ABSTRACT
A quantum dot (QD) is a semiconductor crystal with a size on the nanometer length scale. –e nanometer length scale is key as this is the regime in which quantum con£nement e¢ects arise (the topic of this chapter). –e simplest picture is that the radius of the crystallite should be approximately that of the Bohr radius of the electron (more precisely the exciton). –e Bohr radius of an exciton (a0) in a semiconductor will depend on material parameters which distinguish it from the Bohr radius of an electron in a hydrogen atom (Alivisatos, 1996a). –ese parameters (e¢ective mass and dielectric constant) yield Bohr radii that range from ∼1-20 nm, with a0 = 4πε0εħ2m−1q−2, with the permittivity of vacuum being ε0, dielectric constant ε, reduced Planck constant ħ, mass m, and charge q. When the crystallite is on the order of the excitonic Bohr radius, quantum con£nement e¢ects will arise (Efros and Rosen, 2000) (Figure 10.1).
