- Email: [email protected]
Surface states of GaP (110)
J. Phys. Rimed
Chem. So/i& Vol. in Gnat Britain.
52, No.
S, pp.
705-708,
1991
0022-3697191
$3.00 + 0.00 Pergamon Press pk
SURFACE STATES OF GaP (110) C. K. ONG and K. C. Low Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511 (Received
11 September
1990; accepted 28 November
1990)
Abstract-Chadi’s tight-binding total energy algorithm was used to study the reconstruction of the GaP (110) surface and its intrinsic occupied and unoccupied states. Assuming a rotation-relaxation model, the optimal surface atomic geometry was obtained by minimizing the total energy of the system. The angle of rotation obtained, w = 22”, is near the experimental value of 27.5”. The features of the surface electronic states were determined and described. The calculated intrinsic occupied surface states are in excellent agreement with the experimental data and those for the unoccupied states are about 30% higher than the results of inverse photo-emission experiments. Keywork
Surface states, semiconductor surface, Gap.
1. INTRODUCTION
Recently, there has been a great deal of experimental effort in studying the reconstruction of III-V compound surfaces and their intrinsic occupied and unoccupied states. With the understanding of this information, one may proceed to explain Fermi-level pinning and other metal-semiconductor interface structures. Among the III-V compounds, the GaP (110) surface has drawn most of the attention with its unique characteristic that the unoccupied surface states lie in the energy gap. In the present work, Chadi’s total energy algorithm will be employed, incorporating tight-binding approximation, to study the relaxation of the (110) surface atoms and to determine the stable crystal structure. The calculated surface states will be presented superimposed on the projected bulk bands and are located by visual inspection. 2. THEORY We make use of Chadi’s [l] total energy formalism, E,, = & + U
(1)
where E,,, is the band structure defined as
energy and U is
U=Eii-E,.,
and Koster. The marized in Table the tight-binding The change in
tight-binding parameters are sum1. The l/d2 functional dependence of parameters is imposed throughout. U takes the following form, i>j
AU = c (u,qj+ u,c$), ij
(3)
where 6ij is the fractional change in the distance between two nearest neighbor atoms denoted by i and J ul and u2 are the force-constant parameters and are determined in the usual way as discussed by Chan and Ong [2]: u, = -20.21 eV
u2 = 54.52 eV.
3. RECONSTRUCTED
SURFACE
A 20 atom unit cell as shown in Fig. 1, is used in the present work to represent the ideal terminated GaP (110) surface. Recent ELEED [5-71 and LEED [&lo] experiments on III-V compound semiconductors have shown that the (110) surface is usually distorted with respect to the geometry of an ideal termination of the surface, going through a rotation in such a way that the 1 x 1 periodicity is preserved. The basic feature of these (110) surface reconstruction of III-V compound semiconductors is
(2) Table I. Tight-binding parameters for GaP (110)
the difference between the ion-ion interaction and electron-electron interaction. This term, U, takes into account all other contributions to E,,, . Details of the calculation of Eb. were given by Chadi [l] and Chan and Ong [2]. Basically, the tightbinding model of Slater and Koster [3] was used with the nearest neighbors considered. The tight-binding parameters for the Ga and P interactions are taken from Chadi [4] and converted to the form of Slater
ssu spa
spu ppu ppn
705
E,(Ga) = E,(P) = E,(Ga) = E,(P) = (Ga, P) = (Ga, P) = (P, Ga) = (Ga, P) = (Ga, P) =
-2.72 eV -7.60eV 3.82 eV 3.82 eV - 1.915 eV 2.529 eV 2.308 eV 3.665 eV -0.985 eV
C. K. ONGand K. C. Low ,‘-i
------,~L-_-+-,. pc_ /
,’
/ c-:-1
,/’
‘\ ’ \ j-‘vc I I
z~~::l;+IL--L~ ( PF
;_
/’
I ,
-:
,,’ ---
/’
/q
1 I ---I
_i
---_ T’ / I /’ / /’ I c’ /’ f /I I _I __-__ -I----_,IL---___L/ , , 3FF / / ’ /’ I
,
,/’
I I
j _;T
--
7 I I
_---f 1 /’ I ,/’
o Go l P
.’
Fig. 1. Crystal structure of GaP used in this work. that the relaxation approximately conserved all bond lengths with the top layer anion (P) relaxed outward from the bulk while the top layer cation (Ga) relaxed inward. The calculated optimal displacements of the atoms at the top layer are: Ga:Ay = 0.3880 A
P:Ay = 0.2910 A
AZ = -0.3312 A
AZ = 0.1686 A.
