Determining Locations of Conduction Bands and Valence Bands of Semiconductor Nanoparticles Based on Their Band Gaps

Experimentally, the values of band gaps of semiconductor nanoparticles are generally obtained by the absorption spectrum. Nevertheless, the determinations of the corresponding energy levels of the conduction bands (CBs) or valence bands (VBs) remain a challenge. Correspondingly, an accurate prediction of the CB or VB energy values is highly desired for designing and developing semiconductor devices. Herein, on the basis of the tight-binding approximation, we report a new linear equation that may quantitatively determine the energy levels of CB and VB of semiconductor nanoparticles based on their band gaps: E-CB - E-CB(bulk) = pm(b)/qm(e)+pm(b) x (E-g - E-g(bulk)) and E-VB - E-VB(bulk) = pm(b)/qm(e)+pm(b) x (E-g - E-g(bulk)), where p and q are constants related with the crystal structures, and m(e) and m(h) are the effective mass of electrons and holes, respectively. For single elements and binary crystals with tetrahedral and octahedral unit cells, which represent the majority of important semiconductors, the above equations can be simplified as: E-CB - E-CB(bulk) = m(h)/m(e)+m(h) x (E-g - E-g(bulk)) and E-VB - E-VB(bulk) = m(h)/m(e)+m(h) x (E-g - E-g(bulk)). For Si nanoparticles, E-CB,E-Si = 0.35 x (E-g - 1.1) - 4.0 and E-VB,E-Si = -0.65 x (E-g - 1.1) - 5.1.