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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Formula

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Substrate Bias Coefficient

Formula

`"γ"_{"s"} = sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"N"_{"A"})/"C"_{"ox"}`

Example

`"5.7E^-7"=sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"1.32electrons/cm³")/"3.9F"`

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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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< 21 MOS Transistor Calculators

Sidewall Voltage Equivalence Factor

Go Sidewall Voltage Equivalence Factor = -(2*sqrt(Built in Potential of Sidewall Junctions)/(Final Voltage-Initial Voltage)*(sqrt(Built in Potential of Sidewall Junctions-Final Voltage)-sqrt(Built in Potential of Sidewall Junctions-Initial Voltage)))

Pull down Current in Linear Region

Go Linear Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(2*(Gate Source Voltage-Threshold Voltage)*Output Voltage-Output Voltage^2))

Node Voltage at Given Instance

Go Node Voltage at Given Instance = (Transconductance Factor/Node Capacitance)*int(exp(-(1/(Node Resistance*Node Capacitance))*(Time Period-x))*Current Flowing into Node*x,x,0,Time Period)

Pull down Current in Saturation Region

Go Saturation Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(Gate Source Voltage-Threshold Voltage)^2)

Saturation Time

Go Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)

Drain Current Flowing through MOS Transistor

Go Drain Current = (Channel Width/Channel Length)*Electron Mobility*Oxide Capacitance*int((Gate Source Voltage-x-Threshold Voltage),x,0,Drain Source Voltage)

Time Delay when NMOS Operates in Linear Region

Go Linear Region in Time Delay = -2*Junction Capacitance*int(1/(Transconductance Process Parameter*(2*(Input Voltage-Threshold Voltage)*x-x^2)),x,Initial Voltage,Final Voltage)

Depletion Region Charge Density

Go Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential)))

Depth of Depletion Region Associated with Drain

Go Drain's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*(Built in Junction Potential+Drain Source Voltage))/([Charge-e]*Doping Concentration of Acceptor))

Drain Current in Saturation Region in MOS Transistor

Go Saturation Region Drain Current = Channel Width*Saturation Electron Drift Velocity*int(Charge*Short Channel Parameter,x,0,Effective Channel Length)

Fermi Potential for P Type

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

Maximum Depletion Depth

Go Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))

Fermi Potential for N Type

Go Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)

Equivalent Large Signal Capacitance

Go Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)

Built in Potential at Depletion Region

Go Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential)))

Depth of Depletion Region Associated with Source

Go Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))

Substrate Bias Coefficient

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

Average Power Dissipated over Period of Time

Go Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)

Equivalent Large Signal Junction Capacitance

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

Work Function in MOSFET

Go Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)

Zero Bias Sidewall Junction Capacitance per Unit Length

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

Substrate Bias Coefficient Formula

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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