Built in Potential at Depletion Region 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%
✖Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.ⓘ Bulk Fermi Potential [Φ_f]			+10% -10%

✖Built in Voltage is a characteristic voltage that exists across a semiconductor device.ⓘ Built in Potential at Depletion Region [Φ_B0]

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Formula

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Built in Potential at Depletion Region

Formula

`"Φ"_{"B0"} = -(sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"N"_{"A"}*"modulus"(-2*"Φ"_{"f"})))`

Example

`"-1.6E^-6V"=-(sqrt(2*"[Charge-e]"*"[Permitivity-silicon]"*"1.32electrons/cm³"*"modulus"(-2*"0.25V")))`

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Built in Potential at Depletion Region Solution

STEP 0: Pre-Calculation Summary

Formula Used

Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential)))
Φ_B0 = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(-2*Φ_f)))
This formula uses 2 Constants, 2 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)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

Variables Used

Built in Voltage - (Measured in Volt) - Built in Voltage is a characteristic voltage that exists across a semiconductor device.
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.
Bulk Fermi Potential - (Measured in Volt) - Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.

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)
Bulk Fermi Potential: 0.25 Volt --> 0.25 Volt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_B0 = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(-2*Φ_f))) --> -(sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(-2*0.25)))

Evaluating ... ...

Φ_B0 = -1.57302306783086E-06

STEP 3: Convert Result to Output's Unit

-1.57302306783086E-06 Volt --> No Conversion Required

FINAL ANSWER

-1.57302306783086E-06 ≈ -1.6E-6 Volt <-- Built in Voltage

(Calculation completed in 00.004 seconds)

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Created by banuprakash

Dayananda Sagar College of Engineering (DSCE), Bangalore

banuprakash has created this Calculator and 50+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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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

Built in Potential at Depletion Region Formula

What is the significance of the built-in potential in the depletion region in p-n junctions?

The built-in potential is a crucial parameter that influences the behavior of a p-n junction. It determines the electrostatics of the junction and plays a key role in device characteristics, such as the barrier for majority carriers and the overall behavior in thermal equilibrium.

How to Calculate Built in Potential at Depletion Region?

Built in Potential at Depletion Region calculator uses Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))) to calculate the Built in Voltage, The Built in Potential at Depletion Region formula is defined as the voltage established across this depleted region when the p-n junction is in thermal equilibrium. Built in Voltage is denoted by Φ_B0 symbol.

How to calculate Built in Potential at Depletion Region using this online calculator? To use this online calculator for Built in Potential at Depletion Region, enter Doping Concentration of Acceptor (N_A) & Bulk Fermi Potential (Φ_f) and hit the calculate button. Here is how the Built in Potential at Depletion Region calculation can be explained with given input values -> -1.6E-6 = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*1320000*modulus(-2*0.25))).

FAQ

What is Built in Potential at Depletion Region?

The Built in Potential at Depletion Region formula is defined as the voltage established across this depleted region when the p-n junction is in thermal equilibrium and is represented as Φ_B0 = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*N_A*modulus(-2*Φ_f))) or Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))). Doping Concentration of Acceptor refers to the concentration of acceptor atoms intentionally added to a semiconductor material & Bulk Fermi Potential is a parameter that describes the electrostatic potential in the bulk (interior) of a semiconductor material.

How to calculate Built in Potential at Depletion Region?

The Built in Potential at Depletion Region formula is defined as the voltage established across this depleted region when the p-n junction is in thermal equilibrium is calculated using Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential))). To calculate Built in Potential at Depletion Region, you need Doping Concentration of Acceptor (N_A) & Bulk Fermi Potential (Φ_f). With our tool, you need to enter the respective value for Doping Concentration of Acceptor & Bulk Fermi Potential 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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