Patent Publication Number: US-8531030-B2

Title: IC device having electromigration resistant feed line structures

Description:
FIELD 
     Disclosed embodiments relate to integrated circuit (IC) devices that include feed line structures that improve electromigration (EM) performance. 
     BACKGROUND 
     ICs generally comprise a substrate, active circuitry formed on the topside of the substrate, and a back end of the line (BEOL) structure including alternating metal wiring layers and interlevel dielectric layers (ILD) above the active circuitry. The metal wiring layers comprise various interconnects that provide electrical connections between the active circuitry and external connections. Solder bumps (or solder balls) are commonly utilized to provide a connection between the last (e.g., top) metal wiring level of a semiconductor device and another device, such as from a node in the active circuitry or situations where interconnect plays a passive role where the solder bump/is simply part of a pass-through (e.g., for a stacked die/package). A common type of solder bump is the controlled collapse chip connection (C4) solder bump, often used for jointing for flip chip devices. 
     As dimensions of features (e.g., pads, wires, interconnects, vias) shrink to create smaller devices, the maximum allowable current density decreases rapidly due to EM-based constraints imposed for reliability. EM is a known phenomenon in which atoms of a metal feature are displaced due to the electrical current passing through the metal feature. 
     IC devices such as flip chip devices are requiring higher and higher current carrying capabilities, sometimes to the level of 10 amps or more. Solder is known to have a significantly lower current density handling ability as compared to conventional metal interconnects, such as copper and aluminum. For example, solder has a relatively low EM current limit (e.g., typical EM-limited current density for conventional solder is around 10 4  A/cm 2 , about one hundred times lower than that of copper and aluminum). The current carrying capability of each flip chip solder bump sets the minimum number of solder bumps used to supply this current to limit the current density through the solder bumps due to EM constraints. The conventional flip chip solder bump process suffers from a current distribution non-uniformity over the cross sectional area of the solder bump which accelerates the EM-based degradation of the solder and causes failures earlier than for the case where the current distribution is more uniform. 
     One example of a conventional flip chip bump arrangement includes a copper feed line to an aluminum bond pad formed from a top metal layer, a dielectric (e.g., polyimide) layer including an opening (dielectric opening) over the pad, a thick (e.g., 2 μm thick) nickel under bump metallization (UBM) layer over the dielectric layer and the dielectric opening, and a solder bump over the UBM. This arrangement suffers from significant current non-uniformity across the cross sectional area of the solder bump. 
     For a solder bump with a feed line current coming from one side, the peak current in the solder bump area adjacent to the UBM may exist over a portion of the cross sectional area that is only about 10% of the overall cross sectional area of the solder bump. This is the current crowded region in the solder bump that voids first due to exceeding the EM current density limit of solder. Once this region voids, the solder area next to it will carry the peak current distribution and will void next. This voiding pattern will continue until the whole solder bump over the dielectric opening becomes voided. At this time the outer annulus of the UBM over the dielectric will begin the void, and eventually an open circuit will result. 
     One known solution to this problem involves adding a thick copper stud in the UBM which helps spread current across the cross sectional area of the solder bump. This known solution adds a process step and is only minimally effective since it cannot render uniform current density for typical stud dimensions. There is thus a need for new feed line to bonding feature arrangements that allow the current to be more uniform over the cross sectional area of the solder bump or other bonding feature without adding a process step or significantly increasing the area required to implement the feed line structure. 
     SUMMARY 
     Disclosed embodiments describe integrated circuit (IC) devices that have electromigration (EM) resistant feed line structures to the bonding features that force the current flowing into the bonding feature to be more uniform across its cross sectional area. Such current spreading embodiments solve or at least significantly reduce EM-induced voiding in bonding features, such as solder bumps. 
     By dividing the feed line trace to the bonding feature into at least three electrically parallel sub-trace paths, with the respective sub-trace paths having at least one of (i) appropriate line sizings to make the plurality of feed currents substantially equal currents (i.e., longer lines are wider, and shorter lines are narrower) and ii) a current density provided to the bonding feature conducted through each of the sub-traces being substantially equal, higher total current levels can be handled by the bonding feature without EM-based problems due to better distribution of current (less current crowding) across the cross sectional area of the bonding feature. Disclosed embodiments do not generally add any process steps. 
