## Work Function in MOSFET Solution

STEP 0: Pre-Calculation Summary
Formula Used
Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)
S = +(Ec-EF)
This formula uses 4 Variables
Variables Used
Work Function - (Measured in Volt) - Work Function is the energy required for an electron to move from the Fermi level into free space.
Vaccum Level - (Measured in Joule) - Vaccum Level is a theoretical energy level that provides a baseline for understanding energy levels in the semiconductor and metal regions of the MOSFET.
Conduction Band Energy Level - (Measured in Joule) - Conduction Band Energy Level is an energy band within the semiconductor material where electrons can move freely and contribute to electrical conduction.
Fermi Level - (Measured in Joule) - Fermi Level represents the energy level at which electrons have a 50% probability of being occupied at absolute zero temperature.
STEP 1: Convert Input(s) to Base Unit
Vaccum Level: 5.1 Electron-Volt --> 8.17110438300004E-19 Joule (Check conversion here)
Conduction Band Energy Level: 3.01 Electron-Volt --> 4.82255376330002E-19 Joule (Check conversion here)
Fermi Level: 5.24 Electron-Volt --> 8.39540920920004E-19 Joule (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S = qχ+(Ec-EF) --> 8.17110438300004E-19+(4.82255376330002E-19-8.39540920920004E-19)
Evaluating ... ...
S = 4.59824893710002E-19
STEP 3: Convert Result to Output's Unit
4.59824893710002E-19 Volt --> No Conversion Required
4.59824893710002E-19 4.6E-19 Volt <-- Work Function
(Calculation completed in 00.004 seconds)
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## Credits

Created by banuprakash
Dayananda Sagar College of Engineering (DSCE), Bangalore
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Heritage Insitute of technology (HITK), Kolkata
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## < 20 MOS Transistor Calculators

Sidewall Voltage Equivalence Factor
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
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))
Pull down Current in Saturation Region
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
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
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
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
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
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
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
Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)
Maximum Depletion Depth
Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))
Fermi Potential for N Type
Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)
Equivalent Large Signal Capacitance
Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)
Built in Potential at Depletion Region
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
Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))
Substrate Bias Coefficient
Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance
Average Power Dissipated over Period of Time
Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)
Equivalent Large Signal Junction Capacitance
Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor
Work Function in MOSFET
Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)
Zero Bias Sidewall Junction Capacitance per Unit Length
Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall

## Work Function in MOSFET Formula

Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)
S = +(Ec-EF)

## What is the significance of the work function in MOSFET design?

The work function is crucial in MOSFET design as it determines the energy barrier for electron or hole movement between the metal gate and the semiconductor. It affects the device's electrical characteristics and performance.

## How to Calculate Work Function in MOSFET?

Work Function in MOSFET calculator uses Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level) to calculate the Work Function, The Work Function in MOSFET formula is defined as the energy required to move an electron from the Fermi level of the metal gate electrode to the conduction or valence band of the semiconductor. Work Function is denoted by S symbol.

How to calculate Work Function in MOSFET using this online calculator? To use this online calculator for Work Function in MOSFET, enter Vaccum Level (qχ), Conduction Band Energy Level (Ec) & Fermi Level (EF) and hit the calculate button. Here is how the Work Function in MOSFET calculation can be explained with given input values -> 4.6E-19 = 8.17110438300004E-19+(4.82255376330002E-19-8.39540920920004E-19).

### FAQ

What is Work Function in MOSFET?
The Work Function in MOSFET formula is defined as the energy required to move an electron from the Fermi level of the metal gate electrode to the conduction or valence band of the semiconductor and is represented as S = qχ+(Ec-EF) or Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level). Vaccum Level is a theoretical energy level that provides a baseline for understanding energy levels in the semiconductor and metal regions of the MOSFET, Conduction Band Energy Level is an energy band within the semiconductor material where electrons can move freely and contribute to electrical conduction & Fermi Level represents the energy level at which electrons have a 50% probability of being occupied at absolute zero temperature.
How to calculate Work Function in MOSFET?
The Work Function in MOSFET formula is defined as the energy required to move an electron from the Fermi level of the metal gate electrode to the conduction or valence band of the semiconductor is calculated using Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level). To calculate Work Function in MOSFET, you need Vaccum Level (qχ), Conduction Band Energy Level (Ec) & Fermi Level (EF). With our tool, you need to enter the respective value for Vaccum Level, Conduction Band Energy Level & Fermi Level 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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