Colloidal quantum dots exhibit size-dependent optical properties due to quantum and dielectric confinements at the semiconductor/solvent boundary. To consider both confinement effects, we take a natural potential well approach that assumes separate potential wells for electron and hole which are surrounded by dielectric media. The potential well depths for electron and hole are set by the band offsets at the semiconductor/solvent heterojunction. The kinetic energy is calculated using an effective mass approximation and the electron-hole interaction energy is obtained by taking image charges into account. For cadmium chalcogenides, resulting transition energies agree well with size-dependent optical bandgaps from experiments.

胶体量子点由于在半导体/溶剂边界处的量子和介电限制而表现出与尺寸有关的光学特性。为了同时考虑这两种约束效应，我们采用自然势阱方法，该方法假定电子和空穴的势阱分别被电介质包围。电子和空穴的势阱深度由半导体/溶剂异质结处的带隙设置。使用有效的质量近似值来计算动能，并通过考虑图像电荷来获得电子-空穴相互作用能。对于硫属镉化物，所得的跃迁能量与实验中与尺寸有关的光学带隙非常吻合。