9910
J. Phys. Chem. B 1999, 103, 9910-9914
Temperature and Pressure Dependence of the Oxygen Exchange at the SiO2-Si Interface, O2 T SiO2, during Dry Thermal Oxidation of Silicon T. A° kermark,* J.-J. Ganem, I. Trimaille, I. Vickridge, and S. Rigo UniVersite´ s Paris 6 et 7, Group de Physique des Solides, Tour 23, e´ tage 3, 2, place Jussieu, 75251 Paris Cedex 05, France ReceiVed: June 3, 1999; In Final Form: September 8, 1999
The oxygen exchange reactions can give valuable information concerning the oxidation mechanisms since they can be intermediate reactions. During dry thermal oxidation of silicon there are at least two different oxygen exchange reactions: oxygen exchange between oxygen molecules (O2 T O2, catalyzed by the SiO2) and oxygen exchange between oxygen from the gas phase and the oxygen in SiO2 (O2 T SiO2). The O2 T SiO2 exchange takes place at the surface and more surprisingly also at the SiO2/Si interface. It has been shown that the oxygen exchange rate at the Si/SiO2 interface is at least 25% of the oxygen uptake rate, requiring a movement of oxygen both from the surface to the interface and from the interface to the surface. In this study, we evaluate the oxygen exchange for different pressures and temperatures. The amount exchanged depends marginally on these parameters and can probably be taken as a measure of the thickness of the reacting layer. The chemistry of this reacting layer plays a pronounced role in the oxidation of silicon, since it sets one of the two boundary conditions for diffusion.
Introduction The oxidation process of metals and silicon in pure O2 proceeds by many intermediate reactions. The intermediate reactions usually discussed are adsorption and dissociation of O2 on the oxide surface, charge transfer between oxygen and the metal/silicon, and incorporation of oxygen ions and metal/ silicon ions into the oxide. Some of these intermediate reactions are steps for two of the oxygen exchange reactions, namely the oxygen exchanges between two oxygen molecules (O2 T O2) catalyzed by the oxide surface and between the oxide and molecular oxygen (MexOy T O2 and SiO2 T O2). Adsorption of oxygen is an intermediate reaction of the two exchanges and the dissociation of oxygen1-4 can be an intermediate reaction. The exchange SiO2 T O2 (MexOy T O2) requires that there is a charge transfer and incorporation of oxygen into the oxygen network, as well as the reverse reaction. The studying of oxygen exchange reactions during oxidation can thereby reveal previously unnoticed reaction pathways.5 The dominating experimental procedure to study oxygen exchange during oxidation is two-step oxidation. In a typical experiment the substrate is sequentially oxidized in 16O2 and 18O , and the resulting quantities and isotopic concentration 2 depth profiles are measured by nuclear reaction analysis (NRA), narrow nuclear resonance profiling (NRP), secondary ion mass spectrometry (SIMS), or medium energy ion scattering (MEIS). Such studies have been extensively applied to the oxidation of silicon, showing that oxide growth, except in the initial stage, takes place via interstitial transport of oxygen from the gas through the growing oxide without reaction with the oxide network.6 These studies have also shown a SiO2 T O2 exchange taking place with the surface of the SiO2,7 and more recently at the SiO2-Si interface.4,8-10 The oxygen exchange at the Si* Corresponding author. Current address: Materials Physics-Physics 3, Teknikringen 14, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
SiO2 interface requires transport of oxygen away from the interface in contradiction with the assumption that oxygen is trapped once it reaches the Si-SiO2 interface.11 The interface oxygen exchange occurs only within a thin interfacial reactive layer and a considerable amount of the oxygen reaching this interfacial layer is transported out again through the oxide and is lost to the gas phase. In this paper, we investigate to what extent the total pressure and temperature affect the oxygen exchange at the Si-SiO2. Experimental Section The oxidation procedure is schematically described in Table 1 and is either a sequential three- or four-step oxidation in pure 16O and 18O . The Si samples were 250-300 µm thick polished 2 2 phosphate-doped (100) Czochralski-silicon wafers with a resistance of 3-6 Ω cm, and they were dipped in HF to remove the native oxide before they were introduced into the vacuum furnace system.7 