2.16. Electric-Diffusion Analysis

Use electric-diffusion analysis to perform an electromigration analysis. Applications include the transport of atoms or vacancies in metallic interconnects under intense electric currents.

For theoretical background, see Electric-Diffusion Coupling in the Theory Reference.

The following related topics are available:

 

2.16.1. Elements Used in an Electric-Diffusion Analysis

Table 2.35: Elements Used in Electric-Diffusion Analyses summarizes the elements that you can use to perform a coupled electric-diffusion analysis. For detailed descriptions of the elements and their characteristics (degrees of freedom, KEYOPT options, inputs and outputs, etc.), see the Element Reference.

For a coupled electric-diffusion analysis, you need to select the VOLT and CONC element degrees of freedom by setting KEYOPT(1) to 100100 for the coupled-field element.

Table 2.35: Elements Used in Electric-Diffusion Analyses

Elements Effects Analysis Types

PLANE222 - 4-Node Coupled-Field Quadrilateral

PLANE223 - 8-Node Coupled-Field Quadrilateral

SOLID225 - 8-Node Coupled-Field Hexahedral

SOLID226 - 20-Node Coupled-Field Hexahedral

SOLID227 - 10-Node Coupled-Field Tetrahedral

Electromigration

Static

Full Transient


 

2.16.2. Performing an Electric-Diffusion Analysis

To perform an electric-diffusion analysis:

  1. Select a coupled-field element that is appropriate for the analysis (Table 2.35: Elements Used in Electric-Diffusion Analyses). Use KEYOPT(1) to select the VOLT and CONC element degrees of freedom.

  2. Specify electric material properties:

    • Specify electric resistivities (RSVX, RSVY, RSVZ) (MP).

    • To account for electric transient effects, specify electrical permittivity (PERX, PERY, PERZ) (MP or TB,DPER).

  3. Specify diffusion material properties:

  4. To include the electric transport effect (electromigration):

    • Specify the particle effective charge/Boltzmann constant ratio (Ze/k) using constant C4 (TBDATA) for the migration table, TB,MIGR. Alternatively, you can specify the molar charge/universal gas constant ratio (ZF/R) using the same format. For more information, see Migration Model in the Material Reference.

  5. Apply electric and diffusion loads, initial conditions, and boundary conditions:

    • Electric loads, initial conditions, and boundary conditions include scalar electric potential (VOLT) and current flow (AMPS).

    • Diffusion loads, initial conditions, and boundary conditions include concentration (CONC), diffusion flow rate (RATE), diffusion flux (DFLUX), and diffusing substance generation rate (DGEN).

  6. Specify temperature:

    • Specify temperature load (TEMP) (BF or BFE).

    • Specify temperature offset from absolute zero to zero (TOFFST).

  7. Specify analysis type and solve:

    • Analysis type can be static or full transient.

    • You can use KEYOPT(2) to select a strong (matrix) or weak (load vector) electric-diffusion coupling. Strong coupling produces an unsymmetric matrix. Weak coupling produces a symmetric matrix, but requires more than two iterations to achieve a coupled response.

    • If using TB,MIGR, the analysis is nonlinear, and at least two iterations are required to achieve a coupled response.

    • In a nonlinear analysis, set convergence values (CNVTOL) with:

      1. Electric potential (VOLT) and current flow (AMPS) labels

      2. Concentration (CONC) and diffusion flow rate (RATE) labels

    • For problems having convergence difficulties, activate the line-search capability (LNSRCH).

  8. Post-process electric and diffusion results:

    • Electric results include electric potential (VOLT), electric field (EF), and electric current density (JC).

    • Diffusion results include concentration (CONC), concentration gradient (CG), and diffusion flux (DF).

 

2.16.3. Electric-Diffusion Analysis Example

An electric-diffusion analysis example can be found in the Mechanical APDL Verification Manual: