Sidewall Voltage Equivalence Factor Calculator

✖Built in Potential of Sidewall Junctions refers to the junction formed along the vertical or sidewall surfaces of the transistor structure.ⓘ Built in Potential of Sidewall Junctions [Φ_osw]			+10% -10%
✖Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.ⓘ Final Voltage [V₂]			+10% -10%
✖Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions.ⓘ Initial Voltage [V₁]			+10% -10%

✖Sidewall Voltage Equivalence Factor represents the relationship between the voltage applied to a semiconductor device and the resulting change in sidewall junction capacitance per unit area.ⓘ Sidewall Voltage Equivalence Factor [K_eq(sw)]

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Formula

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Sidewall Voltage Equivalence Factor

Formula

`"K"_{"eq(sw)"} = -(2*sqrt("Φ"_{"osw"})/("V"_{"2"}-"V"_{"1"})*(sqrt("Φ"_{"osw"}-"V"_{"2"})-sqrt("Φ"_{"osw"}-"V"_{"1"})))`

Example

`"1.00009"=-(2*sqrt("0.000032V")/("6.135nV"-"5.42nV")*(sqrt("0.000032V"-"6.135nV")-sqrt("0.000032V"-"5.42nV")))`

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Sidewall Voltage Equivalence Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
K_eq(sw) = -(2*sqrt(Φ_osw)/(V₂-V₁)*(sqrt(Φ_osw-V₂)-sqrt(Φ_osw-V₁)))
This formula uses 1 Functions, 4 Variables

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

Sidewall Voltage Equivalence Factor - Sidewall Voltage Equivalence Factor represents the relationship between the voltage applied to a semiconductor device and the resulting change in sidewall junction capacitance per unit area.
Built in Potential of Sidewall Junctions - (Measured in Volt) - Built in Potential of Sidewall Junctions refers to the junction formed along the vertical or sidewall surfaces of the transistor structure.
Final Voltage - (Measured in Volt) - Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event.
Initial Voltage - (Measured in Volt) - Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions.

STEP 1: Convert Input(s) to Base Unit

Built in Potential of Sidewall Junctions: 3.2E-05 Volt --> 3.2E-05 Volt No Conversion Required
Final Voltage: 6.135 Nanovolt --> 6.135E-09 Volt (Check conversion here)
Initial Voltage: 5.42 Nanovolt --> 5.42E-09 Volt (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_eq(sw) = -(2*sqrt(Φ_osw)/(V₂-V₁)*(sqrt(Φ_osw-V₂)-sqrt(Φ_osw-V₁))) --> -(2*sqrt(3.2E-05)/(6.135E-09-5.42E-09)*(sqrt(3.2E-05-6.135E-09)-sqrt(3.2E-05-5.42E-09)))

Evaluating ... ...

K_eq(sw) = 1.00009028568687

STEP 3: Convert Result to Output's Unit

1.00009028568687 --> No Conversion Required

FINAL ANSWER

1.00009028568687 ≈ 1.00009 <-- Sidewall Voltage Equivalence Factor

(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

Sidewall Voltage Equivalence Factor Formula

How do sidewalls influence MOSFET behavior?

Sidewalls in MOSFETs can affect device characteristics, such as threshold voltage and subthreshold swing. Understanding sidewall properties is crucial for advanced transistor designs, including FinFETs and nanowire transistors.

How to Calculate Sidewall Voltage Equivalence Factor?

Sidewall Voltage Equivalence Factor calculator uses 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))) to calculate the Sidewall Voltage Equivalence Factor, The Sidewall Voltage Equivalence Factor formula is defined as a parameter used in modeling the corner effects of the gate oxide thickness in Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices. Sidewall Voltage Equivalence Factor is denoted by K_eq(sw) symbol.

How to calculate Sidewall Voltage Equivalence Factor using this online calculator? To use this online calculator for Sidewall Voltage Equivalence Factor, enter Built in Potential of Sidewall Junctions (Φ_osw), Final Voltage (V₂) & Initial Voltage (V₁) and hit the calculate button. Here is how the Sidewall Voltage Equivalence Factor calculation can be explained with given input values -> 1.00009 = -(2*sqrt(3.2E-05)/(6.135E-09-5.42E-09)*(sqrt(3.2E-05-6.135E-09)-sqrt(3.2E-05-5.42E-09))).

FAQ

What is Sidewall Voltage Equivalence Factor?

The Sidewall Voltage Equivalence Factor formula is defined as a parameter used in modeling the corner effects of the gate oxide thickness in Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices and is represented as K_eq(sw) = -(2*sqrt(Φ_osw)/(V₂-V₁)*(sqrt(Φ_osw-V₂)-sqrt(Φ_osw-V₁))) or 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))). Built in Potential of Sidewall Junctions refers to the junction formed along the vertical or sidewall surfaces of the transistor structure, Final Voltage refers to the voltage level achieved or measured at the conclusion of a particular process or event & Initial Voltage refer to the voltage present at a specific point in a circuit at the beginning of a certain operation or under specific conditions.

How to calculate Sidewall Voltage Equivalence Factor?

The Sidewall Voltage Equivalence Factor formula is defined as a parameter used in modeling the corner effects of the gate oxide thickness in Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) devices is calculated using 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))). To calculate Sidewall Voltage Equivalence Factor, you need Built in Potential of Sidewall Junctions (Φ_osw), Final Voltage (V₂) & Initial Voltage (V₁). With our tool, you need to enter the respective value for Built in Potential of Sidewall Junctions, Final Voltage & Initial Voltage 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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