- Email: [email protected]
First principal investigation of Fe- and Li- silicon compounds
Available online at www.sciencedirect.com
Physics Procedia
Physics Procedia 0 (2011) 000–000
Physics Procedia 23 (2012) 17 – 20
www.elsevier.com/locate/procedia
Asian School-Conference on Physics and Technology of Nanostructured Materials (ASCO-NANOMAT 2011)
First principal investigation of Fe- and Li- silicon compounds A.S. Fedorova,*, Z.I. Popova, A.A. Kuzubovb, T.A. Kojevnikovab, S.G. Ovchinnikova a
Kirensky Institute of Physics, Akademgorodok 50, Krasnoyarsk, 660036, Russia b Siberian Federal University, av. Svobodny 79,Krasnoyarsk, 660041, Russia
Abstract Electronic and geometric structure of ȕ-phase crystal FeSi2 as well as ȕ-FeSi2 nanofilms and Si/FeSi2 interface is investigated by DFT calculations. It is revealed unusual increasing of the dielectric gap of crystal FeSi 2 under different pressures. It is detected that (001) surface of ȕ-FeSi2 slab, ended by Si atoms, is reconstructed with squares formed by Si atoms. Also FeSi2 nanofilms have conductivity explained by Fe atom layers. It is shown that contact of the (001) Si and ȕ-FeSi2 plate lead to narrow perfect interface having conductivity near Fermi level mainly due to contribution of the silicide surface lavers. Also properties of lithium absorption inside crystal and amorphous silicon as well as inside silicon with impurities were investigated. For that a new method was developed which allow calculating a diffusion rate inside amorphous material when potential barriers are too high to apply conventional molecular dynamic method. It is demonstrated strong increasing of the lithium diffusion rate inside amorphous silicon in comparison with crystal silicon.
©2011 2011Published PublishedbybyElsevier Elsevier Ltd. Selection and/or peer-review under responsibility of Guest Editors of of © B.V. Selection and/or peer-review under responsibility of Publication Committee ASCO-NANOMAT 2011 and Far Eastern Federal University (FEFU)2011 Physics Procedia, Publication Committee of ASCO-NANOMAT Keywords: silicide; ȕ-FeSi2; Li-ion batteries; amorhous silicon; diffusion
1. Investigation of ȕ-FeSi2 crystals, nanofilms and Si/ FeSi2 interface It is known from experiments [1,2] that nanoparticles of transition metal silicides can be produced inside silicon under metal embedding and they can be effective as light emitters and detectors. As
* Corresponding author. Tel.: +7-391-243-2635; fax: +7-391-243-8923. E-mail address: [email protected].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Publication Committee of ASCO-NANOMAT 2011 and Far Eastern Federal University (FEFU) doi:10.1016/j.phpro.2012.01.005
18 2
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
contrasted to pure silicon, such silicides often have direct optical band gap, so they have good luminescent properties. Also using of magnetic properties of such metals in interface layers of transition metal/silicon looks very promising for spintronics elements constructing. At that electronic and optical properties are changed during decreasing of particle size up to nanometers. Unfortunately, these properties of such nanoparticles and nanofilms were not investigated properly yet. So, one of the aim of the work was to investigate these properties of ȕ-phase of crystal FeSi2 under the pressures as well as ȕFeSi2 nanofilms and Si/FeSi2 interface by ab initio calculations. These calculations were made within DFT formalism using GGA-PBE approach using plane wave basis set and ultra soft Vanderbilt pseudopotentials [3] as implemented in the VASP 4.6 code [4]. Remember that nanoparticles undergo the Laplas pressure that can change the optical gap, dependence of the gap of the ȕ-FeSi2 crystal on pressures was investigated. It was detected unusual increasing of the dielectric gap under different pressures. Also the electronic structure of (001) silicon, ȕ-FeSi2 nanofilms and their interface were investigated after the structures optimization. For electronic density of state (DOS) analysis the technique of separation of normal to the surface layers contribution was proposed. By this technique the conductivity of these nanofilms was revealed. It was shown this conductivity arise from surface layers, at that the contribution of inner layers is quickly decreased under moving away the surface. For calculation of equilibrium (001)Si/ȕ-FeSi2 interface structure, the method of damped molecular dynamics was employed and the system was quenched from temperature Tstart=2000 K to 0 K during annealing, see Fig.1. This temperature value had been chosen because both it is greater than silicon melting point (1687 K) and it allowed to modify the interface geometric structure during ~1000 time steps. One can see that the interface has sharp border that is experimentally confirmed in [1]. The partial DOS analysis of every layer in this structure shows main contribution of iron layers into total interface conductivity.
