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Low-energy electron spectroscopy of Si(1 0 0) and Ge(1 0 0) surfaces
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Radiation Physics and Chemistry 68 (2003) 251–256
Low-energy electron spectroscopy of Si(1 0 0) and Ge(1 0 0) surfaces T.Yu. Popika, V.M. Feyera, O.B. Shpenika,*, Yu.V. Popikb a
Institute of Electron Physics, Ukrainian National Academy of Sciences, Universitetska str. 21, Uzhhorod 88017, Ukraine b Uzhhorod National University, Uzhhorod 88000, Ukraine
Abstract Using a high-resolution (DEp40 meV) low-energy electron backscattering technique, the energy loss spectra at various energies of the primary electron beam (Ep ¼ 0:123 eV) for mirror-polished Si(1 0 0) and Ge(1 0 0) surfaces are studied. Our results on the bulk electron states are in good agreement with the known experimental data, obtained from photoemission spectroscopy, electron energy loss spectroscopy as well as bulk electronic structure of silicon and germanium, calculated theoretically by orthogonalized plane wave, local pseudopotential and GWA methods. The presence of the known surface electron states for Si(1 0 0) and Ge(1 0 0) is confirmed and their energy positions are specified more precisely. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Surfaces and interfaces; Electronic states; Electron energy loss spectroscopy
1. Introduction Silicon and germanium surfaces are rather well studied due to their wide applications in electronics. The crystalline structure of Si and Ge is diamond-like, and each of the ideal surfaces of this structure is characterized by dangling hybrid orbitals, directed to vacuum. For Si(1 0 0) and Ge(1 0 0) surface unit cell contains one atom with two dangling bonds (Zangwill, 1988). As it is well known from LEED experiments (Rowe and Ibach, 1974; Nesterenko and Snitko, 1983; Johansson et al., 1990b) and STM studies (Hamers et al., 1986; Kubby et al., 1987), at room temperature for Si(1 0 0) and Ge(1 0 0) surfaces 2 1 reconstruction occurs, being preserved for Si(1 0 0) at T ¼ 300–1450 K (Rowe and Ibach, 1974; Nesterenko and Snitko, 1983; Wachs et al., 1985; Johansson et al., 1990b; Kruger . and Pollmann, 1995), and for Ge(1 0 0) at T ¼ 220–955 K (Laine et al., 1998). The most probable model for the (2 1) surface is a structure, constructed of so-called asymmetric dimers, *Corresponding author. Tel./fax: +380-3122-43650. E-mail address: [email protected] (O.B. Shpenik).
formed by pairwise approaching of surface atoms simultaneous with their displacements normally to the face plane, different in magnitude. Since free (1 0 0) surface is characterized by the presence of two dangling valence bonds for each surface atom, the reconstruction of its surface should be more substantial, than for (1 1 1) and (1 1 0) surfaces. According to the experimental and theoretical data, it covers up to five atomic layers near the boundary with vacuum (Chadi, 1979; Nesterenko and Snitko, 1983; Kruger . and Pollmann, 1995; Rohling et al., 1995; Laine et al., 1998). The most widely used experimental techniques for studying the electron energy structure of Si(1 0 0) and Ge(1 0 0) surfaces are angle-resolved photoemission, inverse photoemission and high-resolution core-level spectroscopy. For Si(1 0 0) 2 1 surface against the background of the bulk valence band surface electron states (SES) with the energies B–0.4 eV (Wachs et al., 1985; Johansson et al., 1990a; Gavioli et al., 1995; Uhrberg et al., 1995), B–0.65 eV (Nesterenko and Snitko, 1983; Gavioli et al., 1995; Uhrberg et al., 1995), B–0.8 eV (Johansson et al., 1990a), B–1.5 eV (Himpsel et al., 1981; Uhrberg et al., 1985) are revealed as well as a
