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1 ISSN , : ,.,. Si(001):..., 17,, 03164,, Si(001),., - B3LYP 6-31 G**., >Si Si<, >Si Ge< >Ge Ge<. : Si(001),,,, -,, [1].,, -.,. ~10. 0 D. 0 D, Si(001) -. Ge/Si [2]., Ge/Si, -, - Si(001),,,., -.,. -.,.,.,.,

2 Si(001),,.., Ge/Si, Si(111). Si(001) Si(001) (. 1), Si(111), (111), Ar + = 1173 K [3]., Si(001)(1 1) (2 1) [4] (. 2) (4 2) [5]. 3). He - Si(001) (2 2) [3] (. 4). - Si(001)(1 1), ), Si Si sp 3. - Si(001)(2 1) Si(001)(2 2) >Si Si<.,. -. Si Si >Si Si< Si(001) ( ),, Si Si ( ) Si(001) [6]. Si Si, - Si(001)(2 1) (. 2)., Si Si Si(001)(2 1). Si Si -, 180,, 180,.,., - Si(001)(p-2 2) Si(001)(c-2 2). Si,,. Si(001)(c-4 2) Si(001) ISSN

3 .,.,.. 2. Si(001)(2 1) [4]. 3. Si(001)(4 2) [5]. 4. Si(001)(2 2) [3] [7] -, Si(001) -. [8], - - Si(001).,,.,,, (HF). ( ),,,. (HO) 258 ISSN

4 Si(001) (LU),. (MCSCF) [9].. (MP) [10] (CI) [11]. (DFT) [12, 13], [14, 15],,,,,. - (MRMP). [16] >Si Si<, - LUMO.., [16], Si(001),.. LUMO -, (RHF),., -,. - Si(001)., [16 19] MCSCF, Si(001) (),, - (HF DFT) [20 24], -. [20],,,. [20] Si 9 H 12, Si(001), DFT, MCSCF (CAS) [10], CASSCF (4,4)., DFT -, CASSCF (4,4) ( C2 ). MRMP, DFT CASSCF (4,4),, 0.9., [20], Si 9 H 12,, MRMP. MRMP,,, -.., Si 9 H 12, DFT Si(001). [21 23], DFT,,. -,, 1.5 3, ISSN

5 .,., , DFT. [8] - Si(001) - ( ) - >Si Si<. Si 15 H 16 ( ), Si 20 H 21 () Si 33 H 28 ( )., CASSCF (4,4), CASSCF (6,6) CASSCF (10,10). Si 15 H G* [25], Si 20 H 21 Si 33 H 28 HW(d) [26]. >Si Si<. -,,.. Si(001)..,.. 1). MRMP (MRMP2), - CASSCF.,. [8],, -,,., DFT, Si(001) - Si 15 H 16 2 CASSCF (4,4) 6-31G* Si 20 H 21 3 CASSCF (6,6) HW (d) Si 33 H 28 5 CASSCF(10,10) HW (d) - (TOF SARS) Si Si, Å 2.28; ; 2.25; ; 2.24; [8] [8] [8] 2.26±0.1 [27] 260 ISSN

6 Si(001) [8] [28] - DFT [11], [29]. -,, DFT [30],. - - [31]. [28],, [8],. 1) - DFT B3LYP [14] Si(001),,. - DFT,,. 2) MRMP2 DFT -. DFT, 1.54 ( ), 4., - MRMP2,, - (4.1, ). 3) -,, DFT. -, -. [28], DFT (, MRMP2). [32] - >Ge Ge<, >Si Si< >Si Ge< Si(001)(1 2), Si(001)(2 2), Ge(001)(1 2) Ge(001)(2 2). DFT - (LGA) [12] - [33]. -, [34]., ,. 7,.. 2 [32], , -, [27]. (1 2) (2 2) Si(001). [35], >Si Si<. ISSN

7 .,.,. >Si Si< - Si(001),,., HF [8], DFT [32, 36],,,.. 5. Si(001)(1 2) Si(001)(2 4) [32] 2., Si(001),, * ( Å, ) [32] A B 1 B D 1 D 2 d 1 d 2 D 3 t 1 Si(001) (1 2) Si(001) (2 2) Si(001) (1 2)-SiGe(up) Si(001) (2 2)-SiGe(up) Si(001) (1 2)-Ge Si(001) (2 2)-Ge *. 5,, Si(001) [8, 28, 36, 37].., DFT, RHF MP2 -, - RHF, [38] (. 6). [28], MCSCF, Si(001),, = 0.,,, - - ( HF (UHF) [39]),, = 0, [28].,,,, , >Si Si<, Si(001) 262 ISSN

