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Submonolayer coverage of Ga and B adatoms on a Ge(111) surface
Applied Surface Science 65/66 (1993) 603-606 North-Holland
applied surface science
Submonolayer coverage of Ga and B adatoms on a Ge(111) surface C. C h e n g a n d K. K u n c Department of Physics, National Cheng Kung University, Tainan, Taiwan, ROC and Laboratoire de Physique des" Solides associd au CNRS, Tour 13, 4 pl. Jussieu, 75252 Paris Cedex 05, France
Received 29 June 1992; accepted for publication 5 August 1992
First-principles calculations based on the density-functional theory are performed to investigate the submonolayer coverage of Ga and B adatoms on a Ge(lll) surface. We study the stability of the three different surface structures of adatoms, viz. the top-site (T4), the hollow-site (H3) and the substitution-site ($5). Calculations show that the T4 structure is favoured over the H3 structure for Ga adatoms and the $5 over the T4 for B adatoms. It is found that for Ga adatoms, the T4 structure induces a much longer range relaxation on the Ge(lll) surface than the H3 one and for B adatoms in the T4 structure, no bond charge between adatoms and surface atoms is formed.
1. Introduction F o r the (111) surfaces o f C, Si a n d Ge, the l I I a a t o m s m a k e p e r f e c t a d a t o m s as they s a t u r a t e the d a n g l i n g b o n d s o f the surface a t o m s with 1 / 3 m o n o l a y e r coverage. T h e t h o r o u g h studies, b o t h e x p e r i m e n t a l a n d t h e o r e t i c a l , on S i ( l l l ) surface show that t h e ( v ~ - x v ~ ) R 3 0 ° surface s t r u c t u r e s a r e f o r m e d for B, AI, G a a n d In a d a t o m s . F o r AI, G a a n d In a d a t o m s [1-4], it is t h e T4 s t r u c t u r e which is m o r e stable t h a n t h e H3 one. T h e T4 a n d H3 s t r u c t u r e s c o r r e s p o n d to the a d a t o m s sitting on t o p o f the a t o m s of t h e s e c o n d layer a n d the f o u r t h layer from the surface, r e s p e c tively. In the case o f B, which is the smallest of t h e I I I a atoms, u n e x p e c t e d l y n e i t h e r a d a t o m s t r u c t u r e is stable. I n s t e a d , the B a d a t o m s form a $5 s t r u c t u r e which is like T4 except that the a d a t o m s a r e s w a p p e d with the Si a t o m s of t h e s e c o n d layer from the surface [5-7]. In the p r e s e n t p a p e r , the G e ( l l l ) surface with B a n d G a a d a t o m s a r e studies with ab initio m e t h o d s . W e f o u n d that, similar to the Si case, the T4 s t r u c t u r e is p r e f e r r e d over the H3 struct u r e for G a a d a t o m s a n d t h e $5 over the T4 for B a d a t o m s . T h e stability o f s t r u c t u r e s is discussed with the h e l p o f investigating the surface c h a r g e
density d i s t r i b u t i o n a n d the r e l a x e d surface structures with a d a t o m s .
