Quantum Dots and Their Emission Properties Cadmium telluride (CdTe) quantum dots are semiconductor nanoparticles known for their unique luminescent properties. When excited with UV light, they exhibit bright emission of different colors. Interestingly, the emission wavelengths depend solely on the size of the nanoparticles. A quantum mechanical effect known as quantum confinement is responsible for this intriguing behavior. Briefly, light directed on a semiconductor at an energy larger than the bandgap will promote an electron from the valence energy band to the conduction band leaving behind a “hole” or vacancy. The electron and the hole form a loosely bound state called an exciton. The radius of the exciton or the Bohr radius is given by ﷯ where ℏ is the reduced Planck constant, e is the electron charge, ε is the dielectric constant, m*e and m*h are the electron and hole effective mass, respectively [1]. The analysis of Eq. 1 shows that the Bohr radius in a semiconductor increases as the dielectric constant of the material increases. Furthermore, it is important to note that the effective masses of the electron and hole are material dependent. In most semiconductors, the exciton is delocalized over a distance that is larger than the crystal lattice constant, and the Bohr radius may reach several Angstroms. This leads to a reasonable assumption that the electron and the hole interact through a shielded Coulomb interaction. In a confined regime, when the semiconductor clusters are smaller than the Bohr radius, the hydrogenic Hamiltonian used to approximately describe shielded Coulomb electron-hole interaction needs to be modified by including terms that take into account potential due to polarization charge at the surface [2]. The solution of the Schrödinger equation yields the following expression for the energy of the first excited state E*: ﷯ where Ebg is the energy of the bandgap of a bulk semiconductor and R is the radius of the cluster. Other parameters in Eq. 2 were defined previously. Eq. 2 needs to be further modified by including a fourth term that describes the spatial correlation effect [3]: ﷯ In Eq. 3, the second term on the right-hand side represents the particle-in-the-box quantum confinement energy. The third term is due to Coulomb interaction. It is inversely proportional to the radius of the cluster and lowers the energy of the first excited state. The fourth term may be neglected in most cases but becomes important in semiconductors with a small dielectric constant. The analysis of Eq. 3 shows that the smaller the quantum dot is, the higher the energy of the photon it will emit. The figure below illustrates this effect. It depicts emission from quantum dots synthesized by the UCalgary BioMod team. Each vial contains particles of the same chemical composition – CdTe core with CdS shell – but the size of the particle increases from the left vial to the rightmost one, due to a thicker CdS shell being grown. As the size of the particle increases, so does the wavelength emitted (inversely related to the energy of the photon). ﷯ Figure 1. Photo of CdTe/CdS core/shell quantum dots under continuous illumination of UV light. The particles, although made of the same material, show dependence of the emission colors on the thickness of CdS shell. [1] Wang, Y. Herron N. Nanometer-Sized Semiconductor Clusters: Materials Synthesis, Quantum Size Effects, and Photophysical Properties. Journal of Physical Chemistry, 95, 1991, 525. [2] L.E. Brus, Electron-Electron and Electron-Hole Interactions in Small Semiconductor Crystallites: the Size Dependence of the Lowest Excited Electronic State. Journal of Chemical Physics, 80, 1984, 4403. [3] Kayanuma, Y. Quantum-Size Effects of Interacting Electrons and Holes in Semiconductor Microcrystals with Spherical Shape. Physical Review B, 38, 1988, 9797.