     For example, disclosed feed structures can replace a conventional single incoming feed line trace (e.g., a 10 micron wide trace from end to end) by a trace that includes a patterned trace portion comprising a plurality of sub-traces (e.g., eight, twelve, sixteen or even more sub-traces). In one embodiment, the current density provided to the bonding feature conducted through each of the sub-traces is substantially equal. As used herein, “substantially equal current density” provided to the bonding feature conducted through each of the sub-traces refers to the current densities each being within a range of the mean current density provided to the bonding feature plus or minus twenty percent. 
     In another embodiment, the sub-traces have different widths and different lengths, where the respective sub-traces each have a substantially equal numbers of squares. As used herein, a “substantially equal number of squares” produces substantially equal sub-trace currents and refers to a number of squares associated with the paths provided by each of the sub-traces all being within a range of a mean number of squares for the sub-traces plus or minus twenty percent, and in one embodiment is within a range of a mean number of squares for the sub-traces plus or minus ten percent. 
     In an embodiment referred to herein as the edge feed embodiment, the sub-traces can be distributed so that the area under the edge (perimeter) of the bonding feature over a dielectric opening has an equal distribution of feed line sub-trace contacts, that is the separation (spacing) between each feed line sub-trace to its neighbors under the bond pad is substantially uniform. In this embodiment “substantially equal separation” refers to the distances along the perimeter between the sub-traces all being within a range of a mean perimeter spacing distance for the plurality of sub-traces plus or minus twenty percent. Since the number of squares and thus the resistance of each feed line sub-trace can be substantially equal in this embodiment, the current in the uniform trace portion will divide itself substantially equally amongst each of the sub-trace paths to the bonding feature available to it. Thus, for the edge feed embodiment the periphery under the bonding feature will see a uniform current into it and a more uniform current distribution in the bonding feature (e.g., solder bump) is generally achieved. 
     In an embodiment referred to herein as the area feed embodiment, substantially the full area of the bonding feature is fed by current. In this embodiment, the bond pad has vias distributed over the substantially the full area under or over the bond pad. In this embodiment, a via pattern can be provided in the dielectric layer over bond pad (e.g., between the bond pad and a UBM pad), or the via pattern can be in the dielectric under bond pad (e.g., between the feed line sub-traces and the bond pad). The area feed embodiment may also be combined with the edge feed embodiment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  shows a depiction of an example electromigration (EM) resistant feed line structure having at least three sub-traces that provide substantially equal sub-trace currents having a substantially equal distribution over the periphery of a dielectric opening under the bonding feature, according to an example embodiment. 
         FIG. 1B  shows a depiction of an example EM resistant feed line structure having at least three sub-traces that provide both substantially equal sub-trace currents and substantially equal sub-trace current densities, as well as substantially equal distribution over the periphery of a dielectric opening under the bonding feature, according to an example embodiment. 
         FIG. 1C  shows a depiction of an example EM resistant feed line structure having a single metal layer that provides both the plurality of sub-traces and the bond pad, where the sub-traces provide substantially equal sub-trace currents to feed the bond pad along its periphery, according to an example embodiment. 
         FIG. 2A  shows a depiction of an example EM resistant feed line structure having at least three sub-traces that provide substantially equal sub-trace currents coupled in a contact region to a bond pad having vias thereon distributed across a full area of a bonding feature above the bond pad, according to an example embodiment. 
         FIG. 2B  shows a depiction of an example EM resistant feed line structure having at least three sub-traces that are coupled in a contact region to a bond pad having vias thereon distributed across a full area of a bonding feature above the bond pad, wherein the sub-trace currents have a range that is outside a mean number of squares for the sub-traces plus or minus twenty percent, and the vias are sized to provide substantially equal current densities to the bonding feature, according to an example embodiment. 
