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Vacancies in a Si(111) thin film
0038-1098/81/460919-03$02.00/O
Solid State Communications, Vol. 40, pp. 919-921. Pergamon Press Ltd. 1981. Printed in Great Britain.
VACANCIES IN A Si( 111) THIN FILM* S. Erkoc, M. Tomak and S. Ciraci Department
of Physics, Middle East Technical University,
Ankara, Turkey
(Received 1 June 1981 by M. Cardona) We investigated the electronic structure of an ideal vacancy in the Si( 111) thin film by using empirical tight binding method. The supercell model used in our calculations predicted vacancy related states in general agreement with previous works. For the vacancy near the surface, it is found that the bound state energies shift to higher energies as the vacancy moves toward the surface. At the surface, however, it was seen that the vacancy bound state mix with the dangling bond surface states. Considering energy locations in the band gap, we propose that vacancies created in the surface region may account for the peak (at about -0.5 eV above the valence band edge) in the density of interface states observed at the interface of the Si-SiOzjunction. _
SINCE metal-oxide-semiconductor transistors have found widespread applications in technology, the physics of the interface forming between oxide and semiconductor has become the focus of attention. In the junction of SiOz-Si, the lattice-mismatch between two crystals may create various defects near the surface of silicon while the oxidation takes place. With regard to these defects, it is believed that vacancies near the surface may induce so-called “interface states” lying in the band gap of silicon and, may play a significant role in determining the electronic properties of the junction
PI. In order to explore the effect of the vacancy on the interface properties we performed calculations by using several models. First, we considered an ideal vacancy in bulk silicon, so that we were able to compare our results with previous studies. In a similar way, we investigated a divacancy, in order to see the effect of second vacancy next to the existing one. Vacancies near the interface were studied in a Si( 111) thin film consisting of 6 atomic-layers. The electronic structure of a vacancy lying at the first, second, and third layer, respectively, are calculated separately. In the present study we use empirical tight binding method with the energy parameters describing only s- and p-atomic-like orbital interactions which were determined by Pandey and Phillips [2]. An isolated vacancy in a crystal is simulated by a supercell of (3 x 3 x 3) for the bulk, and by a surface supercell of (3 x 3) for the thin film (both consisting of 53 atoms and a vacancy). No lattice relaxation is taken into account, and energy parameters * This work is supported by TBTAK, the Scientific and Technical Research Council of Turkey.
belonging to atoms next to the vacancy are assumed to be unaltered. In such a representation vacancy-vacancy interaction between supercells replaces the defect level by a band of - 0.2 eV width [3]. This is expected not to affect our conclusion in any essential manner, [3,4]. By imposing periodic boundary conditions we dialogalize the secular matrix at the center of the Brillouin zone and obtain the energies of the states. Figure 1 presents the energy level diagram of (a) bulk silicon, (b) an ideal vacancy in bulk silicon, (c) a divacancy in bulk silicon, (d) a 6-layer thin film with a vacancy, (e) at the surface, (f) at the second atomic layer, and (g) at the third atomic layer. Now let us discuss our results for the electronic structure and start with Fig. 1(a), where the energies corresponding to the F-point of the supercell are shown. It should be noted that 27-k points of the reduced Brillouin Zone map on to the center of supercell Brillouin Zone. Numbers near the levels denote the degeneracy. In panel (b) the prominent feature of an ideal vacancy appears as a state (illustrated by the dotted lines) in the fundamental gap, 0.4 eV above the valence band maximum. This level consisting of a triplet of t2 symmetry corresponds to vacancy bound-states, which are made up from s + p (dangling bond) orbitals of silicon atoms around the vacancy. 57 and 20% of the charge of these states are localized on the atoms in the first and second neighbourhood of the vacancy, respectively. It is worth noting that calculations using the smaller supercell consisting of 15 atoms and a vacancy predicted boundstates at 0.5 eV indicating higher vacancy-vacancy interactions. Previous studies using different approaches reported different energies, ranging from 0.2 to 0.7 eV for the bound-state energy of the ideal vacancy 919
920
VACANCIES IN A Si(l11)
THIN FILM
Vol. 40, No. 10
2 I
w
I
I
Density
of
b = Vacancy c=Divacancy
-2
g=Vacancy
> -?4
r
z cc
K
3GLayer
f = Vacancy
216 Layer
e= Surface
vacancy
r
Fig. 2. Fundamental band gap region of Si( 1 I l)- 12-layer thin film. Sr (by bold lines) shows the dangling bond surface state bands of the 6-layer thin film. Broken lines correspond to the same surface state bands (with smaller splittings) of 12-layer thin film. Lines labeled by b, c, g, f, e denote various vacancy bound-state of the bulk silicon and 6-layer thin film calculated at the F-point. Density of interface states in the fundamental gap (measured by the conductance technique) is reproduced from [ll].