2. Calculationai methods T h e d e n s i t y functional t h e o r y [8] with local d e n s i t y a p p r o x i m a t i o n [9] is e m p l o y e d to study the system. W e have used the n o r m - c o n s e r v i n g p s e u d o p o t e n t i a l s g e n e r a t e d by B a c h e l e t et al. [10]. E x c h a n g e a n d c o r r e l a t i o n w e r e i n c l u d e d within the local d e n s i t y a p p r o x i m a t i o n using the C e p e r l y a n d A i d e r form [11]. T h e resulting o n e - e l e c t r o n S c h r 6 d i n g e r e q u a t i o n s , k n o w n as K o h n - S h a m e q u a t i o n s [9], w e r e solved self-consistently. T h e wavefunctions w e r e e x p a n d e d in p l a n e waves a n d calculations w e r e p e r f o r m e d in m o m e n t u m space [12]. T h e calculations a r e d o n e with a s u p e r c e l l w h o s e unit cell consists of 5 d o u b l e layers of G e a t o m s a n d 3 d o u b l e layers o f v a c u u m to m o d e l t h e surface structures. P l a n e waves with e n e r g y cut-off up to 5 Ry are i n c l u d e d in the basis-set e x p a n s i o n a n d 3 (for t h e ideal surface s t r u c t u r e ) or 4 (for the r e l a x e d a d a t o m surface structures) special k p o i n t s in the i r r e d u c i b l e zone are used for t h e first BriIlouin zone i n t e g r a t i o n . Exactly the s a m e set o f k p o i n t s is used for all structures
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
604
C. Cheng, K. Kunc / Submonolayer couerage of Ga and B adatoms on a Ge( l l l) surface
considered to achieve high accuracy in energy differences [13]. We shall test the convergence of the energy cut-off and k-point sampling in the near future.
3. R e s u l t s a n d d i s c u s s i o n
The total energy calculations are done for the T4 and $5 structures with B adatoms and for the T4 and H3 structures with Ga adatoms. The first four layers of surface Ge atoms are allowed to relax until the atomic forces are less than 0.6 e V / A . Calculations are also performed for the bulk structure [14], the B and Ga atoms [15] and the ( ~ - × ~/3)R30 ° surface structure with no adatom to obtain surface energy and adsorption energy. The surface energy for the ideal G e ( l l l ) surface, which is defined as the energy required to create the surface from the bulk structure, is found to be 1.66 e V / 1 × 1 cell. This is in good
agreement with the previous calculations done by Meade and Vanderbilt [16] which gives 1.40 e V / 1 x 1 cell. In the case of Ga adatoms, the adsorption energies for the T4 and H3 structures are 1.9 and 1.8 e V / 1 x 1 cell, respectively. These correspond to 5.7 and 5.4 eV per adatom. The absorption energy is the energy released from the ideal Ge(111) surface and adatoms to form the adatom surface structures. The T4 structure is the more stable structure whose energy is 0.3 eV per adatom lower than that of the H3 one. For Si(111) surface, the energy difference between the T4 and H3 structures with Ga adatoms was found to be around 0.3 e V / 1 x 1 cell as well [17]. Both the T4 and H3 structures saturate the surface dangling bonds in the same way for atoms on the first layer of the surface. However, the relaxed structures show that in the T4-type adsorption a much longer range of relaxation is involved. This is demonstrated clearly on the charge density diagrams of fig. 1 which are the contour plots of the
b
O
S Fig. 1. The contour plots of the charge density differences between the T4 structure (a) or the H3 structure (b) for Ga adatoms and the ideal G e ( l l l ) surface on the (110) plane. The solid and employ circles correspond to the Ge and Ga atoms, respectively. The spacing of the contour levels is 0.02 electron per (A) 3 and the lowest level is 0.05 electron per (~,)3.
