Patent Publication Number: US-2023160093-A1

Title: Methods for producing a single crystal silicon ingot using boric acid as a dopant

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Divisional of U.S. Non-provisional patent application Ser. No. 16/875,468, filed May 15, 2020, which claims the benefit of U.S. Provisional Patent Application No. 62/868,573, filed Jun. 28, 2019. Both applications are incorporated herein by reference in their entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     The field of the disclosure relates to methods for producing a single crystal silicon ingot in which the ingot is doped with boron using solid-phase boric acid as the source of boron. The field of the disclosure also relates to ingot puller apparatus that use a solid-phase dopant. 
     BACKGROUND 
     In high resistivity silicon wafer applications, the resistivity of the single crystal silicon ingot from which the wafers are sliced may be controlled by addition of various dopants to the melt. The dopants may be used to compensate for various impurities (e.g., boron or phosphorous) in the source of polycrystalline silicon used to form a melt from which the silicon ingot is withdrawn. 
     When one or more dopants are added to achieve a target resistivity in the ingot, certain dopants and/or impurities may accumulate in the melt due to differences in the segregation coefficients of the compounds. For example, boron has a segregation coefficient of about 0.8 which allows boron to be readily taken up into the growing ingot. Phosphorous has a segregation coefficient of about 0.35 which causes phosphorous to accumulate in the melt relative to boron which is taken up more readily. Accordingly, as the ingot grows and the melt is depleted, phosphorous accumulates in the melt altering the resistivity of the growing ingot. This can cause the resistivity to decrease and fall out of customer specifications and/or for a type-change to occur in the ingot. 
     A need exists for methods for counter-doping a silicon melt during ingot growth to increase the length of the ingot that remains within customer specifications. A need exists for doping methods that allow for use of dopant source materials that are readily available and/or relatively inexpensive and that allow the melt to be doped with relative ease. A need exits for ingot puller apparatus that allow a solid-phase dopant to be used as the source of dopant. 
     This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the disclosure, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     SUMMARY 
     One aspect of the present disclosure is directed to a method for producing a single crystal silicon ingot from a silicon melt held within a crucible. Polycrystalline silicon is added to the crucible. The crucible is disposed within an ingot puller inner chamber. The polycrystalline silicon is heated to cause a silicon melt to form in the crucible. A single crystal silicon ingot is pulled from the silicon melt. A source of solid-phase boric acid is provided. A boron-containing gas is produced from the solid-phase boric acid. The boron-containing gas is contacted with a surface of the melt to cause boron to enter the melt as a dopant while pulling the single crystal silicon ingot from the melt. 
     Yet another aspect of the present disclosure is directed to an ingot puller apparatus for producing a doped single crystal silicon ingot. The ingot puller apparatus includes an ingot puller outer housing and an ingot puller inner chamber formed within the ingot puller outer housing. A crucible is disposed within the ingot puller inner chamber. An outer feed tube is at least partially disposed exterior to the ingot puller outer housing. The outer feed tube defines an outer feed tube chamber. The outer feed tube has a distal end, a proximal end and an outer feed tube axis that extends through the distal end and the proximal end. An elongate member is moveable within the outer feed tube chamber along the outer feed tube axis. A dopant receptacle is coupled to the elongate member. The dopant receptacle is moveable between a loading position in which the dopant receptacle is disposed exterior to the ingot puller outer housing and a feed position in which the dopant receptacle is disposed within the ingot puller inner chamber. 
     Yet another aspect of the present disclosure is directed to an ingot puller apparatus for producing a doped single crystal silicon ingot. The ingot puller apparatus includes an ingot puller outer housing and an ingot puller inner chamber formed within the ingot puller outer housing. A crucible is disposed within the ingot puller inner chamber. A dopant conduit having a gas inlet is disposed exterior to the ingot puller inner chamber and a gas outlet is disposed in the ingot puller inner chamber. A dopant vaporization unit is disposed exterior to the ingot puller chamber. The dopant vaporization unit includes a dopant chamber for holding solid-phase dopant. The dopant vaporization unit includes a heating device for heating the solid-phase dopant and for producing a dopant gas. The dopant vaporization unit includes an outlet through which the dopant gas passes. The outlet is in fluid communication with the dopant conduit. 
