- Email: [email protected]
Low-energy secondary electron spectroscopy of Ge(1 1 1) surface
Solid State Communications, Vol. 101, No. 7, pp. 483-486, 1997 0 1997 Elsevier Science Ltd Printed in Great Britain. All tights reserved 003%1098/97 $17.00+.00
Pergamon
PII:SOO38-1098(96)00655-2
LOW-ENERGY SECONDARY ELECTRON SPECTROSCOPY OF Ge(ll1)
SURFACE
O.F. Panchenko and L.K. Panchenko* Donetsk Institute of Physics & Technology, Ukrainian National Academy of Sciences, Donetsk 340114, Ukraine (Received 6 May 1996; in revised form 24 October 1996 by M. Cardona)
The current spectra of low-energy secondary electron emission (SEE) of a Ge single crystal normal to the surface (11 1) are calculated. The results are compared to existing experimental data. It is shown that the fine structure of SEE spectra is mainly due to the electron build-up of final states, from which electron emission takes place. 0 1997 Elsevier Science Ltd
1. INTRODUCTION The low-energy SEE method is used in the investigations of the surface properties of solids. In this method the regularities of excitation, emittance and energy distribution of electrons emitted by the crystal surface at its excitation by the electron flow are analysed. The method is included in the group of the differential methods of secondary electron spectroscopy [l] as it is based on the definition of the specific features in the secondary electron spectrum at fixed energy of primary electrons Ep, At present the SEE method proved to be good at investigation of the energy structure of near-surface regions of crystals [2]. It is applied both for electron free path length measurements and studies of plasmon and interband transitions in the framework of the characteristic losses of electron energy method (CLEE) [3,4] as well as for studies of electron states in the vicinity of the vacuum level E,, [5-71. In the first case specific features of the energy spectrum of probing electrons with energies Ep - 1 keV are not practically revealed in any way, since broadening of levels at such Ep becomes comparable with characteristic values of band splitting in the crystalline potential, in other words, the electron free path length (relative to inelastic collisions) becomes comparable with the interatomic distance [8], which averages over Bragg diffraction effects. Therefore for the interpretation of results in the indicated region of energies one usually utilizes the free electron approximation [9]. At reduction of energy of registered electrons
*Electronic mail: [email protected]
below the plasma energy hwpr in SEE spectra the fine structure is revealed. For the first time it was observed on W [lo, 111 and associated with the one-dimensional density of electron states. In papers [ 12,131 it was shown that this fine structure reflects band boundaries in the electron dispersion law. Superposed on the background in the form of cascade maximum from electrons dispersed on phonons, surface roughness etc. this tine structure forms the measured energy distribution SEE current along the predetermined direction [14,15]. In this case the fine structure appears if the energy structure of the near-surface region of a crystal corresponds to the energy structure of its volume [l]. The form, intensity and energy position of specific features of SEE experimental spectra are considerably influenced by the following factors: (a) strong energy dependence of probability of occupation states; (b) broadening of peaks because of the finite lifetime of electrons; (c) presence of the background component of the spectrum. The aim of this paper is the investigation and interpretation of the fine structure of SEE spectrum for Ge(1 1 1) and finding how it is associated with the bulk energy band structure. In the paper the model [13, 141 is applied supplemented by consideration of the energy dependence of band energy levels broadening and electron-electron (e-e) and electron-plasmon (e-pf ) contributions to the nonequilibrium electrons distribution function f(E), which allows exclusion of the
483
484
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
experimentally measured background from calculations as it was done in [13]. 2. THEORETICAL MODEL AND DISCUSSION OF RESULTS Distribution of the electron current over energies E and angles 51outside a crystal (ignoring the diffraction effects on the crystal surface) is written as follows [16-181:
h z
xN(E’, 6) (E
W’) l-l2
- E')2 +
T
r2(E’)’
(1)
where S(E)
= 4(E - EvIIC)1’2(E- Eo>‘nl((E - Eva,)‘“+ (E - E0)1n)2 is the coefficient of overcoming of the
crystal-vacuum barrier for one-dimensional motion [19]; E,, y 16.1 eV; E0 = 0 is the bottom of the valence band; N(E, 0) is the branches number of the electron dispersion law Ed along the direction determined by the law of
conserv_ationof the parallel cry@ surface component of vector k at escape in direction 0. Unlike [13] here we consider the final widthhI’ = ii/~(E) of electron levels and the lifetime of the excited state r(E) is determined according to [16] (for E,, c E < E,, + hwP,): W(E)= 7.23 - 10m4(E- EO)ln(E - EF)2 + 0.1 (eV), where EF = 12 eV is the middle of forbidden gap level (Fermi energy). The physical foundations of the relationship (equation (1)) are given in publications [16-181. Here it is to be noted only the following: (1) Strictly speaking the expression in equation (1) is justified when tT coincides with the symmetry axis of crystal (at normal of the electron flow on the sample). (2) At derivation of equation (1) the d-function over energy is substituted by the Lorentzian [19]. (3) The flow of secondary electrons comprises three groups: namely, elastically and non-elastically reflected on the sample surface primary electrons (this p_art,leading to increase of the electron current J(E,Q) up to energies E = EP of the order of several electron-volts, with EP increase is rapidly decreased) and the slow electrons, which are real secondary electrons. According to the generally accepted representation [20] the primary electrons of energy E,, - 0.1 keV, when in side the crystal, create a stationary distribution of real secondary electrons with respect to energy f(E) as a result of the inelastic collision cascade. In the region of interest e-e- and e-pl- scattering prevail. As it was shown in [16, 211 the occupation function of states corresponding to the multiple e-e- scattering can be
SURFACE
Vol. 101, No. 7
represented as: f,(E) - JEIEF - 11e2* T(E) at E,, < E < E,, + T-q+ This expression is an interpolation dependence which rather well describes the behaviour of f,(E) obtained by the numerical calculation for the real energy structure within the approximation of the e-escattering statistical model. A similar value has been obtained in [22, 231 for simple metals at E - EF < EP which, apparently, is the upper limit for semiconductors where the presence of the forbidden band makes the processes of inelastic electron scattering difficult. The process of plasmon decay [24] generated by primary as well as excited electrons in a solid is the second-order process compared with e-e- scattering, especially in the energy region near E,,. However it may be of importance due to the instability of plasmons in Ge. According to CLEE spectrum data for Ge [25] the half-width of the plasmon peak is equal hI’,, = 6eV at energy ho,1 = 16.7eV, which allows (ignoring the plasmon dispersion) to derive from the conservation of energy law a formula for the energy dependence of e-plcontribution to the electron distribution function:
fPl(E)-$)
5 CL?’; I’,, - p(E’)
(E - E’ - T-x+1)2
&I
where E, is the valence band top. The processes of electronic ionization from the last wide maximum in the density of occupied states p(E) are the main contributions to the energy range of interest. At the large broadening of bFp, small details of p(E) are not so important, thus, for simplicity we substitute this maximum by a rectangle having the width E2 - El. Then
where El = 25 eV, E2 = 29 eV are the lower and upper limits (increased on hw,,) of interpolated rectangle. In the general case, as it was shown in [16, 171 by the example of Si the excited level occupation function is written as follows: f(E) = f,(E) +p . fPl(E), where p is the weight. The relation between contributions in f(E) from e-e- scattering and plasmon decay depends on both EP [3] and the angle of incidence of primary electrons on the crystal surface 11).In particular, the form of SEE spectra of W(110) surface and the amplitude of specific features (but not energy position their) vary at EP increase [12]. With EP increase up to 1 keV the fine structure is revealed better and the position of the energy spectrum more and more differs from the cascade
Vol. 101, No. 7