         FIG. 3  shows a depiction of an example EM resistant feed line structure having a first independent feed line comprising a uniform trace portion and a second independent feed line comprising a uniform trace portion, both being coupled to the same bond pad, wherein the feed lines each comprise a patterned trace portion including four sub-traces sized to provide substantially equal sub-trace currents, according to an example embodiment. 
         FIG. 4  shows an example IC device including a substrate having active circuitry, a back end of the line (BEOL) metallization stack including an interconnect metal layer including a disclosed EM resistant feed line structure comprising at least three sub-traces that provide substantially equal sub-trace currents coupled to a bond pad comprising a top metal layer, and a bonding feature on the bond pad, according to an example embodiment. 
         FIG. 5  shows a stacked IC device comprising an IC die having a disclosed EM resistant feed line structure comprising at least three sub-traces that provide substantially equal sub-trace currents bonded to a substrate by a joint that comprises a metal/organic bonding material, according to an example embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Example embodiments are described with reference to the drawings, wherein like reference numerals are used to designate similar or equivalent elements. Illustrated ordering of acts or events should not be considered as limiting, as some acts or events may occur in different order and/or concurrently with other acts or events. Furthermore, some illustrated acts or events may not be required to implement a methodology in accordance with this disclosure. 
       FIG. 1A  shows a depiction of an example EM resistant feed line structure  100  providing edge feed having at least three sub-traces that provide substantially equal sub-trace currents having a substantially equal distribution over the periphery of a dielectric opening  115  under a bonding feature, according to an example embodiment. Although one large dielectric opening  115  is shown in  FIG. 1A , disclosed embodiments can instead include an array of smaller dielectric openings, or both, under a later formed bonding feature. The bonding features are generally described herein as being solder bumps. However, the bonding features can also comprise through substrate vias (TSVs), pillars (e.g., copper pillars), studs (e.g., gold studs), or an organic bonding material having a plurality of metal particles therein. 
     EM resistant feed line structure  100  comprises a uniform (i.e., conventional) trace portion  102  coupled to a patterned trace portion  105  comprising at least three sub-traces  105 ( a ),  105 ( b ),  105 ( c ), etc. that are electrically in parallel and distributed to provide electrical contact along the periphery over the dielectric opening  115  shown that is under the later formed metal stack (not shown) including a bonding feature on a bond pad. The later formed metal stack will be over dielectric opening  115 , which in one particular embodiment can comprise a solder ball/Ni under bump metallization (UMB)/A1 bond pad. 
     Substantially equal sub-trace currents are provided by EM resistant feed line structure  100  because the respective plurality of feed line sub-traces  105 ( a ),  105 ( b ),  105 ( c ), etc. are sized so that a number of squares associated with the respective paths provided by the sub-traces are all within a range of a mean number of squares for the plurality of sub-traces plus or minus twenty percent (±20%). It can be seen that sub-trace  105 ( a ) which is the longest sub-trace shown in  FIG. 1A  is also the widest sub-trace, sub-trace  105 ( b ) which is the shortest sub-trace shown is also the narrowest sub-trace, with sub-trace  105 ( c ) being a sub-trace shown having an intermediate length and an intermediate line width. It is noted that although the sub-traces in patterned trace portion  105  are all shown having a constant line width along their respective path lengths, the line widths need not be constant to provide substantially equal sub-trace currents provided the resulting number of squares for the respective sub-traces are within the numerical range as described above. 
       FIG. 1A  demonstrates that the edge feed embodiment takes up little extra metallization area as compared to a conventional single feed line arrangement for coupling to a bonding feature (e.g., solder bump). Since the edge feed embodiment shown in  FIG. 1A  provides improved current spreading in the overlying bonding feature (e.g. solder bump), this embodiment allows a reduced area for the bonding feature to be used to yield an overall smaller metal area requirement in the upper metal layers of the device for the same EM current performance, thus providing a cost savings for the IC device. 
