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First-principles study of iron segregation into silicon 5 grain boundary T. T. Shi, Y. H. Li, Z. Q. Ma, G. H. Qu, F. Hong et al. Citation: J. Appl. Phys. 107, 093713 (2010); doi: 10.1063/1.3369390 View online: http://dx.doi.org/10.1063/1.3369390 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v107/i9 Published by the American Institute of Physics.

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JOURNAL OF APPLIED PHYSICS 107, 093713 共2010兲

First-principles study of iron segregation into silicon 兺5 grain boundary T. T. Shi,1 Y. H. Li,1,a兲 Z. Q. Ma,1 G. H. Qu,1 F. Hong,1 F. Xu,1 Yanfa Yan,2 and Su-Huai Wei2 1

Department of Physics, SHU-SolarE R&D Laboratory, Shanghai University, 200444, People’s Republic of China 2 National Renewable Energy Laboratory, Golden, Colorado 80401, USA

共Received 27 November 2009; accepted 20 February 2010; published online 7 May 2010兲 Using ab initio density function theory total energy calculations, we have investigated the mechanism of Fe segregation into Si 兺5具310典 grain boundary 共GB兲. We find that the segregation is site selective at the GB—Fe will only segregate to specific sites. We further find that the choice of the segregation site is determined by the segregation-induced stress and effective crystal-field-induce splitting of Fe d orbital at that site. Our results suggest that the revealed mechanism of Fe segregation into the GB should be general for other 3d transition metals with partially filled 3d orbits and for other grain boundaries. © 2010 American Institute of Physics. 关doi:10.1063/1.3369390兴 I. INTRODUCTION

To reduce the cost of Si solar cells, there is currently a steady interest to utilize less pure Si than what is currently used in the industry. A big challenging for utilizing these Si is to deal with their high density of impurities, particularly the 3d transition metals. These impurities typically result in recombination centers, which reduces the minority carrier diffusion length and consequently the cell efficiency.1 Among the 3d transition metal impurities, iron 共Fe兲 is the most detrimental and dominant one in less pure Si.2,3 A number of methods such as nanoprecipitation,4 grain boundary 共GB兲 gettering,5 and boron and phosphorus diffusion6–8 has been developed to reduce the detrimental effects of Fe impurities. Among them, GB gettering is an interesting approach because it involves both GBs and Fe impurities. Understanding how Fe segregates into grain boundaries in Si may help to develop new gettering process. However, so far, only Fe in bulk Si has received extensive attention.1 There are very few investigations on how Fe segregates into Si GBs. The nature of Fe in bulk Si has been studied both experimentally and theoretically.9–15 It is found that the majority individual Fe impurities in Si are at interstitial sites and they can be at positively charged state 共Fe+兲 in p-type doped Si or charge neutral state 共Fe0兲 in undoped Si. The deep donor level is at about 0.4 eV above the top of the valence band of Si. Ludwig and Woodbury9 共LW兲 in the early 1960s proposed a model that can explain qualitatively very well the observed electron paramagnetic-resonance 共EPR兲共Refs. 10–12兲 of interstitial 3d impurities in Si. Deep understanding of this model is further provided by more detailed theoretical calculations.13–15 These include the calculation of the reduction in hyperfine field of Fe in Si, which is consistent with the assumption of the LW model that two Fe 4s valence electrons transfer into the 3d shell, and the calculation of the energy level of Si:Fe by ab initio total energy calculations using a Green’s function technique and explanation of the a兲

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0021-8979/2010/107共9兲/093713/3/$30.00

energetic position based on the coupling with the host states. In this paper, we investigate the mechanism of interstitial Fe segregation into a Si 兺5具310典 GBs using the spinpolarized ab initio density functional theory. We find that the segregation energy depends sensitively on the GB site. We further find that the origin of this behavior is due to the site dependence of segregation-induced stress and the effective crystal field splitting of the Fe d orbitals. Our results suggest that these effects that lead to Fe segregation into the GB should be general for other 3d transition metals with partially filled 3d orbits and for other grain boundaries. II. METHOD

