The electronic structure of GanPm(n+m=5, 17, 29, 35), Ga13P4 (in SiO2) and Ga13P4 (in sodalite) clusters
Introduction
The semiconductor clusters, typically in the size of 3–100 atoms or more, have been the focus of much research in the last years, because of their technological advances in the fabrication of smaller and faster electronic devices. A number of theoretical [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] and experimental [14], [15], [16], [17], [18], [19], [20], [21], [22] attempts have been made to determine the structure and properties of small semiconductor clusters. Compared to homogeneous clusters, such as C, Si and Ge, heterogeneous semiconductor clusters, especially III–V compound ones, like GaAs, GaN and GaP, are more attractive, because their properties can be controlled by changing the composition, in addition to the size. Furthermore, the recent advances in both experimental techniques and computer simulations, made possible to carry out studies on such clusters.
In a recent experimental work GanAsm(n+m≤30) clusters have been produced by a pulsed laser vaporization cluster source and the static polarization of the clusters has been investigated depending on the size [17]. In the same work, the energy transition between Lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) of GanAsm clusters has been modelled by the states similar to defect states in the band gap of bulk semiconductors. In another experimental work, small GaAs molecules were prepared again by laser vaporization and far infrared absorption spectra were observed [18]. In a theoretical work [5], the GaAs clusters based on zinc-blende crystal structure, were studied up to a radius of 100 Å and strong confinement effects were found through a red shifted absorption spectra by decreasing cluster size. In another theoretical work, GaAs clusters have been studied systematically up to eight atoms by Pquini et al. [8]. According to their work, the embryonic forms of these clusters had the geometric and electronic structures based on highly symmetrical configurations formed by the As atoms. In this work, the systematic variation of the optical energy gap between LUMO and HOMO has not been obtained due to the small size of the clusters. In a recent two theoretical works on small GaAs clusters, the As rich clusters were found to be more stable than the Ga rich ones [6], [8]. Besides, the calculated LUMO–HOMO was composition dependent and decreased by increasing GaAs cluster size [6].
GaN is an important wide band-gap semiconductor, and has recently emerged as a material of choice for optoelectronic device applications [22]. This has led to numerous theoretical and experimental studies on structural, electronic and optical properties of both surface and bulk phases of GaN. However, there are a small number of theoretical calculations which are focused on the structural stability and vibrational properties of small GanNm (n, m=1, 2) [9] and GanNn (n=3–6) clusters [10]. Kandalam and co-workers [9], [10] reported that N–N bonds played a crucial role in stabilizing the cluster, and the structures were dominated either by N3 or N2 subunits. In a very recent theoretical work [11], the electronic structure of the Ga3N, GaN3, Ga3N2, and Ga2N3 clusters has been studied in addition to their stability. Bin and co-workers [11] have reported that the Ga3N has a larger gap and the other clusters (GaN3, Ga3N2, and Ga2N3) have smaller ones between LUMO and HOMO than the energy band gap of the wurtzite solid GaN. Furthermore, they have found a strong dominance of the N–N bond over the Ga–N and Ga–Ga bonds to control the structure of GaN clusters, supporting the result obtained by Kandalam and co-workers [9], [10].
In the literature, the stability and confinement effects were also studied on GaP clusters. In one of the theoretical work, the tetrahedral structure of Ga4P6 was satisfied by hydrogenation [12]. In a recent theoretical work [13], the geometric and electronic properties of neutral GaP clusters have been studied by ab initio molecular dynamics simulations starting from a bulk fragment. Tozzini and co-workers [13] have found that small GaP fullerenes have highly symmetric structures, and large LUMO–HOMO gaps. In the same work [13], the energy gap between LUMO and HOMO has been decreased by increasing the size of the cluster for both Ga and P rich clusters. A recent experimental work [21], in which GaP clusters were generated in a laser ablation/pulsed molecular beam source, resulted in little change in the electronic structure of the cluster. In Ref. [5], the calculated indirect exciton energies of GaP clusters with bulk lattice constant were found to be shifted to blue with the decreased cluster size. In the same work [5], the rate of blue shift was lowered by assuming small contractions of the lattice constants in calculations. Micic and co-workers [20] have taken the absorption spectra of passivated GaP quantum dots in 20–30 Å size regime. In this work [20], the main absorption peak which was observed at around 3 eV, showed also the band gap shift to blue for these clusters.
