Patent Publication Number: US-2022231298-A1

Title: Solid-state battery layer structure and method for producing the same

Description:
TECHNICAL FIELD 
     The present invention relates to solid-state battery layer structures and methods of fabricating the same. 
     BACKGROUND 
     Lithium-ion battery technologies, with their high charge capacity levels and rechargeability, have evolved storage of electrical energy and played a significant part in enabling mobile electronic devices such as portable computers and telephones. Lithium-ion batteries have also been of importance for the resurgence of electric vehicles. However, the by now conventional lithium-ion battery technology comes with its own range of issues. In order to achieve battery improvements, essentially across the entire board, battery device designs featuring solid electrolytes, as opposed to traditional liquid electrolytes, are gaining popularity. Batteries comprising a solid electrolyte are generally referred to as solid-state batteries. While solid electrolytes may be very favorable for e.g. reducing the fire risk of batteries, they also come with a need for novel battery designs in regard to morphology and materials in order to realize their full potential of improved performance compared to liquid electrolyte batteries. In particular, improving solid-state battery charge capacity, defined as a ratio of storable charges to a weight of the battery, has not yet been adequately addressed in the prior art. Additionally, material dependent volume expansion is another issue facing prior art solid-state batteries. There is thus need for improvements within the technical field. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to at least mitigate some of the aforementioned issues and to provide solid-state battery layer structures that enable improved battery charge capacity as well as methods of fabricating the same structures. 
     According to a first aspect of the present invention there is provided a solid-state battery layer structure comprising: 
     an anode current collector metal layer; 
     an anode layer arranged on the anode current collector metal layer; 
     a solid electrolyte layer arranged on the anode layer laterally; 
     a cathode layer arranged on the solid electrolyte layer; and 
     a cathode current collector metal layer, 
     wherein the anode layer comprises silicon. 
     The term “arranged on” may refer to having the layers or structures arranged above each other in a vertical direction of the layer structure or stack. The vertical direction may be substantially perpendicular and normal to the surfaces of the layers or structures in the layer structures. The word “comprises” may throughout this disclosure refer to layers and structures at least partially comprising a certain material. The word does not exclude the layer or structure from containing impurities of other materials nor does it exclude the layer or structure substantially consisting of the comprised material. 
     Such a structure may mitigate some of the issues in the prior art. Silicon anodes may be advantageous for increasing the charge capacity for e.g. lithium-ion based batteries. This is due to silicon atoms, often alloyed to form compound anode materials, are better than carbon atoms, in conventional graphite anodes, at binding to and thus holding a larger number of lithium atoms. Battery charge capacity may be recorded in the units ampere hours or coulombs. Additionally, the use of silicon anodes, may simplify production of the battery layer structure and improve yield as sophisticated techniques and methods commonly used in microelectronic fabrication may be utilized. As such, solid-state batteries may be effectively minaturized. Silicon anodes may be based on monocrystalline substrates. As such, solid-state battery layer structures may be formed more integrally with silicon-based microelectronics. Thus, electronic circuits and devices with integrated solid-state batteries may be both enabled and miniaturized. 
     The anode layer may comprise gallium nitride. 
     The use of gallium nitride in the anode layer, e.g. as a thin upper layer of the anode layer otherwise mainly comprising silicon, may mitigate issues in the prior art. The charge capacity of a solid-state battery with a gallium nitride anode material may be ˜2.5 times larger than that of a solid-state battery with conventional graphite anodes. The diffusion barrier for lithium-ion diffusion may also be lower with a gallium nitride anode compared to the same barrier for a graphite anode. This may be advantageous for rapid battery charging. 
     The solid-state battery layer structure may further comprise a plurality of nanowire structures, wherein said nanowire structures are arranged on the anode layer and, wherein said nanowire structures are laterally and vertically enclosed by the solid electrolyte layer. 
     The term “nanowire structure”, also referred to as just nanostructures, may refer to elongated structures with a dimension such as a diameter or a length on the nanometer scale, i.e. 1-100 nm. Nanowire structures may be simple and substantially one-dimensional or contain, along its length, at least one node from which at least two separate branches extend. Such a nanowire structure may be referred to as a nanotree or a nanowire tree structure. 
