HCF calculator

Intrinsic Carrier Concentration Calculator

Engineering Chemistry Financial Health More >>

↳

Electronics Chemical Engineering Civil Electrical More >>

⤿

Solid State Devices Amplifiers Analog Communications Analog Electronics More >>

⤿

Energy Band and Charge Carrier Electrons and Holes Semiconductor Carriers SSD Junction

✖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.ⓘ Effective Density of State in Valence Band [N_v]			+10% -10%
✖Effective Density of State in Conduction Band is defined as the number of equivalent energy minima in the conduction band.ⓘ Effective Density of State in Conduction Band [N_c]			+10% -10%
✖Energy gap in solid-state physics, an energy gap is an energy range in a solid where no electron states exist.ⓘ Energy 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 used to describe the concentration of charge carriers (electrons and holes) in an intrinsic or undoped semiconductor material at thermal equilibrium.ⓘ Intrinsic Carrier Concentration [n_i]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Energy Band and Charge Carrier Formulas PDF PDF Image

Intrinsic Carrier Concentration Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., 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., sqrt(Number)

Variables Used

Intrinsic Carrier Concentration - (Measured in 1 per Cubic Meter) - 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.
Effective Density of State in Valence Band - (Measured in 1 per Cubic Meter) - 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.
Effective Density of State in Conduction Band - (Measured in 1 per Cubic Meter) - Effective Density of State in Conduction Band is defined as the number of equivalent energy minima in the conduction band.
Energy Gap - (Measured in Joule) - Energy gap in solid-state physics, an energy gap is an energy range in a solid where no electron states exist.
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 of State in Valence Band: 240000000000 1 per Cubic Meter --> 240000000000 1 per Cubic Meter No Conversion Required
Effective Density of State in Conduction Band: 640000000 1 per Cubic Meter --> 640000000 1 per Cubic Meter No Conversion Required
Energy Gap: 0.198 Electron-Volt --> 3.17231111340001E-20 Joule (Check conversion here)
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_i = sqrt(N_v*N_c)*exp(-E_g/(2*[BoltZ]*T)) --> sqrt(240000000000*640000000)*exp(-3.17231111340001E-20/(2*[BoltZ]*300))

Evaluating ... ...

n_i = 269195320.407742

STEP 3: Convert Result to Output's Unit

269195320.407742 1 per Cubic Meter --> No Conversion Required

FINAL ANSWER

269195320.407742 ≈ 2.7E+8 1 per Cubic Meter <-- Intrinsic Carrier Concentration

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Electronics » Solid State Devices » Energy Band and Charge Carrier » Intrinsic Carrier Concentration

Credits

Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

Shobhit Dimri has created this Calculator and 900+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< Energy Band and Charge Carrier Calculators

Energy of Electron given Coulomb's Constant

LaTeX Go Energy of Electron = (Quantum Number^2*pi^2*[hP]^2)/(2*[Mass-e]*Potential Well Length^2)

Steady State Electron Concentration

LaTeX Go Steady State Carrier Concentration = Electron Concentration in Conduction Band+Excess Carrier Concentration

Valence Band Energy

LaTeX Go Valence Band Energy = Conduction Band Energy-Energy Gap

Energy Gap

LaTeX Go Energy Gap = Conduction Band Energy-Valence Band Energy

< Semiconductor Carriers Calculators

Fermi Function

LaTeX Go Fermi Function = Electron Concentration in Conduction Band/Effective Density of State in Conduction Band

Distribution Coefficient

LaTeX Go Distribution Coefficient = Impurity Concentration in Solid/Impurity Concentration in Liquid

Photoelectron Energy

LaTeX Go Photoelectron Energy = [hP]*Frequency of Incident Light

Conduction Band Energy

LaTeX Go Conduction Band Energy = Energy Gap+Valence Band Energy

Intrinsic Carrier Concentration Formula

LaTeX Go

How intrinsic concentration is the function of temperature?

If electrons are in the conduction band they will quickly lose energy and fall back to the valence band, annihilating a hole. Therefore, lowering the temperature causes a decrease in the intrinsic carrier concentration, while raising the temperature causes an increase in intrinsic carrier concentration.

How to Calculate Intrinsic Carrier Concentration?

Intrinsic Carrier Concentration calculator 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 calculate 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 calculate Intrinsic Carrier Concentration using this online calculator? To use this online calculator 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. Here is how the Intrinsic Carrier Concentration calculation can be explained with given input values -> 2.7E+8 = sqrt(240000000000*640000000)*exp(-3.17231111340001E-20/(2*[BoltZ]*300)).

FAQ

What is 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 and is represented as n_i = sqrt(N_v*N_c)*exp(-E_g/(2*[BoltZ]*T)) or Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band)*exp(-Energy Gap/(2*[BoltZ]*Temperature)). 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, Effective Density of State in Conduction Band is defined as the number of equivalent energy minima in the conduction band, Energy gap in solid-state physics, an energy gap is an energy range in a solid where no electron states exist & Temperature is the degree or intensity of heat present in a substance or object.

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

Home

FREE PDFs

🔍 Search