ii-6 W
-8
-10
-12
L Fig. 1. Electronic energy level diagram for (a) 54 atomunit cell bulk Si; (b) ideal vacancy in the bulk silicon; (c) ideal divacancy; (d) Si( 111) ~ 6-layer thin film; (e) vacancy at the surface; (f) vacancy at the 2nd layer; (g) vacancy at the 3rd layer. __ = bulk state, . . . = vacancy bound state, *= weakly localised vacancy resonance state, + = strongly localized vacancy resonance state, - - - - - - = surface state. Numbers indicate degeneracy of the state. Energies are measured relative to the valence band edge. [3,5-71. The influence of the vacancy is also seen in the valence and conduction band, where states splitting from bulk degenerate levels appear generally as resonance. In the framework of the tight binding approach we are able to identify resonance states by examining their localization [8,9]. A state 1.4 eV below the valence band edge is formed mainly from pw, P,,, p,-orbitals of four silicon atoms around the vacancy, and 92% of its charge is localized on these atoms. s-Orbitals of the same atoms generate also a resonance state of a1 symmetry positioned at - 7.5 eV. In addition to these highly localized states, resonance states at 3.8 eV (in the conduction band) of tz symmetry, and at -4.2, -6.6, -8.6, - 10.5 eV (in the valence band) could be identified. Some of them are probably induced by the vacancyvacancy interactions.
By removing one more atom lying next to the existing vacancy and leaving the rest of the atoms in their ideal positions we created an ideal divacancy. Since we are mainly interested in the states lying in the fundamental gap, we first concentrate upon the bound-states. In panel (c) we see two doublets (at 0.5 eV and at 0.1 eV) and one singlet (at the edge of valence band) all having s + p orbital character. The two doublets have 40% of their charge localized around the divacancy, whereas the singlet at the edge of the band is less localized. Consistent with the bulk bands, resonance states (at -0.7, - 1.6, - 1.8, -4.2, -7.1, -8.0, -9.5, -10.5 and - 10.7 eV, and 3.8 eV in the conduction band) have considerable s-orbital character below ---8.8 eV, whereas p-orbital contribution is found to increase as one goes towards the top of the valence band. As far as the divacancy is concerned, we are able to compare our results with the Extended-Hiickel calculations performed by Lee and McGill [4], where they found two boundstates at 0.4 eV and resonance states at - 0,19, -0.53 and -0.79 eV in the valence band. So far we have discussed the electronic structure of a bulk vacancy and divacancy. We now confine ourselves to the surface, and start with a thin film free of defects. Panel (d) (Fig. 1) presents energy eigenstates of six-layer slab. The dashed lines near the gap correspond to the dangling bond surface states which form the Sr bands of the (1 x 1) primitive surface unit cell illustrated in Fig. 2. Due to the interactions via backbonds the Sr bands derived from the top and bottom surfaces of the
Vol. 40, No. 10
VACANCIES IN A Si(ll1)
6-layer thin film split (- 0.8 eV at I’), but this splitting is reduced in a 12-layer thin film. As to the dashed lines in deeper energy regions, they belong to surface backbonding and resonance states localized in the 6-layer thin film [8,9]. We now go further, and examine panel (g) corresponding to a thin film having a vacancy at the third atomic layer. The bound state at 0.6 eV is mixed with surface states and exhibits pZ- (perpendicular to the surface) orbital character, whereas the doublet below (at 0.5 eV) is formed from s + pZ orbitals around the vacancy. Below this doublet, dangling bond surface states form a band of 0.8 eV width. The overall behaviour