- Email: [email protected]
Si(1 0 0) interface structure by means of angle-scanned photoelectron spectroscopy and diffraction
Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84
Investigation of the SiO2 /Si(1 0 0) interface structure by means of angle-scanned photoelectron spectroscopy and diffraction S. Dreiner a,b,∗ , M. Schürmann a , C. Westphal a b
a Universität Dortmund, Lehrstuhl für Experimentelle Physik I, Otto-Hahn-Str. 4, 44221 Dortmund, Germany Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany
Available online 19 March 2004
Abstract The local environment of Si at the interface between a thermally grown SiO2 film and Si(1 0 0) was studied by angle-scanned photoelectron spectroscopy and diffraction. Si 2p core-level spectra containing chemically shifted components were recorded. These components were deconvoluted by least squares fitting and assigned to different Si oxidation states. The angular dependence of the photoelectron intensity was obtained from the least squares fit results. A simple statistical model was developed to describe the population and depth distribution of the different suboxide species. Using a simple electron attenuation scheme we can simulate the photoemission polar angle dependence of the various Si oxidation states within the model. The fitting of these model curves to the experimental data results in parameters which indicate a Si–O–Si bridge-bonded interface structure. © 2004 Elsevier B.V. All rights reserved. Keywords: Angle-scanned photoelectron spectroscopy; Photoelectron diffraction; Chemical shift; Silicon oxide
1. Introduction The interface between silicon oxide and silicon plays a crucial role in modern semiconductor technology [1,2]. Due to the advancing miniaturization of semiconductor devices the atomic structure at the interface becomes increasingly important. The experimental access to the interface is limited since the interface is buried below the surface and due to the loss of long range order of the amorphous silicon oxide. Also, a large lattice mismatch between Si and SiO2 causes structural stress. In order to determine the structure, the experimental technique has to be sensitive to the local environment of different atoms present in various structures at the interface. A well suited experimental tool to investigate the structure of the SiO2 /Si interface is high-resolution core-level photoemission spectroscopy. Si 2p photoemission spectra (Fig. 1) show chemically shifted components derived from individual oxidation states (Si0 , Si1+ , Si2+ , Si3+ , Si4+ ) [3,4]. Due to the inelastic scattering of the photoelectrons, the Six+ 2p intensity depends on the population and depth ∗ Corresponding author. Tel.: +49-231-755-3511; fax: +49-231-755-3657. E-mail address: [email protected] (S. Dreiner).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.024
distribution of the Six+ atoms in the surface. Polar-angle and oxidation-state resolved photoemission investigations of the SiO2 /Si(1 1 1) system [5,6] established the statistical cross-linking model. The intensity of the photoemission current as function of angle and/or kinetic energy depends on the local environment of the emitting atom [7]. This dependence is caused by final-state diffraction effects of the photoelectron wave. Photoelectron diffraction (PD) is a well established technique for the determination of surface or interface structures [7]. Structural information is obtained by comparison of the experimental data with simulation calculations. An advantage of photoelectron diffraction compared to many other surface sensitive analytic methods is the high sensitivity to the local arrangement of nearest neighbor atoms within the escape depth of the electrons. A further advantage is that no long-range order is needed. In this Article we report on an investigation of the SiO2 /Si(1 0 0) interface structure using photoelectron spectroscopy and diffraction. Several various interface structure models were proposed, ranging from a chemically graded interface with the suboxides distributed over a range of ∼20 Å [8] to an interface consisting of a single Si2+ layer [9]. Similar to the SiO2 /Si(1 1 1) system the polar-angle dependences of all Si 2p oxidation state intensities contain
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S. Dreiner et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84
information about the population of each suboxide species at the interface. In a previous investigation Oh et al. [10] reported on the polar-angle dependence of the Si 2p oxidation state intensities proposing a graded interface consisting of three layers. In this Report we show that the photoemission polar-angle dependence of the Si suboxides can be explained by a simple statistical model for the atomic populations and depth distributions of the Six+ .
2. Experiment
Fig. 1. Si 2p core level spectra recorded with a photon energy of hν = 180 eV for two different silicon oxide layers on Si(1 0 0) at Θ = 60◦ . The data points are denoted by symbols, the result of least squares fitting is shown as a full line. Also, the decomposition into the bulk component and its chemically shifted components due to the oxidation are shown.