     Applied to wafer chip scale packages (WSCPs), the uniform trace portion  102  and patterned trace portion  105  can both be formed from the redirect layer (RDL). In this embodiment patterned trace portion  105  couples to an RDL pad that is over a bond pad on the IC, while a UBM pad can be on the RDL pad, and a solder bump can be on the UBM pad. In this embodiment, the dielectric opening  115  can be an opening in the dielectric between the RDL and the UBM, such as an opening in a polyimide layer. 
     As described above, some disclosed embodiments can provide both substantially matched sub-currents and substantially matched current densities provided to the bonding feature conducted through each of the sub-traces. For example,  FIG. 1B  shows a depiction of an example EM resistant feed line structure  130  having at least three sub-traces  125 ( a ),  125 ( b ),  125 ( c ) that provide both substantially equal sub-trace currents and substantially equal sub-trace current densities, while also providing a substantially equal physical distribution over the periphery of the dielectric opening  115  under the bonding feature, according to an example embodiment. As known in the art, the current density (J) going into the dielectric opening  115  under the bonding feature is found by dividing the current (I) at the sub-trace contact by the area (A) of the contact, and is given by J=I/A. It can be seen that narrow sub-traces such as sub-trace  125 ( b ) is significantly widened at is distal end  125 ( b )( 1 ) that extends into dielectric opening  115 , as compared to longer sub-traces such as sub-trace  125 ( a ) which shows no widening of its distal end  125 ( a )( 1 ), so that width of the respective sub-traces at their distal ends that extend into dielectric opening  115  are the same width or are about the same width. Sub-trace  125 ( c ) which has an intermediate line width shows moderate widening of its distal end  125 ( c )( 1 ). Since currents in the respective sub-traces are matched to one another, and the area at their contacts are also the same, current density matching is provided. 
       FIG. 1C  shows a depiction of an example EM resistant feed line structure  150  comprising a uniform trace portion  162  coupled to a patterned trace portion  165  having at least three sub-traces  165 ( a ),  165 ( b ),  165 ( c ), etc. that provide substantially equal sub-trace currents that feed the bond pad  170  having a substantially equal distribution along a periphery of the bond pad, according to an example embodiment. In this embodiment the feed line structure  150  and the bond pad  170  are all formed from the same metal layer. This metal layer can be a metal interconnect layer, a top metal layer, or an RDL. 
       FIG. 2A  shows a depiction of an example EM resistant feed line structure  200  demonstrating the area feed embodiment having at least three sub-traces that provide substantially equal sub-trace currents coupled in a contact region  225  across the area of a bond pad, with a plurality of vias  230  formed in a dielectric layer on the bond pad  215 , according to an example embodiment. EM resistant feed line structure  200  comprises a uniform trace portion  102  and a patterned trace portion  205  comprising a plurality of sub-traces  205 ( a ),  205 ( b ),  205 ( c ), etc. The plurality of sub-traces  205 ( a ),  205 ( b ),  205 ( c ), etc. are sized so that a number of squares associated with paths provided by each of the plurality of sub-traces are all within a range of a mean number of squares for the plurality of sub-traces plus or minus twenty percent. 
     In the contact region  225  the respective sub-traces  205 ( a ),  205 ( b ),  205 ( c ) can contact the bond pad  215  using a single dielectric opening (such as dielectric opening  115  shown in  FIG. 1A ) or a plurality of vias formed in a dielectric layer between the sub-traces  205 ( a ),  205 ( b ),  205 ( c ) and the bond pad  215 . The bond pad  215  has an example circular via pattern including vias  230  formed from a dielectric layer thereon at locations that define the respective effective bond pad portions  215 ( a ),  215 ( b ),  215 ( c ). The outer rings  235 ( a ),  235 ( b ),  235 ( c ) shown as dashed rings represent current spreading beyond the bond pad portions  215 ( a ),  215 ( b ),  215 ( c ) as the feed current traverses from the bond pad portions to an example 2 micron thick nickel UBM layer (not shown) that may be over the bond pad  215  in the contact region  225 . As depicted in  FIG. 2A , almost the entire area of an UBM layer over the contact region  225  spreads current for a bonding feature (e.g. solder bump) that can be positioned thereon, virtually guaranteeing uniform current distribution over the full cross sectional area of the bonding feature (e.g. solder bump). 