     Various refinements exist of the features noted in relation to the above-mentioned aspects of the present disclosure. Further features may also be incorporated in the above-mentioned aspects of the present disclosure as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to any of the illustrated embodiments of the present disclosure may be incorporated into any of the above-described aspects of the present disclosure, alone or in any combination. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic of an example method for growing a silicon ingot with boric acid as the source of dopant; 
         FIG.  2    is a partial cross-section side view of an embodiment of an ingot puller apparatus having a dopant receptacle in a dopant loading position; 
         FIG.  3    is a partial cross-section side view of the ingot puller apparatus with the dopant receptacle in a dopant feed position; 
         FIG.  4    is a detailed cross-section side view of the ingot puller apparatus with the dopant receptacle in the dopant feed position; 
         FIG.  5    is a side view of an elongate member that includes a dopant receptacle for holding solid-phase dopant and a translation unit for moving the elongate member; 
         FIG.  6    is a side view of the translation unit; 
         FIG.  7    is a cross-section side view of the joint between the elongate member and the translation unit; 
         FIG.  8    is a perspective cross-section view of the elongate member within an outer tube with the receptacle in the dopant loading position; 
         FIG.  9    is a cross-section side view of the receptacle; 
         FIG.  10    is a cross-section side view of another embodiment of an ingot puller apparatus; 
         FIG.  11    is a cross-section side view of a vaporization unit of the ingot puller apparatus; 
         FIG.  12    is perspective view of the vaporization unit; and 
         FIG.  13    is a detailed cross-section side view of the vaporization unit. 
     
    
    
     Corresponding reference characters indicate corresponding parts throughout the drawings. 
     DETAILED DESCRIPTION 
     Provisions of the present disclosure relate to methods for doping a silicon melt (e.g., counter-doping) that involve boric acid. Additional provisions relate to ingot puller apparatus configured to dope a silicon melt and, in particular, to dope using a solid-phase dopant such as boric acid. 
     Methods for Doping using Boric Acid 
     An example method of the present disclosure is shown in  FIG.  1   . The method may be carried out by use of an ingot puller apparatus that is configured to produce a boron-containing gas from solid-phase boric acid. Example ingot puller apparatus that may be used in accordance with the methods for doping with boric acid are shown in  FIGS.  2 - 13   . While the method may be described with reference to the ingot puller apparatus  100  shown in  FIGS.  2 - 9    or the ingot puller apparatus  400  shown in  FIGS.  10 - 13    to exemplify the method, the method should not be limited to the ingot puller apparatus  100 ,  400  unless stated otherwise. 
     With reference to  FIG.  2   , in accordance with embodiments of the method for preparing a silicon ingot, a silicon melt is prepared in a crucible  104  disposed within the inner chamber  102  of an ingot puller apparatus  100 . The crucible  104  may be supported by a susceptor (not shown). The ingot puller apparatus  100  may be configured to rotate the crucible  104  and/or move the crucible  104  vertically within the ingot puller apparatus  100 . 
     To prepare the silicon melt, polycrystalline silicon is added to the crucible  104 . The polycrystalline silicon is heated to above the melting temperature of silicon (about 1414° C.) to cause the polycrystalline silicon to liquefy into a silicon melt  108 . A heating system is operated to melt-down the polycrystalline silicon. For example, one or more heaters below or to the side of the crucible  104  are operated to melt-down the silicon. 
     Before or after the melt  108  is produced, the melt may be doped with a dopant, typically an n-type dopant, to compensate for p-type impurities (e.g., boron) in the melt. The n-type dopant may be added before growth of the ingot  112  commences. By compensating the melt, the resistivity of the resulting ingot  112  may be increased. For example, the seed end of the ingot (i.e., the portion of the ingot nearest the ingot crown) may have a resistivity of at least about 1,500Ω-cm or, as in other embodiments, at least about 2,000Ω-cm, at least about 4,000Ω-cm, at least about 6,000Ω-cm, at least about 8,000Ω-cm, at least about 10,000Ω-cm or from about 1,500Ω-cm to about 50,000 ohm-cm or from about 8,000Ω-cm to about 50,000Ω-cm. Suitable n-type dopants include phosphorous and arsenic. 