8 Si(001)., - [40] = 300 K. () 180., K,,, [41, 42] Si,. 40 K -, [41, 42], -, - [43]. >Si Ge< Si(001), -,,, 400 Ge Si(001)(2 1),, [44] Ge/Si(001), Si(001). -,, Ge/Si(001), 5 [45]., [46], Si(001),,, , [47] -, Si(001) Ge Si. - Ge/Si(001)(2 1) [38]. Ge/Si(001) - Si(001). Si(001) Ge(001),, Si(001). [30],,,.. Si(001)(2 1) Ge(001)(2 1) Å. - [34]. LGA [12], [48]. - () - >Si Si<, - HO Si, (down- ), Si (up-). LU,, - down Si.. 7, Si(001), Ge Si (. 7 ). >Ge Ge< (. 7 ), - Ge Si(001).. 7, >Ge Ge< ISSN

9 .,.,. (. 7 ), Ge Si Si(001)(2 1). - Ge,, -,,, Ge up (. 7 ),. 7 ) down. Ge Si(001), up Ge >Ge Si<. - [47],, Si(001)(2 1) up Ge (. 7 ). (. 7, ) - Si up >Ge Si<.,, Si(001) (2 2),, (1 2) [49]. - Ge/Si(001).. 7., Si(001). ( ) >Ge Ge< (). (), Ge Si(001) [38] >Ge Si< ( = 20.8 ) >Si Si< Si(001) (2 1) ( = 16.1 ), >Ge Ge< Ge(001) (2 1) ( = 18.7 ).,. >Ge Ge<., [50], dge-ge 2.60 Å. 2.55±0.04 Å, =12.4 [51]. 264 ISSN

10 Si(001) [52] d Ge-Ge 2.51±0.01 Å. d, Ge-Ge [51] [52],,,, [52]. [38], - Si Ge. Si Ge ,,, up. - Si Ge,. 7., [38],, Si Ge., Ge i T pexp E/ kt / exp( E / kt), i i B j B j [38], T = 1000 K 11 %.,., [38] Si(001)(2 1),,, up- Ge (. 7 ), down, , 12 %., - Ge, Si(001)(2 1). >Ge Si< Si(001) [53]. DFT [11]. LGA - [48] [33]., Si Å (5.43 Å). Si(001)(2 1) :,.. Si(001) Si Si, dsi-si 2.27 Å; Si Si sub dsi-si 2.30 Å. [54] ( dsi-si 2.23, sub dsi-si 2.30 Å), LGA. Si(001)(2 1) sub : dsi-si 2.27Å; dsi-si Å down- up- Si (E) [54] : ISSN

11 .,.,. sub dsi-si 2.27, dsi-si Å, 18.3, E =0.12±0.01., [38], - -,. - Si(001)(2 1) [55]. >Ge Si< [53].,, Si(001) (. 8), Ge Si dsi-ge 2.34 Å, Si Ge sub dsi-ge 2.34 Å. d sub Si-Si Si(001)(2 2), >Si Ge< Si(001)(2 1), >Ge Si< (. 9) 0.28., dsi-ge 2.41, dsi-si 2.30 d Si-Ge 2.44 Å, = 20.5., down- Si sp 3 sp 2, up- Ge sp >Ge Si< >Si Si< Si(001)(2 1)., :, Ge (1.22 Å) Si (1.17 Å) [56]. Ge >Ge Si<, Ge/Si(001). >Ge Si<,, Si(001)(2 4). 266 ISSN

12 Si(001) :, - - (. 9 ), (. 9 ),, [57].. d Si-Ge 2.41 Å = ,. 9. Si-Ge 2.42 d Å = Si(2 4), >Si Ge< : - (); (), [53] Si Ge Ge/Si(001), [57] [38]. [53], >Ge(up) Si(down)< Si(up) >Si Si< Si(001) Ge Si Ge,.,. - Si(001),,». - [58]., [59 61], Ge Si(001), >Ge Ge<.,, (. 10). (n) [62 64], n,,. n,, 8, - n 12. :,. ISSN

.,.,. n -, Ge. - m, n. [58] DFT (GGA) -,, -.,, 5 Å.,. 10, n 4 12 n,.. [60, 63], -.. 10. Si(001), n = 6 Si(001) : dge-ge 2.55 Å, sub dge-si 2.48 Å 2.39 Å = 19.2. Si(001)(2 2) E ) ( 9.64.

