The migration model (TB,MIGR) is
used to model electromigration effects. The atomic flux option is used in this example.
For a detailed description of the input for this migration model, including a complete
example, see Atomic Flux Option (TBOPT = 0) in the Material Reference.
The constants and material coefficients in μMKSV units are used as described in the tables below.
Most of the material properties for copper and SAC were taken from Wang and Liang.[2] Some copper material properties, such as the pre-exponential diffusivity coefficient, the activation energy of diffusion, and the change number, were selected from Chao et al.[3]
It is assumed that the electrical resistivity of the solder and the copper plates is not affected by temperature or concentration. The proper direction of atomic flux with respect to the electric current density is specified by the negative sign of the charge numbers. The coefficients of diffusion expansion are specified as positive to ensure the correct sign of the diffusion strain for backstress calculation.
| Constants | ||
|---|---|---|
| Boltzmann constant kB (pJ/K) | 1.3806488E-11 | |
| Boltzmann constant kB_eV (eV/K) | 8.6173324E-5 | |
| Universal gas constant R (J/(K*mol)) | 8.31445 | |
| Reference temperature for thermal strain calculation (°C) | 25 | |
| Reference normalized concentration for diffusion strain calculation | 1.0 | |
| Copper | ||
|---|---|---|
| Property | Value | MP Label |
| Young’s modulus (MPa) | 127.7E3 | EX |
| Poisson’s ratio | 0.31 | PRXY |
| Electrical resistivity (TOhm*μm @ 200°C) | 2.38E-14 | RSVX |
| Pre-exponential diffusivity ((μm)2/s) | 7.8E7 | DXX |
|
Thermal conductivity (pW/(μm*K)) | 393E6 | KXX |
|
Specific heat (pJ/(kg*K) | 385.2E12 | C |
|
Density (kg/(μm)3) | 8900E-18 | DENS |
|
Coefficient of thermal expansion (1/°C) | 17.1E-6 | ALPX |
|
Coefficient of diffusion expansion | 1E-5 | BETX |
| Property | Value | TBDATA Constant |
|
Activation energy of diffusion Qa (J/(K*mol)) | 210E3 | C1 = Qa/R |
| Atomic volume V1 (μm)3 | 1.182E-11 | C2 = V1/kB |
| Charge number Z1 | -4 | C4 = Z1/kB_eV |
| SnAgCu (SAC) | ||
|---|---|---|
| Property | Value | MP Label |
| Young’s modulus (MPa) | 26.2E3 | EX |
| Poisson’s ratio | 0.35 | PRXY |
|
Electrical resistivity (TOhm*μm @ 200°C) | 20.75E-14 | RSVX |
|
Pre-exponential diffusivity ((μm)2/s) | 4.1E7 | DXX |
| Thermal conductivity (pW/(μm*K)) | 57E6 | KXX |
|
Specific heat (pJ/(kg*K)) | 219E12 | C |
| Density (kg/(μm)3) | 7390E-18 | DENS |
|
Coefficient of thermal expansion (1/°C) | 23E-6 | ALPX |
| Coefficient of diffusion expansion | 1E-5 | BETX |
| Property | Value | TBDATA Constant |
| Activation energy of diffusion Ea (eV) | 0.8 | C1 = Ea/kB_eV |
| Atomic volume V2 (μm)3 | 2.71E-11 | C2 = V2/kB |
| Heat of transport Q (eV) | 0.0094 | C3 = Q/kB_eV |
| Charge number Z2 | -23 | C4 = Z2/kB_eV |
The input listing below demonstrates how to use the above properties to define the migration model for solder.
kB=1.3806488e-23*1.e12 ! Boltzmann constant, pJ/K kB_eV=8.6173324e-5 ! Boltzmann constant, eV/K Ea=0.8 ! activation energy, eV V2=2.71e-29*1e18 ! atomic volume, μm^3 Q=0.0094 ! heat of transport, eV Z2=-23 ! charge number tb,migr,2 ! migration model for SAC solder joint tbdata,1,Ea/kB_eV ! activation energy of diffusion/kB_eV tbdata,2,V2/kB ! atomic volume/kB tbdata,3,Q/kB_eV ! coefficient of thermomigration/kB_eV tbdata,4,Z2/kB_eV ! charge number/kB_eV
Following are the contact element properties defined via CONTA174 real constants.
| Contact Properties | ||
|---|---|---|
| Property | Real Constant | Value |
| Structural stiffness | FKN | 1.0 times underlying element stiffness |
| Thermal conductance (pW/((μm)2*°C)) | TCC | 1E6 |
| Electrical conductance (pA/((μm)2*Volt)) | ECC | 1E14 |
| Diffusivity coefficient ((μm)3/s) | DCC | 1E6 |