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
maximum. Besides, temperature T of a sample differently influences the fine structure: a part of peaks practically disappears at T - 1200 K ([12], for W(l10) surface), and other peaks at this temperature remain unchanged. In our case the problem becomes more complicated also by the presence of the crystal-vacuum boundary and the problem of deriving the p(E,, r9,T) dependence requires a special investigation outside the framework of present studies. In Fig. l(a) the calculation results for SEE spectrum using formula from equation (1) for electron emitted normal to plane Ge(ll1) are given. Here for comparison we give also experimental curves from paper [2_5] [Fig. l(b)]. To derive the step function N(E, 0) analogous to [16] and calculate the plasmon contribution to f(E) we utilized the calculation of the band structure EG and of p(E) Ge density-of-states, obtained by the pseudo-potentiai method with parameters from [26]. The
SURFACE
485
curves J(E, Q) have been calculated with the account for (p = 0.7) and with no account (p = 0) for the e-pfcontribution to f(E). The plasmon contribution to the distribution functionf(E) is represented as the wide peak (B) to the right-hand side of the cascade maximum (A) (analogous to [27]). As is shown in [16, 281 in SEE spectra of Si the isotropic component contribution corresponding to elastic scattering on the surface and averaging over directions for a part of emitted electrons is quite great. This background current component presenting a characteristic view of a cascade maximum was considered by addition to N(E, 6) of a constant C, when the energy structure of the near-surface region is described by the model of nearly free electron gas. C variation in the wide range from 0 up to 100 pr$ctically does not change the second derivative J”(E, 0)_[16], which is explained by low dependence of J “(E, 52) on the background component for all E except for the vicinity of the cascade maximum. This proves the usage of double differentiation for, the elimination of background and elucidation of peculiarities fine struct;re of experimental SEE spectra to be correct. In J&62) calculations we assumed C = 100, which gives J(E, fl) dependence close to the experimental one. The experimental spectra change depending on Ep which is connected, apart from other facts, with the change of relationship between e-e- and e-pl- contributions to f(E). Thus, the agreement obtained between the main specific features of theoretical and experimental SEE spectra suggests that the fine structure of SEE current spectra is due to the electron structure of final states, from which the electron emission takes place. This allows us to use experimental data as reference points for more perfect band calculations indicating, which bands namely generate these or other specific features in a spectrum and, thus, to solve the problem of experimental measurement of boundaries of crystal energy bands. Acknowledgement-The
research described in this publication was made possible in part by Grant NK6ElOO from the Joint Fund of the Government of Ukraine and ISF. REFERENCES Komolov, S.A., Zntegrai Secondary Electron Spectroscopy of Surface. LSU Publ., Leningrad,
Fig. 1. The SEE spectra normal to Ge(ll1) surface: (a) theory. Dotted curve shows SEE spectrum with no account for the e-p& scattering; (b) experiment [25] for different energies of primary electrons Ep: (1) 100 eV, (2) 5OOeV, (3) 2 keV. Curves are plotted over coordinate axes in a random way. Energy is calculated beginning from E,,
1986. Christensen, N.E. and Willis, R.F., Phys. Rev., Bl8,1978,5140. Chung, M.S. and Everhart, T.E., Phys. Rev., B15, 1977,4699. Artamonov, O.M., Vinogradov, A.G., Smimov, O.M. and Terekhov, A.N., Fiz. Tverd. Tela, 27, 1985,3138.
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
486
Willis, R.F., Laude, L.D. and Fitton, B., Phys. Rev. Lett., 29, 1972, 220. 6. Best, P.E., Phys. Rev. Lett., 34, 1975, 674. 7. Bazhanova, N.P., Korablev, V.V. and Kochetov, NJ., Fiz. Tverd. Tela, 24, 1982, 1407. 8. Quinn, J.J., Phys. Rev., 126, 1962, 1453. 9. Koval’, I.F., Kryn’ko, Yu.N., Koshevaya, S.V., Mel’nik, P.V. and Nachodkin, N.G., Fiz. Tverd. Tela, 17, 1975, 1138. 10. Willis, R.F., Phys. Rev. Left., 34, 1975, 670. 11. Artamonov, O.M., Smimov, O.M. and Terekhov, A.N., Izv. Akad. Nauk USSR, Ser. Fiz., 46, 1982, 5.
17.
