Fermi Dirac Distribution Function Calculator

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✖Fermi level energy also referred to as fermi level .lt is the highest filled energy level in the energy band at zero kelvin.ⓘ Fermi Level 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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Formula

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Fermi Dirac Distribution Function

Formula

`"f"_{"E"} = 1/(1+e^(("E"_{"f"}-"E"_{"f"})/("[BoltZ]"*"T")))`

Example

`"0.5"=1/(1+e^(("52eV"-"52eV")/("[BoltZ]"*"290K")))`

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Fermi Dirac Distribution Function Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature)))
f_E = 1/(1+e^((E_f-E_f)/([BoltZ]*T)))
This formula uses 2 Constants, 3 Variables

Constants Used

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

Variables Used

Fermi Dirac Distribution Function - 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 Level Energy - (Measured in Joule) - Fermi level energy also referred to as fermi level .lt is the highest filled energy level in the energy band at zero kelvin.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Fermi Level Energy: 52 Electron-Volt --> 8.33132211600004E-18 Joule (Check conversion here)
Temperature: 290 Kelvin --> 290 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_E = 1/(1+e^((E_f-E_f)/([BoltZ]*T))) --> 1/(1+e^((8.33132211600004E-18-8.33132211600004E-18)/([BoltZ]*290)))

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 00.020 seconds)

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Credits

Created by Tejasvini Thakral

Dr. BR Ambedkar National Institute Of Technology (NITJ), Bareilly

Tejasvini Thakral has created this Calculator and 3 more calculators!

Verified by Rachita C

BMS College Of Engineering (BMSCE), Banglore

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< 13 Semiconductor Characteristics Calculators

Conductivity in Semiconductors

Go Conductivity = (Electron Density*[Charge-e]*Mobility of Electron)+(Holes Density*[Charge-e]*Mobility of Holes)

Fermi Dirac Distribution Function

Go Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature)))

Conductivity of Extrinsic Semiconductors for N-type

Go Conductivity of Extrinsic Semiconductors (n-type) = Donor Concentration*[Charge-e]*Mobility of Electron

Conductivity of Extrinsic Semiconductor for P-Type

Go Conductivity of Extrinsic Semiconductors (p-type) = Acceptor Concentration*[Charge-e]*Mobility of Holes

Electron Diffusion Length

Go Electron Diffusion Length = sqrt(Electron Diffusion Constant*Minority Carrier Lifetime)

Energy Band Gap

Go Energy Band Gap = Energy Band Gap at 0K-(Temperature*Material Specific Constant)

Majority Carrier Concentration in Semiconductor for p-type

Go Majority Carrier Concentration = Intrinsic Carrier Concentration^2/Minority Carrier Concentration

Majority Carrier Concentration in Semiconductor

Go Majority Carrier Concentration = Intrinsic Carrier Concentration^2/Minority Carrier Concentration

Fermi Level of Intrinsic Semiconductors

Go Fermi Level Intrinsic Semiconductor = (Conduction Band Energy+Valance Band Energy)/2

Drift Current Density

Go Drift Current Density = Holes Current Density+Electron Current Density

Mobility of Charge Carriers

Go Charge Carriers Mobility = Drift Speed/Electric Field Intensity

Saturation Voltage using Threshold Voltage

Go Saturation Voltage = Gate Source Voltage-Threshold Voltage

Electric Field due to Hall Voltage

Go Hall Electric Field = Hall Voltage/Conductor Width

Fermi Dirac Distribution Function Formula

Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature)))
f_E = 1/(1+e^((E_f-E_f)/([BoltZ]*T)))

What is the 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+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))) to calculate the Fermi Dirac Distribution Function, The Fermi Dirac Distribution Function describes 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 Fermi Level 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+e^((8.33132211600004E-18-8.33132211600004E-18)/([BoltZ]*290))).

FAQ

What is Fermi Dirac Distribution Function?

The Fermi Dirac Distribution Function describes 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+e^((E_f-E_f)/([BoltZ]*T))) or Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))). Fermi level 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 describes 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+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))). To calculate Fermi Dirac Distribution Function, you need Fermi Level Energy (E_f) & Temperature (T). With our tool, you need to enter the respective value for Fermi Level 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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