13 .,.,. n -, Ge. - m, n. [58] DFT (GGA) -,, -.,, 5 Å.,. 10, n 4 12 n,.. [60, 63], Si(001), n = 6 Si(001) : dge-ge 2.55 Å, sub dge-si 2.48 Å 2.39 Å = Si(001)(2 2) E ) ( E Si(001)(2 2), Ge 2, Si(001)(2 2),,, -. E f (n),, - E fin E init, ; E init ; E, fin,,, n. (.. 11), Ef ( n) n, n > 8. n [60, 61].,, 0 E ( n ) n, E ( n ) 0 f f. [58] -,. Si Si,, 2.54 Å 2.36 Å, 268 ISSN

14 Si(001).,, 0.65 Å. up- down- Ge Ge 2,, Si Å,,. E ( n) [58] f,,, n 8 12., i exp ( Ei / kt B ), E i n: 1 ; 2 [58] -,., -, Ge Si(001),., n, n = 8,, Ge 2,. [58], : ) Si(001), ; ) -, - ; ) n = 8, ; ) - -, Si Si,. Si(001), - >Ge Si< >Ge Ge<,,,,. - [65]., [57] >Ge Si<, Ge Si(001)(2 1). Ge 3d, Si 2., Si(001)(2 1) (0,1 ) - >Ge Si<. [57], Si(001) Ge Si up >Si Si<. ISSN

15 .,.,.,.,,. 100,,. -, [57], Si(001)(2 1) >Ge Si< Ge Si 2.43±0.1 Å 31±2 (. 12). [65],. -, [52, 66] Ge 1. Ge Si 2.63±0.01 Å., 0.1, >Ge Si<.. 12, - -, [2 4]). >Ge Si< Si(001) Ge up, Si down. [67] () (), [57] - Si(001), Ge, - >Si Si< >Ge Si<,,,.,,, B3LYP 270 ISSN

16 Si(001) 6-31 G**, Si(001) DFT (B3LYP, 6-31 G**),. Si(001):.,.,...., 17,, 03164,, Si(001),.,, B3LYP 6-31 G**., >Si Si<, >Si Ge< >Ge Ge<. : Si(001),,, Structure and properties of primary surface formations on the Si(001) face: quantum chemical researches O.I. Tkachuk, M.I. Terebinska, V.V. Lobanov Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine, 17 General Naumov Str., Kyiv, 03164, Ukraine, tkachuk_olya@bigmir.net A comparative analysis has been performed on the applicability of quantum chemical methods of different complicability to describe the structure and properties of the clean Si(001) surface, and of that containing a few atoms of germanium. It has been found that the density functional theory within the cluster approximation involving the exchange-correlation functional B3LYP and 6-31 G** basis set is the most rational from the point of view of reproducibility of experimentally found results and considering the moderate cost of computing time and computer resources. It is just this approximation of quantum ISSN

17 .,.,. chemical calculations that properly reproduces the lengths of >Si Si<, >Si Ge<, and >Ge Ge< surface ers bonds as well as the experimentally justified fact of their buckling. Keywords: Si (001) face, Ge atoms on surface, density functional theory, cluster approximation 1..,.,.. - : // , Brunner K. Si/Ge nanostructures // Rep. Prog. Phys V. 65. P ,.. :, Kinoshita T., Kono S., Sagawa T. Angleresolved photoelectron-spectroscopy study of the Si(111) 3 3 -Sn surface: Comparison with Si(111) 3 3 -Al, -Ga, and -In surfaces // Phys. Rev. B V. 34. P Northrup J.E. Si(111) 3 3 -Al: an adatominduced reconstruction // Phys. Rev. Lett V. 53. P Srivastava G.P., Weaire D. The theory of the cohesive energies of solids // Adv. Phys V. 36, N 4. P Chiarotti G., Nannarote S., Postore R., Chiarotti P. Optical absorption of surface states in ultrahigh vacuum cleaved (111) surfaces of Ge and Si // Phys. Rev V. B4. P Jung Y., Akinaga Y., Jordan K.D., Gordon M.S. An ab initio study of the structure of two-, three- and five-er silicon clusters: An approach to the Si(100) surface // Theor. Chem. Acc V P Schmidt M.W., Gordon M.S. The construction and interpretation of MCSCF wavefunctions // Annu. Rev. Phys. Chem V. 4. P Pople J.A., Krisman R., Schleger H.B., Binkley J.S. Electron correlation theories to the study of simple reaction potential surfaces // Int. J. Quantum Chem V. 14, N 5. P Yong D.C. Computation Chemistry. A Practical Guide for Applying Techniques to Real-world Problems. N.Y.: Wiley Interscience, p. 12. Parr R.G., Yang W. Density-functional Theory of Atoms and Molecules // Oxford: Oxford Univ. Press p. 13. Jones R.O., Gunnarsson O. The density functional formalism, its applications and prospects // Rev. Mod. Phys V. 61, N 3. P Becke A.D., Burke K. Correlation energy of an inhomogeneous electron gas: A coordinatespace model // J. Chem. Phys V. 88, N 2. P Becke A.D. Density-functional thermochemistry. 3. The role of exact exchange // J. Chem. Phys V. 98. P Redondo A, Goddard W.A. III Electronic correlation and the Si(100) surface: Buckling versus nonbuckling // J. Vac. Sci. Technol V. 21. P Paulus B. Calculations for the reconstruction of the Si(100) surface // Surf. Sci V P Shoemaker J., Burggraf J.W., Gordon M.S. An ab initio cluster study of the structure of the Si(001) surface // J. Chem. Phys V P Gordon M.S., Shoemaker J.R., Burggraf L.W. Response to Comment on An ab initio cluster study of the structure of the Si(001) surface // J. Chem. Phys V P Hess J.S., Doren D.J. Comment on An ab initio cluster study of the structure of the Si(001) surface // J. Chem. Phys V P Konecny R., Doren D.J. Adsorption of water on Si(100)-(2 1): A study with density functional theory // J. Chem. Phys V P Yang C., Kang H.C. Geometry of er reconstruction on the C(100), Si(100), and Ge(100) surfaces // J. Chem. Phys V P Penev E., Kratzer P., Scheffler M. Effect of the cluster size in modeling the H 2 desorption and dissociative adsorption on Si(001) // J. Chem. Phys V P ISSN

