- Email: [email protected]
The structure of the beryllium-hydrogen complex in silicon
1. Phys. Chem. Solids Vol. 53. No. 4. pp. 58>589. Printed m Great Britain.
1992
0022-X97/92 WI0 + 0.00 PuganIon Press plc
THE STRUCTURE OF THE BERYLLIUM-HYDROGEN COMPLEX IN SILICON L. S. CHIA,t N. K. GoHt and C. K. ONG Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511 (Received 14 May 1991; accepted 4 September 1991)
Abstract-The total energies of the (Be, H) complex in Si have been calculated, when the H atom is moving along the three major axes with the Be atom at a substitutional site, using a self-consistent semi-empirical method. The local minimum for the H atom on the (I IO) plane has also been investigated. The global minimum is found when the H atom is located near the C-site. However, we find that an activation of about 0.49 eV is needed for the H atom to diffuse thermally from one C-site lo the other. Our results further indicate that the H atom has a stronger affinity with the Be rather than the Si atom. A possible mechanism for the passivation of the Be atom by the H atom in crystalline Si is also discussed. Keywordy: Beryllium- hydrogen complex in silicon, CNDO.
1. INTRODUCTION In recent years, the passivation of acceptor impurities in silicon in the presence of hydrogen has attracted a great deal of research interest, because of its implications in developing modern electronic devices. It is interesting to note that different mechanisms have been proposed to explain the effect of hydrogen on passivation [ 141. However, it is still debatable and inconclusive, since not many structures of such Si systems have been studied in detail and revealed in depth. Among the (acceptor, H) in Si systems, (B, H) in Si is supposed to be the only one which is well documented. Its experimental data coincide well with the theoretically derived model [S-9]. On the other hand, information on the theoretical structure of (Be, H) in the Si system is reported only by Denteneer et al. [9]. Their calculations are carried out using the first-principles pseudopotential-density-functional method. Their main findings are as follows. (1) Be binds a H atom rather strongly at several symmetrically equivalent sites in its immediate vicinity. (2) The global minimum is at the C site, with little relaxation of the host crystal. (3) Proton tunnelling between equivalent C sites has been found to be possible. As proton tunnelling is not observed in the case of (B, H) in Si(l I), the structure of (Be, H) in Si should be different from that of (B, H) in Si. Since we have applied the Complete Neglect of the Differential Overlap (CNDO) method successfully
t Permanent address: National Institute of Education, Nanyang Technological University, 469 Bukit Timah Road, Singapore 1025. PCS 13,444
to investigate the structure and properties of (B, H) in Si[l 11, we hope therefore, that by using the same method, we are able to contribute some understanding to the structure and properties of (Be., H) in Si system. Furthermore, it is desirable to compare the results of the two different total energy algorithms, namely the CNDO method and the first-principles pseudopotential-density-functional method.
2. METHOD AND CALCULATIONS
In our study, we employ the Complete Neglect of the Differential Overlap (CNDO) method (I 11. This is based on a semi-empirical self-consistent molecular orbital theory, whereby approximations are systematically applied to the matrix elements of the HartreeFock-Roothaan equations through the introduction of three semi-empirical parameters. These parameters are: (1) the orbital exponent (t); (2) the electronegativity (E), and (3) the bonding parameter (j?). The values of these parameters for the respective atoms are presented in Table 1. The parameters for Si are from Harker and Larkins [12], whereas those for H and Be are from Pople and Beveridge [ 131.Here, we use the Hatwell Moses Code [I41 to perform our calculations for studying the behaviour of H in Si with substitutional Be. The code involves the computation of routines in which equations are solved by self-consistent iterative technique until convergence of the total energy minimum is achieved. The successful applications of the CNDO method to the investigations of the structures and properties of defects and defect complexes in semiconductors have been well documented [lS-181.
585
L. S. CHIA
586
et al.