     The term “laterally and vertically enclosed” may refer to enclosing the nanowire structures both laterally or radially and vertically or longitudinally. The whole nanowire structures, including all eventual branches, faces, and surfaces, may be covered by solid electrolyte material forming the solid electrolyte layer. 
     Such an addition of nanowire structures may advantageously increase the effective interface area between the anode and the solid electrolyte and hence also the battery charge capacity and potentially also increase the rate at which charge carrying ions, e.g. lithium ions, may alloy with the anode material. Additionally, the use of nanowire structures may mitigate the volume expansion of some materials during battery operation. E.g. bulk silicon anodes may expand 300-400% during lithiation, i.e. the process of charging a battery when the charge carriers are lithium ions. Nanostructures, such as e.g. nanowires are advantageous as their volume expansion may be much less severe than that of bulk materials. This advantage of nanostructures may be attributed to their volume expansion being more local and distributed as compared to when a bulk layer expands as one piece. This mitigation of the volume expansion issue may be even more relevant for solid electrolyte batteries as solids generally allow for less mechanical movement than liquids. Furthermore, nanostructures such as these may be produced in a structured and well-defined manner and the effective interface area may still be increased even if irregularities would somehow occur. 
     Each nanowire structure of said plurality of nanowire structures may comprise a vertical stem and a plurality of branches extending from said vertical stem, wherein the vertical stems of said plurality of nanowire structures are arranged perpendicularly to a top surface of the anode layer. 
     The term “arranged perpendicularly” may refer to arranging the whole nanowire structures, and in particular vertical stems, such that they extend in a substantially perpendicular and normal direction to the top surface of the anode layer. This direction may alternatively be understood as corresponding to the vertical direction of the layer structure. Including tree shaped nanowire structures, comprising both stems and branches, may further increase the effective interface area between the anode and the solid electrolyte and the battery charge capacity. Additionally, the tree shaped nanowire structures may further mitigate the volume expansion issue described in the above. 
     The plurality of tree shaped nanowire structures, or nanotrees, may be visually compared or likened to a nanoforest. 
     Said plurality of nanowire structures may comprise silicon. 
     Such nanowire structures may be advantageous for being relatively easy to form due to the numerous silicon formation and processing methods that are available. As the silicon nanowire structures would effectively extend the anode, the same advantages as those of using silicon as an anode material apply, i.e. the charge capacity may be increased. 
     Said plurality of nanowire structures may comprise gallium nitride. 
     Similarly to the above, gallium nitride nanowire structures extending the anode may also improve the charge capacity of the solid-state battery. 
     The anode layer may comprise a plurality of metal vias connecting the plurality of nanowire structures with the anode current collector metal layer. 
     As such, a lower resistance or more ohmic conduction path may be provided to the base of the nanowire structures. 
     The solid electrolyte layer may comprise lithium phosphate. 
     Lithium phosphate, or compounds comprising lithium phosphate, may be considered advantageous materials for the solid electrolyte layer in a solid-state battery layer structure. Lithium phosphate may allow transport of lithium ions between the anode and cathode of the solid-state battery by solid state diffusion via atomic vacancies in the solid electrolyte material lattice. 
     The cathode layer may comprise lithium cobalt oxide or another metal oxide. 
     Lithium cobalt oxide may be considered an advantageous material for the cathode layer. 
     The cathode current collector metal layer may comprise aluminium. 
     Aluminium may provide a low resistance or adequately ohmic conduction path to the cathode layer. 
     The anode current collector metal layer may comprise copper. 
     Copper may provide a low resistance or adequately ohmic conduction path to the anode layer and if present also to the nanowire structures. 
     According to a second aspect of the present invention there is provided a method for producing a solid-state battery layer structure, the method comprising: 
     providing an anode layer; 
     forming a plurality of nanowire structures on the anode layer, each nanowire structure comprising a vertical stem and a plurality of branches extending from the vertical stem, wherein the vertical stems of the nanowire structures are formed perpendicularly to a top surface of the anode layer; 
     depositing a solid electrolyte layer on the anode layer, the solid electrolyte layer laterally and vertically enclosing said plurality of nanowire structures; 
     depositing a cathode layer on the solid electrolyte layer; 
     depositing a cathode current collector metal layer on the cathode layer; and 
     depositing an anode current collector metal layer on a bottom surface of the anode layer. 
