Constraining and size effects in lead-free solder joints J. Cugnoni1, J. Botsis1, J.Janczak2 1 Lab. Applied Mechanics & Reliability, EPFL, Switzerland 2 Füge- und Grenzflächentechnologie, EMPA, Switzerland J.Cugnoni, joel.cugnoni@epfl.ch

J.Cugnoni, joel.cugnoni@epfl.ch Outline Introduction Global project & goals Constraining effects In-situ characterization by inverse numerical methods Experimental Test setup Results: Constrained stress-strain curves of SnAgCu joints Numerical Modelling & inverse identification method Identified constitutive laws (unconstrained) Constraining & size effects Conclusion J.Cugnoni, joel.cugnoni@epfl.ch

Deformation & damage of lead-free solder joints Objectives Plastic constitutive law of Sn-4.0Ag-0.5Cu solder Variable solder gap width Effects of constraints Effects of size Manufacturing Size / Constraining Effects Thermo- mechanical History Micro Structure Interface Nature of Irreversible Deformations Constitutive Equations Global Project ? J.Cugnoni, joel.cugnoni@epfl.ch

Constraints in solder joints Plastic deformation of solder: - constant volume - shrinks in lateral directions Rigid substrates: - impose lateral stresses at the interfaces - additionnal 3D stresses => apparent hardening => constraining effects Solder joint in tension: - stiff elastic substrates - plastic solder (n~=0.5) J.Cugnoni, joel.cugnoni@epfl.ch

Stress field in constrained solder Front surface view 47 MPa 76 MPa Cu Solder FEM 37 MPa 70 MPa Mid-plane view J.Cugnoni, joel.cugnoni@epfl.ch

Stress field in constrained solder Von Mises eq. stress Hydrostatic pressure Front surface view 54 MPa -47 MPa Cu Solder FEM 58 MPa -37 MPa Mid-plane view J.Cugnoni, joel.cugnoni@epfl.ch

Constitutive law & constraints Effects of the constraints: Non-uniform, tri-axial, plasticity dependent, stress field in the solder Constitutive law of the solder Independant of geometry, but may depend on characteristic size & porosity Constraining effects Apparent stress - strain law of the solder confined in a joint Depends on constraints (geometry, base materials) J.Cugnoni, joel.cugnoni@epfl.ch

Constitutive law & constraints 3D FEM: includes all the geometrical effects Apparent stress - strain curve of the solder in a joint is what we usually measure depends on geometry Constitutive law of the solder is needed for FE simulations independent of geometry Inverse numerical identification of a 3D FEM ??? J.Cugnoni, joel.cugnoni@epfl.ch

In-situ characterization Mechanical properties of lead-free solder materials can be process, geometry & size dependant In-situ characterization of the mechanical properties in real solder joints can provide accurate data for modelling and optimization of solder joints Stress / strain fields inside real solder joints are very heterogeneous and classical characterization techniques are not suitable (no analytical solution) By combining the advantages of finite element modelling and in-situ optical strain measurement (digital image correlation), a novell inverse numerical identification procedure can be used to extract accurate constitutive properties of the solder material from a real constrained solder joint J.Cugnoni, joel.cugnoni@epfl.ch

Methodology In-situ characterization of constitutive parameters Experimental Specimen Production Tensile Test (DIC) Experimental Load - Displacement Curve Apparent Stress-Strain Curve (Constrained) Constraining Effects Identification Loop Optimization (Least Square Fitting) Stress - Strain Constitutive Law (Unconstrained) Geometry & Constitutive Model FEM Simulated Load - Displacement Curve Numerical Simulations J.Cugnoni, joel.cugnoni@epfl.ch

J.Cugnoni, joel.cugnoni@epfl.ch Experimental setup Tensile tests: Sn-4.0Ag-0.5Cu solder 0.2 to 2.0 mm gap width Instron 5848 Microtester 2kN load cell Displacement ramp 1 mm/s Digital Image Correlation: 1.3MPix CCD camera 30x optical microscope 3x2 mm observation region Displacement resolution 0.2 mm J.Cugnoni, joel.cugnoni@epfl.ch

Constrained stress-strain curves ~ +/- 5% scatter => averaging J.Cugnoni, joel.cugnoni@epfl.ch

Constrained stress-strain curves Similar results No clear conclusion Identify constitutive properties Stress (Pa) Strain (-) J.Cugnoni, joel.cugnoni@epfl.ch

Finite Element Modelling Imposed displacement & calculated load 3D FEM of 1/8th of the specimen Copper: Elastic behaviour: ECu = 112 GPa, n = 0.3 Solder: Elasto-plastic with isotropic exponential & linear hardening Chosen to fit bulk solder plastic response 5 unknown parameters: Cu Sn-Ag-Cu Simulated load-displacement curve Elongation of solder J.Cugnoni, joel.cugnoni@epfl.ch

Inverse identification procedure Identification parameters: Objective function: relative difference of load-displ. curves with Pexp = measured load-displacement curve and Pnum(a) = simulated load-displacement curve Levenberg-Marquardt non-linear least square optimization algorithm to solve: Gradients of objective function by Finite Differences J.Cugnoni, joel.cugnoni@epfl.ch

