- Email: [email protected]
Infrared properties of ultrathin oxides on Si(1 0 0)
Microelectronic Engineering 80 (2005) 420–423 www.elsevier.com/locate/mee
Infrared properties of ultrathin oxides on Si(100) Feliciano Giustino and Alfredo Pasquarello Ecole Polytechnique Fédérale de Lausanne (EPFL), Institute of Theoretical Physics, CH-1015 Lausanne, Switzerland, Institut Romand de Recherche Numérique en Physique des Materiaux (IRRMA), CH-1015 Lausanne, Switzerland Tel: 41-21-6936563 email: [email protected]
Abstract We study the infrared absorption spectra of ultrathin SiO2 films on Si(100) using a first-principles approach, and adopting a model Si(100)-SiO2 interface with a realistic transition structure. We calculate both the transverse-optical and the longitudinal-optical infrared absorption spectra across the interface, and show that the red shift of the high-frequency peaks observed experimentally with decreasing oxide thickness originates from the softer vibrational frequencies of the substoichiometric interfacial layer. From the calculated infrared properties, we are able to assess the effect of the frequency softening on the corresponding static permittivity. Keywords: Si/SiO2 interface, infrared spectra, dielectric permittivity
1. Introduction While transition metal oxides are currently under consideration for scaling the equivalent oxide thickness in MOS devices, a thin SiO2 layer often forms at the channel interface during the deposition process [1]. Understanding the dielectric and vibrational properties of this interlayer is crucial for assessing its effects on both the gate capacitance and the channel mobility. Recent investigations of the transverse-optical (TO) and longitudinal-optical (LO) infrared absorption spectra of ultrathin oxides on Si(100) recorded a red shift of the asymmetric oxygen stretching mode in Si-O-Si intertetrahedral bridges with decreasing oxide thickness [2, 3]. This
behavior has been alternatively ascribed to the compressive strain of the interfacial oxide, to void incorporation, or to the presence of substoichiometric silica. In this work, we calculate the TO and LO infrared absorption spectra at the Si(100)-SiO2 interface from first principles. Our calculations allow us to assign unambiguously the origin of the red shift to the softening of the Si-O stretching frequency within the substoichiometric interfacial layer. The corresponding mode softening at low frequency is shown to be responsible for an enhancement of the static permittivity of the interfacial layer with respect to bulk SiO2. This effect, together with the larger electronic permittivity of the interfacial layer [4], leads to an equivalent oxide thickness which
0167-9317/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2005.04.025
F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
underestimates the physical thickness by about 0.20.3 nm. 2. Theoretical methods To model the interfacial oxide layer, we adopted a computational cell of size ~ 11×11×30 Å3 containing 9 Si(100) planes and ~ 17 Å of amorphous oxide. The transition from the bulk silicon region to the bulk oxide region takes place through a substoichiometric layer with a thickness of ~ 6 Å. The interfacial transition region has been purposely designed in order to match a large variety of experimental atomic-scale probes such as for instance X-ray photoemission and Rutherford backscattering spectroscopies [5]. The electronic structure of our model was described through the local density approximation to density functional theory. We accounted for the valence electrons through normconserving (Si) and ultrasoft (O) pseudopotentials, and expanded the wave functions and the charge density on plane-wave basis sets with kinetic energy cutoffs of 24 and 200 Ry, respectively [6]. We sampled the Brillouin zone of the supercell at the ī point. The dynamical matrix which defines the vibrational properties was calculated through finite differences of the atomic forces corresponding to atomic displacements of ±0.05 Å. The