Table 1. The CNDO narameters used Atom H Be Si Si*
Orbital exponent tsp (Bohr-‘) 1.20 0.975 1.54 1.54
Electronegativity cs(ev) ep(ev) 7.18 0 5.95 2.56 6.30 4.50 6.30 4.50
With regards to the simulated Be-H complex in Si, we use a 65atom molecular cluster, where we place the Be atom at a substitutional site. The dangling bonds at the edges of this cluster are saturated by single sp3 hybrids of silicon (Si*). We have 36 of these in our 65-atom cluster. These hybrid atoms have the same parameters as Si except that their /I values are set to zero.
Bonding parameter B (ev) - 9.00 - 13.00 - 6.40 l-l
of about 0.50 to 1.30 eV are needed for the H atom to move around the Be atom in a spherical shell which is rather large. (4
3. RESULTS AND DISCUSSION Similarly to our previous study on (B, H) in the Si system [l 11,we first perform our calculations on the Si cluster with the Be atom being placed at the substitutional site, and the H atom moving along the three major axes, namely (1 1 1), (110) and (loo), in the vicinity of the Be atom [Fig. l(a)]. Figure l(b) illustrates the variation of the total energy of the corresponding H atom moving along these axes. The profiles of these total energy curves look very similar and trough-like. They resemble very closely those observed in the (B, H) in Si system [ll], even the order of lowering the total energy, from (111) to (110) to (100) axes, is quite similar for both systems. Such a similarity may suggest that (Be, H) in Si is likely to have the same structure as (B, H) in Si. However, it has been found that H stabilizes at different sites when it pairs with different impurities, and that the nature of the site determines both the electrical activity of the pair and the possibility of thermal and quantum-mechanical motion around the impurity [9]. Thus, the structure of (Be, H) in Si need not be the same as that of (B, H) in Si. The equilibrium distances of the H atom from the substitutional Be atom along the (11 l), (110) and (100) axes are found to be 1.36 A, 1.37 8, and 1.42 A, respectively. All the values here are quite close to that observed for Be-H in BeH [19] which is 1.34 A, but much smaller in comparison with the experimental value of 1.63 8, for the Be-H bridging bond in beryllium borohydride [20]. The local energy minimum along the (100) axis is situated very close to the C-site (being 0.07 A away from the C-site). It is 0.55 eV lower than the minimum along the (110) axis and 1.29 eV lower than that along the (111) axis [which is at the antibonding (AB) site]. Thus, the diffusion channel for the H atom seems to be in a restricted zone. The activation energy
l
0
(b)
Be
atom
Si atom
EneqykVv) -=lll> 4112
\
2.00
180
1.80 s D&invx
of
H
from
Be
&am(A)
Fig. 1. (a) Diagram illustrating the location of the H atom (X,) in the vicinity of the substitutional Be atom in the silicon crystal lattice on the (110) plane. (b) The variation in the total energy of the Be-H complex in the silicon crystal lattice shown in Fig. l(a) along the three major axes.
Beryllium-hydrogen
complex in silicon
We performed further calculations to find out the local minimum on the (110) plane. The equilibrium distance found along the (110) axis (1.37 A) is used as the radius for the circle which represents the path of the H atom around the Be atom. On the (110) plane, when the atoms are not allowed to relax, there are no other local minima besides the ones that correspond to those found along the (100) axis, i.e. A and Q [Fig. 2(b)]. However, we are expecting a large relaxation at some sites for the H atom. One of them is the bond centred (BM) site of Si-Be, as in the case of (B, H) in Si. By allowing Si, H and Be to relax
(4
away along the (111) axis from their original positions by 0.23 A, 0.31 A and 0.28, respectively, and relaxations of their nearest Si atoms by 0.11 A to O.l4A, there is a decrease of the total energy at the local minimum by 9.39 eV. However, the total energy for the H atom of the BM site is still not the global minimum. The other site that we have considered is the C-site [A or Q in Fig. 2(b)]. By allowing the H, Be and Si atoms to move freely along the (100) axis, from their original positions, by about 0.19 A, 0.19 8, and 0.09 A, respectively, and some relaxations of their nearest neighbours, the total energy for the H
a (110 )
/fl-----
587
plane
J
-I- --in” site
I
--Q
-l--
/
/’
lH--I--W semi-circular path of
0 0
0.001
AIQ H atom in (llO)$an@ Be atom
Si atom
/
A
BM
I
Q
Labelled poir& along circular path AIQ in (110)plane
Fig. 2. (a) The semicircular path of the H atom as it is ‘pqved in the (110) plane. (b) The energy profiles as the H atom is moved along the path in 2(a).
