Moritz, Wolfgang

Wolf, D.

English

Universität München: Elektronischen Publikationen

Determination of domain distribution by analysis of LEED beam profiles

Open Access LMU

PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON SOLID SURFACES (A triennal Meeting of the International Union for Vacuum Science, Technique and Applications) and THE THIRD EUROPEAN CONFERENCE ON SURFACE SCIENCE (A topical annual Meeting sponsored by the European Physical Society) September 22 - 26, 1980 Cannes, France Guest Editors : D.A. Degras Commissariat ä TEnergie Atomique M. Costa Centre National de la Recherche Scientifique Host : SOCIETE FRAN£AISE DU VIDE Paris (F) Volume I I (pages 721 ä 1448) Supplement ä la Revue «Le Vide, les Couches Minces» n° 201 . A Bay H.L. Bean S J . Beau me R. 1349 551 95 C Abbati I . 959,1023, Beaunier L. 606 Ca bane Brouty F. 585 1026,1185 Beckmann P. 1299 Calandra C 1162,1185 A bar dam 0. 622 BellierJ.P. 594 Callenas A. 1178 A bo η Μ. 517 Benedek G. 738,818 Cantini P. 830 Achate CA. 1357 Benndorf C. 263, 353 Capiomont Y. 1181 AdachiH. 176 Bennett CO. 529 Cassuto A. 399,509 Ageev G.N. 444,1263 Benninghoven A. 1273,1299 Cavanagh R.R. 750 Akhten P. 42 Bensoussan M. 1197 Celli V. 815 Akimoto K. 1015 Bergner J. 1346 Celotta R J . 1045,1060 Akimov A.S. 1369 Berks A. 213,521 Cerrina F. 1162 Albano E. 291 Berndt K. 370 Chadderton L.T. 933 Albuquerque E.L. 766 BerndtW. 1133 Chadi O.J. 699,1033 Algra A J. 703,1419 Berning G.L.P. 1353 Chao F. 602 Allan G. 11,794 Beuel Ε. 462 Chadwick D. 423, 551 Allen G.C. 453 Bertolini J.C. 209 Chandesris D. 1158 Allison W. 873 Bertoni CM. 1185 Charbonnier M. 1342 Alloneau J.M. 119 Bertonil T. 548 Chazalviel J.N. 634 Alnot M. 399, 509 Besenthal Κ. 345 Cheyssac P. 626 Ais-Nielsen J. 112 Betz G. 1225 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R.B. 842 Fresart (de) E. 431 Dobrzynski L. 50, 774 Freund HJ. 1323 Doyen G. 145 Friedenberg A. 506 Η Drinkwine M. 1380 Froelicher M. 581 Dubois L.H. 287 Froment M. 606 Ducastelle F. 1193 Fusy J. 509 Haberland H. 1248 Ducros R. 329 Habraken F.H.P.M. 555 DudekHJ. 1365 Hachicha S. 498,1125 Dufayard D. 622 G Hagstrum H.D. 1245 Duke C.B. 1407 Hamelin A. 594 Dumas P. 1384 Hanawa T. 987 Dumoulin P. 22 Galli E. 715 Hansen F.Y. 126 Durand R. 573,622 Ganachaud J.P. 164 Hansson G.V. 699,1033 Duraud J.P. 922 Garbout A. 335 Haul R. 366 Dykhne A.M. 96 Garcia N. 815,818 Hay den B. 1125 Garcia-Moliner F. 774 Hayden B.E. 453 Garin F. 420 Haydock R. 1267 Ε Garrigos R. 626 Hayek Κ. 533 Garrison B.J. 1411 Heiland G. 991,1425 Garwin E.L. 1044,1092 Η enzler M. 967 Eberhardt W. 1407 Gaspard J.P. 7,951 Η eras J.M. 291 Ehrhardt J.J. 399,509 Gauthier J.P. 466 Hermann K. 134,196 Eicke A. 1273 Gentil P. 619 Heyrovsky J. 883 Engel T. 801,815,861 Gerardy J.M. 758 Hilaire L. 26 Engelhardt H.A. 1119 Gergely G. 1392 Hilleret N. 1221 Erbudak M. 1056 Ghafouri S.N. 1085 Hincelin G. 1166 Erhart H. 345 Gibbs R A 427 Hinnen C. 630 Erlewein J. 34 Giber J. 38 Hirai Y. 1089 Erljen Z. 865 Gibson W.N. 673 Hirasawa S. 696 Ert iG. 104,108, Gilles J.M. 431,470 Ho P.S. 1376 203,1248,1255 Gillet E. 669 Hoffmann F.M. 307,335 Esser P. 436 Gisler E. 1108 Η ofmann P. 498,541 Etzkorn H.W. 1217 Giuletti D. 46 Η ofmann S. 34 Glassl H. 533 Hohfeld A. 263 Gojsa S.N. 947 Hoinkes H. 87,822 F Goldstein B. 1003 Holland S.P. 427 Gonzalez L. 229 HollowayP.H. 1372 Goodale J.W. 390 Hollo way S. 1154 FabreW. 