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surface resonance near the valence band maximum (B0.0 eV) (Rowe and Ibach, 1973; Johansson et al., 1990a; Rohling et al., 1995). For this surface SES in the gap also exist. The bottom of an empty band and the maximum of the filled band of SES are known to correspond to the energies of B0.83 and B0.34 eV, respectively. The energy gap between them is B0.5 eV (Nesterenko and Snitko, 1983; Zangwill, 1988). The analysis of the results for Ge(1 0 0) 2 1 surface shows that the first group of SES is located against the background of the bulk valence band with the densityof-states maxima at the energies B–0.4 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990; Laine et al., 1998), B–0.6 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990; Kipp et al., 1995), B–0.8 eV (Landemark et al., 1990), B–1.1 eV (Landemark et al., 1990; Kipp et al., 1995) and B–1.4 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990). The SES of the second group are located on both sides of the Fermi level EF which, according to Nesterenko and Snitko (1983), coincides with the valence band maximum. The donor states are by 0.02 eV below EF ; the acceptor states—by 0.02 eV above EF (Henzler, 1968, 1969; Davison and Levine, 1970; Nesterenko and Snitko, 1983; Kipp et al., 1995). These states determine the value and sign of the surface charge and the band curving (Henzler, 1968, 1969; Davison and Levine, 1970; Nesterenko and Snitko, 1983). The third group contains SES, located in the energy gap with the density-of-states maxima at B0.18, B0.27 eV (Popik et al., 2002), B0.35 and B0.45 eV (Nesterenko and Snitko, 1983; Popik et al., 2002). Here we report the results of Si(1 0 0) and Ge(1 0 0) surface studies by low-energy electron backscattering technique which was successfully applied for the investigation of surface and bulk electronic structure of metals (Popik et al., 2001b; Feyer et al., 2002) and semiconductors (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002).
2. Experimental apparatus and samples The experiments were carried out in the Surface Physics Laboratory of the Department of Ion processes, Institute of Electron Physics, Ukr. Nat. Acad. Sci. The studies were performed in an UHV chamber with base pressure B108 Pa. We developed a hypocycloidal electron spectrometer for obtaining monoenergetic electron beam and for the analysis of the reflected (scattered) electrons. The main characteristics of the spectrometer are as follows: primary beam current B108 A, reflected beam current B10–10 A, the beam diameter B0.5 mm, full width of the electron energy spread at half-maximum (FWHM) in the primary beam p20 meV, the analyser energy resolution (FWHM)
B30–40 meV. The technique and the hypocycloidal electron spectrometer design are described in Shpenik et al. (1997, 1998). The measurements were made from the Si(1 0 0) and Ge(1 0 0) surfaces. The Si sample is monocrystalline boron-doped p-type silicon (pB1.04 1017 cm3) with the resistivity 10 O cm. The Ge(1 0 0) surface is nominally ultrapure. The investigated (1 0 0) surfaces of both samples were mirror-polished and X-ray-oriented to within 1 , using Cu Ka radiation. The samples were cleaned by annealing, using a rear electron-beam heating arrangement, to B900 K (Ge) and B1100 K (Si) for about 5–6 h in 1 10–7 Pa vacuum. The cleanliness of the sample surface was checked by the presence of the features in the energy dependences of the reflected electron intensity. As we have shown earlier (Popik et al., 2001a; Feyer et al., 2002), almost no fine structure is revealed in the spectra for not sufficiently cleaned surfaces because of the strong noise of the backscattered electrons due to the adsorption of the residual gas molecules. The reliability and accuracy in determining the energy position of the features in the spectra was provided by high reproducibility of the results in a number of runs. The origin of the scale was put at the energy position of the elastic peak of the scattered electrons. The energy positions of the features were determined with the accuracy of 70.05 eV.