Fig. 1. Structure of ȕ-FeSi2/Si(001) interface after simulated annealing procedure. Black spheres – Si, white spheres – Fe
2. Investigation of lithium absorption and diffusion inside crystalline and amorphous silicon The demand for higher specific energy lithium-ion batteries for applications such as electric vehicles, next generation electronic devices, etc. motivates the research toward electrode materials with larger specific charge capacities. Among several compounds proposed to replace graphite which is conventional material for negative electrode, silicon is very promising material because it has a theoretical specific capacity of 4200 mAh/g due to the incorporation of 4.4 lithium atoms per one Si atom. For comparison, the graphite can be intercalated up to LiC6 compound and his theoretical specific capacity is 372 mAh/g only. So, detail description of lithium absorption process inside silicon is urgent and the second aim of this work was to investigate this process to optimize it for practical using in Li-ion batteries. For that a new method of impurity atoms diffusion rate inside amorphous materials was developed. The method is established on calculations of variety of potential barriers Ebarrier for any possible jump of impurity atom inside the amorphous structure. For crystalline silicon, these barriers were calculated for set of fixed lattice deformations (volume deformations were varied till 9%, shearing deformations- till 9º) by Nudge
19 3
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
Elastic Band (NEB) method [5]. To predict Ebarrier for any local environment of Li atom a linear regression was used for the deformations set data: Ebarrier =a*R1 + b*R2 +c*L +d
(1)
At that regression parameters were chosen as: R1, R2 –radii of circles circumscribed over vertexes of facets of nearest tetrahedrons of Si atoms; L – distance between the circle centers, see Fig.2(a). After regression solving, the calculated parameters were equal: a=-4.62, b=3.12, c=-0.25, d=4.00 with regression inaccuracy: 2.4%. (a)
(b)
Fig. 2. (a) Geometry of Li atom jump through one Si triangle to nearest one inside silicon and the regression parameters (R1, R2, L) used to predict potential barriers Ebarrier of Li jump; (b) Lithium diffusion rate inside amorphous (a-Si) by original method, named Gauss, and inside crystalline silicon (experiment and calculations by different methods)
Then simulation of amorphous silicon was carried out. For that some atoms were removed from Si supercell, consist from 2X2X2 Si unit cells, to reach average experimental amorphous silicon density 2.08 g/cm3 and keep in mind the crystalline silicon density is equal 2.33 g/cm3. After the molecular dynamic (MD) calculations were carried out with temperature slowly decreased from T=2000K to 0K. After that volume of supercell was changed until external pressure became P=0. The both steps were repeated until pressure became ~0 and all atom forces became F<0.05 eV/Å. Finally, for the derived pseudoamorphic silicon structure geometries of all tetrahedrons in which Li atoms can be absorbed were analyzed. Using & & this analysis and the linear regression coefficients, the full set of E barrier ( Ri , R j ) for Li atom jump from & & & tetrahedron centered at Ri into tetrahedron R j was derived. Further, frequencies Q i j of Li jumps from Ri & & & into R j were calculated using of Arrenius formula Q i j A exp(E barrier ( Ri , R j ) / kT ) , where prefactor A was defined using Vineyard formulas [6]. After frequencies determination the diffusion rate D for D
1 k Q a2
