Abstract:
Computer-implemented techniques for modeling the mechanical behavior of integrated circuits using layout-dependent material properties are disclosed. The back end of line wiring that connects an integrated circuit to a substrate undergoes stresses and strains due to many heating and cooling cycles during a chip&#39;s packaging and lifecycle. Depending on integrated circuit design style, there may be vastly different thermal profiles across the integrated circuit. The mechanical behavior caused by the thermal cycles of the wire, vias, and insulators comprising the BEOL materials is simulated. Extraction of the integrated circuit structural information, regarding the BEOL materials, yields anisotropic information. Layout-dependent material volume fractions are computed using integrated circuit structural information. Anisotropic mechanical properties are determined based on the structural information. Mechanical responses are calculated based on the anisotropic material properties and the calculated material-volume fractions.

Description:
FIELD OF ART 
       [0001]    This application relates generally to semiconductor design automation and more particularly to modeling mechanical behavior with layout-dependent material properties. 
       BACKGROUND 
       [0002]    Integrated circuits are ubiquitous in modern electronic devices and systems. These highly complex systems are typically manufactured through exceedingly complicated, multi-step processes which include photolithographic printing, chemical processing, and handling. Such modern systems contain a variety of circuits including digital, analog, and mixed-signal components which are difficult and expensive to manufacture. Feature sizes of the components now comprising such systems are routinely smaller than the wavelength of visible light. In addition, the rapidly changing demands of the various markets which consume the chips drive ever-increasing device count, performance, feature sets, system versatility, and a variety of other system demands which impose contradictory design requirements on the design process. System designers are required to make significant tradeoffs in their designs to balance system performance, physical size, architectural complexity, power consumption, heat dissipation, fabrication complexity, and cost, to name only a few. Each design decision exercises a profound influence on the resulting system design. 
         [0003]    A specification to which system designers design and test their electronic systems is the standard against which a system is compared. Therefore, the systems designers must ensure that their designs conform to the systems specification. The specification defines electrical performance, feature size, power consumption, heat dissipation, operating temperature range, temperature cycles, mechanical performance, and the like, and so on. 
       SUMMARY 
       [0004]    Techniques, used to improve computational efficiency and evaluation accuracy, are implemented to enhance simulation results for back end of line (BEOL) metal interconnects and vias in dielectric layers. An isotropic or “smear” material representation is replaced by layout-dependent anisotropic representation based on material properties and structural information. Each interconnect and via layer that makes up the BEOL stack is evaluated individually. Anisotropic and layout dependent average material properties for each layer and region of interest within a layer or design are obtained. These properties take into account layout specific information such as layer levels, metal line directions, and local pattern densities in order to enhance simulation accuracy. Average materials properties are computed directly by extracting layout and layer geometry information from layout information file formats such as ITF and GDS. A computer-implemented method for design analysis is disclosed comprising: obtaining a design and integrated circuit structural information for the design; extracting anisotropic information from the integrated circuit structural information; computing layout dependent material volume fractions using the integrated circuit structural information; determining anisotropic mechanical properties based on the anisotropic information; and calculating mechanical responses based on the anisotropic mechanical properties and the material volume fractions. 
         [0005]    The computing layout dependent material volume fractions may include computing a dependent material volume fraction for one layer. The one layer may include an interconnect layer, a via layer, or a region of interest. The design may include a plurality of layers. The design may be three dimensional. The structural information may be included in an interconnect technology file (ITF). The structural information may include one or more of vertical geometry information, material thickness, or layout dimensions. The structural information may include one or more of metallization thickness, metallization resistivity, dielectric thickness, dielectric permeability, metallization width, or metallization length. The layout dependent material volume fractions may be computed based on evaluation of three-dimensional structures. The material volume fractions may comprise an amount of metal included within a three-dimensional volume. The anisotropic mechanical properties may be determined using an averaging scheme. The averaging scheme may include serial averaging. The averaging scheme may include parallel averaging. The calculating of mechanical responses may be for a specified layer. The calculating mechanical responses may be for a plurality of layers. The calculating mechanical responses may be for a specified region. The method may further comprise determining critical parameters for the integrated circuit structural information. The critical parameters may include one or more of layer composition, volume, direction, or layer level. The method may further comprise determining volumes from coordinate and thickness information. The method may further comprise determining local material properties from the critical parameters and three-dimensional volumes. The design may include a semiconductor chip. The design may further include a package. The method may further comprise modeling mechanical interaction between the semiconductor chip and the package. The design may include through-silicon vias. The method may further comprise calculating mechanical responses for a plurality of interconnect layers or via layers where each layer is considered individually. The one or more of interconnect line directions, local pattern densities, or level of layers may be analyzed to determine anisotropic mechanical properties. The extracting anisotropic information may be based on information from technology files and design files. The calculating mechanical responses may be based on anisotropic material dependencies and layout dependent material properties. 