18 Si(001) 24. Yang C., Lee S.Y., Kang H.C. An embedded cluster study of er buckling on the Si(100) surface // J. Chem. Phys V P Davidson E. R., Feller D. Basis set selection for molecular calculations // Chem. Rev V. 86, N 4. P Hay P.J., Wadt W.R. Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg // J. Chem. Phys V. 82. P Wang Y., Shi M., Rabalais J. W. Structure of the Si{100} surface in the clean (2 1), (2 1)- H monohydride, (1 1)-H dihydride, and c(4 4)-H phases // Phys. Rev B48. P Jung Y., Shao Y., Gordon M.S. et al. Are both symmetric and buckled ers on Si(100) minima? Density functional and multireference perturbation theory calculations // J. Chem. Phys V P Paz O., da Silva A.J.R., Saenz J.J., Artacho E. Electron correlation in the Si(001) // Surf. Sci V P Neugebauer J., Scheffeler M. Adsorbatesubstrate and adsorbate-adsorbate interactions of Na and K adlayers of Al(111) // Phys. Rev. B V. 46, N 24. P Artacho E., Yndura F. Proposal for symmetric ers at the Si(100)-2 1 surface // Phys. Rev. Lett V. 62. P Gay S.C.A., Srivastava G.P. Dimer length variation for different reconstructions of Si, Ge, and mixed Si-Ge ers on Si(001) and Ge(001) substrates // Phys. Rev V. B 60. P Perdew J.P., Zunger A. Self-interaction correction to density-functional approximations for many-electron systems // Phys. Rev. B V. 23. P Bachelet G.B., Hamann D.R., Schlu ter M. Pseudopotentials that work: From H to Pu // Phys. Rev. B V. 26. P Fritsch J., Pavone P. Ab initio calculation of the structure, electronic states, and the phonon dispersion of the Si(100) surface // Surf. Sci V. 344 P Healy S.B., Filippi C., Kratzer P. et al. Role of electronic correlation in the Si(100) reconstruction: a quantum Monte Carlo study // Phys. Rev. Lett V. 87. P Olson R.M., Gordon M.S. The structure of the Si 9 H 12 cluster: A coupled cluster and multireference perturbation theory study // J. Chem. Phys V P Jenkins S.J., Srivastava G.P. Theoretical evidence concerning mixed er growth on the Si(001)(2 1) Ge surface // J. Phys.: Condens. Matter V. 8. P People J.A., Gill P.M.W., Handy N.C. Spinunrestricted character of Kohn-Sham orbitals for open-shell systems // Int. J. Quantum Chem V. 4. P Wolkow R.A. Direct observation of an increase in buckled ers on Si(001) at low temperature // Phys. Rev. Lett V. 68. P Kondo Y., Amakusa T., Iwatsuki M., Tokumo H. Phase transition of the Si(001) surface below 100 K // Surf. Sci V P. L318 L Lay G.Le, Cricenti A., Ottaviani C., et al. Evidence of asymmetric ers down to 40 K at the clean Si(100) surface // Phys. Rev. B V. 66. P Hata K., Yoshida S., Shigekawa H. p(2 2) Phase of buckled ers of Si(100) observed on n-type substrates below 40 K by scanning tunneling microscopy // Phys. Rev. Lett V. 89. P Mo Y-W, Savage D.E., Swartzentruber B.S., Lagally M.G. Kinetic pathway in Stranski- Krastanov growth of Ge on Si(001) // Phys. Rev. Lett V. 65. P Sasaki M., Abukawa T.A., Yeom H.W. et al. Auger electron diffraction study of the initial stage of Ge heteroepitaxy on Si(001) // Appl. Surf. Sci V. 82/83. P Patthey L., Bullock E.L., Abukawa T. et al. Mixed Ge-Si er growth at the Ge/Si(001)-( 2 1) surface // Phys. Rev. Lett V. 75. P Cho J-H., Jeong S., Kang M-H. Final-state pseudopotential theory for the Ge 3d-corelevel shifts on the Ge/Si(100)-(2 1) surface // Phys. Rev. B V. 50. P Ceperley D.M., Alder B.I. Ground state of the electron gas by a stochastic method // Phys. Rev. Lett V. 45. P Dabrowski J., Pehlke E., Scheffler M. Calculation of the surface stress anisotropy for the buckled Si(001)(1x2) and p(2x2) surfaces // Phys. Rev. B V. 49. P ISSN

