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Certain quantum dot structures can also be modeled by a 2D particle in a box. Quantum dots may be manufactured by creating small circular or square semiconductor deposits on a substrate that is an electric insulator. The electrons of the semiconductor spots are free to move over the entire size of the dot, and the energy levels of the free electrons follow a 2D PiB model [3]. Consequently, the color of electronic transitions can be tuned by varying the size of the quantum dot.

Closely related to these 2‐dimensional quantum dots are 3‐dimensional nanoparticles, such as spheres of metallic or semiconductor materials. The free electrons on the surface of such spheres can assume wave patterns known as “spherical harmonic functions” that are the solutions for particle on a sphere. Similar functions will be discussed in Chapter 7 during the treatment of the hydrogen atom wavefunctions. Again, the optical properties of such nanoparticles can be tuned by adjusting the size of the nanoparticle. This is shown in Figure 2.7.