Calculation of the Energy Spectrum of Nano-Meter-Sized Silicon
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CALCULATION OF THE ENERGY SPECTRUM OF NANO-METER-SIZED SILICON Vladimir Gavrilenko* , Peter Vogl** and Frederick Koch* "*Technical University of Munich, Physics Department E16, W-8046 Garching, Germany "**W.Schottky Institute, Technical University of Munich, W-8046 Garching, Germany
ABSTRACT A large number of experiments on porous silicon has reliably demonstrated that the onset of optical absorption is shifted to energies significantly above the band edge of bulk Si. This increased transparency of the small nanometer-sized crystallites with their H-covered surfaces is a fact that asks for theoretical interpretation. Handwaving arguments about quantum size effect can only be a qualitative guide. We present here a tight binding calculation of a Si slab with nanometer dimensions covered with hydrogen. This is a model system for one-dimensional confinement. We consider the effect on the electron energy structure, the total and local densities of states of Si covered with hydrogen in two phases: monohydride - Si : H (2xl) symmetric dimer, and dihydride phases - Si : H2 (lxl) A total energy minimization method in the framework of the self-consistent tight binding theory has been used to investigate the structural reconstruction of the Si-surface after the adsorption of hydrogen. We find, that the band gap of the slab covered with H on both sides (monohydride phase) shifts to higher energies (typically -1.8 eV for 1.16 nm thick slab). The adsorption of hydrogen removes all the electronic states from the gap for both phases investigated. In nanometer sized slabs the lowest electronic states in the conduction band are localized on the surface Si-atoms, in contrast to thicker slabs. We discuss the implication of this model calculation to light emission in porous Si. INTRODUCTION There has been great interest recently in the study of porous silicon (PS), which is known to exhibit photoluminescence (PL) well above the band-gap energy of crystalline Si (1], [2], [3]. A large number of experiments on PS has reliably demonstrated, that the onset of optical absorption is shifted to energies significantly above the band edge of bulk Si [1] to [5]. Handwaving arguments about quantum size effect can only be a qualitative guide . In some work [1] to [3], quantum size effect has been suggested to be responsible for the photoluminescence in PS. In [6] has been suggested that siloxene is present in PS and is the source of the visible luminescence in PS. In [7] the controversial arguments have been presented to the siloxene nature of the PL in porous silicon. In (4] has been suggested that PL i's most affected by total surface area in PS and the PL peak position be determined by the hydride complex on the Si-surface. Most of the specimens of PS have been prepared by electrochemical dissolution of (001) silicon wafers in hydrofluoric solution. Theoretically, the electron energy structure (EES) of the (001) Si surface covered with hydrogen has been considered in many publications. Theoretically the reconstruction of (001) surface of silic
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