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Ab initio restricted Hartree-Fock method within the framework of large unit cell formalism is used to simulate silicon nanocrystals between 216 and 1000 atoms (1.6–2.65 nm in diameter) that include Bravais and primitive cell multiples. The investigated properties include core and oxidized surface properties. Results revealed that electronic properties converge to some limit as the size of the nanocrystal increases. Increasing the size of the core of a nanocrystal resulted in an increase of the energy gap, valence band width, and cohesive energy. The lattice constant of the core and oxidized surface parts shows a decreasing trend as the nanocrystal increases in a size that converges to 5.28 Ǻ in a good agreement with the experiment. Surface and core convergence to the same lattice constant reflects good adherence of oxide layer at the surface. The core density of states shows highly degenerate states that split at the oxygenated (001)-(

Silicon has many industrial uses and is considered one of the most important semiconductors [

Electronic structure of silicon has been studied extensively because it is widely used in electronic products [

Large unit cell method (LUC) coupled with ab initio Hartree-Fock self-consistent electronic structure calculations are used in the present work. LUC method was formulated and used before for several kinds of bulk materials including diamond structured materials [

In most of the previous calculations of Si nanocrystals no clear distinction between core and surface properties of nanocrystals is made to the best of our knowledge. The distinction is important to understand the behavior of the different electronic properties and their relation to surface and core parts of the nanocrystal as we will see in present work. Another important reason for performing core and surface parts separately, is to reach a higher total number of atoms by summing the contributions of the different smaller parts of specific symmetry or size.

Ab initio self-consistent Hartree-Fock is used to obtain silicon nanocrystal molecular orbitals. Correlation corrections are neglected in the present calculations relying on Koopmans theorem [

In the present work, we divided calculations into two parts, core and surface parts which is the traditional method used in microscopic-size solid-state calculations as shown in Figure

(color online) A cross-section in Si cubic nanocrystal in which the outer area is the externally oxidized surface of one lattice constant width, while the inner area is the nanocrystal core and has nearly the exact diamond structure.

Two kinds of core LUCs are investigated, namely cubic and parallelepiped cells. The cubic cells are multiples of diamond structure Bravais unit cells, while the parallelepiped cells are multiples of primitive diamond structure unit cells [

We will perform the core part calculations using 3-D large unit cell method (LUC). The 2-D calculations for the oxygenated (001)-(

In Figure

Total energy of 216 Si atom nanocrystal core as a function of lattice constant.

Lattice constant as a function of number of core atoms for Si nanocrystal.

Three periodic slab stoichiometries were investigated to examine oxygenated (001)-(

Because of symmetry, silicon nanocrystal core part has a unique single structure in one of its allotropies, namely, the diamond structure in the present work. This is the opposite case of surface multiple structures in which orientation, passivating atoms, and other situations in which surface structure changes accordingly. Figure

energy gap, valence band width and cohesive energy of the core part plotted against the number of core atoms in Figures

Energy gap of Si nanocrystal core as a function of number of atoms.

Valence band width of Si nanocrystals core as a function of number of atoms.

Cohesive energy for Si nanocrystal core as a function of number of atoms.

Energy gap of Si nanocrystal oxygenated (001)-(

Degeneracy of states of 8 atoms LUC as a function of levels energy (a), and (b) surface density of states of oxygenated (001)-(

Ionic charges of oxygenated (001)-(

In Table 3 of [

Figure _{2} matrix is 1.7 eV [

Hydrogenated silicon nanocrystals [

The high value of the present core energy gap (3.5 eV) is a trend of Hartree-Fock theory [

The present value of the cohesive energy and other properties can be greatly enhanced by merely changing the simple STO-3G basis used in the present calculations to a more sophisticated basis states. However, more sophisticated basis states consume more memory and computer time and will eventually prevent us from reaching a large number of atoms. As an example [

Mesoscopic thermal conductance fluctuations of silicon nanowires are measured in [

Figure

Figure

Summarizing the above mentioned conclusions, the core part has a converging fluctuating energy gap, valence band width, and cohesive energy. These fluctuations are related to the geometry of the nanocrystal. The energy gap is controlled by the surface part of the nanocrystal with descending values that show its obedience to quantum confinement effects. The surface has damping oscillatory successive negative and positive layer charges. The surface part has a lower symmetry than the core part with smaller energy gap and wider valence and conduction bands. Surface and core parts have approximately the same lattice constant that reflects the good adherence of oxide layer at the surface.

_{2}having interface silicon suboxides