3. Experimental results and discussion At the energy of the primary electron beam Ep o10 eV, inelastic interaction of the electrons with the solid surface becomes so strong and localized in a thin subsurface region that optical selection rules break down (Ibach, 1977). While in the case of photoemission, the photon momentum can be neglected in comparison with the emitted electron momentum, in the present case the primary electron momentum should also be taken into account (at Ep B10 eV the electron wave vector kB1:6 1010 m–1, which is comparable with the Brillouin zone in the k-space). Since under excitation by electrons with the energy Ep B0210 eV both direct and indirect allowed and forbidden transitions of electrons from the filled to the empty states are possible, the studies of slow electron backscattering processes, contrary to other, well-known, techniques, enable one to obtain information on the excitation of such transitions across the entire reduced Brillouin zone, including the SES. In the present paper, the studies of the energy loss spectra at electron backscattering from Si(1 0 0) and Ge(1 0 0) surfaces at different Ep from 0.5 to 3.0 eV are reported (Fig. 1). As has been shown earlier (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002; Feyer et al., 2002), the
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Fig. 1. Electron energy loss spectra for the Si(1 0 0) and Ge(1 0 0) surfaces at different incident electron energies: (a) Ep ¼ 0:5 eV; (b) Ep ¼ 1:0 eV; (c) Ep ¼ 1:5 eV; (d) Ep ¼ 2:0 eV; (e) Ep ¼ 2:5 eV; and (f) Ep ¼ 3:0 eV.
processes of electron transition excitation in the lowenergy range (0–5 eV) are of ‘‘resonance’’ character: the fine structure, revealed in the spectra, depends on Ep : Thus, the features at 0.22 and 0.34 eV are distinctly manifested for Ge(1 0 0) surface at Ep ¼ 0:5 eV (Fig. 1a), not being revealed at higher Ep for this surface (Fig. 1b– f). The feature at the energy 0.45 eV is manifested as a maximum at Ep ¼ 1:0 eV (Fig. 1b), as a shoulder at Ep ¼ 1:5 eV (Fig. 1c), and is not detected at higher energies (Fig. 1d–f). Other features in the energy loss spectra for Ge(1 0 0) surface have a similar character of excitation. The fine structure, revealed in the spectra for Si(1 0 0), also essentially depends on Ep : As seen from Fig. 1a, at Ep ¼ 0:5 eV no features in the energy loss spectra are detected, and at Ep ¼ 1:023:0 eV (Fig. 1b–f) a rich fine structure is observed in the spectra. The probability of the primary electron energy loss for the excitation of interband transitions is closely related to the features of the energy structure of the density-ofstates in the bands and is maximal between the points of
Fig. 2. Si(1 0 0) and Ge(1 0 0) SES spectra.
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the reduced Brillouin zone with the maximal densities of filled and empty electron states (gradk EðkÞ-0) (Komolov, 1986). Thus, the features in the energy loss spectra result from the excitation of the electron transitions between the maxima of the density of surface and bulk electron states (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002; Feyer et al., 2002). While discussing the experimental data, we use the known band structures of silicon and germanium, calculated by local pseudopotential (Cohen and Chelikowsky, 1989), orthogonalized plane wave (Tsidilkovski, 1978) and GWA (Hedin, 1999) methods. The features in the spectra, whose energy does not correspond to the electron transitions in the bulk, are related to the presence of SES. The SES spectra for the Si(1 0 0) 2 1 and Ge(1 0 0) 2 1 surfaces are shown in Fig. 2. The energy positions of the features, detected in the loss spectra (Fig. 1), and possible electron transitions between the density-of-states maxima for Si (1 0 0) and Ge (1 0 0) are listed in Table 1. As seen from Fig. 2, the SES spectra against the background of the bulk valence band for Si(1 0 0) 2 1,