The ideal terminated surface and the relaxed surface are shown in Fig. 2. From Fig. 2, the relative displacement of the cations and anions within the outermost layer defines
a rotation angle of 22”. However, low-energy electron diffraction (LEED) [12] has determined this angle to be 21.5”. We examined a configuration with this rotation angle and with the following displacements: Ga : Ay = 0.4608 A AZ = -0.4095 A
P:Ay = 0.2910a AZ = 0.1686 A.
The total energy for this particular configuration was calculated to be higher than that for the earlier configuration, so the optimal configuration used in this work is that with the lower total energy.
4. ELECTRONIC SURFACE STATES
Side view
(Ideally
Side view
(after
terminated)
relaxation)
__-________
I 1 I
I I I -_-________ <
s
Top view (otter 000
mloxation) lP
Fig. 2. Atomic geometry of the GaP (110)surface before and after relaxation.
The calculated electronic states of the ideal terminated and relaxed surface structure of GaP (110) along the principal symmetric directions of the Brillouin zone are displayed in Figs 3 and 4, respectively. The surface states of the relaxed structure of GaP (110) can be located by visual inspection. From Fig. 3, it can be seen that two prominent states exist at around 0.7 eV and 2.3 eV above the valence band maximum (VBM). After relaxation (from Fig. 4 and by comparing with Fig. 3), the lower surface state (at 0.7 eV) can be seen to be pushed down to 1.1 eV below VBM while the other (at 2.3 eV) is pushed higher to 3.1 eV above VBM. Other surface states can also be similarly detected and are shown as bold lines in Fig. 5. It can be seen from Fig. 5 that the band structure of the GaP (110) relaxed surface is quite flat with a band gap of about 2.9 eV. From the same figure, it can also be seen that the surface states in the gap are not completely removed. In other III-V compound semi-conductors, it had been determined experimentally and theoretically that relaxation of the (110) surface is responsible for the removal of the dangling-bond surface states from the gap [13-l 51. However, for GaP (1 lo), relaxation does not completely remove the surface states from the gap [16,17]. Other surface states, as can be
Surface states of GaP (110)
r
r
J’ Wavevector
(k)
r
107
r
J’ Wavevector
(k)
(110) surface
Fig. 5. Band structure of GaP (110) after relaxation with the bold lines indicating intrinsic surface states.
Seen from Fig. 5, are at around 5 eV, 9.5 eV above VBM. These results are tabulated in Table 2 together with experimental and other theoretical results. Flat band structure had been detected by Chiaradia and co-workers [ 1l] from photo-emission spectroscopy
of ultrahigh-vacuum cleaved GaP (110) surface, for P-type samples. For n-type samples, a certain amount of band-bending is observed. But they had discovered that these are due to extrinsic surface states, probably cleavage defects. Our result of this feature agrees quite well with the experimental results. Manghi and co-workers [12] using self-consistent pseudo-potential approach had predicted the direct band gap, Fn + F, to be 3.41 eV. In the same paper, they had also reported the experimental value for this direct band gap to be 2.94 eV. From our results, the band gap is calculated to be 2.9 eV at the F point which agrees well with the reported experimental value. Our results predict an occupied surface state at 1.1 eV below VBM. Similarly, Manghi and co-workers [12] using a pseudo-potential approach had also predicted an occupied surface state at 1.2 eV below VBM. Experimental results on this feature of the GaP (110) surface also indicate an occupied surface state around this region. Cerrina and co-workers [18] using a photo-emission technique determined the occupied surface state to be at around 1 eV below VBM. Thus, it can be seen that the agreement for the occupied intrinsic state is excellent. There are several empty intrinsic surface states for the GaP (110) surface. The lowest unoccupied surface state was detected to be at 2.2 eV above VBM, by Straub and co-workers [19] using inverse photoemission. Straub and other co-workers [20] using high resolution inverse photo-emission study also detected the lowest empty surface state, at 1.96 eV above VBM.
