Hydrodynamic Semiconductor Transport L1-489

Semiconductor PhysicsEnergy-balance transportδ=5 · challengingL_DAG = 4.2📋 Stub — not mineable

📋

Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

Read the contribution guide →Open a claim issue →

Forward model E

d n / d t + d i v (n \cdot v) = - R; m \cdot (d v / d t + (v . g r a d) v) = - q E - g r a d (n \cdot k_{B} \cdot T_{e}) / n - m \cdot v / t a u_{p} (T_{e}); d (n \cdot U) / d t + d i v (n \cdot U \cdot v + J_{S}) = J . E - n \cdot (U - U_{0}) / t a u_{E}

Blotekjaer-Stratton hydrodynamic equations: continuity + momentum + energy, derived from Boltzmann moments with closure at second order; captures hot-carrier and velocity-overshoot effects missed by drift-diffusion.

L-DAG

E.continuity -> E.momentum_balance -> E.energy_balance -> O.iter -> O.hot_carrier_IV

E.continuityE.momentum_balanceE.energy_balanceO.iterO.hot_carrier_IV

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 1500

Stiff hyperbolic-parabolic system; shocks at hot-carrier fronts; closure model breaks down in ballistic regime.

Solvability C

Solver class:: Implicit Gummel + ENO/WENO for convection; adjoint inversion for closure parameters
Convergence rate q:: 2
Complexity:: O(N_mesh^{1.5}) per step with CFL constraint

Specs (0)

No L2 specs registered yet for this principle.