Ge(1 0 0) 2 1 are similar. For both surfaces the presence of SES at the energies –0.4, –0.6–0.65, –0.8– 0.85, –1.4–1.5 eV is characteristic. However, the excitation of these electron states for each surface occurs at different energies of the incident electrons. Since the maxima in the loss spectra in the energy range under investigation are related to the excitation of the electrons from the filled to the empty states, and in photoemission spectra only the features of the filled states of the valence band are revealed, then the detected fine structure in the backscattering spectra can result from the excitation of electrons across the whole reduced Brillouin zone including the valence and conduction bands as well as the energy gap. For example, for Ge(1 0 0) surface the feature at the energy B0.45 eV can result from both excitation of electrons from the SES in the valence band S5 to the empty SES Sr2 ; located near EF ; as well as from the filled SES Sr1 in the vicinity of EF and from the bulk valence band maximum in G025 point to the empty SES in the gap S9 (See Fig. 2). The unambiguity of assignment of the specific features is encumbered by the absence of theoretical calculations
Table 1 Energy positions of the features in the electron energy loss spectra by Si(1 0 0) and Ge(1 0 0) surfaces and their relation to the transitions of excited electrons p-Si(1 0 0) Energy loss spectra (eV)
Ge(1 0 0) Reference data (eV)
Possible electron transitions between states
Energy loss spectra (eV)
Reference data (eV)
Possible electron transitions between states
0.34 0.4 0.49
S4 G025 ðlÞ (p-type) G025 ðhÞ S5 S4 G025 ðhÞ (p-type) S 5 S6
0.22 0.34
0.27 0.35
Sr1 S7 =G025 S7 Sr1 S8 =G025 S8
0.45
0.45 0.4
0.62 0.67 0.75 0.85
0.7 0.8 0.85
0.94 1.05 1.15
1.1 1.0–1.3
1.64
S3 G025 ðlÞ (p-type) S3 G025 ðhÞ (p-type) G025 ðhÞ S6 G025 ðlÞ S6 S2 G025 ðhÞ (p-type) S5 X1 ðS1 Þ G025 ðhÞ X1 ðD1 Þ G025 ðhÞ X1 ðS3 Þ G025 ðlÞ X1 ðD1 Þ S4 S6 S3 S6 S4 X1 ðD1 Þ S1 G025 ðhÞ (p-type) S4 X1 ðS3 Þ
Sr1 S9 =S5 Sr2 G025 S9 S4 Sr2 =S5 S6 G025 L1 =S5 S7 G025 G02 =S5 S8 S3 Sr2 =S5 S9 S4 S7 S4 S 8 S4 S 9 S2 S5 =S4 S7 G025 X1
1.76 1.93 2.04 2.17 2.27 2.49 2.59
L1 S5 S3 X1 ðD1 Þ S3 X1 ðS3 Þ G025 ðhÞ L1 G025 ðlÞ L1 L03 X1 ðD1 Þ L03 X1 ðS3 Þ
1.7 1.83 2.25 2.76
0.23 0.35 0.52 0.59 0.66 0.74 0.83 1.00 1.10 1.26
1.43 1.54
0.65 0.83 0.8 1.16–1.7 1.22–1.32 1.25 1.48 1.5
2.11–2.15 2.44–2.53
1.24 1.34 1.52
2.8
S1 S6 S4 L1 =S2 S7 S3 S9 S1 S6 =S2 S9 S3 L 1 S4 X1 =S3 G02 S1 S9 =S2 L1 S1 G02 =S2 X1 G025 G15 =S1 X1
Note: (1) X 1; G02 ; G15 ; G025 ; L1 ; L03 —reduced Brillouin zone high-symmetry points; (2) Sr Sr1 ; Sr2 ; S1 2S9 —surface electron states.
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for the energy loss spectra at the interaction of slow electrons with the surface of the investigated objects.
4. Conclusions As seen from our experiments, the loss spectra at the backscattering of low-energy electrons by surface are very sensitive to both bulk and surface electron energy structure of the materials under investigation. The excitation of electron states at Si(1 0 0) and Ge(1 0 0) surfaces is shown to be of ‘‘resonance’’ character: the fine structure, revealed in the spectra in the energy range 0.5–3 eV, depends on the incident electron energy. The SES spectra with ES oEV for both surfaces under investigation are shown to be similar, but their excitation for Si(1 0 0) and Ge(1 0 0) occurs at different energies of incident electrons. The obtained results confirm and complement the data on the bulk and surface electron density-of-states for Si(1 0 0) and Ge(1 0 0), obtained by UPS, XPS, inverse photoemission and EELS.
Acknowledgements The authors would like to thank Dr. Yu.M. Azhniuk and Dr. A.V. Snegursky for their help in manuscript preparation.