605
c. Cheng, K. Kunc / Submonolayer coverage of Ga and B adatoms on a G e ( l l l ) surface
b
0
Fig. 2. The contour plots of the charge density differences between the T4 structure (a) or the $5 structure (b) for B adatoms and the ideal Ge(lll) surface on the (110) plane. The solid and emply circles correspond to the Ge and B atoms, respectively. The spacing of the contour levels is 0.04 electron per (~)3 and the lowest level is 0.05 electron per (,~)3. charge density differences between the a d a t o m structures and the ideal surface structure on the zig-zag atomic plane (110). Except the longer range interaction induced in the T4 structure, the bonding characteristics of the adatoms on the surface atoms for the T4 and H3 structures are rather similar. For B adatoms, the adorption energies of the T4 and $5 structures are 5.1 and 5.8 eV per adatom, respectively. T h e energy of the $5 structure is lower than that of T4 by 0.7 eV per adatom. For the S i ( l l l ) surface, this energy difference is 0.93 e V / 1 × 1 cell [6]. The lower energy of the $5 structure for the B a d a t o m on the Si(ll 1) surface has been discussed with the charge transfer from the dangling-bond orbital to the B atom [6]. Similar charge tranfer occurred for the B $5 structure of the Ge(111) surface (fig. 2b). F r o m comparison of the T4 structures for G a and B adatoms, one can also understand why the T4 structure for B adatoms is not favoured. In fig. 2a, we show the differences in the charge density between the T4 and the ideal surface structures
with B adatoms. Contrary to that of the Ga a d a t o m T4 structure (fig. la), there is no bond charge whatsoever between the B adatoms and the surface atoms. Thus the small and no-p orbital core of B atom prefers to b e c o m e an anion rather than a cation, therefore the $5 structure is favoured. In conclusion, we have p e r f o r m e d ab initio total energy calculations on the G a and B a d a t o m structures of a G e ( l l l ) surface. The more stable a d a t o m structures for G a and B adatoms are the T4 and $5 structures, respectively, similar to the Si case. Investigation of the surface charge density suggests that the lower energy state of T4 for G a adatoms might be due to the longer range relaxation and the anion-like property of B atoms accounts for the stability of $5 structure.
Acknowledgements This work has been supportted by the National Science Council in R O C (project n u m b e r N S C 80-0208-M-006-45) and the C N R S in France. The
606
C. Cheng, K. Kunc / Submonolayer coverage of Ga and B adatoms on a G e ( l l l ) surface
computer resources were provided by the Scientific Committee of the CCVR (Centre de Calcul Vectoriel pour la Recherche), Palaiseau, France and the CRAY-Xmp of the National Taiwan University, Taipei, Taiwan.
References [1] G.V. Hansson, R.Z. Bachrach, R.S. Bauer and P. Chiaradia, Phys. Rev. Lett. 46 (1981) 1033. [2] J.M. Nicholls, B. Reihl and J.E. Northrup, Phys. Rev. B 35 (1987) 4137. [3] J. Nogami, S. Park and C.F. Quate, Phys. Rev. B 36 (1987) 6221. [4] R.J. Hamers and J.E. Demuth, Phys. Rev. Lett. 60 (1988) 2527. [5] R . L Headrick, I.K. Robinson, E. Vlieg and L.C. Feldman, Phys. Rev. Lett. 63 (1989) 1253. [6] P. Bedrossian, R.D. Meade, K. Mortersen, D.M. Chen, J.A. Golovchendo and D. Vanderbilt, Phys. Rev. Lett. 63 (1989) 1257. [7] I.-W. Lyo, E. Kaxiras and Ph. Avouris, Phys. Rev. Lett. 63 (1989) 1261.
[8] P. Hohenberg and W. Kohn, Phys. Rev. B 136 (1964) 864. [9] W. Kohn and L.J. Sham, Phys. Rev. A 140 (1965) 1133. [10] G.C. Bachelet, D.R. H a m a n n and M. Schluter, Phys. Rev. B 26 (1982) 2314. [11] D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. [12] J. Ihm, A. Z u n g e r and M . L Cohen J. Phys. C: Solid State Phys. 12 (1979) 4409. [13] C. Cheng, R.J. Needs and V. Heine, J. Phys. C: Solid State Phys. 2t (1988) 1049. [14] With the choice of a unit cell with 8 double layer, we obtain the bulk energy from the wurtzite structure of Ge in order to use exactly the same k points as other structures calculated. It has been shown that the energy difference between the diamond and wurtzite structure for Si is less than 0.02 e V / p e r atom pair, i.e., the uncertainty is less than 0.1 eV for the surface energy of order of 1 e V / l × 1 cell. [15] The energy of B and Ga atoms are calculated by using exactly the same unit cell as that of surface structures and having two atoms in a unit cell. The calculation is justified as the stresses of the system are tiny (less than 4 kbar). [16] R.D. Meade and D. Vanderbilt, Phys. Rev. B 40 (1989) 3905. [17] J.E. Northrup, Phys. Rev. Lett. 53 (1984) 683.
