Quantum Capacitance of Quantum Dot Calculator

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✖Ionization Potential of N Particle is defined as the total amount of energy required to free an electron, which is revolving in the outermost shell of any atom.ⓘ Ionization Potential of N Particle [IP_N]			+10% -10%
✖Electron Affinity of N Particle System is the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion.ⓘ Electron Affinity of N Particle System [EA_N]			+10% -10%

✖Quantum capacitance of Quantum Dot is a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics.ⓘ Quantum Capacitance of Quantum Dot [C_N]

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Formula

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Quantum Capacitance of Quantum Dot

Formula

`"C"_{"N"} = ("[Charge-e]"^2)/("IP"_{"N"}-"EA"_{"N"})`

Example

`"3E^-20F"=("[Charge-e]"^2)/("6.11eV"-"0.75eV")`

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Quantum Capacitance of Quantum Dot Solution

STEP 0: Pre-Calculation Summary

Formula Used

Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System)
C_N = ([Charge-e]^2)/(IP_N-EA_N)
This formula uses 1 Constants, 3 Variables

Constants Used

[Charge-e] - Charge of electron Value Taken As 1.60217662E-19

Variables Used

Quantum Capacitance of Quantum Dot - (Measured in Farad) - Quantum capacitance of Quantum Dot is a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics.
Ionization Potential of N Particle - (Measured in Joule) - Ionization Potential of N Particle is defined as the total amount of energy required to free an electron, which is revolving in the outermost shell of any atom.
Electron Affinity of N Particle System - (Measured in Joule) - Electron Affinity of N Particle System is the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion.

STEP 1: Convert Input(s) to Base Unit

Ionization Potential of N Particle: 6.11 Electron-Volt --> 9.78930348630005E-19 Joule (Check conversion here)
Electron Affinity of N Particle System: 0.75 Electron-Volt --> 1.20163299750001E-19 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_N = ([Charge-e]^2)/(IP_N-EA_N) --> ([Charge-e]^2)/(9.78930348630005E-19-1.20163299750001E-19)

Evaluating ... ...

C_N = 2.98913416044833E-20

STEP 3: Convert Result to Output's Unit

2.98913416044833E-20 Farad --> No Conversion Required

FINAL ANSWER

2.98913416044833E-20 ≈ 3E-20 Farad <-- Quantum Capacitance of Quantum Dot

(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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Verified by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

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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)

Quantum Capacitance of Quantum Dot Formula

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

What are Quantum Dots?

Quantum dots (QDs), also called semiconductor nanocrystals, are semiconductor particles a few nanometres in size, having optical and electronic properties that differ from those of larger particles as a result of quantum mechanical effects.

How to Calculate Quantum Capacitance of Quantum Dot?

Quantum Capacitance of Quantum Dot calculator uses Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System) to calculate the Quantum Capacitance of Quantum Dot, The Quantum Capacitance of Quantum Dot formula is defined as a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics. Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density. Quantum Capacitance of Quantum Dot is denoted by C_N symbol.

How to calculate Quantum Capacitance of Quantum Dot using this online calculator? To use this online calculator for Quantum Capacitance of Quantum Dot, enter Ionization Potential of N Particle (IP_N) & Electron Affinity of N Particle System (EA_N) and hit the calculate button. Here is how the Quantum Capacitance of Quantum Dot calculation can be explained with given input values -> 3E-20 = ([Charge-e]^2)/(9.78930348630005E-19-1.20163299750001E-19).

FAQ

What is Quantum Capacitance of Quantum Dot?

The Quantum Capacitance of Quantum Dot formula is defined as a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics. Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density and is represented as C_N = ([Charge-e]^2)/(IP_N-EA_N) or Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System). Ionization Potential of N Particle is defined as the total amount of energy required to free an electron, which is revolving in the outermost shell of any atom & Electron Affinity of N Particle System is the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion.

How to calculate Quantum Capacitance of Quantum Dot?

The Quantum Capacitance of Quantum Dot formula is defined as a fundamental quantity that can directly reveal many-body interactions among electrons and is expected to play a critical role in nanoelectronics. Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density is calculated using Quantum Capacitance of Quantum Dot = ([Charge-e]^2)/(Ionization Potential of N Particle-Electron Affinity of N Particle System). To calculate Quantum Capacitance of Quantum Dot, you need Ionization Potential of N Particle (IP_N) & Electron Affinity of N Particle System (EA_N). With our tool, you need to enter the respective value for Ionization Potential of N Particle & Electron Affinity of N Particle System 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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