588
L. S. CHIA
atom at this position (global minimum) is the lowest, which is 0.49 eV lower than that at the BM site (after relaxation). The equilibrium distance for Si-H at the global minimum is 1.84 A, which is much longer than the experimental value of 1.48 di found for Si-H in SiH, [21]. The corresponding distance for Be-H becomes I .42 8, which is identical to that of Be-H found at the local minimum along the (100) axis, and also close to the reported value of I .34 8, for Be-H in BeH [19]. The above observations suggest that: (I) the H atom has a stronger affinity with the Be atom than the Si atom; (2) the movement of the H atom into the bond-centred position of the Si-Be is not favoured, in contrast to the case of (B, H) in Si. A similar treatment has been applied to the AB site. By allowing the H, Be and Si atoms to relax away, along the (I 11) axis, from their original positions by 0.085 A, 0.113 8, and 0.113 A, respectively, and some relaxations of their nearest Si atoms, a local minimum is obtained. However, the total energy for the H atom at this local minimum is 1.20 eV higher than that at the global minimum (i.e. the one near the C site). In order to have a better understanding of the structure of the Be-H complex in Si, we have also investigated the movement of H in the environment of four Si atoms, where one of the Si atoms is tetrahedrally bonded to a Be atom. The treatment similar to that mentioned earlier has been applied to the H atom to move it along the three major axes, namely (I 1I), (1 IO) and (loo), in the vicinity of the central Si atom. The equilibrium distances of the H atom from the Si atom along the (I 1l), (1 IO) and (100) axes are found to be I.55 A, 1.61 A and 1.63 A, respectively. All these values are in good agreement with the equilibrium distance of 1.53 A for Si-H found in the EH complex in Si [I 11 and are also compatible with the experimental value of 1.488, for Si-H in SiH, 1211. Furthermore the profiles of these total energy curves are similar and trough-like. However, the total energies of the local minima along the three major axes are all much higher than those mentioned before. For example, before relaxation, the energy minimum along the (100) axis, which is the lowest one for this case, has a total energy about 2.54eV higher than that at the C-site, indicating that the H atom prefers to combine with the Be atom rather than the Si atom. In addition, the local minimum along the (100) axis, in this case, has a total energy about 3.50eV higher than the global minimum of the system, indicating that the diffusion of H atom from the global minimum to this location is not favourable.
f?! ai.
4. POSSIBLE STRUCTURE OF THE (R+H) COMPLEX IN Si Intuitively we believed that the H atom in the (Be, Si) system would be at the bond-centred position of Be-Si, just as H behaves in the (B, Si) system [ 1I]. This belief relies strongly on the fact that both Be and B belong to the second period of the periodic table and that they both cannot extend their outermost shell electronic configuration to occupy more than eight electrons. However, no global minimum energy could be obtained for the Be-H-Si bond-centred configuration even after the relaxation. The reluctance for the Be-Si bond to be relaxed, as compared to the B-Si bond, when the H atom is placed at the respective bond-centred, could be explained by the much greater relaxation energy required by the Be-Si bond (9.39eV) than that required by the B-Si bond (5.3 eV) [I I]. The bonding of the Be atom with the H atom situated close to the C-site seems to face the problem of violating the ‘octet rule’. One way to overcome this problem is to have more ionic bond character between the Be and H atoms by assuming that the H atom could donate a partial charge to the Be atom to become H6+, whereas the Be atom becomes Be’-. This non-directional character of ionic bonding might further be supported by, and