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• 21. [Article] Analysis of a Short Beam with Application to Solder Joints: Could Larger Stand-Off Heights Relieve Stress?

  Physically meaningful and easy-to-use analytical (mathematical) stress model is developed for a short beam with clamped and known-in-advance offset ends. The analysis is limited to elastic deformations. ...

  Citation × Citation Citation Abstract Copy Title: Analysis of a Short Beam with Application to Solder Joints: Could Larger Stand-Off Heights Relieve Stress? Author: Suhir, Ephraim Year: 2015 Physically meaningful and easy-to-use analytical (mathematical) stress model is developed for a short beam with clamped and known-in-advance offset ends. The analysis is limited to elastic deformations. While the classical Timoshenko short-beam theory seeks the beam’s deflection caused by the combined bending and shear deformations for the given loading, an inverse problem is considered here: the lateral force is sought for the given ends offset. In short beams this force is larger than in long beams, since, in order to achieve the given displacement (offset), the applied force has to overcome both bending and shear resistance of the beam. It is envisioned that short beams could adequately mimic the state of stress in solder joint interconnections, including ball-grid-array (BGA) systems, with large, compared to conventional joints, stand-off heights. When the package/printed-circuit-board (PCB) assembly is subjected to the change in temperature, the thermal expansion (contraction) mismatch of the package and the PCB results in an easily predictable relative displacement (offset) of the ends of the solder joint. This offset can be determined from the known external thermal mismatch strain (determined as the product of the difference in the coefficients of thermal expansion and the change in temperature) and the position of the joint with respect to the mid-cross-section of the assembly. The maximum normal and shearing stresses could be viewed as suitable criteria of the beam’s (joint’s) material long-term reliability. It is shown that these stresses can be brought down by employing beam-like joints, i.e., joints with an increased stand-off height compared to conventional joints. It is imperative, of course, that, if such joints are employed, there is still enough interfacial real estate, so that the BGA bonding strength is not compromised. On the other hand, owing to the lower stress level, reliability assurance might be much less of a challenge than in the case of conventional joint configuration. By employing beam-like solder joints one can even manage to avoid inelastic deformations of the joints, thereby increasing dramatically their fatigue lifetime. Future work will include, but might not be limited to, the finite-element computations, experimental evaluations (such as, e.g., shear-off testing), and analyses of the occurrence and the role of the inelastic strains, if any. The paper is intended for materials-, reliability- and industrial- physicists and applied scientists. Title: Analysis of a Short Beam with Application to Solder Joints: Could Larger Stand-Off Heights Relieve Stress? Author: Suhir, Ephraim Year: 2015 Physically meaningful and easy-to-use analytical (mathematical) stress model is developed for a short beam with clamped and known-in-advance offset ends. The analysis is limited to elastic deformations. While the classical Timoshenko short-beam theory seeks the beam’s deflection caused by the combined bending and shear deformations for the given loading, an inverse problem is considered here: the lateral force is sought for the given ends offset. In short beams this force is larger than in long beams, since, in order to achieve the given displacement (offset), the applied force has to overcome both bending and shear resistance of the beam. It is envisioned that short beams could adequately mimic the state of stress in solder joint interconnections, including ball-grid-array (BGA) systems, with large, compared to conventional joints, stand-off heights. When the package/printed-circuit-board (PCB) assembly is subjected to the change in temperature, the thermal expansion (contraction) mismatch of the package and the PCB results in an easily predictable relative displacement (offset) of the ends of the solder joint. This offset can be determined from the known external thermal mismatch strain (determined as the product of the difference in the coefficients of thermal expansion and the change in temperature) and the position of the joint with respect to the mid-cross-section of the assembly. The maximum normal and shearing stresses could be viewed as suitable criteria of the beam’s (joint’s) material long-term reliability. It is shown that these stresses can be brought down by employing beam-like joints, i.e., joints with an increased stand-off height compared to conventional joints. It is imperative, of course, that, if such joints are employed, there is still enough interfacial real estate, so that the BGA bonding strength is not compromised. On the other hand, owing to the lower stress level, reliability assurance might be much less of a challenge than in the case of conventional joint configuration. By employing beam-like solder joints one can even manage to avoid inelastic deformations of the joints, thereby increasing dramatically their fatigue lifetime. Future work will include, but might not be limited to, the finite-element computations, experimental evaluations (such as, e.g., shear-off testing), and analyses of the occurrence and the role of the inelastic strains, if any. The paper is intended for materials-, reliability- and industrial- physicists and applied scientists. Close

