L1 ⚛ L1-488 ⊙ Testnet

Drift-Diffusion Semiconductor Transport (TCAD)

Semiconductor Physics · Device transport

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⬇ L1-488.md

# ⚛ L1 Principle — Drift-Diffusion Semiconductor Transport (TCAD) **ID:** `L1-488` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Device transport* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** device IV curves and field profiles > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554130 --- ## 🧠 1. Introduction **Drift-Diffusion Semiconductor Transport (TCAD)** is a **nonlinear inverse problem** whose unknown lives in **device IV curves and field profiles** space, within the **Device transport** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **terminal IV CV** sensing mechanism. The forward operator applies, in order: E · poisson operator; E · continuity n operator; E · continuity p operator; a fixed-point or gradient iteration on the unknown; O · terminal IV operator. Observations are corrupted by additive Gaussian noise. 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). ## ⚙ 2. Forward Model Physical chain: **x** → E · poisson → E · continuity n → E · continuity p → O · terminal IV → **y** (detector). ``` y = `O.terminal_IV` `E.continuity_p` `E.continuity_n` `E.poisson` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.poisson` | E · poisson operator | | `E.continuity_n` | E · continuity n operator | | `E.continuity_p` | E · continuity p operator | | `O.terminal_IV` | O · terminal iv operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.iter` | A fixed-point or gradient iteration on the unknown | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Semiconductor Physics | | Sub domain | Device transport | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | device_IV_curves_and_field_profiles | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model 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). | Metric | Value | |---|---| | Metric | IV_log_relative_error | | Secondary | Vth_error_mV | ## 📏 5. Operating Range (Ω) **Center problem class:** `device_parameter_inversion` · **Forward operator:** `drift_diffusion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | T k | — | 300 | | Mesh n | N | 64 | | N a cm3 | — | 100000000000000000 | | N d cm3 | — | 1000000000000000000 | | T ox nm | nm | 2 | | L channel nm | nm | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T k | — | 200 – 500 | | Mesh n | N | 32 – 512 | | N a cm3 | — | 1000000000000000.0 – 100000000000000000000 | | N d cm3 | — | 1000000000000000.0 – 100000000000000000000 | | T ox nm | nm | 0.5 – 20 | | L channel nm | nm | 5 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** log10(I_D) error <= 0.03 | Metric | Range | |---|---| | Iv log relative error | 0.005 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **IV_log_relative_error**, with κ = `800` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xac30a5d9507b3f0c2be5058d1f997da330ca02cfaa2350bc5059acf1447878e8` - **Chain tx hash:** `0x1aa1ba71a065c90c7d6a0380ac73b50f77f82db64b73d56b2000e17973fa0476` - **Chain block:** `41554130` --- ## File Mapping This bundle consists of: `L1-488.md`, `L1-488.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-488.md` | Source of truth — edit this | Human or LLM | | `L1-488.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-488`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-488.md).
Regenerate L1-488.json so every field matches the Markdown.
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L2-488-001 Drift-Diffusion Semiconductor Transport (TCAD) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554130,
  "chain_hash": "0xac30a5d9507b3f0c2be5058d1f997da330ca02cfaa2350bc5059acf1447878e8",
  "chain_tx_hash": "0x1aa1ba71a065c90c7d6a0380ac73b50f77f82db64b73d56b2000e17973fa0476",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 800,
    "metric": "IV_log_relative_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "IV_log_relative_error",
    "regime": "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).",
    "secondary": "Vth_error_mV"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Semiconductor Physics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "E.poisson",
      "E.continuity_n",
      "E.continuity_p",
      "O.iter",
      "O.terminal_IV"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "terminal_IV_CV",
    "solution_space": "device_IV_curves_and_field_profiles",
    "sub_domain": "Device transport",
    "title": "Drift-Diffusion Semiconductor Transport (TCAD)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "drift_diffusion_forward"
    ],
    "allowed_omega_dimensions": [
      "L_channel_nm",
      "T_ox_nm",
      "N_D_cm3",
      "N_A_cm3",
      "T_K",
      "mesh_N"
    ],
    "allowed_problem_classes": [
      "device_parameter_inversion"
    ],
    "center_spec": {
      "epsilon_fn_center": "log10(I_D) error \u003c= 0.03",
      "forward_operator": "drift_diffusion_forward",
      "input_format": "measurement_only",
      "omega": {
        "L_channel_nm": 50,
        "N_A_cm3": 100000000000000000,
        "N_D_cm3": 1000000000000000000,
        "T_K": 300,
        "T_ox_nm": 2.0,
        "mesh_N": 64
      },
      "problem_class": "device_parameter_inversion"
    },
    "epsilon_bounds": {
      "IV_log_relative_error": [
        0.005,
        0.3
      ]
    },
    "omega_bounds": {
      "L_channel_nm": [
        5,
        1000
      ],
      "N_A_cm3": [
        1000000000000000.0,
        100000000000000000000
      ],
      "N_D_cm3": [
        1000000000000000.0,
        100000000000000000000
      ],
      "T_K": [
        200,
        500
      ],
      "T_ox_nm": [
        0.5,
        20
      ],
      "mesh_N": [
        32,
        512
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Device transport",
  "title": "Drift-Diffusion Semiconductor Transport (TCAD)"
}

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