Micro mechanical anchor for 3D architecture

Components and methods of making the same are disclosed herein. In one embodiment, a method of forming a component comprises forming metal anchoring elements at a first surface of a support element having first and second oppositely facing surfaces, the support element having a thickness extending in a first direction between the first and second surfaces, wherein each anchoring element has a downwardly facing overhang surface; and then forming posts having first ends proximate the first surface and second ends disposed above the respective first ends and above the first surface, wherein a laterally extending portion of each post contacts at least a first area of the overhang surface of the respective anchoring element and extends downwardly therefrom, and the overhang surface of the anchoring element resists axial and shear forces applied to the posts at positions above the anchoring elements.

FIELD OF THE INVENTION

The present application describes structures such as that which can be incorporated into a microelectronic assembly which may include an unpackaged semiconductor die or packaged semiconductor die, as well as methods for making such structures.

BACKGROUND OF THE INVENTION

Microelectronic devices such as semiconductor chips typically require many input and output connections to other electronic components. The input and output contacts of a semiconductor chip or other comparable device are generally disposed in grid-like patterns that substantially cover a surface of the device (commonly referred to as an “area array”) or in elongated rows which may extend parallel to and adjacent each edge of the device's front surface, or in the center of the front surface. Typically, devices such as chips must be physically mounted on a substrate such as a printed circuit board, and the contacts of the device must be electrically connected to electrically conductive features of the circuit board.

Semiconductor chips are commonly provided in packages that facilitate handling of the chip during manufacture and during mounting of the chip on an external substrate such as a circuit board or other circuit panel. For example, many semiconductor chips are provided in packages suitable for surface mounting. Numerous packages of this general type have been proposed for various applications. Most commonly, such packages include a dielectric element, commonly referred to as a “chip carrier” with terminals formed as plated or etched metallic structures on the dielectric. These terminals typically are connected to the contacts of the chip itself by features such as thin traces extending along the chip carrier itself and by fine leads or wires extending between the contacts of the chip and the terminals or traces. In a surface mounting operation, the package is placed onto a circuit board so that each terminal on the package is aligned with a corresponding contact pad on the circuit board. Solder or other bonding material is provided between the terminals and the contact pads. The package can be permanently bonded in place by heating the assembly so as to melt or “reflow” the solder or otherwise activate the bonding material.

Many packages include solder masses in the form of solder balls, typically between about 0.005 mm and about 0.8 mm in diameter, attached to the terminals of the package. A package having an array of solder balls projecting from its bottom surface is commonly referred to as a ball grid array or “BGA” package. Other packages, referred to as land grid array or “LGA” packages have thin layers or lands, which fit into a socket or are secured to the substrate by solder. Packages of this type can be quite compact. Certain packages, commonly referred to as “chip scale packages,” occupy an area of the circuit panel equal to, or only slightly larger than, the area of the device incorporated in the package. This is advantageous in that it reduces the overall size of the assembly and permits the use of short interconnections between various devices on the circuit panel, which in turn limits signal propagation time between devices and thus facilitates operation of the assembly at high speeds.

An interposer can be provided as an interconnection element having contacts and top and bottom surfaces thereof electrically connected with one or more packaged or unpackaged semiconductor dies at one of the top or bottom surface thereof, and electrically connected with another component at the other one of the top or bottom surfaces. The other component may in some cases be a package substrate which in turn may be electrically connected with another component which may be or may include a circuit panel.

Despite all of the above-described advances in the art, still further improvements in microelectronics assemblies, the individual components thereof, such as interposers and microelectronics elements, and methods of making the same would be desirable.

BRIEF SUMMARY OF THE INVENTION

Components and methods of making the same are disclosed herein. In one embodiment, a method of forming a component comprises forming metal anchoring elements at a first surface of a support element having first and second oppositely facing surfaces. The support element can have a thickness extending in a first direction between the first and second surfaces. Each anchoring element can have a downwardly facing overhang surface. The method includes then forming posts having first ends proximate the first surface and second ends disposed above the respective first ends and above the first surface. A laterally extending portion of each post contacts at least a first area of the overhang surface of the respective anchoring element and extends downwardly therefrom. The overhang surface of the anchoring element resists axial and shear forces applied to the posts at positions above the anchoring elements.

In one embodiment, the anchoring elements further comprise metal elements that are supported by structures extending towards the second surface, each metal element having an upper surface facing away from the first surface and a lower surface remote from the upper surface, wherein a portion of the lower surface, which extends beyond the structure, defines the overhang surface.

In one embodiment, the structure is associated with at least a portion of the support element.

In one embodiment, the posts extend more than 50 micrometers above the metal elements.

In one embodiment, the posts extend between 50 and 500 micrometers above the metal elements.

In one embodiment, the posts have heights and widths, the heights being 1.5 times the respective widths.

In one embodiment, the posts include polymer elements having electrically conductive coatings at exterior surfaces thereof.

In one embodiment, forming the posts further comprises injecting polymer materials into a molding overlying the anchoring elements to form the posts.

In one embodiment, the metal element defines an opening and the structure at least partially defines a cavity aligned with the opening, and the overhang surface extends beyond a wall of the cavity.

In one embodiment, the overhang surface extends beyond a periphery of the structure.

In one embodiment, forming the anchoring elements further comprises forming the metal elements overlying the structure; and undercutting material of the structures to form the overhang surfaces of the metal elements.

In one embodiment, forming the anchoring elements further comprises patterning openings in the metal elements, wherein the undercutting of the material of the structures is formed by processing applied through the openings.

In one embodiment, patterning openings in the metal elements further comprises forming photoresist layers overlying portions of upper surfaces of the structures; forming the metal elements overlying remaining portions of the upper surfaces of the structures; and removing the photoresist layers to expose the openings in the metal elements.

In one embodiment, a method of forming a component comprises forming metal anchoring elements at a first surface of a support element having first and second oppositely facing surfaces. The support element can have a thickness extending in a first direction between the first and second surfaces. Each anchoring element can have one or more recesses extending towards the second surface of the support element. The method includes then forming posts having first ends proximate the first surface and second ends disposed above the respective first ends and above the first surface. An axially extending portion of each post contacts at least a portion of the one or more cavities of the respective anchoring element and extends downwardly therefrom. The one or more cavities of the anchoring element resists axial and shear forces applied to the posts at positions above the anchoring elements.

In one embodiment, a component comprises a support element having first and second oppositely facing surfaces and having a thickness extending in a first direction between the first and second surfaces, metal anchoring elements at the first surface, each anchoring element having an overhang surface extending in a direction along the first surface, the overhang surface facing toward the second surface; and posts having first ends proximate the first surface and second ends disposed above the respective first ends and above the first surface, wherein a laterally extending portion of each post contacts at least a first area of the overhang surface of the respective anchoring element and extends downwardly therefrom, and the overhang surface of the anchoring element resists axial and shear forces applied to the post above the anchoring elements.

In one embodiment, at least some anchoring elements further comprise metal elements that are supported by structure extending towards the second surface, each metal element having an upper surface facing away from the first surface and a lower surface remote from the upper surface, wherein a portion of the lower surface, which extends beyond the structure, defines the overhang surface.

In one embodiment, the metal element defines an opening and the structure at least partially defines a cavity aligned with the opening, and the overhang surface extends beyond a wall of the cavity.

In one embodiment, the structure further comprises a second metal element overlying the first surface of the support structure, wherein the second metal element at least partially defines the cavity.

In one embodiment, the overhang surface extends beyond a periphery of the structure.

In one embodiment, the component further includes electrically conductive interconnects supported by the support element and extending in the first direction for electrically coupling conductive elements at the respective first and second surfaces, wherein the conductive posts contact at least some of the conductive interconnects.

In one embodiment, the posts extend more than 50 micrometers above the metal elements.

In one embodiment, the posts extend between 50 and 500 micrometers above the metal elements.

In one embodiment, the posts have heights and widths, the heights being at least about 1.5 times the respective widths.

In one embodiment, the posts include polymer elements having electrically conductive coatings at exterior surfaces thereof.

DETAILED DESCRIPTION

Embodiments in accordance with the present invention will be described in more detail below.

All ranges recited herein include the endpoints, including those that recite a range “between” two values. Terms such as “about,” “generally,” “substantially,” and the like are to be construed as modifying a term or value such that it is not an absolute, but does not read on the prior art. Such terms will be defined by the circumstances and the terms that they modify as those terms are understood by those of skill in the art. This includes, at very least, the degree of expected experimental error, technique error and instrument error for a given technique used to measure a value.