In experimental works [23], [24], [25], the optically active systems have been obtained by the growth of small semiconductor clusters in host materials, in particular zeolite cages, glasses, and liquid suspensions. Pal and co-workers [23] have prepared GaAs nanoparticles of different sizes embedded successfully in SiO2 by radio frequency co-sputtering technique. In this work [23], the optical absorption spectra of the GaAs particles were significantly blue shifted from the bulk absorption edge, due to the strong quantum confinement. In two other experimental works [24], [25], the GaP clusters in the 20–30 Å size regime have been produced in the cavities of zeolite Y. The synthesis of the small clusters of GaP, particularly Ga28P13, has been accomplished in the periodic environment of zeolite with the use of inclusion chemistry. In these works [24], [25], the optical spectra have showed peaks that are blue shifted relative to bulk GaP and extended to the red of the indirect gap in bulk GaP. In a theoretical work [26], Porto and co-workers have indicated that, the effect of the zeolite host has facilitated the stabilization of the Ga28P13 cluster in the tetrahedral structure via its oxygen atoms. In a recent theoretical work [27], the calculated LUMO–HOMO energy gap for the GaP clusters embedded in zeolite with different Ga:P ratios was found to be ∼1.5 eV which was much smaller than the one expected on the basis of quantum confinement in nanometer size dots. In the same work [27], the LUMO–HOMO energy gap was calculated to be 1.9 eV which was again much smaller than the band gap of GaP (2.79 eV [5]). In another recent work [28], the stability and the role of quantum confinement were studied on small GaP and GaN clusters in sodalite; it was found that the alternated tetrahedral bulk structure was lost after molecular dynamics simulations and contrary to the expectation of quantum confinement, the LUMO–HOMO energy gap was increased by an increased cluster size. In all experimental and theoretical works mentioned above, the presence of the SiO2 matrix or zeolite framework around the small semiconductor clusters (GaAs, GaN, GaP) plays an important role in the stabilization and the final structure of the clusters. Furthermore, the SiO2 matrix or zeolite framework offers opportunities for creating new three- dimensional arrays of clusters (nanocrystal) whose dimensionality and electronic properties can be controlled [23], [24], [25], [26], [27], [28], [29].
To the best of authors' knowledge, the electronic structure of different sized spherical GaP clusters with Td symmetry has not been studied theoretically. In the present work, to complete this lacking of literature, the electronic structure of optimized Ga4P, Ga13P4, Ga16P13, Ga19P16, GaP4, Ga4P13, Ga13P16, and Ga16P19 clusters has been calculated and the results have been evaluated by considering the binding energy and the energy gap between LUMO and HOMO. Furthermore, the electronic structure of Ga13P4 cluster in SiO2 and sodalite has been studied to understand the role of SiO2 matrix and sodalite cage on the energy gap between LUMO and HOMO. In the present work, the Ga13P4 (in SiO2) and Ga13P4 (in sodalite) clusters have been proposed to be the cluster models of three dimensional Ga13P4–SiO2 and Ga13P4–sodalite nanocrystals.
Section snippets
Cluster models and theoretical method
In the first stage of this work, the spherical GaP clusters are generated shell by shell from an ideal zincsulfide type crystalline structure of Gallium phosphide. All the Ga and P atoms are initially at their crystalline positions and belong to the Td symmetry group. In these cluster structures, the first and second nearest neighbor distances between the Ga and P atoms are 2.36, and 4.52 Å, respectively. Therefore the Ga rich (Ga4P, Ga13P4, Ga16P13, Ga19P16) and P rich (GaP4, Ga4P13, Ga13P16, Ga
Calculations and results
In the present work, the spherical Ga and P rich clusters with Td symmetry are optimized by PM3 method [30] in gaussian98 package [31], to find out the geometry of GanPm((n+m)=5, 17, 29, 35)) isomers. In the first stage of the work, the hydrogenated and oxidized Ga4P and Ga13P4 clusters are tried to be optimized to see the roles of both hydrogen and oxygen on conserving the Td symmetry of the clusters. The hydrogenated and oxidized Ga4P and Ga13P4 are dispersed after optimization. For this
Summary and discussion
In the present work, the electronic structure calculations have been performed on GanPm (Ga4P, Ga13P4, Ga16P13, Ga19P16, GaP4, Ga4P13, Ga13P16, Ga16P19), Ga13P4(in SiO2) and Ga13P4(in sodalite) clusters by HF method with STO-3g basis set in gaussian98 [31] code to understand the effect of cluster size and Ga-O bonds on the variation of the optical gap between LUMO and HOMO. All the GanPm clusters considered in this work are generated by tetrahedral symmetry of GaP bulk. The dielectric layer
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