Electrodes and boundary conditions

Table of Contents

• Boundary conditions
  • Specifying the field and/or potential
  • Electric potential boundary conditions
  • Species boundary conditions
• Specifying an electrode

Boundary conditions

Specifying the field and/or potential

The applied electric field or voltage can be set through the option field_given_by, which can take the following forms:

field_given_by = voltage <value in V>"
field_given_by = field <value in V/m>"
field_given_by = voltage_table <filename>"
field_given_by = field_table <filename>"

In case of a table, the format of the table should be as follows:

voltage_vs_time (or field_vs_time)
--------
t1 v1
t2 v2
...
--------

where t1, t2, etc. are times and v1, v2, etc. are values. The lines with dashes should contain at least five dashes.

Electric potential boundary conditions

There is a parameter field_bc_type, that can be set to:

• 'homogeneous': Neumann zero on the sides, zero voltage at the bottom, and a fixed applied voltage on top.
• 'neumann': Neumann zero on the sides, zero voltage at the bottom, and a Neumann boundary at the top corresponding to the applied electric field

To have more flexibility, a custom routine for boundary conditions can be defined in the m_user.f90 file, which will override the above setting, see the m_user documentation.

Species boundary conditions

There is a parameter species_boundary_condition, that can be set to:

• 'neumann_zero': Neumann zero for all species on all domain boundaries. This means that electrons can flow out of electrodes.
• 'dirichlet_zero': Dirichlet zero for all species on all domain boundaries. Electrons can still flow into electrodes, but not out.

Specifying an electrode

To enable an electrode, set use_electrode = T. The electrode can be controlled with the following parameters:

    call cfg_add_get(cfg, "field_electrode_grounded", field_electrode_grounded, &
         "Whether electrode 1 is grounded or at the applied voltage")
    call cfg_add_get(cfg, "field_electrode2_grounded", field_electrode2_grounded, &
         "Whether electrode 2 is grounded or at the applied voltage")
    call cfg_add_get(cfg, "field_rod_r0", rod_r0, &
         "Electrode 1: first relative coordinate")
    call cfg_add_get(cfg, "field_rod_r1", rod_r1, &
         "Electrode 1: second relative coordinate")
    call cfg_add_get(cfg, "field_rod2_r0", rod2_r0, &
         "Electrode 2: first relative coordinate")
    call cfg_add_get(cfg, "field_rod2_r1", rod2_r1, &
         "Electrode 2: second relative coordinate")
    call cfg_add_get(cfg, "field_rod_radius", rod_radius, &
         "Electrode 1 radius (in m)")
    call cfg_add_get(cfg, "field_rod2_radius", rod2_radius, &
         "Electrode 2 radius (in m)")
    call cfg_add_get(cfg, "cone_tip_radius", cone_tip_radius, &
         "Electrode 1: tip radius (if conical)")
    call cfg_add_get(cfg, "cone_length_frac", cone_length_frac, &
         "Electrode 1: fraction of conical part (if conical)")
    call cfg_add_get(cfg, "cone2_tip_radius", cone2_tip_radius, &
         "Electrode 2: tip radius (if conical)")
    call cfg_add_get(cfg, "cone2_length_frac", cone2_length_frac, &
         "Electrode 2: fraction of conical part (if conical)")
 
    rod_r0 = st_domain_origin + rod_r0 * st_domain_len
    rod_r1 = st_domain_origin + rod_r1 * st_domain_len
    rod2_r0 = st_domain_origin + rod2_r0 * st_domain_len
    rod2_r1 = st_domain_origin + rod2_r1 * st_domain_len
 
    electrode_type = "rod"
    call cfg_add_get(cfg, "field_electrode_type", electrode_type, &
         "Electrode: sphere, rod, rod_cone_top, rod_rod, sphere_rod, user")

The parameter field_electrode_type can be set to:

• sphere: a spherical electrode
• rod (default): a cylindrical electrode with a semi-spherical tip
• rod_cone_top: a cylindrical electrode with a conical tip
• rod_rod: two electrodes of rod type
• user: a user-defined electrode

For a rod electrode, the relative coordinates field_rod_r0 and field_rod_r0 need to be defined. For the conical tip, field_rod_r2 also needs to be specified. See the electrode tutorial for examples.