As used in this disclosure with reference to a component, a statement that an element, e.g., a conductive element, contact, metal post, terminal, structure, or other element, is “at” a surface of a component, e.g., microelectronic element, interposer, circuit panel, or other substrate, indicates that, when the component is not assembled with any other element, the element is available for contact with a theoretical point moving in a direction perpendicular to the surface of the component toward the surface of the component from outside the component. Thus, an element which is at a surface of a component may project from such surface; may be flush with such surface; or may be recessed relative to such surface in a hole or depression in the component.

FIGS. 1-1 through 1-5depict components in accordance with some embodiments of the invention. The various embodiments of the components disclosed herein may be utilized alone, or combination. The components described in accordance with the invention can advantageously facilitate a more robust structure supported by anchoring elements. The anchoring elements can further facilitate improved fabrication of the components in some aspects.

FIG. 1-1depicts a side schematic view of a component100in accordance with some embodiments of the invention. The component100includes a support element102having a first surface104and a second oppositely facing surface106. The support element102has a thickness108extending in a first direction110between the first and second surfaces104,106. The support element102can consist essentially of one or more of a dielectric material, semiconductor material, or electrically conductive material. In one embodiment, the support element102consists essentially of a dielectric material.

The component100includes a metal anchoring element112at the first surface104of the support element102. In some aspects of the present invention, the anchoring element112has an overhang surface114extending in a direction along the first surface104of the support element102. The overhang surface114faces toward the second surface106of the support element.

FIG. 1-1depicts the anchoring element112according to one aspect of the present invention. The anchoring element includes a metal element116that is supported by a structure118extending towards the second surface106of the support element102. In one example, the structure118includes a second metal element120overlying the first surface104of the support structure102. The second metal element120can have a thickness extending in the first direction110from a lower surface119, which is adjacent to the first surface104of the support element102, to an upper surface121. The second metal element120at least partially defines a cavity122of the anchoring element112.

The metal element116includes an upper surface124facing away from the first surface104of the support element104and an oppositely facing lower surface126. The lower surface126of the metal element defines the overhang surface114. The overhang surface114is defined by an area of the lower surface126of the metal element116that extends beyond the structure. In one example, the metal element116overlies the second metal element120as depicted inFIG. 1-1. The metal element116defines an opening128. The opening128can be aligned with the cavity122, where the overhang surface114is defined as an area of the lower surface126of the metal element116that extends beyond a wall of the cavity122. The overhang surface114overlies and confronts a bottom surface130of the cavity122. In one exemplary embodiment depicted inFIG. 1-1, the cavity122has a rectangular cross section having vertical and horizontal surfaces. The cavity122can have any suitable cross section, such as having curved surfaces or the like. In one aspect, the cross section of the cavity122can be a cross section resultant from isotropic or anisotropic etching.

The component100includes posts132having first ends134proximate the first surface104of the support element102and second ends136disposed above the respective first ends134and above the first surface104. The posts132include a laterally extending portion138that contacts a first area of the overhang surface114of a respective anchoring element112and extends downwardly therefrom. In one example, the laterally extending portion138extends downward into the cavity122as depicted inFIG. 1-1and contacts the bottom surface130of the cavity122. Though illustrated as contacting the entirety of the overhang surface114, and the walls and bottom surface130of the cavity122, the laterally extending portion138may contact these surfaces only partially or not at all in some embodiments. The first end134and laterally extending portion138of the posts132can have any suitable shape, include those shapes that conform to the shape of the cavity122.

The overhang surface114and the anchoring elements112can resist axial and shear forces applied to the posts132above the anchoring elements112. In one example, when the laterally extending portion138of a respective post132contacts the bottom surface130of the cavity122, the bottom surface130can resist axial and shear forces applied to the posts132above the anchoring elements112.

The posts132can include electrically conducting materials. For example, the posts may be plated metal structures, polymer elements having electrically conductive coatings, solder posts, or metal posts comprising any suitable metal and formed by any suitable means. The posts132can extend more than about 50 microns above the metal elements116of the anchoring elements112. In one embodiment, the posts132can extend between about 50 microns to about 500 microns above the metal elements116. The posts132can have an aspect ratio, wherein the height of a respective post is about twice its width. In one embodiment, the height of a respective post may be about 2.5 to about 3 times its width. The pitch of the posts132can be less than the height of the posts132. In one example, the pitch in one or more directions parallel to the first surface104can be less than about 400 microns.

