^{1,a)}, Dmitri G. Fedorov

^{2}, Pavel B. Sorokin

^{3,4,5}, Leonid A. Chernozatonskii

^{5}and Sergei G. Ovchinnikov

^{3,4}

### Abstract

Motivated by the experimental discovery of branched siliconnanowires, we performed theoretical electronic structure calculations of icosahedral siliconquantum dots embedded into pentagonal siliconnanowires. Using the semiempirical method, we studied the quantum confinement effect in the fully optimized embedded structures. It was found that (a) the band gaps of the embedded structures are closely related to the linear sizes of the longest constituting part rather than to the total linear dimension and (b) the discovered atypical quantum confinement with a plateau and a maximum can be attributed to the substantial interactions of near Fermi level electronic states of the quantum dots and nanowire segments.

This work was, in part, partially supported by a Core Research for Evolutional Science and Technology (CREST) grant in the area of high performance computing for multiscale and multiphysics phenomena from the Japan Science and Technology Agency (JST) as well as by the Russian Fund of Basic Researches (Grant No. 05-02-17443) (L.A.C.). One of the authors (P.V.A.) acknowledges the encouragement of Dr. Keiji Morokuma, Research Leader at Fukui Institute. The geometry of all presented structures was visualized by ChemCraft software.^{23} L.A.C. acknowledges I. V. Stankevich for help and fruitful discussions. P.B.S. is grateful to the Joint Supercomputer Center of the Russian Academy of Sciences for access to a cluster computer for quantum-chemical calculations.

I. INTRODUCTION

II. CALCULATION TECHNIQUE AND OBJECTS UNDER STUDY

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

## Figures

(a) Atomic structure of silicon nanowires, illustrated for and . describes the number of prism layers in the nanowire cross section (1 and 2). gives the number of the lengthwise segments (1, 2, 3, and 4). The asterisk denotes the formation of silicon dimers on the facets of the nanowires. (b) Quantum dot with the 20-atom core of symmetry (shown in red sticks). is the number of layers of silicon atoms including the core. (c) Side and top views of the quantum dot attached to the nanowire . The silicon atoms of the quantum dot, nanowire and the shared interface are shown in red (gray off line), blue (black off line), and green (light gray off line), respectively. Hydrogen atoms are not shown.

(a) Atomic structure of silicon nanowires, illustrated for and . describes the number of prism layers in the nanowire cross section (1 and 2). gives the number of the lengthwise segments (1, 2, 3, and 4). The asterisk denotes the formation of silicon dimers on the facets of the nanowires. (b) Quantum dot with the 20-atom core of symmetry (shown in red sticks). is the number of layers of silicon atoms including the core. (c) Side and top views of the quantum dot attached to the nanowire . The silicon atoms of the quantum dot, nanowire and the shared interface are shown in red (gray off line), blue (black off line), and green (light gray off line), respectively. Hydrogen atoms are not shown.

(a) Scanning electron microscopy image of a branched silicon nanowire (adapted from Ref. 10 and reproduced pending the permission from Nano Lett.). b) Atomic structures of silicon nanowires with embedded quantum dots (see main text for the notation). The linear sizes of the schematic systems are shown for some actual systems, along with their diameters . Only very few of the computed systems are illustrated, and the sizes and symmetry of all systems are provided in Table I. Silicon and hydrogen atoms are shown in red and blue, respectively.

(a) Scanning electron microscopy image of a branched silicon nanowire (adapted from Ref. 10 and reproduced pending the permission from Nano Lett.). b) Atomic structures of silicon nanowires with embedded quantum dots (see main text for the notation). The linear sizes of the schematic systems are shown for some actual systems, along with their diameters . Only very few of the computed systems are illustrated, and the sizes and symmetry of all systems are provided in Table I. Silicon and hydrogen atoms are shown in red and blue, respectively.

Band gap energy dependence on the linear size , showing the quantum confinement effect in (a) simple nanowires : black lines with circles, : red lines with triangles, and complex connected nanowires : green lines with squares; (b) quantum dot–nanowire junctions of : green lines with triangles, : black lines with circles, : red lines with circles, and : red lines with triangles and blue lines with squares . Numbers show the number of segments in nanowires. Pairs of numbers are given if more than one nanowire is present, giving the two independent numbers of segments. pairs are equivalent to single and are so shown to elucidate the structure connection.

Band gap energy dependence on the linear size , showing the quantum confinement effect in (a) simple nanowires : black lines with circles, : red lines with triangles, and complex connected nanowires : green lines with squares; (b) quantum dot–nanowire junctions of : green lines with triangles, : black lines with circles, : red lines with circles, and : red lines with triangles and blue lines with squares . Numbers show the number of segments in nanowires. Pairs of numbers are given if more than one nanowire is present, giving the two independent numbers of segments. pairs are equivalent to single and are so shown to elucidate the structure connection.

(a) Total and partial DOS of complex nanoclusters. Partial DOS are shown in the same color as the corresponding atomic structures. (b) The detailed total and partial DOS of occupied electronic states of cluster near the Fermi level region. Peaks , , and correspond to the , , and fragments respectively.

(a) Total and partial DOS of complex nanoclusters. Partial DOS are shown in the same color as the corresponding atomic structures. (b) The detailed total and partial DOS of occupied electronic states of cluster near the Fermi level region. Peaks , , and correspond to the , , and fragments respectively.

Molecular orbital diagram elucidating the quantum confinement. When system is elongated with producing , nearly degenerate occupied and virtual orbitals are shifted by the interaction (e.g., the HOMO and LUMO orbital energies shifted by and , respectively), reducing the band gap from to .

Molecular orbital diagram elucidating the quantum confinement. When system is elongated with producing , nearly degenerate occupied and virtual orbitals are shifted by the interaction (e.g., the HOMO and LUMO orbital energies shifted by and , respectively), reducing the band gap from to .

## Tables

Atomic and electronic structure of complex nanostructures.

Atomic and electronic structure of complex nanostructures.

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