Inverse identification Blue: initial load-displ. curve Red: identified load-displ. curve Black: measured load-displ. curve Load - displacement curves Relative errors Solution time: 4 iterations / 50 FE solutions required to identify the material properties (~1h30) Accuracy: max error +/-4% on load – displacement curve Convergence Very robust convergence even with bad initial guess of the parameters J.Cugnoni, joel.cugnoni@epfl.ch

Identified constitutive parameters Mechanical properties decreasing for smaller joints due to a visible increase of the porosity: Manufacturing process is also size dependant !! J.Cugnoni, joel.cugnoni@epfl.ch

Fractography & Porosity Metallography after testing Fractography Porosity: Responsible for the scatter in exp. data Concentrated at the interface: critical !! Size of pores ~constant for all gap widths => more influence in thinner joints Porous metal constitutive law ?? J.Cugnoni, joel.cugnoni@epfl.ch

Constraining effects 2 mm + 16 % J.Cugnoni, joel.cugnoni@epfl.ch

Constraining effects 1 mm + 22 % J.Cugnoni, joel.cugnoni@epfl.ch

Constraining effects 0.5 mm + 30 % J.Cugnoni, joel.cugnoni@epfl.ch

Constraining effects 0.2 mm + 37 % J.Cugnoni, joel.cugnoni@epfl.ch

Size effects decrease of yield & ultimate stress ~7-8 MPa increase of constraining effects ~ 10 MPa J.Cugnoni, joel.cugnoni@epfl.ch

Constraining effects / gap Gap (mm) J.Cugnoni, joel.cugnoni@epfl.ch

Plastic deformations: 1mm Gap Average Strain: 2% Max Strain: 10% 1 Outside Inside Two plastic deformation regions: At the interface on the outside surface In the center of the joint 2 J.Cugnoni, joel.cugnoni@epfl.ch

J.Cugnoni, joel.cugnoni@epfl.ch Conclusions In-situ characterization by optical measurement & inverse numerical method: Versatile & powerfull: real joints (geometry & processing) highly heterogeneous stress fields in test specimens Can determine real constitutive properties from constrained materials: provide geometry-independant mechanical properties ideal for further modelling & optimization of joints / packages A general tool for characterization of small size & thin layer materials produced with realistic processing and geometry conditions J.Cugnoni, joel.cugnoni@epfl.ch

J.Cugnoni, joel.cugnoni@epfl.ch Conclusions Size & scale effects in lead-free solders Actual constitutive properties are size dependant: In the present case, ult. stress decreases by 13% from 2 mm to 0.2 mm joints due to increased porosity in thinner joints. material scale effects & the "scaling" of the production methods have a combined influence. Constraining effects: Constraining effects are size dependant ~(1/Gap)0.6 Up to 37% of additionnal hardening due to constraints Constrained & constitutive properties are NOT equivalent Apparent stress-strain curves are geometry dependant !! J.Cugnoni, joel.cugnoni@epfl.ch

Constraining & size effects: Future developments Constraining & size effects: Microstructure analysis / measure porosity Additionnal test with 0.1mm and 2mm gap widths Improvement of manufacturing quality / porosity Industrial aspects: Apply the in-situ characterization method (DIC / mixed num./exp. Identification) to a real industrial package (for example BGA) Determination of the mechanical properties of a solder joint under realistic loading conditions (power-cycles) Realistic Experiment (DIC) Mixed num-exp identification: realistic properties Design / process validation FE Analysis & optimization J.Cugnoni, joel.cugnoni@epfl.ch

STSM: ESPI measurements Pr. Karalekas, Univ. Piraeus, Greece, STSM at EPFL Incremental loading by step of 9 microns Measurement of global incremental displacement field by phase difference between the n-th & n+1-th load state Reconstruction of the total displacement field by summation of the increments Theoretical sensitivity: ~ 0.7 microns J.Cugnoni, joel.cugnoni@epfl.ch

Results: sp1, 0.2mm joint, global view J.Cugnoni, joel.cugnoni@epfl.ch

Results: sp1, 0.2mm joint, displ. distrib. J.Cugnoni, joel.cugnoni@epfl.ch

Results: sp1, 0.2mm joint, strain distrib. J.Cugnoni, joel.cugnoni@epfl.ch

Results: 0.2mm joint, local view J.Cugnoni, joel.cugnoni@epfl.ch

Results: sp3, 1mm joint, displ. distrib. J.Cugnoni, joel.cugnoni@epfl.ch

Results: sp3, 1mm joint, strain distrib. J.Cugnoni, joel.cugnoni@epfl.ch

Results: stress-strain curves J.Cugnoni, joel.cugnoni@epfl.ch

ESPI measurement for joints + Sensitivity independant from magnification: excellent for global observations Full field measurement Monitoring of the damage evolution - Decorrelation when increasing magnification: not suitable for local measurements Very sensitive to out of plane displacements: decorrelates Incremental loading not suitable with creep In general: difficult to master, takes a lot of time J.Cugnoni, joel.cugnoni@epfl.ch