The density functional total energy calculations were performed using the VIENNA AB INITIO SIMULATION 16 PROGRAM. We used the general gradient approximation for exchange correlation and the ultrasoft Vanderbilt-type pseudopotentials.17 For exchange correlation functional, we use the parameters proposed by Perdew and Wang known as PW91.18 A cutoff energy of 320 eV was used for the planewave basis. To build the 兺5 GB, we adopted a super-cell including 128 atoms, which is small enough to simulate the doped GB and large enough to neglect the interaction of impurity irons. In addition, the super-cell had two twin GBs in order to guarantee the periodic boundary condition. The influence of different k-points was tested by a series of calculations and we find that calculations performed with 4 ⫻ 1 ⫻ 3 Monkhorst–Pack k-point sampling are relatively converged. All atoms were relaxed until all force components at each atomic site is less than 0.01 eV/Å. III. RESULTS AND DISCUSSIONS A. Atomic structure of Si 兺5Š310‹ GBs

Si 兺5具310典 GBs had been studied by the tight binding method and the first-principles method.19,20 The 兺5具310典 GB composes alternating threefold and fivefold rings. There are

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FIG. 1. 共Color online兲 Structure model of z-type 共310兲兺5 GB. The label a-f, indicate six possible GB sites for interstitial Fe. g is an interstitial site at the bulk region.

two types of 兺5, the zigzag 共z-type兲 and straight 共s-type兲 ones, due to the different arrangement of 3–5 units deduced from varied edge dislocation in the GB. We constructed the 兺5具310典 GB structures by adapting the previously published models and calculated the GB energies ␴GB using the firstprinciple method. To obtain ␴GB, we first calculate the GB formation energy defined21 as Eform = 1 / 2共EGB − Ebulk兲, where EGB is the total energy of a super-cell containing two GBs and Ebulk is the total energy of bulk Si with an equivalent number of atoms. In the two total energy calculations, the cutoff energies were kept the same and the k-point grid was kept equivalent. The GB energy ␴GB is then given by Eform / A, where A is the area of the periodic unit cell of the boundary in the 具310典 plane. Our calculations show that the interface energy of z-type 共0.368 J / m2兲 is smaller than the s-type 共0.444 J / m2兲. This result agrees with the highresolution transmission electron microscopy experiment22 in Ge that the z-type was the stable structure. In the following discussions, we will use the stable z-type 具310典兺5 model 共Fig. 1兲 for investigation. Considering the symmetry, we select six special sites 共a-f in Fig. 1兲 to represent the GB and select the g site as the reference bulk site. We define the GB segregation energy as the total energy difference between iron at the GB sites and at the bulk site. Negative GB segregation energy indicates that Fe would like to segregate to the GB site. The calculated values are shown in Table I. We find that the interstitial iron has a negative GB segregation energy only at c site. In most Si solar cells, the concentration for Fe in bulk is around 1013 to 1014 / cm3. Because of the small segregation energy, the concentration for Fe in the GB should be also around 1013 to 1014 / cm3. To understand the calculated trend, we have calculated the bond length and bond angle distortion, ⌬bmax and ⌬amax, TABLE I. Segregation energy of Fe at different GB sites in z-type 兺5具310典 GB. The bond length and bond angle distortions and the t2-e energy splitting of the Fe spin-down d state are also given.

Fe site a b c d e f

Segregation energy 共eV兲

⌬bmax 共Å兲

⌬amax 共 °兲

t2-e splitting 共eV兲

0.20 0.25 ⫺0.08 0.48 0.13 0.11

0.644 0.121 0.049 0.064 0.040 0.038

12.97 14.67 9.06 16.52 11.01 14.72

1.45 0.76 0.91 0.66 0.98 1.00

FIG. 2. 共Color online兲 Simplified energy level diagram for the tetrahedral interstitial Fe in silicon. 共a兲 The atomic Fe d single particle levels; 共b兲 and 共b⬘兲 are the levels with the exchange splitting included; 共c兲 and 共c⬘兲 include the effect of the crystalline field splitting; 共d兲 and 共d⬘兲 include the resulting energy levels due to the coupling to the antibonding p t2 levels. For clarity, the coupling with bonding p states is not shown.

when interstitial Fe is introduced at one of the GB sites. These distortion values are defined as the maximum differences between the nearest Si–Si bond lengths, bond angles of the doped sites and those in pure GB which are in the most stable structure. In general, larger strain means higher energy. Considering the changes of bond length and bond angle from Table I, we find that c, f, and e sites have one of the least length and angle change. This is consistent with the fact that the c site is the most stable one. Similarly, the f and e sites have lower energy because of their smaller angle and bond change. We also find that at a, b, and d sites the GB segregation energies are much higher because they are located at the vertex of the threefold ring, thus they have larger deviation from the standard tetrahedral symmetry. This can partly explain the energy trends of Fe in different GB sites. On the other hand, besides the strain, the electronic properties of Fe interstitial also plays role in determine the stability. B. Electronic structures