The experiment was performed in a -metal UHV chamber equipped with a hemispherical electron analyzer. Before preparation, the sample holder and the sample were thoroughly degassed at a temperature of 700–750 ◦ C. With the hot sample, the base pressure was at 4 × 10−10 mbar after this procedure. A clean Si sample was obtained by heating the sample to 1050 ◦ C for 2 min followed by a slow temperature decrease to room temperature. Thin SiO2 films were grown in-situ by thermal oxidation, the oxygen pressure was kept at 5 × 10−6 mbar (1.2 × 10−7 mbar) for 10 min equivalent to 3000 L (72 L) while the crystal was at a temperature of 650 ◦ C (530 ◦ C). The electron energy resolution was about 50 meV and the photon energy resolution at a photon energy of 180 eV was set to 90 meV. At a fixed polar angle, photoemission spectra were recorded at the BESSY II U-41 PGM beamline over 360◦ azimuth range with an azimuth angle increment of Φ = 2◦ . Subsequently, a new polar angle was set with an increment of Θ = 2◦ and a new azimuth-scan was recorded. This was repeated until the full polar and azimuth range were covered (0◦ < Θ < 84◦ , 0◦ < Φ < 360◦ ).
(a) T
SiO2
t, R3 t, R2 t, R1
uppermost layer middle layer bottom layer Si
(b) Probabilities (each bond to O( ) is twice as likely as a bond to Si( )):
Si0
Si1+
Si2+
Si2+
Si3+
uppermost layer (bonds to the layer above are bonds to O): p= 1/9
Si4+
4/9
4/9
middle layer: p = 1/81
4/81
4/81
16/81
4/81
4/81
16/81
16/81
16/81
bottom layer: (bonds to the layer below are bonds to Si): p = 1/9
4/9
4/9
Fig. 2. Three layer interface model (a) with all possible local bonding configurations and their probabilities (b).
S. Dreiner et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84 4.5
I(Si
x+
0
)/I(Si )
4.0
Si
3.5
Si
3.0
Si Si
1+ 2+ 3+ 4+
2.5 2.0 1.5 1.0 0.5 0.0 0˚
10˚
20˚
30˚
40˚
50˚
60˚
70˚
80˚
polar angle Θ
Fig. 3. Intensity ratios of Si1+ , Si2+ , Si3+ , and Si4+ components normalized to the bulk component as a function of polar emission angle for the 3000 L film. The symbols represent data points, and the solid lines are obtained fits using the model displayed in Fig. 2. The details are described in the text.
3. Results and discussion Fig. 1 shows typical photoemission spectra of both oxidized surfaces after the secondary background has been subtracted. The line-shape consists of seven resolved components, which correspond to the electron signals of Si0 (B, α, β), Si1+ , Si2+ , Si3+ , and Si4+ . The Si0 -signal was composed of the bulk signal (B) and two extra components (α, β). These components are assumed to be due to strained interfacial Si without any Si–O bonds [10]. Each measured spectrum was decomposed by a least squares fitting into seven components, each of which consisting of a pair of spin-orbit split Gaussian peaks. All peak positions (energy shifts: Si␣ = −0.22 eV, Si = 0.34 eV, Si1+ = 0.95 eV, Si2+ = 1.78 eV, Si3+ = 2.60 eV, Si4+ = 3.72 eV) agree well within a few percent to previously published results [10]. For the Si signal we obtain a binding energy shift of 0.34 eV in comparison to 0.2 eV by Oh et al. [10]. In our model of the SiO2 /Si(1 0 0) system, the interface consists of three layers (Fig. 2a). The uppermost layer is
81
connected with the SiO2 film and the bottom layer is connected with the silicon crystal. A silicon atom located in the middle layer may be bond to silicon and oxygen in both directions. In Fig. 2b, all possible bonding configurations of Si atoms at the interface are displayed. In the easiest configuration the silicon atom in the center of the cluster is bonded to silicon neighbors only (Fig. 2b, Si0 -cluster). Each silicon bond can be replaced with an oxygen bond so that all Si oxidation states are possible. Since oxidation of the Si surface is considered to be a relatively random and local process [5], we derive the probability of each configuration from a statistical analysis. Taking into account the symmetry-equivalent configurations and assuming that each bond to oxygen is twice as likely as a bond to silicon, the probabilities (p) of the suboxides are obtained as displayed in Fig. 2. This assumption can be traced back to the