Drift-Diffusion Semiconductor Transport (TCAD) L1-488

Semiconductor PhysicsDevice transportδ=5 · challengingL_DAG = 4📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

g r a d . (e p s \cdot g r a d (p hi)) = - q \cdot (p - n + N_{D} - N_{A}); J_{n} = q \cdot m u_{n} \cdot n \cdot E + q \cdot D_{n} \cdot g r a d (n); d n / d t = (1/ q) \cdot d i v (J_{n}) - R (n, p); ana l o g o u s f or h o l es

Van Roosbroeck system: Poisson + electron/hole continuity, with drift-diffusion currents; solved self-consistently across a 2D/3D device mesh.

L-DAG

E.poisson -> E.continuity_n -> E.continuity_p -> O.iter -> O.terminal_IV

E.poissonE.continuity_nE.continuity_pO.iterO.terminal_IV

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 800

Well-posed elliptic-parabolic system with Dirichlet/mixed BC at contacts; inversion for (mu, tau) from I-V is moderately ill-conditioned (mobility-lifetime trade-off).

Solvability C

Solver class:: Scharfetter-Gummel FV + Gummel or full Newton; inversion via BFGS/adjoint-TCAD
Convergence rate q:: 2
Complexity:: O(N_mesh^{1.5}) per Newton step

Specs (0)

No L2 specs registered yet for this principle.