dynamical charges required for the infrared intensities were calculated by taking finite differences of the atomic forces with respect to externally applied electric fields of ±0.05 VÅ-1 [7]. The calculated spectra were broadened through Gaussian functions with a standard deviation of 40 cm-1 in order to overcome the limited statistics. The spatial decomposition of the transverse and longitudinal absorption intensities was performed by determining the dielectric functions of atomically thin layers parallel to the interface. This was achieved through the evaluation of localized infrared dipoles induced by an external electric field [8]. The formalism adopted here constitutes a generalization of the methods developed in Ref. [9] for the static and high-frequency permittivities to the whole infrared spectral range. 3. Red shift of the TO and LO peaks In Fig. 1 we show the change of the calculated infrared absorption spectra across our model of the
421
Si(100)-SiO2 interface. Far from the Si substrate (curves 8 in Fig. 1), the structural and electronic properties of the oxide correspond to bulk vitreous silica. In this region, we found TO peaks at 457, 810 and 1097 cm-1 and LO peaks at 529, 820 and 1260 cm-1, in excellent agreement with the corresponding experimental values of 457, 810 and 1076 cm-1 for the TO spectrum, and of 507, 820 and 1256 cm-1 for the LO spectrum, respectively [10]. At a distance of 5-7 Å from the substrate (curves 6 and 7 in Fig. 1), the high-frequency shoulder at 1260 cm-1 in the TO spectrum disappears, and a shoulder develops at 1077 cm-1 in the LO spectrum. The low-frequency peaks are found to be red-shifted with respect to the bulk oxide by about 30 cm-1 in both the LO and TO spectra. In this region, the oxide is slightly oxygendeficient and Si+3 species are found. Even closer to the substrate (curves 3 to 5 in Fig. 1), the TO spectrum develops a shoulder, and then a peak, at 939 cm-1, while the shoulder at 1077 cm-1 in the LO spectrum becomes the principal peak.
Fig.1 Local infrared absorption spectra calculated across the adopted model structure of the Si(100)-SiO2 interface: transverse (left) and longitudinal (right) spectrum. The central panel shows a ball-and-stick representation of the adopted model interface. Dashed lines are guides to the eye and indicate the red shift of the high-frequency peaks in the LO and TO spectra.
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F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
The low-frequency part of the TO spectrum becomes quite broad, with the lowest frequency satellite at ∼ 230 cm-1. In this region the Si atoms are onefold and twofold oxidized. The largest calculated red shifts of the absorption peaks are 158 cm-1 for the high-frequency region of the TO spectrum, and 183 cm-1 for the corresponding peak in the LO spectrum. Since these values refer to the local absorption intensities, they cannot be compared directly to experiments on the Si-SiO2 interface. Indeed, the latter probe the average behavior of an oxide characterized by a strong chemical grading. Nonetheless, the calculated data can be confronted with experiments on bulk sub-stoichiometric silica (SiOx). While to our knowledge there are no experimental data available for the LO spectrum, several investigations on the high-frequency region of the TO spectrum reported peak frequencies within the range 940-987 cm-1 for SiOx with low O content [11, 12, 13]. In addition, a recent study of ultrathin SiO2 layers on Si(100) recorded a shoulder at 980 cm-1, and proposed the assignment of this feature to a substoichiometric interfacial layer [2]. Our calculated TO peak at 939 cm-1 is in agreement with experimental data on sub-stoichiometric silica with low oxygen content, and supports the latter assignment of the shoulder at 980 cm-1 to the suboxide layer. Hence, our results indicate that the origin of TO and LO red shifts in ultrathin oxide films on Si(100) resides in the softer vibrational modes of the substoichiometric interfacial layer.
