# What is quantum dot light?

Jul 8, 2018

Quantum dots (QDs) are semiconductor particles, typically on the order of a few $\text{nm}$ in diameter, capable of emitting pure colors.

The following is a simplified energy diagram for a quantum dot, showing its band gap, or HOMO-LUMO gap (more on the HOMO-LUMO gap is described here):

The idea is that applied electric fields will draw electrons (solid circles, ""_(-1)^(0) e) and positrons (dashed circles, ""_(+1)^(0) e) into the QD, where they recombine and annihilate each other, emitting photons (packets of light) as seen in the following nuclear equation:

${\text{_(-1)^(0) e + ""_(+1)^(0) e -> 2 }}_{0}^{0} \gamma$

Or if you prefer, a diagram:

Depending on the dot size, they can be made to emit different colors of light; the wavelength emitted is directly proportional to the QD size.

This relationship can be seen by modeling semiconductors using the one-dimensional Particle in a Box energy levels:

${E}_{n} = \frac{{n}^{2} {h}^{2}}{8 {m}_{e} {L}^{2}}$

where:

• $h = 6.626 \times {10}^{- 34} \text{J"cdot"s}$
• ${m}_{e} = 9.109 \times {10}^{- 31} \text{kg}$

• $L$ is the length of the "box".

• $n = 1 , 2 , 3 , . . .$ is the principal quantum number.

So, since $L \propto \frac{1}{\sqrt{E}}$ and $E \propto \frac{1}{\lambda}$, adjusting their size allows one to tune to the right wavelength, and hence color, of light emitted.

Common applications for them are in transistors, solar cells, and quantum computing. You can find out how they are made by looking here.