Charge transfer energy for Y₂O₃:Eu³⁺ nanophosphor

Based on the Kronig–Penney model, the changing tendency of the bandgap or of a particular level with the volume deformation in crystalline materials has been derived. On the basis of this changing tendency, the zero-phonon charge transfer (CT) energy is deduced to be decreased when the size of Y₂O₃:Eu³⁺ phosphor decreases into the nanoscale. In addition, the rigidity decrease of the lattice environment in Y₂O₃:Eu³⁺ nanophosphor leads to the enlargement of the CT state coordinate offset of the optical centers; this means that an optical center would reach a higher vibration level in CT excitation. The increasing magnitude of the vibration energy is smaller than the decreasing magnitude of the zero-phonon CT energy when the size of the Y₂O₃:Eu³⁺ phosphor decreases into the nanoscale. As a result, the CT energy is decreased, and the CT excitation spectrum shifts to a lower energy.