Composition dependent properties of GaAs clusters

Transcription

1 Computer Physics Communications 142 (2001) Composition dependent properties of GaAs clusters H.H. Kwong, Y.P. Feng,T.B.Boo Department of Physics, National University of Singapore, Singapore , Singapore Abstract We used a combination of first principles electronic structure calculation and semi-empirical methods to study the composition dependence of physical properties of small and medium sized GaAs clusters. Structures and physical properties of Ga 10 n As n (n = 0, 1, 2,...,10) clusters were determined using the ab initio Hartree Fock method, with the STO-3G basis set. It was found that the structures of these clusters strongly depend on the composition and generally As-rich clusters are more stable than Ga-rich clusters. The dipole moment, HOMO-LUMO gap, vertical ionization energy, vertical electron affinity also depend on composition of the clusters and show an even/odd alteration with the number of Ga atoms (or As atoms) in the cluster Elsevier Science B.V. All rights reserved. PACS: 31.15; 36.40; 61.46; 71.20; Keywords: Cluster; Nanoparticles; GaAs; Electronic structure; Semiconductor; Ab initio calculations With the rapid increase in density of electronic components and the downsizing of electronic devices, it is predicted that the building blocks for future electronic devices will be semiconductor quantum dots and clusters [1,2]. Progress in semiconductor technology has already made it possible to fabricate semiconductor clusters. Besides their small sizes, clusters mark the transition between molecular and solid-state regimes. Microscopic study of clusters provides insights into the evolution of material properties from molecules and surfaces to solids. In the case of semiconductors, this evolution is remarkable. Semiconductor clusters have been shown to exhibit exotic properties quite different from those in molecules and solids. Compared to homogeneous clusters such as carbon and silicon, heterogeneous semiconductor clusters like gallium arsenide are more attractive because their properties can * Corresponding author. address: phyfyp@nus.edu.sg (Y.P. Feng). be controlled by changing the composition, in addition to the size. For these reasons, theoretical studies on clusters are critical to the design and synthesis of advanced materials with desired optical, electronic, and chemical properties. However, theoretical studies of heterogeneous semiconductor clusters have been limited due to computational difficulties arising from the large number of structural and permutational isomers formed due to multiple elements. On one hand, sophisticated computational method such as self-consistent quantum mechanical calculation is required to make reliable prediction on the properties of these clusters, in the absence of comprehensive experimental results. On the other hand, the amount of computational work is enormous in order to find all the stable isomers for a given cluster size and composition. A number of theoretical and experimental [3 15] attempts have been made to determine the structure and properties of small Ga m As n clusters. Most of the theoretical studies have /01/$ see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S (01)

2 H.H. Kwong et al. / Computer Physics Communications 142 (2001) been focused on clusters of a few atoms due to the above mentioned difficulties. In this article, we report some preliminary results of our study on the 10-atom GaAs clusters, Ga n As 10 n. The objective of our study is to investigate the composition dependence of structure and various physical properties of these clusters. For each composition of the Ga n As 10 n cluster, we used various less expensive approaches, such as geometric optimization based on semi-empirical force field, simulated annealing, and permutations of elements based on known structures, to pre-select a group of stable isomers. Quantum mechanical calculation was then performed on these isomers to refine their structures and to make prediction for their properties. Actually, for very small clusters, it is possible to enumerate all possible stable isomers [16]. They can be used as initial configurations for the quantum mechanical calculation which further optimizes the bond lengths, bond angles, etc. For clusters beyond a few atoms ( 5), we used molecular dynamics, based on semi-empirical methods (MOPAC PM3 [17]), and the simulated annealing technique to shortlist a number of candidates for each composition, before carrying out quantum mechanical calculation. On average, about half of the configurations can be rejected on the basis of those simulations. Among all the stable isomers found, the one with the lowest total energy was taken as the ground state for the given composition. Our quantum mechanical calculation was based on the Hartree Fock self-consistent field method, with the minimal basis set, STO-3G, as it is implemented in the Gaussian program [18]. All calculations are performed using the computing facilities provided by the Supercomputing and Visualization Unit of the Computer Centre, National University of Singapore. The geometric structures of the Ga n As 10 n (n = 0, 1, 2,...,10) clusters were determined by full geometric optimization. For each different composition, a number of stable structures were obtained. The structure corresponding to the lowest total energy is shown in Fig. 1 for each composition. It can be seen that Fig. 1. Structures of the Ga n As 10 n clusters.

