MOSFET Threshold Voltage Calculator
Free calculate threshold voltage from material and process parameters. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
Typically -0.8 to -1.0 V for n-MOS
Typical: 3.45 nF/cm² for 10 nm oxide
Acceptor (N_A) for n-MOS, Donor (N_D) for p-MOS
Results
Enter parameters to calculate
What is Threshold Voltage?
The threshold voltage (V_th) is the minimum gate-source voltage required to create a conducting channel in a MOSFET. Below V_th, the device is off (cutoff region). Above V_th, current can flow.
Threshold voltage depends on material properties (work function difference), oxide properties (thickness, capacitance), and substrate doping. It's typically 0.5-2 V for modern MOSFETs, but can be adjusted through process parameters.
V_th is critical in circuit design - it determines when transistors turn on, affects power consumption, and influences switching speed. Lower V_th enables faster switching but increases leakage current.
Threshold Voltage Formula
Where:
- • V_th = Threshold voltage (V)
- • V_FB = Flatband voltage (V)
- • φ_F = Fermi potential = (kT/q)ln(N_A/n_i) (V)
- • ε_s = Silicon permittivity ≈ 11.7ε₀ (F/cm)
- • q = Electron charge = 1.602×10⁻¹⁹ C
- • N_A = Acceptor doping concentration (cm⁻³)
- • C_ox = Oxide capacitance per unit area (F/cm²)
Note: Simplified formula shown. Full calculation includes body effect and other factors.
How to Calculate
-
1
Determine flatband voltage
V_FB depends on work function difference and oxide charge. Typical: -0.8 to -1.0 V for n-MOS.
-
2
Calculate Fermi potential
φ_F = (kT/q)ln(N_A/n_i), where n_i ≈ 1.5×10¹⁰ cm⁻³ for silicon at 300K.
-
3
Calculate depletion charge term
Q_dep = (2ε_s qN_A)^½. This represents charge in depletion region.
-
4
Calculate threshold voltage
V_th = V_FB + 2φ_F + Q_dep/C_ox. Sum all components.
Practical Examples
Example 1: Typical n-MOS
V_FB = -0.8 V, C_ox = 3.45 nF/cm², N_A = 1×10¹⁶ cm⁻³.
Solution:
Using simplified calculation with typical values:
V_th ≈ 0.7-1.0 V (typical range)
Applications
IC Design
Designing integrated circuits, optimizing threshold voltage for performance and power, and ensuring proper switching behavior.
Process Engineering
Controlling threshold voltage through doping, oxide thickness, and work function engineering in semiconductor manufacturing.
Device Physics
Understanding MOSFET operation, analyzing device characteristics, and studying semiconductor physics.
Education
Teaching semiconductor device physics, understanding MOSFET operation, and demonstrating threshold voltage concepts.
Frequently Asked Questions
What is flatband voltage?
Flatband voltage (V_FB) is the gate voltage where there's no band bending in the semiconductor. It accounts for work function difference between gate and substrate, and oxide charge.
How does doping affect threshold voltage?
Higher doping (N_A) increases threshold voltage because more charge is needed in the depletion region to invert the surface. Lower doping reduces V_th but increases body effect.
What is body effect?
Body effect increases threshold voltage when source is not at substrate potential. V_th increases with |V_SB|. This is important in circuits where source voltage varies.
Can threshold voltage be negative?
Yes! Depletion-mode MOSFETs have negative V_th (normally on). Enhancement-mode MOSFETs have positive V_th (normally off). Most modern MOSFETs are enhancement-mode.
How is threshold voltage measured?
V_th is typically measured as the gate voltage where drain current reaches a specific value (e.g., I_D = 1 μA × W/L) at low V_DS. It's extracted from I_D vs V_GS characteristics.