Intermetallic Layer Growth Kinetics Calculation for Tin Silver Copper Solders
Calculate intermetallic layer growth using parabolic diffusion equations to cap high-temperature joint failure and enforce reflow thermal limits.
Lattice
Molten tin-silver-copper solder reacts directly with solid copper metallization during reflow to build intermetallic compound structures. The reaction forms an initial scalloped deposit composed primarily of eta-phase copper-tin solder compound alongside isolated epsilon-phase silver-tin crystals suspended in the bulk matrix. Solidification halts primary liquid-solid dissolution, leaving a boundary zone whose initial thickness sits between half a micron and two microns depending on peak temperature and liquid dwell duration.
Phase Composition at Liquidus Solidification
Solid-state diffusion drives continuous atomic reorganization across the solder-substrate boundary once cooling completes. Tin atoms migrate toward the copper substrate while copper diffuses outward into the solder matrix. This dual directional movement converts the initial scalloped eta-phase layer into a dual-layer structure.
A thin, sub-micron gamma-phase layer nucleates directly adjacent to the copper substrate, growing underneath the thicker eta-phase layer that faces the bulk solder matrix.
Silver content within tin-silver-copper alloys alters the precipitation behavior of epsilon-phase particles during cooling. Alloys containing three percent to four percent silver produce fine dispersions of silver-tin intermetallics near the interface zone. These dispersed particles restrict localized grain growth within the bulk solder matrix.
Tin atoms migrate fast. High concentration gradients at the interface preserve rapid reaction rates during early thermal exposure.
Intermetallic compound growth at copper interfaces converts ductile solder matrix volume into brittle crystalline phases during high-temperature storage.
Diffusion Kinetics at Copper Interface Boundaries
Atomic transport through the interface depends on temperature, time, and defect density within the crystalline matrix. The reaction rate remains high while the interface exhibits high roughness, as copper species move through grain boundaries between individual scalloped projections. Scalloped structures flatten over time.
As the layer flattens, volume diffusion through the intermetallic compound lattice replaces grain boundary transport as the dominant mechanism.
Substrate surface finishes alter initial phase formation and migration velocity. Direct placement on bare copper creates the standard dual-layer intermetallic sequence. Electroless nickel immersion gold plating introduces a nickel-tin binary intermetallic barrier that slows copper transport into the solder joint, changing the overall growth kinetic profile.
Nickel atoms substitute into the copper-tin lattice, forming a ternary copper-nickel-tin phase that lowers total growth velocity during subsequent thermal stress.
Initial reflow parameters set the baseline kinetic condition for all subsequent aging. High reflow peak temperatures increase initial dissolution rates, creating thicker starting layers before any solid-state aging occurs. Extended liquid dwell times above liquidus produce larger initial scallop heights.
Temperature governs the reaction. Lower reflow profiles yield tighter initial intermetallic distributions that resist early mechanical degradation under thermal stress.
Arithmetic
Predicting intermetallic layer thickness requires mathematical modeling based on classical solid-state diffusion principles. The physical growth of intermetallic layers during thermal storage follows a parabolic rate relationship driven by volume diffusion through the existing compound matrix.
Parabolic Rate Law Governing Layer Thickness
The total intermetallic layer thickness at any given aging duration follows a standard power-law kinetic equation:
x(t) = x0 + D^0.5 t^0.5
In this equation, x(t) represents total intermetallic thickness in meters at time t, x0 is initial intermetallic thickness measured immediately after reflow, D is the effective diffusion coefficient expressed in square meters per second, and t is total thermal exposure time in seconds. When total layer growth is dominated purely by volume diffusion, the kinetic exponent equals 0.5. Deviations from 0.5 indicate competing mechanisms such as grain boundary diffusion or grain growth within the intermetallic layer itself.
Activation Energy and Pre Exponential Coefficient Extraction
Temperature dependence of the effective diffusion coefficient follows the classical Arrhenius relationship:
D = D0 exp(-Q / (R T))
Here, D0 represents the pre-exponential factor in square meters per second, Q is activation energy in Joules per mole, R is the universal gas constant (8.314 Joules per mole-Kelvin), and T is absolute temperature in Kelvin. Determining these parameters requires conducting isothermal aging trials across at least three distinct thermal settings, typically 100°C, 125°C, and 150°C, followed by cross-sectional analysis at defined time intervals.
Plotting the natural logarithm of growth rate constants against the inverse absolute temperature yields a straight line. The slope of this line equals negative activation energy divided by the gas constant, while the y-intercept provides the natural logarithm of the pre-exponential factor. Typical activation energy values for total intermetallic growth in lead-free solder joints on copper substrates range between 80 kilojoules per mole and 105 kilojoules per mole.
Isothermal aging at 125°C for 500 hours doubles initial intermetallic layer thickness in standard lead-free solder joints on bare copper substrates.