3 292 H.H. Kwong et al. / Computer Physics Communications 142 (2001) these structures are quite different from each other, indicating that the structures of GaAs clusters depend strongly on composition. Even though it is not so obvious due to the small sizes of the clusters, it seems that the As atoms have a tendency to segregate to the surface of the clusters. The overall shapes of these clusters are relatively compact compared to smaller GaAs clusters. Detailed examinations on the bond lengths and angles showed that the average bond lengths remain fairly constant in different clusters and are close to the bond lengths in the corresponding bulk materials. The bond angles, however, have large variations, due to severe structural distortion. Lou et al. [7] studied two 10-atom clusters, Ga 6 As 4 and Ga 4 As 6 among other GaAs clusters of different sizes and predicted that the most stable structure of the Ga 4 As 6 cluster has a C 3v symmetry while the most stable structure of the Ga 4 As 6 cluster has a C s symmetry. Compared to these, the structures obtained in our study have lower symmetries. To compare the relative stability of the Ga n As 10 n clusters, we calculated the binding energy of each cluster, given by E b = ne(ga) + (10 n)e(as) E(Ga n As 10 n ), where E(As), E(Ga) and E(Ga n As 10 n ) are the energies of an isolated As atom, a Ga atom and the Ga n As 10 n cluster, respectively. The calculated binding energy is shown in Fig. 2(a) as a function of n. First of all, the average binding energy is about 1 2 ev per atom which is much larger than the thermal energy at an ambient temperature. All these clusters are, therefore, stable under normal conditions. The binding energy decreases as the number of Ga atoms increases in the cluster. This means that the Asrich clusters are more stable than the Ga-rich clusters, in good agreement with previous studies [10]. Furthermore, the Ga 5 As 5,Ga 8 As 2 and Ga 10 clusters have lower binding energies compared to others with close compositions and are thus less stable. In particular, Ga 5 As 5 being among the least stable Ga n As 10 n clusters is peculiar since bulk GaAs has and large GaAs clusters are expected to be stoichiometric. The relative stability concerning Ga 4 As 6 and Ga 6 As 4 agrees with prediction by Lou et al. [7] using local spin density method, i.e. Ga 4 As 6 is more stable than Ga 6 As 4. Dipole moment is an important quantity for clusters since it measures the relative separation of positive and negative charges in space. The variation of the dipole moment of the Ga n As 10 n clusters with composition Fig. 2. Variations of binding energies (a), dipole moments (b), HOMO-LUMO gaps (c), vertical ionization energies (d) and vertical electron affinity (e) with composition (number of Ga atoms n)of the Ga n As 10 n clusters. is shown in Fig. 2(b). It is interesting to note that the dipole moment shows strong even/odd alternation with the composition. Clusters with odd number of Ga atoms generally have higher dipole moments than those clusters with even number of Ga atoms, with the only exception at n = 7. Pure Ga and pure As clusters have lower dipole moments which is expected since they are composed of similar atoms. The energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), or the HOMO- LUMO gap is the equivalent of the energy gap in a bulk semiconductor and it is of considerable importance in the study of semiconductor materials. For small clusters, the trend followed by the HOMO- LUMO gap is still of considerable interest, although a comparison with bulk values should require much bigger clusters. The change of HOMO-LUMO gap for the Ga n As 10 n cluster with the cluster composition is shown in Fig. 2(c). The HOMO-LUMO gaps

