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Substrate Bias Coefficient Formula

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Substrate Bias Coefficient is a parameter used in the modeling of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices. Check FAQs

γ s = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot N A}}{C ox}

γ_s - Substrate Bias Coefficient?N_A - Doping Concentration of Acceptor?C_ox - Oxide Capacitance?[Charge-e] - Charge of electron?[Permitivity-silicon] - Permittivity of silicon?

Substrate Bias Coefficient Example

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Here is how the Substrate Bias Coefficient equation looks like with Values.

Here is how the Substrate Bias Coefficient equation looks like with Units.

Here is how the Substrate Bias Coefficient equation looks like.

5.7E-7 = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32}}{3.9}

5.7E-7 = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³}}{3.9F}

5.7E-7 = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.32}}{3.9}

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Substrate Bias Coefficient Solution

Follow our step by step solution on how to calculate Substrate Bias Coefficient?

FIRST Step Consider the formula

γ s = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot N A}}{C ox}

Next Step Substitute values of Variables

∴

γ s = \frac{\sqrt{2 \cdot [Charge-e] \cdot [Permitivity-silicon] \cdot 1.32electrons/cm³}}{3.9F}

Next Step Substitute values of Constants

∴

γ s = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.32electrons/cm³}}{3.9F}

Next Step Convert Units

∴

γ s = \frac{\sqrt{2 \cdot 1.6E-19C \cdot 11.7 \cdot 1.3E+6electrons/m³}}{3.9F}

Next Step Prepare to Evaluate

∴

γ s = \frac{\sqrt{2 \cdot 1.6E-19 \cdot 11.7 \cdot 1.3E+6}}{3.9}

Next Step Evaluate

∴

γ s = 5.70407834987726E-07

LAST Step Rounding Answer

∴

γ s = 5.7E-7

Substrate Bias Coefficient Formula Elements

Variables

Constants

Functions

Substrate Bias Coefficient

Substrate Bias Coefficient is a parameter used in the modeling of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices.

Symbol: γ_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Substrate Bias Coefficient

Doping Concentration of Acceptor

Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.

Symbol: N_A

Measurement: Electron DensityUnit: electrons/cm³

Note: Value should be greater than 0.

Formulas to find Doping Concentration of Acceptor

Oxide Capacitance

Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs.

Symbol: C_ox

Measurement: CapacitanceUnit: F

Note: Value should be greater than 0.

Formulas to find Oxide Capacitance

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Permittivity of silicon

Permittivity of silicon measures its ability to store electrical energy in an electric field, vital in semiconductor technology.

Symbol: [Permitivity-silicon]

Value: 11.7

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in MOS Transistor category

Go Zero Bias Sidewall Junction Capacitance per Unit Length

C jsw = C j0sw \cdot x j

Go Equivalent Large Signal Junction Capacitance

C eq(sw) = P \cdot C jsw \cdot K eq(sw)

Go Fermi Potential for P Type

Φ Fp = \frac{[BoltZ] \cdot T a}{[Charge-e]} \cdot \ln (\frac{n i}{N A})

Go Sidewall Voltage Equivalence Factor

K eq(sw) = - (2 \cdot \frac{\sqrt{Φ osw}}{V 2 - V 1} \cdot (\sqrt{Φ osw - V 2} - \sqrt{Φ osw - V 1}))

How to Evaluate Substrate Bias Coefficient?

Substrate Bias Coefficient evaluator uses Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance to evaluate the Substrate Bias Coefficient, The Substrate Bias Coefficient formula is defined as a parameter used in the modeling of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices. Substrate Bias Coefficient is denoted by γ_s symbol.

How to evaluate Substrate Bias Coefficient using this online evaluator? To use this online evaluator for Substrate Bias Coefficient, enter Doping Concentration of Acceptor (N_A) & Oxide Capacitance (C_ox) and hit the calculate button.

FAQs on Substrate Bias Coefficient

What is the formula to find Substrate Bias Coefficient?

The formula of Substrate Bias Coefficient is expressed as Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance. Here is an example- 5.7E-7 = sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000)/3.9.

How to calculate Substrate Bias Coefficient?

With Doping Concentration of Acceptor (N_A) & Oxide Capacitance (C_ox) we can find Substrate Bias Coefficient using the formula - Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance. This formula also uses Charge of electron, Permittivity of silicon constant(s) and Square Root (sqrt) function(s).

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Substrate Bias Coefficient Formula

Substrate Bias Coefficient Example

Substrate Bias Coefficient Solution

Substrate Bias Coefficient Formula Elements

Other formulas in MOS Transistor category

How to Evaluate Substrate Bias Coefficient?

FAQs on Substrate Bias Coefficient

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