1096 Göpel W. 366,436, Honjo G. 267, 683, If adley CS. 865 995,1011,1040 1007 Fasana A. 1185 GorohT. 696 Hoogewijs R. 180 Fasolino A. 679 Goto K. 1081 Hopster H. 275 Faure R. 573,622 Gozzini A. 46 Hora R. 1147 Feder R. 1104 Grefte (de) H.A.M. 1238 Höring N.J.N. 83,918 Feierabend R. 436 Greiner L. 822 Horn K. 335,541 Fei eher G.P. 1045 Gries W.H. 1122 Hosoki S. 1089 c Houston J.E. 205 Kassa bovS.G. 1263 Landolt N. 1064 Hoyt E.W. 1092 KätzelW. 370 Lange W. 1273 Huber M. 663 Κ a wa bat a S. 696 Langer E. 217 Hugot-LeGoff A. 581 Kawasaki Κ. 317 Langowski H.C. 995 Hulpke E. 846 Kawase S. 1089 Langeron J.P. 1277,1346 Hülse J. 104,108 Kawazu Α. 955,1015 Lapeyre G J . 1162 Hupkens T.M. 1229 Kempa Κ. 907 Lapujoulade J. 826,857 Kessler R.W. 1338 Larere A. 22 Kinbara A. 61 Lassabatere L. 1129,1137, 1 King D.A. 237,403 1141 Kinqham D. 1267 Lassailly Y. 1158.1204 Kinöshita K. 6/3 Laszloffy L. 1052 Ibach H. 221,458 Kinosita K. 696 Lauter J. 122 Ibanez J. 415 KiokaT. 317 LeBossoJ.C. 184 Ichimura S. 922 Kirby R.E. 1044,1092 Lecante J. 1158,1204 Ichinikawa T. 983 Kirschneri. 1052 Lecayon G. 633 Ignatiev A. 677 Kirschner J. 19,1104, Le Cruer Y. 826 Ilyasov A.Z. 1303 1217 Lefort M. 826 Ishi S. 141,853 Kirstein W. 345 LSgare* P. 26, 537 Ishikawa Y. 983 Kiskinova M.P. 502 Legendre JJ. 663 I toT . 440 Kiso G. 1052 Le Gressus C. 283, 638, Kiso J. 213,521 922,983,1400 Kitson M. 474 Le H6ricy J. 1277,1346 J Klauber C. 1170 Lehmpfuhl G. 569 Klein R. 361 Lehwald S. 221 Klemperer D.F. 453 Lejay Y. 826,857 Jablonski A. 1307 Klissurski D.G. 545 Le Moel A. 638 Jackson D.P. 659 Kobayashi K. 683 Levi A.C. 812 Jacobi K. 256 Koestner R J. 287 Lewis J.E. 1376 Jacucci J. 54 Kofman RJ. 626 Lichtman D. 1380 Jardin C. 466 Kohl 0. 991 Liänard G. 419 Jaunet J. 77 Kolb D.M. 256,569, Lindau 1. 979 Jirikowsky M. 1273 614 Lindauer G. 537 Jobic H. 746 KonoS. 665 Lindgren S.A. 349 Johansson L.l. 1178 Kornelsen E.V. 1415 Lindroos M. 707,1174 Johansson P.K. 156 Koval A.F. 947 Lipski M. 407 Johnson G. 933 Koziol C. 299 Litovchenko G. 895 Joud J.C. 65 Kramer H.M. 217 Lloyd J.T. 665 Jovancicevic V. 581 Kramer R. 533 Long K.A. 887 Jugnet Y. 1159, 1204 Krebs HJ. 411 Lopez J. 184, 794 Junack M. 1273 Kühnemann B. 1040 Lopez-Sancho J.M. 332,376 Jupille J. 509 Küppers J. 104,108, Lopez-Sancho M.P. 332 1248,1255 Lorenzi (de) G. 54 LosJ. 849 Κ Losch W. 19,1357 L Lourens J.A.J. 1353 Lucchesi M. 46 Kaarman H. 822 Luches A. 715 Kahn A. 711 Ladouceur H.D. 786 Luitjens S.B. 703,1419 Kamarinos G. 619 Lambert R.M. 242,381, Lukovits 1. 910 Kam be Κ. 569,879 474 Lundström 1. 