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Radiation Physics and Chemistry 68 (2003) 251–256
Low-energy electron spectroscopy of Si(1 0 0) and Ge(1 0 0) surfaces T.Yu. Popika, V.M. Feyera, O.B. Shpenika,*, Yu.V. Popikb a
Institute of Electron Physics, Ukrainian National Academy of Sciences, Universitetska str. 21, Uzhhorod 88017, Ukraine b Uzhhorod National University, Uzhhorod 88000, Ukraine
Abstract Using a high-resolution (DEp40 meV) low-energy electron backscattering technique, the energy loss spectra at various energies of the primary electron beam (Ep ¼ 0:123 eV) for mirror-polished Si(1 0 0) and Ge(1 0 0) surfaces are studied. Our results on the bulk electron states are in good agreement with the known experimental data, obtained from photoemission spectroscopy, electron energy loss spectroscopy as well as bulk electronic structure of silicon and germanium, calculated theoretically by orthogonalized plane wave, local pseudopotential and GWA methods. The presence of the known surface electron states for Si(1 0 0) and Ge(1 0 0) is confirmed and their energy positions are specified more precisely. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Surfaces and interfaces; Electronic states; Electron energy loss spectroscopy
1. Introduction Silicon and germanium surfaces are rather well studied due to their wide applications in electronics. The crystalline structure of Si and Ge is diamond-like, and each of the ideal surfaces of this structure is characterized by dangling hybrid orbitals, directed to vacuum. For Si(1 0 0) and Ge(1 0 0) surface unit cell contains one atom with two dangling bonds (Zangwill, 1988). As it is well known from LEED experiments (Rowe and Ibach, 1974; Nesterenko and Snitko, 1983; Johansson et al., 1990b) and STM studies (Hamers et al., 1986; Kubby et al., 1987), at room temperature for Si(1 0 0) and Ge(1 0 0) surfaces 2 1 reconstruction occurs, being preserved for Si(1 0 0) at T ¼ 300–1450 K (Rowe and Ibach, 1974; Nesterenko and Snitko, 1983; Wachs et al., 1985; Johansson et al., 1990b; Kruger . and Pollmann, 1995), and for Ge(1 0 0) at T ¼ 220–955 K (Laine et al., 1998). The most probable model for the (2 1) surface is a structure, constructed of so-called asymmetric dimers, *Corresponding author. Tel./fax: +380-3122-43650. E-mail address: [email protected] (O.B. Shpenik).
formed by pairwise approaching of surface atoms simultaneous with their displacements normally to the face plane, different in magnitude. Since free (1 0 0) surface is characterized by the presence of two dangling valence bonds for each surface atom, the reconstruction of its surface should be more substantial, than for (1 1 1) and (1 1 0) surfaces. According to the experimental and theoretical data, it covers up to five atomic layers near the boundary with vacuum (Chadi, 1979; Nesterenko and Snitko, 1983; Kruger . and Pollmann, 1995; Rohling et al., 1995; Laine et al., 1998). The most widely used experimental techniques for studying the electron energy structure of Si(1 0 0) and Ge(1 0 0) surfaces are angle-resolved photoemission, inverse photoemission and high-resolution core-level spectroscopy. For Si(1 0 0) 2 1 surface against the background of the bulk valence band surface electron states (SES) with the energies B–0.4 eV (Wachs et al., 1985; Johansson et al., 1990a; Gavioli et al., 1995; Uhrberg et al., 1995), B–0.65 eV (Nesterenko and Snitko, 1983; Gavioli et al., 1995; Uhrberg et al., 1995), B–0.8 eV (Johansson et al., 1990a), B–1.5 eV (Himpsel et al., 1981; Uhrberg et al., 1985) are revealed as well as a