Korablev, V.V. and Kudinov, Yu.A., Izv. Akad. Korablev, V.V., Kudinov, Yu.A. and Sysoev, S.N.,
Korablev, V.V., Kudinov, Yu.A., Panchenko, O.F., Panchenko, L.K. and Shatalov, V.M., Fiz. Tverd.
19. 20. 21.
Landau, L.D. and Liphshits, E.M., Quantum Mechanics, Nonrelativistic Theory, Nauka, Moscow, 1974. Wolff, P.A., Phys. Rev., 95, 1954, 56. Shatalov, V.M. and Panchenko, O.F., Solid State
22.
Panchenko, O.F. and Shatalov, V.M., Sov. Phys.
Tela, 36, 1994, 2373.
Commun., 69, 1989, 937. JETP, 66,1987,
Korablev, V.V., Kudinov, Yu.A. and Sysoev, S.N.,
24. 25.
Pahnberg,
1976,741.
Fiz. Tverd Tela, 28, 1986, 2648.
15.
Artamonov, O.M. and Terekhov, A.N., Fiz. Tverd.
P.W., J. Appl.
Phys.,
38,
1967,
2137. 26.
Cohen, M.L. and Bergstresser, T.K., Phys. Rev.,
Shatalov, V.M., Panchenko, O.F., Artamonov, O.M., Vinogradov, A.G. and Terekhov, A.N.,
27.
Solid State Commun., 68, 1988, 719.
28.
Rosier, M. and Brauer, W., Phys. Status Solidi (b), 104,1981,161,575. Best, P.E., Phys. Rev., B14, 1976, 606.
141,1966,789.
Tela, 28, 1986, 862.
16.
127.
Panchenko, O.F. and Panchenko, L.K., J. Electr. Spectr. and Rel. Phenom., (in press). Pillon, J., Roptin, D. and Cailler, M., Surf. Sci., 57,
23,
Fiz. Tverd. Tela, 29, 1987, 702.
14.
Panchenko, O.F. and Shatalov, V.M., Zh. Tekhn.
18.
Nauk USSR, Ser. Fiz., 49, 1985, 1775.
13.
Vol. 101, No. 7
Fiz., 63, 1993, 144.
1383.
12.
SURFACE
Pergamon
PII:SOO38-1098(96)00655-2
LOW-ENERGY SECONDARY ELECTRON SPECTROSCOPY OF Ge(ll1)
SURFACE
O.F. Panchenko and L.K. Panchenko* Donetsk Institute of Physics & Technology, Ukrainian National Academy of Sciences, Donetsk 340114, Ukraine (Received 6 May 1996; in revised form 24 October 1996 by M. Cardona)
The current spectra of low-energy secondary electron emission (SEE) of a Ge single crystal normal to the surface (11 1) are calculated. The results are compared to existing experimental data. It is shown that the fine structure of SEE spectra is mainly due to the electron build-up of final states, from which electron emission takes place. 0 1997 Elsevier Science Ltd
1. INTRODUCTION The low-energy SEE method is used in the investigations of the surface properties of solids. In this method the regularities of excitation, emittance and energy distribution of electrons emitted by the crystal surface at its excitation by the electron flow are analysed. The method is included in the group of the differential methods of secondary electron spectroscopy [l] as it is based on the definition of the specific features in the secondary electron spectrum at fixed energy of primary electrons Ep, At present the SEE method proved to be good at investigation of the energy structure of near-surface regions of crystals [2]. It is applied both for electron free path length measurements and studies of plasmon and interband transitions in the framework of the characteristic losses of electron energy method (CLEE) [3,4] as well as for studies of electron states in the vicinity of the vacuum level E,, [5-71. In the first case specific features of the energy spectrum of probing electrons with energies Ep - 1 keV are not practically revealed in any way, since broadening of levels at such Ep becomes comparable with characteristic values of band splitting in the crystalline potential, in other words, the electron free path length (relative to inelastic collisions) becomes comparable with the interatomic distance [8], which averages over Bragg diffraction effects. Therefore for the interpretation of results in the indicated region of energies one usually utilizes the free electron approximation [9]. At reduction of energy of registered electrons
*Electronic mail: [email protected]
below the plasma energy hwpr in SEE spectra the fine structure is revealed. For the first time it was observed on W [lo, 111 and associated with the one-dimensional density of electron states. In papers [ 12,131 it was shown that this fine structure reflects band boundaries in the electron dispersion law. Superposed on the background in the form of cascade maximum from electrons dispersed on phonons, surface roughness etc. this tine structure forms the measured energy distribution SEE current along the predetermined direction [14,15]. In this case the fine structure appears if the energy structure of the near-surface region of a crystal corresponds to the energy structure of its volume [l]. The form, intensity and energy position of specific features of SEE experimental spectra are considerably influenced by the following factors: (a) strong energy dependence of probability of occupation states; (b) broadening of peaks because of the finite lifetime of electrons; (c) presence of the background component of the spectrum. The aim of this paper is the investigation and interpretation of the fine structure of SEE spectrum for Ge(1 1 1) and finding how it is associated with the bulk energy band structure. In the paper the model [13, 141 is applied supplemented by consideration of the energy dependence of band energy levels broadening and electron-electron (e-e) and electron-plasmon (e-pf ) contributions to the nonequilibrium electrons distribution function f(E), which allows exclusion of the
