What Is the MOSFET Threshold Voltage & Subthreshold Swing Calculator?
MOSFET threshold voltage is the gate-to-source voltage where an inversion conduction channel forms under the gate.
How Does the MOSFET Threshold Voltage & Subthreshold Swing Calculator Work?
Sums flatband potential, surface inversion band bending (2phi_B), and depletion charge over oxide capacitance.
MOSFET Threshold Voltage & Subthreshold Swing Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
V_{ ext{th}} = V_{ ext{fb}} + 2phi_B + rac{sqrt{4 q epsilon_{ ext{si}} N_a phi_B}}{C_{ ext{ox}}}, quad S = ln(10) rac{k_B T}{q}left(1 + rac{C_{ ext{dep}}}{C_{ ext{ox}}}
ight)
Classical strong-inversion threshold equation and subthreshold swing slope.
How to Use the MOSFET Threshold Voltage & Subthreshold Swing Calculator
- Input substrate doping Na, gate oxide thickness Tox in nanometers, and flatband voltage Vfb.
Step-by-Step Example Calculation
Advanced CMOS NMOS Transistor
Input Values:
substrateDopingNaCm3:100000000000000000
oxideThicknessNm:2
flatbandVoltageVolts:-0.85
Worked Steps: Threshold voltage V_th = 0.385 V with subthreshold swing S = 69.8 mV/decade.
Understanding Your Result
Shows threshold voltage, gate capacitance C_ox, and subthreshold slope (ideal lower bound is 60 mV/dec at 300 K).
Factors That Affect the Result
- Thinning the oxide increases C_ox, improving subthreshold slope and reducing short-channel effects.
When Should You Use This Calculator?
- CMOS digital logic library characterization, analog amplifier biasing, and low-power circuit optimization.
Assumptions & Limitations
- Applies long-channel 1D MOS capacitor theory; ignores drain-induced barrier lowering (DIBL).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard 1D Poisson-Boltzmann MOS capacitor inversion formulation.