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Intrinsic Concentration Formula

GoIntrinsic Carrier Concentration under Non-Equilibrium Conditions Formula

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Intrinsic Carrier Concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material. Check FAQs

n i = \sqrt{N c \cdot N v} \cdot e^{\frac{- E g}{2 \cdot [BoltZ] \cdot T}}

n_i - Intrinsic Carrier Concentration?N_c - Effective Density in Valence Band?N_v - Effective Density in Conduction Band?E_g - Temperature Dependence of Energy Band Gap?T - Temperature?[BoltZ] - Boltzmann constant?

Intrinsic Concentration Example

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Here is how the Intrinsic Concentration equation looks like with Values.

Here is how the Intrinsic Concentration equation looks like with Units.

Here is how the Intrinsic Concentration equation looks like.

1.3E+8 = \sqrt{1E+18 \cdot 5E+17} \cdot e^{\frac{- 1.12}{2 \cdot 1.4E-23 \cdot 290}}

1.3E+81/m³ = \sqrt{1E+181/m³ \cdot 5E+171/m³} \cdot e^{\frac{- 1.12eV}{2 \cdot 1.4E-23J/K \cdot 290K}}

1.3E+8 = \sqrt{1E+18 \cdot 5E+17} \cdot e^{\frac{- 1.12}{2 \cdot 1.4E-23 \cdot 290}}

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Intrinsic Concentration Solution

Follow our step by step solution on how to calculate Intrinsic Concentration?

FIRST Step Consider the formula

n i = \sqrt{N c \cdot N v} \cdot e^{\frac{- E g}{2 \cdot [BoltZ] \cdot T}}

Next Step Substitute values of Variables

∴

n i = \sqrt{1E+181/m³ \cdot 5E+171/m³} \cdot e^{\frac{- 1.12eV}{2 \cdot [BoltZ] \cdot 290K}}

Next Step Substitute values of Constants

∴

n i = \sqrt{1E+181/m³ \cdot 5E+171/m³} \cdot e^{\frac{- 1.12eV}{2 \cdot 1.4E-23J/K \cdot 290K}}

Next Step Convert Units

∴

n i = \sqrt{1E+181/m³ \cdot 5E+171/m³} \cdot e^{\frac{- 1.8E-19J}{2 \cdot 1.4E-23J/K \cdot 290K}}

Next Step Prepare to Evaluate

∴

n i = \sqrt{1E+18 \cdot 5E+17} \cdot e^{\frac{- 1.8E-19}{2 \cdot 1.4E-23 \cdot 290}}

Next Step Evaluate

∴

n i = 132370745.7517481/m³

LAST Step Rounding Answer

∴

n i = 1.3E+81/m³

Intrinsic Concentration Formula Elements

Variables

Constants

Functions

Intrinsic Carrier Concentration

Intrinsic Carrier Concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.

Symbol: n_i

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Intrinsic Carrier Concentration

Effective Density in Valence Band

Effective density in valence band is defined as the density of electron concentration in the valance band of an element.

Symbol: N_c

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Effective Density in Valence Band

Effective Density in Conduction Band

Effective density in conduction band is defined as the density of electron concentration in the conduction band of an element.

Symbol: N_v

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Effective Density in Conduction Band

Temperature Dependence of Energy Band Gap

Temperature Dependence of Energy Band Gap describes the influence of photons on band-gap energy.

Symbol: E_g

Measurement: EnergyUnit: eV

Note: Value should be greater than 0.

Formulas to find Temperature Dependence of Energy Band Gap

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

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.

Syntax: sqrt(Number)

Other Formulas to find Intrinsic Carrier Concentration

Go Intrinsic Carrier Concentration under Non-Equilibrium Conditions

n i = \sqrt{n 0 \cdot p 0}

Other formulas in Charge Carrier Characteristics category

Go Electrons Diffusion Constant

D n = μ n \cdot (\frac{[BoltZ] \cdot T}{[Charge-e]})

Go Hole Diffusion Length

L p = \sqrt{D p \cdot τ p}

Go Current Density due to Electrons

J n = [Charge-e] \cdot N e \cdot μ n \cdot E I

Go Current Density due to Holes

J p = [Charge-e] \cdot N p \cdot μ p \cdot E I

How to Evaluate Intrinsic Concentration?

Intrinsic Concentration evaluator uses Intrinsic Carrier Concentration = sqrt(Effective Density in Valence Band*Effective Density in Conduction Band)*e^((-Temperature Dependence of Energy Band Gap)/(2*[BoltZ]*Temperature)) to evaluate the Intrinsic Carrier Concentration, The intrinsic concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material. Intrinsic Carrier Concentration is denoted by n_i symbol.

How to evaluate Intrinsic Concentration using this online evaluator? To use this online evaluator for Intrinsic Concentration, enter Effective Density in Valence Band (N_c), Effective Density in Conduction Band (N_v), Temperature Dependence of Energy Band Gap (E_g) & Temperature (T) and hit the calculate button.

FAQs on Intrinsic Concentration

What is the formula to find Intrinsic Concentration?

The formula of Intrinsic Concentration is expressed as Intrinsic Carrier Concentration = sqrt(Effective Density in Valence Band*Effective Density in Conduction Band)*e^((-Temperature Dependence of Energy Band Gap)/(2*[BoltZ]*Temperature)). Here is an example- 1.3E+8 = sqrt(1.02E+18*5E+17)*e^((-1.79443860960001E-19)/(2*[BoltZ]*290)).

How to calculate Intrinsic Concentration?

With Effective Density in Valence Band (N_c), Effective Density in Conduction Band (N_v), Temperature Dependence of Energy Band Gap (E_g) & Temperature (T) we can find Intrinsic Concentration using the formula - Intrinsic Carrier Concentration = sqrt(Effective Density in Valence Band*Effective Density in Conduction Band)*e^((-Temperature Dependence of Energy Band Gap)/(2*[BoltZ]*Temperature)). This formula also uses Boltzmann constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Intrinsic Carrier Concentration?

Here are the different ways to Calculate Intrinsic Carrier Concentration-

Intrinsic Carrier Concentration=sqrt(Majority Carrier Concentration*Minority Carrier Concentration)

Can the Intrinsic Concentration be negative?

No, the Intrinsic Concentration, measured in Carrier Concentration cannot be negative.

Which unit is used to measure Intrinsic Concentration?

Intrinsic Concentration is usually measured using the 1 per Cubic Meter[1/m³] for Carrier Concentration. 1 per Cubic Centimeter[1/m³], per Liter[1/m³] are the few other units in which Intrinsic Concentration can be measured.

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Intrinsic Concentration Formula

​GoIntrinsic Carrier Concentration under Non-Equilibrium Conditions Formula

Intrinsic Concentration Example

Intrinsic Concentration Solution

Intrinsic Concentration Formula Elements

Other Formulas to find Intrinsic Carrier Concentration

Other formulas in Charge Carrier Characteristics category

How to Evaluate Intrinsic Concentration?

FAQs on Intrinsic Concentration

Variable Name

GoIntrinsic Carrier Concentration under Non-Equilibrium Conditions Formula