fact that the number of O atoms is twice the number of Si atoms in SiO2 . The probabilities of Si in the upper layer are calculated with all bonds to the layer above being bonds to oxygen. In the case of Si in the lower layer all bonds to the layer below are bonds to silicon. Due to the different Si densities of crystalline silicon and SiO2 we allow a change of the Si density in the various interface layers. The Si 2p intensity variation as a function of polar angle of each oxidation component (I 0 , I 1+ , . . . ) can be calculated using a simple electron damping scheme, including the probabilities obtained from our model I 0 = nSi [D3 + ( 19 R1 D +
1 81 R2 )D(1 − D)]C
I 1+ = nSi [( 49 R1 D + I 2+ = I 3+ =
8 81 R2 )D(1 − D)]C 1 nSi [( 49 R1 D2 + 24 81 R2 D + 9 R3 )(1 − D)]C 4 nSi [( 32 81 R2 D + 9 R3 )(1 − D)]C
4 I 4+ = nSi [( 16 81 R2 D + 9 R3 )(1 − D)]C + nSiO2 (1 − C)
with
−t D = exp λ cos θ −T C = exp λ cos θ
Fig. 4. Side view of the bridge-bond interface model that halves the number of dangling bonds of the silicon layer (Si: grey circles, O: black circles).
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Fig. 5. Experimental Si 2p diffraction patterns of the Six+ obtained for a photon energy of 180 eV. The left column displays the diffraction patterns of the 72 L and the right column these of the 3000 L silicon oxide film.
S. Dreiner et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84
where θ denotes the internal angle which is related by the simple inner potential refraction rule to the observed external angle [5], nSi is the surface atom density of pure Si (nSi = 6.8×1014 cm−2 ) and t = 1.37 Å is the thickness of a silicon layer. We assume a uniform mean free path of λ = 4.2 Å for Si according to the TPP2 formula [11]. The factor Rx describes the change of the Si density in each interface layer x. The only free parameters within this model are the Rx factors, the SiO2 film thickness T , and the inner potential. We used this model to simulate the experimental intensity ratios (I x+ /I 0 ) between each suboxide and the Si0 intensity as a function of the polar angle, where I 0 denotes the total intensity of silicon which is not directly bonded to oxygen (I 0 = I B + I ␣ + I  ). In order to eliminate photoelectron diffraction effects in the experimental data at a given polar angle all spectra at this polar angle are added up. Fig. 3 shows an excellent agreement between the experimental intensity ratios (symbols) with the simulated ratios for the 3000 L film. In contrast to the results of Oh et al. [10] our experimental data of the Si1+ and Si2+ signals show individual dependence on the polar angle. As the polar angle increases, the I 2+ /I 0 ratio exhibits a steeper increase than the I 1+ /I 0 ratio. This is also obtained by the intensity ratios of the simulation. Within the model we expect more Si2+ atoms than Si1+ atoms in the second and third interface layer because of statistical reasons. In agreement with Oh et al., the normalized I 3+ intensity exhibits a steeper increase than the I 2+ and the I 1+ as a function of the polar angle. The fitting parameters for the simulated curves are R1 = 0.77 ± 0.05, R2 = 0.45 ± 0.08, R3 = 0.93 ± 0.05, and T = 1.37±0.01 Å. The decrease of the Si density in the second interface layer to a value of R2 ≈ 0.5 can be explained by the bridge-bonded interface structure which was found by the theoretical investigations of Tu and Tersoff [9]. The silicon crystal terminating Si–O–Si brigde bonds are consistently proposed by various structure models of the SiO2 /Si interface [9,12–14]. The bridge-bonds eliminate half of the bonds from the Si side, correcting the mismatch between the bond densities in the two different materials (cf. Fig. 4). Fig. 5 displays the experimental diffraction patterns of the Si atoms in various oxidation states for both SiO2 /Si films. The patterns display the anisotropy function A(Θ, Φ) = [I(Θ, Φ) − I0 (Θ)]/I0 (Θ) in a strictly linear grey scale, where I(Θ, Φ) denotes the photoelectron intensity obtained by the above-mentioned fitting procedure and I0 (Θ) denotes the mean intensity for a given polar angle. The maximum anisotropy Amax calculated as Amax = max(A(Θ, Φ)) − min(A(Θ, Φ)) is indicated within each diffraction pattern. The diffraction pattern of the bulk signal (SiB ) does not vary considerably depending on the layer thickness. A very similar diffraction pattern was obtained for the clean Si(1 0 0)-2 × 1 and the Si(1 0 0):H-2 × 1 surface [15]. The suboxide signals of Si1+ , Si2+ and Si3+ show a similar angular dependence. The diffraction patterns consist of elongated maxima in Φ = 45◦ , 135◦ , 225◦ , 315◦ azimuth direction. The change of the Si3+ diffraction pat-