         [0006]    In embodiments, a computer system for design analysis comprises: a memory which stores instructions; one or more processors coupled to the memory wherein the one or more processors are configured to: obtain a design and integrated circuit structural information for the design; extract anisotropic information from the integrated circuit structural information; compute layout dependent material volume fractions using the integrated circuit structural information; determine anisotropic mechanical properties based on the anisotropic information; and calculate mechanical responses based on the anisotropic mechanical properties and the material volume fractions. In some embodiments, a computer program product embodied in a non-transitory computer readable medium for design analysis comprises: code for obtaining a design and integrated circuit structural information for the design; code for extracting anisotropic information from the integrated circuit structural information; code for computing layout dependent material volume fractions using the integrated circuit structural information; code for determining anisotropic mechanical properties based on the anisotropic information; and code for calculating mechanical responses based on the anisotropic mechanical properties and the material volume fractions. 
         [0007]    Various features, aspects, and advantages of various embodiments will become more apparent from the following further description. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    The following detailed description of certain embodiments may be understood by reference to the following figures wherein: 
           [0009]      FIG. 1  is a flow diagram for design information analysis. 
           [0010]      FIG. 2  is a flow diagram for calculating responses. 
           [0011]      FIG. 3  is a design automation flow for modeling mechanical response. 
           [0012]      FIG. 4  is an example chip and package profile. 
           [0013]      FIG. 5  is an example BEOL profile for a semiconductor ship. 
           [0014]      FIG. 6  shows an example region of interest. 
           [0015]      FIG. 7  is an example of layer analysis. 
           [0016]      FIG. 8  is a system diagram for mechanical modeling of BEOL structures. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]    Modern semiconductor systems are often composed of many circuits and circuit types contained on semiconductor chips. Semiconductor chips typically have a vast number of connections where the uppermost layer of the chip is often covered with input/output (I/O) pads. The chips that make up the system are mounted into packages using solder bumps. The solder bumps form connections between the I/O pads of the chip and the corresponding connections of the package. The solder bumps are surrounded by an underfill material which provides, among other things, a better mechanical connection between the chip and the package and improves chip reliability by environmentally sealing the chip connections. To make pad connections, the chip is typically inverted and then attached to the substrate. This inversion, called “flip chip” technology, is common in the semiconductor industry. The connections within a chip typically involve numerous layers of wires, vias, and contacts surrounded by dielectric or insulator layers. 
         [0018]    The chips making up the electronic systems operate by sourcing, sinking, and steering current to the various circuits and subcircuits that make up the chip. The many paths through the circuits and subcircuits of the chip are, among their other properties, resistive. Thus, heat results from current switching throughout the chip. This heating of the chip results even under normal operating conditions. In the case of high power chips, such heating may be extreme. Further, since some of the circuits and subcircuits of the chip are more active than others, there are regions of the chips that are relatively hotter than others. The thermal profiles of the chip, package substrate, and interconnection layers are not constant. The thermal coefficients of expansion of the chip, interconnecting layers of the BEOL, and package cause the chips and interconnecting layers to undergo stress. The mismatch between coefficients of thermal expansion also introduces residual stress during fabrication and package process steps. The metal wires, vias, and insulating underfill materials making up the layers between the chips and the substrate may be damaged, as may the physically delicate chip. 