of the resonance states is similar to that of a bulk vacancy, but their energy positions are shifted. Next, the vacancy is moved toward the surface until it reaches the second atomic layer. Here, the first boundstate moved to higher energy and is positioned at 0.7 eV. It is generated from the p,-orbitals, and has 47% localization. The doublet 0.6 eV above the valence band maximum is strongly localized on the surface and on second layer atoms lying around the vacancy, but not on the third layer. Dangling bond surface states and vacancyrelated resonance states in panel (f) continue to exhibit similar characters as described in the previous case. The doublet just below the surface states (at -0.5 eV) seems to present an exception. Highly perturbed back-bonds are believed to generate the localized states of this doublet. Finally, we move to the surface, remove one atom, and thus create the surface vacancy. At this point one recognizes that the surface vacancy differs from the bulk vacancy, as far as the number of broken bonds are concerned. Therefore one may expect that the spectra exhibit significant changes. This is, in fact, demonstrated in panel (e), where the highest localized states in the band gap become dangling bond surface states, whereas the vacancy-related doublet moves to lower energy. The states of this doublet are formed from pX and py orbitals of the second layer atoms and behave like a resonance state in the surface state band. In the valence band, most of the vacancy-related resonance states disappear, leaving only the s-orbital state at - 8.7 eV. In conclusion, the electronic structure of a vacancy is affected as the vacancy moves towards the surface such that a tz bound-state splits and moves to higher
THIN FILM
921
energy. Similar behaviour was reported previously for the neutral cation vacancy on the GaAs(ll0) surface [lo]. When the vacancy reaches the surface, the spectra exhibit significant changes: vacancy bound-states move to lower energy and eventually into the dangling bond surface states. This signifies that vacancy bound-states become resonance states. As the oxidation takes place on the Si(ll1) surface, oxygen atoms saturate dangling bonds and remove surface states from the fundamental gap. In the meantime, many vacancies are created due to the lattice-mismatch. Bound-states of these vacancies distributed in the energy range from 0.7 to 0.5 eV may contribute to the peak (at about -0.5 eV above the valence band maximum) in the density of interface states observed at the interface of Si-SiOZ junction [ 11, 121 (see Fig. 2). Acknowledgements - The authors would like to thank Dr B. Katircioglu and Dr M.E. iSzsan for helpful discussions and members of the Computer Center of METU for providing computer facilities. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12.
Y.C. Cheng,Prog. Surt Sci 8,181 (1977). K.C. Pandey & J.C. Phillips, P&s. Rev. Lett. 32, 1433 (1974). F. Casula, S. Ossicini & A. Selloni, Solid State Commun. 28, 141 (1978). T.F. Lee & T.C. McGill, J. P&s. C: Solid State Phys. 6,3438 (1973). J. Bernholc & S.T. Pantelides, Phvs. . Rev. B18. 1780 (1978). G.A. Baraff, E.O. Kane & M. Schliiter, Phys. Rev. B21,5662 (1980). D.A. Papaconstantopoulos & E.N. Economou, Phys. Rev. B22,2903 (1980). S. Ciraci, I.P. Batra & W.A. Tiller, Phys. Rev. B12, 5811 (1975). S. Ciraci & I.P. Batra, Phys. Rev. B15,3254 (1977). Murray S. Daw & D.L. Smith, Phys. Rev. B20, 5150 (1979). M. Schulz, Insulating Films on Semiconductors 1979 (Edited by G.G. Roberts and M.J. Morant), p. 87. The Institute of Physics, Bristol, London (1979). P.W. Chye, I. Lindau, P. Pianetta, C.M. Garner, C.Y. Su & W.E. Spicer, Phys. Rev. B18,5545 (1978).