     Once the melt  108  is prepared, a single crystal silicon ingot  112  is pulled from the melt  108 . A seed crystal  118  is secured to a seed chuck  114 . The seed chuck  114  and crystal  118  are lowered until the seed crystal  118  contacts the surface of the silicon melt  108 . Once the seed crystal  118  begins to melt, a pulling mechanism slowly raises the seed crystal  118  up to grow the monocrystalline ingot  112 . 
     A process gas (e.g., argon) is caused to circulate through the inner chamber  102  of the ingot puller apparatus  100 . The process gas creates an atmosphere within the chamber  102 . 
     As shown in  FIG.  1   , embodiments of methods of the present disclosure include providing a source of solid-phase boric acid (H 3 BO 3 ). The boric acid may be relatively pure such as about 99% pure or more, 99.9% pure or more, or 99.99% pure or more. In some embodiments, the boric acid may be relatively isotopically pure (i.e., boron-11). For example, boric acid may be provided within the inner chamber  102  of the ingot puller apparatus  100  (i.e., within the housing  116 ) such as in the receptacle  156  ( FIG.  4   ) of the ingot puller apparatus  100  of  FIGS.  2 - 9   . Alternatively, the solid-phase boric acid may be disposed exterior to the ingot puller outer housing  416  such as within the dopant chamber  424  of the vaporization unit  414  of the ingot puller apparatus  400  of  FIGS.  10 - 13   . 
     A boron-containing gas is produced from the solid-phase boric acid. The gas that is produced is generally in the form of boric acid (H 3 BO 3 ) or derivatives thereof (B x O y H z   +  complexes) and not other compounds (e.g., diborane (B 2 H 6 ) or boron dihydride (BH 2 )). However, it should be understood that other boron compounds may be added to the boron-containing gas. 
     The solid-phase boric acid may be heated to above its melting temperature (about 171° C.) to liquefy the solid-phase boric acid and to produce a boric acid liquid. The boric acid liquid is then heated above its vaporization temperature (about 300° C.) to produce a boron-containing gas. For example, the solid-phase boric acid may be heated by heat radiated from the silicon melt  108  in the ingot puller apparatus of  FIGS.  2 - 9    or by a heating device  428  ( FIG.  12   ) of the vaporization unit  414  of the ingot puller apparatus of  FIGS.  10 - 13   . 
     Once the boron-containing gas is produced, the boron-containing gas contacts the surface of the melt  108  to allow boron to diffuse into the melt. For example, the flow path of the boron-containing gas in the exit tube  168  ( FIG.  4   ) may be restricted such that the boron-containing gas may only move through the tube outlet  170  as in the ingot puller apparatus  100  of  FIGS.  2 - 9    or the boron-containing gas may be carried by a process gas as in the ingot puller apparatus  400  of  FIGS.  10 - 13   . 
     Once boron enters the melt, boron compensates for phosphorous which has concentrated in the melt due to the relatively low segregation coefficient of phosphorous, thereby increasing the resistivity of the remaining portion of the ingot  112  that forms in the ingot puller apparatus. 
     Ingot Puller Apparatus for Doping by use of Solid Dopants 
     An example ingot puller apparatus  100  is generally shown in  FIGS.  2 - 9    and another example ingot puller apparatus  400  is shown in  FIGS.  10 - 13   . The apparatus  100  of  FIGS.  2 - 9    and the apparatus  400  of  FIGS.  10 - 13    may be used to dope the ingot with boron using solid-phase boric acid as in the method described above or may be used with other solid-phase dopants that may be vaporized below the melting point of silicon (about 1414° C.) in either the native form, or a hydrated form, or in a compound that is non-contaminating to the crystal growth process (e.g., doped glass with a relatively high concentration of B 2 O 3  intermixed with SiO 2  or a heavily doped Si—B alloy). 
     Referring now to  FIG.  2   , the ingot puller apparatus  100  includes an ingot puller outer housing  116  that defines an ingot puller inner chamber  102  within the housing  116 . A crucible  104  is disposed within the ingot puller inner chamber  102 . The crucible  104  contains the silicon melt  108  from which the silicon ingot  112  is pulled. The ingot  112  is shrouded by a heat shield  120 . 
     The ingot puller apparatus  100  includes a dopant feed system  126 . The dopant feed system  126  includes an outer feed tube  130  that is at least partially disposed exterior to the ingot puller housing  116 . The outer feed tube  130  defines an outer feed tube chamber  136  therein. The outer tube  130  has a distal end  140  furthest from the outer housing  116  and a proximal end  144  nearest the housing  116 . An outer feed tube axis A 130  extends through the distal end  140  and the proximal end  144  of the outer feed tube  130 . The outer feed tube  130  may be made of stainless steel or other suitable materials. 
