Fermi dirac distribution function Calculator

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✖Energy to calculate f(e) refers to the energy where we want to determine fermi energy.ⓘ Energy to calculate f(E) [E]			+10% -10%
✖Fermi energy also referred to as fermi level .lt is the highest filled energy level in the energy band at zero kelvin.ⓘ Fermi Energy [E_f]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Fermi Dirac Distribution Function is probability distribution function. The Fermi function determines the probability that an energy state (E) is filled with an electron, under equilibrium conditions.ⓘ Fermi dirac distribution function [f(E)]

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Credits

Created by Tejasvini Thakral

Mahatma Jyotiba Phule Rohilkhand University (M.J.P.R.U), Bareilly

Tejasvini Thakral has created this Calculator and 3 more calculators!

Verified by Rachita C

BMS College Of Engineering (BMSCE), Banglore

Rachita C has verified this Calculator and 50+ more calculators!

Fermi dirac distribution function Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fermi Dirac Distribution Function = 1/(1+exp((Energy to calculate f(E)-Fermi Energy)/([BoltZ]*Temperature)))
f(E) = 1/(1+exp((E-E_f)/([BoltZ]*T)))
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23 Joule/Kelvin

Functions Used

exp - Exponential function, exp(Number)

Variables Used

Energy to calculate f(E) - Energy to calculate f(e) refers to the energy where we want to determine fermi energy. (Measured in Joule)
Fermi Energy - Fermi energy also referred to as fermi level .lt is the highest filled energy level in the energy band at zero kelvin. (Measured in Joule)
Temperature - Temperature is the degree or intensity of heat present in a substance or object. (Measured in Kelvin)

STEP 1: Convert Input(s) to Base Unit

Energy to calculate f(E): 52 Joule --> 52 Joule No Conversion Required
Fermi Energy: 52 Joule --> 52 Joule No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f(E) = 1/(1+exp((E-E_f)/([BoltZ]*T))) --> 1/(1+exp((52-52)/([BoltZ]*85)))

Evaluating ... ...

f(E) = 0.5

STEP 3: Convert Result to Output's Unit

0.5 --> No Conversion Required

FINAL ANSWER

0.5 <-- Fermi Dirac Distribution Function

(Calculation completed in 00.016 seconds)

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< 10+ EDC Calculators

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Temperature dependence of energy bandgap = Fitting parameter 1-((Alpha*(Temperature^2))/(Temperature+Beta)) Go

Current density due to electrons

Current density due to electrons = [Charge-e]*Density of electron*Mobility of electron*Electric Field Go

Current density due to holes

Current density due to holes = [Charge-e]*Density of holes*Mobility of holes*Electric Field Go

Einstein Equation for electrons

Einstein Equation for electron = Mobility of electron*[BoltZ]*Temperature Go

Conductivity in Metals

Conductivity = Density of electron*[Charge-e]*Mobility of electron Go

Electron Diffusion Length

Electron Diffusion Length = (Electron Diffusion Constant*Electron minority carrier lifetime)^1/2 Go

Hole Diffusion Length

Hole Diffusion Length = (Hole Diffusion Constant*Hole carrier minority lifetime)^1/2 Go

Mobility of charge carriers

Mobility of charge carriers = Drift Speed/Electric Field Intensity Go

Electric Field Intensity

Electric Field Intensity = Force/Charge Go

Voltage Equivalent of Temperature

Volts-Equivalent of Temperature = Temperature/11600 Go

Fermi dirac distribution function Formula

Fermi Dirac Distribution Function = 1/(1+exp((Energy to calculate f(E)-Fermi Energy)/([BoltZ]*Temperature)))
f(E) = 1/(1+exp((E-E_f)/([BoltZ]*T)))

Significance of fermi level?

The significance of the Fermi energy is most clearly seen by setting T=0. At absolute zero, the probability is =1 for energies less than the Fermi energy and zero for energies greater than the Fermi energy. We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy. This is entirely consistent with the Pauli exclusion principle where each quantum state can have one but only one particle.

How to Calculate Fermi dirac distribution function?

Fermi dirac distribution function calculator uses Fermi Dirac Distribution Function = 1/(1+exp((Energy to calculate f(E)-Fermi Energy)/([BoltZ]*Temperature))) to calculate the Fermi Dirac Distribution Function, The Fermi dirac distribution function gives the probability that an available energy state E will be occupied by an electron at temperature T, under thermal equilibrium. Fermi Dirac Distribution Function is denoted by f(E) symbol.

How to calculate Fermi dirac distribution function using this online calculator? To use this online calculator for Fermi dirac distribution function, enter Energy to calculate f(E) (E), Fermi Energy (E_f) & Temperature (T) and hit the calculate button. Here is how the Fermi dirac distribution function calculation can be explained with given input values -> 0.5 = 1/(1+exp((52-52)/([BoltZ]*85))).

FAQ

What is Fermi dirac distribution function?

The Fermi dirac distribution function gives the probability that an available energy state E will be occupied by an electron at temperature T, under thermal equilibrium and is represented as f(E) = 1/(1+exp((E-E_f)/([BoltZ]*T))) or Fermi Dirac Distribution Function = 1/(1+exp((Energy to calculate f(E)-Fermi Energy)/([BoltZ]*Temperature))). Energy to calculate f(e) refers to the energy where we want to determine fermi energy, Fermi energy also referred to as fermi level .lt is the highest filled energy level in the energy band at zero kelvin & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Fermi dirac distribution function?

The Fermi dirac distribution function gives the probability that an available energy state E will be occupied by an electron at temperature T, under thermal equilibrium is calculated using Fermi Dirac Distribution Function = 1/(1+exp((Energy to calculate f(E)-Fermi Energy)/([BoltZ]*Temperature))). To calculate Fermi dirac distribution function, you need Energy to calculate f(E) (E), Fermi Energy (E_f) & Temperature (T). With our tool, you need to enter the respective value for Energy to calculate f(E), Fermi Energy & Temperature 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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