83
tern depending on the layer thickness indicates that each maximum consists of several maxima. These maxima affiliate with each other if the layer thickness increases. The Si4+ signal displays a different diffraction pattern compared to the previous discussed ones . The main maxima of the Si4+ diffraction pattern are observed in Φ = 0◦ , 90◦ , 180◦ , 270◦ azimuth direction. In Fig. 5, the anisotropy of the Si0 diffraction pattern of the thicker film is reduced compared to the film prepared at 72 L. However, the suboxide diffraction patterns show a increased anisotropy compared to the thinner film. This indicates that a locally ordered interface structure is to be expected rather for the thicker than for the thinner film. The perfect interface proposed by Tu and Tersoff [9] consists of Si2+ and Si4+ atoms in very different local atomic environments. The Si2+ and Si4+ signals show very different diffraction patterns. A comparison of the experimental data with multiple scattering calculations will show if this diffraction pattern can be explained within the brigde-bonded interface model as well.
4. Conclusions In summary, we investigated the local atomic environment of Si at the interface between a thermally grown SiO2 film and Si(1 0 0). We utilized the chemically shifted Si 2p core-level photoelectrons as a local probe at the interface. The photoemission polar angle dependence of the various Six+ signals contains information about the depth distribution and population of each oxidation state. We developed a statistical model for the Six+ depth distribution and population over an interface range of three layers. This model and a simple electron attenuation scheme were used to obtain the simulated photoemission polar angle dependence of each Six+ . The model curves can successfully and quantitatively describe the experimental data of the Si/SiO2 interface. The free parameters to fit these curves to the experimental data are the silicon densities in the various interface layers. The fitting procedure results in a significant reduction of the Si density in the second interface layer which can be explained by a Si–O–Si bridge-bond interface model obtained by theoretical investigations. The Six+ photoelectron diffraction patterns contain information about the structural environment of Si in the various oxidation states. The comparison of the diffraction patterns with multiple scattering calculations is in progress.
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (No. We 1649/3) and by the German Federal Ministry of Education, Science, Research and Technology (BMBF) under contract number 05 SE8PMB 9. We thank the BESSY-team (especially C. Jung, M. Mast and W. Braun) for technical support during the measurements.
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References [1] T. Hattori, Crit. Rev. Solid State Sci. 20 (1995) 339, and references therein. [2] Y.J. Chabal (Ed.), Fundamental Aspects of Silicon Oxidation, Springer Series in Materials Science, vol. 46, Springer-Verlag, Berlin, Heidelberg, 2001. [3] F.J. Grunthaner, P.J. Grunthaner, R.P. Vasquez, B.F. Lewis, J. Maserjian, A. Madhukar, Phys. Rev. Lett. 43 (1979) 1683. [4] F.J. Himpsel, F.R. McFeely, A. Taleb-Ibrahimi, J.A. Yarmoff, G. Hollinger, Phys. Rev. B 38 (1988) 6084. [5] D.-A. Luh, T. Miller, T.-C. Chiang, Phys. Rev. Lett. 79 (1997) 3014. [6] S. Dreiner, M. Schürmann, C. Westphal, H. Zacharias, Phys. Rev. Lett. 86 (2001) 4068. [7] C.S. Fadley, R.Z. Bachrach (Eds.), Synchrotron Radiation Research: Advances in Surface and Interface Science, vol. 1, Plenum Press, New York, 1992.