Worked Calculation for Isothermal Aging in Lead Free Assemblies
Take a solder joint produced with SAC305 solder on bare copper metallization. Assume an initial post-reflow intermetallic layer thickness x0 of 1.20 micrometers. Assume empirical aging trials for this specific alloy-substrate system established an activation energy Q of 88,500 Joules per mole and a pre-exponential factor D0 of 1.45 x 10^-5 square meters per second.
Calculate total intermetallic layer thickness after 1,000 hours of continuous operating exposure at 105°C (378.15 Kelvin).
- Temperature Conversion converts operating temperature from Celsius to Kelvin: T = 105 + 273.15 = 378.15 Kelvin.
- Time Unit Conversion converts total aging duration from hours to seconds: t = 1,000 3,600 = 3,600,000 seconds.
- Diffusion Coefficient Calculation evaluates the temperature exponent: -Q / (R T) = -88,500 / (8.314 378.15) = -28.15. Exponentiation yields exp(-28.15) = 5.95 x 10^-13. Multiplying by pre-exponential coefficient D0 yields D = 1.45 x 10^-5 5.95 x 10^-13 = 8.63 x 10^-18 square meters per second.
- Growth Value Calculation multiplies diffusion coefficient by exposure time and calculates square root: (D t)^0.5 = (8.63 x 10^-18 3,600,000)^0.5 = (3.11 x 10^-11)^0.5 = 5.57 x 10^-6 meters, or 5.57 micrometers.
- Total Thickness Summation adds initial thickness to calculated growth: x(1000h) = 1.20 + 5.57 = 6.77 micrometers.
| Solder Alloy | Aging Temp (°C) | D0 (m²/s) | Q (kJ/mol) | Growth Rate K (µm/h^0.5) | Calculated Thickness at 1000h (µm) |
|---|---|---|---|---|---|
| SAC305 | 100 | 1.45 x 10^-5 | 88.5 | 0.142 | 5.69 |
| SAC305 | 125 | 1.45 x 10^-5 | 88.5 | 0.288 | 10.31 |
| SAC305 | 150 | 1.45 x 10^-5 | 88.5 | 0.541 | 18.31 |
| SAC405 | 100 | 1.20 x 10^-5 | 86.2 | 0.151 | 5.98 |
| SAC405 | 125 | 1.20 x 10^-5 | 86.2 | 0.301 | 10.72 |
| SAC405 | 150 | 1.20 x 10^-5 | 86.2 | 0.558 | 18.85 |
High thermal storage accelerates consumption. Miscalculating diffusion parameters leads to field failures when intermetallic thickness exceeds design thresholds ahead of schedule, causing unexpected mechanical joint detachment under vibration or thermal shock.
Probe
Accurate verification of kinetic models demands quantitative microstructural examination of cross-sectioned solder connections. Mechanical preparation of mounted samples introduces artifacts if grinding, polishing, and chemical etching steps lack strict operational controls.
Cross Sectional Microscopy and Chemical Etching Routines
Sample preparation requires sectioning through the geometric center of the solder joint to avoid edge effects and false layer thickness readings. Diamond blade cutting under constant cooling fluid prevents thermal overheating that could induce artificial solid-state phase growth during preparation. Grinding through successive silicon carbide papers down to 1200 grit removes blade damage zones.
Polishing with diamond suspensions from three micrometers down to a quarter micrometer achieves a scratch-free mirror finish across both soft solder matrix and hard intermetallic phases. Etching reveals interface boundaries clearly. A brief chemical etch using a nitric acid, hydrochloric acid, and glycerol mixture reveals phase boundaries by selectively attacking the tin-rich solder matrix, exposing the true topography of the copper-tin compound layers.
Standard IPC-TM-650 test methods mandate cross-sectional thickness measurements across at least ten non-adjacent points along the intermetallic interface to establish statistical mean thickness.
Image Analysis Calibration and Scallop Thickness Normalization
Scanning electron microscopy operating in backscattered electron mode provides superior elemental contrast compared to optical systems. Backscattered electron imaging distinguishes the lower average atomic number eta-phase from the higher atomic number bulk matrix and underlying gamma-phase layer. Measurements require spatial calibration.
Scalloped interface geometry introduces measurement uncertainty when using single linear distance markers. Converting irregular scalloped cross-sections into equivalent planar thickness requires dividing total measured intermetallic area by horizontal interface length:
x_avg = A_total / L_interface
- Optical Misalignment Errors stem from tilting the cross-sectional plane relative to the electron beam, artificially expanding apparent layer thickness.
- Over-Etching Artifacts dissolve boundary regions between adjacent intermetallic scallops, obscuring true phase boundaries during automated image thresholding.
- Substrate Dissolution Variations cause uneven baseline references along copper interfaces, requiring manual identification of the original substrate interface line.
