Brus Equation Calculator

Brus Equation Formula:

\[ E_{emission} = E_{gap} + \frac{h^2}{8a^2} \left( \frac{1}{m_e^* m_e} + \frac{1}{m_h^* m_e} \right) \]

Band Gap Energy:

Radius of Quantum Dot:

Effective Mass of Electron:

Effective Mass of Hole:

Emission Energy of Quantum Dot (J):

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1. What is the Brus Equation Calculator?

Definition: This calculator computes the emission energy of quantum dots using the Brus equation, which describes the quantum confinement effect.

Purpose: It helps researchers and engineers in nanotechnology determine the optical properties of quantum dots based on their size and material properties.

2. How Does the Calculator Work?

The calculator uses the Brus equation:

\[ E_{emission} = E_{gap} + \frac{h^2}{8a^2} \left( \frac{1}{m_e^* m_e} + \frac{1}{m_h^* m_e} \right) \]

Where:

\( E_{emission} \) — Emission energy of quantum dot (Joules)
\( E_{gap} \) — Band gap energy (Joules)
\( h \) — Planck constant (6.626070040 × 10⁻³⁴ J·s)
\( a \) — Radius of quantum dot (meters)
\( m_e^* \) — Effective mass of electron
\( m_h^* \) — Effective mass of hole
\( m_e \) — Mass of electron (9.10938356 × 10⁻³¹ kg)

Explanation: The equation accounts for both the bulk band gap energy and the quantum confinement effects that become significant at nanoscale dimensions.

3. Importance of Quantum Dot Emission Energy

Details: Accurate calculation of emission energy is crucial for designing quantum dots with specific optical properties for applications in displays, solar cells, and biomedical imaging.

4. Using the Calculator

Tips: Enter the band gap energy in Joules, quantum dot radius in meters, and effective masses (default values are for CdSe quantum dots). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for effective masses?
A: For CdSe quantum dots: mₑ* ≈ 0.21, mₕ* ≈ 0.81. These vary for different materials.

Q2: How does quantum dot size affect emission energy?
A: Smaller dots have higher emission energies (blue shift) due to stronger quantum confinement.

Q3: Where can I find band gap energy values?
A: Band gap values are material-specific and can be found in semiconductor material databases.

Q4: What units should I use?
A: Use Joules for energy, meters for radius, and dimensionless numbers for effective masses.

Q5: How accurate is this calculation?
A: The Brus equation provides a good first approximation but may need corrections for very small dots or strong confinement.