483
484
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
experimentally measured background from calculations as it was done in [13]. 2. THEORETICAL MODEL AND DISCUSSION OF RESULTS Distribution of the electron current over energies E and angles 51outside a crystal (ignoring the diffraction effects on the crystal surface) is written as follows [16-181:
h z
xN(E’, 6) (E
W’) l-l2
- E')2 +
T
r2(E’)’
(1)
where S(E)
= 4(E - EvIIC)1’2(E- Eo>‘nl((E - Eva,)‘“+ (E - E0)1n)2 is the coefficient of overcoming of the
crystal-vacuum barrier for one-dimensional motion [19]; E,, y 16.1 eV; E0 = 0 is the bottom of the valence band; N(E, 0) is the branches number of the electron dispersion law Ed along the direction determined by the law of
conserv_ationof the parallel cry@ surface component of vector k at escape in direction 0. Unlike [13] here we consider the final widthhI’ = ii/~(E) of electron levels and the lifetime of the excited state r(E) is determined according to [16] (for E,, c E < E,, + hwP,): W(E)= 7.23 - 10m4(E- EO)ln(E - EF)2 + 0.1 (eV), where EF = 12 eV is the middle of forbidden gap level (Fermi energy). The physical foundations of the relationship (equation (1)) are given in publications [16-181. Here it is to be noted only the following: (1) Strictly speaking the expression in equation (1) is justified when tT coincides with the symmetry axis of crystal (at normal of the electron flow on the sample). (2) At derivation of equation (1) the d-function over energy is substituted by the Lorentzian [19]. (3) The flow of secondary electrons comprises three groups: namely, elastically and non-elastically reflected on the sample surface primary electrons (this p_art,leading to increase of the electron current J(E,Q) up to energies E = EP of the order of several electron-volts, with EP increase is rapidly decreased) and the slow electrons, which are real secondary electrons. According to the generally accepted representation [20] the primary electrons of energy E,, - 0.1 keV, when in side the crystal, create a stationary distribution of real secondary electrons with respect to energy f(E) as a result of the inelastic collision cascade. In the region of interest e-e- and e-pl- scattering prevail. As it was shown in [16, 211 the occupation function of states corresponding to the multiple e-e- scattering can be
SURFACE
Vol. 101, No. 7
represented as: f,(E) - JEIEF - 11e2* T(E) at E,, < E < E,, + T-q+ This expression is an interpolation dependence which rather well describes the behaviour of f,(E) obtained by the numerical calculation for the real energy structure within the approximation of the e-escattering statistical model. A similar value has been obtained in [22, 231 for simple metals at E - EF < EP which, apparently, is the upper limit for semiconductors where the presence of the forbidden band makes the processes of inelastic electron scattering difficult. The process of plasmon decay [24] generated by primary as well as excited electrons in a solid is the second-order process compared with e-e- scattering, especially in the energy region near E,,. However it may be of importance due to the instability of plasmons in Ge. According to CLEE spectrum data for Ge [25] the half-width of the plasmon peak is equal hI’,, = 6eV at energy ho,1 = 16.7eV, which allows (ignoring the plasmon dispersion) to derive from the conservation of energy law a formula for the energy dependence of e-plcontribution to the electron distribution function:
fPl(E)-$)
5 CL?’; I’,, - p(E’)
(E - E’ - T-x+1)2
&I
where E, is the valence band top. The processes of electronic ionization from the last wide maximum in the density of occupied states p(E) are the main contributions to the energy range of interest. At the large broadening of bFp, small details of p(E) are not so important, thus, for simplicity we substitute this maximum by a rectangle having the width E2 - El. Then