     The word “forming” may refer to any method or technique for forming a layer or structure. The word “depositing” may refer to any method or the use of a technique for forming a layer or structure by addition of material. Examples of deposition techniques may include chemical vapor deposition (CVD), physical vapor deposition (PVD), metalorganic vapor-phase epitaxty (MOVPE), sputtering, evaporation, etc. Thus, a step of forming may refer to depositing. The anode current collector metal layer should be understood as beeing deposited on the bottom surface of the anode layer, i.e. not on or above the anode layer when considering the vertical direction of the layer structure or stack. 
     Such a method may be used to produce solid-state battery layer structures according to the first aspect. Therefore, advantages may closely correspond to those described for the first aspect. In summary, the method may provide a relatively low complexity way to produce a solid-state battery layer structure by using existing, microelectronic, fabrication methods and techniques. Close integration with electronic devices and miniaturization may be enabled by the method. 
     The method may further comprise etching, from the bottom surface of the anode layer, holes through the anode layer, wherein the step of depositing the anode current collector metal layer on the bottom surface of the anode layer further comprises filling the holes with a same material as a material of the anode current collector metal layer. 
     This addition of etching and filling may be understood as corresponding to forming the vias to the bases of the nanowire structures as described in the first aspect. Thus, similar advantages and beneficial effect apply. Such backside wafer vias may be provided by plasma etching of silicon oxide or silicon nitride as a hard mask for deep reactive-ion etching (DRIE) of silicon. 
     The method may further comprise aligning the holes through the anode layer with said plurality of nanowire structures. 
     As such, a more ideal conduction path between anode contacts and nanowire strucutres may be obtained. 
     The step of forming said plurality of nanowire structures may comprise: 
     forming a plurality of stem seed particles on the top surface of the anode layer; 
     epitaxially growing the vertical stems of said plurality of nanowire structures from said plurality of stem seed particles; 
     depositing branch seed particles on the vertical stems; and 
     epitaxially growing the branches of said plurality of nanowire structures from said branch seed particles. 
     Forming nanowire structures by particle formation, e.g. deposition, and subsequent particle mediated epitaxy may be an effective way to form tree shaped nanowire structures comprising first order nanowire structures, i.e. vertical stems, and second order nanowire structures, i.e. branches wherein the first order nanowire structures act as bases for second order nanowire structures. 
     The branches may be understood as being grown substantially radially out from the vertical stems. The branch seed particles may be understood as being deposited on radial or lateral surface faces, and along the entire length, of the vertical stems. 
     A further scope of applicability of the present invention will become apparent from the detailed description given below. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the scope of the invention will become apparent to those skilled in the art from this detailed description. 
     Hence, it is to be understood that this invention is not limited to the particular component parts of the device described or acts of the methods described as such device and method may vary. It is also to be understood that the terminology used herein is for purpose of describing particular embodiments only and is not intended to be limiting. 
     It must be noted that, as used in the specification and the appended claims, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements unless the context clearly dictates otherwise. Thus, for example, reference to “a unit” or “the unit” may include several devices, and the like. Furthermore, the words “comprising”, “including”, “containing” and similar wordings does not exclude other elements or steps. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects of the present invention will, in the following, be described in more detail with reference to appended figures. The figures should not be considered limiting; instead they should be considered for explaining and understanding purposes. 
       As illustrated in the figures, the sizes of layers and regions may be exaggerated for illustrative purposes and, thus, are provided to illustrate the general structures. Like reference numerals refer to like elements throughout. 
         FIG. 1  shows a cross section of a solid-state battery layer structure. 
         FIG. 2  shows a cross section of a solid-state battery layer structure comprising nanowire structures. 
         FIG. 3  shows a cross section of a solid-state battery layer structure comprising nanowire structures and vias. 
         FIG. 4  shows a flowchart with steps for forming solid-state battery layer structures. 
         FIG. 5 a - h    show cross sections of a solid-state battery layer structure during various stages of its production. 
         FIG. 6  shows a flowchart with steps for forming nanowire structures. 
         FIG. 7 a - d    show cross sections of nanowire structures during different stages of their formation. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which currently preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided for thoroughness and completeness, and to fully convey the scope of the invention to the skilled person. 
