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Intrinsic Carrier Concentration Formula

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Intrinsic Carrier Concentration is used to describe the concentration of charge carriers (electrons and holes) in an intrinsic or undoped semiconductor material at thermal equilibrium. Check FAQs

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

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

Intrinsic Carrier Concentration Example

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

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

Here is how the Intrinsic Carrier Concentration equation looks like.

2.7E+8 = \sqrt{2.4E+11 \cdot 6.4E+8} \cdot \exp (- \frac{0.198}{2 \cdot 1.4E-23 \cdot 300})

2.7E+81/m³ = \sqrt{2.4E+111/m³ \cdot 6.4E+81/m³} \cdot \exp (- \frac{0.198eV}{2 \cdot 1.4E-23J/K \cdot 300K})

2.7E+8 = \sqrt{2.4E+11 \cdot 6.4E+8} \cdot \exp (- \frac{0.198}{2 \cdot 1.4E-23 \cdot 300})

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Intrinsic Carrier Concentration Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

n i = \sqrt{2.4E+111/m³ \cdot 6.4E+81/m³} \cdot \exp (- \frac{0.198eV}{2 \cdot [BoltZ] \cdot 300K})

Next Step Substitute values of Constants

∴

n i = \sqrt{2.4E+111/m³ \cdot 6.4E+81/m³} \cdot \exp (- \frac{0.198eV}{2 \cdot 1.4E-23J/K \cdot 300K})

Next Step Convert Units

∴

n i = \sqrt{2.4E+111/m³ \cdot 6.4E+81/m³} \cdot \exp (- \frac{3.2E-20J}{2 \cdot 1.4E-23J/K \cdot 300K})

Next Step Prepare to Evaluate

∴

n i = \sqrt{2.4E+11 \cdot 6.4E+8} \cdot \exp (- \frac{3.2E-20}{2 \cdot 1.4E-23 \cdot 300})

Next Step Evaluate

∴

n i = 269195320.4077421/m³

LAST Step Rounding Answer

∴

n i = 2.7E+81/m³

Intrinsic Carrier Concentration Formula Elements

Variables

Constants

Functions

Intrinsic Carrier Concentration

Intrinsic Carrier Concentration is used to describe the concentration of charge carriers (electrons and holes) in an intrinsic or undoped semiconductor material at thermal equilibrium.

Symbol: n_i

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Intrinsic Carrier Concentration

Effective Density of State in Valence Band

Effective Density of State in Valence Band is defined as the band of electron orbitals that electrons can jump out of, moving into the conduction band when excited.

Symbol: N_v

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Effective Density of State in Valence Band

Effective Density of State in Conduction Band

Effective Density of State in Conduction Band is defined as the number of equivalent energy minima in the conduction band.

Symbol: N_c

Measurement: Carrier ConcentrationUnit: 1/m³

Note: Value should be greater than 0.

Formulas to find Effective Density of State in Conduction Band

Energy Gap

Energy gap in solid-state physics, an energy gap is an energy range in a solid where no electron states exist.

Symbol: E_g

Measurement: EnergyUnit: eV

Note: Value should be greater than 0.

Formulas to find Energy 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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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 in Energy Band and Charge Carrier category

Go Distribution Coefficient

k d = \frac{C solid}{C L}

Go Photoelectron Energy

E photo = [hP] \cdot f

Go Fermi Function

f E = \frac{n 0}{N c}

Go Conduction Band Energy

E c = E g + E v

How to Evaluate Intrinsic Carrier Concentration?

Intrinsic Carrier Concentration evaluator uses Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band)*exp(-Energy Gap/(2*[BoltZ]*Temperature)) to evaluate the Intrinsic Carrier Concentration, Intrinsic Carrier Concentration formula is defined as number of electrons in conduction band or number of holes in valence band in intrinsic material. This number of carriers depends on band gap of material and on temperature of material. Intrinsic Carrier Concentration is denoted by n_i symbol.

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

FAQs on Intrinsic Carrier Concentration

What is the formula to find Intrinsic Carrier Concentration?

The formula of Intrinsic Carrier Concentration is expressed as Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band)*exp(-Energy Gap/(2*[BoltZ]*Temperature)). Here is an example- 2.7E+8 = sqrt(240000000000*640000000)*exp(-3.17231111340001E-20/(2*[BoltZ]*300)).

How to calculate Intrinsic Carrier Concentration?

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

Can the Intrinsic Carrier Concentration be negative?

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

Which unit is used to measure Intrinsic Carrier Concentration?

Intrinsic Carrier 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 Carrier Concentration can be measured.

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Intrinsic Carrier Concentration Formula

Intrinsic Carrier Concentration Example

Intrinsic Carrier Concentration Solution

Intrinsic Carrier Concentration Formula Elements

Other formulas in Energy Band and Charge Carrier category

How to Evaluate Intrinsic Carrier Concentration?

FAQs on Intrinsic Carrier Concentration

Variable Name