The component100can, optionally, include electrically conductive interconnects140. The interconnects140can be supported by the support element102and extending in the first direction110for electrically coupling conductive elements at, or adjacent to, the first and second surfaces104,106of the support element102. In one example, the posts132can be electrically coupled to at least some of the interconnects140at the first surface104. For example, as depicted inFIG. 1-1, the posts132can be electrically coupled to the interconnects140through the anchoring elements112. The anchoring elements112need not be directly coupled to and/or aligned with the interconnects140as depicted inFIG. 1-1. For example, the anchoring elements112may be coupled to the interconnects140by a trace that extends along the surface104and/or one or more of the interconnects may be omitted entirely. As disclosed herein, embodiments of any anchoring element can be optionally coupled to an interconnect140in any suitable configuration.

The component100can include terminals at the first and second surfaces104,106of the support structure102. The terminals can be used to connect the component100to other components of a microelectronic assembly. The terminals can be part of a redistribution structure, pin array, or the surfaces of the interconnects140. In one example, at least some of the terminals at the first surface104are the posts132. In one example, terminals142coupled to the interconnects140at the second surface106of the support element102are part of a redistribution structure143. The terminals142can contact the interconnects140, or be electrically coupled with the interconnects140through a trace144as depicted in top down view of the component100inFIG. 1-6.

The component100can be a component of a microelectronic assembly. Exemplary components100can include an interposer, a package substrate, a microelectronic element, a printed circuit board (PCB), other components, or any electronic substrate.FIG. 1-7depicts an exploded view of one exemplary microelectronic assembly160, where the component100is part of a vertically stacked structure. The component100can be electrically coupled to other components in a vertical arrangement by the posts132at a first side of the component100and by the terminals142at an opposing second side of the component100, respectively. For example, one or more first components162, such as microelectronic element, can be stacked adjacent to the second side of the component100and overlying the component100, and the component100in turn can be stacked at the first side thereof to overlie a circuit panel164, or another component, such as an interposer. In one example, the posts132may be inserted into corresponding sockets at a surface of the circuit panel164. Many vertical stacking arrangements and components are possible, and not limited to the exemplary embodiment depicted inFIG. 1-7.

FIG. 1-2depicts a side schematic view of an anchoring element150in accordance with some embodiments of the invention. The anchoring element150can include any embodiments and/or permutations as described for the anchoring element112, except where otherwise noted. In one embodiment of the invention, as shown for the anchoring element150, the overhang surface114extends beyond the periphery of the second metal element120. Further, the cavity122is absent from the anchoring element150. The overhang surface114overlies and confronts an area152of the first surface104, where the area152extends beyond the periphery of the second metal element120. The laterally extending portion138of a respective post132extends laterally inward towards the periphery of the second metal element120as depicted inFIG. 1-2. The laterally extending portion138contacts at least a first area of the overhang surface114and extends downward therefrom towards the first surface104. In one example, the laterally extending portion138contacts the area152of the first surface104. The area152can resist axial and shear forces applied to the post114above the anchoring element150. Though depicted as contacting the entirety of the overhang surface114, periphery of the second metal element120and area152, the laterally extending portion138may contact these surfaces only partially or not at all in some embodiments.

FIG. 1-3depicts a side schematic view of an anchoring element154in accordance with some embodiments of the invention. The anchoring element154can include any embodiments and/or permutations as described for the anchoring element112, except where otherwise noted. In one embodiment of the invention, as shown for the anchoring element154, the anchoring element154includes the metal element116but not the second metal element120. As depicted inFIG. 1-3, the cavity112of the anchoring element154is formed in the first surface104of the support element102and extends towards the second surface106. The metal element116overlies the first surface104of the support element102and the overhang surface114extends inwardly beyond the walls of the cavity122. The metal element116defines the opening128and the cavity122is aligned with the opening128.