where El = 25 eV, E2 = 29 eV are the lower and upper limits (increased on hw,,) of interpolated rectangle. In the general case, as it was shown in [16, 171 by the example of Si the excited level occupation function is written as follows: f(E) = f,(E) +p . fPl(E), where p is the weight. The relation between contributions in f(E) from e-e- scattering and plasmon decay depends on both EP [3] and the angle of incidence of primary electrons on the crystal surface 11).In particular, the form of SEE spectra of W(110) surface and the amplitude of specific features (but not energy position their) vary at EP increase [12]. With EP increase up to 1 keV the fine structure is revealed better and the position of the energy spectrum more and more differs from the cascade
Vol. 101, No. 7
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
maximum. Besides, temperature T of a sample differently influences the fine structure: a part of peaks practically disappears at T - 1200 K ([12], for W(l10) surface), and other peaks at this temperature remain unchanged. In our case the problem becomes more complicated also by the presence of the crystal-vacuum boundary and the problem of deriving the p(E,, r9,T) dependence requires a special investigation outside the framework of present studies. In Fig. l(a) the calculation results for SEE spectrum using formula from equation (1) for electron emitted normal to plane Ge(ll1) are given. Here for comparison we give also experimental curves from paper [2_5] [Fig. l(b)]. To derive the step function N(E, 0) analogous to [16] and calculate the plasmon contribution to f(E) we utilized the calculation of the band structure EG and of p(E) Ge density-of-states, obtained by the pseudo-potentiai method with parameters from [26]. The
SURFACE
485
curves J(E, Q) have been calculated with the account for (p = 0.7) and with no account (p = 0) for the e-pfcontribution to f(E). The plasmon contribution to the distribution functionf(E) is represented as the wide peak (B) to the right-hand side of the cascade maximum (A) (analogous to [27]). As is shown in [16, 281 in SEE spectra of Si the isotropic component contribution corresponding to elastic scattering on the surface and averaging over directions for a part of emitted electrons is quite great. This background current component presenting a characteristic view of a cascade maximum was considered by addition to N(E, 6) of a constant C, when the energy structure of the near-surface region is described by the model of nearly free electron gas. C variation in the wide range from 0 up to 100 pr$ctically does not change the second derivative J”(E, 0)_[16], which is explained by low dependence of J “(E, 52) on the background component for all E except for the vicinity of the cascade maximum. This proves the usage of double differentiation for, the elimination of background and elucidation of peculiarities fine struct;re of experimental SEE spectra to be correct. In J&62) calculations we assumed C = 100, which gives J(E, fl) dependence close to the experimental one. The experimental spectra change depending on Ep which is connected, apart from other facts, with the change of relationship between e-e- and e-pl- contributions to f(E). Thus, the agreement obtained between the main specific features of theoretical and experimental SEE spectra suggests that the fine structure of SEE current spectra is due to the electron structure of final states, from which the electron emission takes place. This allows us to use experimental data as reference points for more perfect band calculations indicating, which bands namely generate these or other specific features in a spectrum and, thus, to solve the problem of experimental measurement of boundaries of crystal energy bands. Acknowledgement-The
research described in this publication was made possible in part by Grant NK6ElOO from the Joint Fund of the Government of Ukraine and ISF. REFERENCES Komolov, S.A., Zntegrai Secondary Electron Spectroscopy of Surface. LSU Publ., Leningrad,
Fig. 1. The SEE spectra normal to Ge(ll1) surface: (a) theory. Dotted curve shows SEE spectrum with no account for the e-p& scattering; (b) experiment [25] for different energies of primary electrons Ep: (1) 100 eV, (2) 5OOeV, (3) 2 keV. Curves are plotted over coordinate axes in a random way. Energy is calculated beginning from E,,
1986. Christensen, N.E. and Willis, R.F., Phys. Rev., Bl8,1978,5140. Chung, M.S. and Everhart, T.E., Phys. Rev., B15, 1977,4699. Artamonov, O.M., Vinogradov, A.G., Smimov, O.M. and Terekhov, A.N., Fiz. Tverd. Tela, 27, 1985,3138.
