Size-dependent change in energy bands of nanoparticles of white tin

For white-Sn particles smaller than about 5000.3em0ex in diameter, interband absorption, arising from transitions between nearly parallel bands, has been studied experimentally. In particle sizes smaller than about 3000.3em0ex in diameter, interband absorption appearing at about 3.1 and 3.80.3em0exeV is shifted to higher energies with decreasing particle size. In particle sizes smaller than about 1000.3em0ex in diameter, interband absorption appearing at about 5.00.3em0exeV is shifted to lower energies with decreasing particle size. The shift to the lower and higher energies can qualitatively be attributed to the energy-band narrowing by low coordination-number of surface atoms and to the energy-band broadening by lattice contraction, respectively. Thus, both the low coordination-number and the lattice contraction cause depending on size the change in energy bands. The interband absorption weakened with shifting and finally disappeared, indicating a decrease in the joint density of states. Thus, the initial and final bands are considered to depart from nearly parallel with energy-band narrowing and broadening.