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surface resonance near the valence band maximum (B0.0 eV) (Rowe and Ibach, 1973; Johansson et al., 1990a; Rohling et al., 1995). For this surface SES in the gap also exist. The bottom of an empty band and the maximum of the filled band of SES are known to correspond to the energies of B0.83 and B0.34 eV, respectively. The energy gap between them is B0.5 eV (Nesterenko and Snitko, 1983; Zangwill, 1988). The analysis of the results for Ge(1 0 0) 2 1 surface shows that the first group of SES is located against the background of the bulk valence band with the densityof-states maxima at the energies B–0.4 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990; Laine et al., 1998), B–0.6 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990; Kipp et al., 1995), B–0.8 eV (Landemark et al., 1990), B–1.1 eV (Landemark et al., 1990; Kipp et al., 1995) and B–1.4 eV (Nelson et al., 1983; Hsieh et al., 1984; Landemark et al., 1990). The SES of the second group are located on both sides of the Fermi level EF which, according to Nesterenko and Snitko (1983), coincides with the valence band maximum. The donor states are by 0.02 eV below EF ; the acceptor states—by 0.02 eV above EF (Henzler, 1968, 1969; Davison and Levine, 1970; Nesterenko and Snitko, 1983; Kipp et al., 1995). These states determine the value and sign of the surface charge and the band curving (Henzler, 1968, 1969; Davison and Levine, 1970; Nesterenko and Snitko, 1983). The third group contains SES, located in the energy gap with the density-of-states maxima at B0.18, B0.27 eV (Popik et al., 2002), B0.35 and B0.45 eV (Nesterenko and Snitko, 1983; Popik et al., 2002). Here we report the results of Si(1 0 0) and Ge(1 0 0) surface studies by low-energy electron backscattering technique which was successfully applied for the investigation of surface and bulk electronic structure of metals (Popik et al., 2001b; Feyer et al., 2002) and semiconductors (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002).
2. Experimental apparatus and samples The experiments were carried out in the Surface Physics Laboratory of the Department of Ion processes, Institute of Electron Physics, Ukr. Nat. Acad. Sci. The studies were performed in an UHV chamber with base pressure B108 Pa. We developed a hypocycloidal electron spectrometer for obtaining monoenergetic electron beam and for the analysis of the reflected (scattered) electrons. The main characteristics of the spectrometer are as follows: primary beam current B108 A, reflected beam current B10–10 A, the beam diameter B0.5 mm, full width of the electron energy spread at half-maximum (FWHM) in the primary beam p20 meV, the analyser energy resolution (FWHM)
B30–40 meV. The technique and the hypocycloidal electron spectrometer design are described in Shpenik et al. (1997, 1998). The measurements were made from the Si(1 0 0) and Ge(1 0 0) surfaces. The Si sample is monocrystalline boron-doped p-type silicon (pB1.04 1017 cm3) with the resistivity 10 O cm. The Ge(1 0 0) surface is nominally ultrapure. The investigated (1 0 0) surfaces of both samples were mirror-polished and X-ray-oriented to within 1 , using Cu Ka radiation. The samples were cleaned by annealing, using a rear electron-beam heating arrangement, to B900 K (Ge) and B1100 K (Si) for about 5–6 h in 1 10–7 Pa vacuum. The cleanliness of the sample surface was checked by the presence of the features in the energy dependences of the reflected electron intensity. As we have shown earlier (Popik et al., 2001a; Feyer et al., 2002), almost no fine structure is revealed in the spectra for not sufficiently cleaned surfaces because of the strong noise of the backscattered electrons due to the adsorption of the residual gas molecules. The reliability and accuracy in determining the energy position of the features in the spectra was provided by high reproducibility of the results in a number of runs. The origin of the scale was put at the energy position of the elastic peak of the scattered electrons. The energy positions of the features were determined with the accuracy of 70.05 eV.