might account for, the observed experimental evidence on the tunnelling effect [IO] of the H atom around the vicinity of the Be atom through all the equivalent C-sites over the corresponding small energy wells. The fact that the hydrogen is able to tunnel further indicates that this hydrogen is most likely to be the H or H’ species rather than the H- species because of the size effect. The above discussion leads to some insight of the mechanism of the passivation of Be with H in Si. The negatively charged Be will be compensated by the positively charged H by interacting with each other to form an ion pair as follows; Be*,. + H6+ +(Be6-H6+)‘. 5. CONCLUSION In this study, we used the CNDO method to find out the behaviour of the H atom in the silicon crystal lattice with a substituted Be atom. The structure of (Be, H) in Si is somewhat different from that of (B, H) in Si. At the global minimum, the H atom is found to be situated not at the BM site, but at the location which is along the (100) axis and close to the C-site, with the relaxation of the nearest Si atoms as well as the Be atom. Based on the calculated energy profiles, the diffusion path of the H atom, from one global minimum to another equivalent global minimum,
Beryllium-hydrogen Table 2. Energy _. difference between the C-site and other sites Site
Denteneer ef a/. [9]
Present study
C-site BM-site AB-site
0 0.1 eV 0.4 eV
0 0.49 eV 1.20eV
may be via the BM-site. Here the barrier is 0.49eV. With this low energy barrier and the fact that the relaxation around the C-site is small, it is likely that the H atom is tunnelling around these locations. This finding is qualitatively in good agreement with that reported by Denteneer et al. [9]. However, other than the finding that the global minimum is located at the C-site, our energy results are in general larger than those reported by Denteneer et al., as can be seen from Table 2. REFERENCES Pankove J. I., Zanzucchi P. J., Magee C. W. and Lucovsky G., Appi. Phys. Left. 46, 421 (1985). Assali L. V. C. and Leite J. R.. Phys. Rev. Lear. 55,980 (1985); 56, 403 (1986). Capizzi M., Mittiga A. and Frova A., in Proceedings of the 18th International Conference on the Physics of Semiconducrors, Stockholm, p. 995, 11-15 August (1986). Pantelides S., in Proceedings of the 18th International Conference on the Physics of Semiconductors, Stockholm, p. 987, II-15 August (1986).
complex in silicon
589
5. Johnson N. M. and Mover M. D. AI&. . . Phvs. , Lert. 46. 787 (1985). 6. Pandove 1. I., Carlson D. E., Berkeyheiser J. E. and Wance R. 0.. Phvs. Rev. Lett. 51. 2224 (1983). 7. DeLeo G. G..and Fowler W. B., i. Elect;. Maier. 148, 745 (1985). 8. Denteneer P. J. H., Van de Walle C. G. and Pantelides S. T., Phys. Rev. B39, 10,809 (1989). 9. Denteneer P. J. H.. Van de Walle C. G. and Pantelides S. T., Phys. Rev. ierr. 62, 1884 (1989). 10. Muro K. and Sievers A. J., Phys. Rev. Lerf. 57, 897 (1986).
I I. bng C. K. and Khoo G. S., J. Phys. Cond. Mat!. 3,675 (1991). 12. Harker A. H. and Larkins F. P., J. Phys. C: Solid State Phys. 12, 2489 (1979).
13. Pople J. A. and Beveridge D. L., Approximate Molecuhr Orbiral Theory. McGraw-Hill, London (1970). 14. Harker A. H. and Lyon J. B., Hanvell Report AERE
R8598 (1979). 15. Mainwdod A. and Stoneham A. M., Physica 116B. 101
(1963). 16. Khoo G. S. and Ong C. K., J. Phys. C: Solid State Phys. 20, 1385 (1987). 17. Khoo G. S. and Ong C. K., J. Phys. C: Solid Stare Phys. 20, 5037 (1987). 18. Khoo G. S. and Ong C. K., J. Phys. Chem. Solids 51, 1177 (1990). 19. Pople J. A. and Beveridge D. L., Approximate Molecular Orbital Theory, p. 89. McGraw-Hill, London
(1970). 20. Bailar J. C., Emeleus H. J., Nyholm R. and TrotmanDickenson A. F., Comprehensive Inorganic Chemistry, Vol. 1, p. 545. Pergamon Press, Oxford (1973). 21. Bailar J. C., Emeleus H. J., Nyholm R. and TrotmanDickenson A. F., Comprehensive Inorganic Chemistry, Vol. I, p. 1381. Pergamon Press, Oxford (1973).