482 Kanamori Η. 683 Lampe U. 366, 1011 Lüth H. 762 Kanchera N.M. 545 Lamson S.H. 152 Lutz H. 1425 Kansky J. 971 Landoldt D. 1319 LuxJ. 991 D Μ Morgan A.E. 1238 Oura K. 987 Morgen P. 303,1361 Oyama T. 955,1015 Moritz W. 1295 Maca F. 1151 Mosser A. 1330 MadeyT.E. 205 Mowery R.L. 786 Ρ Madix RJ. 448 MrozS. 299 Magil J. 887 Muchielli F. 1252 Maglietta M. 365 Mulak A. 1112 Pajonk G.M. 529 Mag υ ire H.G. 929 Müller K. 1315 Palau J.M. 1129,1137 Mahmoud E.A. 1085 Muller N. 248 Palcewska W. 407 Μ aire G. 26.490, Mummy Μ. 394 Papageorgopouios C. 688 537 Munoz-Yague Α. 1096 Papp H. 245 Makh S.S. 1209 Murray CA. 770 Parke A.W. 699 Manghi F. 1185 Parsons R. 610, 630 Mann K. 846 Pastorino P. 838 Maradudin A.A. 50,891 Ν Paterson P.J.K. 1287 Marcus P. 610 Pedersen F.F. 563 Marilier A. 314 Pellerin F. 283,1400 Marinova T.S. 192,1263 Nagai S. 141,853 Pennino (del) U. 959,1026 Mark P. 711 Namba H. 470 Perraillon B. 69 Marti C. 119,122 Nassisi U. 715 Persson B.N.J. 790 Martin B.G. 939 NekerF.P. 462 Pescia D. 1056 Martinas K. 1052 Neumann M. 357 PessaM. 707,1174 Marvin A.M. 754 Neyens A. 339 Peto G. 971 Marx R. 100 Nguyen T.T.A. 1181 Philibert J. 77 Masri P. 742 Niehaus A. 1229 Picq G. 577 Massignon 0. 922,983 Nielsen M. 112 Pierce D.T. 1045,1060 Mathieu HJ. 1319 Niewenhuys B.E. 279 Pindor A J . 707 Mattera L. 838 Nishijima M. 205 Piqueras J. 1096 Mattews W. 1287 Nizzoli F. 754 Pivin J.C. 283 Matz R. 762 Nöbl C. 353 Plummer E.W. 1323,1407 Maurel E. 826 NoffkeJ. 134 Pockrand I . 778 Mazur A. 975 Nooman J.R. 1100 Poelsema B. 834 Mechtersheimer G. 834 Norman D. 271 Polanski J. 283 Meckler R. 822 Nuvolone R. 1252 Pollmann J. 7,975 Meier F. 1056 Pontikis V. 54, 73 688 Menzel D. 260,1259 Poppa H. Menyhard M. 1388 0 Pouliquen J. 116 Messmer R.P. 152 Praline G. 399 Μ et ίο Μ 168 Pratesi F. 321 Mezey L.Z. 38 O'Callagan P. 225 Prince K.C. 1170 Michel P. 466 Oechsner H. 1234,1291 Michelis (de) B. 1023 Oelkrug D. 1338 Mikhailin A.V. 1303 OhiS. 955 Q Miki H. 317 OhnoY. 141,853 Miranda R. 229,415 Ohse R.W. 887 Miyazaki E. 176 Ohuchi F. 1372 Quinn J.J. 939 Mogami A. 1283 Onsgaard J. 303,1361 Mohammed M.H. 938 Opitz Μ. 1225 Moison J.M 1197 Ortega A. 335 R Molinari C. 65 Osakabe N. 1007 Moller PJ. 563, 933 Ottaviani G. 715 MomoseT. 1092 Otto A. 782 Rafanelli G. 918 Monard E. 339 Oudar J. 610,645 Rasser B. 849 Ε DETERMINATION OF DOMAIN DISTRIBUTION BY ANALYSIS OF LEED BEAM PROFILES. W. Moritz and D. Wolf I n s t i t u t f . K r i s t a l l o g r a p h i e , Universität München, T h e r e s i e n s t r . 41, D-8000 München 2, W.-Germany A b s t r a c t Angular p r o f i l e s of LEED beams from A u ( l l 0 ) - ( l x 2 ) have been measured and analyzed with r e s p e c t to shape, h a l f - w i d t h s and energy dependence of h a l f - w i d t h s . Beam broadening i s mainly caused by s t e p s . The d i s -t r i b u t i o n of t e r r a c e widths has been determined, ana l y z i n g the shape of the p r o f i l e s which have been found to be w e l l described by a Cauchy f u n c t i o n . T h i s p r o f i l e i s caused by an exponential decrease of domain s i z e p r o b a b i l i t i e s . 