MOSFET Threshold Voltage Calculator

MOSFET Threshold Voltage

Example: -0.5V for typical MOSFETs
Metal-Semiconductor Work Function Difference
Substrate Doping Concentration
Oxide Capacitance per Unit Area
Fermi Potential

Results

Threshold Voltage (Vth):
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Understanding MOSFET Threshold Voltage (Vth)

Understanding MOSFET Threshold Voltage (Vth)

The threshold voltage (Vth) is a crucial parameter for MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors). It represents the gate-source voltage (VGS) required to create a conducting channel between the source and drain terminals. When VGS exceeds Vth, the MOSFET turns "on," allowing current to flow. This article provides a breakdown of the key components affecting Vth and illustrates its calculation.

Key Components of Threshold Voltage

The threshold voltage is determined by several factors, captured in the following equation:

Vth = VFB + ΦMS + (Qdep/Cox) + 2ΦF

Where:

  • Vth: Threshold voltage (the voltage needed to turn the MOSFET on)
  • VFB: Flat-band voltage (voltage required to "flatten" the energy bands at the semiconductor surface)
  • ΦMS: Metal-semiconductor work function difference
  • Qdep: Charge density of the depletion region
  • Cox: Oxide capacitance per unit area
  • ΦF: Fermi potential (related to the doping concentration of the semiconductor)

Calculating the Depletion Region Charge (Qdep)

The charge density of the depletion region (Qdep) is calculated using the following formula:

Qdep = √(2qεSiNAΦF)

Where:

  • q: Elementary charge (1.60 x 10-19 Coulombs)
  • εSi: Permittivity of silicon (εr * ε0, where εr is the relative permittivity and ε0 is the vacuum permittivity)
  • NA: Acceptor doping concentration (for a p-type substrate)
  • ΦF: Fermi potential

Example Calculation

Let's consider a hypothetical example to illustrate the calculation of Qdep.

Given the following values:

  • q = 1.60 x 10-19 C
  • εSi = 1.04 x 10-12 F/m (This assumes εr = 11.7 and ε0 = 8.854e-12 F/m)
  • NA = 9 x 1017 cm-3 (Convert cm-3 to m-3: 9e17 * 1e6 = 9e23 m-3)
  • ΦF = 0.057 V (Convert 57mV to V: 0.057V)

Then:

Qdep = √(2qεSiNAΦF) = √(2 × 1.60e-19 × 1.04e-12 × 9e23 × 0.057)

Therefore:

Qdep ≈ √(1.79e-7) ≈ 4.23e-4 C/m2

Note the important unit conversions and realistic scaling of values to acheive meaningful numerical results. With Qdep now computed we could then proceed to finish the full calculation of the threshold voltage Vth if VFB, ΦMS, and Cox are known.

Conclusion

Understanding the factors influencing the threshold voltage is crucial for designing and analyzing MOSFET circuits. By carefully considering these parameters and performing accurate calculations, engineers can optimize circuit performance and ensure proper device operation.