6 0 crystalline periodical structure can be found using formula (Einstein equation), where a is defined as the jump length and k0 is correction coefficient responsible for deviation of this structure from the cubic structure. But this method does not fit for amorphous media. So, the universal formula D lim 'R 2 (t ) / 2Zt (Free walk method) for calculations of impurity atom random walk can be used. t of
Here 'R 2 (t ) define rms atom displacement at time t, Z is space dimensionality. But here we have developed the original method (Gauss distribution evolution method) which is established on calculation )& of the temporal evolution of impurity atoms density distribution P ( R, T ) . The initial impurity atom
20 4
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
)&
)& )&
2
distribution centered at any tetrahedron R0 was chosen as gauss function: P(R,T) exp( RR0 /2V02) . For the distribution evolution set of dynamic equations (master equation) were evaluated for increasing time:
dP(i, tk ) dt
¦
W ji P( j , tk )(1 P(i, tk )) Wij P(i, tk )(1 P( j, tk ))
j neib
& & Here W ji define probability of the impurity atom jump from Rj into Ri tetrahedron, calculated with help of Arrenius formula mentioned above. This Gauss method can be applied for any amorphous material, even when the potential barriers are too high to apply conventional MD method. As the result, the lithium diffusion rate inside amorphous and crystalline silicon for different temperatures was defined, see Fig.2(b). One can see lithium diffusion acceleration inside amorphous silicon on 2-3 orders at usual temperatures in comparison with crystalline silicon. This fact was indirectly confirm in experiments [7]. 3. Conclusions By DFT calculations the electronic and geometric structure of Li-Si compounds, ȕ-phase crystal FeSi 2 as well as ȕ-FeSi2 nanofilms and Si/FeSi2 interface were investigated. It was established that ȕ-FeSi2/Si interface can form perfect structure having conductivity along interface surface. In consideration of slabs of ȕ-FeSi2 it was found «square» reconstruction of (001) surface terminated by Si atoms and slight reconstruction of all other surfaces. At that the slab conductivity via Fe layers was detected. Considering Li impurity inside amorphous silicon, the linear dependence of lattice volume on lithium concentration was detected. Using original Gauss distribution evolution method, it was shown that Li diffusion rate inside amorphous silicon is increased at usual temperatures on 2-3 orders in comparison with crystalline silicon. Acknowledgements The work was supported by the federal program "Scientific and pedagogical specialists in innovative Russia 2009-2013". We thank the Institute of Computer Modeling (Siberian Division, RAS, Russia). References [1] Galkin NG, Goroshko DL, Polyarnyi VO, Chusovitin EA, Gutakovsky AK, Latyshev AV, Khang Y. Formation, crystal structure and properties of silicon with buried iron disilicide nanocrystallites on Si (100) substrates. Fizika i tekhnika poluprovodnikov 2007;41:1085. [2] Galkin NG, Goroshko DL, Polyarnyi VO, Chusovitin EA, Korobtsov VV, Balashev VV, Khang Y, Dozsa L, Gutakovsky AK, Latyshev AV, Shamirzaev TS, Zhuravlev KS. Investigation of Multilayer Silicon Structures with Buried Iron Silicide Nanocrystallites: Growth, Structure, and Properties. J. Nanosci. Nanotechnol. 2008;8:527. [3] Vanderbilt D. Soft self-consistent pseudopotentials in generalized eigenvalue formalism. Phys. Rev. B. 1990;41:7892. [4] Kresse G, Furthmöller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996; 6:15. [5] Henkelman G, Uberuaga BP, Jܞnsson H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000;113:9901 [6] Vineyard GH. Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 1957;3:121. [7] Kulova TL, Pleskov YuV, Skundin AM, Terukov EI, Kon'kov OI. Lithium intercalation into amorphous-silicon thin films: An electrochemical-impedance study. Russian Journal of Electrochemistry 2006;42:791-798.
