH 4 ) and germane (GeH 4 ). The specific precursor used will dictate the nanowire composition. For example, if SiH 4  is employed as the precursor, then Si nanowire growth (as described in step  108 , below) will result. Similarly, if GeH 4  is employed as the precursor, then Ge nanowire growth (as described in step  108 , below) will result. A combination of SiH 4  and GeH 4  will result in SiGe nanowire growth, wherein the relative concentration of Si and Ge will depend on the ratio of partial pressures of SiH 4  and GeH 4  in the growth ambient, as well as, on the growth temperature. Suitable partial pressures of the precursor(s) and temperature parameters are provided below. 
     By way of example only, suitable growth conditions for Si nanowires include a temperature of between about 400° C. and about 500° C. and a partial pressure of the precursor of between about 0.1 torr and about 100 torr. Suitable growth conditions for Ge nanowires include a temperature of between about 250° C. and about 300° C. and a partial pressure of the precursor of between about 0.1 torr and about 100 torr. 
     Optionally, an n-type and/or a p-type doping agent may be introduced to the ambient during nanowire growth. For example, some embodiments, described below, include n-type and/or p-type doped nanowires. Suitable doping agents include, but are not limited to, B 2 H 6  and PH 3 . By way of example only, if substrate  110  is exposed to an ambient of GeH 4  and B 2 H 6 , boron-doped (B-doped), p-type Ge nanowire growth will result. Similarly, if substrate  110  is exposed to an ambient of GeH 4  and PH 3 , phosphorous-doped (P-doped), n-type Ge nanowire growth will result. 
     In step  108 , droplets  114  will mediate CVD growth of crystals, namely nanowires  118 . According to an exemplary embodiment, when droplets  114  comprise Au as the catalyst metal, and the growth conditions outlined above are employed, highly anisotropic Si or Ge nanowires are produced. 
     The diameters of the nanowires produced are determined by the diameters (i.e., sizes) of the respective droplets  114 . The lengths of the nanowires produced are determined by the growth time and growth pressure. For example, at a partial pressure of GeH 4  in the CVD reactor of 0.5 ton and a temperature of 285° C., the longitudinal growth rate for Ge nanowires is about five μm/hour. At constant temperature, e.g., 285° C., the nanowire growth rate depends linearly on the partial pressure of GeH 4  in the growth ambient. At constant pressure, the growth rate depends exponentially on the temperature (i.e., in a limited temperature window, because at higher temperatures the nanowire growth can be complicated by conformal growth). 
     As described above, the nanowires produced can have diameters of between about ten nm and about 70 nm and lengths of between about 0.1 μm and about 100 μm. For example, the nanowires produced can have diameters of between about 20 nm and about 50 nm and lengths of between about one μm and about ten μm. 
       FIG. 2  is scanning electron micrograph image  200  of exemplary nanowire forest  202 , e.g., produced according to methodology  100 , described in conjunction with the description of  FIG. 1 , above. Nanowire forest  202  comprises Ge nanowires grown predominately in a vertical direction. The substrate employed is an n-type doped Si wafer. 
     As will be described in detail below, the nanowire forests possess a very high absorption coefficient of incident, visible electromagnetic waves (light). According to the present techniques, these high light-absorptive properties can be utilized by incorporating the nanowire forests into photovoltaic devices, such as photocells, to convert light into electricity with enhanced efficiency and to reduce the overall size of the devices to minimize use of costly production materials. 
       FIG. 3  is a diagram illustrating exemplary methodology  300  for forming a photovoltaic device. As will be described in detail below, the photovoltaic device is formed using CVD growth techniques. 
     In step  302 , the starting structure for the photocell is a nanowire forest formed in accordance with exemplary methodology  100 , described above, and comprises nanowires  301  on substrate  303 . Substrate  303  comprises a semiconductor material doped with a doping agent, so as to be conductive. The doping of a semiconductor substrate material is described, for example, in conjunction with the description of  FIG. 1 , above. 