     An elongate member  150  is moveable within the outer feed tube  130  along the outer feed tube axis A 130 . The elongate member  150  may be lowered into the ingot puller inner chamber  102  as shown in  FIG.  4   . In the illustrated embodiment, the elongate member  150  is a tube. In other embodiments, a rod or shaft may be used. The elongate member  150  may be made of any material that withstands the environment within the ingot puller chamber  102  such as quartz. 
     A dopant receptacle  156  is coupled to the elongate member  150  ( FIG.  4   ) (e.g., nested within it). As shown in  FIG.  8   , the receptacle  156  may abut a ledge  160  of the elongate member  150 . The receptacle  156  may include a shoulder  162  ( FIG.  9   ) that is seated on the ledge  160 . By moving the elongate member  150 , the dopant receptacle  156  moves between a raised position ( FIG.  2   , which may also be referred to as a “dopant loading position”) in which the dopant receptacle  156  is disposed exterior to the ingot puller outer housing  116  and a lowered position ( FIGS.  3  and  4   , which may also be referred to as a “dopant feed position”) in which the receptacle  156  is disposed within the ingot puller inner chamber  102  near the surface of the melt  108 . The heat shield  120  may include a channel  124  ( FIG.  2   ) formed therein to provide a pathway for the elongate member  150  and dopant receptacle  156  coupled thereto to approach the melt  108 . 
     The receptacle  156  may be separable from the elongate member  150 . The elongate member  150  includes a notch  164  ( FIG.  5   ) that enables access to the receptacle  156 . In the loading position ( FIG.  2   ), the receptacle  156  may be removed from the elongate member  150  to charge it with dopant. The notch  164  is aligned with an access port  166  when the receptacle  156  is in the loading position to allow access to the receptacle  156 . The receptacle  156  may be grasped by a connecting loop  172  of the receptacle  156  to pull the receptacle  156  through the notch  164  and access port  166 . In other configurations, dopant may be added to the receptacle  156  when the receptacle  156  is disposed in the elongate member  150 . 
     In the feed position of the receptacle ( FIGS.  3  and  4   ), a dopant gas is produced from the solid-phase dopant. The dopant gas travels down an exit tube  168  and through an outlet  170  where it is directed to the surface of the melt  108 . 
     In the illustrated embodiment, the receptacle  156  is a capsule  158  ( FIG.  9   ) that holds the solid-phase dopant. The capsule  158  includes an outer capsule housing  180 . A weir  182  is disposed within the outer capsule housing  180 . The weir  182  forms a channel  184  therein. The weir  182  has an upper end  188  and a lower end  190  that are each open such that gas may pass through the channel  184 . An annular chamber  194  is disposed between the weir  182  and the outer capsule housing  180 . Solid dopant  174  (e.g., boric acid) is disposed within the annular chamber  194  and rests on the capsule floor. When the receptacle  156  is in its lowered position ( FIGS.  3  and  4   ), the solid-phase dopant  174  heats which causes the dopant to either sublime or to melt and evaporate. The dopant gas rises in the annular chamber  194  and enters the weir channel  184  through the upper end  188  of the weir  182 . The gas continues to pass down through the channel  184  and exits through the open lower end  190  of the weir  182 . The dopant gas proceeds through the exit tube  168  ( FIG.  4   ), through the tube outlet  170  and toward the surface of the melt. 
     The elongate member  150  includes a gas barrier wall  240  ( FIG.  8   ) which prevents gas from back-flowing up the elongate member  150 . Alternatively, the elongate member may be a rod or shaft which does not include a pathway for gas to back-flow. 
     Referring now to  FIG.  4   , the ingot puller apparatus  100  includes an isolation valve  200  within the outer feed tube  130 . The isolation valve  200  seals the ingot puller inner chamber  102  when the elongate member  150  is withdrawn from the ingot puller inner chamber  102 . This allows the dopant receptacle  156  to be accessed through the access port  166  while the port  156  is isolated from the inner chamber  102 . When the elongate member  150  is lowered, the access port  166  may be closed or connected to a source of process gas (e.g., argon). The isolation valve  200  is connected to a valve controller  202  which actuates the valve  200 . 
