513.001 Molecular and Solid State Physics

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Quantum Dot

A quantum dot is a small semiconducting crystal. Suppose the crystal is cubic L×L×L so the 3-D potential square well model can be used. The quantum dot contains one electron. A frequently used wavelength in telecommunications is 1.5 μm. How long would the side of the quantum dot have to be to absorb radiation of this wavelength? Assume that the electron makes a transition from the lowest energy level (ground state) to the first excited level when the photon is absorbed.

L = m

Quantum dots are nanometre-scale semiconductor crystals. When semiconductors are hit by a beam of light, some of their electrons are excited into higher energy states. As the electrons fall back to the ground state, they emit photons of light in a colour that is characteristic of the material.

When the electrons in a semiconductor are excited, they prefer to dwell at a certain fixed distance from the positive charges they leave behind, called the exciton radius. For the semiconductors used to make fluorescent quantum dots, this radius is around 5–10 nanometres.

If the entire crystal's size is less than the exciton radius, however, an effect called quantum confinement comes into play, and shifts the colour of the emitted light towards shorter wavelengths. For crystals of this size, more energy than normal is required to force electrons out of the ground state. So when the electrons return to the ground state, the photons they release have more energy — and therefore a shorter wavelength — than normal.

There is a simple linear relationship between crystal size and colour: the smaller the size, the shorter the wavelength. For cadmium selenide — one of the most popular materials for making fluorescent quantum dots — varying the size of the crystals over a range of 2–6 nanometres covers the entire visible spectrum.

Erica Klarreich, Nature 413, 450-452(4 October 2001)