Intrinsic Concentration Calculator

✖Effective density in valence band is defined as the density of electron concentration in the valance band of an element.ⓘ Effective Density in Valence Band [N_c]			+10% -10%
✖Effective density in conduction band is defined as the density of electron concentration in the conduction band of an element.ⓘ Effective Density in Conduction Band [N_v]			+10% -10%
✖Temperature Dependence of Energy Band Gap describes the influence of photons on band-gap energy.ⓘ Temperature Dependence of Energy Band Gap [E_g]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Intrinsic Carrier Concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.ⓘ Intrinsic Concentration [n_i]

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Intrinsic Concentration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Intrinsic Carrier Concentration = sqrt(Effective Density in Valence Band*Effective Density in Conduction Band)*e^((-Temperature Dependence of Energy Band Gap)/(2*[BoltZ]*Temperature))
n_i = sqrt(N_c*N_v)*e^((-E_g)/(2*[BoltZ]*T))
This formula uses 2 Constants, 1 Functions, 5 Variables

Constants Used

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

Functions Used

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., sqrt(Number)

Variables Used

Intrinsic Carrier Concentration - (Measured in 1 per Cubic Meter) - Intrinsic Carrier Concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material.
Effective Density in Valence Band - (Measured in 1 per Cubic Meter) - Effective density in valence band is defined as the density of electron concentration in the valance band of an element.
Effective Density in Conduction Band - (Measured in 1 per Cubic Meter) - Effective density in conduction band is defined as the density of electron concentration in the conduction band of an element.
Temperature Dependence of Energy Band Gap - (Measured in Joule) - Temperature Dependence of Energy Band Gap describes the influence of photons on band-gap energy.
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

Effective Density in Valence Band: 1.02E+18 1 per Cubic Meter --> 1.02E+18 1 per Cubic Meter No Conversion Required
Effective Density in Conduction Band: 5E+17 1 per Cubic Meter --> 5E+17 1 per Cubic Meter No Conversion Required
Temperature Dependence of Energy Band Gap: 1.12 Electron-Volt --> 1.79443860960001E-19 Joule (Check conversion here)
Temperature: 290 Kelvin --> 290 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_i = sqrt(N_c*N_v)*e^((-E_g)/(2*[BoltZ]*T)) --> sqrt(1.02E+18*5E+17)*e^((-1.79443860960001E-19)/(2*[BoltZ]*290))

Evaluating ... ...

n_i = 132370745.751748

STEP 3: Convert Result to Output's Unit

132370745.751748 1 per Cubic Meter --> No Conversion Required

FINAL ANSWER

132370745.751748 ≈ 1.3E+8 1 per Cubic Meter <-- Intrinsic Carrier Concentration

(Calculation completed in 00.004 seconds)

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Created by Rachita C

BMS College Of Engineering (BMSCE), Banglore

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< Charge Carrier Characteristics Calculators

Current Density due to Electrons

LaTeX Go Electron Current Density = [Charge-e]*Electron Concentration*Mobility of Electron*Electric Field Intensity

Current Density due to Holes

LaTeX Go Holes Current Density = [Charge-e]*Holes Concentration*Mobility of Holes*Electric Field Intensity

Electrons Diffusion Constant

LaTeX Go Electron Diffusion Constant = Mobility of Electron*(([BoltZ]*Temperature)/[Charge-e])

Hole Diffusion Length

LaTeX Go Holes Diffusion Length = sqrt(Holes Diffusion Constant*Hole Carrier Lifetime)

Intrinsic Concentration Formula

LaTeX Go

What are the factors intrinsic concentration depends on?

This number of carriers depends on the bandgap of the material and on the temperature of the material. A large band gap will make it more difficult for a carrier to be thermally excited across the bandgap, and therefore the intrinsic carrier concentration is lower in higher bandgap materials.

How to Calculate Intrinsic Concentration?

Intrinsic Concentration calculator 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 calculate 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 calculate Intrinsic Concentration using this online calculator? To use this online calculator 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. Here is how the Intrinsic Concentration calculation can be explained with given input values -> 1.3E+8 = sqrt(1.02E+18*5E+17)*e^((-1.79443860960001E-19)/(2*[BoltZ]*290)).

FAQ

What is Intrinsic 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 and is represented as n_i = sqrt(N_c*N_v)*e^((-E_g)/(2*[BoltZ]*T)) or Intrinsic Carrier Concentration = sqrt(Effective Density in Valence Band*Effective Density in Conduction Band)*e^((-Temperature Dependence of Energy Band Gap)/(2*[BoltZ]*Temperature)). Effective density in valence band is defined as the density of electron concentration in the valance band of an element, Effective density in conduction band is defined as the density of electron concentration in the conduction band of an element, Temperature Dependence of Energy Band Gap describes the influence of photons on band-gap energy & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Intrinsic 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 is calculated using 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 calculate Intrinsic Concentration, you need Effective Density in Valence Band (N_c), Effective Density in Conduction Band (N_v), Temperature Dependence of Energy Band Gap (E_g) & Temperature (T). With our tool, you need to enter the respective value for Effective Density in Valence Band, Effective Density in Conduction Band, Temperature Dependence of Energy Band Gap & Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Intrinsic Carrier Concentration?

In this formula, Intrinsic Carrier Concentration uses Effective Density in Valence Band, Effective Density in Conduction Band, Temperature Dependence of Energy Band Gap & Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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