This cleaning procedure results in a passivated Si surface, with an approximately 2 nm thick layer of water and hydrocarbons (hydrogen contaminates due to the air exposure). It is well-known that the oxidation kinetics of silicon are extremely sensitive to water and even ppm of water increase the oxidation rate considerably.6,12 At elevated temperatures, the hydrogen contaminates will desorb and react with oxygen to form water and carbon dioxide.5 To avoid this, the hydrogen contaminates were removed by outgassing for 10 min at 600 °C in the vacuum furnace before the samples were oxidized. The vacuum pressure was below 10-7 mbar before the outgassing started, and the pressure increase was less than 10-8 mbar when outgassing ended. This outgassing procedure was also used before the third oxidation step for samples 001-024 and before the fourth oxidation step for samples 030-044, since they were exposed to air in order to analyze them with NRA. The outgassing did not give any measurable effect to the measured depth profiles.
10.1021/jp991788e CCC: $18.00 © 1999 American Chemical Society Published on Web 10/21/1999
Oxygen Exchange at the SiO2-Si Interface
J. Phys. Chem. B, Vol. 103, No. 45, 1999 9911
TABLE 1: Experimental Conditions and Analysis Sequence for the Samplea sample
temp. [°C] II step
pressure [mbar] II step
time [h] II step
001 010 011 012 013 020 021 022 023 024 030 031 032 033 040 041 042
1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1000 900 800 800 1100 1100 1100
210 210 210 210 210 210 210 210 210 210 210 210 210 210 20 2 2
1 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 2/3 2 3 3 2 10 10
outg. yes yes yes yes yes yes yes yes yes yes no no no no no no no
time [h] III step 6 1/4 1/2 1 6 1 1 1 1 25/60 0.75 1.5 25/60 1 10 1
outg.
time [h] IV step
yes yes yes yes yes yes yes
a Step I: in 210 mbar 16O for 12h at 1100. Samples 001, 010-013, and 020-024: step II in 2 040-042: step II in 16O2, step III in 18O2, step IV in 16O2.
The first step, for all oxidations, was in 210 mbar O2 for 12 h at 1100 °C to form a ∼120 nm thick SiO2 film. The second to fourth steps are specified in Table 1. As mentioned previously, a low water content of the O2 is desired, so during all the oxidation steps a liquid nitrogen trap was used and the water vapor content was less than 1 ppm. The difference between the samples 001-024 and 030-044 is an additional oxidation step in 16O2 before the 18O2 step. This additional oxidation step for samples 001-024 was made to obtain an 16O-interface representative for the temperatures and pressures used in the later steps. To have as stable pressures and low levels of water as possible, we waited 5 min (after introducing the O2 gas) before the samples were moved into the hot part of the furnace. After each step, the samples were allowed to cool for 10 min before the gas was removed. The NRA analyses were made twice: for samples 001-024 after the second step (first analysis) and after the third step (second analysis), and for samples 030-042 after the third and fourth step. The aerial densities of 16O and 18O were measured by the reaction 16O(d,p)17O at 850 keV and 18O(p,R)15N at 730 keV,13,14 calibrated by using well-defined standards. The 18O depth profiles were determined by using the narrow and isolated resonance of the reaction 18O(p,R)15N at 151 keV.15,16 Results Figure 1 shows the resonance excitation curves after the third and fourth oxidation step for sample 041. The excitation curve (yield of R particles) is a distorted image of the isotopic (18O) concentration profile. In the interpretation of the excitation curves, we do not need a complicated analysis, since the two peaks are well separated. We approximate that the energy of the incident beam may be related linearly to depth in the sample via the rate of energy loss of the incoming protons (protons of 151 keV lose 12.5 eV per Å in SiO2). A proton energy of ∼151 keV is equivalent to zero depth, and a proton energy of ∼166 keV is equivalent to a depth of 120 nm in the sample (oxide). The excitation curve of a 10 Å thick Si18O2 layer will, independently of where it is in the oxide, have the same integrated area, but a peak from a layer at the interface (∼166 keV) will be, due to straggling,17 lower and broader than a peak from a layer at the surface (∼151 keV). Shown in the figure is a decrease of the two peaks, both at the surface (∼151 keV) and at the interface (∼166 keV) after the fourth oxidation step.