         [0019]    Modeling the mechanical behavior of the connections between the solder bumps of a chip and the interconnecting layers of the BEOL involves a computationally complex and prohibitively expensive three-dimensional (3D) simulation problem. Attempts to simplify this simulation problem have traditionally included calculating the volume percent average for all of the interconnecting wires, vias, and insulating materials in the layers within a semiconductor chip to estimate an averaged volume “smear” of the materials. However, calculating the smear has proven an unreliable method of simplifying the simulation problem. For example, the smear does not take into account critical design parameters such as metal density variation from location to location, directional arrangements of metal interconnects from layer to layer, pattern characteristic changes, and metal changes from lower interconnect layers to upper interconnect layers. The computational simplicity of the smear masks critical potential design problems such as the uneven distribution of metalization or an unreliable structure with high stress. 
         [0020]    In the disclosed concept, efficient modeling of the BEOL mechanical behavior is supported by layout-dependent anisotropic material properties. Each interconnect and via layer that makes up the BEOL layers between the chip and the substrate is considered individually. Anisotropic and layout dependent average material properties for each layer and region of interest are obtained. These properties take into account metal line directions, local pattern densities, and layer levels. Average material properties are computed directly using geometry information extracted from process geometry files such as ITF and GDS files. The local material properties are obtained using serial, parallel, or a combination of serial and parallel averaging to obtain the local material properties for any specified layers or regions of interest. 
         [0021]      FIG. 1  is a flow diagram for design information analysis. A flow  100  for modeling mechanical behavior is described and comprises a computer-implemented method for design analysis. The flow  100  includes obtaining a design  110  and integrated circuit structural information for the design. The obtaining can include importing a design and supporting information or it can involve having the design and information already within a software tool. The obtaining can be part of an electronic design automation (EDA) process. The design may comprise various types of structural information describing critical features about the design. The structural information may include layer information including type of material, dimensions, and the like. The design may be three-dimensional, describing, for example, the connections between a chip and a substrate or package. In embodiments, the structural information is included in an interconnect technology file (ITF). The layout may be in the form of GDSII, OASIS™, or some other format for describing various shapes, sizes, and relationships of elements in a semiconductor layout. 
         [0022]    The flow  100  includes extracting anisotropic information  120  from the integrated circuit structural information. The extracted information may include details about the structure of the layers within a chip. The structural information may include one or more of vertical geometry information, material thickness, layout dimensions and the like. The extracting of anisotropic information may be based on the information from technology files and design files. The structural information may include one or more of metallization thickness, metallization resistivity, dielectric thickness, dielectric permeability, metallization width, or metallization length. The flow  100  may further comprise determining critical parameters  122  for the integrated circuit structural information. The critical information may be based on a layer or a collection of layers—for example, interconnect layers, vias, or dielectric materials. The critical information may include a variety of parameters including one or more of layer composition, volume, direction, or layer level. The critical parameters may be determined for each layer within the BEOL layers. 
         [0023]    The flow  100  may further comprise determining volumes  130  from coordinate and thickness information. The determined volumes will depend on the length, width, and height of a layer for a region of interest. Each layer can have a separate volume calculated as heights vary from layer to layer. The flow  100  includes computing layout dependent material volume fractions  140  using the integrated-circuit structural information and layout. Based on the determined volumes, the wiring and insulator within a layer can be analyzed to determine how much of the layer is metalization and how much is insulator. These amounts are used to compute the material volume fraction. The layout dependent material volume fractions may be computed based on evaluation of three-dimensional structures. The layout in a specific region impacts the fraction value and will vary from region to region and will also vary in different directions across a chip. Depending on the numbers of connections within a chip there may be a higher or lower concentration of wire and vias and therefore changes in the fraction values. The metalization on a chip often has a predominant direction for each layer. The direction of the metalization can impact the mechanical expansion in that direction due to the thermal coefficient for that metal. 
         [0024]    The computation of volume factions can be done based on averaging  142 . The averaging scheme may include serial averaging to obtain local material properties for any specified layers or regions of interest. When traversing a layer, the sequence of structures (i.e. metalization and insulator) can be evaluated and the average amount of the metallization present can be determined. The averaging scheme may include parallel averaging to obtain local material properties for layers or regions of interest. In some cases, a region can have a group of structures neighboring each other. When a region is traversed, the neighboring structures can be averaged in parallel to evaluate an overall average. When evaluating a vertical region with a stack, the vias and metalization can be averaged in parallel through the vertical region. 