Fig. 3. Band structure of an ideally teminated of GaP.
r
r-
J’ Wavrvrctor
tk)
Fig. 4. Band structure of GaP (110) after relaxation. PCS 5215-E
C. K. ONG and K. C. Low
Table 2. Features of the band structure and surface states of GaP (110) with optimal energy configuration for the surface
Features
Results
Rotation angle Band
22 Flat
Band gap Occupied intrinsic states BmPtY intrinsic states
2.9 eV 1.1 eV below VBM 3.1 eV, 5 eV and 9.5 eV above VBM
However, Chiaradia and co-workers [1 11, using photoelectron spectroscopy on a clean GaP (110) surface, determined the lowest empty surface state to be at 0.5 eV above, near the bottom of the conduction band. Our result for this lowest surface is as shown in Fig. 5. It can be seen this surface state is about 3.1 eV above VBM, but at the r point, this surface state is about 0.2 eV above the edge of thcconduction band. Our result agrees better with that of Chiaradia. Inverse photo-emission [19] had also detected other empty surface states at 4 eV and 7.5 eV above VBM. Our calculations predict the other empty surface states to be at about 5 eV and 9.5 eV above VBM. The discrepancy of about 30% could be due to the fact that our calculation is an eigenvalue calculation while inverse photo-emission results involve the creation of holes and relaxation of electrons around it.
Experimental results 27.5”[12] Flat (p-type) [1 1] band-bending (n-type) 1111 2.94 eV [12] 1 eV below VBM [18] 2.2 eV [19] (1.96 eV [20]), 4 eV [19] and 7.5 eV [19] above VBM
Other theoretical results 3.41eV [12] 1.2eV below VBM [ 121 1.53eV [12] above VBM
experimental results. The unoccupied surface states at 3.1 eV, 5 eV and 9.5 eV above VBM are higher than the results of inverse photo-emission technique. REFERENCES 1. Chadi D. J., Whys.Rev. Mt.
41, 1062 (1978). 2. Ong C. K. and Chan B. C., J. Phys. Chem. Soiiak 51, 343 (1989).
3. Slater J. C. and Koster G. F., Phys. Rev. 94, 1498 (1954).
4. 5. 6. 7. 8.
Chadi D. J., Phys. Rev. B 16, 790 (1977). Duke C. B. and Paton A., Surf: Sci. 164, L797 (1985). Kahn A., Surf. Sci. Repot-r 3, 193 (1983). Wing Y. R. and Duke C. B., Surf. Sci. 205, L755 (1988). Lubinsky A. R., Duke C. B., Lee B. W. and Mark P., Phys. Rev. Zmr. 36, 1058 (1976).
9. Tong S. Y., Lubinsky A. R., Mrstik B. J. and van Hove M. A., Phys. Rw. B 17, 3303 (1978).
10. Duke C. B., Meyer R. J., Paton A., Mark A., Kahn A.,
5. CONCLUSION
11.
We have made use of Chadi’s total energy formalism to determine the optimal surface structure of GaP (110) assuming a rotation-relaxation model by minimizing the total energy of the system. The angle of rotation for the optimal structure is obtained to be 22” against the experimental value of 27.5”. The projected bulk bands of both the ideal terminated and relaxed surfaces were calculated. By comparing these two structures, the surface states were determined by visual inspection. Using experimental and other theoretical results, our predicted results are compared. The flatness of the band structure, the band gap of 2.9 eV and the occupied surface state at 1.1 eV below VBM are in excellent agreement, especially with
12. 13. 14. 15. 16.
So E. and Yeh J. L., J. Vat. Sci. Technol. 16, 1252 (1979). Chiaradia P., Fanfoni M., Nataletti P. and De Padova P., Phys. Rev. E 39, 5128 (1989). Manghi F., Bertoni C. M., Calandra C. and Molinari E., Phys. Rev. B24, 6029 (1981). Calandra C., Manghi F. and Bertoni C. M., J. Phys. C. 10, 1911 (1977). Chelikowsky J. R. and Cohen M. L., Phys. Rw. B 20, 4150 (1979). Miller D. J. and Haneman D., J. Vat. Sci. Technol. 15. 1267 (1978). Bertoni C. M.. Bishi 0.. Manehi F. and Calandra C.. J. Vat. Sci. Technol. 15; 1256-(1978).
17. Nishida M., Solid State Commun. 28, 551 (1978). 18. Cerrina F., Bommannavar A., Benhow R. A. and Hurych Z., Phys. Rev. B 31, 8314 (1985).
19. Straub D., Dose V. and Altmann W., Surf. Sci. 133, 9 (1983).
20. Straub D., Skibowski M. and Himpsel F. J., J. Vat. Sci. Technol. A3(3), 1484 (1985).
Chem. So/i& Vol. in Gnat Britain.
