Which phenomenon produces discrete energy levels for an electron confined to a small region?

Quantum confinement produces discrete energy levels for an electron confined to a small region.

When a particle is restricted to a dimension comparable with its de Broglie wavelength, its allowed wave patterns become limited. Only certain standing-wave solutions fit inside the region, so the particle’s energy takes separated values instead of a continuous range.

This effect is especially important in semiconductor nanostructures such as quantum wells, quantum wires, and quantum dots. A quantum dot confines carriers in all three spatial dimensions and can behave like an artificial atom. Changing a dot’s size changes its energy spacing and therefore the color of light it absorbs or emits.

Quantum confinement is not the same as quantum tunnelling. Confinement limits the allowed states inside a structure, whereas tunnelling describes a particle’s probability of crossing a classically forbidden barrier. Both effects become prominent at nanoscale dimensions.