Thermal Annealing 

#include <models/psAnneal.hpp>

Anneal evolves dopant concentration and optional activation and defect fields on a ViennaCS cell set. It supports constant or Arrhenius diffusivity, isothermal steps, temperature ramps, and material-specific diffusion barriers. The domain must already have a cell set containing the species field, for example from ion implantation.

Set the anneal duration or schedule on the model and use zero duration for the enclosing Process. The model updates volume fields without moving the level sets.

Example: diffuse an implanted profile

These snippets continue from the implantation example, with B_total stored in nm⁻³. The constant diffusivity is illustrative.

auto anneal = ps::SmartPointer<ps::Anneal<double, 2>>::New();
anneal->setSpeciesLabel("B_total");
anneal->setTemperature(1273.15); // kelvin
anneal->setDuration(30.0);      // seconds
anneal->setDiffusionCoefficient(1.0); // nm²/s
anneal->setMode(ps::AnnealMode::GaussSeidel);
anneal->setDiffusionMaterials({ps::Material::Si});
anneal->setBlockingMaterials(
    {ps::Material::Air, ps::Material::Mask, ps::Material::SiO2});
ps::Process<double, 2>(domain, anneal, 0.0).apply();
domain->getCellSet()->writeVTU("post_anneal");

anneal = vps.Anneal()
anneal.setSpeciesLabel("B_total")
anneal.setTemperature(1273.15) # kelvin
anneal.setDuration(30.0)      # seconds
anneal.setDiffusionCoefficient(1.0) # nm²/s
anneal.setMode(vps.AnnealMode.GaussSeidel)
anneal.setDiffusionMaterials([vps.Material.Si])
anneal.setBlockingMaterials(
    [vps.Material.Air, vps.Material.Mask, vps.Material.SiO2])
vps.Process(domain, anneal, 0.0).apply()
domain.getCellSet().writeVTU("post_anneal")

Temperature schedules and solver controls

setTemperatureSchedule(durations, temperatures) accepts either:

  • N durations and N temperatures for N isothermal steps, or
  • N durations and N+1 temperatures for linear ramps between endpoints.

For a ramp-up, soak, and ramp-down schedule:

anneal.setTemperatureSchedule(
    [9.0, 5.0, 9.0],
    [873.15, 1323.15, 1323.15, 873.15])

Use clearTemperatureSchedule() before returning to a single isothermal duration. Steps can also be appended with addIsothermalStep and addRampStep.

Method Purpose
setArrheniusParameters(D0, Ea) Temperature-dependent diffusivity; D0 in geometry unit²/s and Ea in eV.
setMode(mode) Choose AnnealMode::Explicit or AnnealMode::GaussSeidel.
setTimeStep(dt) Time step in seconds; nonpositive values request automatic selection.
setStabilityFactor(factor) Stability factor for explicit time stepping.
setImplicitSolverOptions(maxIterations, relativeTolerance, relaxation) Iteration controls for Gauss–Seidel mode.
setDiffusionMaterials(materials) Restrict diffusion to selected materials; an empty list allows all materials.
setBlockingMaterials(materials) Select materials that block diffusion.

Activation and defects

enableSolidActivation() enables a solubility-limited active concentration field. Name it with setActiveLabel(...) and configure the solubility with setSolidSolubilityArrhenius(C0, Ea), using concentrations consistent with the cell-set fields and energy in eV.

The model also exposes damage-dependent activation, interstitial/vacancy diffusion and reactions, transient enhanced diffusion (TED), defect clustering, and interface trapping/segregation. These options require corresponding parameters and fields. Match setDamageLabels(...) to the implant’s cumulative and most-recent damage labels when coupling an implant and anneal.

The public model database supplies literature-based diffusion and selected activation/TED parameters. Its effective damage-driven TED does not supply a full dynamic defect parameter set. For C++ setup helpers, use AnnealSetup, lookupAnneal, and applyAnnealSetup from <models/psAnnealSetup.hpp>; direct setters are available in both C++ and Python.

Activation and electrical output

applyActivation(domain) computes active concentration without running diffusion. Configure the temperature, species label, active label, and solubility model first. For the nm-based boron example above, the following uses the public table’s boron solubility parameters (C0 converted to nm⁻³):

anneal.setActiveLabel("B_active")
anneal.enableSolidActivation(True)
anneal.setSolidSolubilityArrhenius(1e3, 0.91)
anneal.applyActivation(domain)

sheet = vps.SheetResistance()
sheet.setCellSet(domain.getCellSet())
sheet.setConcentrationLabel("B_active")
sheet.setLengthUnit(1e-7) # nm to cm; also sets concentration conversion
rsh = sheet.computeHole() # ohms per square for p-type silicon

SheetResistance uses the active concentration and a Masetti–Severi mobility model; use computeElectron() for n-type silicon. If concentrations were already converted to cm⁻³, call setConcentrationUnit(1.0) after setLengthUnit(...).

For multiple species, NetDoping combines donor and acceptor fields. Attach the cell set, register active fields with addDonorLabel("P_active") and addAcceptorLabel("B_active"), then call apply() to write net_doping. junctionDepth() and junctionDepths() extract sign changes along the depth profile; depths use the geometry length unit. Both analysis classes allow setDepthAxis and setSurfacePosition to configure the depth coordinate.

The Python names are vps.SheetResistance and vps.NetDoping. C++ users can access the corresponding viennacs::SheetResistance<T, D> and viennacs::NetDoping<T, D> classes through <csSheetResistance.hpp> and <csNetDoping.hpp>.