[8] A. Pasquarello, M.S. Hybertsen, R. Car, Nature 396 (1998) 58. [9] Y. Tu, J. Tersoff, Phys. Rev. Lett. 84 (2000) 4393. [10] J.H. Oh, H.W. Yeom, Y. Hagimoto, K. Ono, M. Oshima, N. Hirashita, M. Nywa, A. Toriumi, A. Kakizaki, Phys. Rev. B 63 (2001) 205310. [11] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. 20 (1993) 77; C.J. Powell, A. Jablonski, S. Tanuma, D.R. Penn, J. Electron Spectrosc. Rel. Phenom. 63 (1994) 605. [12] A. Pasquarello, M.S. Hybertsen, R. Car, Appl. Phys. Lett. 68 (1996) 625. [13] K.-O. Ng, D. Vanderbilt, Phys. Rev. B 59 (1999) 10132. [14] R. Buczko, S.J. Pennycook, S.T. Pantelides, Phys. Rev. Lett. 84 (2000) 943. [15] S. Dreiner, C. Westphal, M. Schürmann, H. Zacharias, Thin Solid Films 428 (2003) 123.
Investigation of the SiO2 /Si(1 0 0) interface structure by means of angle-scanned photoelectron spectroscopy and diffraction S. Dreiner a,b,∗ , M. Schürmann a , C. Westphal a b
a Universität Dortmund, Lehrstuhl für Experimentelle Physik I, Otto-Hahn-Str. 4, 44221 Dortmund, Germany Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany
Available online 19 March 2004
Abstract The local environment of Si at the interface between a thermally grown SiO2 film and Si(1 0 0) was studied by angle-scanned photoelectron spectroscopy and diffraction. Si 2p core-level spectra containing chemically shifted components were recorded. These components were deconvoluted by least squares fitting and assigned to different Si oxidation states. The angular dependence of the photoelectron intensity was obtained from the least squares fit results. A simple statistical model was developed to describe the population and depth distribution of the different suboxide species. Using a simple electron attenuation scheme we can simulate the photoemission polar angle dependence of the various Si oxidation states within the model. The fitting of these model curves to the experimental data results in parameters which indicate a Si–O–Si bridge-bonded interface structure. © 2004 Elsevier B.V. All rights reserved. Keywords: Angle-scanned photoelectron spectroscopy; Photoelectron diffraction; Chemical shift; Silicon oxide
1. Introduction The interface between silicon oxide and silicon plays a crucial role in modern semiconductor technology [1,2]. Due to the advancing miniaturization of semiconductor devices the atomic structure at the interface becomes increasingly important. The experimental access to the interface is limited since the interface is buried below the surface and due to the loss of long range order of the amorphous silicon oxide. Also, a large lattice mismatch between Si and SiO2 causes structural stress. In order to determine the structure, the experimental technique has to be sensitive to the local environment of different atoms present in various structures at the interface. A well suited experimental tool to investigate the structure of the SiO2 /Si interface is high-resolution core-level photoemission spectroscopy. Si 2p photoemission spectra (Fig. 1) show chemically shifted components derived from individual oxidation states (Si0 , Si1+ , Si2+ , Si3+ , Si4+ ) [3,4]. Due to the inelastic scattering of the photoelectrons, the Six+ 2p intensity depends on the population and depth ∗ Corresponding author. Tel.: +49-231-755-3511; fax: +49-231-755-3657. E-mail address: [email protected] (S. Dreiner).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.02.024
distribution of the Six+ atoms in the surface. Polar-angle and oxidation-state resolved photoemission investigations of the SiO2 /Si(1 1 1) system [5,6] established the statistical cross-linking model. The intensity of the photoemission current as function of angle and/or kinetic energy depends on the local environment of the emitting atom [7]. This dependence is caused by final-state diffraction effects of the photoelectron wave. Photoelectron diffraction (PD) is a well established technique for the determination of surface or interface structures [7]. Structural information is obtained by comparison of the experimental data with simulation calculations. An advantage of photoelectron diffraction compared to many other surface sensitive analytic methods is the high sensitivity to the local arrangement of nearest neighbor atoms within the escape depth of the electrons. A further advantage is that no long-range order is needed. In this Article we report on an investigation of the SiO2 /Si(1 0 0) interface structure using photoelectron spectroscopy and diffraction. Several various interface structure models were proposed, ranging from a chemically graded interface with the suboxides distributed over a range of ∼20 Å [8] to an interface consisting of a single Si2+ layer [9]. Similar to the SiO2 /Si(1 1 1) system the polar-angle dependences of all Si 2p oxidation state intensities contain
80
S. Dreiner et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84
information about the population of each suboxide species at the interface. In a previous investigation Oh et al. [10] reported on the polar-angle dependence of the Si 2p oxidation state intensities proposing a graded interface consisting of three layers. In this Report we show that the photoemission polar-angle dependence of the Si suboxides can be explained by a simple statistical model for the atomic populations and depth distributions of the Six+ .