(2)
Physics Procedia
Physics Procedia 0 (2011) 000–000
Physics Procedia 23 (2012) 17 – 20
www.elsevier.com/locate/procedia
Asian School-Conference on Physics and Technology of Nanostructured Materials (ASCO-NANOMAT 2011)
First principal investigation of Fe- and Li- silicon compounds A.S. Fedorova,*, Z.I. Popova, A.A. Kuzubovb, T.A. Kojevnikovab, S.G. Ovchinnikova a
Kirensky Institute of Physics, Akademgorodok 50, Krasnoyarsk, 660036, Russia b Siberian Federal University, av. Svobodny 79,Krasnoyarsk, 660041, Russia
Abstract Electronic and geometric structure of ȕ-phase crystal FeSi2 as well as ȕ-FeSi2 nanofilms and Si/FeSi2 interface is investigated by DFT calculations. It is revealed unusual increasing of the dielectric gap of crystal FeSi 2 under different pressures. It is detected that (001) surface of ȕ-FeSi2 slab, ended by Si atoms, is reconstructed with squares formed by Si atoms. Also FeSi2 nanofilms have conductivity explained by Fe atom layers. It is shown that contact of the (001) Si and ȕ-FeSi2 plate lead to narrow perfect interface having conductivity near Fermi level mainly due to contribution of the silicide surface lavers. Also properties of lithium absorption inside crystal and amorphous silicon as well as inside silicon with impurities were investigated. For that a new method was developed which allow calculating a diffusion rate inside amorphous material when potential barriers are too high to apply conventional molecular dynamic method. It is demonstrated strong increasing of the lithium diffusion rate inside amorphous silicon in comparison with crystal silicon.
©2011 2011Published PublishedbybyElsevier Elsevier Ltd. Selection and/or peer-review under responsibility of Guest Editors of of © B.V. Selection and/or peer-review under responsibility of Publication Committee ASCO-NANOMAT 2011 and Far Eastern Federal University (FEFU)2011 Physics Procedia, Publication Committee of ASCO-NANOMAT Keywords: silicide; ȕ-FeSi2; Li-ion batteries; amorhous silicon; diffusion
1. Investigation of ȕ-FeSi2 crystals, nanofilms and Si/ FeSi2 interface It is known from experiments [1,2] that nanoparticles of transition metal silicides can be produced inside silicon under metal embedding and they can be effective as light emitters and detectors. As
* Corresponding author. Tel.: +7-391-243-2635; fax: +7-391-243-8923. E-mail address: [email protected].
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Publication Committee of ASCO-NANOMAT 2011 and Far Eastern Federal University (FEFU) doi:10.1016/j.phpro.2012.01.005
18 2
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
contrasted to pure silicon, such silicides often have direct optical band gap, so they have good luminescent properties. Also using of magnetic properties of such metals in interface layers of transition metal/silicon looks very promising for spintronics elements constructing. At that electronic and optical properties are changed during decreasing of particle size up to nanometers. Unfortunately, these properties of such nanoparticles and nanofilms were not investigated properly yet. So, one of the aim of the work was to investigate these properties of ȕ-phase of crystal FeSi2 under the pressures as well as ȕFeSi2 nanofilms and Si/FeSi2 interface by ab initio calculations. These calculations were made within DFT formalism using GGA-PBE approach using plane wave basis set and ultra soft Vanderbilt pseudopotentials [3] as implemented in the VASP 4.6 code [4]. Remember that nanoparticles undergo the Laplas pressure that can change the optical gap, dependence of the gap of the ȕ-FeSi2 crystal on pressures was investigated. It was detected unusual increasing of the dielectric gap under different pressures. Also the electronic structure of (001) silicon, ȕ-FeSi2 nanofilms and their interface were investigated after the structures optimization. For electronic density of state (DOS) analysis the technique of separation of normal to the surface layers contribution was proposed. By this technique the conductivity of these nanofilms was revealed. It was shown this conductivity arise from surface layers, at that the contribution of inner layers is quickly decreased under moving away the surface. For calculation of equilibrium (001)Si/ȕ-FeSi2 interface structure, the method of damped molecular dynamics was employed and the system was quenched from temperature Tstart=2000 K to 0 K during annealing, see Fig.1. This temperature value had been chosen because both it is greater than silicon melting point (1687 K) and it allowed to modify the interface geometric structure during ~1000 time steps. One can see that the interface has sharp border that is experimentally confirmed in [1]. The partial DOS analysis of every layer in this structure shows main contribution of iron layers into total interface conductivity.
