Public evidence

electrical.mosfet.vth

Machine-checked verification for calculation version 1.3.1 · tier expert_verified

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· Model Vth ≠ datasheet VGS(th); kn not temperature-scaled · Protocol · Schema · Production report

Declared partition coverage: PASS · 4/4 declared partitions (overdrive, id, vth, invalid-domain)
Versions: Calculation 1.3.1 · CVP protocol 1.0.0-proposed
CVP identity: 11/11 property · digest df4f29a72c29

Verification

Legacy regression suite: 26/26 calculation tests · Production surface contract 10/10

Three distinct suites: educational examples on the calculator page, this legacy regression count (26/26 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.3.1 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Calculation version 1.3.1. CVP 1.0.0-proposed. 4/4 golden · 5/5 CVP boundary · 5/5 invalid · 11/11 property · 2/2 cross-interface · 10/10 CVP contract. digest df4f29a72c29.

Golden (oracle-backed) 4 / 4
CVP boundary 5 / 5
Invalid input 5 / 5
Property 11 / 11
Cross-interface 2 / 2
CVP contract 10 / 10
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Engineering

contract page version PASS
contract capability version PASS
contract input schema version PASS
contract output schema version PASS
evidence version matches manifest PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
subthreshold warning codes PASS
cutoff id zero subthreshold warning PASS

Fingerprint sha256:62d830442da390bacca788207a7c0cde30c1f11982f6a67aa61d54533e60497a

Input schema sha256:8aaf0a70ca3197d145c41aebca84830791334284c7830b197771ba8e83f8178e · Output schema sha256:07ec52f59e9a4a0172410ab1152a5879545b7d79b2f2a48a1355a4135ea860cf · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: mosfet-vth
Engine: mosfet-vth
Engine build: 2026-09-10
Evidence core: 2026-09-05T02:35:39.217Z
Rendered: 2026-09-16T22:03:43.747Z
Last reviewed: 2026-08-17

Assumptions

Ideal long-channel square-law NMOS model. Not BSIM, velocity saturation, or short-channel.
Vth is the model threshold parameter, not datasheet VGS(th) and not recommended gate drive.
kn = μn·Cox·W/L such that Id_sat = ½·kn·Vod². The ½ factor is not included in kn.
When Vds is omitted, Id uses the saturation equation and region is above_threshold or cutoff.
When Vds is provided: cutoff if Vod≤0; linear if 0≤Vds<Vod; saturation if Vds≥Vod.
Vod > 0 means above the model threshold, not strong inversion.
Cutoff returns Id = 0 A. Subthreshold current is not modeled.
Solve-Vth always uses the saturation extract Vth=Vgs−√(2Id/kn) at the measurement temperature.
Linear Vth(Tj) does not scale kn or μ(T).
Default α = −0.002 V/°C is a Si planning value, not a datasheet TCV of VGS(th).

Limitations

Long-channel square-law only — not BSIM, velocity saturation, or short-channel
Vth is the model threshold parameter, not datasheet VGS(th) and not recommended gate drive
kn = μn·Cox·W/L such that Id_sat = ½·kn·Vod²; the ½ is not included in kn
Without Vds, Id uses the saturation equation; with Vds, region is cutoff / linear / saturation
Cutoff returns Id = 0 A; subthreshold leakage is not modeled
Linear Vth(Tj) does not scale kn / μ(T); default α = −0.002 V/°C is a Si planning value, not datasheet TCV

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Sedra/Smith — Microelectronic Circuits — MOSFET DC / square-law saturation and Vth(T)
Supports: Id_sat=½ kn (Vgs−Vth)² and Id_lin=kn[(Vgs−Vth)Vds−Vds²/2]; Vth typically falls with T (~−2 mV/°C planning scale)
Toshiba — Power MOSFET Electrical Characteristics — Gate threshold voltage VGS(th)
Supports: Datasheet VGS(th) is measured at a specified drain current; onset of conduction, not recommended gate drive
Nexperia AN11158 — Understanding power MOSFET data sheet parameters — Threshold voltage
Supports: Datasheet VGS(th) definition differs from the textbook device-physics threshold parameter; TCV of VGS(th) is not model Vth(T)
Texas Instruments SLUA618 — Fundamentals of MOSFET and IGBT Gate Driver Circuits — Gate drive versus threshold
Supports: VGS(th) indicates the start of conduction; it is not the gate voltage for full enhancement