     The ingot puller apparatus  100  includes a translation device  208  ( FIG.  2   ) for moving the dopant receptacle  156  between the dopant loading position ( FIG.  2   ) and the dopant feed position ( FIGS.  3  and  4   ). The translation device  208  moves the elongate member  150  and dopant receptacle  156  in and out of the inner chamber  102  of the ingot puller apparatus  100  and within the outer feed tube chamber  136  (i.e., along outer feed tube axis A 130 ). Generally, any translation device  208  that allows the receptacle  156  to be moved between the dopant loading and dopant feed positions of the receptacle  156  may be used unless stated otherwise. 
     In the illustrated embodiment, the translation device  208  is a magnetically coupled through-wall translation unit. The translation device  208  includes an outer tube  212  and an inner member  214  that moves within the outer tube  212 . The inner member  214  is magnetically coupled to a translation device handle  216 . The outer tube  212  may be made of stainless steel (non-magnetic) or other suitable materials. The translation device handle  216  and inner member  214  may have magnets embedded therein to enable magnetic coupling between the handle  216  and inner member  214 . 
     The inner member  214  is also connected to the elongate member  150  at a joint  220  ( FIG.  7   ). The example joint  220  includes a threaded member  224  that engages threads on a sleeve  218  that surrounds and is pinned to a lower portion of the inner member  214 . The joint  220  includes first and second o-rings  228 ,  232  and a bushing  236  disposed between the o-rings  228 ,  232 . The threaded member  224  compresses the o-rings  228 ,  232  causing them to move radially outward to facilitate a frictional connection between the translation device inner member  214  and the elongate member  150 . 
     The handle  216  of the translation device  208  may be moved up and down along axis A 130  ( FIG.  2   ). As the handle  216  moves, the inner member  214  moves within the outer tube  212 . Because the inner member  214  is coupled to the elongate member  150 , the elongate member  150  and receptacle  256  are caused to move in and out of the inner chamber  102  of the ingot puller apparatus  100 . In some embodiments, when the receptacle  156  is in a lowered position for feeding dopant, the distance between the receptacle  156  and the melt  108  may be changed (e.g., by an operator) to vary the heat applied to the receptacle  156  and solid-phase dopant therein to control the rate at which dopant gas is produced. In other embodiments, the receptacle  156  may be moved between its loading position ( FIG.  2   ) and the dopant feed position ( FIGS.  3  and  4   ) by an actuator rather than manually. 
     As noted above, the translation device  208  may have other configurations. Other example translation devices may include a bellows system or an externally operated linear translation device (e.g., a rod attached to either an externally isolated linear rail or pneumatic cylinder). Any external actuator should be isolated from the heat and vacuum inside the inner chamber  102 . 
     Another example ingot puller apparatus  400  is shown in  FIGS.  10 - 11   . The ingot puller apparatus  400  may operate similar to the ingot puller apparatus  100  described above and the operation of the apparatus  100  should be considered to be applicable to apparatus  400  (i.e., in aspects not related to use of the solid-phase dopant). For example, the ingot puller apparatus  400  includes an outer housing  416  that forms an inner chamber  402  within the housing  416 . A crucible  404  for holding a silicon melt  408  therein is disposed in the chamber  402 . The apparatus  400  includes a heat shield (not shown) that shrouds the ingot that is pulled from the melt. 
     The ingot puller apparatus  400  includes a dopant vaporization unit  414  that feeds doped gas to a dopant conduit  430 . The doped gas passes through the dopant conduit  430  to contact the melt  408  to cause the melt  408  to be doped. The dopant conduit  430  includes a gas inlet  422  ( FIG.  11   ) disposed exterior to the ingot puller chamber  402  and a gas outlet  426  disposed in the ingot puller inner chamber  402  and positioned relatively near the surface of the melt  408 . 
     The dopant vaporization unit  414  is disposed exterior to the ingot puller inner chamber  402 . The dopant vaporization unit  414  includes a dopant chamber  424  ( FIG.  13   ) for holding the solid-phase dopant (e.g., boric acid as discussed in the method above). A process gas (e.g., argon) may be circulated through the vaporization unit  414  through first and second process gas inlets  436 ,  440 . A doped gas outlet  452  of the vaporization unit  414  is in fluid communication with the dopant conduit  430  ( FIG.  11   ) to move doped gas to the surface of the melt  408 . 