Fig. 1. Structure of ȕ-FeSi2/Si(001) interface after simulated annealing procedure. Black spheres – Si, white spheres – Fe
2. Investigation of lithium absorption and diffusion inside crystalline and amorphous silicon The demand for higher specific energy lithium-ion batteries for applications such as electric vehicles, next generation electronic devices, etc. motivates the research toward electrode materials with larger specific charge capacities. Among several compounds proposed to replace graphite which is conventional material for negative electrode, silicon is very promising material because it has a theoretical specific capacity of 4200 mAh/g due to the incorporation of 4.4 lithium atoms per one Si atom. For comparison, the graphite can be intercalated up to LiC6 compound and his theoretical specific capacity is 372 mAh/g only. So, detail description of lithium absorption process inside silicon is urgent and the second aim of this work was to investigate this process to optimize it for practical using in Li-ion batteries. For that a new method of impurity atoms diffusion rate inside amorphous materials was developed. The method is established on calculations of variety of potential barriers Ebarrier for any possible jump of impurity atom inside the amorphous structure. For crystalline silicon, these barriers were calculated for set of fixed lattice deformations (volume deformations were varied till 9%, shearing deformations- till 9º) by Nudge
19 3
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
Elastic Band (NEB) method [5]. To predict Ebarrier for any local environment of Li atom a linear regression was used for the deformations set data: Ebarrier =a*R1 + b*R2 +c*L +d
(1)
At that regression parameters were chosen as: R1, R2 –radii of circles circumscribed over vertexes of facets of nearest tetrahedrons of Si atoms; L – distance between the circle centers, see Fig.2(a). After regression solving, the calculated parameters were equal: a=-4.62, b=3.12, c=-0.25, d=4.00 with regression inaccuracy: 2.4%. (a)
(b)
Fig. 2. (a) Geometry of Li atom jump through one Si triangle to nearest one inside silicon and the regression parameters (R1, R2, L) used to predict potential barriers Ebarrier of Li jump; (b) Lithium diffusion rate inside amorphous (a-Si) by original method, named Gauss, and inside crystalline silicon (experiment and calculations by different methods)
Then simulation of amorphous silicon was carried out. For that some atoms were removed from Si supercell, consist from 2X2X2 Si unit cells, to reach average experimental amorphous silicon density 2.08 g/cm3 and keep in mind the crystalline silicon density is equal 2.33 g/cm3. After the molecular dynamic (MD) calculations were carried out with temperature slowly decreased from T=2000K to 0K. After that volume of supercell was changed until external pressure became P=0. The both steps were repeated until pressure became ~0 and all atom forces became F<0.05 eV/Å. Finally, for the derived pseudoamorphic silicon structure geometries of all tetrahedrons in which Li atoms can be absorbed were analyzed. Using & & this analysis and the linear regression coefficients, the full set of E barrier ( Ri , R j ) for Li atom jump from & & & tetrahedron centered at Ri into tetrahedron R j was derived. Further, frequencies Q i j of Li jumps from Ri & & & into R j were calculated using of Arrenius formula Q i j A exp(E barrier ( Ri , R j ) / kT ) , where prefactor A was defined using Vineyard formulas [6]. After frequencies determination the diffusion rate D for D
1 k Q a2
6 0 crystalline periodical structure can be found using formula (Einstein equation), where a is defined as the jump length and k0 is correction coefficient responsible for deviation of this structure from the cubic structure. But this method does not fit for amorphous media. So, the universal formula D lim 'R 2 (t ) / 2Zt (Free walk method) for calculations of impurity atom random walk can be used. t of
