Substrate Bias Coefficient Calculator

✖Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.ⓘ Doping Concentration of Acceptor [N_A]			+10% -10%
✖Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs.ⓘ Oxide Capacitance [C_ox]			+10% -10%

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

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Substrate Bias Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance
γ_s = sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A)/C_ox
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[Permitivity-silicon] - Permittivity of silicon Value Taken As 11.7
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19

Functions Used

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., sqrt(Number)

Variables Used

Substrate Bias Coefficient - Substrate Bias Coefficient is a parameter used in the modeling of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices.
Doping Concentration of Acceptor - (Measured in Electrons per Cubic Meter) - Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material.
Oxide Capacitance - (Measured in Farad) - Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs.

STEP 1: Convert Input(s) to Base Unit

Doping Concentration of Acceptor: 1.32 Electrons per Cubic Centimeter --> 1320000 Electrons per Cubic Meter (Check conversion here)
Oxide Capacitance: 3.9 Farad --> 3.9 Farad No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ_s = sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A)/C_ox --> sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000)/3.9

Evaluating ... ...

γ_s = 5.70407834987726E-07

STEP 3: Convert Result to Output's Unit

5.70407834987726E-07 --> No Conversion Required

FINAL ANSWER

5.70407834987726E-07 ≈ 5.7E-7 <-- Substrate Bias Coefficient

(Calculation completed in 00.004 seconds)

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< MOS Transistor Calculators

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Fermi Potential for P Type

LaTeX Go Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)

Equivalent Large Signal Junction Capacitance

LaTeX Go Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor

Zero Bias Sidewall Junction Capacitance per Unit Length

LaTeX Go Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall

Substrate Bias Coefficient Formula

LaTeX Go

Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance
γ_s = sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A)/C_ox

How Does Substrate Bias Influence Device Performance?

Substrate bias can affect the threshold voltage, carrier mobility, and other electrical characteristics of semiconductor devices. It is often used to control the device's behavior and optimize performance.

How to Calculate Substrate Bias Coefficient?

Substrate Bias Coefficient calculator uses Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance to calculate 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 calculate Substrate Bias Coefficient using this online calculator? To use this online calculator for Substrate Bias Coefficient, enter Doping Concentration of Acceptor (N_A) & Oxide Capacitance (C_ox) and hit the calculate button. Here is how the Substrate Bias Coefficient calculation can be explained with given input values -> 5.7E-7 = sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000)/3.9.

FAQ

What is 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 and is represented as γ_s = sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A)/C_ox or Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance. Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material & Oxide Capacitance refers to the capacitance associated with the insulating oxide layer in a Metal-Oxide-Semiconductor (MOS) structure, such as in MOSFETs.

How to calculate 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 is calculated using Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance. To calculate Substrate Bias Coefficient, you need Doping Concentration of Acceptor (N_A) & Oxide Capacitance (C_ox). With our tool, you need to enter the respective value for Doping Concentration of Acceptor & Oxide Capacitance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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