• 22. [Article] Microstructural Evolution of SAC305 Solder Joints in Wafer Level Chip-Scale Packaging (WLCSP) with Continuous and Interrupted Accelerated Thermal Cycling

  Four high-strain design wafer level chip scale packages were given accelerated thermal cycling with a 10°C/min ramp rate and 10 min hold times between 0°C and 100°C to examine the effects of continuous ...

  Citation × Citation Citation Abstract Copy Title: Microstructural Evolution of SAC305 Solder Joints in Wafer Level Chip-Scale Packaging (WLCSP) with Continuous and Interrupted Accelerated Thermal Cycling Author: Zhou, Quan, Zhou, Bite, Lee, Tae-Kyu, Bieler, Thomas Year: 2016 Four high-strain design wafer level chip scale packages were given accelerated thermal cycling with a 10°C/min ramp rate and 10 min hold times between 0°C and 100°C to examine the effects of continuous and interrupted thermal cycling on the number of cycles to failure. The interruptions given two of the samples were the result of periodic examinations using electron backscattered pattern mapping, leading to room temperature aging of 30 days–2.5 years after increments of about 100 cycles at several stages of the cycling history. The continuous thermal cycling resulted in solder joints with a much larger degree of recrystallization, whereas the interrupted thermal cycling tests led to much less recrystallization, which was more localized near the package side, and the crack was more localized near the interface and had less branching. The failure mode for both conditions was still the same, with cracks nucleating along the high angle grain boundaries formed during recrystallization. In conditions where there were few recrystallized grains, recovery led to formation of subgrains that strengthened the solder, and the higher strength led to a larger driving force for crack growth through the solder, leading to failure after less than half of the cycles in the continuous accelerated thermal cycling condition. This work shows that there is a critical point where sufficient strain energy accumulation will trigger recrystallization, but this point depends on the rate of strain accumulation in each cycle and various recovery processes, which further depends on local crystal orientations, stress state evolution, and specific activated slip and twinning systems. Title: Microstructural Evolution of SAC305 Solder Joints in Wafer Level Chip-Scale Packaging (WLCSP) with Continuous and Interrupted Accelerated Thermal Cycling Author: Zhou, Quan, Zhou, Bite, Lee, Tae-Kyu, Bieler, Thomas Year: 2016 Four high-strain design wafer level chip scale packages were given accelerated thermal cycling with a 10°C/min ramp rate and 10 min hold times between 0°C and 100°C to examine the effects of continuous and interrupted thermal cycling on the number of cycles to failure. The interruptions given two of the samples were the result of periodic examinations using electron backscattered pattern mapping, leading to room temperature aging of 30 days–2.5 years after increments of about 100 cycles at several stages of the cycling history. The continuous thermal cycling resulted in solder joints with a much larger degree of recrystallization, whereas the interrupted thermal cycling tests led to much less recrystallization, which was more localized near the package side, and the crack was more localized near the interface and had less branching. The failure mode for both conditions was still the same, with cracks nucleating along the high angle grain boundaries formed during recrystallization. In conditions where there were few recrystallized grains, recovery led to formation of subgrains that strengthened the solder, and the higher strength led to a larger driving force for crack growth through the solder, leading to failure after less than half of the cycles in the continuous accelerated thermal cycling condition. This work shows that there is a critical point where sufficient strain energy accumulation will trigger recrystallization, but this point depends on the rate of strain accumulation in each cycle and various recovery processes, which further depends on local crystal orientations, stress state evolution, and specific activated slip and twinning systems. Close

• 23. [Article] Distribution of Mean Kinetic Energy Around an Isolated Wind Turbine and a Characteristic Wind Turbine of a Very Large Wind Farm

  An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying ...

