L1 ⚛ L1-495 ⊙ Testnet

Thermionic Emission at Metal-Semiconductor Interfaces

Semiconductor Physics · Schottky barrier transport

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⬇ L1-495.md

# ⚛ L1 Principle — Thermionic Emission at Metal-Semiconductor Interfaces **ID:** `L1-495` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Semiconductor Physics — *Schottky barrier transport* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** phi B A star R s vector > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554142 --- ## 🧠 1. Introduction **Thermionic Emission at Metal-Semiconductor Interfaces** is a **nonlinear inverse problem** whose unknown lives in **phi B A star R s vector** space, within the **Schottky barrier transport** sub-domain of **Semiconductor Physics**. Measurements consist of electrons collected by an electron detector via a **schottky IV vs T** sensing mechanism. The forward operator applies, in order: E · richardson emission operator; E · barrier lowering operator; time evolution of the state; O · IV vs T operator. Observations are corrupted by additive Gaussian noise. Well-posed away from breakdown; inversion of (phi_B, A*) ambiguous at single T — requires T-series. ## ⚙ 2. Forward Model Physical chain: **x** → E · richardson emission → E · barrier lowering → Time derivative → O · IV vs T → **y** (detector). ``` y = `O.IV_vs_T` ∂_t `E.barrier_lowering` `E.richardson_emission` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.richardson_emission` | E · richardson emission operator | | `E.barrier_lowering` | E · barrier lowering operator | | `D.time` | Time evolution of the state | | `O.IV_vs_T` | O · iv vs t operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Semiconductor Physics | | Sub domain | Schottky barrier transport | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | phi_B_A_star_R_s_vector | | Noise model | gaussian | | Integration axis | bias_and_temperature | | Difficulty delta | 3 | | L dag | 3.1 | ## 📡 4. Measurement Model Well-posed away from breakdown; inversion of (phi_B, A*) ambiguous at single T — requires T-series. | Metric | Value | |---|---| | Metric | phi_B_error_meV | | Secondary | IV_log_relative_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `schottky_barrier_fit` · **Forward operator:** `thermionic_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | A cm2 | — | 0.0001 | | V max v | — | 0.5 | | N points | — | 100 | | Material | — | Au_on_Si | | T k range | — | 200 – 400 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | A cm2 | — | 1e-08 – 1 | | T k max | — | 300 – 600 | | T k min | — | 77 – 300 | | V max v | — | 0.1 – 5.0 | | N points | — | 20 – 5000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** phi_B error <= 10 meV | Metric | Range | |---|---| | Phi b error mev | 5.0 – 200.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **phi_B_error_meV**, with κ = `80` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x630c015fbc32169d1dbe067bc6a1d2a492b45f7fac124408f46ad5549e44a4bb` - **Chain tx hash:** `0xb5625709800937c6b2fe2456d349ea0a5a96000b06117e09036389b8304271a9` - **Chain block:** `41554142` --- ## File Mapping This bundle consists of: `L1-495.md`, `L1-495.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-495.md` | Source of truth — edit this | Human or LLM | | `L1-495.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 `L1-495`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-495-001 Thermionic Emission at Metal-Semiconductor Interfaces Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-495",
  "chain_block": 41554142,
  "chain_hash": "0x630c015fbc32169d1dbe067bc6a1d2a492b45f7fac124408f46ad5549e44a4bb",
  "chain_tx_hash": "0xb5625709800937c6b2fe2456d349ea0a5a96000b06117e09036389b8304271a9",
  "domain": "Semiconductor Physics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 80,
    "metric": "phi_B_error_meV",
    "type": "epsilon_fn"
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  "observable_profile": {
    "metric": "phi_B_error_meV",
    "regime": "Well-posed away from breakdown; inversion of (phi_B, A*) ambiguous at single T \u2014 requires T-series.",
    "secondary": "IV_log_relative_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.1,
    "carrier": "electron",
    "difficulty_delta": 3,
    "domain": "Semiconductor Physics",
    "integration_axis": "bias_and_temperature",
    "noise_model": "gaussian",
    "primitives": [
      "E.richardson_emission",
      "E.barrier_lowering",
      "D.time",
      "O.IV_vs_T"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "schottky_IV_vs_T",
    "solution_space": "phi_B_A_star_R_s_vector",
    "sub_domain": "Schottky barrier transport",
    "title": "Thermionic Emission at Metal-Semiconductor Interfaces"
  },
  "size_tiers": {
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      "thermionic_forward"
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    "allowed_omega_dimensions": [
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      "V_max_V",
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      "material",
      "N_points"
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    ],
    "center_spec": {
      "epsilon_fn_center": "phi_B error \u003c= 10 meV",
      "forward_operator": "thermionic_forward",
      "input_format": "measurement_only",
      "omega": {
        "A_cm2": 0.0001,
        "N_points": 100,
        "T_K_range": [
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        "V_max_V": 0.5,
        "material": "Au_on_Si"
      },
      "problem_class": "schottky_barrier_fit"
    },
    "epsilon_bounds": {
      "phi_B_error_meV": [
        5.0,
        200.0
      ]
    },
    "omega_bounds": {
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        1
      ],
      "N_points": [
        20,
        5000
      ],
      "T_K_max": [
        300,
        600
      ],
      "T_K_min": [
        77,
        300
      ],
      "V_max_V": [
        0.1,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Schottky barrier transport",
  "title": "Thermionic Emission at Metal-Semiconductor Interfaces"
}

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