2 4 8 8 10 10 10 18O
2,
temp. [°C] III-IV step
pressure [mbar] III-IV step
1100 1100 1100 1100 1100 1000 950 900 800
210 210 210 210 210 210 210 210 210
1000 900 800 800 1100 1100 1100
210 210 210 210 20 2 2
step III in
16O
2.
Samples 030-033 and
Figure 1. Measured excitation curves near the 18O(p,R)15N narrow (full width at half-maximum ) 100 eV) resonance at 151 keV after the second and third oxidations (see text for details) for sample 041, clearly showing the oxygen exchange at the surface and at the SiSiO2 interface. The excitation curves were measured with 30 µC of incident protons for each point and a total beam current of 300 nA.
The decrease of 18O at the surface is due to surface exchange,7 and the decrease of 18O at the interface is due to oxygen exchange at the SiO2-Si interface.4,8-10 In this study, we are primarily interested in the Si-SiO2 interface peak (peak at ∼166 keV). The full width at half-maximum (fwhm) for the two peaks at 166 keV is the same (3.2 ( 0.2 keV) and equal to the expected broadening of a peak due to straggling. Straggling of 3 keV will give a depth resolution of 1.5 keV or ∼150 Å, and that is much broader than the amount incorporated in the third step (∼12 Å of SiO2). It is thereby not possible to extract information from the shape of this peak. The shape of the peaks can otherwise give information on depth distribution of 18O and, from this, the diffusion of oxygen belonging to the oxygen network can be evaluated.18 The only information one can extract out of this figure is the amount of oxygen exchanged between the Si-SiO2 interface region and oxygen in the gas (O2). This can be seen in the figure by the higher number of counts and a broader peak at the interface after the third step. The mean peak height was calculated (mean value of the six highest counts) after the third step and fourth step to 59.2 ( 3.1 and 46.7 ( 2.8 counts of R-particles, respectively. The error is calculated from counting statistics and given as one standard deviation, σ.
9912 J. Phys. Chem. B, Vol. 103, No. 45, 1999 The area under the curves in Figure 1 is equivalent to an amount of 18O. The amount exchanged after each exposure was measured in two ways. First, it was measured as a fraction of the integrated area of a thick Si18O2 reference sample with an aerial density of 257 × 1015 atoms cm-2 (580 Å) for samples 030-044 and 336 × 1015 atoms cm-2 (760 Å) for samples 001024. Second, it was measured in relation to the total amount measured by NRA. The integrated areas of the two curves (in the unit [(counts of R particles) × (proton energy in keV)], which in the following section will be neglected since it contains no physical information) are 842 (after the third step) and 465 (after the fourth step), respectively. The loss is thereby 377 (842-465) of which 53 (236 - 183 ) 53, areas of the interface peaks) is the loss at the Si-SiO2 interface. The number 53 can be related to the integral of the reference sample (12310) and the loss can be calculated to 1.1 × 1015 atoms cm-2 (53/12310 × 257 × 1015 atoms cm-2). One can also calculate the amount 18O at the interface after the third and fourth step by the relation between the integral of the peak at the Si-SiO2 interface and the total integral multiplied with the total amount 18O measured by NRA, 16.8 × 1015 atoms cm-2 and 8.6 × 1015 atoms cm-2, respectively. The amounts of 18O at the interface are then after the third step: 236/842 × 16.8 × 1015 ) 4.7 × 1015 atoms cm-2, and after the fourth step 183/465 × 6.8 × 1015 ) 3.4 × 1015 atoms cm-2. The difference between these two amounts is the oxygen exchange at the Si-SiO2 interface, (4.7-3.4) × 1015 ) 1.3 × 1015 atoms cm-2, which is essentially the same as 1.1 × 1015 atoms cm-2. A similar evaluation has been made for all samples and, independently of which of