     In this embodiment, the top metal layer in which the bond pad  215  comprises (e.g., an aluminum layer) which can connect the UBM to the patterned trace portion  205  of the underlying metal (e.g., copper) sub-traces is effectively patterned. This patterning can be performed so that the openings over the bond pad  215  comprises array of vias, which can be shaped in a variety of shapes including, but not limited to, round or square depending upon the metal patterning requirements. The area of the vias can be based on the thickness of the bond pad metal and the UBM metal thereon, so that the area of the vias increase as the thickness of the bond pad metal and the UBM metal increase. For example, in embodiments including an UBM on the bond pad  215 , where the vias  230  are round, the diameter of the vias  230  can be twice the UBM thickness plus twice the bond pad metal thickness plus or minus twenty percent. Thus, for a 1 micron thick bond pad  215  and a 2 micron thick UBM layer, the vias  230  can be six microns in diameter plus or minus twenty percent in diameter. 
     The spacing between adjacent vias  230  can also be based on the overlying metal thickness. For example, the via spacing can be so that the maximum distance to the next via is twice the UBM metal thickness plus or minus twenty percent. Thus, for a two micron thick UBM, the via-to-via distance can be four microns plus or minus twenty percent. 
     Each via  230  is thus fed by individual sub-traces  205 ( a ),  205 ( b ),  205 ( c ) from uniform trace portion  102  in a manner such that the number of squares and thus the resistance of each sub-trace is substantially equal, but significantly higher than the sum of the resistance of the bonding feature stack (e.g. solder bump on UBM) plus the via resistance over the bond pad  215 . Thus for a conventional dielectric (e.g., polyimide) via opening between the bond pad  215  and the UBM (e.g., solder bump opening) of 35 microns in diameter, and a 1 micron bond pad layer (e.g. aluminum) and 2 micron UBM (e.g., nickel), a conventional single dielectric opening over the bond pad can be replaced by 14 six micron circular vias  230  with 14 individual feed line sub-traces as shown in  FIG. 2A . The vias may be shaped asymmetrically to allow easier routing of the sub-traces  205 ( a ),  205 ( b ),  205 ( c ) should this be helpful. The overall (summed) widths of the sub-traces  205 ( a ),  205 ( b ),  205 ( c ) to the effective bond pad portions  215 ( a ),  215 ( b ),  215 ( c ) can be made equal to that of the uniform trace portion  102  to minimize the total resistance to the bonding feature (e.g., solder bump). 
     In another embodiment, a via pattern may be formed in the contact region  225  between the sub-traces and the bond pad  215 , instead of vias over the bond pad  215  as shown in  FIG. 2A , to yield a similar but enhanced current spreading feed line structure as compared to the feed line structure  200  shown in  FIG. 2A . This embodiment has the advantage of additional current spreading as current traverses the thickness of bond pad  215  (e.g., 1 μm aluminum) before it reaches the UBM layer in embodiments including a UBM layer on the bond pad  215 . 
     The area feed embodiment shown in  FIG. 2A  for bonding features on a UBM provides a uniform current distribution over substantially the entire bonding feature cross-section at the UBM to the bonding feature interface. This embodiment takes up very little if any extra metallization area as compared to a standard bump feed structure and has the advantage of a smaller bump structure which lowers the overall area for the bonding feature. Improved uniformity of the current distribution in the bonding feature and reduced area of the metal feed structure combine to yield an overall smaller metal area requirement in the upper metal layers of the IC device for the same current EM performance, thus leading to a cost savings for the IC device. 