1. I n t r o d u c t i o n Imperfections i n the s u r f a c e r e g i s t r y , such as s t a t i s t i c a l l y d i s t r i b u t -ed domains or s t e p s , cause broadening or s p l i t t i n g of the LEED beams. The average number of d e f e c t s can be obtained from the h a l f - w i d t h s of the angular p r o f i l e s whereas the information about the d i s t r i b u t i o n of d e f e c t s i s contained i n the shape of the p r o f i l e . I n a f i r s t approxi-mation the angular p r o f i l e - a f t e r deconvolution with the instrumental f u n c t i o n - i s given by the F o u r i e r transform of the c o r r e l a t i o n func-t i o n . A G a u a s i a n - l i k e d i s t r i b u t i o n of domain s i z e s causes s a t e l l i t e r e f l e c t i o n s or s p l i t t i n g of the beams s t i l l a t r a t h e r broad d i s t r i b u -t i o n s [ l ] . As Henzler [ 2 ] has shown, such s p l i t t i n g disappears and a continuously broadened beam with a Gaussian shape appears a t asymmetric d i s t r i b u t i o n s of domain s i z e s where s t i l l a preference f o r a c e r t a i n domain s i z e e x i s t s but short domains are s t r o n g l y suppressed. A d i f -f e r e n t type of d i s t r i b u t i o n i s given by an exponential decrease of do-main s i z e p r o b a b i l i t i e s where the s h o r t e s t domain has the maximum p r o b a b i l i t y . Such a d i s t r i b u t i o n leads to a Cauchy f u n c t i o n i n the beam p r o f i l e s and i s p r e f e r a b l y described by continuing p r o b a b i l i t i e s r a t h e r than domain s i z e s , t h a t means, the d i s t r i b u t i o n i s r u l e d by the p r o b a b i l i t y t h a t one step or domain boundary i s followed by another at the next p o s s i b l e l a t t i c e p lace [ 3 ] · The p h y s i c a l process produc-ing t h i s d i s t r i b u t i o n i s d i f f e r e n t from t h a t one which causes a Gaus-s i a n shape of the p r o f i l e . 2. Experimental R e s u l t s An A u ( l l O ) surface has been prepared by spark erosion and e l e c t r o c h e -mical p o l i s h i n g [ 4 ] . A f t e r ion bombardment and annealing the surface shows a ( l x 2 ) s u p e r s t r u c t u r e with s l i g h t d i f f u s e n e s s of the d i f f r a c -t i o n spots i n [OOl] · Measurements were performed with a Faraday cup w i t h Q a n entrance s l i t of 0.45x4 mm corresponding to an aperture of 0.44 χ 3 . 7 8 . Angular p r o f i l e s of (Ok) r e f l e c t i o n s . i n t e g e r and h a l f order beams, have been measured p a r a l l e l to [OOl] a t energies between 20 and 220 eV a t angles of i n c i d e n t = 7 5 and £0 , and of the (hO) r e f l e c t i o n s i n the perpendicular d i r e c t i o n [ΪΙΟ] at the same energies and angles of i n c i d e n c e . 1 2 9 5 The instrumental f u n c t i o n has been determined i n a way d e s c r i b e d by Wang and LagaJ.ly [ 5 ] from the minima of the h a l f - w i d t h s of the (OO) beam i n [ l i o ] , assuming a Gaussian f u n c t i o n of the primary beam con­voluted with the Faraday cup s l i t f u n c t i o n . 