the two methods was used, the same result was obtained. The region in between the two peaks has approximately the same number of counts after the third and after the fourth step. The mean number of counts in this region (six points) is after the third step 13.3 ( 1.4 counts and after the fourth step 9.9 ( 1.1 counts. One can, as in the previous section, relate this to an amount by taking the width between the two peaks (15 keV) and multiplying this by the difference, and this would give (13.3-9.9) × 15 ) 51, equal to 51/842 × 16.8 × 1015 ) 1 × 1015 atoms cm-2 which is 20% of the oxide growth. This region can also be seen as a plateau, i.e., a constant concentration over a depth interval in the oxide much wider than the resolution. The concentration in this interval can be calculated by comparing the measured counts (9.9) with the counts (1990) in the plateau of the reference sample (thick 18O-oxide). This gives a concentration of 0.5% 18O in the Si16O2. The 16O2 used in this study is, due to the experimental procedure, slightly enriched in 18O (natural aboundence ) 0.2% 18O), which was also confirmed by measuring the 18O concentration in 16O2 by a mass spectrometry. A measurable difference in concentration of 18O between the two peaks was only found for samples 040-043. There might be an exchange in between the oxygen passing through the oxide, but it is small in comparison with the oxide growth. In Figure 2, the oxygen exchange at the Si-SiO2 interface is plotted vs temperature, and there is no large change with temperature. Considering the error bars, the exchange does not decrease with temperatures and it might increase slightly with temperature. Figure 3 shows the Si-SiO2 interface loss plotted vs pressure for oxidation at 1100 °C, and, as can be seen, the pressure is not an essential parameter. Another way of illustrating this can be found in Figure 4. This figure shows the oxygen (18O) uptake at the Si-SiO2 interface in the first 18O2 step for oxidation at different pressures for 1 h at 1100 °C. The oxidation
A° kermark et al.
Figure 2. Amount 18O lost from the Si-SiO2 interface during oxidation in 210 mbar O2 vs temperature [°C].
Figure 3. Amount 18O lost from the Si-SiO2 interface during oxidation at 1100 °C vs pressure [mbar].
Figure 4. Amount 18O incorporated in the Si-SiO2 interface after the oxidation step in 18O2 vs pressure, and since we are in the parabolic region, the oxidation growth varies linearly with pressure and the oxide growth is small and can be estimated to linear growth.
kinetics are parabolic for the thickness used in this study and the parabolic rate constant has a linear pressure dependency.11 The oxide growth is however small in comparison to the oxide thickness, thereby the parabolic kinetics can be, with very high accuracy, represented by a linear growth.19 The 18O uptake can thereby be extrapolated to zero giving an incorporation of 1 × 1015 18O atoms cm-2 at zero pressure, which agrees well with the measured exchange. Figure 5 summarize the results for all the excitation curves of the samples in Table 1. This is of interest since neither the temperature nor the pressure had any major effect on the amount
Oxygen Exchange at the SiO2-Si Interface
J. Phys. Chem. B, Vol. 103, No. 45, 1999 9913 concentrations of oxygen at the interfaces, and x is the thickness. This equation can be separated into a flux in the forward direction (JF) and a flux in the backward direction (JB), by
C1 - C2 C1 C2 ) -D + D x x x
J ) JF - JB ) -D
(2)
Identification gives that JF ) -D(C1/x) and JB ) +D(C2/x). The ratio between the forward and backward fluxes can thereby be expressed by
C1 JF ) -JB C2
Figure 5. Amount 18O lost from the Si-SiO2 interface vs amount 18O incorporated in the Si-SiO2 interface after the oxidation step in 18O2 for all samples in Table 1.