Solid State Communications, Vol. 40, pp. 919-921. Pergamon Press Ltd. 1981. Printed in Great Britain.
VACANCIES IN A Si( 111) THIN FILM* S. Erkoc, M. Tomak and S. Ciraci Department
of Physics, Middle East Technical University,
Ankara, Turkey
(Received 1 June 1981 by M. Cardona) We investigated the electronic structure of an ideal vacancy in the Si( 111) thin film by using empirical tight binding method. The supercell model used in our calculations predicted vacancy related states in general agreement with previous works. For the vacancy near the surface, it is found that the bound state energies shift to higher energies as the vacancy moves toward the surface. At the surface, however, it was seen that the vacancy bound state mix with the dangling bond surface states. Considering energy locations in the band gap, we propose that vacancies created in the surface region may account for the peak (at about -0.5 eV above the valence band edge) in the density of interface states observed at the interface of the Si-SiOzjunction. _
SINCE metal-oxide-semiconductor transistors have found widespread applications in technology, the physics of the interface forming between oxide and semiconductor has become the focus of attention. In the junction of SiOz-Si, the lattice-mismatch between two crystals may create various defects near the surface of silicon while the oxidation takes place. With regard to these defects, it is believed that vacancies near the surface may induce so-called “interface states” lying in the band gap of silicon and, may play a significant role in determining the electronic properties of the junction
PI. In order to explore the effect of the vacancy on the interface properties we performed calculations by using several models. First, we considered an ideal vacancy in bulk silicon, so that we were able to compare our results with previous studies. In a similar way, we investigated a divacancy, in order to see the effect of second vacancy next to the existing one. Vacancies near the interface were studied in a Si( 111) thin film consisting of 6 atomic-layers. The electronic structure of a vacancy lying at the first, second, and third layer, respectively, are calculated separately. In the present study we use empirical tight binding method with the energy parameters describing only s- and p-atomic-like orbital interactions which were determined by Pandey and Phillips [2]. An isolated vacancy in a crystal is simulated by a supercell of (3 x 3 x 3) for the bulk, and by a surface supercell of (3 x 3) for the thin film (both consisting of 53 atoms and a vacancy). No lattice relaxation is taken into account, and energy parameters * This work is supported by TBTAK, the Scientific and Technical Research Council of Turkey.
belonging to atoms next to the vacancy are assumed to be unaltered. In such a representation vacancy-vacancy interaction between supercells replaces the defect level by a band of - 0.2 eV width [3]. This is expected not to affect our conclusion in any essential manner, [3,4]. By imposing periodic boundary conditions we dialogalize the secular matrix at the center of the Brillouin zone and obtain the energies of the states. Figure 1 presents the energy level diagram of (a) bulk silicon, (b) an ideal vacancy in bulk silicon, (c) a divacancy in bulk silicon, (d) a 6-layer thin film with a vacancy, (e) at the surface, (f) at the second atomic layer, and (g) at the third atomic layer. Now let us discuss our results for the electronic structure and start with Fig. 1(a), where the energies corresponding to the F-point of the supercell are shown. It should be noted that 27-k points of the reduced Brillouin Zone map on to the center of supercell Brillouin Zone. Numbers near the levels denote the degeneracy. In panel (b) the prominent feature of an ideal vacancy appears as a state (illustrated by the dotted lines) in the fundamental gap, 0.4 eV above the valence band maximum. This level consisting of a triplet of t2 symmetry corresponds to vacancy bound-states, which are made up from s + p (dangling bond) orbitals of silicon atoms around the vacancy. 57 and 20% of the charge of these states are localized on the atoms in the first and second neighbourhood of the vacancy, respectively. It is worth noting that calculations using the smaller supercell consisting of 15 atoms and a vacancy predicted boundstates at 0.5 eV indicating higher vacancy-vacancy interactions. Previous studies using different approaches reported different energies, ranging from 0.2 to 0.7 eV for the bound-state energy of the ideal vacancy 919
920
VACANCIES IN A Si(l11)
THIN FILM
Vol. 40, No. 10
2 I
w
I
I
Density
of
b = Vacancy c=Divacancy
-2
g=Vacancy
> -?4
r
z cc
K
3GLayer
f = Vacancy
216 Layer
e= Surface
vacancy
r
Fig. 2. Fundamental band gap region of Si( 1 I l)- 12-layer thin film. Sr (by bold lines) shows the dangling bond surface state bands of the 6-layer thin film. Broken lines correspond to the same surface state bands (with smaller splittings) of 12-layer thin film. Lines labeled by b, c, g, f, e denote various vacancy bound-state of the bulk silicon and 6-layer thin film calculated at the F-point. Density of interface states in the fundamental gap (measured by the conductance technique) is reproduced from [ll].