applied surface science
Submonolayer coverage of Ga and B adatoms on a Ge(111) surface C. C h e n g a n d K. K u n c Department of Physics, National Cheng Kung University, Tainan, Taiwan, ROC and Laboratoire de Physique des" Solides associd au CNRS, Tour 13, 4 pl. Jussieu, 75252 Paris Cedex 05, France
Received 29 June 1992; accepted for publication 5 August 1992
First-principles calculations based on the density-functional theory are performed to investigate the submonolayer coverage of Ga and B adatoms on a Ge(lll) surface. We study the stability of the three different surface structures of adatoms, viz. the top-site (T4), the hollow-site (H3) and the substitution-site ($5). Calculations show that the T4 structure is favoured over the H3 structure for Ga adatoms and the $5 over the T4 for B adatoms. It is found that for Ga adatoms, the T4 structure induces a much longer range relaxation on the Ge(lll) surface than the H3 one and for B adatoms in the T4 structure, no bond charge between adatoms and surface atoms is formed.
1. Introduction F o r the (111) surfaces o f C, Si a n d Ge, the l I I a a t o m s m a k e p e r f e c t a d a t o m s as they s a t u r a t e the d a n g l i n g b o n d s o f the surface a t o m s with 1 / 3 m o n o l a y e r coverage. T h e t h o r o u g h studies, b o t h e x p e r i m e n t a l a n d t h e o r e t i c a l , on S i ( l l l ) surface show that t h e ( v ~ - x v ~ ) R 3 0 ° surface s t r u c t u r e s a r e f o r m e d for B, AI, G a a n d In a d a t o m s . F o r AI, G a a n d In a d a t o m s [1-4], it is t h e T4 s t r u c t u r e which is m o r e stable t h a n t h e H3 one. T h e T4 a n d H3 s t r u c t u r e s c o r r e s p o n d to the a d a t o m s sitting on t o p o f the a t o m s of t h e s e c o n d layer a n d the f o u r t h layer from the surface, r e s p e c tively. In the case o f B, which is the smallest of t h e I I I a atoms, u n e x p e c t e d l y n e i t h e r a d a t o m s t r u c t u r e is stable. I n s t e a d , the B a d a t o m s form a $5 s t r u c t u r e which is like T4 except that the a d a t o m s a r e s w a p p e d with the Si a t o m s of t h e s e c o n d layer from the surface [5-7]. In the p r e s e n t p a p e r , the G e ( l l l ) surface with B a n d G a a d a t o m s a r e studies with ab initio m e t h o d s . W e f o u n d that, similar to the Si case, the T4 s t r u c t u r e is p r e f e r r e d over the H3 struct u r e for G a a d a t o m s a n d t h e $5 over the T4 for B a d a t o m s . T h e stability o f s t r u c t u r e s is discussed with the h e l p o f investigating the surface c h a r g e
density d i s t r i b u t i o n a n d the r e l a x e d surface structures with a d a t o m s .
2. Calculationai methods T h e d e n s i t y functional t h e o r y [8] with local d e n s i t y a p p r o x i m a t i o n [9] is e m p l o y e d to study the system. W e have used the n o r m - c o n s e r v i n g p s e u d o p o t e n t i a l s g e n e r a t e d by B a c h e l e t et al. [10]. E x c h a n g e a n d c o r r e l a t i o n w e r e i n c l u d e d within the local d e n s i t y a p p r o x i m a t i o n using the C e p e r l y a n d A i d e r form [11]. T h e resulting o n e - e l e c t r o n S c h r 6 d i n g e r e q u a t i o n s , k n o w n as K o h n - S h a m e q u a t i o n s [9], w e r e solved self-consistently. T h e wavefunctions w e r e e x p a n d e d in p l a n e waves a n d calculations w e r e p e r f o r m e d in m o m e n t u m space [12]. T h e calculations a r e d o n e with a s u p e r c e l l w h o s e unit cell consists of 5 d o u b l e layers of G e a t o m s a n d 3 d o u b l e layers o f v a c u u m to m o d e l t h e surface structures. P l a n e waves with e n e r g y cut-off up to 5 Ry are i n c l u d e d in the basis-set e x p a n s i o n a n d 3 (for t h e ideal surface s t r u c t u r e ) or 4 (for the r e l a x e d a d a t o m surface structures) special k p o i n t s in the i r r e d u c i b l e zone are used for t h e first BriIlouin zone i n t e g r a t i o n . Exactly the s a m e set o f k p o i n t s is used for all structures
0169-4332/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
604
C. Cheng, K. Kunc / Submonolayer couerage of Ga and B adatoms on a Ge( l l l) surface
considered to achieve high accuracy in energy differences [13]. We shall test the convergence of the energy cut-off and k-point sampling in the near future.