oxygen exchanged. There is an almost constant exchange after incorporation of 3 × 1015 O atoms cm-2 and it depends marginally on the amount of 18O incorporated in the oxidation step with 18O2. As in ref 4, one can relate the oxygen exchange to the amount incorporated in the 18O2 oxidation step in order to get an estimation of how much oxygen is transported to the Si-SiO2 interface and from the Si-SiO2 interface. The two lines in the figure represent an optimistic (90%) and a pessimistic (35%) relation between the amount of oxygen incorporation and the amount of exchange. 100% represent only oxygen exchange but no growth, and 0% represent only growth but no exchange. We use here a definition of the reacting layer as the thickness of the layer in which oxygen exchange occurs. This definition is probably appropriate since the oxygen in this layer is difficult to define as belonging to the lattice or dissolved in the interface layer. The reacting layer is less than 3 × 1015 atoms cm-2 (7.5 Å of SiO2) and at least 1 × 1015 atoms cm-2 (2.5 Å of SiO2) thick. This thickness agrees well with the reported 5 Å thickness of the Si-SiO2 interface.20,21 Discussion It was assumed in the original model used for describing the reacting layer between the Si and growing SiO2 that the reacting layer consists of a mixture of Si in the oxidation states 0, +1, +2, +3, and +4 and that Sin+ was the mobile species in the reactive layer.22 An interface consisting of Si in the oxidation states 0, +1, +2, +3, and +4 was based on X-ray photoelectron spectroscopy (XPS) measurements, but the interpretation of the XPS results has recently been experimentally questioned.23 Furthermore, the finding of an oxygen exchange at the SiSiO2 interface strongly suggests that the mobile species is oxygen. A new model of the reacting layer is thereby needed, but the chemical structure of the interface has to be settled before a new model can be presented. The oxygen exchange can also be used to evaluate the concentration of oxygen at the Si-SiO2 interface. If we assume steady-state diffusion and no chemical diffusion (diffusion driven by an oxygen potential), Fick’s law can be applied. The diffusion of oxygen through the oxide can then be described by
C1 - C2 x
J ) -D
(1)
where D is the diffusion coefficient, C1 and C2 are the
(3)
We can, from Figure 5, extract the ratio of the forward and backward flux to between 35% and 90%; therefore, the concentration of oxygen at the Si-SiO2 interface is also between 35% and 90% of the concentration of oxygen at the SiO2-O2 interface. Considering also a chemical potential driving the diffusion in the forward direction it is possible that we have uphill diffusion,24 i.e., that the concentration at the Si-SiO2 interface is higher than the concentration at the SiO2-O2 interface. However, even if the concentration of oxygen at the Si-SiO2 interface is between 35 and 90% of the concentration of oxygen at the SiO2-O2 interface, the situation is very different for oxidation of Si from what is generally assumed. Namely, that the concentration of oxygen at the Si-SiO2 interface is negligible in comparison to that at the SiO2-O2 interface.11 In the case of a zero concentration at the Si-SiO2 interface (C ) 0 in eq 2), there are two ways of changing the oxidation kinetics: changing the surface concentration by the surface reactions or changing the diffusion coefficient. A zero concentration can thereby not explain the oxidation kinetics dependency of crystal structure of the underlaying Si. This dependency can, on the other hand, be understood if concentration of oxygen at the Si-SiO2 interface is not zero, since it