1992
0022-X97/92 WI0 + 0.00 PuganIon Press plc
THE STRUCTURE OF THE BERYLLIUM-HYDROGEN COMPLEX IN SILICON L. S. CHIA,t N. K. GoHt and C. K. ONG Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511 (Received 14 May 1991; accepted 4 September 1991)
Abstract-The total energies of the (Be, H) complex in Si have been calculated, when the H atom is moving along the three major axes with the Be atom at a substitutional site, using a self-consistent semi-empirical method. The local minimum for the H atom on the (I IO) plane has also been investigated. The global minimum is found when the H atom is located near the C-site. However, we find that an activation of about 0.49 eV is needed for the H atom to diffuse thermally from one C-site lo the other. Our results further indicate that the H atom has a stronger affinity with the Be rather than the Si atom. A possible mechanism for the passivation of the Be atom by the H atom in crystalline Si is also discussed. Keywordy: Beryllium- hydrogen complex in silicon, CNDO.
1. INTRODUCTION In recent years, the passivation of acceptor impurities in silicon in the presence of hydrogen has attracted a great deal of research interest, because of its implications in developing modern electronic devices. It is interesting to note that different mechanisms have been proposed to explain the effect of hydrogen on passivation [ 141. However, it is still debatable and inconclusive, since not many structures of such Si systems have been studied in detail and revealed in depth. Among the (acceptor, H) in Si systems, (B, H) in Si is supposed to be the only one which is well documented. Its experimental data coincide well with the theoretically derived model [S-9]. On the other hand, information on the theoretical structure of (Be, H) in the Si system is reported only by Denteneer et al. [9]. Their calculations are carried out using the first-principles pseudopotential-density-functional method. Their main findings are as follows. (1) Be binds a H atom rather strongly at several symmetrically equivalent sites in its immediate vicinity. (2) The global minimum is at the C site, with little relaxation of the host crystal. (3) Proton tunnelling between equivalent C sites has been found to be possible. As proton tunnelling is not observed in the case of (B, H) in Si(l I), the structure of (Be, H) in Si should be different from that of (B, H) in Si. Since we have applied the Complete Neglect of the Differential Overlap (CNDO) method successfully
t Permanent address: National Institute of Education, Nanyang Technological University, 469 Bukit Timah Road, Singapore 1025. PCS 13,444
to investigate the structure and properties of (B, H) in Si[l 11, we hope therefore, that by using the same method, we are able to contribute some understanding to the structure and properties of (Be., H) in Si system. Furthermore, it is desirable to compare the results of the two different total energy algorithms, namely the CNDO method and the first-principles pseudopotential-density-functional method.
2. METHOD AND CALCULATIONS
In our study, we employ the Complete Neglect of the Differential Overlap (CNDO) method (I 11. This is based on a semi-empirical self-consistent molecular orbital theory, whereby approximations are systematically applied to the matrix elements of the HartreeFock-Roothaan equations through the introduction of three semi-empirical parameters. These parameters are: (1) the orbital exponent (t); (2) the electronegativity (E), and (3) the bonding parameter (j?). The values of these parameters for the respective atoms are presented in Table 1. The parameters for Si are from Harker and Larkins [12], whereas those for H and Be are from Pople and Beveridge [ 131.Here, we use the Hatwell Moses Code [I41 to perform our calculations for studying the behaviour of H in Si with substitutional Be. The code involves the computation of routines in which equations are solved by self-consistent iterative technique until convergence of the total energy minimum is achieved. The successful applications of the CNDO method to the investigations of the structures and properties of defects and defect complexes in semiconductors have been well documented [lS-181.
585
L. S. CHIA
586
et al.
Table 1. The CNDO narameters used Atom H Be Si Si*
Orbital exponent tsp (Bohr-‘) 1.20 0.975 1.54 1.54
Electronegativity cs(ev) ep(ev) 7.18 0 5.95 2.56 6.30 4.50 6.30 4.50
With regards to the simulated Be-H complex in Si, we use a 65atom molecular cluster, where we place the Be atom at a substitutional site. The dangling bonds at the edges of this cluster are saturated by single sp3 hybrids of silicon (Si*). We have 36 of these in our 65-atom cluster. These hybrid atoms have the same parameters as Si except that their /I values are set to zero.
