Impurity effects on adatom density of state

Transcription

1 Ipurity effects on adato density of state HIROMU UE BA and SHOJI ICHIMURA Departent of Electronics, Faculty of Engineering Abstract The influence of both ipurity and surface states on the adato electronic properties is studied using the Dyson equation approach. The surface Green function of a seiinfinite crystal containated by a single ipurity ato is calculated. It is found that the surface state energy depends on the location of the ipurity ato. A siilar calculation is perfored for the case where an adato interacts with the containated substrate and the energy Ea of an electron localized on the adato is deterined as a function of the ipurity ato location and potential. The adato density is also calculated to discuss the significant effect of the ipurity near the surface. 1. Introduction It is well known that the cheisorption properties of a etal surface are closely connected with those of the etallic substrate. The Newns-Anderson ( 1, 2) enabled the relationship between cheisorption phenoena and the local electronic properties of the etal surface to be derived, i. e., the adato self-energy, due to its interaction with the substrate, ay be deterined by the surface Green function. The presence of a surface and the resultant perturbation, produces the inherent surface electronic properties, such as localized surface states. Foo and Davison ( 3 ) studied the effect of Schockley surface states of a sp-hybrid substrate on the hydrogen cheisorption process. They pointed out that the presence of Schockley state reoves soe charge fro the adato and strengthens the cheisorption bond. Siilar effect ay be expected when an ipurity is present near the surface. The growing AE S experiental data akes it reasonable to assue that crystals contain soe kind of ipurities or defects. As discussed by previous authors ( 4, 5 ), the presence of an ipurity ay change the surface electronic properties as it approaches the surface. The purpose of this paper is to investigate the influence of both ipurity and surface states on those of an adato. The odel treated here is that of a sei- infinite linear chain containing an ipurity with an adato attached to its end. The sei- infinite crystal is fored by Kalkstein and Soven ethod ( 6 ), the presence of an ipurity ato in the substrate being accounted for by the difference of its ionization energy fro that of *Present Address: Departent of Applied Matheatics, University of Waterloo, Wate r loo, Canada

2 Bulletin of Faculty of Engineering Toyaa University 1980 the substrate atos. Using the Dyson equation approach, the surface Green function of a sei-infinite crystal, containated by a single ipurity ato, is expressed in ters of the Green function of the infinite crystal, the scatter ing potentials being introduced by the surface and ipurity ato. The surface Green function thus obtained depends on the location of the ipurity ato. The localized surface state energy, whicn depends on the ipurity site and its potential, is calculated. A siilar calculation is perfored for the case where an adato interacts with such a containated surface, using the adato Green function. The adato density of states is also calculated to discuss the significance of the surface and ipurity states. 2. Surface Green Function The syste consists of a sei-infinite linear chain with an ipurity at the ith site and an adato attached to the surface ato at n 0 (Fig. l). Let G and g be the Green = a 0 Fig. l Orbilal ode l of adato a inte racting with a containated crystal [., [, and [, are the electronic energies of the adato, crystal a!ds and ipurity a!d, respective ly f! (f!' ) is the resonance in tegral between the crystal atos (the adato and the crystal ato) function of a sei-infinite crystal with and without an ipurity ato, respective ly. The Green function G ay be expressed in ters of g and the scattering potential V due to the ipurity via the Dyson equation A G = g + A gvg (1) v = E, I i > < i I ( 2) where c, 1s the ipurity electronic energy and I i > denote s the atoic orbital of the ipurity at the ith site. Fro (1) and (2), the explicit for of G is A G ( n, ) _ - g ( n, ) + g(n, i)c,g( i, ) 1 - E,g (. l, l. ) ( 3) The Green function g of a sei-infinite crystal satisfies the equation ( E - H, - 2.) g = 1. (4) The unperturbed Hailtonian H, for an infinite crystal is given by the usual tignt-binding for, H, = L E, I n> < n l + /3 L In > < I ( 5 ) n ni' - 60-