       FIG. 1  shows a cross sectional view of a solid-state battery layer structure  100 . The solid-state battery layer structure comprises: 
     an anode current collector metal layer  110 ; 
     an anode layer  120  arranged on the anode current collector metal layer; 
     a solid electrolyte layer  140  arranged on the anode layer laterally; 
     a cathode layer  150  arranged on the solid electrolyte layer; and 
     a cathode current collector metal layer  160 , wherein the anode layer comprises silicon. 
     The anode current collector metal layer  110  may comprise or substantially consist of copper. The anode current collector metal layer  110  may alternatively or additionally comprise one of the other metal materials: gold, silver, platina, nickel, titanium, zinc, chromium, tin, lead, manganese, cobalt, and iron. The anode current collector metal layer  110  may comprise an alloy material. 
     The anode layer  120  may comprise &lt; 111 &gt;silicon. The anode layer  120  may be a crystaline silicon substrate or wafer. The anode layer  120  may comprise or substantially consist of gallium nitride. The anode layer  120  may comprise a thin upper sublayer of gallium nitride arranged on a lower sublayer of silicon. The anode layer comprising  120  GaN may be passivated with hydrogen. Lithium may be incorporated or alloyed into the anode layer  120 . 
     The solid electrolyte layer  140  may comprise or substantially consist of lithium phosphate (Li 3 PO 4 ). The solid electrlyte layer  140  may additionally or alternatively comprise or substantially consist of other materials such as lithium iron phosphate (Li 3 FePO 4 ) or lithium phosphorus oxynitride (LiPON). 
     Other lithium compounds may also be availble for the solid electrolyte layer  140 . 
     The solid electrolyte layer  140  may feature atomic vacancies at lithium atom lattice locations to allow for conduction by diffusion of lithium ions through the solid electrolyte layer  140 . The solid electrolyte layer  140  may comprise magnesium replacment or impurity atoms to restore the equlibrium of charges in the lattice that may be lost by introducing the lattice lithium vacancies. 
     The solid electrolyte layer  140  may have a thickness in the range 500-5000 nm. 
     The cathode layer  150  may comprise or substantially consist of lithium cobalt oxide (LiCoO 2 ). The cathode layer  150  may alternatively or additionally comprise other metal oxide based materials. 
     The cathode current collector metal layer  160  may comprise or substantially consist of aluminium. The cathode current collector metal layer  160  may alternatively or additionally comprise one of the other metal materials: gold, silver, platina, nickel, titanium, zinc, chromium, tin, lead, manganese, cobalt, and iron. The cathode current collector metal layer  160  may comprise an alloy material. 
       FIG. 2  shows the solid-state battery  100  layer structure further comprising a plurality of nanowire structures  130 . Said nanowire structures  130  may be arranged on the anode layer  120 . Said nanowire structures  130  may be laterally and vertically enclosed by the solid electrolyte layer  140 . 
     Each nanowire structure  130  of said plurality of nanowire structures may comprise a vertical stem  132  and a plurality of branches  134  extending from said vertical stem  132 . The vertical stems of said plurality of nanowire structures may be arranged perpendicularly to a top surface  122  of the anode layer  120 . 
     The nanowire structures  130  may be arranged in a hexagonal pattern on the top surface  122  of the anode layer  120 . The vertical stems  132  of the nanowire structures  130  may be arranged with a spacing to the nearest other vertical stem  132  in the range 100-1000 nm. More preferably, the spacing is in the range 250-750 nm. Most preferably, the spacing is in the range 400-600 nm. 
     The nanowire structures  130  may alternatively be arranged on the anode layer  120  with arbitrary orientations of each individual nanowire structure  130 . Such formation may be less complex while still increasing the effective anode-electrolyte interface area. 
     The vertical stems  132  may have a length in the range 500-5000 nm. More preferably, the length is in the range 1000-3000 nm. Most preferably, the length is in the range 1500 nm-2500 nm. 
     The branches  134  may have a length in the range 50-500 nm. More preferably, the length is in the range 50-250 n. Most preferably, the length is in the range 50-150 nm. 