19 .,.,. 50. Fontes E., Patel J.R., Comin F. Direct measurement of the asymmetric er buckling of Ge on Si(001) // Phys. Rev. Lett V. 70. P Fontes E., Patel J. R., Comin F. Bond-length of Ge mers at Si(001) Reply// Phys. Rev. Lett V. 72. P Oyanagi H., Sakamoto K., Shioda R. et al. Ge overlayers on Si(001) studied by surfaceextended X-ray-absorption fine structure // Phys. Rev. B V. 52. P Niwa R. H. Theoretical study of Si Ge mixed ers on Si(001) surfaces // Surf. Sci V P Ramstad A., Brocks G., Kelly J. P. Theoretical study of the Si(100) surface reconstruction // Phys. Rev. B V. 51. P Lin D. S., Miller T., Chiang T. C. Dimer charge asymmetry determined by photoemission from epitaxial Ge on Si(100)-(2 1) // Phys. Rev. Lett V. 67. P :.-.., Chen X., Patthey L., Bullock E. L. et al. Atomic geometry of mixed Ge-Si ers in the initial-stage growth of Ge on Si(001)2 1 // Phys. Rev. B V. 55. P Oviedo J.A. First principles study of submonolayer Ge on Si(001) // Surf. Sci V P Keöhler U., Jusko O., Mëuller B. et al. Layerby-layer growth of germanium on Si(100): strain-induced morphology and the influence of surfactants // Ultramicroscopy V P Tersoff J. Stress-induced layer-by-layer growth of Ge on Si(100) // Phys. Rev. B V. 43. P Tersoff J. Missing ers and strain relief in Ge films on Si(100) // Phys. Rev. B V. 45. P Chen X., Wu F., Zhang Z., Lagally M. G. Vacancy-vacancy interaction on Ge-covered Si(001) // Phys. Rev. Lett V. 73. P Liu F., Lagally M. G. Interplay of stress, structure, and stoichiometry in Ge-covered Si(001) // Phys. Rev. Lett V. 76. P Voigtlëander B., Këastner M. Evolution of the strain relaxation in a Ge layer on Si(001) by reconstruction and intermixing // Phys. Rev. B V. 60. P Patthey L., Bullock E. L., Abukawa T. et al. Mixed Ge-Si er growth at the Ge/Si(001)- (2 1) Surface // Phys. Rev. Lett V. 75. P Cho J. H., Kang M. H. Atomic structure of the Ge/Si(100)(2 1) surface // Phys. Rev. B V. 59. P Iwawaki F., Tomitori M., Nishikawa O. STM study of Ge overlayers on Si(001) // Surf. Sci V P , ISSN

Prerequisites for reliable modeling with first-principles methods. P. Kratzer Fritz-Haber-Institut der MPG D Berlin-Dahlem, Germany

Prerequisites for reliable modeling with first-principles methods P. Kratzer Fritz-Haber-Institut der MPG D-14195 Berlin-Dahlem, Germany Prerequisites for modeling (I) Issues to consider when applying