(∆İions)ox ∼2.0. In Fig. 2 we analyze the contribution of each eigenmode to the static permittivity by showing, as a function of the frequency Ȧ, the ∆İions obtained by summing only over the modes with frequency Ȧn > Ȧ in Eq. (1). The mode contribution to the static permittivity has been evaluated separately for the bulk oxide and for the interfacial layer in our model Si(100)-SiO2 interface, following the formalism introduced in Ref. [8]. For comparison we also report in Fig. 2 the corresponding imaginary dielectric functions. The high-frequency modes are clearly not involved in the enhanced ionic screening of the suboxide, the extra screening (from 2.0 to 2.6) arising from a suboxide peak around 230 cm-1 (Fig. 2,
4. Enhanced permittivity of the interfacial layer The ionic contribution to the dielectric permittivity ∆İions scales with the inverse of the vibrational eigenfrequencies squared:
∆İions ∼ ¦n Sn2/Ȧn2,
(1)
the sum running over the eigenmodes of frequency
Ȧn and strength Sn2. Therefore, the red shift of the infrared spectra of the interfacial oxide could imply an enhanced ionic contribution to the permittivity close to the Si substrate. Indeed, our calculations indicate that the ionic contribution to the permittivity of the interfacial layer amounts to (∆İions)inter ∼2.6, while the corresponding value for the bulk oxide is
Fig.2 Upper panel: vibrational mode contribution to the static permittivity, evaluated within the interfacial layer (solid) and the bulk oxide (dashed) of our model Si(100)SiO2 interface. Lower panel: imaginary part of the dielectric function vs. frequency, for the interfacial layer (solid) and the bulk oxide (dashed). The shaded region indicates the contribution of Si+2O2 structural units, giving rise to the peak at ∼ 230 cm-1. The vertical line indicates that, in proximity of this resonance, the mode contribution to the static permittivity of the suboxide starts exceeding the corresponding one of bulk SiO2.
F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
shaded area). Indeed, when the modes between 220 and 240 cm-1 are forced to be silent in Eq. (1), the suboxide ionic permittivity drops to the value calculated for the bulk oxide. By inspecting the atomic displacements corresponding to these modes within the suboxide, we found that the main contribution to the extra screening arises from Si+2 atoms together with their O nearest neighbors. The large polarizability of the Si+2O2 structural units is a consequence of both the large dynamical charges of Si+2 atoms [8] and the small associated vibrational frequency of 230 cm-1 (to be compared to the corresponding modes of bulk SiO2 around 450 cm-1). The enhanced ionic screening, combined with a larger electronic polarizability of the Si-Si bonds in the interfacial layer [4], leads to an enhanced static permittivity of ∼ 6-7, as compared to the bulk silica value of ∼ 4. As a result, the equivalent oxide thickness of this region is by 0.2-0.3 nm smaller than the corresponding physical thickness, with a limited yet beneficial effect on the capacitance of high-k gate stacks incorporating an interfacial oxide. 5. Conclusions In conclusion, we calculated the infrared absorption spectra at the Si(100)-SiO2 interface within a first-principles approach. The frequencies of the main peaks corresponding to the stoichiometric oxide region are in excellent agreement with experiment. Similarly, the calculated peaks within the interfacial layer agree with experiments on substoichiometric oxides and on Si(100)-SiO2 interfaces with ultrathin oxides. Our calculations allowed us to assign the origin of the TO and LO high-frequency red shift with decreasing oxide thickness to the softer vibrational modes of the interfacial suboxide layer. In addition, we found that the interfacial layer carries an enhanced ionic contribution to the static permittivity, arising from vibrational modes with frequency around 230 cm-1.
Acknowledgements The calculations were performed on the JANUS and the PLEIADES platforms of the Ecole Polytechnique Fédérale de Lausanne.