2. Experiment
Fig. 1. Si 2p core level spectra recorded with a photon energy of hν = 180 eV for two different silicon oxide layers on Si(1 0 0) at Θ = 60◦ . The data points are denoted by symbols, the result of least squares fitting is shown as a full line. Also, the decomposition into the bulk component and its chemically shifted components due to the oxidation are shown.
The experiment was performed in a -metal UHV chamber equipped with a hemispherical electron analyzer. Before preparation, the sample holder and the sample were thoroughly degassed at a temperature of 700–750 ◦ C. With the hot sample, the base pressure was at 4 × 10−10 mbar after this procedure. A clean Si sample was obtained by heating the sample to 1050 ◦ C for 2 min followed by a slow temperature decrease to room temperature. Thin SiO2 films were grown in-situ by thermal oxidation, the oxygen pressure was kept at 5 × 10−6 mbar (1.2 × 10−7 mbar) for 10 min equivalent to 3000 L (72 L) while the crystal was at a temperature of 650 ◦ C (530 ◦ C). The electron energy resolution was about 50 meV and the photon energy resolution at a photon energy of 180 eV was set to 90 meV. At a fixed polar angle, photoemission spectra were recorded at the BESSY II U-41 PGM beamline over 360◦ azimuth range with an azimuth angle increment of Φ = 2◦ . Subsequently, a new polar angle was set with an increment of Θ = 2◦ and a new azimuth-scan was recorded. This was repeated until the full polar and azimuth range were covered (0◦ < Θ < 84◦ , 0◦ < Φ < 360◦ ).
(a) T
SiO2
t, R3 t, R2 t, R1
uppermost layer middle layer bottom layer Si
(b) Probabilities (each bond to O( ) is twice as likely as a bond to Si( )):
Si0
Si1+
Si2+
Si2+
Si3+
uppermost layer (bonds to the layer above are bonds to O): p= 1/9
Si4+
4/9
4/9
middle layer: p = 1/81
4/81
4/81
16/81
4/81
4/81
16/81
16/81
16/81
bottom layer: (bonds to the layer below are bonds to Si): p = 1/9
4/9
4/9
Fig. 2. Three layer interface model (a) with all possible local bonding configurations and their probabilities (b).
S. Dreiner et al. / Journal of Electron Spectroscopy and Related Phenomena 137–140 (2004) 79–84 4.5
I(Si
x+
0
)/I(Si )
4.0
Si
3.5
Si
3.0
Si Si
1+ 2+ 3+ 4+
2.5 2.0 1.5 1.0 0.5 0.0 0˚
10˚
20˚
30˚
40˚
50˚
60˚
70˚
80˚
polar angle Θ
Fig. 3. Intensity ratios of Si1+ , Si2+ , Si3+ , and Si4+ components normalized to the bulk component as a function of polar emission angle for the 3000 L film. The symbols represent data points, and the solid lines are obtained fits using the model displayed in Fig. 2. The details are described in the text.