3. Experimental results and discussion At the energy of the primary electron beam Ep o10 eV, inelastic interaction of the electrons with the solid surface becomes so strong and localized in a thin subsurface region that optical selection rules break down (Ibach, 1977). While in the case of photoemission, the photon momentum can be neglected in comparison with the emitted electron momentum, in the present case the primary electron momentum should also be taken into account (at Ep B10 eV the electron wave vector kB1:6 1010 m–1, which is comparable with the Brillouin zone in the k-space). Since under excitation by electrons with the energy Ep B0210 eV both direct and indirect allowed and forbidden transitions of electrons from the filled to the empty states are possible, the studies of slow electron backscattering processes, contrary to other, well-known, techniques, enable one to obtain information on the excitation of such transitions across the entire reduced Brillouin zone, including the SES. In the present paper, the studies of the energy loss spectra at electron backscattering from Si(1 0 0) and Ge(1 0 0) surfaces at different Ep from 0.5 to 3.0 eV are reported (Fig. 1). As has been shown earlier (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002; Feyer et al., 2002), the
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Fig. 1. Electron energy loss spectra for the Si(1 0 0) and Ge(1 0 0) surfaces at different incident electron energies: (a) Ep ¼ 0:5 eV; (b) Ep ¼ 1:0 eV; (c) Ep ¼ 1:5 eV; (d) Ep ¼ 2:0 eV; (e) Ep ¼ 2:5 eV; and (f) Ep ¼ 3:0 eV.
processes of electron transition excitation in the lowenergy range (0–5 eV) are of ‘‘resonance’’ character: the fine structure, revealed in the spectra, depends on Ep : Thus, the features at 0.22 and 0.34 eV are distinctly manifested for Ge(1 0 0) surface at Ep ¼ 0:5 eV (Fig. 1a), not being revealed at higher Ep for this surface (Fig. 1b– f). The feature at the energy 0.45 eV is manifested as a maximum at Ep ¼ 1:0 eV (Fig. 1b), as a shoulder at Ep ¼ 1:5 eV (Fig. 1c), and is not detected at higher energies (Fig. 1d–f). Other features in the energy loss spectra for Ge(1 0 0) surface have a similar character of excitation. The fine structure, revealed in the spectra for Si(1 0 0), also essentially depends on Ep : As seen from Fig. 1a, at Ep ¼ 0:5 eV no features in the energy loss spectra are detected, and at Ep ¼ 1:023:0 eV (Fig. 1b–f) a rich fine structure is observed in the spectra. The probability of the primary electron energy loss for the excitation of interband transitions is closely related to the features of the energy structure of the density-ofstates in the bands and is maximal between the points of
Fig. 2. Si(1 0 0) and Ge(1 0 0) SES spectra.
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the reduced Brillouin zone with the maximal densities of filled and empty electron states (gradk EðkÞ-0) (Komolov, 1986). Thus, the features in the energy loss spectra result from the excitation of the electron transitions between the maxima of the density of surface and bulk electron states (Popik et al., 2000, 2001a, 2002; Shpenik et al., 2002; Feyer et al., 2002). While discussing the experimental data, we use the known band structures of silicon and germanium, calculated by local pseudopotential (Cohen and Chelikowsky, 1989), orthogonalized plane wave (Tsidilkovski, 1978) and GWA (Hedin, 1999) methods. The features in the spectra, whose energy does not correspond to the electron transitions in the bulk, are related to the presence of SES. The SES spectra for the Si(1 0 0) 2 1 and Ge(1 0 0) 2 1 surfaces are shown in Fig. 2. The energy positions of the features, detected in the loss spectra (Fig. 1), and possible electron transitions between the density-of-states maxima for Si (1 0 0) and Ge (1 0 0) are listed in Table 1. As seen from Fig. 2, the SES spectra against the background of the bulk valence band for Si(1 0 0) 2 1,