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References [1] D. A. Muller and G. D. Wilk, Atomic scale measurements of the interfacial electronic structure and chemistry of zirconium silicate gate dielectrics, Appl. Phys. Lett. 79 (2001) 4915-4197. [2] K.T. Queeney, M.K. Weldon, J.P. Chang, Y.J. Chabal, A.B. Gurevich, J. Sapjeta and R. L. Opila, Infrared spectroscopic analysis of the Si/SiO2 interface structure of thermally oxidized silicon, J. Appl. Phys. 87 (2000) 1322-1330. [3] R. A. B. Devine, Structural nature of the Si/SiO2 interface through infrared spectroscopy, Appl. Phys. Lett. 68 (1996) 3108-3110. [4] F. Giustino, P. Umari and A. Pasquarello, Dielectric discontinuity at interfaces in the atomic-scale limit: Permittivity of ultrathin oxide films on silicon, Phys. Rev. Lett. 91 (2003) 267601. [5] A. Bongiorno, A. Pasquarello, M. S. Hybertsen and L. C. Feldman, Transition structure at the Si(100)-SiO2 interface, Phys. Rev. Lett. 90 (2003) 186101. [6] A. Pasquarello, K. Laasonen, R. Car, C. Lee and D. Vanderbilt, Ab initio molecular dynamics for delectron systems: Liquid copper at 1500 K, Phys. Rev. Lett. 69 (1992) 1982-1985; K. Laasonen, A. Pasquarello, R. Car, C. Lee and D. Vanderbilt, CarParrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B 47 (1993) 10142-10153. [7] P. Umari and A. Pasquarello, Ab initio molecular dynamics in a finite homogeneous electric field, Phys. Rev. Lett. 89 (2002) 157602. [8] F. Giustino, Infrared properties of the Si-SiO2 interface from first principles, Ph.D. Thesis, Ecole Polytechnique Fédérale de Lausanne, 2005. [9] F. Giustino and A. Pasquarello, Theory of atomicscale dielectric permittivity at insulator interfaces, Phys. Rev. B 71 (2005) 144104. [10] C. T. Kirk, Quantitative analysis of the effect of disorder-induced mode coupling on infrared absorption in silica, Phys. Rev. B 38 (1998) 12551273. [11] P. G. Pai, S. S. Chao, Y. Takagi and G. Lucovsky, Infrared spectroscopic study of SiOx films produced by plasma enhanced chemical vapor deposition, J. Vac. Sci. Technol. A 4 (1986) 689-694. [12] M. Nakamura, Y. Mochizuki, K. Usami, Y. Itoh and T. Nozaki, Infrared absorption spectra and composition of evaporated silicon oxides (SiOx), Solid State Commun. 50 (1984) 1079. [13] L. Schumann, A. Lehmann, H. Sobotta, V. Riede, U. Teschner and K. Hübner, Infrared studies of reactively sputtered SiOx films in the composition range 0.2 x 1.9, Phys. Status Solidi B 110 (1982) K69.
Infrared properties of ultrathin oxides on Si(100) Feliciano Giustino and Alfredo Pasquarello Ecole Polytechnique Fédérale de Lausanne (EPFL), Institute of Theoretical Physics, CH-1015 Lausanne, Switzerland, Institut Romand de Recherche Numérique en Physique des Materiaux (IRRMA), CH-1015 Lausanne, Switzerland Tel: 41-21-6936563 email: [email protected]
Abstract We study the infrared absorption spectra of ultrathin SiO2 films on Si(100) using a first-principles approach, and adopting a model Si(100)-SiO2 interface with a realistic transition structure. We calculate both the transverse-optical and the longitudinal-optical infrared absorption spectra across the interface, and show that the red shift of the high-frequency peaks observed experimentally with decreasing oxide thickness originates from the softer vibrational frequencies of the substoichiometric interfacial layer. From the calculated infrared properties, we are able to assess the effect of the frequency softening on the corresponding static permittivity. Keywords: Si/SiO2 interface, infrared spectra, dielectric permittivity
1. Introduction While transition metal oxides are currently under consideration for scaling the equivalent oxide thickness in MOS devices, a thin SiO2 layer often forms at the channel interface during the deposition process [1]. Understanding the dielectric and vibrational properties of this interlayer is crucial for assessing its effects on both the gate capacitance and the channel mobility. Recent investigations of the transverse-optical (TO) and longitudinal-optical (LO) infrared absorption spectra of ultrathin oxides on Si(100) recorded a red shift of the asymmetric oxygen stretching mode in Si-O-Si intertetrahedral bridges with decreasing oxide thickness [2, 3]. This