00 0 . 1 0 r e c . u n i t s F i g , 1 Half-widths of d i f f e r e n t beams as a f u n c t i o n of the s c a t t e r i n g v e c t o r , measured i n two l a t ­t i c e d i r e c t i o n s [001^ and [ΪΙΟ]. The dashed l i n e s i n ­d i c a t e t h e t h e o r e t i ­c a l f u n c t i o n . R e c i p r o c a l u n i t s of the bulk l a t t i c e are used. 3 · A n a l y s i s of P r o f i l e s Deconvolution of narrow p r o f i l e s d i r e c t l y by F o u r i e r transform causes numerical problems which are overcome by a f i t procedure i n which a t h e o r e t i c a l f u n c t i o n i s convoluted w i t h the i n s t r u m e n t a l f u n c t i o n and compared with the measured p r o f i l e s . I n a l l cases b e s t f i t has been achieved with a Cauchy f u n c t i o n as t h e o r e t i c a l p r o f i l e . 0.1 r e c . u n i t s F i g . 2 Angular beam p r o f i l e s i n [OOl] and [ΪΙΟ] . I n both d i r e c t i o n s the pro­f i l e s are f a i r l y w e l l r e p r e s e n t e d by Cauchy f u n c t i o n s . S o l i d l i n e : Cauchy f u n c t i o n dashed l i n e : Gauss f u n c t i o n f u l l dots: measurement The t h i n dashed l i n e i s the i n s t r u m e n t a l f u n c t i on 1 2 9 6 I t should be mentioned t h a t the information ahout the c o r r e l a t i o n f u n c t i o n i s contained i n the p r o f i l e wings, whereas the h a l f - w i d t h s can be determined n e a r l y as w e l l by use of a Gaussian f u n c t i o n . 4. D i s c u s s i o n The energy dependence of the peak widths i n d i c a t e s a stepped surface s t r u c t u r e . The i n t e g e r order beams broaden a l t e r n a t e l y as can be seen i n F i g , 1, and the s u p e r s t r u c t u r e beams broaden and sharpen i n the same way but are s h i f t e d by a q u a r t e r of the p e r i o d . This behaviour i s produced by steps which are d i s p l a c e d by a q u a r t e r of the super-s t r u c t u r e l a t t i c e s p a c i n g . The step h e i g h t corresponds approximately to the bulk value of 1.442 A more p r e c i s e determination of the step height seems d i f f i c u l t because of the u n c e r t a i n t i e s i n the measure-ments · -1 — o u o u o u oSo 0 o 0 o 0 o 0 o 0 o 0 o 0 o 0 o 0 o 0 F i g . 3 Two types of l a t t i c e f a u l t s i n the m i s s i n g row model. The arrow i n d i c a t e s an antiphase boundary ( s e e t e x t f o r explana-t i o n ) . T e r r a c e widths are r e l a t e d to the s u p e r s t r u c t u r e s p a c i n g . A l l observations are c o n s i s t e n t with the m i s s i n g row model d i s t o r t e d by s t e p s . Of course, p r o f i l e a n a l y s i s i s not s u i t e d f o r s t r u c t u r e de-t e r u i i i i t t t i on , b u t t i n y other s t r u c t u r e model must permit the e x i s t -ence of t e r r a c e s s h i f t e d p a r a l l e l and normal by a q u a r t e r of a s u p e r l a t t i c e spacing and a bulk l a y e r spacing, r e -s p e c t i v e l y , as shown i n F i g . 