  Citation × Citation Citation Abstract Copy Title: Distribution of Mean Kinetic Energy Around an Isolated Wind Turbine and a Characteristic Wind Turbine of a Very Large Wind Farm Author: Cortina, Gerard, Calaf, Marc, Cal, Raul Bayoan Year: 2016 An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying surface temperature extracted from a selected period of the CASES-99 field experiment. A control volume approach is used to directly compare the transfer of mean kinetic energy around a characteristic wind turbine throughout a diurnal cycle considering both scenarios. For the very large wind farm case, results illustrate that the recovery of mean kinetic energy around a wind turbine is dominated by the vertical flux, regardless of atmospheric stratification. Contrarily, for an isolated wind turbine, the recovery is dependent on the background atmospheric stratification and it is produced by a combination of advection, vertical flux, and pressure redistribution. The analysis also illustrates that during the unstable stratification periods vertical entrainment of mean kinetic energy dominates, whereas during the stable regime horizontal entrainment is predominant. Finally, it is observed that in both scenarios, the single wind turbine and the large wind farm cases, turbulent mixing is driven by the background convective stratification during the unstable period and by the effect of the wind turbine during the stable regime. Title: Distribution of Mean Kinetic Energy Around an Isolated Wind Turbine and a Characteristic Wind Turbine of a Very Large Wind Farm Author: Cortina, Gerard, Calaf, Marc, Cal, Raul Bayoan Year: 2016 An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying surface temperature extracted from a selected period of the CASES-99 field experiment. A control volume approach is used to directly compare the transfer of mean kinetic energy around a characteristic wind turbine throughout a diurnal cycle considering both scenarios. For the very large wind farm case, results illustrate that the recovery of mean kinetic energy around a wind turbine is dominated by the vertical flux, regardless of atmospheric stratification. Contrarily, for an isolated wind turbine, the recovery is dependent on the background atmospheric stratification and it is produced by a combination of advection, vertical flux, and pressure redistribution. The analysis also illustrates that during the unstable stratification periods vertical entrainment of mean kinetic energy dominates, whereas during the stable regime horizontal entrainment is predominant. Finally, it is observed that in both scenarios, the single wind turbine and the large wind farm cases, turbulent mixing is driven by the background convective stratification during the unstable period and by the effect of the wind turbine during the stable regime. Close

• 24. [Article] Could Application of Column-Grid-Array (CGA) Technology Result in Inelastic-Strain-Free State-of-Stress in Solder Material?

  Physically meaningful and easy-to-use analytical stress model is developed for a short cylinder (beam) clamped at the ends and subjected to bending caused by the ends offset. The offset is due, in its ...