Ge(1 0 0) 2 1 are similar. For both surfaces the presence of SES at the energies –0.4, –0.6–0.65, –0.8– 0.85, –1.4–1.5 eV is characteristic. However, the excitation of these electron states for each surface occurs at different energies of the incident electrons. Since the maxima in the loss spectra in the energy range under investigation are related to the excitation of the electrons from the filled to the empty states, and in photoemission spectra only the features of the filled states of the valence band are revealed, then the detected fine structure in the backscattering spectra can result from the excitation of electrons across the whole reduced Brillouin zone including the valence and conduction bands as well as the energy gap. For example, for Ge(1 0 0) surface the feature at the energy B0.45 eV can result from both excitation of electrons from the SES in the valence band S5 to the empty SES Sr2 ; located near EF ; as well as from the filled SES Sr1 in the vicinity of EF and from the bulk valence band maximum in G025 point to the empty SES in the gap S9 (See Fig. 2). The unambiguity of assignment of the specific features is encumbered by the absence of theoretical calculations
Table 1 Energy positions of the features in the electron energy loss spectra by Si(1 0 0) and Ge(1 0 0) surfaces and their relation to the transitions of excited electrons p-Si(1 0 0) Energy loss spectra (eV)
Ge(1 0 0) Reference data (eV)
Possible electron transitions between states
Energy loss spectra (eV)
Reference data (eV)
Possible electron transitions between states
0.34 0.4 0.49
S4 G025 ðlÞ (p-type) G025 ðhÞ S5 S4 G025 ðhÞ (p-type) S 5 S6
0.22 0.34
0.27 0.35
Sr1 S7 =G025 S7 Sr1 S8 =G025 S8
0.45
0.45 0.4
0.62 0.67 0.75 0.85
0.7 0.8 0.85
0.94 1.05 1.15
1.1 1.0–1.3
1.64
S3 G025 ðlÞ (p-type) S3 G025 ðhÞ (p-type) G025 ðhÞ S6 G025 ðlÞ S6 S2 G025 ðhÞ (p-type) S5 X1 ðS1 Þ G025 ðhÞ X1 ðD1 Þ G025 ðhÞ X1 ðS3 Þ G025 ðlÞ X1 ðD1 Þ S4 S6 S3 S6 S4 X1 ðD1 Þ S1 G025 ðhÞ (p-type) S4 X1 ðS3 Þ
Sr1 S9 =S5 Sr2 G025 S9 S4 Sr2 =S5 S6 G025 L1 =S5 S7 G025 G02 =S5 S8 S3 Sr2 =S5 S9 S4 S7 S4 S 8 S4 S 9 S2 S5 =S4 S7 G025 X1
1.76 1.93 2.04 2.17 2.27 2.49 2.59
L1 S5 S3 X1 ðD1 Þ S3 X1 ðS3 Þ G025 ðhÞ L1 G025 ðlÞ L1 L03 X1 ðD1 Þ L03 X1 ðS3 Þ
1.7 1.83 2.25 2.76
0.23 0.35 0.52 0.59 0.66 0.74 0.83 1.00 1.10 1.26
1.43 1.54
0.65 0.83 0.8 1.16–1.7 1.22–1.32 1.25 1.48 1.5
2.11–2.15 2.44–2.53
1.24 1.34 1.52
2.8
S1 S6 S4 L1 =S2 S7 S3 S9 S1 S6 =S2 S9 S3 L 1 S4 X1 =S3 G02 S1 S9 =S2 L1 S1 G02 =S2 X1 G025 G15 =S1 X1
Note: (1) X 1; G02 ; G15 ; G025 ; L1 ; L03 —reduced Brillouin zone high-symmetry points; (2) Sr Sr1 ; Sr2 ; S1 2S9 —surface electron states.
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for the energy loss spectra at the interaction of slow electrons with the surface of the investigated objects.
4. Conclusions As seen from our experiments, the loss spectra at the backscattering of low-energy electrons by surface are very sensitive to both bulk and surface electron energy structure of the materials under investigation. The excitation of electron states at Si(1 0 0) and Ge(1 0 0) surfaces is shown to be of ‘‘resonance’’ character: the fine structure, revealed in the spectra in the energy range 0.5–3 eV, depends on the incident electron energy. The SES spectra with ES oEV for both surfaces under investigation are shown to be similar, but their excitation for Si(1 0 0) and Ge(1 0 0) occurs at different energies of incident electrons. The obtained results confirm and complement the data on the bulk and surface electron density-of-states for Si(1 0 0) and Ge(1 0 0), obtained by UPS, XPS, inverse photoemission and EELS.
Acknowledgements The authors would like to thank Dr. Yu.M. Azhniuk and Dr. A.V. Snegursky for their help in manuscript preparation.
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