Bonding parameter B (ev) - 9.00 - 13.00 - 6.40 l-l
of about 0.50 to 1.30 eV are needed for the H atom to move around the Be atom in a spherical shell which is rather large. (4
3. RESULTS AND DISCUSSION Similarly to our previous study on (B, H) in the Si system [l 11,we first perform our calculations on the Si cluster with the Be atom being placed at the substitutional site, and the H atom moving along the three major axes, namely (1 1 1), (110) and (loo), in the vicinity of the Be atom [Fig. l(a)]. Figure l(b) illustrates the variation of the total energy of the corresponding H atom moving along these axes. The profiles of these total energy curves look very similar and trough-like. They resemble very closely those observed in the (B, H) in Si system [ll], even the order of lowering the total energy, from (111) to (110) to (100) axes, is quite similar for both systems. Such a similarity may suggest that (Be, H) in Si is likely to have the same structure as (B, H) in Si. However, it has been found that H stabilizes at different sites when it pairs with different impurities, and that the nature of the site determines both the electrical activity of the pair and the possibility of thermal and quantum-mechanical motion around the impurity [9]. Thus, the structure of (Be, H) in Si need not be the same as that of (B, H) in Si. The equilibrium distances of the H atom from the substitutional Be atom along the (11 l), (110) and (100) axes are found to be 1.36 A, 1.37 8, and 1.42 A, respectively. All the values here are quite close to that observed for Be-H in BeH [19] which is 1.34 A, but much smaller in comparison with the experimental value of 1.63 8, for the Be-H bridging bond in beryllium borohydride [20]. The local energy minimum along the (100) axis is situated very close to the C-site (being 0.07 A away from the C-site). It is 0.55 eV lower than the minimum along the (110) axis and 1.29 eV lower than that along the (111) axis [which is at the antibonding (AB) site]. Thus, the diffusion channel for the H atom seems to be in a restricted zone. The activation energy
l
0
(b)
Be
atom
Si atom
EneqykVv) -=lll> 4112
\
2.00
180
1.80 s D&invx
of
H
from
Be
&am(A)
Fig. 1. (a) Diagram illustrating the location of the H atom (X,) in the vicinity of the substitutional Be atom in the silicon crystal lattice on the (110) plane. (b) The variation in the total energy of the Be-H complex in the silicon crystal lattice shown in Fig. l(a) along the three major axes.
Beryllium-hydrogen
complex in silicon
We performed further calculations to find out the local minimum on the (110) plane. The equilibrium distance found along the (110) axis (1.37 A) is used as the radius for the circle which represents the path of the H atom around the Be atom. On the (110) plane, when the atoms are not allowed to relax, there are no other local minima besides the ones that correspond to those found along the (100) axis, i.e. A and Q [Fig. 2(b)]. However, we are expecting a large relaxation at some sites for the H atom. One of them is the bond centred (BM) site of Si-Be, as in the case of (B, H) in Si. By allowing Si, H and Be to relax
(4
away along the (111) axis from their original positions by 0.23 A, 0.31 A and 0.28, respectively, and relaxations of their nearest Si atoms by 0.11 A to O.l4A, there is a decrease of the total energy at the local minimum by 9.39 eV. However, the total energy for the H atom of the BM site is still not the global minimum. The other site that we have considered is the C-site [A or Q in Fig. 2(b)]. By allowing the H, Be and Si atoms to move freely along the (100) axis, from their original positions, by about 0.19 A, 0.19 8, and 0.09 A, respectively, and some relaxations of their nearest neighbours, the total energy for the H
a (110 )
/fl-----
587
plane
J
-I- --in” site
I
--Q
-l--
/
/’
lH--I--W semi-circular path of
0 0
0.001
AIQ H atom in (llO)$an@ Be atom
Si atom
/
A
BM
I
Q
Labelled poir& along circular path AIQ in (110)plane
Fig. 2. (a) The semicircular path of the H atom as it is ‘pqved in the (110) plane. (b) The energy profiles as the H atom is moved along the path in 2(a).