3. Results and discussion Fig. 1 shows typical photoemission spectra of both oxidized surfaces after the secondary background has been subtracted. The line-shape consists of seven resolved components, which correspond to the electron signals of Si0 (B, α, β), Si1+ , Si2+ , Si3+ , and Si4+ . The Si0 -signal was composed of the bulk signal (B) and two extra components (α, β). These components are assumed to be due to strained interfacial Si without any Si–O bonds [10]. Each measured spectrum was decomposed by a least squares fitting into seven components, each of which consisting of a pair of spin-orbit split Gaussian peaks. All peak positions (energy shifts: Si␣ = −0.22 eV, Si = 0.34 eV, Si1+ = 0.95 eV, Si2+ = 1.78 eV, Si3+ = 2.60 eV, Si4+ = 3.72 eV) agree well within a few percent to previously published results [10]. For the Si signal we obtain a binding energy shift of 0.34 eV in comparison to 0.2 eV by Oh et al. [10]. In our model of the SiO2 /Si(1 0 0) system, the interface consists of three layers (Fig. 2a). The uppermost layer is
81
connected with the SiO2 film and the bottom layer is connected with the silicon crystal. A silicon atom located in the middle layer may be bond to silicon and oxygen in both directions. In Fig. 2b, all possible bonding configurations of Si atoms at the interface are displayed. In the easiest configuration the silicon atom in the center of the cluster is bonded to silicon neighbors only (Fig. 2b, Si0 -cluster). Each silicon bond can be replaced with an oxygen bond so that all Si oxidation states are possible. Since oxidation of the Si surface is considered to be a relatively random and local process [5], we derive the probability of each configuration from a statistical analysis. Taking into account the symmetry-equivalent configurations and assuming that each bond to oxygen is twice as likely as a bond to silicon, the probabilities (p) of the suboxides are obtained as displayed in Fig. 2. This assumption can be traced back to the fact that the number of O atoms is twice the number of Si atoms in SiO2 . The probabilities of Si in the upper layer are calculated with all bonds to the layer above being bonds to oxygen. In the case of Si in the lower layer all bonds to the layer below are bonds to silicon. Due to the different Si densities of crystalline silicon and SiO2 we allow a change of the Si density in the various interface layers. The Si 2p intensity variation as a function of polar angle of each oxidation component (I 0 , I 1+ , . . . ) can be calculated using a simple electron damping scheme, including the probabilities obtained from our model I 0 = nSi [D3 + ( 19 R1 D +
1 81 R2 )D(1 − D)]C
I 1+ = nSi [( 49 R1 D + I 2+ = I 3+ =
8 81 R2 )D(1 − D)]C 1 nSi [( 49 R1 D2 + 24 81 R2 D + 9 R3 )(1 − D)]C 4 nSi [( 32 81 R2 D + 9 R3 )(1 − D)]C
4 I 4+ = nSi [( 16 81 R2 D + 9 R3 )(1 − D)]C + nSiO2 (1 − C)
with
−t D = exp λ cos θ −T C = exp λ cos θ
Fig. 4. Side view of the bridge-bond interface model that halves the number of dangling bonds of the silicon layer (Si: grey circles, O: black circles).
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Fig. 5. Experimental Si 2p diffraction patterns of the Six+ obtained for a photon energy of 180 eV. The left column displays the diffraction patterns of the 72 L and the right column these of the 3000 L silicon oxide film.
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where θ denotes the internal angle which is related by the simple inner potential refraction rule to the observed external angle [5], nSi is the surface atom density of pure Si (nSi = 6.8×1014 cm−2 ) and t = 1.37 Å is the thickness of a silicon layer. We assume a uniform mean free path of λ = 4.2 Å for Si according to the TPP2 formula [11]. The factor Rx describes the change of the Si density in each interface layer x. The only free parameters within this model are the Rx factors, the SiO2 film thickness T , and the inner potential. We used this model to simulate the experimental intensity ratios (I x+ /I 0 ) between each suboxide and the Si0 intensity as a function of the polar angle, where I 0 denotes the total intensity of silicon which is not directly bonded to oxygen (I 0 = I B + I ␣ + I  ). In order to eliminate photoelectron diffraction effects in the experimental data at a given polar angle all spectra at this polar angle are added up. Fig. 3 shows an excellent agreement between the experimental intensity ratios (symbols) with the simulated ratios for the 3000 L film. In contrast to the results of Oh et al. [10] our experimental data of the Si1+ and Si2+ signals show individual dependence on the polar angle. As the polar angle increases, the I 2+ /I 0 ratio exhibits a steeper increase than the I 1+ /I 0 ratio. This is also obtained by the intensity