behavior has been alternatively ascribed to the compressive strain of the interfacial oxide, to void incorporation, or to the presence of substoichiometric silica. In this work, we calculate the TO and LO infrared absorption spectra at the Si(100)-SiO2 interface from first principles. Our calculations allow us to assign unambiguously the origin of the red shift to the softening of the Si-O stretching frequency within the substoichiometric interfacial layer. The corresponding mode softening at low frequency is shown to be responsible for an enhancement of the static permittivity of the interfacial layer with respect to bulk SiO2. This effect, together with the larger electronic permittivity of the interfacial layer [4], leads to an equivalent oxide thickness which
0167-9317/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2005.04.025
F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
underestimates the physical thickness by about 0.20.3 nm. 2. Theoretical methods To model the interfacial oxide layer, we adopted a computational cell of size ~ 11×11×30 Å3 containing 9 Si(100) planes and ~ 17 Å of amorphous oxide. The transition from the bulk silicon region to the bulk oxide region takes place through a substoichiometric layer with a thickness of ~ 6 Å. The interfacial transition region has been purposely designed in order to match a large variety of experimental atomic-scale probes such as for instance X-ray photoemission and Rutherford backscattering spectroscopies [5]. The electronic structure of our model was described through the local density approximation to density functional theory. We accounted for the valence electrons through normconserving (Si) and ultrasoft (O) pseudopotentials, and expanded the wave functions and the charge density on plane-wave basis sets with kinetic energy cutoffs of 24 and 200 Ry, respectively [6]. We sampled the Brillouin zone of the supercell at the ī point. The dynamical matrix which defines the vibrational properties was calculated through finite differences of the atomic forces corresponding to atomic displacements of ±0.05 Å. The dynamical charges required for the infrared intensities were calculated by taking finite differences of the atomic forces with respect to externally applied electric fields of ±0.05 VÅ-1 [7]. The calculated spectra were broadened through Gaussian functions with a standard deviation of 40 cm-1 in order to overcome the limited statistics. The spatial decomposition of the transverse and longitudinal absorption intensities was performed by determining the dielectric functions of atomically thin layers parallel to the interface. This was achieved through the evaluation of localized infrared dipoles induced by an external electric field [8]. The formalism adopted here constitutes a generalization of the methods developed in Ref. [9] for the static and high-frequency permittivities to the whole infrared spectral range. 3. Red shift of the TO and LO peaks In Fig. 1 we show the change of the calculated infrared absorption spectra across our model of the
421
Si(100)-SiO2 interface. Far from the Si substrate (curves 8 in Fig. 1), the structural and electronic properties of the oxide correspond to bulk vitreous silica. In this region, we found TO peaks at 457, 810 and 1097 cm-1 and LO peaks at 529, 820 and 1260 cm-1, in excellent agreement with the corresponding experimental values of 457, 810 and 1076 cm-1 for the TO spectrum, and of 507, 820 and 1256 cm-1 for the LO spectrum, respectively [10]. At a distance of 5-7 Å from the substrate (curves 6 and 7 in Fig. 1), the high-frequency shoulder at 1260 cm-1 in the TO spectrum disappears, and a shoulder develops at 1077 cm-1 in the LO spectrum. The low-frequency peaks are found to be red-shifted with respect to the bulk oxide by about 30 cm-1 in both the LO and TO spectra. In this region, the oxide is slightly oxygendeficient and Si+3 species are found. Even closer to the substrate (curves 3 to 5 in Fig. 1), the TO spectrum develops a shoulder, and then a peak, at 939 cm-1, while the shoulder at 1077 cm-1 in the LO spectrum becomes the principal peak.
Fig.1 Local infrared absorption spectra calculated across the adopted model structure of the Si(100)-SiO2 interface: transverse (left) and longitudinal (right) spectrum. The central panel shows a ball-and-stick representation of the adopted model interface. Dashed lines are guides to the eye and indicate the red shift of the high-frequency peaks in the LO and TO spectra.