588
L. S. CHIA
atom at this position (global minimum) is the lowest, which is 0.49 eV lower than that at the BM site (after relaxation). The equilibrium distance for Si-H at the global minimum is 1.84 A, which is much longer than the experimental value of 1.48 di found for Si-H in SiH, [21]. The corresponding distance for Be-H becomes I .42 8, which is identical to that of Be-H found at the local minimum along the (100) axis, and also close to the reported value of I .34 8, for Be-H in BeH [19]. The above observations suggest that: (I) the H atom has a stronger affinity with the Be atom than the Si atom; (2) the movement of the H atom into the bond-centred position of the Si-Be is not favoured, in contrast to the case of (B, H) in Si. A similar treatment has been applied to the AB site. By allowing the H, Be and Si atoms to relax away, along the (I 11) axis, from their original positions by 0.085 A, 0.113 8, and 0.113 A, respectively, and some relaxations of their nearest Si atoms, a local minimum is obtained. However, the total energy for the H atom at this local minimum is 1.20 eV higher than that at the global minimum (i.e. the one near the C site). In order to have a better understanding of the structure of the Be-H complex in Si, we have also investigated the movement of H in the environment of four Si atoms, where one of the Si atoms is tetrahedrally bonded to a Be atom. The treatment similar to that mentioned earlier has been applied to the H atom to move it along the three major axes, namely (I 1I), (1 IO) and (loo), in the vicinity of the central Si atom. The equilibrium distances of the H atom from the Si atom along the (I 1l), (1 IO) and (100) axes are found to be I.55 A, 1.61 A and 1.63 A, respectively. All these values are in good agreement with the equilibrium distance of 1.53 A for Si-H found in the EH complex in Si [I 11 and are also compatible with the experimental value of 1.488, for Si-H in SiH, 1211. Furthermore the profiles of these total energy curves are similar and trough-like. However, the total energies of the local minima along the three major axes are all much higher than those mentioned before. For example, before relaxation, the energy minimum along the (100) axis, which is the lowest one for this case, has a total energy about 2.54eV higher than that at the C-site, indicating that the H atom prefers to combine with the Be atom rather than the Si atom. In addition, the local minimum along the (100) axis, in this case, has a total energy about 3.50eV higher than the global minimum of the system, indicating that the diffusion of H atom from the global minimum to this location is not favourable.
f?! ai.
4. POSSIBLE STRUCTURE OF THE (R+H) COMPLEX IN Si Intuitively we believed that the H atom in the (Be, Si) system would be at the bond-centred position of Be-Si, just as H behaves in the (B, Si) system [ 1I]. This belief relies strongly on the fact that both Be and B belong to the second period of the periodic table and that they both cannot extend their outermost shell electronic configuration to occupy more than eight electrons. However, no global minimum energy could be obtained for the Be-H-Si bond-centred configuration even after the relaxation. The reluctance for the Be-Si bond to be relaxed, as compared to the B-Si bond, when the H atom is placed at the respective bond-centred, could be explained by the much greater relaxation energy required by the Be-Si bond (9.39eV) than that required by the B-Si bond (5.3 eV) [I I]. The bonding of the Be atom with the H atom situated close to the C-site seems to face the problem of violating the ‘octet rule’. One way to overcome this problem is to have more ionic bond character between the Be and H atoms by assuming that the H atom could donate a partial charge to the Be atom to become H6+, whereas the Be atom becomes Be’-. This non-directional character of ionic bonding might further be supported by, and