Floating bonds and gap states in a-Si and a-Si:H from first principles calculations

– We study in detail by means of ab-initio pseudopotential calculations the electronic structure of five-fold coordinated (T5) defects in a-Si and a-Si:H, also during their formation and their evolution upon hydrogenation. The atom-projected densities of states (DOS) and an accurate analysis of the valence charge distribution clearly indicate the fundamental contribution of T5 defects in originating gap states through their nearest neighbors. The interaction with hydrogen can reduce the DOS in the gap annihilating T5 defects. The atomic origin of the midgap energy levels in a-Si has been commonly ascribed to three-fold (T3) coordinated atoms, and the observed reduction upon hydrogenation has been explained with the passivation of the “dangling bonds” by H [1]. This picture has been proposed in analogy with the well known mechanism occurring in undercoordinated configurations such as at surfaces and vacancies in crystalline silicon (c-Si) [2]. The dangling bond picture for a-Si has been widely supported by many electronic structure calculations [3, 4, 5, 6, 7], although it has been recognized that gap states can be induced also by other coordination defects [4, 7], e.g. five-fold (T5) coordinated “floating bonds” and anomalous four-fold (T4) coordinated atoms. We focus our attention here on the role of T5 defects. Their importance in a-Si has been clearly stated by Pantelides [8, 9] and Kelires and Tersoff [10] a douzen of years ago. Pantelides [8, 9] suggested that the presence and the role of T5 defects must be seriously reconsidered in order to explain some theoretical and experimental data (effective electron correlation [11], (∗) Present address: Naval Research Laboratory Code 6391, Washington DC 20375-5345; e-mail: [email protected] Typeset using EURO-TEX 2 EUROPHYSICS LETTERS hyperfine structure from electron paramagnetic resonance data [12], relationship between intensity of paramagnetic signal and density of Si-H bonds [13]) that otherwise would remain unexplained in the common picture involving only dangling bonds, and he gave some arguments suggesting that T5 defects could be predominant. He argued that T3 and T5 are conjugated defects, since a bond elongation can transform a T4 + T5 structure into a T3 + T4 one [8]; furthermore, he proposed a mechanism for H diffusion based on floating-bond switching and annihilation/formation of T5’s through interaction with H [9]. The empirical simulation by Kelires and Tersoff [10] has shown that T5 atoms have lower energy than T3 atoms, and therefore should be favoured in general. Also some ab-initio molecular dynamics simulations of a-Si structures indicate a predominance of T5 defects with respect to T3 [14, 15]. The ideas of Pantelides have then been applied mainly in discussing the geometrical characterization of defects [6, 7, 16, 17, 18]. Our aim is to discuss their soundness in terms of electronic properties, by analyzing charge distributions and atom-projected DOS obtained from accurate ab initio calculations, also following some possible process of formation of T5 defects and of evolution upon hydrogenation. To this purpose, we start from some selected samples generated by other authors [14, 15, 19] using Car-Parrinello molecular dynamics (CPMD). These structures are a good starting point for this study, since they contain floating bonds; furthermore, they reproduce quite well the experimental pair correlation function and bond angle distribution function using a reasonable number of atoms and hence they are suitable for accurate ab-initio studies. The small number of defects, which is however larger than in experiment, allows to easily single out effects associated to local features. The configurations studied are cubic supercells of side a = 2 a0, where a0 is the equilibrium lattice parameter of c-Si. With respect to the original configuration, where a0 was fixed to the experimental value, we use the theoretical equilibrium lattice parameter a0 = 10.17a.u., which also corresponds —in our calculations— to the optimized density of a-Si and a-Si:H. The starting configurations contain respectively 64 Si atoms to describe a-Si [14, 15] and 64 Si atoms plus 8 H atoms for a-Si:H [14, 19]. We have studied both the mean configuration at room temperature and a snapshot of the CPMD run, in order to check for possible anomalies due to statistical average, and also to single out the effect on the electronic features of tiny structural variations. The CPMD configurations, aiming mainly at reproducing the structural properties, have been obtained using a kinetic energy cutoff Ecut=12 Ry and the Γ point only for Brillouin Zone (BZ) sampling [14, 15, 19]. Since electronic structure studies require better accuracy, we improve in our calculations the BZ sampling using 4 inequivalent special k points for self-consistency and 75 k points for DOS. These parameters have been chosen as a reasonable compromise between accuracy and computational cost, after tests with Ecut=16 Ry and with the Γ point or 32 special k points for self-consistency. We have used for Si the pseudopotential by Gonze et al. [20] and for H a smoothed Coulomb potential. The optimization of the a-Si and a-Si:H structures with the new computational parameters is accompanied only by small structural rearrangements. The results for the structural and electronic properties of the mean relaxed configurations that we present here are essentially valid also for the others (snapshot, unrelaxed). The mean structural properties of these configurations are similar to those discussed in refs. [14, 15, 19]. We only report here that in a-Si the mean bond length is d ≃ 4.47 a.u., quite similar to the crystalline one which is 4.40 a.u.. The location of the first minimum of the radial distribution function defines geometrically the cutoff distance for the nearest neighbors (NN), which for Si-Si turns out to be RNN = 5.08 a.u. and RNN = 5.49 a.u. in a-Si and a-Si:H respectively. In a-Si:H each H is bound to one Si atom with an average distance dH = 2.95 a.u.. With those values of RNN , the resulting average coordination number for Si in a-Si M. FORNARI et al.: FLOATING BONDS AND GAP STATES IN a-SI ETC. 3