  Citation × Citation Citation Abstract Copy Title: Could Application of Column-Grid-Array (CGA) Technology Result in Inelastic-Strain-Free State-of-Stress in Solder Material? Author: Suhir, Ephraim, Ghaffarian, Reza, Nicolics, Johann Year: 2015 Physically meaningful and easy-to-use analytical stress model is developed for a short cylinder (beam) clamped at the ends and subjected to bending caused by the ends offset. The offset is due, in its turn, to an external lateral force that has to be determined from the known offset. It is envisioned that such a beam can adequately represent the state of stress in a column-grid-array (CGA) solder joint interconnection experiencing thermal loading due to the thermal expansion/contraction mismatch of the IC package and the printed circuit board (PCB). The CGA designs are characterized by considerably higher stand-off heights than ball-grid-array (BGA) systems. The offset Δ = lΔαΔt for a CGA solder joint located at the distance l from the mid-cross-section of the package/PCB assembly (the neutral point (DNP)), can be determined, in an approximate analysis, as a product of this distance and the “external” thermal mismatch strain ΔαΔt between the IC package and the printed circuit board (PCB). Here Δα is the difference in the effective coefficients of thermal expansion (CTE) of the PCB and package materials, and Δt is the change in temperature. The objective of the analysis is to demonstrate that the application of a CGA design, in which the solder joints are configured as short clamped–clamped beams, enables one not only to significantly relieve the thermally induced stresses, compared to the BGA system, but possibly to do that to an extent that the stresses in the solder material would remain within the elastic range. If this is achieved, the low-cycle-fatigue condition for the solder material will be replaced by the elastic-fatigue condition, thereby leading to a significantly longer fatigue lifetime of the joint. The elastic fatigue lifetime can be assessed, as is known, based on the Palmgren–Miner rule of linear accumulation of damages. Our analysis is limited therefore to elastic deformations. Title: Could Application of Column-Grid-Array (CGA) Technology Result in Inelastic-Strain-Free State-of-Stress in Solder Material? Author: Suhir, Ephraim, Ghaffarian, Reza, Nicolics, Johann Year: 2015 Physically meaningful and easy-to-use analytical stress model is developed for a short cylinder (beam) clamped at the ends and subjected to bending caused by the ends offset. The offset is due, in its turn, to an external lateral force that has to be determined from the known offset. It is envisioned that such a beam can adequately represent the state of stress in a column-grid-array (CGA) solder joint interconnection experiencing thermal loading due to the thermal expansion/contraction mismatch of the IC package and the printed circuit board (PCB). The CGA designs are characterized by considerably higher stand-off heights than ball-grid-array (BGA) systems. The offset Δ = lΔαΔt for a CGA solder joint located at the distance l from the mid-cross-section of the package/PCB assembly (the neutral point (DNP)), can be determined, in an approximate analysis, as a product of this distance and the “external” thermal mismatch strain ΔαΔt between the IC package and the printed circuit board (PCB). Here Δα is the difference in the effective coefficients of thermal expansion (CTE) of the PCB and package materials, and Δt is the change in temperature. The objective of the analysis is to demonstrate that the application of a CGA design, in which the solder joints are configured as short clamped–clamped beams, enables one not only to significantly relieve the thermally induced stresses, compared to the BGA system, but possibly to do that to an extent that the stresses in the solder material would remain within the elastic range. If this is achieved, the low-cycle-fatigue condition for the solder material will be replaced by the elastic-fatigue condition, thereby leading to a significantly longer fatigue lifetime of the joint. The elastic fatigue lifetime can be assessed, as is known, based on the Palmgren–Miner rule of linear accumulation of damages. Our analysis is limited therefore to elastic deformations. Close

• 25. [Article] Positive Matrix Factorization of PM2.5 - Eliminating the Effects of Gas/Particle Partitioning of Semivolatile Organic Compounds

  Gas-phase concentrations of semi-volatile organic compounds (SVOCs) were calculated from gas/particle (G/P) partitioning theory using their measured particle-phase concentrations. The particle-phase data ...