         [0025]    The flow  100  includes determining anisotropic mechanical material properties  150  based on the anisotropic information. The mechanical properties may be determined for local material properties based on the critical parameters and volumes as well as the volume fractions for metallization. The mechanical material properties can be determined for an individual layer as opposed to multiple layers in a smear. Once mechanical material properties are determined for multiple layers individually, the mechanical material impact of the multiple layers can be evaluated. Various steps in the flow  100  may be changed in order, repeated, omitted, or the like without departing from the disclosed concepts. Various embodiments of the flow  100  may be included in a computer program product embodied in a non-transitory computer readable medium that includes code executable by one or more processors. 
         [0026]      FIG. 2  is a flow diagram for calculating responses. A flow  200  may continue from or be part of the previous flow  100 . The flow  200  includes determining anisotropic mechanical properties  210  based on the anisotropic information. Each interconnect and via layer of a BEOL stack may be evaluated individually. Anisotropic and layout dependent average material properties for each layer may be determined based on metal line direction of interconnect, pattern densities, layer levels, and the like. Local anisotropic mechanical properties may be determined. For example, anisotropic and layout-dependent average material properties for each region of interest may be determined based on the metal line direction of the interconnect, local pattern densities, layer levels, vias, and the like. A region of interest may be a stack of metalization layers and vias connecting the metallization layers. Therefore, the region could cover multiple layers with each layer being evaluated individually or the combination of layers being evaluated collectively to determine their mechanical properties. 
         [0027]    The flow  200  may further comprise modeling the mechanical interaction  220  between a semiconductor chip and a package. A flip-chip technology may utilize solder bumps and surrounding underfill material to attach a chip to a package. The anisotropic mechanical material properties can be used to model mechanical interactions between the chip and the package on which the chip is mounted. The BEOL on-chip wiring includes multiple layers of interconnect, vias, and dielectric material. The heating of the chip due to normal operation may cause stresses and strains among the semiconductor, BEOL, and the package. A model of the mechanical interaction between a semiconductor chip and a package may comprise a 3-D model of the BEOL layers. 
         [0028]    The flow  200  includes calculating mechanical responses  230  based on the anisotropic mechanical properties and the material volume fractions. Such calculating may evaluate 2-D and 3-D models of the layers of the BEOL materials between a chip and a package or substrate. The calculating may be based on layout-dependent material volume fractions and determined volumes. The calculating of mechanical responses  230  may be based on anisotropic material dependencies and layout dependent material properties. The calculating of mechanical responses may be for a specified region. The flow  200  may further comprise calculating mechanical responses  232  for a plurality of interconnect layers or via layers where each layer is considered individually. Various steps in the flow  200  may be changed in order, repeated, omitted, or the like without departing from the disclosed concepts. Various embodiments of the flow  200  may be included in a computer program product embodied in a non-transitory computer readable medium that includes code executable by one or more processors. 
         [0029]      FIG. 3  is a design automation flow for modeling mechanical response. A flow  300  may continue from or be a superset or a subset of the previous flow  100  or the previous flow  200 . The flow  300  includes selecting regions and/or layers of interest  310  for modeling from a mechanical perspective. The mechanical modeling can be very useful in evaluating the impact of thermal effects in producing stress and strain within a semiconductor chip or between a chip and its package. The layers can include any of the metallization wiring or via layers as well as the insulator layers. A region can be for a portion of one layer. A region can be for a portion of multiple layers, such as through a stack of wires and vias. The flow  300  includes determining layout dependent anisotropic mechanical properties  320 . For the region or layer of interest, directional mechanical properties can be determined. The directions can include those in x, y, and z directions along a chip. The flow  300  includes replacing original regions and layers with a homogeneous representation  330  or representations. By determining a volume for a layer and a fraction of that volume which includes metallization, the layer can be modeled with homogeneity rather than including all of the wires and insulators between the wires. The multiple layers can be combined so that what would have been previously modeled as a whole smeared material can now be modeled as separate homogeneous layers. The flow  300  includes modeling the smeared materials with layout dependent anisotropic mechanical properties  340 . The layers can be modeled separately and each layer can have its own directional dependence for mechanical behavior. The flow  300  can include computing mechanical responses  350  using the anisotropic mechanical properties. As temperature change on a semiconductor chip, the thermal impact on the BEOL metal and insulator can be evaluated to determine the mechanical behavior based on the thermal expansion. The mechanical response can be evaluated for the x, y, and z directions. Various steps in the flow  300  may be changed in order, repeated, omitted, or the like without departing from the disclosed concepts. Various embodiments of the flow  300  may be included in a computer program product embodied in a non-transitory computer readable medium that includes code executable by one or more processors. 
