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The Elastic Continuum Limit of the tight binding model

Chinese Annals of Mathematics,Series B 2007年第6期28卷 665-676页

作者： Weinan E Jianfeng LU Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

关键词： Continuum limit Elasticity theory Cauchy-Born rule tight binding model

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Surface brightens up Si quantum dots: direct bandgap-like size-tunable emission

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Light(Science & Applications) 2013年第1期2卷 242-247页

作者： Katerina Dohnalova Alexander N Poddubny Alexei A Prokofiev Wieteke DAM de Boer Chinnaswamy P Umesh Jos MJ Paulusse Han Zuilhof Tom Gregorkiewicz Van der Waals-Zeeman Institute University of AmsterdamNL-1098 XH AmsterdamThe Netherlands Laboratory of Organic Chemistry Wageningen University6703 HB WageningenThe Netherlands Department of Chemical and Materials Engineering King Abdulaziz UniversityJeddahSaudi Arabia Ioffe Physical-Technical Institute RAS 26 Polytechnicheskaya194021 Saint-PetersburgRussia Current address:MIRA Institute Department of Biomedical ChemistryUniversity of TwenteBuilding Zuidhorst EnschedeThe Netherlands

Colloidal semiconductor quantum dots(QDs)constitute a perfect material for ink-jet printable large area displays,photovoltaics,light-emitting diode,bio-imaging luminescent markers and many other *** this purpose,efficient light emission/absorption and spectral tunability are necessary *** are currently fulfilled by the direct bandgap ***-QDs could offer the solution to major hurdles posed by these materials,namely,toxicity(e.g.,Cd-,Pb-or As-based QDs),scarcity(e.g.,QD with In,Se,Te)and/or *** we show that by combining quantum confinement with dedicated surface engineering,the biggest drawback of Si—the indirect bandgap nature—can be overcome,and a‘direct bandgap’variety of Si-QDs is *** demonstrate this transformation on chemically synthesized Si-QDs using state-of-the-art optical spectroscopy and theoretical *** carbon surface termination gives rise to drastic modification in electron and hole wavefunctions and radiative transitions between the lowest excited states of electron and hole attain‘direct bandgap-like’(phonon-less)*** results in efficient fast emission,tunable within the visible spectral range by QD *** findings are fully justified within a tight-binding theoretical *** the C surface termination is replaced by oxygen,the emission is converted into the well-known red luminescence,with microsecond decay and limited spectral *** that way,the‘direct bandgap’Si-QDs convert into the‘traditional’indirect bandgap form,thoroughly investigated in the past.

关键词： direct bandgap optical spectroscopy optoelectronics organic capping silicon quantum dots tight binding model

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