is likely that solubility of oxygen in the interface is different for different crystal orientations. The exchange at the Si-SiO2 interface also tells us that the oxygen reaching this interface is not bound strongly to Si and it is difficult to distinguish it from oxygen as the transported species. A nonzero concentration at the SiO2-O2 interface indicates that the chemical interfacial reactions define the concentration gradient for oxidation and thereby set the transport rate of the migrating species. The change to a nonzero concentration can be taken into account by a small modification of the dominating model.9 The oxidation process can probably be described by calculating the equilibrium for the reactions at the interfaces (thermodynamics) and then using the diffusion coefficient for the migrating species. This is basically valid for both the Wagner theory (oxidation of metals)25-27 and the Deal and Grove theory (ref 11). The question is only: are the right equilibriums and migrating species used?28 The catalytic properties of the interfaces have a pronounced effect on the equilibrium conditions for a chemical reaction. Chemical reactions occur probably on active sites, both at the Si-SiO2 interface and at the SiO2-O2 interface, and active sites are thereby closely related to the catalytic activity of an interface. One can expect that the catalytic activity depends on both the defect density (number of sites) and the stresses (additional surface energy). In the case of the SiO2-O2 interface, it has been found, in studies of the exchange O2 T O2 catalyzed by SiO2, that the catalytic properties depend strongly on oxide thickness.5 It has also been shown that the change in catalytic activity with thickness of the growing oxide could explain the
A° kermark et al.
9914 J. Phys. Chem. B, Vol. 103, No. 45, 1999 deviation from the linear-parabolic oxidation theory for oxide thickness less than 20 nm.4 Even though the catalytic activity of the SiO2-O2 interface most likely changes with oxide thickness, one can, at present, only speculate on the mechanisms for this. An increased understanding of the mechanisms could lead to a better understanding of the oxidation kinetics. The result of an exchange at zero pressure, see Figure 4, can explain why it is possible to reduce SiO2 films on Si substrates by vacuum annealing even for oxygen activities where SiO2 should be stable.29 It was reported for annealing of a 600 Å thick SiO2 on Si that evaporation of SiO occurs. In an initial induction period no SiO was measured and it is believed that during the induction period channels through the oxide were formed. When this has happened, SiO evaporates directly from the Si-SiO2 interface (or rather a Si-SiO2-vacuum interface). The number of channels does not increase with time of annealing and thereby the nuclei for the channels is likely present before the annealing starts. These nuclei can be the already existing preferential fast diffusion paths. The first step in the annealing process can thereby be a widening of already existing diffusion paths by transport of oxygen to the surface where it reacts to O2(g). The presence of preferential diffusion paths can also explain the behaviour of the oxygen exchange. The oxygen can quickly move in and out through these preferential diffusion paths in the oxide. In this scheme, the oxygen must also have a high mobility in the reactive layer, otherwise the result would be an uneven oxide growth, which is not the case. Conclusions In conclusion, the vital parameters for the oxygen exchange at the Si-SiO2 interface are neither the temperature (800-1100 °C) nor the pressure (2-200 