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`od`	golden	pass	Expected Vod_V=2 · region=above_threshold · Actual mode=overdrive · Vgs_V=3 · Vth_V=1 · Vod_V=2 · region=above_threshold · strong_inversion=true
`id`	golden	pass	Expected Id_A=1 · Vod_V=2 · region=above_threshold · Actual mode=id · Vgs_V=3 · Vth_V=1 · kn_A_per_V2=0.5 · Vod_V=2 · Id_A=1 · region=above_threshold · strong_inversion=true
`id-linear`	golden	pass	Expected Id_A=0.75 · Vod_V=2 · region=linear · Actual mode=id · Vgs_V=3 · Vth_V=1 · kn_A_per_V2=0.5 · Vod_V=2 · Id_A=0.75 · region=linear · strong_inversion=true
`id-sat-vds`	golden	pass	Expected Id_A=1 · Vod_V=2 · region=saturation · Actual mode=id · Vgs_V=3 · Vth_V=1 · kn_A_per_V2=0.5 · Vod_V=2 · Id_A=1 · region=saturation · strong_inversion=true
`vth`	golden	pass	Expected Vth_V=1 · Vod_V=2 · Actual mode=vth · Vgs_V=3 · Id_A=1 · kn_A_per_V2=0.5 · Vod_V=2 · Vth_V=1 · region=above_threshold · strong_inversion=true
`cutoff`	golden	pass	Expected Id_A=0 · region=cutoff · Actual mode=id · Vgs_V=1 · Vth_V=2 · kn_A_per_V2=1 · Vod_V=-1 · Id_A=0 · region=cutoff · strong_inversion=false
`near`	golden	pass	Expected Vod_V=0.01 · region=above_threshold · Actual mode=overdrive · Vgs_V=1.01 · Vth_V=1 · Vod_V=0.010000000000000009 · region=above_threshold · strong_inversion=true
`bad-kn`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`bad-vds`	boundary	pass	Expected VALUE_MUST_BE_NON_NEGATIVE · Actual VALUE_MUST_BE_NON_NEGATIVE
`vth-tj`	golden	pass	Expected Vod_V=2.2 · Vth_Tj_V=0.8 · Vth_Tref_V=1 · Actual mode=overdrive · Vgs_V=3 · Vth_V=0.8 · Vod_V=2.2 · region=above_threshold · strong_inversion=true · temperature_model=linear · Tj_C=125
`id-tj`	golden	pass	Expected Id_A=1.21 · Vod_V=2.2 · Actual mode=id · Vgs_V=3 · Vth_V=0.8 · kn_A_per_V2=0.5 · Vod_V=2.2 · Id_A=1.2100000000000002 · region=above_threshold · strong_inversion=true
`extract-tj`	golden	pass	Expected Vth_V=1 · Vth_Tref_V=1.2 · Actual mode=vth · Vgs_V=3 · Id_A=1 · kn_A_per_V2=0.5 · Vod_V=2 · Vth_V=1 · region=above_threshold · strong_inversion=true
`linear-no-tj`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`tj-abs-zero`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-vth-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`property-od`	property	pass	2
`property-id`	property	pass	½ kn Vod² (½ not in kn)
`property-vth-roundtrip`	property	pass	1
`property-cutoff`	property	pass	0 A cutoff
`property-near-threshold`	property	pass	NEAR_THRESHOLD
`property-id-linear`	property	pass	0.75 A linear
`property-id-sat-edge`	property	pass	Id continuous at Vds=Vod
`property-vth-tj`	property	pass	Vth(Tj)=0.8 Vod=2.2
`property-id-tj`	property	pass	1.21 A hot Id
`property-extract-tref`	property	pass	extract Vth_Tref=1.2
`property-temp-ignored`	property	pass	TEMPERATURE_NOT_APPLIED