52, No.
S, pp.
705-708,
1991
0022-3697191
$3.00 + 0.00 Pergamon Press pk
SURFACE STATES OF GaP (110) C. K. ONG and K. C. Low Department of Physics, National University of Singapore, Kent Ridge, Singapore 0511 (Received
11 September
1990; accepted 28 November
1990)
Abstract-Chadi’s tight-binding total energy algorithm was used to study the reconstruction of the GaP (110) surface and its intrinsic occupied and unoccupied states. Assuming a rotation-relaxation model, the optimal surface atomic geometry was obtained by minimizing the total energy of the system. The angle of rotation obtained, w = 22”, is near the experimental value of 27.5”. The features of the surface electronic states were determined and described. The calculated intrinsic occupied surface states are in excellent agreement with the experimental data and those for the unoccupied states are about 30% higher than the results of inverse photo-emission experiments. Keywork
Surface states, semiconductor surface, Gap.
1. INTRODUCTION
Recently, there has been a great deal of experimental effort in studying the reconstruction of III-V compound surfaces and their intrinsic occupied and unoccupied states. With the understanding of this information, one may proceed to explain Fermi-level pinning and other metal-semiconductor interface structures. Among the III-V compounds, the GaP (110) surface has drawn most of the attention with its unique characteristic that the unoccupied surface states lie in the energy gap. In the present work, Chadi’s total energy algorithm will be employed, incorporating tight-binding approximation, to study the relaxation of the (110) surface atoms and to determine the stable crystal structure. The calculated surface states will be presented superimposed on the projected bulk bands and are located by visual inspection. 2. THEORY We make use of Chadi’s [l] total energy formalism, E,, = & + U
(1)
where E,,, is the band structure defined as
energy and U is
U=Eii-E,.,
and Koster. The marized in Table the tight-binding The change in
tight-binding parameters are sum1. The l/d2 functional dependence of parameters is imposed throughout. U takes the following form, i>j
AU = c (u,qj+ u,c$), ij
(3)
where 6ij is the fractional change in the distance between two nearest neighbor atoms denoted by i and J ul and u2 are the force-constant parameters and are determined in the usual way as discussed by Chan and Ong [2]: u, = -20.21 eV
u2 = 54.52 eV.
3. RECONSTRUCTED
SURFACE
A 20 atom unit cell as shown in Fig. 1, is used in the present work to represent the ideal terminated GaP (110) surface. Recent ELEED [5-71 and LEED [&lo] experiments on III-V compound semiconductors have shown that the (110) surface is usually distorted with respect to the geometry of an ideal termination of the surface, going through a rotation in such a way that the 1 x 1 periodicity is preserved. The basic feature of these (110) surface reconstruction of III-V compound semiconductors is
(2) Table I. Tight-binding parameters for GaP (110)
the difference between the ion-ion interaction and electron-electron interaction. This term, U, takes into account all other contributions to E,,, . Details of the calculation of Eb. were given by Chadi [l] and Chan and Ong [2]. Basically, the tightbinding model of Slater and Koster [3] was used with the nearest neighbors considered. The tight-binding parameters for the Ga and P interactions are taken from Chadi [4] and converted to the form of Slater
ssu spa
spu ppu ppn
705
E,(Ga) = E,(P) = E,(Ga) = E,(P) = (Ga, P) = (Ga, P) = (P, Ga) = (Ga, P) = (Ga, P) =
-2.72 eV -7.60eV 3.82 eV 3.82 eV - 1.915 eV 2.529 eV 2.308 eV 3.665 eV -0.985 eV
C. K. ONGand K. C. Low ,‘-i
------,~L-_-+-,. pc_ /
,’
/ c-:-1
,/’
‘\ ’ \ j-‘vc I I
z~~::l;+IL--L~ ( PF
;_
/’
I ,
-:
,,’ ---
/’
/q
1 I ---I
_i
---_ T’ / I /’ / /’ I c’ /’ f /I I _I __-__ -I----_,IL---___L/ , , 3FF / / ’ /’ I
,
,/’
I I
j _;T
--
7 I I
_---f 1 /’ I ,/’
o Go l P
.’
Fig. 1. Crystal structure of GaP used in this work. that the relaxation approximately conserved all bond lengths with the top layer anion (P) relaxed outward from the bulk while the top layer cation (Ga) relaxed inward. The calculated optimal displacements of the atoms at the top layer are: Ga:Ay = 0.3880 A
P:Ay = 0.2910 A
AZ = -0.3312 A
AZ = 0.1686 A.