3 Ipurity effects on adato density of state HIROMU UEBA and SHOJI ICHIMURA where E, is the electronic energy of the substrate ato and fl is the resonance integral between the nearest-ne ighbour atos. crystal fro an infinite one 1s given by The cleavage perturbation to for a sei-infinite t:,. = - fj ( I O > < I- 1 > < o 1). (6) Fro ( 4 ) and (6) coes g(n, ) = 1 1+f]g. (O, - 1 ) [ g. ( n, ) + t-fl g. ( n, ) g. (0, - 1 ) - g. ( n, - 1 ) g. ( 0, ) f ] ( 7 ) where the Green function g. of the unperturbed infinite crystal, which satisfies (E - H, ) g, = 1 is given by where g. (n, ) -ik (n-)a e --= = k E-coska 1 t l + I o- I fl 1 - t' ( 8) IE -, E > 1 t = E +JE' - 1, E < 1 E - i J1 - E' ' IE I < 1 ( 9 ) The energy E is easured relative to, in unit of 2fl. Inserting ( 7) and ( 8) in ( 3 ) leads to the site-diagonal Green function of a sei-infinite crystal with an ipurity ato, viz., G (n, n) = G(l+(f]t- c;, ) g. (O) -fjc;,t ( 1 - t" ) g: ( o))-' (10) whe re c = g. ( o) + Cflt ( 1 -t'") - c, l 1 - t'< '-"> f ) g; ( o). ( 11) Here, the equation g. ( n) =g. ( O ) t" has been used. surface Green function Equation (10) and (11) yield the G, = G O, O) = ( g. ( 0 ) ( 1 -, t" f g. ( 0 ) ) 1 +(f]t-c;, ) g. (O) - fjc;,t ( 1 - t" ) g; ( o ) (12) It is clear fro (12 ) that the surface Green function depends on the location of the ipurity ato. The effect of thp ipurity on the surface electronic properties becoes less pronounced as the ipurity recedes frr> the surface. Since t" 0, as i 00, (13) reduces to - g. (0) G, flt g. (O) (13) agreeent with the surface Green function of a sei-infinite pure crystal. The Green function G, ( i ro ) has no real pole, which iplies that the localized surface state

4 Bulletin o ( Faculty of Engineering Toyaa University 1980 does not appear without the change of the substrate electronic energy due to the presence of the surface ( 7). When the ipurity resides at the surface ato location ( i 0), the corresponding = surface Green function is G, = g.(o) 1 + (/3t - c:, ) g.(o) The energy of the ipurity state, localized at the surface, of the denoinator of ( 14) to be 1 E, = y y ( 14) is calculated fro the zeros (15) and its intensity is 1 I, = 1 - -, 4 y (16) under the condition I y l > Yz, where = y c:, /2/3. The energies of any possible surface states can be deterined fro the real poles of ( 12) as a function of the ipurity site i and the ipurity paraeter y. After soe anipulations, the surface state energy is given by the solution of t- - 2 y [1 + t ' (1 + t ' t "-')] = 0. (17) The effect of both the surface and ipurity states on the adato electronic properties is discussed in Sect. 4. te rs of the adato- sub 3. Adato Green Function The adato Green function G, is, in general, expressed strate coupling ter (3' and the surface Green function G., G. (E) = [ E- c:. - ( (3' )'- G, (E)r (18) = [ E - c:. - A ( E ) + it, (E) r ( 19 J where c:. is the unperturbed adato energy. The real and iaginary part of the adato self-energy is defined as A( E) ( (3' )' Re [ G, (E)] (20) t.(e) - ((3' )' I. [G, (E)] = 7T((3' )' p, (E) (21).,p, (E) being the surface density of states. Pa (E) = 1 -I. [G. (E)] 7T 1 t.(e) 1r [E - c:. - A(E)]' + t, ' (E) The adato density of states is (22 ) -62-

5 Ipurity effects on adato density of state HIROMU UEBA and SHOJI ICHIMURA The adato electronic properties thus depend on the surface Green function, which is influenced by the presence of the ipurity. Before perforing the detailed calculation for the surface and adato density of states for arbitrary value of it is of interest to discuss the case i = 0, where and A(E) = L:l(E) I (/3' )' (E-2y) ± v'e' -1 (/3' )'(E-2y) (E-2y)'+ (1-E') (/3' )' J1- E' (E-2y)' + (1-E').,-( (3' )' I, o(e-e,). + E > 1, -E< - 1 l E I < 1 lei < 1 I E I > 1 and I rl > Yz (23) (24) 0 ; otherwise Since L:l(E) = 0 outside the band, except at the energy of the localized ipurity state at the surface, the poles of Ga (E) in ( 19) are given by E-Ea - A(E) = 0 (25) After a straight forward cal whose solutions are the localized adato state energies. culation, ( 23) in ( 26) gives where A. E' + A, E' + A, E + A, 0 ( 26) Ao = 4 Y, A, = 4/3' 2-8 Ea )' - 4 )' 2-1 A, = 2 a (4y'+1) + 4)' : - 4(3" (Ea + 2)') A, = : ( 4 y' + 1) - 8(3'' )'Ea + /3'4 However, not all the roots of ( 26) satisfy ( 25), because extra ones are introduced by the rationalization procedure. The energy Ea of an electron localized on the adato, which is a function of the position of the ipurity and its potential y, is given by the solution of E-Ea - (/3' )' [ 1-2 yt( 1 + t' t"-') ] - t ' -2yt l 1+ t' (1 + t' + + t" ')f - O (27) As i increases, the surface state starts to disappear into the band, and the energy of the localized adato state approaches that given by Newns (1), i. e., Ea = ( 1-2(3'') Ea ± 2(3'' J 4(3" + : - 1 (1-4/3'') (28)