mbar) but the characteristic of a thin reactive interfacial layer. Oxygen reaching this reactive layer is not fixed but has a considerable chance of being transported back to the SiO2-O2 interface. The oxygen transport rate from the Si-SiO2 interface is between 35% and 90% of the oxygen transport rate to the Si-SiO2 interface. This indicates that the concentration of oxygen at the Si-SiO2 interface is almost the same as the concentration at the SiO2-O2 interface. In fact, the concentration at the Si-SiO2 interface can be the highest of the two, i.e., uphill diffusion, when considering that there is also a chemical potential driving the diffusion. The found characteristics of the oxygen exchange indicate also that the chemistry at the Si-SiO2 interface plays a major role for the oxidation kinetics. This is in contrast to the situation of having
a zero concentration at the Si-SiO2 interface, when the diffusion coefficient and the surface chemistry are the only parameters that can change the oxidation kinetics. References and Notes (1) Boreskov, G. K. In Catalysis: Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Berlin, 1982; Chapter 2, pp 39137. (2) Winter, E. R. S. J. Chem. Soc. A 1968, 2889-2902. (3) Nova´kova´, J. Catal. ReV. J. 1970, 4, 77-113. (4) A° kermark, T. Oxid. Met. 1998, 50 (1/2), 167-188. (5) A° kermark, T.; Hultquist, G. J. Electrochem. Soc. 1997, 144 (4), 1456-1471. (6) Rigo, S. In Instabilities in Silicon DeVices; Barbottin, G., Vapaille, A., Eds.; North-Holland/Elsevier Science Publishers: New York, 1986; Vol. 1, pp 8-100. (7) Rochet, F.; Agius, B.; Rigo, S. J. Electrochem. Soc. 1984, 131 (4), 914-922. (8) A° kermark, T. Oxide Formation: Much more than Oxygen Uptake. Doctaral Thesis, Royal Institute of Technology, Stockholm, Sweden, 1996. (9) A° kermark, T.; Gosset, L. G.; Ganem, J.-J.; Trimaille, I.; Vickridge, I.; Rigo, S. J. Electrochem. Soc. 1999, 146 (9), 3389-3392. (10) A° kermark, T.; Gosset, L. G.; Ganem, J.-J.; Trimaille, I.; Vickridge, I.; Rigo, S. J. Appl. Phys. 1999, 86 (2), 1153-1155. (11) Deal, B. E.; Grove, A. S. J. Appl. Phys. 1965, 34 (12), 37703778. (12) Irene, E. A. CRC Crit. ReV. Solid State Mater. Sci. 1988; 14 (2), 175. (13) Cohen, D. D.; Rose, E. K. Nucl. Instr. Methods Phys. Res. 1992, B66, 158-190. (14) Amsel, G.; Nadai, J. P.; D’Artemare, E.; Girard, E.; Moulin, J. Nucl. Instrum. Methods 1971, 92, 481-498. (15) Battistig, G.; Amsel, G.; D’Artemare, E.; Vickridge, I. Nucl. Instrum. Methods Phys. Res. 1991, B61, 369-376. (16) Battistig, G.; Amsel, G.; D’Artemare, E.; Vickridge, I. Nucl. Instrum. Methods Phys. Res. 1992, B66, 1-10. (17) Vickridge, I.; Amsel, G. Nucl. Instrum. Methods Phys. Res. 1990, B45, 6-11. (18) Ganem, J.-J.; Trimaille, I.; Andre´, P.; Rigo, S.; Stedile, F. C.; Baumvol, I. J. R. J. Appl. Phys. 1997, 81 (12), 8109-8111. (19) Trimaille, I.; Rigo, S. Appl. Surf. Sci. 1989, 39, 65-80. (20) Pascaquarello, A.; Hybertsen, M. S.; Car, R. Phys. ReV. B 1996, 53 (16), 10942-10950. (21) Grunthaner, F. J.; Grunthaner, P. J. Mater. Sci. Rep. 1986, 1 (3), 65-160. (22) Stoneham, A. M.; Grovenor, C. R. M.; Cerezo, A. Philos. Mag. 1987, 55 (2), 201.10. (23) Greeley, J. N.; Meeuwenberg, L. M.; Banaszak Holl, M. M. J. Am. Chem. Soc. 1998, 120, 7776-7782. (24) Darken, S. Trans. AIME 1949, 180, 430-438. (25) Wagner, C. Z. Physik. Chem. 1933, B21, 25-47. (26) Kofstad, P. High-Temperature Corrosion; Elsevier Applied Science: London, New York, 1988. (27) Fromhold, A. T., Jr. Theory of Metal Oxidation, Vol. 1 Fundamentals; North-Holland: Amsterdam, 1976. (28) Α˙ kermark, T. J. Electrochem. Soc., submitted. (29) Engel, T. Surf. Sci. Rep. 1993, 18 (4), 91-144.