     Said plurality of nanowire structures may comprise or substantially consist of silicon. Said nanowire structures  130  may comprise crystaline silicon with a crystal lattice direction &lt; 111 &gt;corresponding to the vertical direction of the nanowire structures. 
     Said plurality of nanowire structures may comprise or substantially consist of gallium nitride. Said nanowire structures  130  may comprise crystaline gallium nitride with a crystal lattice direction &lt; 0001 &gt;corresponding to the vertical direction of the nanowire structures. Gallium nitride nanowire structures  130  may feature a hydrogen passivation layer on the surfaces and faces of the nanowire structures  130  to saturate unsaturated dangling bonds at the gallium nitride surface. 
     The nanowire structures  130  may incorporate or alloy Li into their surface or bulk lattice. 
       FIG. 3  shows the anode layer  120  comprising a plurality of metal vias  224  connecting the plurality of nanowire structures  130  with the anode current collector metal layer  110 . The metal vias  224  may comprise or substantially consist of a same material existing in the anode current collector metal layer  110 . 
       FIG. 4  shows a flowchart of a method for producing a solid-state battery layer structure  100 . The method is shown to comprise steps of: 
     providing S 1002  an anode layer  120 ; 
     forming S 1004  a plurality of nanowire structures  130  on the anode layer  120 , each nanowire structure  130  comprising a vertical stem  132  and a plurality of branches  134  extending from the vertical stem  132 , wherein the vertical stems  132  of the nanowire structures  130  are formed perpendicularly to a top surface  122  of the anode layer  120 ; 
     depositing S 1006  a solid electrolyte layer  140  on the anode layer  120 , the solid electrolyte layer  140  laterally and vertically enclosing said plurality of nanowire structures  130 ; 
     depositing S 1008  a cathode layer  150  on the solid electrolyte layer  140 ; 
     depositing S 1010  a cathode current collector metal layer  160  on the cathode layer  140 ; and 
     depositing S 1012  an anode current collector metal layer  110  on a bottom surface  326  of the anode layer  120 . 
     The plurality of nanowires structures  130  may be formed by a MOVPE, or a CVD process. The process may be seed particle mediated. The pattern in which the nanowire structures  130  are arranged may be formed using lithography techniques such as ultra-violet lithography (UVL), electron beam lithography (EBL), and nanoimprint lithography (NIL). Pattern transfer may be achieved through etching methods. 
     Nanosphere lithography (NSL) may be used together with chlorine-based plasma etching to etch out entire vertical stems  132 . As such, the need for MOVPE may be circumvented, at least for the formation of the vertical stems  132 .The nanowire structures  130  may be passivated in-situ before, during, or after MOVPE processing. The nanowire structure  130  may be passivated with hydrogen. 
     The method may further comprise incorporating or alloying lithium into the surface or bulk lattice of the nanowire structures  130 . This may be achieved through electrochemical processing. Lithium may be deposited onto the nanowire structures  130  before solid electrolyte layer  140  deposition S 1006 . Lithium may be deposited by thermal evaporation. 
     The solid electrolyte layer  140  may be deposited S 1006  by a CVD process. The solid electrolyte layer  140  may be deposited by PVD or sputtering process. The sputtering process may be a pulsed DC (direct current) or RF (radio frequency) based sputtering process. The solid electrolyte layer  140  may encapsulate any lithium deposited onto the nanowire structures  130 . 
     The cathode layer  150  may be deposited S 1008  by a CVD process. The cathode current collector metal layer  160  may be deposited S 1010  by a PVD process. The anode current collector metal layer  110  may be deposited S 1012  by a PVD process. 
       FIG. 4  also shows how the method may further comprise etching S 3002 , from the bottom surface  326  of the anode layer  120 , holes  328  through the anode layer  120 . In this eventuallity, the step of depositing S 1012  the anode current collector metal layer  110  on the bottom surface  326  of the anode layer  120  further comprises filling the holes  328  with a same material as a material of the anode current collector metal layer  110 . The filled in holes  328  may correspond to the vias  224  in  FIG. 3 . 
     Also shown in  FIG. 4 , the method may further comprise aligning S 4002  the holes  328  through the anode layer  120  with said plurality of nanowire structures  130  i.e. so that each hole  328  corresponds to the position of a nanowire structure  130 . 
