Ab initio large unit cell calculations of the electronic structure of diamond nanocrystals

In order to reduce computational efforts, and separate surface and core properties, diamond nanocrystals in the present model is represented by a heterojunction between the surface and the core in which the surface represents the outer most four layers and the core by the rest of the internal region of nanocrystal. Ab initio restricted Hartree-Fock (RHF) method coupled with the large unit cell method (LUC) is used to determine the electronic structure and physical properties of diamond nanocrystals core part with different sizes. The use of STO-3G basis choice is made to be able to compare to semiempirical methods using the complete neglect of differential overlap (CNDO) that uses Slater type orbitals (STO). The oxygenated (001)-(1 × 1) facet that expands with larger sizes of nanocrystals is also investigated to determine the rule of the surface in nanocrystals electronic structure. The results show that the present method agrees with semiempirical method contraction of lattice constant with increasing nanocrystal size but disagrees with energy gap variation with nanocrystal size in some regions. After nearly 1.4 nm the energy gap which is controlled by surface states begins to rise. The lowest unoccupied molecular orbital (LUMO) is attributed to surface states that largely reduce the value of energy gap. The sources of disagreement between semiempirical and ab initio results are discussed. The present method shows a maximum increment of the lattice constant by 3.3% over the calculated bulk for the smallest diamond nanocrystals. The surface states are found mostly non-degenerated because of the effect of surface discontinuity and oxygen atoms. Valance and conduction bands are wider on the surface due to splitting and oxygen atoms. The method also shows fluctuations in the converged energy gap, valence band width and cohesive energy of the core part of nanocrystal. These fluctuations might partially explain the controversial experimental results for diamond nanocrystals greater than 1.4 nm in size. The method of the present model has threefold results; it can be used to obtain the electronic structure of bulk, surface, and nanocrystals.

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