  Citation × Citation Citation Abstract Copy Title: Positive Matrix Factorization of PM2.5 - Eliminating the Effects of Gas/Particle Partitioning of Semivolatile Organic Compounds Author: Xie, Mingjie, Barsanti, Kelley, Hannigan, Michael P., Dutton, Steven J., Vedal, Sverre Year: 2013 Gas-phase concentrations of semi-volatile organic compounds (SVOCs) were calculated from gas/particle (G/P) partitioning theory using their measured particle-phase concentrations. The particle-phase data were obtained from an existing filter measurement campaign (27 January 2003-2 October 2005) as a part of the Denver Aerosol Sources and Health (DASH) study, including 970 observations of 71 SVOCs (Xie et al., 2013). In each compound class of SVOCs, the lighter species (e.g. docosane in n-alkanes, fluoranthene in PAHs) had higher total concentrations (gas + particle phase) and lower particle-phase fractions. The total SVOC concentrations were analyzed using positive matrix factorization (PMF). Then the results were compared with source apportionment results where only particle-phase SVOC concentrations were used (filter-based study; Xie et al., 2013). For the filter-based PMF analysis, the factors primarily associated with primary or secondary sources (n-alkane, EC/sterane and inorganic ion factors) exhibit similar contribution time series (r = 0.92-0.98) with their corresponding factors (n-alkane, sterane and nitrate + sulfate factors) in the current work. Three other factors (light n-alkane/PAH, PAH and summer/odd n-alkane factors) are linked with pollution sources influenced by atmospheric processes (e.g. G/P partitioning, photochemical reaction), and were less correlated (r = 0.69-0.84) with their corresponding factors (light SVOC, PAH and bulk carbon factors) in the current work, suggesting that the source apportionment results derived from filter-based SVOC data could be affected by atmospheric processes. PMF analysis was also performed on three temperature-stratified subsets of the total SVOC data, representing ambient sampling during cold (daily average temperature20°C) periods. Unlike the filter-based study, in this work the factor characterized by the low molecular weight (MW) compounds (light SVOC factor) exhibited strong correlations (r = 0.82-0.98) between the full data set and each sub-data set solution, indicating that the impacts of G/P partitioning on receptor-based source apportionment could be eliminated by using total SVOC concentrations. Title: Positive Matrix Factorization of PM2.5 - Eliminating the Effects of Gas/Particle Partitioning of Semivolatile Organic Compounds Author: Xie, Mingjie, Barsanti, Kelley, Hannigan, Michael P., Dutton, Steven J., Vedal, Sverre Year: 2013 Gas-phase concentrations of semi-volatile organic compounds (SVOCs) were calculated from gas/particle (G/P) partitioning theory using their measured particle-phase concentrations. The particle-phase data were obtained from an existing filter measurement campaign (27 January 2003-2 October 2005) as a part of the Denver Aerosol Sources and Health (DASH) study, including 970 observations of 71 SVOCs (Xie et al., 2013). In each compound class of SVOCs, the lighter species (e.g. docosane in n-alkanes, fluoranthene in PAHs) had higher total concentrations (gas + particle phase) and lower particle-phase fractions. The total SVOC concentrations were analyzed using positive matrix factorization (PMF). Then the results were compared with source apportionment results where only particle-phase SVOC concentrations were used (filter-based study; Xie et al., 2013). For the filter-based PMF analysis, the factors primarily associated with primary or secondary sources (n-alkane, EC/sterane and inorganic ion factors) exhibit similar contribution time series (r = 0.92-0.98) with their corresponding factors (n-alkane, sterane and nitrate + sulfate factors) in the current work. Three other factors (light n-alkane/PAH, PAH and summer/odd n-alkane factors) are linked with pollution sources influenced by atmospheric processes (e.g. G/P partitioning, photochemical reaction), and were less correlated (r = 0.69-0.84) with their corresponding factors (light SVOC, PAH and bulk carbon factors) in the current work, suggesting that the source apportionment results derived from filter-based SVOC data could be affected by atmospheric processes. PMF analysis was also performed on three temperature-stratified subsets of the total SVOC data, representing ambient sampling during cold (daily average temperature20°C) periods. Unlike the filter-based study, in this work the factor characterized by the low molecular weight (MW) compounds (light SVOC factor) exhibited strong correlations (r = 0.82-0.98) between the full data set and each sub-data set solution, indicating that the impacts of G/P partitioning on receptor-based source apportionment could be eliminated by using total SVOC concentrations. Close