might account for, the observed experimental evidence on the tunnelling effect [IO] of the H atom around the vicinity of the Be atom through all the equivalent C-sites over the corresponding small energy wells. The fact that the hydrogen is able to tunnel further indicates that this hydrogen is most likely to be the H or H’ species rather than the H- species because of the size effect. The above discussion leads to some insight of the mechanism of the passivation of Be with H in Si. The negatively charged Be will be compensated by the positively charged H by interacting with each other to form an ion pair as follows; Be*,. + H6+ +(Be6-H6+)‘. 5. CONCLUSION In this study, we used the CNDO method to find out the behaviour of the H atom in the silicon crystal lattice with a substituted Be atom. The structure of (Be, H) in Si is somewhat different from that of (B, H) in Si. At the global minimum, the H atom is found to be situated not at the BM site, but at the location which is along the (100) axis and close to the C-site, with the relaxation of the nearest Si atoms as well as the Be atom. Based on the calculated energy profiles, the diffusion path of the H atom, from one global minimum to another equivalent global minimum,
Beryllium-hydrogen Table 2. Energy _. difference between the C-site and other sites Site
Denteneer ef a/. [9]
Present study
C-site BM-site AB-site
0 0.1 eV 0.4 eV
0 0.49 eV 1.20eV
may be via the BM-site. Here the barrier is 0.49eV. With this low energy barrier and the fact that the relaxation around the C-site is small, it is likely that the H atom is tunnelling around these locations. This finding is qualitatively in good agreement with that reported by Denteneer et al. [9]. However, other than the finding that the global minimum is located at the C-site, our energy results are in general larger than those reported by Denteneer et al., as can be seen from Table 2. REFERENCES Pankove J. I., Zanzucchi P. J., Magee C. W. and Lucovsky G., Appi. Phys. Left. 46, 421 (1985). Assali L. V. C. and Leite J. R.. Phys. Rev. Lear. 55,980 (1985); 56, 403 (1986). Capizzi M., Mittiga A. and Frova A., in Proceedings of the 18th International Conference on the Physics of Semiconducrors, Stockholm, p. 995, 11-15 August (1986). Pantelides S., in Proceedings of the 18th International Conference on the Physics of Semiconductors, Stockholm, p. 987, II-15 August (1986).
complex in silicon
589
5. Johnson N. M. and Mover M. D. AI&. . . Phvs. , Lert. 46. 787 (1985). 6. Pandove 1. I., Carlson D. E., Berkeyheiser J. E. and Wance R. 0.. Phvs. Rev. Lett. 51. 2224 (1983). 7. DeLeo G. G..and Fowler W. B., i. Elect;. Maier. 148, 745 (1985). 8. Denteneer P. J. H., Van de Walle C. G. and Pantelides S. T., Phys. Rev. B39, 10,809 (1989). 9. Denteneer P. J. H.. Van de Walle C. G. and Pantelides S. T., Phys. Rev. ierr. 62, 1884 (1989). 10. Muro K. and Sievers A. J., Phys. Rev. Lerf. 57, 897 (1986).
I I. bng C. K. and Khoo G. S., J. Phys. Cond. Mat!. 3,675 (1991). 12. Harker A. H. and Larkins F. P., J. Phys. C: Solid State Phys. 12, 2489 (1979).
13. Pople J. A. and Beveridge D. L., Approximate Molecuhr Orbiral Theory. McGraw-Hill, London (1970). 14. Harker A. H. and Lyon J. B., Hanvell Report AERE
R8598 (1979). 15. Mainwdod A. and Stoneham A. M., Physica 116B. 101
(1963). 16. Khoo G. S. and Ong C. K., J. Phys. C: Solid State Phys. 20, 1385 (1987). 17. Khoo G. S. and Ong C. K., J. Phys. C: Solid Stare Phys. 20, 5037 (1987). 18. Khoo G. S. and Ong C. K., J. Phys. Chem. Solids 51, 1177 (1990). 19. Pople J. A. and Beveridge D. L., Approximate Molecular Orbital Theory, p. 89. McGraw-Hill, London
(1970). 20. Bailar J. C., Emeleus H. J., Nyholm R. and TrotmanDickenson A. F., Comprehensive Inorganic Chemistry, Vol. 1, p. 545. Pergamon Press, Oxford (1973). 21. Bailar J. C., Emeleus H. J., Nyholm R. and TrotmanDickenson A. F., Comprehensive Inorganic Chemistry, Vol. I, p. 1381. Pergamon Press, Oxford (1973).