ii-6 W
-8
-10
-12
L Fig. 1. Electronic energy level diagram for (a) 54 atomunit cell bulk Si; (b) ideal vacancy in the bulk silicon; (c) ideal divacancy; (d) Si( 111) ~ 6-layer thin film; (e) vacancy at the surface; (f) vacancy at the 2nd layer; (g) vacancy at the 3rd layer. __ = bulk state, . . . = vacancy bound state, *= weakly localised vacancy resonance state, + = strongly localized vacancy resonance state, - - - - - - = surface state. Numbers indicate degeneracy of the state. Energies are measured relative to the valence band edge. [3,5-71. The influence of the vacancy is also seen in the valence and conduction band, where states splitting from bulk degenerate levels appear generally as resonance. In the framework of the tight binding approach we are able to identify resonance states by examining their localization [8,9]. A state 1.4 eV below the valence band edge is formed mainly from pw, P,,, p,-orbitals of four silicon atoms around the vacancy, and 92% of its charge is localized on these atoms. s-Orbitals of the same atoms generate also a resonance state of a1 symmetry positioned at - 7.5 eV. In addition to these highly localized states, resonance states at 3.8 eV (in the conduction band) of tz symmetry, and at -4.2, -6.6, -8.6, - 10.5 eV (in the valence band) could be identified. Some of them are probably induced by the vacancyvacancy interactions.
By removing one more atom lying next to the existing vacancy and leaving the rest of the atoms in their ideal positions we created an ideal divacancy. Since we are mainly interested in the states lying in the fundamental gap, we first concentrate upon the bound-states. In panel (c) we see two doublets (at 0.5 eV and at 0.1 eV) and one singlet (at the edge of valence band) all having s + p orbital character. The two doublets have 40% of their charge localized around the divacancy, whereas the singlet at the edge of the band is less localized. Consistent with the bulk bands, resonance states (at -0.7, - 1.6, - 1.8, -4.2, -7.1, -8.0, -9.5, -10.5 and - 10.7 eV, and 3.8 eV in the conduction band) have considerable s-orbital character below ---8.8 eV, whereas p-orbital contribution is found to increase as one goes towards the top of the valence band. As far as the divacancy is concerned, we are able to compare our results with the Extended-Hiickel calculations performed by Lee and McGill [4], where they found two boundstates at 0.4 eV and resonance states at - 0,19, -0.53 and -0.79 eV in the valence band. So far we have discussed the electronic structure of a bulk vacancy and divacancy. We now confine ourselves to the surface, and start with a thin film free of defects. Panel (d) (Fig. 1) presents energy eigenstates of six-layer slab. The dashed lines near the gap correspond to the dangling bond surface states which form the Sr bands of the (1 x 1) primitive surface unit cell illustrated in Fig. 2. Due to the interactions via backbonds the Sr bands derived from the top and bottom surfaces of the
Vol. 40, No. 10
VACANCIES IN A Si(ll1)
6-layer thin film split (- 0.8 eV at I’), but this splitting is reduced in a 12-layer thin film. As to the dashed lines in deeper energy regions, they belong to surface backbonding and resonance states localized in the 6-layer thin film [8,9]. We now go further, and examine panel (g) corresponding to a thin film having a vacancy at the third atomic layer. The bound state at 0.6 eV is mixed with surface states and exhibits pZ- (perpendicular to the surface) orbital character, whereas the doublet below (at 0.5 eV) is formed from s + pZ orbitals around the vacancy. Below this doublet, dangling bond surface states form a band of 0.8 eV width. The overall behaviour