     According to one exemplary embodiment, substrate  303  comprises an n-type doped Si wafer and nanowires  301  comprise Ge. The use of Ge nanowires, in particular, significantly decreases reflectivity (e.g., to below 10 −4  across the whole visible light spectrum), i.e., rendering the nanowire forest a black body, and thus enhances the desirable light absorptive properties of the nanowire forest. 
     In step  304 , doped semiconductor layer  310 , which may comprise either a p-type or an n-type doped layer, is formed over the nanowire forest by conformal CVD growth (so as to have the same relative shape as the underlying structure, i.e., the nanowire forest). According to one exemplary embodiment, wherein doped semiconductor layer  310  comprises a p-type doped layer, doped semiconductor layer  310  is formed by exposing the nanowire forest to an ambient of GeH 4  and B 2 H 6 . This results in B-doped, p-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 torr and a B 2 H 6 /GeH 4  ratio of about 0.0001, the growth rate of a p-type doped semiconductor layer  310  will be on the order of about 200 nm/hour, with a doping concentration of about 10 18  cm− 3 . 
     According to another exemplary embodiment, wherein doped semiconductor layer  310  comprises an n-type doped layer, doped semiconductor layer  310  is formed by exposing the nanowire forest to an ambient of GeH 4  and PH 3 . This results in P-doped, n-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 ton and a PH 3 /GeH 4  ratio of about 0.0001, the growth rate of an n-type doped semiconductor layer  310  will be on the order of about 210 nm/hour, with a doping concentration of about 10 18  cm− 3 . The growth rates and doping concentrations given can vary based on temperature and gas flow ratios, and therefore are merely exemplary. 
     In step  306 , doped semiconductor layer  312 , which may comprise either a p-type or an n-type doped layer, is formed over doped semiconductor layer  310  by conformal CVD growth. The doping of doped semiconductor layer  310  has to be different from the doping of doped semiconductor layer  312 . Namely, if doped semiconductor layer  310  comprises a p-type doped layer, then doped semiconductor layer  312  must comprise an n-type doped layer. Similarly, if doped semiconductor layer  310  comprises an n-type doped layer, then doped semiconductor layer  312  must comprise a p-type doped layer. 
     According to one exemplary embodiment, wherein doped semiconductor layer  312  comprises a p-type doped layer, doped semiconductor layer  312  is formed by exposing the nanowire forest/doped semiconductor layer  310  structure to an ambient of GeH 4  and B 2 H 6 . As described above, this results in B-doped, p-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 torr and a B 2 H 6 /GeH 4  ratio of about 0.0001, the growth rate of a p-type doped semiconductor layer  312  will be on the order of about 200 nm/hour, with a doping concentration of about 10 18  cm− 3 . 
     According to another exemplary embodiment, wherein doped semiconductor layer  312  comprises an n-type doped layer, doped semiconductor layer  312  is formed by exposing the nanowire forest/doped semiconductor layer  310  structure to an ambient of GeH 4  and PH 3 . As described above, this results in P-doped, n-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 torr and a PH 3 /GeH 4  ratio of about 0.0001, the growth rate of n-type doped semiconductor layer  312  will be on the order of about 210 nm/hour, with a doping concentration of about 10 18  cm− 3 . The growth rate and doping concentration given can vary based on temperature and gas flow ratios, and therefore are merely exemplary. 
     In step  308 , the nanowire forest/doped semiconductor layer  310 /doped semiconductor layer  312  structure is capped with transparent electrode layer  314 . Transparent electrode layer  314  may be disposed using CVD. According to an exemplary embodiment, transparent electrode layer  314  comprises indium tin oxide (ITO). 
     As a result of methodology  300 , a p-n junction is formed over the nanowire forest. As will be described, for example, in conjunction with the description of  FIG. 5 , below, the resulting structure can be used as a photocell. 
       FIG. 4  is a diagram illustrating exemplary methodology  400  for forming a photovoltaic device. As will be described in detail below, the photovoltaic device is formed using CVD growth techniques. 
