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Fermi Dirac Distribution Function Formula

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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. Check FAQs

f E = \frac{1}{1 + e^{\frac{E f - E f}{[BoltZ] \cdot T}}}

f_E - Fermi Dirac Distribution Function?E_f - Fermi Level Energy?T - Temperature?[BoltZ] - Boltzmann constant?

Fermi Dirac Distribution Function Example

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Here is how the Fermi Dirac Distribution Function equation looks like with Values.

Here is how the Fermi Dirac Distribution Function equation looks like with Units.

Here is how the Fermi Dirac Distribution Function equation looks like.

0.5 = \frac{1}{1 + e^{\frac{52 - 52}{1.4E-23 \cdot 290}}}

0.5 = \frac{1}{1 + e^{\frac{52eV - 52eV}{1.4E-23J/K \cdot 290K}}}

0.5 = \frac{1}{1 + e^{\frac{52 - 52}{1.4E-23 \cdot 290}}}

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Fermi Dirac Distribution Function Solution

Follow our step by step solution on how to calculate Fermi Dirac Distribution Function?

FIRST Step Consider the formula

f E = \frac{1}{1 + e^{\frac{E f - E f}{[BoltZ] \cdot T}}}

Next Step Substitute values of Variables

∴

f E = \frac{1}{1 + e^{\frac{52eV - 52eV}{[BoltZ] \cdot 290K}}}

Next Step Substitute values of Constants

∴

f E = \frac{1}{1 + e^{\frac{52eV - 52eV}{1.4E-23J/K \cdot 290K}}}

Next Step Convert Units

∴

f E = \frac{1}{1 + e^{\frac{8.3E-18J - 8.3E-18J}{1.4E-23J/K \cdot 290K}}}

Next Step Prepare to Evaluate

∴

f E = \frac{1}{1 + e^{\frac{8.3E-18 - 8.3E-18}{1.4E-23 \cdot 290}}}

LAST Step Evaluate

∴

f E = 0.5

Fermi Dirac Distribution Function Formula Elements

Variables

Constants

Fermi Dirac Distribution Function

Symbol: f_E

Measurement: NAUnit: Unitless

Note: Value should be between -2 to 2.

Formulas to find Fermi Dirac Distribution Function

Fermi Level Energy

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

Symbol: E_f

Measurement: EnergyUnit: eV

Note: Value can be positive or negative.

Formulas to find Fermi Level Energy

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Other formulas in Semiconductor Characteristics category

Go Fermi Level of Intrinsic Semiconductors

E Fi = \frac{E c + E v}{2}

Go Mobility of Charge Carriers

μ = \frac{V d}{E I}

Go Electron Diffusion Length

L n = \sqrt{D n \cdot τ n}

Go Conductivity in Semiconductors

σ = (ρ e \cdot [Charge-e] \cdot μ n) + (ρ h \cdot [Charge-e] \cdot μ p)

How to Evaluate Fermi Dirac Distribution Function?

Fermi Dirac Distribution Function evaluator uses Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))) to evaluate 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 evaluate Fermi Dirac Distribution Function using this online evaluator? To use this online evaluator for Fermi Dirac Distribution Function, enter Fermi Level Energy (E_f) & Temperature (T) and hit the calculate button.

FAQs on Fermi Dirac Distribution Function

What is the formula to find Fermi Dirac Distribution Function?

The formula of Fermi Dirac Distribution Function is expressed as Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))). Here is an example- 0.5 = 1/(1+e^((8.33132211600004E-18-8.33132211600004E-18)/([BoltZ]*290))).

How to calculate Fermi Dirac Distribution Function?

With Fermi Level Energy (E_f) & Temperature (T) we can find Fermi Dirac Distribution Function using the formula - Fermi Dirac Distribution Function = 1/(1+e^((Fermi Level Energy-Fermi Level Energy)/([BoltZ]*Temperature))). This formula also uses Boltzmann constant .

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