Lifetime Model for Solder Layers

Transcription

1 Lifetime Model for Solder Layers I. Kovačević-Badstübner, A. Stupar, and J.W. Kolar ETH Zurich, Switzerland Power Electronic Systems Laboratory / kovacevic@lem.ee.ethz.ch

2 2/23 Overview Reliability of Power Modules Failure Mechanism of Power Modules Power Cycling (PC) tests, Temperature Cycling (TC) tests Analytical vs. Physical Lifetime Modeling Physical lifetime model based on Clech s algorithm for Solder Interconnections Solder Interconnection Failure Solder equations (elastic, plastic and creep deformation) Energy-based modeling Lifetime Estimation based on PC tests

3 3/23 Reliability of Power Modules Power Module: layers with typically different thermal constants have great influence on heating and cooling rate of module Thermo-mechanical Stress: temperature gradients and CTE (Coefficient of Thermal Expansion) difference between layers Mission Profile Lifetime Modeling

4 4/23 Failure of Power Modules Bond wire fatigue (lift off, heel cracking) Aluminium reconstruction Brittle cracking, fatigue crack propagation Corrosion of interconnections Solder fatigue Burnout failures Ref [D. C. Katsis, Thermal Characterization of Die-Attach Degradation in the Power MOSFET ] Ref [Lefranc, G., et al. (2003) Aluminium bondwire properties after 1 billion cycles ] Ref [Lefranc, G., eta al. (2003) Aluminium bond-wire properties after 1 billion cycles ] Ref [U. Scheuermann, R. Schmidt (EPE 2011), Impact of Solder Fatigue on Module Lifetime in Power Cycling Tests ]

5 5/23 Lifetime Modeling Analytical Models Basic N f Model: Coffin-Manson f ÿ D cyc N f Number of Cycles to Failure f ÿ D cyc exp E A k B T jm Rain Flow Algorithm (counting DT cyc in mission profile) + Miner s rule 1 DT j - Junction Temperature Swing

6 6/23 Accelerated Power Cycling Tests Accelerated Power Cycling Tests

7 7/23 Lifetime Modeling Physical Models Failure and deformation mechanism have to be known in advance * Bond Wire Lift-off : Crack Propagation * Solder Failure: Stress-/Strain-/Damage /Energy-based model Thermo-mechanical behaviour: stress (t, s) and strain (g, e)

8 8/23 Physical Lifetime Modeling Dg, Dt, D, D d d = 1 D 1 2 Dg 2e / D ÿ K Parameterization of models? Ref [M. Ciappaet al., Lifetime Prediction and Design of Reliability Tests for High-Power Devices in Automotive Applications ]

9 9/23 Stress-Strain Relation for Solder Joint How does stress appear and act within materials? Correlate stress/strain values with observed failures? Shear force Hysteresis: stress-strain response of solder joint to periodical temperature cycling Shear strain Ref [M. Hall, Forces, moments, and displacements during thermal chamber cycling of leadless ceramic chip carriers soldered to printed boards ] Energy based models DW tot g g t g

10 10/23 Proposed Lifetime Modeling Approach Main idea of energy-based models * D : Total deformation energy accumulated within module DW acc g g t g * End-of-Life (EOL): device fails when deformation work D reaches critical value D Clech s algorithm Constitutive solder equations

11 11/23 Solder Physics Equations (1) Fatigue: elastic and plastic time-independent deformation T 0 1 ÿ 273K t g pl p ÿ g el t

12 12/23 Solder Physics Equations (2) tot Creep: time-dependent plastic deformation creep primary creep secondary creep tertiary creep g g 1ÿ ÿ t ÿ / 2 ÿ ÿ t ÿ / g g ÿ + ÿ Sn37Pb aÿt sinh ÿ / sinh aÿt ÿ / g g 1ÿ aÿt sinh ÿ / 0 Time Material parameters (alloy-dependent) g g 1ÿt ÿ / ÿ t/s + 2 ÿt ÿ / ÿ t/s t g g ÿ ÿ 1 ÿg ÿ Sn3.5Ag

13 14/23 Stress-Reduction Lines of Solder Material Solder geometry properties: height-h, length-l, area-a of solder joint Geometry dependent parameters which has to be found: Mechanical modeling of power module based on Finite Element Analysis Optimization Approach g t 1ÿ 0 º, 1º

14 15/23 Numerical Modeling of Stress-Strain Clech s algorithm g 1 - g 12 : fast time-independent transient stress-strain state (g 1, t 1 ) at time t stress-strain state (g 2, t 2 ) at time t + Dt

15 16/23 Lifetime Model Parameterization Input: 3 PC Tests 1,, f1 2, f2, 3, f3, 1,2, 3 Exponent depends on solder material Optimization routine is used to find best set, 1 º1 Relative Lifetime Estimation t 1 dg 1 t 2 dg 2

16 17/23 Input Data for Lifetime Estimation Solder material data from Literature X. Q. Shi et al., Creep Behaviour and Deformation Mechanism Map of SnPb Sutectic Solder Alloy, 2003; J-P. Clech, An obstacle controlled creep model for SnPb and Sn-based lead-free solders, 2004; Power Cycling (PC) Data: Temperature Profiles - T solder (t) & Number of Cycles to Failure - N f Solder geometry data: First task: Parameterization of the proposed lifetime model to determine geometry solder parameters Searching for optimal parameter set [K, D 1 ] Second task: Lifetime estimation for given PC and mission profiles

17 18/23 Verification based on PC Test Data PCs with solder (chip solder layer) failure as dominant failure mode PC Temperature Profiles: T solder (t) extracted based on thermal model of power module [K, D 1 ] selected based on min parameterization error (for = 2.2, f hys ) PC 1-3 used for parameterization: PC1: DT = 115 K, T max = 155±C, t on = 50s PC2: DT = 70 K, T max = 150±C, t on = 0.95s PC3: DT = 70 K, T max = 150±C, t on = 5s PC1 PC2 PC3

18 19/23 Results for PC1-3 Error of parameterization = 1.71 W tot1, W tot2, W tot3 (N fmin, N fmax ) N f1 = , N fcalc1 = (31 302, , 53654) N f2 = N fcalc2 = ( , , ) N f3 = , N fcalc3 = ( , , )

19 20/23 Results for PC1-3 Strain deformation under given T(t)

20 21/23 Lifetime Estimation based on PC1-3 Verification for PC A-E PCA: DT = 134 K, T max = 174±C, t on = 64.5s N fa = , ( ) d max =-19% PCB: DT = 67 K, T max = 146±C, t on = 0.95s N fb = , ( ) d max =-0.3% PCC: DT = 70 K, T max = 150±C, t on = 1.2s N fc = , ( ) d max =-10.8% PCD: DT = 73K, T max = 150±C, t on = 2.9s N fd = , ( ) d max =-9.6% PCE: DT = 109K, T max = 148±C, t on = 13.6s N fe = , ( ) d max =-18.3% Fast or slow temperature rate during T max level determine strain development Longer pulse: stationary situation is reached, more deformation Parameter DT influence lifetime PCX: DT = 136K, T max = 176±C, t on = 2s N fx = , ( ) d max =-23.5%

21 N f vs. DT Curves 22/23

22 23/23 MATLAB Graphical User Interface MATLAB GUI Options Search Parameters Procedure Load Input Data Set Simulation Settings Modeling for selected [K, D 1 ] PC Lifetime Estimation Analyze Stress-Strain Response Rel. Lifetime Calculation Readme File

23 Thank You!