MOSFET Threshold Voltage Calculator — V_th for NMOS and PMOS

What Is a MOSFET Threshold Voltage Calculator?

Our MOSFET threshold voltage calculator helps you determine the critical gate voltage at which a MOSFET transitions from the "off" state to the "on" state — the threshold voltage (V_th). Whether you're a student studying semiconductor physics, an electrical engineer designing integrated circuits, or a researcher modeling transistor behavior, this tool provides fast, accurate results.

What Is a MOSFET?

A MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) is the most fundamental building block of modern electronics. Nearly every digital circuit — from microprocessors to smartphones — relies on billions of MOSFETs switching on and off billions of times per second.

Unlike bipolar junction transistors (BJTs), a MOSFET is controlled by a voltage applied to its gate terminal rather than a base current. This makes MOSFETs highly efficient. The three main terminals are:

• Gate (G) — controls the channel conductivity via electric field
• Source (S) — the terminal where carriers enter the channel
• Drain (D) — the terminal where carriers exit the channel
• Body/Substrate (B) — the bulk semiconductor material

A thin insulating layer of silicon dioxide (SiO₂) separates the gate metal from the semiconductor — hence "metal-oxide-semiconductor."

The Types of MOSFETs

There are two main types based on the doping of the substrate:

• N-channel MOSFET (NMOS) — The substrate is p-type (doped with acceptors, N_A). Current flows through electrons. The source and drain are n⁺-doped. Threshold voltage is typically positive (enhancement mode) or negative (depletion mode).
• P-channel MOSFET (PMOS) — The substrate is n-type (doped with donors, N_D). Current flows through holes. The source and drain are p⁺-doped. Threshold voltage is typically negative.

MOSFETs can also be classified as:

• Enhancement-mode — No channel exists at V_GS = 0; the device is normally OFF
• Depletion-mode — A channel exists at V_GS = 0; the device is normally ON

How Does a MOSFET Operate?

In an NMOS transistor, applying a positive gate voltage (V_GS) creates an electric field through the oxide layer. This field repels holes from the p-type substrate directly beneath the gate, creating a depletion region. As V_GS increases, the surface potential increases until a thin layer of electrons — an inversion layer — forms at the oxide–semiconductor interface. This inversion layer is the channel that allows current to flow between source and drain.

What Is the MOSFET Threshold Voltage?

The threshold voltage (V_th) is the minimum gate-to-source voltage required to create a conducting channel between the source and drain. At V_GS = V_th, the surface potential equals 2φ_F (strong inversion condition).

The threshold voltage formula for an NMOS is:

V_th0 = V_fb + 2φ_F + √(2ε_Si·q·N_A·2φ_F) / C_ox

Where:

• V_fb — Flat-band voltage (accounts for work function differences and oxide charges)
• φ_F — Fermi potential = V_T · ln(N_A/n_i)
• ε_Si — Silicon permittivity = 11.7 × ε₀
• N_A — Acceptor doping concentration (cm⁻³)
• C_ox — Oxide capacitance = ε_ox/t_ox
• q — Elementary charge = 1.602 × 10⁻¹⁹ C

The Body Effect in MOSFETs

When the source-body voltage V_SB ≠ 0 (the source is not connected to the substrate), the threshold voltage changes. This is called the body effect. The modified threshold voltage is:

V_th = V_th0 + γ · (√(2φ_F + V_SB) − √(2φ_F))

Where γ (body effect coefficient) = √(2ε_Si·q·N_A) / C_ox

For NMOS, increasing V_SB (reverse body bias) increases V_th, requiring a higher gate voltage to turn on the device.

Regimes of Operation: Above and Below Threshold Voltage

• V_GS < V_th — Subthreshold (weak inversion): The channel is not fully formed. A small exponentially-dependent current still flows (subthreshold leakage).
• V_GS = V_th — Strong inversion begins: channel is just formed.
• V_GS > V_th, V_DS < V_GS−V_th — Linear (triode) region: MOSFET acts like a voltage-controlled resistor.
• V_GS > V_th, V_DS ≥ V_GS−V_th — Saturation region: current is relatively independent of V_DS, used for amplification.

How to Use Our MOSFET Threshold Voltage Calculator

1. Select MOSFET type — Choose N-channel (NMOS) or P-channel (PMOS)
2. Choose unit system — Metric (nm for oxide thickness) or American (Å for oxide thickness)
3. Enter doping concentration — Substrate doping N_A (NMOS) or N_D (PMOS) in cm⁻³. Typical values: 10¹⁶ to 10¹⁸ cm⁻³.
4. Enter gate oxide thickness — t_ox in nm or Å. Typical modern values: 2–20 nm.
5. Enter flat-band voltage — V_fb in volts. For n⁺ polysilicon gate on p-type Si, typical value is about −1 V.
6. Enter source-body voltage — V_SB = 0 for no body effect, or a positive value to see the body effect on V_th.
7. Enter temperature — Default is 300 K (room temperature). Affects the thermal voltage V_T and Fermi potential.
8. Click Calculate Threshold Voltage to see all results instantly.

What About Depletion-Mode MOSFETs?

In a depletion-mode MOSFET, a channel is implanted during fabrication, so the device conducts current even at V_GS = 0. For NMOS depletion-mode, the threshold voltage is negative — meaning you need to apply a negative gate voltage to turn it off. Our calculator automatically detects this: if V_th0 < 0 for NMOS (or V_th0 > 0 for PMOS), it is labeled "Depletion-Mode."

Frequently Asked Questions

What is a typical MOSFET threshold voltage?

For enhancement-mode NMOS in CMOS technology, V_th is typically 0.3–0.7 V. For PMOS, it is typically −0.3 to −0.7 V. Older technologies had higher thresholds (~1 V).

Why does threshold voltage decrease with temperature?

As temperature increases, the Fermi potential φ_F decreases (because thermal voltage V_T = kT/q increases and n_i increases with temperature), which lowers V_th. This is why hot chips can malfunction — transistors may turn on unintentionally.

What is the flat-band voltage?

The flat-band voltage V_fb = φ_ms − Q_ox/C_ox, where φ_ms is the work function difference between gate metal and semiconductor, and Q_ox is the oxide charge density. It represents the gate voltage at which there is no band bending at the surface.

What is the difference between V_th and V_GS(th)?

These are the same quantity — the threshold voltage. V_GS(th) is the notation commonly used in datasheets, while V_th or V_T is used in textbook analysis.

Does threshold voltage affect power consumption?

Yes. A lower V_th allows faster switching and lower supply voltages, but increases leakage current (subthreshold current), raising static power consumption. Modern low-power design involves careful threshold voltage optimization.