ratios of the simulation. Within the model we expect more Si2+ atoms than Si1+ atoms in the second and third interface layer because of statistical reasons. In agreement with Oh et al., the normalized I 3+ intensity exhibits a steeper increase than the I 2+ and the I 1+ as a function of the polar angle. The fitting parameters for the simulated curves are R1 = 0.77 ± 0.05, R2 = 0.45 ± 0.08, R3 = 0.93 ± 0.05, and T = 1.37±0.01 Å. The decrease of the Si density in the second interface layer to a value of R2 ≈ 0.5 can be explained by the bridge-bonded interface structure which was found by the theoretical investigations of Tu and Tersoff [9]. The silicon crystal terminating Si–O–Si brigde bonds are consistently proposed by various structure models of the SiO2 /Si interface [9,12–14]. The bridge-bonds eliminate half of the bonds from the Si side, correcting the mismatch between the bond densities in the two different materials (cf. Fig. 4). Fig. 5 displays the experimental diffraction patterns of the Si atoms in various oxidation states for both SiO2 /Si films. The patterns display the anisotropy function A(Θ, Φ) = [I(Θ, Φ) − I0 (Θ)]/I0 (Θ) in a strictly linear grey scale, where I(Θ, Φ) denotes the photoelectron intensity obtained by the above-mentioned fitting procedure and I0 (Θ) denotes the mean intensity for a given polar angle. The maximum anisotropy Amax calculated as Amax = max(A(Θ, Φ)) − min(A(Θ, Φ)) is indicated within each diffraction pattern. The diffraction pattern of the bulk signal (SiB ) does not vary considerably depending on the layer thickness. A very similar diffraction pattern was obtained for the clean Si(1 0 0)-2 × 1 and the Si(1 0 0):H-2 × 1 surface [15]. The suboxide signals of Si1+ , Si2+ and Si3+ show a similar angular dependence. The diffraction patterns consist of elongated maxima in Φ = 45◦ , 135◦ , 225◦ , 315◦ azimuth direction. The change of the Si3+ diffraction pat-
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tern depending on the layer thickness indicates that each maximum consists of several maxima. These maxima affiliate with each other if the layer thickness increases. The Si4+ signal displays a different diffraction pattern compared to the previous discussed ones . The main maxima of the Si4+ diffraction pattern are observed in Φ = 0◦ , 90◦ , 180◦ , 270◦ azimuth direction. In Fig. 5, the anisotropy of the Si0 diffraction pattern of the thicker film is reduced compared to the film prepared at 72 L. However, the suboxide diffraction patterns show a increased anisotropy compared to the thinner film. This indicates that a locally ordered interface structure is to be expected rather for the thicker than for the thinner film. The perfect interface proposed by Tu and Tersoff [9] consists of Si2+ and Si4+ atoms in very different local atomic environments. The Si2+ and Si4+ signals show very different diffraction patterns. A comparison of the experimental data with multiple scattering calculations will show if this diffraction pattern can be explained within the brigde-bonded interface model as well.
4. Conclusions In summary, we investigated the local atomic environment of Si at the interface between a thermally grown SiO2 film and Si(1 0 0). We utilized the chemically shifted Si 2p core-level photoelectrons as a local probe at the interface. The photoemission polar angle dependence of the various Six+ signals contains information about the depth distribution and population of each oxidation state. We developed a statistical model for the Six+ depth distribution and population over an interface range of three layers. This model and a simple electron attenuation scheme were used to obtain the simulated photoemission polar angle dependence of each Six+ . The model curves can successfully and quantitatively describe the experimental data of the Si/SiO2 interface. The free parameters to fit these curves to the experimental data are the silicon densities in the various interface layers. The fitting procedure results in a significant reduction of the Si density in the second interface layer which can be explained by a Si–O–Si bridge-bond interface model obtained by theoretical investigations. The Six+ photoelectron diffraction patterns contain information about the structural environment of Si in the various oxidation states. The comparison of the diffraction patterns with multiple scattering calculations is in progress.
Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (No. We 1649/3) and by the German Federal Ministry of Education, Science, Research and Technology (BMBF) under contract number 05 SE8PMB 9. We thank the BESSY-team (especially C. Jung, M. Mast and W. Braun) for technical support during the measurements.
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