     In step  402 , the starting structure for the photovoltaic device is a nanowire forest formed in accordance with exemplary methodology  100 , described above, and comprises nanowires  401  on substrate  403 . Substrate  403  comprises a semiconductor material and is doped with a doping agent, so as to be conductive. The doping of a semiconductor substrate material is described, for example, in conjunction with the description of  FIG. 1 , above. According to one exemplary embodiment, substrate  403  comprises an n-type doped Si wafer. 
     Nanowires  401  are doped with either a p-type or an n-type doping agent and thus are conductive. Namely, nanowires  401  may comprise either p-type or n-type doped nanowires. According to one exemplary embodiment, nanowires  401  comprise p-type or n-type doped Ge nanowires. The doping of nanowires is described, for example, in conjunction with the description of  FIG. 1 , above. 
     In step  404 , doped semiconductor layer  410 , which may comprise either a p-type or an n-type doped layer, is formed over the nanowire forest by conformal CVD growth (so as to have the same relative shape as the underlying structure, i.e., the nanowire forest). The doping of doped semiconductor layer  410  has to be different from the doping of nanowires  401 . Namely, if nanowires  401  comprise p-type doped nanowires, then doped semiconductor layer  410  must comprise an n-type doped layer. Similarly, if nanowires  401  comprise n-type doped nanowires, then doped semiconductor layer  410  must comprise a p-type doped layer. 
     According to one exemplary embodiment, wherein doped semiconductor layer  410  comprises a p-type doped layer, doped semiconductor layer  410  is formed by exposing the nanowire forest to an ambient of GeH 4  and B 2 H 6 . This results in B-doped, p-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 torr and a B 2 H 6 /GeH 4  ratio of about 0.0001, the growth rate of a p-type doped semiconductor layer  410  will be on the order of about 200 nm/hour, with a doping concentration of about 10 18  cm− 3 . 
     According to another exemplary embodiment, wherein doped semiconductor layer  410  comprises an n-type doped layer, doped semiconductor layer  410  is formed by exposing the nanowire forest to an ambient of GeH 4  and PH 3 . This results in P-doped, n-type Ge layer growth. At a temperature of about 350° C., a GeH 4  partial pressure of about 0.33 torr and a PH 3 /GeH 4  ratio of about 0.0001, the growth rate of an n-type doped semiconductor layer  410  will be on the order of about 210 nm/hour, with a doping concentration of about 10 18  cm− 3 . The growth rates and doping concentrations given can vary based on temperature and gas flow ratios, and therefore are merely exemplary. 
     In step  406 , the nanowire forest/doped semiconductor layer  410  structure is capped with transparent electrode layer  414 . Transparent electrode layer  414  may be disposed using CVD. According to an exemplary embodiment, transparent electrode layer  414  comprises ITO. 
     As a result of methodology  400 , a p-n junction is formed with the doped nanowires. As will be described, for example, in conjunction with the description of  FIG. 5 , below, the resulting structure can be used as a photocell. 
       FIG. 5  is a diagram illustrating exemplary photocell  502 . Photocell  502  comprises, e.g., n-type, doped substrate  504 , nanowire-based p-n junctions  506  and transparent electrode layer  508 . The use of nanowire-based p-n junctions in a photocell increases the surface area of the p-n junctions, which is beneficial in enhancing light absorption. 
     Further, the use of nanowire-based p-n junctions in a photocell takes advantage of the single crystal structure of a nanowire. Namely, the performance of a photocell can be degraded if the underlying material has defects. For example, grain boundaries enhance minority carrier recombination, thus reducing carrier lifetime and increasing the dark current. The grain boundaries also reduce majority carrier mobility and increase the series resistance of the photocell. See, for example, H. C. Card et al.,  Electronic Processes At Grain Boundaries in Polycrystalline Semiconductors Under Optical Illumination , IEEE T RANS . E LECTRON  D EVICES  ED-24, 397-402 (1977), the disclosure of which is incorporated by reference herein. As such, single crystal structures, such as nanowires, can minimize or eliminate the presence of material defects and the decrease in performance associated therewith. 