4 H.H. Kwong et al. / Computer Physics Communications 142 (2001) of the Ga n As 10 n clusters depend strongly on cluster composition. Clusters with even number of Ga atoms generally have larger HOMO-LUMO gaps than those clusters with odd number of Ga atoms. The smallest HOMO-LUMO gap is about 6.5 ev. This is quite large compared to the band gap of bulk GaAs but could be expected for clusters. Our computational result shows that all the lowest energy clusters are singlet state with large HOMO-LUMO gap, in good agreement with the experimental observation from photo-emission studies which showed that even numbered clusters are singlet with large HOMO-LUMO gap [19,20]. This is due to the fact that these clusters have even number of valence electrons and furthermore all the electrons are paired together in their respective molecular orbitals. There is some interesting correlation between the dipole moment and the HOMO-LUMO gap of the clusters. A cluster having large dipole moment typically has small HOMO-LUMO gap and vice versa. The vertical ionization energy is the energy needed to remove an electron from the neutral cluster, assuming that the geometry of the positively charged ionized cluster remains unchanged. Fig. 2(d) shows how the vertical ionization energy of the Ga n As 10 n cluster changes with the number of Ga atoms in the cluster. It is interesting to observe that the vertical ionization energy shows some degree of even/odd alternation except for n around 4 and 9, where the vertical ionization energy decreases almost linearly with the number of Ga atoms in the cluster. There are some similarities between the trends of the vertical ionization energy and the HOMO-LUMO gap, as functions of the cluster composition, except for n around 7. It has been observed experimentally that ionization energy of clusters exhibits the even/odd alteration as a function of cluster size [19]. Here we observe that the vertical ionization potential has a tendency to show the same even/odd alternation with cluster composition. Those clusters with even number of Ga atoms generally have higher vertical ionization energies than those clusters with odd number of Ga atoms. The ionization energies for the Ga 4 As 6 and Ga 6 As 4 obtained in our calculation qualitatively agree with the results of the local spin density studies of tetra-capped trigonal prism of Ga 4 As 6 and Ga 6 As 4 [7]. Both studies showed that the vertical ionization energy of Ga 4 As 6 is smaller than that of Ga 6 As 4. The ionization energy obtained in our calculation is smaller than the experimental values and results of other calculations due to the fact that experimental ionization potential corresponds to the adiabatic case instead of the vertical ionization potential. The adiabatic ionization energy is the energy required to remove an electron from a cluster with a corresponding change in the geometry of the positively charged ionized cluster. This may lead to a change in energy of the positively charged ionized cluster. This, however, was not considered in our present study because the energy change induced by such a change in geometry would be small within the Hartree Fock level of theory coupled with a small basis set. The vertical electron affinity is the amount of energy released when the cluster gains an electron from its neutral state, with the assumption that the geometry of the negatively charged cluster remains unchanged. Fig. 2(e) shows the behavior of the vertical electron affinity with the number of Ga atoms, n, in the cluster. All clusters investigated have positive vertical electron affinity. Thus the clusters have a tendency to gain an electron under normal conditions, as it is energetically favorable to do so. Interpreted in another way, the negatively charged clusters are lower in energy than the corresponding neutral clusters. This is in agreement with results of earlier theoretical studies on smaller GaAs clusters [11] and mass spectrometry results for clusters that are spontaneously generated in random processes [21]. The vertical electron affinity shows only a certain degree of even/odd alternation with cluster composition, n. Local spin density studies of tetra-capped trigonal prism of Ga 4 As 6 and Ga 6 As 4 [7]gavehighervalues of 2.0 and 2.6 ev for the vertical electron affinity as compared to our values of about 1.5 and 2.3 ev, respectively. Both results indicated that the electron affinity of Ga 4 As 6 is smaller than that of Ga 6 As 4. In conclusion, structures of 11 clusters in the form of Ga n As 10 n (n = 0, 1, 2,...,10) were determined and their properties were investigated using ab initio quantum mechanical calculation. It is found that the structure of these clusters depend strongly on the composition. The As-rich clusters are generally more stable than the Ga-rich clusters. Various physical properties of these clusters have strong dependence on the composition. Some properties even exhibit peculiar even/odd alternation with composition.

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