         [0030]      FIG. 4  is an example chip and package profile. The example profile  400  shows a chip  410  connected to a package  440 . The chip is inverted and connected by the various layers of the BEOL structure in region  420  to an array of solder bumps  432 . As the semiconductor chip  410  heats up, there can be mechanical stresses as a function of temperature. One direction&#39;s stress is illustrated by the arrow  412  where stress increases as the chip heats up further. The BEOL structure has previously been represented by a smear of the whole region. Using the disclosed concepts, the BEOL region  420  can be modeled anisotropically on a layer by layer basis. The interstitial space between the chip and the substrate which is not otherwise occupied by solder bumps can be filled with an underfill material  430 . The underfill material helps to attach the chip to the substrate and to hold and protect the chip. The solder bumps are in turn connected to a package  440 . The package may, in some cases, be part of a multichip module. In some cases the design may include through-silicon vias. 
         [0031]      FIG. 5  is an example BEOL profile  500  for a semiconductor ship. This profile  500  is a cross-section of a portion of a semiconductor BEOL region. Part of the semiconductor substrate  540  for the chip is shown. Beyond this substrate  540 , a first layer  542  including insulator in this region is shown as well as a second layer  544  with a mixture of metalization and insulator. A third layer  546 , in this case insulator is followed by a fourth layer  548  which is mostly metalization. A fifth layer  550  that is entirely insulator is shown followed by a sixth layer  552  and a seventh layer  554 , which is mostly insulator but includes a via  520  between metalization on the sixth layer  552  and the eighth layer  556 . The eighth layer  556  includes a wire  530  above which is the ninth layer  558 . Above these layers can be various structures including solder bumps. The structures shown in this example should be considered illustrative and not viewed as a limitation to the disclosed concepts. Layout-dependent material volume fractions may be computed for each layer. The material volume fractions may comprise an amount of metal included within a three-dimensional volume. One stress  512  direction is shown where increases in temperature would cause an increase in stress. Anisotropic analysis can be performed on a layer by layer basis to model the mechanical response. For example, wire  530  runs in the same direction as stress  512  and as the metal expands that makes up the wire  530 , the stress  512  may increase. 
         [0032]      FIG. 6  shows an example region of interest  600 . Multiple layers of an example region of interest  600  are shown. The layers may include an interconnect layer  610 , a via layer  620 , an interconnect layer  630 , and a via layer  640 . The layers of the region of interest may be used to compute layout-dependent material volume fractions. For example, layer  610  may comprise a dielectric portion  611 , a wire  612 , a dielectric portion  613 , a wire  614 , a dielectric portion  615 , a wire  616 , and a dielectric portion  617 . A layout-dependent material volume fraction may be computed for layer  610  using these structures. For layer  620 , a dielectric portion  622 , a via  624 , and a dielectric portion  626  may be examined to determine volumes. A layout-dependent material volume fraction may be computed for layer  620  using these structures. Similarly, for layer  630 , a dielectric portion  632 , a wire  634 , and a dielectric portion  636  may be examined to determine volumes. A layout-dependent material volume fraction may be computed for layer  630  using these structures. The layer  640  may be examined in the same manner with a dielectric portion  642 , a via  644 , and a dielectric portion  646  to determine volumes. A layout-dependent material volume fraction may be computed for layer  640  using these structures. The structures shown in this example region of interest  600  should be considered illustrative and not viewed as a limitation to the disclosed concepts. Based on volumes and fractions, mechanical analysis may be performed. The analysis may include calculating mechanical responses for a plurality of interconnect layers and via layers where each layer is considered individually. Other layout-dependent parameters and structural information may be considered for calculating mechanical responses based on interconnect. These parameters and information can be analyzed to determine anisotropic mechanical properties. Analysis may include determining volumes from coordinate and thickness information extracted from a design format file such as an ITF or GDSII file. Analysis may include determining local material properties from the critical parameters and three-dimensional volumes. A stress  650  direction is shown for the example profile. As the semiconductor heats up, thermal expansion can occur in the various layers based on the metalization contained within the layer. Layer  610  can have a stress  652  while layer  620  can have a stress  654 . Layer  630  can have a stress  656  while layer  640  can have a stress  658 . These stresses are shown in the direction of stress  650 . Similarly, directional stress can be modeled for direction  660  and/or direction  662 . 
