Fermi Potential for N Type Calculator

✖Absolute Temperature is a measure of the thermal energy in a system and is measured in kelvins.ⓘ Absolute Temperature [T_a]			+10% -10%
✖Donor Dopant Concentration is the concentration of donor atoms per unit volume.ⓘ Donor Dopant Concentration [N_d]			+10% -10%
✖Intrinsic Carrier Concentration is a fundamental property of a semiconductor material and represents the concentration of thermally generated charge carriers in the absence of any external influences.ⓘ Intrinsic Carrier Concentration [n_i]			+10% -10%

✖Fermi Potential for N Type is a key parameter that describes the energy level at which the probability of finding an electron is 0.5.ⓘ Fermi Potential for N Type [Φ_Fn]

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Fermi Potential for N Type

Formula

`"Φ"_{"Fn"} = ("[BoltZ]"*"T"_{"a"})/"[Charge-e]"*ln("N"_{"d"}/"n"_{"i"})`

Example

`"0.081443V"=("[BoltZ]"*"24.5K")/"[Charge-e]"*ln("1.7E^23electrons/m³"/"3000000electrons/m³")`

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Fermi Potential for N Type Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)
Φ_Fn = ([BoltZ]*T_a)/[Charge-e]*ln(N_d/n_i)
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Fermi Potential for N Type - (Measured in Volt) - Fermi Potential for N Type is a key parameter that describes the energy level at which the probability of finding an electron is 0.5.
Absolute Temperature - (Measured in Kelvin) - Absolute Temperature is a measure of the thermal energy in a system and is measured in kelvins.
Donor Dopant Concentration - (Measured in Electrons per Cubic Meter) - Donor Dopant Concentration is the concentration of donor atoms per unit volume.
Intrinsic Carrier Concentration - (Measured in Electrons per Cubic Meter) - Intrinsic Carrier Concentration is a fundamental property of a semiconductor material and represents the concentration of thermally generated charge carriers in the absence of any external influences.

STEP 1: Convert Input(s) to Base Unit

Absolute Temperature: 24.5 Kelvin --> 24.5 Kelvin No Conversion Required
Donor Dopant Concentration: 1.7E+23 Electrons per Cubic Meter --> 1.7E+23 Electrons per Cubic Meter No Conversion Required
Intrinsic Carrier Concentration: 3000000 Electrons per Cubic Meter --> 3000000 Electrons per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_Fn = ([BoltZ]*T_a)/[Charge-e]*ln(N_d/n_i) --> ([BoltZ]*24.5)/[Charge-e]*ln(1.7E+23/3000000)

Evaluating ... ...

Φ_Fn = 0.081443344057026

STEP 3: Convert Result to Output's Unit

0.081443344057026 Volt --> No Conversion Required

FINAL ANSWER

0.081443344057026 ≈ 0.081443 Volt <-- Fermi Potential for N Type

(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!

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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

Fermi Potential for N Type Formula

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

How does the Fermi potential impact carrier concentration in N-type semiconductors?

The Fermi potential serves as a reference energy level that dictates the distribution of electrons in the conduction band. A higher Fermi potential corresponds to a higher electron concentration in the conduction band.

How to Calculate Fermi Potential for N Type?

Fermi Potential for N Type calculator uses Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration) to calculate the Fermi Potential for N Type, The Fermi Potential for N Type formula is defined as a key parameter that describes the energy level at which the probability of finding an electron is 0.5. Fermi Potential for N Type is denoted by Φ_Fn symbol.

How to calculate Fermi Potential for N Type using this online calculator? To use this online calculator for Fermi Potential for N Type, enter Absolute Temperature (T_a), Donor Dopant Concentration (N_d) & Intrinsic Carrier Concentration (n_i) and hit the calculate button. Here is how the Fermi Potential for N Type calculation can be explained with given input values -> 0.008144 = ([BoltZ]*24.5)/[Charge-e]*ln(1.7E+23/3000000).

FAQ

What is Fermi Potential for N Type?

The Fermi Potential for N Type formula is defined as a key parameter that describes the energy level at which the probability of finding an electron is 0.5 and is represented as Φ_Fn = ([BoltZ]*T_a)/[Charge-e]*ln(N_d/n_i) or Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration). Absolute Temperature is a measure of the thermal energy in a system and is measured in kelvins, Donor Dopant Concentration is the concentration of donor atoms per unit volume & Intrinsic Carrier Concentration is a fundamental property of a semiconductor material and represents the concentration of thermally generated charge carriers in the absence of any external influences.

How to calculate Fermi Potential for N Type?

The Fermi Potential for N Type formula is defined as a key parameter that describes the energy level at which the probability of finding an electron is 0.5 is calculated using Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration). To calculate Fermi Potential for N Type, you need Absolute Temperature (T_a), Donor Dopant Concentration (N_d) & Intrinsic Carrier Concentration (n_i). With our tool, you need to enter the respective value for Absolute Temperature, Donor Dopant Concentration & Intrinsic Carrier Concentration 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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