E3 Quantum Confinement

Topic

When the size of this semiconductor nanoparticle approaches the exciton Bohr radius of the same material—the characteristic separation between the electron and hole forming the exciton in the bulk material—the nanoparticle enters the strong confinement regime. In bulk material, the exciton has ample space to maintain this characteristic separation without restriction; however, within a nanoparticle whose size approaches that exciton Bohr radius, the physical boundaries of the nanoparticle itself begin to restrict the space available to the exciton. Further reduction in the nanoparticle's size—bringing it closer to or even below the exciton Bohr radius—consequently intensifies this strong confinement regime.

Entering this strong confinement regime means that, according to the Brus equation, the nanoparticle's band gap ceases to be the fixed constant found in bulk material and instead becomes directly dependent on the nanoparticle's size; the Brus equation describes how the nanoparticle's band gap widens beyond that of the equivalent bulk material as its size decreases within this strong confinement regime. Thus, within this regime, a smaller nanoparticle size results in a larger band gap, as dictated by the Brus equation. Thus, this model—characterized by the strong confinement regime and the size-dependent bandgap—establishes that this very size dependence is the physical signature defining a quantum dot, distinguishing it from any other semiconductor nanoparticle of the same material that has not yet reached this strong confinement regime: whereas the bandgap remains constant for any particle size outside this regime, within it, two particles of the same material but different sizes each possess their own characteristic bandgap. The fact that this size-dependent bandgap can be experimentally verified—via the energy of the light emitted by the nanoparticle through photoluminescence, as described by another model in this set—allows that model to confirm whether the strong confinement regime is indeed present; conversely, the loss of this size-dependent bandgap—occurring when thermal coalescence (described by a different model in the set) causes the nanoparticle to grow beyond the exciton Bohr radius—results in the destruction of both the quantum confinement and the physical quantum-dot signature it defined.

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