3. R e s u l t s a n d d i s c u s s i o n
The total energy calculations are done for the T4 and $5 structures with B adatoms and for the T4 and H3 structures with Ga adatoms. The first four layers of surface Ge atoms are allowed to relax until the atomic forces are less than 0.6 e V / A . Calculations are also performed for the bulk structure [14], the B and Ga atoms [15] and the ( ~ - × ~/3)R30 ° surface structure with no adatom to obtain surface energy and adsorption energy. The surface energy for the ideal G e ( l l l ) surface, which is defined as the energy required to create the surface from the bulk structure, is found to be 1.66 e V / 1 × 1 cell. This is in good
agreement with the previous calculations done by Meade and Vanderbilt [16] which gives 1.40 e V / 1 x 1 cell. In the case of Ga adatoms, the adsorption energies for the T4 and H3 structures are 1.9 and 1.8 e V / 1 x 1 cell, respectively. These correspond to 5.7 and 5.4 eV per adatom. The absorption energy is the energy released from the ideal Ge(111) surface and adatoms to form the adatom surface structures. The T4 structure is the more stable structure whose energy is 0.3 eV per adatom lower than that of the H3 one. For Si(111) surface, the energy difference between the T4 and H3 structures with Ga adatoms was found to be around 0.3 e V / 1 x 1 cell as well [17]. Both the T4 and H3 structures saturate the surface dangling bonds in the same way for atoms on the first layer of the surface. However, the relaxed structures show that in the T4-type adsorption a much longer range of relaxation is involved. This is demonstrated clearly on the charge density diagrams of fig. 1 which are the contour plots of the
b
O
S Fig. 1. The contour plots of the charge density differences between the T4 structure (a) or the H3 structure (b) for Ga adatoms and the ideal G e ( l l l ) surface on the (110) plane. The solid and employ circles correspond to the Ge and Ga atoms, respectively. The spacing of the contour levels is 0.02 electron per (A) 3 and the lowest level is 0.05 electron per (~,)3.
