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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 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" ], "boundary_conditions": [ "Unknown mode or temperature_model → INVALID_MODE", "Missing Vgs / Vth / Id / kn / Tj when required → MISSING_REQUIRED_INPUT", "Non-finite → INVALID_NUMBER", "Id or kn ≤ 0 → VALUE_MUST_BE_POSITIVE", "Vds < 0 → VALUE_MUST_BE_NON_NEGATIVE", "Tj or Tref < −273.15 °C → VALUE_OUT_OF_RANGE", "id mode Vgs ≤ Vth_used → Id_A=0, region=cutoff, warning SUBTHRESHOLD_NOT_MODELED (CUTOFF_NOT_MODELED deprecated alias)", "0 < Vod < 0.1 V → warning NEAR_THRESHOLD", "Every success includes warning MODEL_VTH_NOT_DATASHEET_VGS_TH", "id/vth with Vds omitted and Vod>0 → warning SATURATION_ASSUMED", "Vds < Vod and Vod>0 → region=linear, warning LINEAR_REGION (id) or SATURATION_EXTRACT_ASSUMED (vth)", "linear with omitted α → warning VTH_TEMP_COEFF_DEFAULT", "temperature_model=none with Tj/α present → warning TEMPERATURE_NOT_APPLIED", "linear id/vth → warning KN_TEMP_NOT_MODELED", "α > 0 → warning VTH_TEMP_COEFF_POSITIVE" ], "sources": [ { "title": "Sedra/Smith — Microelectronic Circuits", "section": "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)", "kind": "reference" }, { "title": "Toshiba — Power MOSFET Electrical Characteristics", "section": "Gate threshold voltage VGS(th)", "url": "https://toshiba.semicon-storage.com/info/docget.jsp?did=13415", "supports": "Datasheet VGS(th) is measured at a specified drain current; onset of conduction, not recommended gate drive", "kind": "reference", "accessed": "2026-08-16" }, { "title": "Nexperia AN11158 — Understanding power MOSFET data sheet parameters", "section": "Threshold voltage", "url": "https://assets.nexperia.com/documents/application-note/AN11158.pdf", "supports": "Datasheet VGS(th) definition differs from the textbook device-physics threshold parameter; TCV of VGS(th) is not model Vth(T)", "kind": "reference", "accessed": "2026-08-16" }, { "title": "Texas Instruments SLUA618 — Fundamentals of MOSFET and IGBT Gate Driver Circuits", "section": "Gate drive versus threshold", "url": "https://www.ti.com/lit/pdf/slua618", "supports": "VGS(th) indicates the start of conduction; 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