# ⚛  L1 Principle — BSIM Compact MOSFET Model

**ID:** `L1-492` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Semiconductor Physics — *Compact device modeling*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** bsim parameter vector
> **📡 Carrier:** electron · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554141

---

## 🧠 1. Introduction

**BSIM Compact MOSFET Model** is a **nonlinear inverse problem** whose unknown lives in **bsim parameter vector** space, within the **Compact device modeling** sub-domain of **Semiconductor Physics**.

Measurements consist of electrons collected by an electron detector via a **compact IV CV fit** sensing mechanism.

The forward operator applies, in order: E · threshold model operator; E · mobility model operator; K · filter operator; O · IV operator.

Observations are corrupted by additive Gaussian noise. Parameter-rich (>100 fitting knobs); non-unique locally; regularized fits required.

## ⚙ 2. Forward Model

Physical chain: **x** → E · threshold model → E · mobility model → O · IV → **y** (detector).

```
y = `O.IV` `E.mobility_model` `E.threshold_model` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `E.threshold_model` | E · threshold model operator |
| `E.mobility_model` | E · mobility model operator |
| `O.IV` | O · iv operator |

**🛰 Estimator components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `K.filter` | K · filter operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Semiconductor Physics |
| Sub domain | Compact device modeling |
| Carrier | electron |
| Problem class | nonlinear_inverse |
| Solution space | bsim_parameter_vector |
| Noise model | gaussian |
| Integration axis | bias_sweep |
| Difficulty delta | 3 |
| L dag | 3.2 |

## 📡 4. Measurement Model

Parameter-rich (>100 fitting knobs); non-unique locally; regularized fits required.

| Metric | Value |
|---|---|
| Metric | IV_log_relative_error |
| Secondary | Vth_distribution_error |

## 📏 5. Operating Range (Ω)

**Center problem class:** `compact_model_fit` · **Forward operator:** `bsim_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| T k | — | 300 |
| L nm | nm | 20 |
| W nm | nm | 100 |
| Vds range v | — | 1.2 |
| Vgs range v | — | 1.2 |
| N bias points | — | 400 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| T k | — | 200 – 400 |
| L nm | nm | 5 – 1000 |
| W nm | nm | 20 – 10000 |
| Vds range v | — | 0.5 – 3.3 |
| Vgs range v | — | 0.5 – 3.3 |
| N bias points | — | 50 – 10000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** log10(Ids) error <= 0.02

| 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 = `100` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xaa2037be22bf03ddeb45405a114f23f2d3a258b3dc029ae27ea54cb1e5342aec`
- **Chain tx hash:** `0x9b643ab8a8a60bb4976c56cf034513b7c83fefed0ece7dd0c34870b4226c3246`
- **Chain block:** `41554141`

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## File Mapping

This bundle consists of: `L1-492.md`, `L1-492.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-492.md` | Source of truth — edit this | Human or LLM |
| `L1-492.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 `L1-492`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._