         [0033]      FIG. 7  is an example of layer analysis. A group of layers  700  is shown similar to the region of interest  600  previously shown. A first layer  710  is shown similar to the layer  610 . The first layer  710  is a homogenous representation of the layer  610  where the homogeneous representation is based on the layout-dependent material volume fraction of layer  610 . A second layer  720  is shown similar to the layer  620 . The second layer  720  is a homogenous representation of the layer  620  where the homogeneous representation is based on the layout-dependent material volume fraction of layer  620 . A third layer  730  is shown similar to the layer  630 . The third layer  730  is a homogenous representation of the layer  630  where the homogeneous representation is based on the layout-dependent material volume fraction of layer  630 . A fourth layer  740  is shown similar to the layer  640 . The fourth layer  740  is a homogenous representation of the layer  640  where the homogeneous representation is based on the layout-dependent material volume fraction of layer  640 . A stress direction  750  is shown for the semiconductor. Layer  710  can have a stress  752  while layer  720  can have a stress  754 . Layer  730  can have a stress  756  while layer  740  can have a stress  758 . These stresses are shown in the direction of stress  750 . Similarly, other directions can be evaluated and modeled. The structures shown in this example group of layers  700  should be considered illustrative and not viewed as a limitation to the disclosed concepts. The layers may represent a BEOL arrangement and may comprise interconnect layers, via layers, and dielectric layers. 
         [0034]      FIG. 8  is a system diagram for mechanical modeling of BEOL structures. A system  800  for modeling such mechanical behavior with layout-dependent properties may include one or more processors  810  coupled to a memory  812  and a display  814 . The memory  812  can store code, mechanical analysis, thermal analysis, design data, instructions, system support data, intermediate data, analysis results and the like. The display  814  may be any electronic display, including but not limited to, a computer display, a laptop screen, a net-book screen, a tablet computer screen, a cell phone display, a mobile device display, a remote with a display, a television, a projector, or the like. 
         [0035]    The processors  810  may access a design repository  820 , use an extracting module  830  to extract materials properties, use a determining module  840  to determine layout-dependent material volume fractions and anisotropic mechanical properties based on anisotropic information, and use a calculating module  850  to calculate mechanical responses based on anisotropic mechanical properties and the volume fractions. In at least one embodiment, the one or more processors  810  may accomplish the functions of the extracting module  830 , the determining module  840 , and the calculating module  850 . 
         [0036]    The system  800  may include computer program product including code for obtaining a design and integrated circuit structural information for the design, code for extracting anisotropic information from the integrated circuit structural information, code for computing layout-dependent material volume fractions using the integrated circuit structural information, code for determining anisotropic mechanical properties based on the anisotropic information, and code for calculating mechanical responses based on the anisotropic mechanical properties and the material volume fractions, and the like. 
         [0037]    Each of the above methods may be executed on one or more processors on one or more computer systems. Embodiments may include various forms of distributed computing, client/server computing, and cloud based computing. Further, it will be understood that the depicted steps or boxes contained in this disclosure&#39;s flow charts are solely illustrative and explanatory. The steps may be modified, omitted, repeated, or re-ordered without departing from the scope of this disclosure. Further, each step may contain one or more sub-steps. While the foregoing drawings and description set forth functional aspects of the disclosed systems, no particular implementation or arrangement of software and/or hardware should be inferred from these descriptions unless explicitly stated or otherwise clear from the context. All such arrangements of software and/or hardware are intended to fall within the scope of this disclosure. 