Here 'R 2 (t ) define rms atom displacement at time t, Z is space dimensionality. But here we have developed the original method (Gauss distribution evolution method) which is established on calculation )& of the temporal evolution of impurity atoms density distribution P ( R, T ) . The initial impurity atom
20 4
A.S. Fedorov et al. / Physics Procedia 23 (2012) 17 – 20 A.S. Fedorov et al./ Physics Procedia 00 (2011) 000–000
)&
)& )&
2
distribution centered at any tetrahedron R0 was chosen as gauss function: P(R,T) exp( RR0 /2V02) . For the distribution evolution set of dynamic equations (master equation) were evaluated for increasing time:
dP(i, tk ) dt
¦
W ji P( j , tk )(1 P(i, tk )) Wij P(i, tk )(1 P( j, tk ))
j neib
& & Here W ji define probability of the impurity atom jump from Rj into Ri tetrahedron, calculated with help of Arrenius formula mentioned above. This Gauss method can be applied for any amorphous material, even when the potential barriers are too high to apply conventional MD method. As the result, the lithium diffusion rate inside amorphous and crystalline silicon for different temperatures was defined, see Fig.2(b). One can see lithium diffusion acceleration inside amorphous silicon on 2-3 orders at usual temperatures in comparison with crystalline silicon. This fact was indirectly confirm in experiments [7]. 3. Conclusions By DFT calculations the electronic and geometric structure of Li-Si compounds, ȕ-phase crystal FeSi 2 as well as ȕ-FeSi2 nanofilms and Si/FeSi2 interface were investigated. It was established that ȕ-FeSi2/Si interface can form perfect structure having conductivity along interface surface. In consideration of slabs of ȕ-FeSi2 it was found «square» reconstruction of (001) surface terminated by Si atoms and slight reconstruction of all other surfaces. At that the slab conductivity via Fe layers was detected. Considering Li impurity inside amorphous silicon, the linear dependence of lattice volume on lithium concentration was detected. Using original Gauss distribution evolution method, it was shown that Li diffusion rate inside amorphous silicon is increased at usual temperatures on 2-3 orders in comparison with crystalline silicon. Acknowledgements The work was supported by the federal program "Scientific and pedagogical specialists in innovative Russia 2009-2013". We thank the Institute of Computer Modeling (Siberian Division, RAS, Russia). References [1] Galkin NG, Goroshko DL, Polyarnyi VO, Chusovitin EA, Gutakovsky AK, Latyshev AV, Khang Y. Formation, crystal structure and properties of silicon with buried iron disilicide nanocrystallites on Si (100) substrates. Fizika i tekhnika poluprovodnikov 2007;41:1085. [2] Galkin NG, Goroshko DL, Polyarnyi VO, Chusovitin EA, Korobtsov VV, Balashev VV, Khang Y, Dozsa L, Gutakovsky AK, Latyshev AV, Shamirzaev TS, Zhuravlev KS. Investigation of Multilayer Silicon Structures with Buried Iron Silicide Nanocrystallites: Growth, Structure, and Properties. J. Nanosci. Nanotechnol. 2008;8:527. [3] Vanderbilt D. Soft self-consistent pseudopotentials in generalized eigenvalue formalism. Phys. Rev. B. 1990;41:7892. [4] Kresse G, Furthmöller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996; 6:15. [5] Henkelman G, Uberuaga BP, Jܞnsson H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000;113:9901 [6] Vineyard GH. Frequency factors and isotope effects in solid state rate processes. J. Phys. Chem. Solids 1957;3:121. [7] Kulova TL, Pleskov YuV, Skundin AM, Terukov EI, Kon'kov OI. Lithium intercalation into amorphous-silicon thin films: An electrochemical-impedance study. Russian Journal of Electrochemistry 2006;42:791-798.
(2)