LOW-ENERGY ELECTRON SPECTROSCOPY OF Ge(ll1)
486
Willis, R.F., Laude, L.D. and Fitton, B., Phys. Rev. Lett., 29, 1972, 220. 6. Best, P.E., Phys. Rev. Lett., 34, 1975, 674. 7. Bazhanova, N.P., Korablev, V.V. and Kochetov, NJ., Fiz. Tverd. Tela, 24, 1982, 1407. 8. Quinn, J.J., Phys. Rev., 126, 1962, 1453. 9. Koval’, I.F., Kryn’ko, Yu.N., Koshevaya, S.V., Mel’nik, P.V. and Nachodkin, N.G., Fiz. Tverd. Tela, 17, 1975, 1138. 10. Willis, R.F., Phys. Rev. Left., 34, 1975, 670. 11. Artamonov, O.M., Smimov, O.M. and Terekhov, A.N., Izv. Akad. Nauk USSR, Ser. Fiz., 46, 1982, 5.
17.
Korablev, V.V. and Kudinov, Yu.A., Izv. Akad. Korablev, V.V., Kudinov, Yu.A. and Sysoev, S.N.,
Korablev, V.V., Kudinov, Yu.A., Panchenko, O.F., Panchenko, L.K. and Shatalov, V.M., Fiz. Tverd.
19. 20. 21.
Landau, L.D. and Liphshits, E.M., Quantum Mechanics, Nonrelativistic Theory, Nauka, Moscow, 1974. Wolff, P.A., Phys. Rev., 95, 1954, 56. Shatalov, V.M. and Panchenko, O.F., Solid State
22.
Panchenko, O.F. and Shatalov, V.M., Sov. Phys.
Tela, 36, 1994, 2373.
Commun., 69, 1989, 937. JETP, 66,1987,
Korablev, V.V., Kudinov, Yu.A. and Sysoev, S.N.,
24. 25.
Pahnberg,
1976,741.
Fiz. Tverd Tela, 28, 1986, 2648.
15.
Artamonov, O.M. and Terekhov, A.N., Fiz. Tverd.
P.W., J. Appl.
Phys.,
38,
1967,
2137. 26.
Cohen, M.L. and Bergstresser, T.K., Phys. Rev.,
Shatalov, V.M., Panchenko, O.F., Artamonov, O.M., Vinogradov, A.G. and Terekhov, A.N.,
27.
Solid State Commun., 68, 1988, 719.
28.
Rosier, M. and Brauer, W., Phys. Status Solidi (b), 104,1981,161,575. Best, P.E., Phys. Rev., B14, 1976, 606.
141,1966,789.
Tela, 28, 1986, 862.
16.
127.
Panchenko, O.F. and Panchenko, L.K., J. Electr. Spectr. and Rel. Phenom., (in press). Pillon, J., Roptin, D. and Cailler, M., Surf. Sci., 57,
23,
Fiz. Tverd. Tela, 29, 1987, 702.
14.
Panchenko, O.F. and Shatalov, V.M., Zh. Tekhn.
18.
Nauk USSR, Ser. Fiz., 49, 1985, 1775.
13.
Vol. 101, No. 7
Fiz., 63, 1993, 144.
1383.
12.
SURFACE