FIG. 1-4 through 1-5depict side and top down schematic views, respectively, of an anchoring element156in accordance with some embodiments of the invention. The anchoring element156can include any embodiments and/or permutations as described for the anchoring element112, except where otherwise noted. In one embodiment, as shown for the anchoring element156, the anchoring element156includes the second metal element120and not the metal element116. The second metal element120includes one or more cavities158formed therein. The one or more cavities158can be arranged in any arrangement suitable for the anchoring element156to resist axial and shear forces applied to a respective post114. One exemplary arrangement of the one or more cavities158is depicted in top down view inFIG. 1-5. The one or more cavities158can include any embodiments and/or permutations as described for the cavity122, except where otherwise noted. In one embodiment, the post132includes one or more axial extending portions159, where the one or more axially extending portions159contact at least a portion of the one or more cavities158and extend downwardly therefrom. The one or more cavities158resist axial and shear forces applied to the post114at positions above the anchoring element158.

FIG. 2depicts a flow chart of a method200for fabrication of the component100in accordance with some embodiments of the present invention. The method200is described below in accordance with the stages of fabrication of the component100having anchoring element112depicted inFIGS. 3-1 through 3-6, andFIGS. 4-1 through 4-5, having anchoring element150depicted inFIGS. 5-1 through 5-2, and having anchoring element154depicted inFIGS. 6-1 through 6-6. However, the method200may be applied to other embodiments of the present invention, or other components within the scope of the invention.

FIG. 3-1depicts stages in a method of fabricating the anchoring element112in accordance with some embodiments of the invention. At202, the anchoring element112is formed at the first surface104of the support element102. As depicted inFIG. 3-1, the component100includes the second metal element120overlying the first surface104of the support element102. In one aspect, the conductive interconnect140may be formed in the support element102prior to formation of the anchoring element112. The second metal element120can be deposited at the first surface104by any suitable process. The second metal element120can be formed by any suitable method. In one aspect, the second metal element120can be formed by plating a metal layer overlying the surface104, and then etching the plated metal layer to form the second metal element120. In another aspect, a patterned layer may be formed overlying the first surface104, and then the second metal elements120may be formed in the patterned layer by plating or another deposition process.

FIG. 3-2depicts a photoresist layer302formed overlying a portion of the upper surface121of the second metal element120. The photoresist layer302does not contact at least some of the edges of the upper surface121. In some aspects, the photoresist layer302may overlie the peripheral walls of the second metal element120. The metal layer116is formed overlying the remaining portions of the upper surface121of the second metal element120as depicted inFIG. 3-3. The photoresist layer302is removed to expose the opening128in the metal element116as depicted inFIG. 3-4. Material of the second metal element120is undercut to form the overhang surface114and the cavity122. In one aspect, the materials of the metal elements116,120are different. In one example, the metal element116includes nickel (Ni) and the second metal element120includes copper (Cu). Copper can be selectively etched relative to nickel to form the cavity122and the overhang surface114. Other exemplary materials that may be used for the metal elements116,120, respectively, include gold and copper, tin and copper, chrome and copper, nickel and gold, solder mask and copper, or dielectric material and copper.

In one aspect, when the photoresist302does not overlie the walls of the second metal element120, the walls of the second metal element120can be etched to form another overhang surface, similar to that in the anchoring element150. The additional overhang surface may also be contacted by a lateral extending portion of the post132, and may resist axial and shear forces applied to the post132above the anchoring element112.

At202, the posts132are formed in a manner anchored by the anchoring element112. The posts132may be formed in corresponding openings306of a mold304overlying anchoring elements112as depicted inFIG. 3-6. In one aspect, the post132may be formed by plating one or more metals into the opening306of the mold304. In another aspect, the post132may be formed by injecting a polymer material into the opening306in the mold304. The anchoring elements112may advantageously secure the posts132, once formed, against axial and shear forces caused by the removal of the mold. One or more plating or metal or metal-containing coatings may be applied to surfaces of the posts132after removing the mold, such as, but not limited to, when polymer elements are formed in the mold304.

FIGS. 4-1 through 4-5depict stages in a method of fabricating the anchoring element110in accordance with another aspect of the invention. As depicted inFIG. 4-1, the second metal element120is deposited overlying the first surface104of the support element102. Then, the metal element116is deposited overlying the upper surface121of the second metal element120.FIG. 4-2depicts a patterned photoresist layer402deposited overlying the upper surface124of the metal element116. In one aspect, the photoresist layer402may overlie the peripheral walls of the metal elements116,120as depicted inFIG. 4-2. The photoresist layer402includes an opening404overlying a portion of the upper surface124of the metal element116.FIG. 4-3depicts material removed from the metal element116underlying the opening404to form the opening128in the metal element116. Once the opening128is formed in the metal element116, material is removed from processes applied through the opening128to form the cavity122and overhang surface114as depicted inFIG. 4-5. The cavity122and overhang surface114can be formed by processes discussed above with regards toFIGS. 3-1 through 3-6. The photoresist layer402can be removed, and the posts132are formed as depicted inFIG. 4-5. Removal of the photoresist layer402and formation of the posts132can be accomplished by methods discussed above with regards toFIGS. 3-1 through 3-6.

