Silicon clusters models

The ultrahigh vacuum STM was used to investigate the addition of the 2,2,6,6-tetramethyI-l-piperidinyloxy (TEMPO) radical to the dangling bond of Si(l 0 0)-2 X 1 surface. ° ° The TEMPO can bond with a single dangling bond to form stable Si-O coupling products, in contrast to the thermal decomposition of TEMPO-silicon compounds. Semiempiiical and DFT calculations of TEMPO bound to a three-dimer silicon cluster model yielded... 

Redondo and Goddard28 first reported that the lowest energy configuration for a dimer in a small silicon cluster model, SigH, shown in Figure la, is the symmetric geometry. 

Rev. A., 73, 053203 (2006). Modified Genetic Algorithm to Model Cluster Structures in Medium-Sized Silicon Clusters Si18-Sifi0-... 

With roughly 1000 atoms, the size of the silicon clusters that constitute the micro PS network is between the bulk crystal and a molecule. Hence models of the luminescence process based on size reduction of the crystal, as well as models based on molecular sttuctures, have been proposed, which are reviewed in detail in [Ca7, Ju3]. Generally the various models of the luminescence of PS can be classified into three major categories ... 

Fig. 9. Cluster model of the coordinative adsorption of a H20 molecule on (a) the face and (b) the edge of a silicon-oxygen tetrahedron in Si02.

In this paper, we only focus on the properties of hydrogen-terminated silicon clusters and the surface reconstructions are ignored. All the cluster models, we used in the present work, were cut out of crystalline silicon and the surfaces were terminated with hydrogen atoms. 

Figure 1 Models of (a) 1-D, (b) 2-D, and (c) 3-D silicon clusters. Si2He, SiioH22, and Si2oH42 are shown as examples for 1-D clusters, Si2oH3<, SisoHyo are shown as examples for 2-D clusters, and SisHi2, SiasHsg, and SinHeo are shown as examples for 3-D clusters.

Figure 3 Eg values of 1-D silicon clusters as a function of the size. The calculated Eg values are with ( ) and without (A) silicon 3d orbitals plotted by broken curves. The solid curve shows the Eg values evaluated from Matsumoto s QW model.

Figure 3 shows the Eg values of 1-D silicon clusters ls a function of size. The calculated Eg value decreases with increase of the number of silicon atoms, that is, the cluster size. Figure 3 also indicates the Eg values evaluated by Matsumoto s quantum-well (QW) modell l in which the wavefunctions are confined in the potential well and asolute Eg values were determined by interpolating the experimental Eg values of disilane (6.5eV) and polysilane (4eV) by the size dependance of the energy levels of the wavefunctions. 

Figures 4 and 5 show the Eg values of 2-D and 3-D silicon clusters also as a function of their size, respectively. The Eg values of of QW-model derived 1-D, 2-D, and 3-D silicon clusters of infinite size were determined by the experimental Eg values of disilane (6.5eV), polysilane (4eV), siloxene (2.5eV) and crystalline silicon (l.leV), respectively. When the cluster size increases, the Eg values in 2-D and 3-D clusters decrease similar to the decrease in the Eg values in 1-D clusters. Also, the Eg values decrease as the number of dimensions of the cluster increases. These decrease in Eg values have been explained by the fact that the delocalized skeleton u-electrons form both band edge levels including HOMO and LUMO.

Figures 3, 4 and 5 also show the Eg values when silicon 3d orbitals are added to the basis sets. All of the calculated Eg values without Si 3d orbitals are about leV higher than those of the QW model. However, when Si 3d orbitals are taken into account, the calculated Eg values decrease by about leV and good agreement with the values given by the QW model is obtciined. These results imply that the energy levels around HOMO and LUMO of silicon clusters are well modeled by the quantum confinement of delocalized wavefunc-...

We calculated the electronic structure of 1-D, 2-D, and 3-D silicon clusters using (DV)-Xa MO method. The calculated energy gap Eg) between HOMO and LUMO decreases with increase of the cluster size and the number of dimensions of the cluster. It is found that including silicon 3d orbitals as basis sets results in lowering the Eg values by about leV. The results also show that the components of silicon 3d orbitals in the unoccupied levels near LUMO axe over 50%. In the case of silicon clusters, the size effect on the Eg value is well described by the quantum-well(QW) model in which the delocalized wavefunc-tions are confined in the potential well. The calculated results predict that Eg... 

Si atoms representing the dimer structure, four second layer silicon atoms, two third layer silicon atoms, and one fourth layer silicon atom. Although this cluster can be used to simulate the bulk feature of sihcon, the one dimer cluster does not describe the surface reaction adequately [17]. In order to adequately describe the surface at low computational cost, we adopt the three dimer cluster model S121H20. As the energy gain per dimer for the three-dimer cluster is between 0.15-0.20eV and in agreement with the slab results to... 

Fig. 15. Illustrations of modified HK adsorption models, (a) Geometric representation slit pore filled with adsorbate [110]. (b) Two-stage HK mesopore isotherm model [114] in which capillary condensation (1) to the filled state (2) is preceded by a wetting transition (3) from an empty state (4) to an intermediate condition characterized by film growth on the pore walls (5). (Reproduced with permission from S. Ramalingam, E. S. Aydil, and D. Maroudas. Molecular dynamics study of the interactions of small thermal and energetic silicon clusters with crystalline and amorphous silicon surfaces. Journal of Vacuum Science and Technology B, 2000 19 634-644. Copyright 2001, AVS.)...

Miyazaki, T, Uda, T, Stich, I., and Terakura, K., Theoretical study of the structural evolution of small hydrogenated silicon clusters Si(,I I. Chem. Phys. Lett. 261,346-352 (1996). Mousseau, N., and Lewis, L. J., Dynamical models of hydrogenated amorphous silicon. Phys. 

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