For Fe 共s2d6兲 at the Si interstitial site, the coupling between the Fe 4s orbital and the host pushes the 4s orbital to a higher energy level, so the two s electron transfer to the lower energy Fe 3d orbital.14 Therefore, Fe in Si has a 共d8兲 configuration.9,10 The energy levels of Fe 3d states split into spin-up and spin-down level under the spin exchange interaction. The fivefold degenerated d orbital further splits into triply degenerated t2 and doubly degenerated e states due to the crystal field of neighboring Si atoms 共Fig. 2兲. In general, considering the electron Coulomb repulsion, the e level should be below the t2 level in a tetrahedral environment. However, for the interstitial iron atom because it is located at the antibonding site of the four nearest Si, the Coulomb repulsion between the t2 state and the neighboring Si s and p electrons is weak. Moreover, the lobes of e orbital point to the direction of the next nearest neighboring Si atoms, forming an octahedral environment, whose electron Coulomb repulsion pushes the e level up. Consequently, the crystal field splitting between the t2 and e levels due to the overall Coulomb potential is small. On the other hand, the d orbital hybridize strongly with the host p orbital.14 The strong level repulsion between the Fe t2g d level and the antibonding Si p state pushes the Fe t2 d level down, so that the t2 d level is


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IV. CONCLUSIONS

Using ab initio density function theory total energy calculations, we have investigated the mechanism of Fe segregation into Si 兺5具310典 GB. We find that the segregation is site selective at the GB—Fe will only segregate to specific sites. We further find that the choice of the segregation site is determined by the segregation-induced stress and crystalfield-induce splitting of Fe d orbital at that site. Our results suggest that the effects that lead to Fe segregation into the GB should be general for other 3d transition metals with partially filled 3d orbitals and for other grain boundaries. ACKNOWLEDGMENTS FIG. 3. 共Color online兲 The calculated total DOS 共black lines兲 and the partial DOS of Fe d t2 共⫻10, blue lines兲 and e 共⫻10, red lines兲 orbitals at the six GB sites, a-f, as well as the g site in the bulk region. The energy zero is at highest occupied level. For reference, the DOS of the undoped system is also given.

lower in energy than the e level. Therefore, the exact energy position of the spin-up t2 and e states is determined by the effective crystal field splitting, consisting of overall Coulomb potential and p-d coupling. Our calculation reveals that for Fe interstitial in Si, the spin-up t2 and e states are occupied, whereas the spin-down t2 is occupied but the spin-down e orbital is unoccupied 共Fig. 2兲, meaning the p-d couplinginduced splitting is larger than the Coulomb potentialinduced splitting. The occupied spin-down t2 level determines the position of the deep donor level, which can become a recombination center when it is partially ionized. Because the spin-down d level is closer to the conduction band minimum, the level repulsion between the occupied t2 d level and unoccupied t2 antibonding p level is larger in the spin-down channel than in the spin-up channel, so the effective crystal field induced t2 and e splitting is larger in the spin-down channel than in the spin-up channel 共Fig. 2兲. This level repulsion lowers the energy of the occupied states and raises the energy of the unoccupied state, so it gains energy. This analysis indicate that when the effective crystal field splitting between t2 and e levels is large at a certain site, the Fe atom will tend to be more stable. Figure 3 plots the total density of states 共DOS兲 and partial DOS of interstitial Fe d orbital in different GB sites. The average values of t2-e splitting of these sites are listed in Table I. These t2-e split values are calculated through weighted average of each t2 and e peaks as shown in Fig. 3. In Table I, Fe at d site has the smallest t2-e splitting, which is consistent with the fact that Fe in this site has the highest energy. On the other hand, the c, e, and f sites are all have relatively large t2-e splittings, which are consistent with the fact that they have relatively small GB segregation energy.

The work at Shanghai University was supported by the Natural Science Foundation of China 共Grant No. 60876045兲 and Shanghai Leading Basic Research Project 共Grant No. 09JC1405900兲. The work at NREL was supported by the U.S. Department of Energy 共DOE兲, under Contract No. DEAC36-08GO28308. Computing resources is provided by the High Performance Computing Center of Shanghai University. 1

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