FIGS. 5-1 through 5-2depict the stages in a method of fabricating the anchoring element150in accordance with another aspect of the invention. As depicted inFIG. 5-1, a structure is provided which includes the metal element116overlying the second metal element120, the structure at the first surface104. For example, the metal element116can be deposited on the upper surface121of the second metal element120. As depicted inFIG. 5-2, material is selectively removed from the peripheral walls of the second metal element120to form an overhang surface114of the metal element116, where the metal element116extends beyond the periphery of the second metal element120. In one aspect, the materials of the metal elements116,120are different. In one example, the metal element116includes nickel (Ni) and the second metal element120includes copper (Cu). Copper can be selective etched relative to nickel to form the overhang surface114as depicted inFIG. 5-2. The posts132can be formed such that the laterally extending portion128contacts at least a portion of the overhang surface114. Formation of the posts132can be accomplished by methods discussed above with regards toFIGS. 3-1 through 3-6.

FIGS. 6-1 through 6-5depict the stages in a method of fabricating the anchoring element154in accordance with another aspect of the invention.FIG. 6-1depicts metal element116overlying the first surface104of the support element102. Optionally, the metal element116may be overlying the conductive interconnect140in embodiments where the conductive interconnect140is present.

FIG. 6-2depicts a patterned photoresist layer602overlying the upper surface124of the metal element116. The patterned photoresist layer602includes an opening604overlying a portion of the upper surface124the metal element116. In one aspect, the portion of the metal element116is a non-peripheral edge portion of the upper surface124.FIG. 6-3depicts material removed from the metal element116underlying the opening604to form the opening128in the metal element116. Once the opening128is formed in the metal element116, material is removed from processes applied through the opening128to form the cavity122in the support element102and the overhang surface114as depicted inFIG. 6-4. The cavity122and overhang surface114can be formed by an etching process to remove materials from the support element102. In one aspect, when the conductive interconnect140is present, an etching solution or gas suitable for etching a metal or semiconductor material may be used to etch the cavity122at least partially in the conductive interconnect140. In another aspect, when the conductive interconnect140is not present, an etching solution or gas suitable for etching a dielectric material may be used to etch the cavity122. The posts132can be formed, and then the photoresist layer602can be removed as depicted inFIG. 6-5. Removal of the photoresist layer602and formation of the posts132can be accomplished by methods discussed above with regards toFIGS. 3-1 through 3-6.

FIGS. 7-1 through 7-2depict stage in a method of fabricating the anchoring element156in accordance with another aspect of the invention.FIG. 7-1depicts the second metal element120deposited overlying the first surface104of the support element102.FIG. 7-2depicts a patterned photoresist layer702deposited overlying the upper surface121of the second metal element120. The patterned photoresist layer702includes one or more openings704overlying one or more portions of the upper surface121of the second metal element120. Material is removed by processes applied through the openings704to form the one or more cavities158in the second metal element120. The photoresist layer702can be removed, and the posts132can be formed as depicted inFIG. 7-3. Removal of the photoresist layer702and formation of the posts132can be accomplished by methods discussed above with regards toFIGS. 3-1 through 3-6.

For example, the order in which particular steps in patterning one or more of metal layers shown to form the first or second metal elements116,120can be varied from the foregoing description. Thus, the processing described above relative toFIGS. 3-1 through 3-6can be carried out with respect to a continuous metal layer in place of second metal element120, and can be carried out with respect to a metal layer overlying such layer in place of metal element116as depicted inFIG. 3-3. Final patterning to define the extent, i.e, peripheral edges123of these elements can be postponed until later stages of the process, such as before or after forming posts132. Similar variations in the order of patterning metal layers can also be made to the methods described above with respect toFIGS. 4-1 through 4-5,FIGS. 6-1 through 6-5, andFIGS. 7-1 through 7-2.