Why does a quantum dot's band gap increase as it shrinks?

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Why does the quantum dot's band gap increase as in shrinks in size? What is the principle behind this? Is the Heisenberg's uncertainty principle?
 

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The short answer is that the bandgap increases for the same reason that the energy spacing for the particle-in-a-box increases as the box size gets smaller.

This quantum confinement effect becomes resolvable when when the size of the dot approaches the thermal deBroglie wavelength of an electron in the dot. So, at low temperatures, the effect of quantum confinement can be seen in slightly larger dots, but the phenomenon is perfectly visible at room temperature. As an undergrad, I looked at the absorption and emission spectra of Cadmium Sulfide quantum dots as a function of size, and we could clearly see the effect at room temperature.