The ideal terminated surface and the relaxed surface are shown in Fig. 2. From Fig. 2, the relative displacement of the cations and anions within the outermost layer defines
a rotation angle of 22”. However, low-energy electron diffraction (LEED) [12] has determined this angle to be 21.5”. We examined a configuration with this rotation angle and with the following displacements: Ga : Ay = 0.4608 A AZ = -0.4095 A
P:Ay = 0.2910a AZ = 0.1686 A.
The total energy for this particular configuration was calculated to be higher than that for the earlier configuration, so the optimal configuration used in this work is that with the lower total energy.
4. ELECTRONIC SURFACE STATES
Side view
(Ideally
Side view
(after
terminated)
relaxation)
__-________
I 1 I
I I I -_-________ <
s
Top view (otter 000
mloxation) lP
Fig. 2. Atomic geometry of the GaP (110)surface before and after relaxation.
The calculated electronic states of the ideal terminated and relaxed surface structure of GaP (110) along the principal symmetric directions of the Brillouin zone are displayed in Figs 3 and 4, respectively. The surface states of the relaxed structure of GaP (110) can be located by visual inspection. From Fig. 3, it can be seen that two prominent states exist at around 0.7 eV and 2.3 eV above the valence band maximum (VBM). After relaxation (from Fig. 4 and by comparing with Fig. 3), the lower surface state (at 0.7 eV) can be seen to be pushed down to 1.1 eV below VBM while the other (at 2.3 eV) is pushed higher to 3.1 eV above VBM. Other surface states can also be similarly detected and are shown as bold lines in Fig. 5. It can be seen from Fig. 5 that the band structure of the GaP (110) relaxed surface is quite flat with a band gap of about 2.9 eV. From the same figure, it can also be seen that the surface states in the gap are not completely removed. In other III-V compound semi-conductors, it had been determined experimentally and theoretically that relaxation of the (110) surface is responsible for the removal of the dangling-bond surface states from the gap [13-l 51. However, for GaP (1 lo), relaxation does not completely remove the surface states from the gap [16,17]. Other surface states, as can be
Surface states of GaP (110)
r
r
J’ Wavevector
(k)
r
107
r
J’ Wavevector
(k)
(110) surface
Fig. 5. Band structure of GaP (110) after relaxation with the bold lines indicating intrinsic surface states.
Seen from Fig. 5, are at around 5 eV, 9.5 eV above VBM. These results are tabulated in Table 2 together with experimental and other theoretical results. Flat band structure had been detected by Chiaradia and co-workers [ 1l] from photo-emission spectroscopy
of ultrahigh-vacuum cleaved GaP (110) surface, for P-type samples. For n-type samples, a certain amount of band-bending is observed. But they had discovered that these are due to extrinsic surface states, probably cleavage defects. Our result of this feature agrees quite well with the experimental results. Manghi and co-workers [12] using self-consistent pseudo-potential approach had predicted the direct band gap, Fn + F, to be 3.41 eV. In the same paper, they had also reported the experimental value for this direct band gap to be 2.94 eV. From our results, the band gap is calculated to be 2.9 eV at the F point which agrees well with the reported experimental value. Our results predict an occupied surface state at 1.1 eV below VBM. Similarly, Manghi and co-workers [12] using a pseudo-potential approach had also predicted an occupied surface state at 1.2 eV below VBM. Experimental results on this feature of the GaP (110) surface also indicate an occupied surface state around this region. Cerrina and co-workers [18] using a photo-emission technique determined the occupied surface state to be at around 1 eV below VBM. Thus, it can be seen that the agreement for the occupied intrinsic state is excellent. There are several empty intrinsic surface states for the GaP (110) surface. The lowest unoccupied surface state was detected to be at 2.2 eV above VBM, by Straub and co-workers [19] using inverse photoemission. Straub and other co-workers [20] using high resolution inverse photo-emission study also detected the lowest empty surface state, at 1.96 eV above VBM.