605
c. Cheng, K. Kunc / Submonolayer coverage of Ga and B adatoms on a G e ( l l l ) surface
b
0
Fig. 2. The contour plots of the charge density differences between the T4 structure (a) or the $5 structure (b) for B adatoms and the ideal Ge(lll) surface on the (110) plane. The solid and emply circles correspond to the Ge and B atoms, respectively. The spacing of the contour levels is 0.04 electron per (~)3 and the lowest level is 0.05 electron per (,~)3. charge density differences between the a d a t o m structures and the ideal surface structure on the zig-zag atomic plane (110). Except the longer range interaction induced in the T4 structure, the bonding characteristics of the adatoms on the surface atoms for the T4 and H3 structures are rather similar. For B adatoms, the adorption energies of the T4 and $5 structures are 5.1 and 5.8 eV per adatom, respectively. T h e energy of the $5 structure is lower than that of T4 by 0.7 eV per adatom. For the S i ( l l l ) surface, this energy difference is 0.93 e V / 1 × 1 cell [6]. The lower energy of the $5 structure for the B a d a t o m on the Si(ll 1) surface has been discussed with the charge transfer from the dangling-bond orbital to the B atom [6]. Similar charge tranfer occurred for the B $5 structure of the Ge(111) surface (fig. 2b). F r o m comparison of the T4 structures for G a and B adatoms, one can also understand why the T4 structure for B adatoms is not favoured. In fig. 2a, we show the differences in the charge density between the T4 and the ideal surface structures
with B adatoms. Contrary to that of the Ga a d a t o m T4 structure (fig. la), there is no bond charge whatsoever between the B adatoms and the surface atoms. Thus the small and no-p orbital core of B atom prefers to b e c o m e an anion rather than a cation, therefore the $5 structure is favoured. In conclusion, we have p e r f o r m e d ab initio total energy calculations on the G a and B a d a t o m structures of a G e ( l l l ) surface. The more stable a d a t o m structures for G a and B adatoms are the T4 and $5 structures, respectively, similar to the Si case. Investigation of the surface charge density suggests that the lower energy state of T4 for G a adatoms might be due to the longer range relaxation and the anion-like property of B atoms accounts for the stability of $5 structure.
Acknowledgements This work has been supportted by the National Science Council in R O C (project n u m b e r N S C 80-0208-M-006-45) and the C N R S in France. The
606
C. Cheng, K. Kunc / Submonolayer coverage of Ga and B adatoms on a G e ( l l l ) surface
computer resources were provided by the Scientific Committee of the CCVR (Centre de Calcul Vectoriel pour la Recherche), Palaiseau, France and the CRAY-Xmp of the National Taiwan University, Taipei, Taiwan.
References [1] G.V. Hansson, R.Z. Bachrach, R.S. Bauer and P. Chiaradia, Phys. Rev. Lett. 46 (1981) 1033. [2] J.M. Nicholls, B. Reihl and J.E. Northrup, Phys. Rev. B 35 (1987) 4137. [3] J. Nogami, S. Park and C.F. Quate, Phys. Rev. B 36 (1987) 6221. [4] R.J. Hamers and J.E. Demuth, Phys. Rev. Lett. 60 (1988) 2527. [5] R . L Headrick, I.K. Robinson, E. Vlieg and L.C. Feldman, Phys. Rev. Lett. 63 (1989) 1253. [6] P. Bedrossian, R.D. Meade, K. Mortersen, D.M. Chen, J.A. Golovchendo and D. Vanderbilt, Phys. Rev. Lett. 63 (1989) 1257. [7] I.-W. Lyo, E. Kaxiras and Ph. Avouris, Phys. Rev. Lett. 63 (1989) 1261.
[8] P. Hohenberg and W. Kohn, Phys. Rev. B 136 (1964) 864. [9] W. Kohn and L.J. Sham, Phys. Rev. A 140 (1965) 1133. [10] G.C. Bachelet, D.R. H a m a n n and M. Schluter, Phys. Rev. B 26 (1982) 2314. [11] D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. [12] J. Ihm, A. Z u n g e r and M . L Cohen J. Phys. C: Solid State Phys. 12 (1979) 4409. [13] C. Cheng, R.J. Needs and V. Heine, J. Phys. C: Solid State Phys. 2t (1988) 1049. [14] With the choice of a unit cell with 8 double layer, we obtain the bulk energy from the wurtzite structure of Ge in order to use exactly the same k points as other structures calculated. It has been shown that the energy difference between the diamond and wurtzite structure for Si is less than 0.02 e V / p e r atom pair, i.e., the uncertainty is less than 0.1 eV for the surface energy of order of 1 e V / l × 1 cell. [15] The energy of B and Ga atoms are calculated by using exactly the same unit cell as that of surface structures and having two atoms in a unit cell. The calculation is justified as the stresses of the system are tiny (less than 4 kbar). [16] R.D. Meade and D. Vanderbilt, Phys. Rev. B 40 (1989) 3905. [17] J.E. Northrup, Phys. Rev. Lett. 53 (1984) 683.