     Surrounding the dopant chamber  424  is a heating chamber  472  ( FIG.  13   ). A heating device  428  (e.g., resistive heating element) heats gases circulating in the vaporization unit  414 . The heated gases contact the solid-phase dopant in the dopant chamber  242  causing a dopant gas to be produced (e.g., through sublimation or by liquefaction and vaporization of the solid-phase dopant). The dopant gas is picked up the process gas to produce a doped process gas that is discharged through the doped gas outlet  452  and into the dopant conduit  430  ( FIG.  11   ). The vaporization unit  414  includes a thermal shield  476  to reduce heat lost through the walls of the heating chamber  472 . The heating chamber  472  may be made of quartz to reduce contamination. 
     An isolation valve  460  is within the process gas pathway downstream of the heating chamber  472  and dopant chamber  424 . The isolation valve  460  isolates the vaporization unit  414  from the inner chamber  402  of the ingot puller apparatus  400  to seal the chamber  402  when dopant is not being added to the melt  408 . A valve controller  464  may be used to actuate the valve  460 . 
     The vaporization unit  414  includes a temperature sensor  448  ( FIG.  12   ) to measure the temperature of the heating chamber  472  ( FIG.  13   ). The temperature sensor  448  may send a signal to a control unit to vary the output of the heating device  428  based on the sensed temperature. The vaporization unit  414  includes a vacuum port  456  for pump-down, leak testing and to equalize the pressure with the ingot puller apparatus inner chamber  402  prior to opening isolation valve  460  for doping. 
     Compared to conventional methods for producing a single crystal silicon ingot from a silicon melt, the methods of embodiments of the present disclosure have several advantages. In embodiments in which the melt is counter-doped by using boric acid, a larger portion of the ingot may be within customer specifications (e.g., high resistivity) and/or a type-change in the ingot may be prevented. Solid-phase boric acid has a relatively low melting and vaporization temperatures which allows a dopant gas to be produced with relative ease. 
     Compared to conventional ingot puller apparatus, the ingot puller apparatus of embodiments of the present disclosure have several advantages. In embodiments in which a dopant receptacle is used to hold solid dopant, the receptacle may be placed in relative proximity to the melt surface which allows the heat of the melt to melt and vaporize the dopant. Positioning the receptacle near the melt also reduces or prevents the formation of precipitation or condensation of elemental boron or boron compounds that result in loss of crystal structure or integrity. Use of a dopant receptacle that includes a weir allows dopant particles to move within the receptacle without being propelled out of the receptacle and into the melt. Entry of dopant particles directly into the melt may cause loss of zero dislocation in the ingot. Use of an isolation valve allows the inner chamber of the ingot puller to be isolated from the solid-phase dopant system which prevents contamination of the melt and enables reloading of solid-phase dopant. Use of a magnetically coupled through-wall translation unit simplifies sealing and allows the system to be more robust (e.g., no separate seals) to maintain a gas-tight environment. 
     In embodiments in which the solid-phase dopant is converted to a gas by a vaporization unit exterior to the ingot puller housing, a heating device may be used to heat the dopant which allows for improved control of the rate at which dopant is added to the melt. The rate at which process gas is circulated through the vaporization unit may also be used to control the rate at which the melt is doped. In embodiments in which a feed tube or conduit is moveable within the ingot puller apparatus, the distance from the melt may be controlled which allows the rate of dopant addition to the melt to be controlled. 
     As used herein, the terms “about,” “substantially,” “essentially” and “approximately” when used in conjunction with ranges of dimensions, concentrations, temperatures or other physical or chemical properties or characteristics is meant to cover variations that may exist in the upper and/or lower limits of the ranges of the properties or characteristics, including, for example, variations resulting from rounding, measurement methodology or other statistical variation. 
     When introducing elements of the present disclosure or the embodiment(s) thereof, the articles “a”, “an”, “the” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” “containing” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. The use of terms indicating a particular orientation (e.g., “top”, “bottom”, “side”, etc.) is for convenience of description and does not require any particular orientation of the item described. 
     As various changes could be made in the above constructions and methods without departing from the scope of the disclosure, it is intended that all matter contained in the above description and shown in the accompanying drawing[s] shall be interpreted as illustrative and not in a limiting sense.