Fig. 3. Band structure of an ideally teminated of GaP.
r
r-
J’ Wavrvrctor
tk)
Fig. 4. Band structure of GaP (110) after relaxation. PCS 5215-E
C. K. ONG and K. C. Low
Table 2. Features of the band structure and surface states of GaP (110) with optimal energy configuration for the surface
Features
Results
Rotation angle Band
22 Flat
Band gap Occupied intrinsic states BmPtY intrinsic states
2.9 eV 1.1 eV below VBM 3.1 eV, 5 eV and 9.5 eV above VBM
However, Chiaradia and co-workers [1 11, using photoelectron spectroscopy on a clean GaP (110) surface, determined the lowest empty surface state to be at 0.5 eV above, near the bottom of the conduction band. Our result for this lowest surface is as shown in Fig. 5. It can be seen this surface state is about 3.1 eV above VBM, but at the r point, this surface state is about 0.2 eV above the edge of thcconduction band. Our result agrees better with that of Chiaradia. Inverse photo-emission [19] had also detected other empty surface states at 4 eV and 7.5 eV above VBM. Our calculations predict the other empty surface states to be at about 5 eV and 9.5 eV above VBM. The discrepancy of about 30% could be due to the fact that our calculation is an eigenvalue calculation while inverse photo-emission results involve the creation of holes and relaxation of electrons around it.
Experimental results 27.5”[12] Flat (p-type) [1 1] band-bending (n-type) 1111 2.94 eV [12] 1 eV below VBM [18] 2.2 eV [19] (1.96 eV [20]), 4 eV [19] and 7.5 eV [19] above VBM
Other theoretical results 3.41eV [12] 1.2eV below VBM [ 121 1.53eV [12] above VBM
experimental results. The unoccupied surface states at 3.1 eV, 5 eV and 9.5 eV above VBM are higher than the results of inverse photo-emission technique. REFERENCES 1. Chadi D. J., Whys.Rev. Mt.
41, 1062 (1978). 2. Ong C. K. and Chan B. C., J. Phys. Chem. Soiiak 51, 343 (1989).
3. Slater J. C. and Koster G. F., Phys. Rev. 94, 1498 (1954).
4. 5. 6. 7. 8.
Chadi D. J., Phys. Rev. B 16, 790 (1977). Duke C. B. and Paton A., Surf: Sci. 164, L797 (1985). Kahn A., Surf. Sci. Repot-r 3, 193 (1983). Wing Y. R. and Duke C. B., Surf. Sci. 205, L755 (1988). Lubinsky A. R., Duke C. B., Lee B. W. and Mark P., Phys. Rev. Zmr. 36, 1058 (1976).
9. Tong S. Y., Lubinsky A. R., Mrstik B. J. and van Hove M. A., Phys. Rw. B 17, 3303 (1978).
10. Duke C. B., Meyer R. J., Paton A., Mark A., Kahn A.,
5. CONCLUSION
11.
We have made use of Chadi’s total energy formalism to determine the optimal surface structure of GaP (110) assuming a rotation-relaxation model by minimizing the total energy of the system. The angle of rotation for the optimal structure is obtained to be 22” against the experimental value of 27.5”. The projected bulk bands of both the ideal terminated and relaxed surfaces were calculated. By comparing these two structures, the surface states were determined by visual inspection. Using experimental and other theoretical results, our predicted results are compared. The flatness of the band structure, the band gap of 2.9 eV and the occupied surface state at 1.1 eV below VBM are in excellent agreement, especially with
12. 13. 14. 15. 16.
So E. and Yeh J. L., J. Vat. Sci. Technol. 16, 1252 (1979). Chiaradia P., Fanfoni M., Nataletti P. and De Padova P., Phys. Rev. E 39, 5128 (1989). Manghi F., Bertoni C. M., Calandra C. and Molinari E., Phys. Rev. B24, 6029 (1981). Calandra C., Manghi F. and Bertoni C. M., J. Phys. C. 10, 1911 (1977). Chelikowsky J. R. and Cohen M. L., Phys. Rw. B 20, 4150 (1979). Miller D. J. and Haneman D., J. Vat. Sci. Technol. 15. 1267 (1978). Bertoni C. M.. Bishi 0.. Manehi F. and Calandra C.. J. Vat. Sci. Technol. 15; 1256-(1978).
17. Nishida M., Solid State Commun. 28, 551 (1978). 18. Cerrina F., Bommannavar A., Benhow R. A. and Hurych Z., Phys. Rev. B 31, 8314 (1985).
19. Straub D., Dose V. and Altmann W., Surf. Sci. 133, 9 (1983).
20. Straub D., Skibowski M. and Himpsel F. J., J. Vat. Sci. Technol. A3(3), 1484 (1985).