of the resonance states is similar to that of a bulk vacancy, but their energy positions are shifted. Next, the vacancy is moved toward the surface until it reaches the second atomic layer. Here, the first boundstate moved to higher energy and is positioned at 0.7 eV. It is generated from the p,-orbitals, and has 47% localization. The doublet 0.6 eV above the valence band maximum is strongly localized on the surface and on second layer atoms lying around the vacancy, but not on the third layer. Dangling bond surface states and vacancyrelated resonance states in panel (f) continue to exhibit similar characters as described in the previous case. The doublet just below the surface states (at -0.5 eV) seems to present an exception. Highly perturbed back-bonds are believed to generate the localized states of this doublet. Finally, we move to the surface, remove one atom, and thus create the surface vacancy. At this point one recognizes that the surface vacancy differs from the bulk vacancy, as far as the number of broken bonds are concerned. Therefore one may expect that the spectra exhibit significant changes. This is, in fact, demonstrated in panel (e), where the highest localized states in the band gap become dangling bond surface states, whereas the vacancy-related doublet moves to lower energy. The states of this doublet are formed from pX and py orbitals of the second layer atoms and behave like a resonance state in the surface state band. In the valence band, most of the vacancy-related resonance states disappear, leaving only the s-orbital state at - 8.7 eV. In conclusion, the electronic structure of a vacancy is affected as the vacancy moves towards the surface such that a tz bound-state splits and moves to higher
THIN FILM
921
energy. Similar behaviour was reported previously for the neutral cation vacancy on the GaAs(ll0) surface [lo]. When the vacancy reaches the surface, the spectra exhibit significant changes: vacancy bound-states move to lower energy and eventually into the dangling bond surface states. This signifies that vacancy bound-states become resonance states. As the oxidation takes place on the Si(ll1) surface, oxygen atoms saturate dangling bonds and remove surface states from the fundamental gap. In the meantime, many vacancies are created due to the lattice-mismatch. Bound-states of these vacancies distributed in the energy range from 0.7 to 0.5 eV may contribute to the peak (at about -0.5 eV above the valence band maximum) in the density of interface states observed at the interface of Si-SiOZ junction [ 11, 121 (see Fig. 2). Acknowledgements - The authors would like to thank Dr B. Katircioglu and Dr M.E. iSzsan for helpful discussions and members of the Computer Center of METU for providing computer facilities. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12.
Y.C. Cheng,Prog. Surt Sci 8,181 (1977). K.C. Pandey & J.C. Phillips, P&s. Rev. Lett. 32, 1433 (1974). F. Casula, S. Ossicini & A. Selloni, Solid State Commun. 28, 141 (1978). T.F. Lee & T.C. McGill, J. P&s. C: Solid State Phys. 6,3438 (1973). J. Bernholc & S.T. Pantelides, Phvs. . Rev. B18. 1780 (1978). G.A. Baraff, E.O. Kane & M. Schliiter, Phys. Rev. B21,5662 (1980). D.A. Papaconstantopoulos & E.N. Economou, Phys. Rev. B22,2903 (1980). S. Ciraci, I.P. Batra & W.A. Tiller, Phys. Rev. B12, 5811 (1975). S. Ciraci & I.P. Batra, Phys. Rev. B15,3254 (1977). Murray S. Daw & D.L. Smith, Phys. Rev. B20, 5150 (1979). M. Schulz, Insulating Films on Semiconductors 1979 (Edited by G.G. Roberts and M.J. Morant), p. 87. The Institute of Physics, Bristol, London (1979). P.W. Chye, I. Lindau, P. Pianetta, C.M. Garner, C.Y. Su & W.E. Spicer, Phys. Rev. B18,5545 (1978).