       FIG. 2B  shows a depiction of an example EM resistant feed line structure  250  having at least three sub-traces  255 ( a ),  255 ( b ) and  255 ( c ) coupled in the contact region  225  to a bond pad  215 , with a plurality of vias  230 ( a ),  230 ( b ) and  230 ( c ) formed in a dielectric layer on the bond pad  215  that are distributed across an area of the bond pad  215 , wherein the sub-trace currents have a range that is outside a mean number of squares for the sub-traces plus or minus twenty percent, and the vias are sized to provide substantially equal current densities to a bonding feature above the bond pad, according to an example embodiment. In this embodiment, the vias  230 ( a ),  230 ( b ) and  230 ( c ) are sized so that the shorter sub-traces such as  255 ( b ) that result in higher currents are coupled to larger area via areas as compared to sub-traces that carry lower current such as sub-trace  255 ( a ) that have smaller via areas. The outer rings are shown as  235 ( a ),  235 ( b ),  235 ( c ) which have sizes that reflect the size of their corresponding vias  230 ( a ),  230 ( b ) and  230 ( c ), depict current spreading beyond the bond pad portions  215 ( a ),  215 ( b ),  215 ( c ) as the current traverses from the bond pad portions to a metal layer thereon (not shown) that is typically over the bond pad  215  in the contact region  225 . 
     Disclosed embodiments can also be applied to IC designs where there are two or more independent feed lines (i.e., from different nodes on the IC) coupled to the same bonding feature (e.g., solder bump). Discretion may be used to determine whether the feeds should combined to maximize current uniformity, or be split based upon expected current loading on each incoming line. Thus, for a uniform split, the independent feed lines can be tied together before being split into sub-traces. For the cases where the expected current from each independent feed line is known by design, the number of contact vias feeding the bonding feature may be divided per input line to yield a uniform current distribution over the area of the bonding feature. Thus, if there are two independent feed lines with equal current on each line, then half of the vias can be assigned to one of the feed lines and half of the vias to the other feed line. 
       FIG. 3  shows a depiction of an example EM resistant feed line structure  300  having a first independent feed line  310  comprising uniform trace portion  312  and a second independent feed line  320  comprising uniform trace portion  322  that are both coupled to a bond pad  215 , wherein the feed lines  310  and  320  each comprise a patterned trace portion  315  and  325  that each comprise four sub-traces  315 ( a )-( d ) and  325 ( a )-( d ), that provide substantially equal sub-trace currents, according to an example embodiment. First feed line  310  and second feed line are shown formed from different metal interconnects. First feed line  310  is shown formed from metal layer N (e.g., seventh level metal), while second feed line  320  is shown formed from metal layer N−1 (e.g. sixth level metal). First feed line  310  is shown feeding a feed current of while second feed line  320  is shown feeding a current I 2 . I 1  and I 2  are generally not equal currents. 
       FIG. 4  shows an example IC device  400  including a back end of the line (BEOL) metallization stack  420  comprising a top interconnect metal layer shown as METn  412  that includes a disclosed EM resistant feed line  401  comprising a uniform trace portion  402  and a patterned trace portion  406  comprising a plurality of sub-traces that couple to a bump pad  419  comprising METn (e.g., a copper bump pad), such as by a dielectric opening analogous to the dielectric opening  115  shown in  FIG. 1A  or a plurality of vias (not shown). BEOL stack  420  also includes first dielectric layer  431  and second dielectric layer  432 . IC device  400  includes a substrate  405  having active circuitry  409 , where a node  417  in the active circuitry is shown coupled to uniform trace portion  402  by a connection through the BEOL  420 . 
     A bond pad  415  formed from a top metal layer (e.g., aluminum) is on the bump pad  419 , a UBM pad that provides a current spreading layer is on bond pad  415 , and a bonding feature shown as a solder bump  435  is on the UBM pad  418 . Although METn  412  is shown in  FIG. 4  providing the EM resistant feed lines, any of the metal interconnect layers on IC  400  may generally be used to provide EM resistant feed lines, such as underlying metal interconnect layers. It is noted that for certain bonding features, the UBM pad  418  shown may not be needed. For example, when the bonding feature comprises a cooper pillar, the copper pillar can be formed directly on a copper bond pad. 