     Photocell  502  may be fabricated using either methodology  300  or methodology  400  described, for example, in conjunction with the description of  FIGS. 3 and 4 , respectively, above. Thus, for example, if photocell  502  is fabricated using methodology  300 , then nanowire-based p-n junctions  506  comprise two doped semiconductor layers formed, i.e., disposed conformally, over a nanowire forest. Similarly, if photocell  502  is fabricated using methodology  400 , then nanowire-based p-n junctions  506  comprise a single doped semiconductor layer formed, i.e., disposed conformally, over a doped nanowire forest. 
     One of the challenges in photovoltaic device, i.e., photocell, applications is to maximize solar light absorption. The design of photocell  502  incorporating a plurality of nanowire-based p-n junctions is based on the discovery that a plurality of nanowires enables very high light absorption. Specifically, the absorption spectrum of various films of Ge nanowires have been measured, and showed 99 percent absorption over most of the relevant spectral range. 
     Photocell  502  can be configured to optimize the absorption of incoming light. One way to achieve this is by employing an irregular configuration of nanowire-based p-n junctions  506 . Such an irregular configuration is shown in  FIG. 5 , wherein some of nanowire-based p-n junctions  506  are oriented perpendicular to substrate  504 , e.g., at an angle θ 1  between about 75 degrees to about 90 degrees relative to substrate  504 , and others of nanowire-based p-n junctions  506  are oriented nearly parallel to substrate  504 , e.g., at an angle θ 2  up to about 45 degrees relative to substrate  504 . 
     This irregular configuration helps optimize the orientations of nanowire-based p-n junctions  506  with respect to the angles of incoming light. For example, the nanowire-based p-n junctions  506  oriented nearly parallel to substrate  504  enhance absorption by aligning with the electric field vectors of the incoming light. 
     An irregular nanowire configuration can be produced using either a non-crystalline substrate, or a crystalline substrate with a rough, faceted surface (i.e., a crystalline Si substrate with a rough, faceted surface). A certain degree of irregularity is typically observed due to the ubiquitous imperfections of the substrate surface. However, according to an exemplary embodiment, the substrate surface is intentionally roughened or rendered non-crystalline (for example, by ion treatment) to increase irregular nanowire growth. Preferably, the spatial wavelengths of the surface roughness are smaller than the wavelength of the absorbed light (the wavelengths of absorbed light can be, e.g., between about 400 nm and about 800 nm). 
     Further, while most of the enhanced light absorption is caused by “roughness” of the nanowire film (see, for example, H. Kaplan,  Black Coatings Are Critical In Optical Design,  31 P HOTON . S PECTRA  48-50 (1997) and C. Amra,  From Light Scattering to the Microstructure of Thin Film Multilayers,  32 A PPL . O PT.  5481-5491 (1993), the disclosures of which are incorporated by reference herein) a plurality of nanowires also show altered absorption/reflection properties due to coupling between the nanowires, which is not found with individual nanowires. 
     These coupling modes can be further exploited for optimum light absorption. For example, the optical properties of a plurality of nanowires (or clusters of nanowires) can be governed by dipole-dipole interactions. For example, the individual nanowires can interact as “quasi-antennas” with the incident electrical field. The radiation field from these antennas will interact with other nanowires, thus altering the collective optical properties of the nanowire film. Further, the wavefunction of nanowires can overlap (couple quantum mechanically), which will alter the optical properties of nanowire films. In addition, the dielectric constants can be a function of the size, e.g., length and/or diameter, of the nanowire. 
     Although illustrative embodiments of the present invention have been described herein, it is to be understood that the invention is not limited to those precise embodiments, and that various other changes and modifications may be made by one skilled in the art without departing from the scope of the invention.