Confinement Energy Calculator

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✖Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots.ⓘ Radius of Quantum Dot [a]			+10% -10%
✖Reduced Mass of Exciton is the reduced mass of an electron and a hole that are attracted to each other by the Coulomb force which can form a bound state called exciton.ⓘ Reduced Mass of Exciton [μ_ex]			+10% -10%

✖Confinement Energy in the particle in a box model is also used in modeling the exciton. Variance of particle size allows for control of the confinement energy.ⓘ Confinement Energy [E_confinement]

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Formula

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Confinement Energy

Formula

`"E"_{"confinement"} = (("[hP]"^2)*(pi^2))/(2*("a"^2)*"μ"_{"ex"})`

Example

`"9.702653eV"=(("[hP]"^2)*(pi^2))/(2*(("3nm")^2)*"0.17me")`

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Confinement Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton)
E_confinement = (([hP]^2)*(pi^2))/(2*(a^2)*μ_ex)
This formula uses 2 Constants, 3 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Confinement Energy - (Measured in Joule) - Confinement Energy in the particle in a box model is also used in modeling the exciton. Variance of particle size allows for control of the confinement energy.
Radius of Quantum Dot - (Measured in Meter) - Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots.
Reduced Mass of Exciton - (Measured in Kilogram) - Reduced Mass of Exciton is the reduced mass of an electron and a hole that are attracted to each other by the Coulomb force which can form a bound state called exciton.

STEP 1: Convert Input(s) to Base Unit

Radius of Quantum Dot: 3 Nanometer --> 3E-09 Meter (Check conversion here)
Reduced Mass of Exciton: 0.17 Electron Mass (Rest) --> 1.54859625024252E-31 Kilogram (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_confinement = (([hP]^2)*(pi^2))/(2*(a^2)*μ_ex) --> (([hP]^2)*(pi^2))/(2*(3E-09^2)*1.54859625024252E-31)

Evaluating ... ...

E_confinement = 1.55453706487244E-18

STEP 3: Convert Result to Output's Unit

1.55453706487244E-18 Joule -->9.70265298206678 Electron-Volt (Check conversion here)

FINAL ANSWER

9.70265298206678 ≈ 9.702653 Electron-Volt <-- Confinement Energy

(Calculation completed in 00.004 seconds)

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Created by Sangita Kalita

National Institute of Technology, Manipur (NIT Manipur), Imphal, Manipur

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< 7 Quantum Dots Calculators

Exciton Bohr Radius

Go Exciton Bohr Radius = Dielectric Constant of Bulk Material*(Effective Mass of Electron/((Effective Mass of Electron*Effective Mass of Hole)/(Effective Mass of Electron+Effective Mass of Hole)))*[Bohr-r]

Brus Equation

Go Emission Energy of Quantum Dot = Band Gap Energy+(([hP]^2)/(8*(Radius of Quantum Dot^2)))*((1/([Mass-e]*Effective Mass of Electron))+(1/([Mass-e]*Effective Mass of Hole)))

Reduced Mass of Exciton

Go Reduced Mass of Exciton = ([Mass-e]*(Effective Mass of Electron*Effective Mass of Hole))/(Effective Mass of Electron+Effective Mass of Hole)

Coulombic Attraction Energy

Go Coulombic Attraction Energy = -(1.8*([Charge-e]^2))/(2*pi*[Permeability-vacuum]*Dielectric Constant of Bulk Material*Radius of Quantum Dot)

Total Energy of Particle in Quantum Dot

Go Total Energy of a Particle in Quantum Dot = Band Gap Energy+Confinement Energy+(Coulombic Attraction Energy)

Quantum Capacitance of Quantum Dot

Go Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System)

Confinement Energy

Go Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton)

Confinement Energy Formula

Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton)
E_confinement = (([hP]^2)*(pi^2))/(2*(a^2)*μ_ex)

What is a Quantum Dot?

Quantum dots are theoretically described as a point-like, or zero dimensional (0D) entity. Most of their properties depend on the dimensions, shape, and materials of which QDs are made.

How to Calculate Confinement Energy?

Confinement Energy calculator uses Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton) to calculate the Confinement Energy, The Confinement Energy formula in as particle in a box model is also used in modelling the exciton. Confinement energy is a term used to explain the confinement effect inside the nanospace. Variance of particle size allows for control of the confinement energy. Confinement Energy is denoted by E_confinement symbol.

How to calculate Confinement Energy using this online calculator? To use this online calculator for Confinement Energy, enter Radius of Quantum Dot (a) & Reduced Mass of Exciton (μ_ex) and hit the calculate button. Here is how the Confinement Energy calculation can be explained with given input values -> 6.1E+19 = (([hP]^2)*(pi^2))/(2*(3E-09^2)*1.54859625024252E-31).

FAQ

What is Confinement Energy?

The Confinement Energy formula in as particle in a box model is also used in modelling the exciton. Confinement energy is a term used to explain the confinement effect inside the nanospace. Variance of particle size allows for control of the confinement energy and is represented as E_confinement = (([hP]^2)*(pi^2))/(2*(a^2)*μ_ex) or Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton). Radius of Quantum Dot is the distance from the center to any point on the boundary of Quantum dots & Reduced Mass of Exciton is the reduced mass of an electron and a hole that are attracted to each other by the Coulomb force which can form a bound state called exciton.

How to calculate Confinement Energy?

The Confinement Energy formula in as particle in a box model is also used in modelling the exciton. Confinement energy is a term used to explain the confinement effect inside the nanospace. Variance of particle size allows for control of the confinement energy is calculated using Confinement Energy = (([hP]^2)*(pi^2))/(2*(Radius of Quantum Dot^2)*Reduced Mass of Exciton). To calculate Confinement Energy, you need Radius of Quantum Dot (a) & Reduced Mass of Exciton (μ_ex). With our tool, you need to enter the respective value for Radius of Quantum Dot & Reduced Mass of Exciton and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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