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))
ni = sqrt(Nv*Nc) *exp(-Eg/(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
ni = sqrt(Nv*Nc) *exp(-Eg/(2*[BoltZ]*T)) --> sqrt(240000000000*640000000) *exp(-3.17231111340001E-20/(2*[BoltZ]*300))
Evaluating ... ...
ni = 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 00.019 seconds)

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!

20 Energy Band & Charge Carrier Calculators

Intrinsic Carrier Concentration
Go Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band) *exp(-Energy Gap/(2*[BoltZ]*Temperature))
Carrier Lifetime
Go Carrier Lifetime = 1/(Proportionality for Recombination*(Holes Concentration in Valance Band+Electron Concentration in Conduction Band))
Energy of Electron given Coulomb's Constant
Go Energy of Electron = (Quantum Number^2*pi^2*[hP]^2)/(2*[Mass-e]*Potential Well Length^2)
Steady State Electron Concentration
Go Steady State Carrier Concentration = Electron Concentration in Conduction Band+Excess Carrier Concentration
Effective Density of State
Go Effective Density of State in Conduction Band = Electron Concentration in Conduction Band/Fermi Function
Fermi Function
Go Fermi Function = Electron Concentration in Conduction Band/Effective Density of State in Conduction Band
Concentration in Conduction Band
Go Electron Concentration in Conduction Band = Effective Density of State in Conduction Band*Fermi Function
Effective Density State in Valence Band
Go Effective Density of State in Valence Band = Holes Concentration in Valance Band/(1-Fermi Function)
Recombination Lifetime
Go Recombination Lifetime = (Proportionality for Recombination*Holes Concentration in Valance Band)^-1
Concentration of Holes in Valence Band
Go Holes Concentration in Valance Band = Effective Density of State in Valence Band*(1-Fermi Function)
Thermal Generation Rate
Go Thermal Generation = Proportionality for Recombination*(Intrinsic Carrier Concentration ^2)
Distribution Coefficient
Go Distribution Coefficient = Impurity Concentration in Solid/Impurity Concentration in Liquid
Liquid Concentration
Go Impurity Concentration in Liquid = Impurity Concentration in Solid/Distribution Coefficient
Net Rate of Change in Conduction Band
Go Proportionality for Recombination = Thermal Generation/(Intrinsic Carrier Concentration^2)
Excess Carrier Concentration
Go Excess Carrier Concentration = Optical Generation Rate*Recombination Lifetime
Optical Generation Rate
Go Optical Generation Rate = Excess Carrier Concentration/Recombination Lifetime
Photoelectron Energy
Go Photoelectron Energy = [hP]*Frequency of Incident Light
Conduction Band Energy
Go Conduction Band Energy = Energy Gap+Valence Band Energy
Valence Band Energy
Go Valence Band Energy = Conduction Band Energy-Energy Gap
Energy Gap
Go Energy Gap = Conduction Band Energy-Valence Band Energy

15 Semiconductor Carriers Calculators

Intrinsic Carrier Concentration
Go Intrinsic Carrier Concentration = sqrt(Effective Density of State in Valence Band*Effective Density of State in Conduction Band) *exp(-Energy Gap/(2*[BoltZ]*Temperature))
Carrier Lifetime
Go Carrier Lifetime = 1/(Proportionality for Recombination*(Holes Concentration in Valance Band+Electron Concentration in Conduction Band))
Radius of Nth Orbit of Electron
Go Radius of nth Orbit of Electron = ([Coulomb]*Quantum Number^2*[hP]^2)/(Mass of Particle*[Charge-e]^2)
Quantum State
Go Energy in Quantum State = (Quantum Number^2*pi^2*[hP]^2)/(2*Mass of Particle*Potential Well Length^2)
Electron Flux Density
Go Electron Flux Density = (Mean Free Path Electron/(2*Time))*Difference in Electron Concentration
Fermi Function
Go Fermi Function = Electron Concentration in Conduction Band/Effective Density of State in Conduction Band
Effective Density State in Valence Band
Go Effective Density of State in Valence Band = Holes Concentration in Valance Band/(1-Fermi Function)
Distribution Coefficient
Go Distribution Coefficient = Impurity Concentration in Solid/Impurity Concentration in Liquid
Electron Multiplication
Go Electron Multiplication = Number of Electron Out of Region/Number of Electron in Region
Excess Carrier Concentration
Go Excess Carrier Concentration = Optical Generation Rate*Recombination Lifetime
Electron Current Density
Go Electron Current Density = Total Carrier Current Density-Hole Current Density
Hole Current Density
Go Hole Current Density = Total Carrier Current Density-Electron Current Density
Mean Time Spend by Hole
Go Mean Time Spend by Hole = Optical Generation Rate*Majority Carrier Decay
Photoelectron Energy
Go Photoelectron Energy = [hP]*Frequency of Incident Light
Conduction Band Energy
Go Conduction Band Energy = Energy Gap+Valence Band Energy

Intrinsic Carrier Concentration 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))
ni = sqrt(Nv*Nc) *exp(-Eg/(2*[BoltZ]*T))

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 ni 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 (Nv), Effective Density of State in Conduction Band (Nc), Energy Gap (Eg) & 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 ni = sqrt(Nv*Nc) *exp(-Eg/(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 (Nv), Effective Density of State in Conduction Band (Nc), Energy Gap (Eg) & 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!