Establish a current-convergence acceptance criterion for drift-diffusion runs

[emircbngl]

Summary

The 1D and 2D drift-diffusion solvers stop on the potential-step criterion alone. current_rel_change is measured and recorded, but there is no established acceptance criterion for it.

The current wording is appropriately narrow (potential-step-converged), but the CLI still exits 0 and writes a completed artifact. A caller therefore has no machine verdict for whether the current iteration has settled; exit 4 is reached only when the potential step fails.

This is already acknowledged in AGENTS.md and pinned by test_pn1d_grid_robustness.py, but it has no GitHub issue tracking the missing criterion.

Reproduction

Public main at 5100ab0:

tarhan --format json run solve \
  semiconductor.pn.drift-diffusion.1d.steady \
  --bias 0.1 --output /tmp/tarhan-low

tarhan --format json run solve \
  semiconductor.pn.drift-diffusion.1d.steady \
  --bias 0.4 --output /tmp/tarhan-high

Both commands exit 0 after three Gummel iterations and report potential-step-converged:

bias	psi_step	current_rel_change
0.1 V	1.2079e-13	3.4901e-04
0.4 V	1.2914e-10	2.7995e-09

The 0.1 V artifact records the distinction honestly:

{
  "solver_status": "potential-step-converged",
  "current_convergence": "measured:3.490e-04"
}

Code path

• models/pn1d.py: the loop breaks when psi_step < gummel_tol; current_rel_change is diagnostic only.
• models/pn2d.py: the same stopping structure is used.
• cli.py: the diagnostic is copied into metrics/provenance, while the successful run remains exit 0.

What this issue does not claim

This is not evidence that either reported current is wrong. In particular, 0.1 V is one of the current-validation points in the capability record. The demonstrated problem is narrower: the solver contract has no current-based acceptance verdict, so potential convergence and current convergence cannot be distinguished by exit status.

Definition of done

1. Establish a defensible current-convergence metric and threshold for 1D and 2D, including the difficult cases already documented:
   • equilibrium, where net current is a cancellation and a relative change may be undefined;
   • a first/single pass, where there is no previous current;
   • platform-dependent floating-point variation.
2. Decide how that verdict affects solver_status and EXIT_NO_CONVERGENCE without relabelling the existing phase/potential criterion.
3. Add negative-control tests showing the criterion rejects a sequence that is still materially changing and accepts a genuinely settled sequence.
4. Keep the existing measured diagnostic in artifacts so the decision remains auditable.

Until a threshold is established, retaining the current honest potential-step-converged wording is preferable to inventing one from the two measurements above.