     The holes  328  may be etched S 3002  by a reactive ion etching (RIE) process. The RIE process may be a dry RIE process. 
       FIGS. 5 a -5 h    show cross sectional views of layers and structures of the solid-state battery layer structure  100  during various stages of its production. 
       FIG. 5 a    shows the anode layer  120  having been provided S 1002 , the anode layer  120  being the base for subsequent processing steps. 
       FIG. 5 b    shows the plurality of nanowire structures  130 , each comprising vertical stems  132  and branches  134 , having been formed S 1004  wherein the vertical stems  132  of the nanowire structures  130  are formed perpendicularly to the top surface  122  of the anode layer  120 . 
       FIG. 5 c    shows the solid electrolyte layer  140  having been deposited S 1006  on the anode layer  120  such that it laterally and vertically encloses the plurality of nanowire structures  130 . 
       FIG. 5 d    shows the cathode layer  150  having been deposited S 1008  on the solid electrolyte layer  140 . 
       FIG. 5 e    shows the cathode current collector metal layer  160  having been deposited S 1010  on the cathode layer  150 . The battery layer structure may be flipped after step S 1010  in order to accommodate subsequent processing steps. 
       FIG. 5 f    shows the anode current collector metal layer  110  having been deposited S 1012  on the bottom surface  326  of the anode layer  120 , thus completing the solid-state battery layer structure  100 . 
       FIGS. 5 g - h    show an alternative route to complete the layer structure  100  compared to the route shown in  FIG. 5   f.    
       FIG. 5 g    shows the holes  328  having been etched S 3002  from the bottom through the anode layer  120 , from its bottom surface  326 . The holes  328  are also shown to have been aligned S 4002  with the nanowire structures  130 . 
       FIG. 5 h    shows the anode current collector metal layer  110  having been deposited S 1012  on the bottom surface  326  of the anode layer  120  and into the holes  328  through the anode layer  120 , thus completing the solid-state battery layer structure  100 . 
       FIG. 6  shows a flowchart of the step of forming S 1004  said plurality of nanowire structures  130 . The step S 1004  may comprise: 
     forming S 2002  a plurality of stem seed particles  436  on the top surface  122  of the anode layer  120 ; 
     epitaxially growing S 2004  the vertical stems  132  of said plurality of nanowire structures  130  from said plurality of stem seed particles  436 ; 
     depositing S 2006  branch seed particles  438  on the vertical stems  132 ; and 
     epitaxially growing S 2008  the branches  134  of said plurality of nanowire structures  130  from said branch seed particles  438 . 
     The stem seed and branch seed particles  436 ,  438  may be e.g. gold seed particles. The stem seed and branch seed particles  436 ,  438  may comprise other materials than gold such as e.g. silver, palladium, cobalt, bismuth, and platina. The stem seed and branch seed particles  436 ,  438  may be deposited using aerosol deposition. Deposition or formation of the plurality of seed particles  436 ,  438  may be formed with or without preferred co-alignment onto their respective surfaces or structures. The stem seed particle  436  may be formed using lithography-based patterning techniques. Such a technique may include forming a gold layer onto the anode layer  120  through electroplating, evaporation, or sputtering followed by lithography-based patterning, e.g. with resist coating, exposure, and etching steps to achieve a well-defined pattern of remaining stem seed particles  436  on the top surface  122  of the anode layer  120 . 
     The nanowire structures  130  may be grown using seed particle mediated epitaxy. Essentially, this may mean that crystalline nanowire structures  130  are epitaxially grown from the seed particles  436 ,  438 . The seed particles  436 ,  438  may first absorb precursor gases. 
       FIGS. 7 a - d    show a cross sectional, or side views, of nanowire structures  130  during different stages of their formation. 
       FIG. 7 a    shows a plurality of stem seed particles  436  having been formed S 2002  on the top surface  122  of the anode layer  120 . 
       FIG. 7 b    shows the vertical stems  132  having been epitaxially grown S 2004 . 
       FIG. 7 c    shows branch seed particles  438  having been deposited S 2006  on the vertical stems  132 . 
       FIG. 7 d    shows the branches  134  having been epitaxially grown S 2008 . 
     Additionally, variations to the disclosed embodiments can be understood and effected by the skilled person in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.