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F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
The low-frequency part of the TO spectrum becomes quite broad, with the lowest frequency satellite at ∼ 230 cm-1. In this region the Si atoms are onefold and twofold oxidized. The largest calculated red shifts of the absorption peaks are 158 cm-1 for the high-frequency region of the TO spectrum, and 183 cm-1 for the corresponding peak in the LO spectrum. Since these values refer to the local absorption intensities, they cannot be compared directly to experiments on the Si-SiO2 interface. Indeed, the latter probe the average behavior of an oxide characterized by a strong chemical grading. Nonetheless, the calculated data can be confronted with experiments on bulk sub-stoichiometric silica (SiOx). While to our knowledge there are no experimental data available for the LO spectrum, several investigations on the high-frequency region of the TO spectrum reported peak frequencies within the range 940-987 cm-1 for SiOx with low O content [11, 12, 13]. In addition, a recent study of ultrathin SiO2 layers on Si(100) recorded a shoulder at 980 cm-1, and proposed the assignment of this feature to a substoichiometric interfacial layer [2]. Our calculated TO peak at 939 cm-1 is in agreement with experimental data on sub-stoichiometric silica with low oxygen content, and supports the latter assignment of the shoulder at 980 cm-1 to the suboxide layer. Hence, our results indicate that the origin of TO and LO red shifts in ultrathin oxide films on Si(100) resides in the softer vibrational modes of the substoichiometric interfacial layer.
(∆İions)ox ∼2.0. In Fig. 2 we analyze the contribution of each eigenmode to the static permittivity by showing, as a function of the frequency Ȧ, the ∆İions obtained by summing only over the modes with frequency Ȧn > Ȧ in Eq. (1). The mode contribution to the static permittivity has been evaluated separately for the bulk oxide and for the interfacial layer in our model Si(100)-SiO2 interface, following the formalism introduced in Ref. [8]. For comparison we also report in Fig. 2 the corresponding imaginary dielectric functions. The high-frequency modes are clearly not involved in the enhanced ionic screening of the suboxide, the extra screening (from 2.0 to 2.6) arising from a suboxide peak around 230 cm-1 (Fig. 2,
4. Enhanced permittivity of the interfacial layer The ionic contribution to the dielectric permittivity ∆İions scales with the inverse of the vibrational eigenfrequencies squared:
∆İions ∼ ¦n Sn2/Ȧn2,
(1)
the sum running over the eigenmodes of frequency
Ȧn and strength Sn2. Therefore, the red shift of the infrared spectra of the interfacial oxide could imply an enhanced ionic contribution to the permittivity close to the Si substrate. Indeed, our calculations indicate that the ionic contribution to the permittivity of the interfacial layer amounts to (∆İions)inter ∼2.6, while the corresponding value for the bulk oxide is
Fig.2 Upper panel: vibrational mode contribution to the static permittivity, evaluated within the interfacial layer (solid) and the bulk oxide (dashed) of our model Si(100)SiO2 interface. Lower panel: imaginary part of the dielectric function vs. frequency, for the interfacial layer (solid) and the bulk oxide (dashed). The shaded region indicates the contribution of Si+2O2 structural units, giving rise to the peak at ∼ 230 cm-1. The vertical line indicates that, in proximity of this resonance, the mode contribution to the static permittivity of the suboxide starts exceeding the corresponding one of bulk SiO2.
F. Giustino, A. Pasquarello / Microelectronic Engineering 80 (2005) 420–423
shaded area). Indeed, when the modes between 220 and 240 cm-1 are forced to be silent in Eq. (1), the suboxide ionic permittivity drops to the value calculated for the bulk oxide. By inspecting the atomic displacements corresponding to these modes within the suboxide, we found that the main contribution to the extra screening arises from Si+2 atoms together with their O nearest neighbors. The large polarizability of the Si+2O2 structural units is a consequence of both the large dynamical charges of Si+2 atoms [8] and the small associated vibrational frequency of 230 cm-1 (to be compared to the corresponding modes of bulk SiO2 around 450 cm-1). The enhanced ionic screening, combined with a larger electronic polarizability of the Si-Si bonds in the interfacial layer [4], leads to an enhanced static permittivity of ∼ 6-7, as compared to the bulk silica value of ∼ 4. As a result, the equivalent oxide thickness of this region is by 0.2-0.3 nm smaller than the corresponding physical thickness, with a limited yet beneficial effect on the capacitance of high-k gate stacks incorporating an interfacial oxide. 5. Conclusions In conclusion, we calculated the infrared absorption spectra at the Si(100)-SiO2 interface within a first-principles approach. The frequencies of the main peaks corresponding to the stoichiometric oxide region are in excellent agreement with experiment. Similarly, the calculated peaks within the interfacial layer agree with experiments on substoichiometric oxides and on Si(100)-SiO2 interfaces with ultrathin oxides. Our calculations allowed us to assign the origin of the TO and LO high-frequency red shift with decreasing oxide thickness to the softer vibrational modes of the interfacial suboxide layer. In addition, we found that the interfacial layer carries an enhanced ionic contribution to the static permittivity, arising from vibrational modes with frequency around 230 cm-1.