       FIG. 5  shows a stacked IC device  500  comprising an IC die  510  having a disclosed EM resistant feed line structure in a flip chip arrangement coupled to a pad  511  bonded to a substrate  520  having a pad  521  by a joint  525  that comprises a metal/organic bonding material, according to an example embodiment. Disclosed embodiments may be particularly helpful for bonding materials with low EM resistance such as the metal/organic bonding material shown by current spreading provided across substantially the entire cross sectional area of the joint  525  provided by disclosed feed line structures. 
     Disclosed embodiments can generally be applied to any feed line structure coupled to a bonding feature. WCSPs including a ball is only one example. Other feed structures that can benefit from disclosed embodiments include TSV to RDL to remote pad arrangements. 
     Simulations were performed to compare the EM performance using the mean time to failure (MTTF) parameter obtained from Black&#39;s equation for the EM resistant feed line structure  100  shown in  FIG. 1A  (edge feed), the EM resistant feed line structure  200  shown in  FIG. 2A  (area feed), both with fourteen feed line sub-traces sized to provide substantially equal sub-trace currents coupled to a bond pad, with a 2 micron Ni UMB on the bond pad and a solder bump on the UBM, vs. two different reference structures. The first reference structure comprised fourteen feed line sub-traces equivalent to feed line structure  200  other than having the same uniform sub-trace line width throughout their lengths, and the second reference structure comprised a conventional single feed line arrangement with the same layer stack on the bond pad. Black&#39;s Equation (shown below) is a mathematical model for the MTTF of a semiconductor circuit due to EM: 
               M   ⁢           ⁢   T   ⁢           ⁢   T   ⁢           ⁢   F     =     A   ⁢           ⁢     ωj     -   n       ⁢     ⅇ     (     Q   kT     )               
where A is a constant, j is the current density, n is a model parameter, Q is the activation energy in eV (electron volts), k is Boltzmann constant, T is the absolute temperature in K, and w is the width of the metal line/wire.
 
     Based on simulations performed, the first reference structure having fourteen feed line sub-traces all having the same uniform line width over their respective lengths provided an improvement in solder lifetime by about 20 to 40% as compared to the conventional single feed line arrangement. In contrast, feed line structure  100  shown in  FIG. 1A  was found to provide an improvement in solder lifetime of 200 to 300%. The feed line structure  200  shown in  FIG. 2A  was found to provide an improvement in solder lifetime of more than an order of magnitude, i.e. &gt;1,000%. 
     The magnitude of the MTTF performance impact found to be obtained by disclosed embodiments including sub-trace sizing for matching sub-trace currents evidenced an unexpected result that demonstrates criticality based on the magnitude of the improvement. Specifically, the 200 to 300% improvement in solder lifetime for the edge feed embodiment and &gt;1,000% improvement in solder lifetime for the area feed embodiment both represent a marked improvement over the results achieved from the conventional feed line structure as well as the first reference structure, as to be properly considered a difference in kind, rather than a difference of degree. 
     The active circuitry formed on the wafer semiconductor substrate comprises circuit elements that may generally include transistors, diodes, capacitors, and resistors, as well as signal lines and other electrical conductors that interconnect the various circuit elements and are configured to provide an IC circuit function. As used herein “provide an IC circuit function” refers to circuit functions from ICs, that for example may include an application specific integrated circuit (ASIC), a digital signal processor, a radio frequency chip, a memory, a microcontroller and a system-on-a-chip or a combination thereof. Disclosed embodiments can be integrated into a variety of process flows to form a variety of devices and related products. The semiconductor substrates may include various elements therein and/or layers thereon. These can include barrier layers, other dielectric layers, device structures, active elements and passive elements, including source regions, drain regions, bit lines, bases, emitters, collectors, conductive lines, conductive vias, etc. Moreover, disclosed embodiments can be used in a variety of semiconductor device fabrication processes including bipolar, CMOS, BiCMOS and MEMS processes. 
     Those skilled in the art to which this disclosure relates will appreciate that many other embodiments and variations of embodiments are possible within the scope of the claimed invention, and further additions, deletions, substitutions and modifications may be made to the described embodiments without departing from the scope of this disclosure.