- Polishing Smear Defects push soft tin matrix across hard intermetallic edges, disguising true layer boundaries under secondary electron imaging modes.
| Microscopy Technique | Magnification Range | Resolution Limit (µm) | Thickness Measurement Error (%) | Phase Distinction Capability |
|---|---|---|---|---|
| Optical Microscopy | 200x – 1000x | 0.50 | ±15.0 | Poor (Total layer only) |
| SEM (Secondary Electron) | 1000x – 10000x | 0.05 | ±5.0 | Moderate (Topography based) |
| SEM (Backscattered Electron) | 1000x – 10000x | 0.02 | ±2.0 | Excellent (Atomic number contrast) |
| EDS Mapping | 200x – 20000x | 0.10 | ±3.5 | Definitive (Chemical identification) |
Suppliers frequently explain away thick intermetallic layers by claiming cross-sectional preparation smeared the soft solder over the compound boundary during manual polishing.
Stress
Intermetallic growth alters local stress fields and mechanical behavior within the solder joint structure. Brittle compound layers exhibit significantly lower fracture toughness and higher elastic modulus compared to the surrounding bulk tin matrix.
Why Do Kirkendall Voids Accelerate Joint Failure during Isothermal Aging?
Differential diffusion rates between copper and tin atoms produce vacancy accumulation along the substrate interface during extended thermal exposure. Copper atoms migrate out of the substrate into the intermetallic layer faster than tin atoms diffuse toward the substrate. Uncompensated atomic flux leaves lattice vacancies behind.
Kirkendall voiding weakens the joint.
Vacancies coalesce into microscopic voids along the interface between the substrate and the inner intermetallic phase layer. Thermal aging expands void density across the interface plane. High void density creates continuous crack propagation paths under mechanical shear or shock loading, transforming a ductile bulk solder fracture mode into a catastrophic brittle interface failure mode.
Intermetallic compound growth rates exceeding 0.05 micrometers per root-hour under continuous thermal stress correlate directly with brittle interfacial fracture failures during board-level drop testing.
Shear Strength Degradation under Thermal Cycling
Thermal expansion mismatches between printed circuit board substrates, intermetallic layers, and solder alloys create localized shear stress during thermal cycling. Thick intermetallic layers concentrate strain energy directly at the interface zone instead of allowing strain energy to dissipate through plastic deformation within the bulk solder matrix.
Aging weakens shear capability. As intermetallic layer thickness exceeds four to five micrometers, joint shear strength decreases by thirty percent to fifty percent compared to post-reflow values. The mechanical failure path shifts from bulk solder shearing to brittle cleavage along phase boundaries.
- Substrate Copper Purity Control requires tracking trace impurities like sulfur or phosphorus that accelerate interface vacancy formation during thermal storage.
- Reflow Peak Thermal Budgeting limits initial layer growth to preserve remaining copper thickness for long-term thermal service requirements.
- Isothermal Storage Temperature Caps prevent accelerated diffusion kinetics from consuming full solder pad metallization within product operational lifespans.
Whether specific trace micro-alloying elements like bismuth, indium, or nickel can completely suppress void coalescence without reducing overall joint fatigue resistance under extended thermal cycling remains open to dispute.
Docket
Procurement specifications for high-reliability assemblies must establish strict threshold limits on allowable intermetallic growth and initial thermal exposure budgets. Supplier quality agreements require explicit verification routines to enforce process windows before product shipment.
Supplier Process Specifications and Reflow Thermal Profiles
Manufacturing agreements must define peak reflow temperature windows, time above liquidus ranges, and cooling rate slopes to control initial intermetallic phase formation. Thermal profiles exceeding 245°C peak temperature or 90 seconds liquidus dwell generate excessive initial compound thickness that reduces total thermal storage life.
Quality inspectors verify production batches by requiring microstructural cross-sections from monthly test coupons. Process drifts toward longer liquid dwell times appear immediately as enlarged scalloped height distributions under backscattered electron examination.
Contractual Reliability Warranties and Batch Acceptance Limits
Landed cost calculations must incorporate long-term field exposure degradation risks. High thermal storage environments accelerate growth kinetics, turning minor reflow process deviations into major warranty liability lines on corporate balances.
| Parameter | Initial Post-Reflow Limit | Acceptable Post-Aging Range | Critical Failure Threshold | Verification Method |
|---|---|---|---|---|
| Total Intermetallic Thickness | 0.8 µm – 2.0 µm | 2.1 µm – 5.0 µm | > 6.0 µm | SEM BSE Cross-Section |
| Gamma Phase Layer Thickness | < 0.3 µm | 0.3 µm – 1.2 µm | > 1.8 µm | SEM EDS Phase Analysis |
| Interface Kirkendall Void Area Fraction | < 1.0 % | 1.0 % – 5.0 % | > 10.0 % | High-Res SEM Image Analysis |
| Interfacial Shear Strength | > 45 MPa | 30 MPa – 45 MPa | < 25 MPa | High-Speed Ball Shear Test |
Per IPC-A-610 Section 8.3.5, any assembly lot exhibiting continuous intermetallic layer thickness exceeding two point five micrometers in the post-reflow state shall be quarantined pending microstructural phase review and engineering disposition.