Abstract
A review of the ground state confinement energy term in the Brus equation for the bandgap energy of a spherically shaped semiconductor quantum dot was made within the framework of effective mass approximation. The Schrodinger wave equation for a spherical nanoparticle in an infinite spherical potential well was solved in spherical polar coordinate system. Physical reasons in contrast to mathematical expediency were considered and solution obtained. The result reveals that the shift in the confinement energy is less than that predicted by the Brus equation as was adopted in most literatures.
Highlights
Solid state materials, in general are classified either as metals, semiconductors or insulators
The confinement energy is inversely proportional to the square of the diameter of the quantum dot, in contrast to the Brus equation which predicts an inverse square relationship in the radius
The confinement energy based on the brus equation is not entirely new
Summary
In general are classified either as metals, semiconductors or insulators. Carrier confinement increases the band gap energy of a semiconductor and alters the density of state of the bulk semiconductor material (Pohl, 2013). It extends the frontiers of application of the semiconductor. The second additive term in the right hand side of equation (1) represents the additional energy due to quantum confinement It can be thought of as the infinite square-well contribution to the band gap energy. The effect of quantum confinement on the band gap energy of a semiconductor is determined by this term. The confinement energy is important because it determines the emission energy as well as the wavelength of the quantum dot
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