3 . The e x i s t -ence of antiphase boundaries produced by an occurrence of the bulk l a t t i c e spacing can be w i d e l y excluded s i n c e f o r t h i s model the i n t e g e r order beams remain sharp and the h a l f order beams are d i f f u s e , independent of energy. A formerly d i s c u s s e d model [ 6 ] i n which both types of l a t t i c e f a u l t s have been assumed to occur w i t h equal p r o b a b i l i t y does not produce a s u f f i c i e n t v a r i a t i o n of the h a l f -widths of the s u p e r s t r u c t u r e beams. We t h e r e f o r e conclude t h a t mainly steps occur a t the s u r f a c e . The e x i s t e n c e of other types of f a u l t s cannot be excluded completely s i n c e the r e f l e c t i o n s do not get p e r f e c t -l y sharp a t any energy i n [OOl] . F i g . 4 D i s t r i b u t i o n of t e r r a c e widths. U n i t i s a s u p e r l a t t i c e spacing. 1 2 3 4 5 6 7 8 9 1 2 9 7 T h i s e f f e c t could a l s o be a consequence of m u l t i p l e s c a t t e r i n g pro­cesses* The d i s t r i b u t i o n of t e r r a c e widths f o l l o w s from the "Cauchy" shape of the p r o f i l e s . The p r o b a b i l i t y of f i n d i n g a domain with a s i n g l e l a t t i c e spacing i s determined from the maxima of the half-widtha shown i n F i g . 1. The average t e r r a c e widths are 3-4 s u p e r l a t t i c e spacings (25-35 i n [OOl] and 25-35 l a t t i c e spacings (70-100 A ) i n [ΪΙΟ]. The main u n c e r t a i n t y i n the a n a l y s i s of h a l f - w i d t h s and p r o f i l e shapes i s due to the e r r o r s made i n the determ i n a t i o n of the i n s t r u m e n t a l f u n c t i o n . A f u r t h e r l i m i t a t i o n a r i s e s from the f a c t t h a t c o n t r i b u ­t i o n s from thermal d i f f u s e s c a t t e r i n g to the p r o f i l e cannot be r e ­solved. Acknowledgement The authors thank P r o f . Dr. Η· J a g o d z i n s k i and Dr. W. A d l h a r t f o r help f u l d i s c u s s i o n s and the "Deutsche Forschungsgemeinschaft (SFB 1 2 8 ) " f o r f i n a n c i a l support. References 1. I . E . Houston and R.L. Park, S u r f . S e i . 2 1 , 213 (ΐ97θ) S u r f . S e i . 2^, 269 (1971) 2. M. Henzler, i n : Topics i n Current P h y s i c s , V o l . 4, S p r i n g e r Ver­l a g , Berlin-Heidelberg-New York, 1977 3. H. J a g o d z i n s k i , A c t a C r y s t . I, 201, 208, 298 (1949) 4. W. Moritz and D. Wolf, Suf. S e i . 88, 229 (1979) 5 . G.C. Wang and M.G. L a g a l l y , S u r f . S e i . 81_, 69 (1979) 6. D. Wolf, H. J a g o d z i n s k i and W. Moritz, S u r f . S e i . 22» 2 8 5 (1978) 1 2 9 8 

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Determination of domain distribution by analysis of LEED beam profiles

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Universität München: Elektronischen Publikationen

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