6 Bulletin of Faculty of Engineering Toyaa University Results and Discussion The energies of the localized adato states calculated fro (27) are shown in Fig. 2 as a function of i and y, when Ea = and (3' = 0.3. For any value of y, Ea approaches that of the pure crystal case (28), within the first few atoic sites, as the ipurity recedes fro the surface. Moreover, as can be seen, the ipurity effect becoes ore pronounced as y increases. As pointed out by Newns (1), the localized state starts to disappear into the band as I Ea I decreases. For Ea = -0.5 and (3' = 0.3, the localized state does not appear for the pure substrate, but does appear for the containated one, though as i increases it again disappears into the band (Fig. 2) (a) (b) Fig. 2 Variation of the localized adato energy with the ipurity site i fo r different values of E, and y. ( a ) E, =-1.0, fj' =0.3 and y =1.0 ( I ), 0.4( Il ), 0.2( Ill ). (b) E, = -0.5, fj' =0.3 and y = -0.6( I ), -0.8( II ), -1.0( Ill ). The adato electronic properties are thus influenced by the presence of an ipurity situated within the first few atoic layers of the surface. The ipurity effects are, therefore, iportant for the surface and ada to electronic properties, because ipurity atos ay be distributed near the surface even when the substrate aterial has been prepared as supposedly pure crystal. The adato density of states (ADOS) was also calculated for the situation where the ipurity resides at the surface location as a function of y and (3' for Ea -0.5(Fig. = 3 ). The corresponding surface density of state ( SDOS) of the containated crystal is (c) b: -ID Fig. 3 Adato density of state p, fo r i= 0 as a function of y and fj'. The corresponding surface density of state p, is also shown. E, is fixed at ( a ) y=-0.2, (b) y=-0.4 and ( c) y=-1.0 fj' =0.5( I ), 0.3( II ), O.l(Ill ), throughout figures

7 Ipurity effects on adato density of state HIROMU UEBA and SHOJI ICHIMURA also shown in the figure. For y = -0.2, no localized state exists. However, as y increases, a localized adato state starts to separate fro the band with (3'. This adato localized state ay be interpreted as the ipurity-assisted one fro the fact that the ada to localized state does not appear for pure substates when Ea = -0.5 and (3' ;;:;; 0.5. For I y I > Yz, the localized ipurity states, whose energy is given by ( 15), appears in the SDOS. In this case, two types of localized state exist in the ADOS. One is identified as the ipurity state and the other as the adato state, since, as (3' increases, the energy of the adato state oves to a lower energy side, while that of the ipurity reains fixed. Siilar calculations were perfored for the case where the ipurity is located at the second surface site (Fig. 4). In this case, the condition for the existence ~ Qb (b) I l.o Fig. 4 Ada to density of state p, for i = 1. Paraeters are sae as in.f ig. 4 execpt (a) y=-0.2. (b) y=-0.4. _,-L o E of a surface state 1s given by I y I > 1_4, Two types of localized state entioned above appear for y = - 0.4, whereas only the ipurity-assisted state appears for i = 0 under the sae set of paraeters. On increasing y or fj', two peaks appear in the band sta tes. Their origins are quite different fro each other. The peak near E = -0.5 is, of course, due to the adato. The other peak, located at the higher energy side, is attributed to its counterpart of the virtual bound state in the SDOS. The adato peak is therefore repelled to the lower energy side with the growing additional structure. As discussed above, an ipurity near the surface plays an iportant role in deter ining the adato electronic structure. In spite of the present siple odel, the results enable us to draw significant effects of an ipurity on adato states. The odel treated here is very priitive, in several respects, and a ore realistic treatent is needed for an understanding of such phenoena as adato charge transfer and cheisorption energy of the containated substrate. The self-consistent treatent including the indirect interaction between adato and ipurity via the substate is currently being studied and will be reported elsewhere. Acknowledgeent The authors would like to express their sincere thanks to Professor S. G. useful discussions and the critical reading of the anuscript. Davison for

8 Bulletin of Faculty of Engineering Toyaa University 1980 References 1. D. M. Newns, Phys. Rev. 178, 1123 (1969 ). 2, T. B. Griley, Prog. Surface and Mebrance Sci. 9, 71 (1975 ). 3. E - Ni Foo and S. G. Davison, Surface Sci. 55, 274 (1976), 4. S. G. Davison and Y. C. Cheng, Intn. J. Quantu Chern. 23, 313 ( 1968 ). 5, W. F. Fairbairn, Surface Sci. 25, 587 (1971 ). 6. D. Kalkste in and P. Soven, Surface Sci. 26, 85 ( 1971 ). 7. H. Ueba and S. Ichiura, J. Chern. Phys. 70, 1945 (1979 ). (Received October ) - 66-