What is the MOSFET threshold voltage?

The MOSFET threshold voltage (Vth) is the minimum gate-to-source voltage required to form an inversion layer in the channel and allow current to flow between drain and source. It is a fundamental parameter in transistor circuit design.

How does the MOSFET Threshold Voltage Calculator compute Vth?

In formula mode, the MOSFET Threshold Voltage Calculator uses the process-parameter equation: Vth = VFB + 2φF + γ(√(2φF + VSB) − √(2φF)). In extraction mode it interpolates the constant-current method or applies linear extrapolation on √ID vs VGS data.

What is the body effect in MOSFETs?

The body effect refers to the increase in threshold voltage when a reverse bias VSB is applied between source and body. The MOSFET Threshold Voltage Calculator shows the body-effect table across multiple VSB values so you can assess its impact on circuit performance.

What is the difference between NMOS and PMOS threshold voltage?

NMOS transistors have a positive Vth (typically 0.3–1 V), while PMOS transistors have a negative Vth (typically −0.3 to −1 V). The MOSFET Threshold Voltage Calculator applies the correct sign convention automatically when you select the device type.

What is the linear extrapolation method for extracting Vth?

The linear extrapolation method fits a straight line to the √ID versus VGS data in the saturation region. The x-intercept of this line (where √ID = 0) gives the threshold voltage.

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MOSFET Threshold Voltage Calculator

How to Use MOSFET Threshold Voltage Calculator

The MOSFET Threshold Voltage Calculator provides two independent methods for determining Vth. Select the method that matches your available data.

Formula Mode (Process Parameters)

Select the device type — NMOS or PMOS — using the toggle buttons.
Enter the Flat-Band Voltage (VFB) in volts. For NMOS this is typically a small negative value such as −0.5 V.
Enter the Fermi Potential (φF), usually in the range 0.3–0.4 V for silicon at room temperature.
Enter the Body-Effect Coefficient (γ) in V^0.5, typically 0.2–0.8 V^0.5 depending on substrate doping.
Enter the Source-Body Voltage (VSB). Use 0 V when source and body are tied together.
The MOSFET Threshold Voltage Calculator instantly shows Vth, the derivation steps, and a table of how Vth changes with VSB from 0 to 3 V.

Extraction Mode (Transfer Curve)

Choose the extraction method: Constant-Current or Linear Extrapolation.
Enter paired (VGS, ID) measurement data from your SPICE simulation or lab measurements.
For the constant-current method, specify the drain current threshold (e.g., 100 nA). The calculator interpolates Vth at that current.
For linear extrapolation, the calculator fits √ID vs VGS in the saturation region and finds the x-intercept.

Formula & Theory — MOSFET Threshold Voltage Calculator

The MOSFET Threshold Voltage Calculator is based on the standard MOS physics model.

Process-Parameter Formula

The threshold voltage of an MOS transistor is:

V_th = V_FB + 2φF + γ × (√(2φF + V_SB) − √(2φF))

Parameters:

Symbol	Name	Typical Range
V_FB	Flat-band voltage	−1 to 0 V (NMOS)
φF	Fermi potential	0.3–0.4 V
γ	Body-effect coefficient	0.2–0.8 V^0.5
V_SB	Source-body voltage	0–5 V

Flat-Band Voltage (VFB):

V_FB = φ_ms − Q_ox / C_ox

where φ_ms is the work-function difference between gate and semiconductor, Q_ox is the oxide charge density, and C_ox is the gate oxide capacitance per unit area.

Fermi Potential (φF):

φF = (kT / q) × ln(N_A / n_i)

where N_A is the acceptor doping concentration, n_i is the intrinsic carrier concentration (~1.45 × 10^10 cm^−3 for silicon at 300 K), and kT/q ≈ 0.026 V at room temperature.

Body-Effect Coefficient (γ):

γ = √(2 × ε_Si × q × N_A) / C_ox

where ε_Si ≈ 11.7 ε_0 is the silicon permittivity and C_ox = ε_ox / t_ox.

PMOS Sign Convention

For PMOS devices, the threshold voltage is negative. The MOSFET Threshold Voltage Calculator adjusts the formula:

V_th,PMOS = V_FB − 2|φF| − γ × (√(2|φF| + |V_SB|) − √(2|φF|))

Enter φF and γ as positive values; the sign convention is applied automatically.

Extraction Methods

Constant-Current Method: The threshold voltage is defined as the VGS value at which ID equals a small pre-defined current (typically 100 nA × W/L). This method is widely used in industry because it is less sensitive to series resistance and short-channel effects.

Linear Extrapolation: √ID is plotted versus VGS. A linear fit to the steepest portion of the curve is extrapolated to √ID = 0. The x-intercept gives Vth. This method is straightforward and works well for long-channel devices.

Use Cases for MOSFET Threshold Voltage Calculator

The MOSFET Threshold Voltage Calculator is useful in a wide range of engineering and academic contexts:

Circuit Design Verification: Confirm that the process-given Vth is consistent with your circuit operating point. Designs that rely on a specific overdrive voltage (VGS − Vth) need an accurate Vth estimate before simulation.
Body-Effect Analysis: Understand how Vth shifts when source-body bias is applied. This is critical in stacked transistor circuits, switched-capacitor designs, and pass-gate logic where body bias varies dynamically.
Process Characterization: Extract Vth from measured IV curves during wafer testing to monitor process uniformity and compare against SPICE model parameters.
Education and Teaching: The MOSFET Threshold Voltage Calculator provides a transparent step-by-step derivation, making it ideal for semiconductor device courses, textbook exercises, and lab report preparation.
SPICE Model Calibration: Compare hand-calculated Vth with the SPICE model VTHO parameter to spot discrepancies between the model card and measured device behavior.
Technology Scaling Study: Explore how Vth decreases with oxide thickness scaling or substrate doping changes, which is fundamental to understanding short-channel effects and power management in advanced CMOS nodes.