         [0038]    The block diagrams and flowchart illustrations depict methods, apparatus, systems, and computer program products. The elements and combinations of elements in the block diagrams and flow diagrams, show functions, steps, or groups of steps of the methods, apparatus, systems, computer program products and/or computer-implemented methods. Any and all such functions—generally referred to herein as a “circuit,” “module,” or “system”—may be implemented by computer program instructions, by special-purpose hardware-based computer systems, by combinations of special purpose hardware and computer instructions, by combinations of general purpose hardware and computer instructions, and so on. 
         [0039]    A programmable apparatus which executes any of the above mentioned computer program products or computer-implemented methods may include one or more microprocessors, microcontrollers, embedded microcontrollers, programmable digital signal processors, programmable devices, programmable gate arrays, programmable array logic, memory devices, application specific integrated circuits, or the like. Each may be suitably employed or configured to process computer program instructions, execute computer logic, store computer data, and so on. 
         [0040]    It will be understood that a computer may include a computer program product from a computer-readable storage medium and that this medium may be internal or external, removable and replaceable, or fixed. In addition, a computer may include a Basic Input/Output System (BIOS), firmware, an operating system, a database, or the like that may include, interface with, or support the software and hardware described herein. 
         [0041]    Embodiments of the present invention are neither limited to conventional computer applications nor the programmable apparatus that run them. To illustrate: the embodiments of the presently claimed invention could include an optical computer, quantum computer, analog computer, or the like. A computer program may be loaded onto a computer to produce a particular machine that may perform any and all of the depicted functions. This particular machine provides a means for carrying out any and all of the depicted functions. 
         [0042]    Any combination of one or more computer readable media may be utilized including but not limited to: a non-transitory computer readable medium for storage; an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor computer readable storage medium or any suitable combination of the foregoing; a portable computer diskette; a hard disk; a random access memory (RAM); a read-only memory (ROM), an erasable programmable read-only memory (EPROM, Flash, MRAM, FeRAM, or phase change memory); an optical fiber; a portable compact disc; an optical storage device; a magnetic storage device; or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
         [0043]    It will be appreciated that computer program instructions may include computer executable code. A variety of languages for expressing computer program instructions may include without limitation C, C++, Java, JavaScript™, ActionScript™, assembly language, Lisp, Perl, Tcl, Python, Ruby, hardware description languages, database programming languages, functional programming languages, imperative programming languages, and so on. In embodiments, computer program instructions may be stored, compiled, or interpreted to run on a computer, a programmable data processing apparatus, a heterogeneous combination of processors or processor architectures, and so on. Without limitation, embodiments of the present invention may take the form of web-based computer software, which includes client/server software, software-as-a-service, peer-to-peer software, or the like. 
         [0044]    In embodiments, a computer may enable execution of computer program instructions including multiple programs or threads. The multiple programs or threads may be processed approximately simultaneously to enhance utilization of the processor and to facilitate substantially simultaneous functions. By way of implementation, any and all methods, program codes, program instructions, and the like described herein may be implemented in one or more threads which may in turn spawn other threads, which may themselves have priorities associated with them. In some embodiments, a computer may process these threads based on priority or other order. 
         [0045]    Unless explicitly stated or otherwise clear from the context, the verbs “execute” and “process” may be used interchangeably to indicate execute, process, interpret, compile, assemble, link, load, or a combination of the foregoing. Therefore, embodiments that execute or process computer program instructions, computer-executable code, or the like may act upon the instructions or code in any and all of the ways described. Further, the method steps shown are intended to include any suitable method of causing one or more parties or entities to perform the steps. The parties performing a step, or portion of a step, need not be located within a particular geographic location or country boundary. For instance, if an entity located within the United States causes a method step, or portion thereof, to be performed outside of the United States then the method is considered to be performed in the United States by virtue of the causal entity. 
         [0046]    While the invention has been disclosed in connection with preferred embodiments shown and described in detail, various modifications and improvements thereon will become apparent to those skilled in the art. Accordingly, the forgoing examples should not limit the spirit and scope of the present invention; rather it should be understood in the broadest sense allowable by law.