Acknowledgements The calculations were performed on the JANUS and the PLEIADES platforms of the Ecole Polytechnique Fédérale de Lausanne.
423
References [1] D. A. Muller and G. D. Wilk, Atomic scale measurements of the interfacial electronic structure and chemistry of zirconium silicate gate dielectrics, Appl. Phys. Lett. 79 (2001) 4915-4197. [2] K.T. Queeney, M.K. Weldon, J.P. Chang, Y.J. Chabal, A.B. Gurevich, J. Sapjeta and R. L. Opila, Infrared spectroscopic analysis of the Si/SiO2 interface structure of thermally oxidized silicon, J. Appl. Phys. 87 (2000) 1322-1330. [3] R. A. B. Devine, Structural nature of the Si/SiO2 interface through infrared spectroscopy, Appl. Phys. Lett. 68 (1996) 3108-3110. [4] F. Giustino, P. Umari and A. Pasquarello, Dielectric discontinuity at interfaces in the atomic-scale limit: Permittivity of ultrathin oxide films on silicon, Phys. Rev. Lett. 91 (2003) 267601. [5] A. Bongiorno, A. Pasquarello, M. S. Hybertsen and L. C. Feldman, Transition structure at the Si(100)-SiO2 interface, Phys. Rev. Lett. 90 (2003) 186101. [6] A. Pasquarello, K. Laasonen, R. Car, C. Lee and D. Vanderbilt, Ab initio molecular dynamics for delectron systems: Liquid copper at 1500 K, Phys. Rev. Lett. 69 (1992) 1982-1985; K. Laasonen, A. Pasquarello, R. Car, C. Lee and D. Vanderbilt, CarParrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B 47 (1993) 10142-10153. [7] P. Umari and A. Pasquarello, Ab initio molecular dynamics in a finite homogeneous electric field, Phys. Rev. Lett. 89 (2002) 157602. [8] F. Giustino, Infrared properties of the Si-SiO2 interface from first principles, Ph.D. Thesis, Ecole Polytechnique Fédérale de Lausanne, 2005. [9] F. Giustino and A. Pasquarello, Theory of atomicscale dielectric permittivity at insulator interfaces, Phys. Rev. B 71 (2005) 144104. [10] C. T. Kirk, Quantitative analysis of the effect of disorder-induced mode coupling on infrared absorption in silica, Phys. Rev. B 38 (1998) 12551273. [11] P. G. Pai, S. S. Chao, Y. Takagi and G. Lucovsky, Infrared spectroscopic study of SiOx films produced by plasma enhanced chemical vapor deposition, J. Vac. Sci. Technol. A 4 (1986) 689-694. [12] M. Nakamura, Y. Mochizuki, K. Usami, Y. Itoh and T. Nozaki, Infrared absorption spectra and composition of evaporated silicon oxides (SiOx), Solid State Commun. 50 (1984) 1079. [13] L. Schumann, A. Lehmann, H. Sobotta, V. Riede, U. Teschner and K. Hübner, Infrared studies of reactively sputtered SiOx films in the composition range 0.2 x 1.9, Phys. Status Solidi B 110 (1982) K69.