KINETICS OF OXIDE GROWTH ON METAL SURFACES

Transcription

1 KINETICS OF OXIDE GROWTH ON METAL SURFACES A. Vlad Faculty of Science, University of Oradea, RO Oradea, Romania Max-Planck-Institut für Metallforschung, D-70569, Stuttgart, Germany Abstract: A short review of the principles governing the oxidation of metals is presented. The initial stage of the oxidation process involves the chemisorption of oxygen, frequently followed by dissociation and at least partial ionization. The growth of continuous oxide films or scales is considered in terms of various rate-limiting processes such as anion or cation diffusion through the bulk oxide, mass or electron transport across one of the interfaces, or electron transfer processes associated with the chemisorption step. INTRODUCTION Metals are generally unstable in the climatic conditions of Earth. Thermodynamically, only a metal as noble as gold should survive as a native metal, resisting conversion into a oxide, halide, sulfide or other compound. The destruction of metals by corrosion is the costly aspect of the low temperature oxidation: the important metals used in engineering and construction, like iron, copper, aluminium all corrode to different degrees. However, the oxides are not just harmful and under specific conditions a passivating oxide may form which acts as a protective layer against further oxidation. The discovery of Atalla et. al. [1] in 1959 that the thermal oxidation of silicon passivates its surface was a crucial step in the semiconductor device technology. There are also other fields were oxide layers play an important role, like in heterogeneous catalysis or in the high temperature resistant coatings. In order to control the oxidation and use it as a tool, understanding the mechanism at an atomic scale is mandatory. INITIAL STAGES OF GAS-METAL INTERACTION The initial stages of the gas-metal interaction may be very complex and imply a number of different physical or chemical processes. Oxygen molecules from the gas phase must first come into contact with the metallic surface. The rate of impingement of the molecules on the unit surface area is

2 given by the kinetic theory as being directly proportional to the gas pressure, p and inversely proportional to the square root of the mass of the gas molecule, m, and of the temperature, T: p/(2πmk B T) 1/2 (1.1) where k B is the Boltzmann constant. A fundamental property of the gas-surface interaction is the sticking probability, that is the probability that an gas atom or molecule which hits the surface ends up is an adsorbed state on the surface. The sticking probability is influenced by several external variables, like the surface structure, cleanliness of the surface, the temperature and the gas pressure. Two main adsorption mechanisms can be distinguished: physisorption and chemisorption. Physisorption In the process of physisorption of a molecule on a surface, the electronic structure the adsorbate and of the substrate is hardly perturbed. The bonding takes place via weak van der Waals interactions, where an attractive force appears due to the mutually induced dipole moments. The interaction of a diatomic molecule, like O 2, with a metallic surface may be described by the potential energy diagrams such as that shown in Fig. 1.1 [2]. The curve I (blue) represents the potential energy of the molecule as it is attracted to the surface by the long-range forces and becomes physisorbed in a non-activated process. Hp denotes the heat of physisorption. The potential has a shallow minimum at a few Ǻ from the surface. At closer distances, the electron wave function of the adsorbate and the surface atoms start to overlap leading to a strong repulsion. Characteristic for the physisorption is a low bonding energy (5-100 mev). Thus, it is assumed that it becomes important at relatively high gas pressures and low temperatures (RT: k B T» 25 mev) and primarily as a precursor to chemisorption [2]. Figure 1.1: Schematic potential energy diagram for the interaction of a diatomic gas with a metallic substrate. 42

3 Chemisorption The strongest adsorption mechanism is the chemisorption which involves a rearrangement of the valence electrons of the metal and adsorbate in order for a chemical bond to form. The bonding energies of chemisorption are relatively high (> 1 ev) and involve short bond distances of a few Ǻ. The curve II (red) in Fig. 1.1 represents the potential energy of a molecule which has been dissociated prior to chemisorption. E a and E d represent the activation energies for chemisorption and desorption, respectively, whereas Hc denotes the heat of chemisorption. Depending on the point of intersection between the two curves, chemisorption can be either an activated or a non-activated process: it the point of intersection P is above the zero potential energy an activation energy, E a, will be required for the chemisorption to occur. On the other hand, if P lies below zero, no activation energy is necessary for chemisorption. In a simplified picture, whether a molecule will be physisorbed or chemisorbed on a surface depends primarily upon the energetic position of the molecular orbitals of oxygen molecule with respect to the Fermi level of the metal. In the frame of the Molecular Orbital Theory, the bonding within a molecule is described in terms of bonding (σ, π,..) and anti-bonding (σ, π,..) molecular orbitals which are constructed by combining the available atomic orbitals. The molecular orbital energy level diagram for an oxygen molecule in the ground state is presented in Fig Figure 1.2: Molecular orbital energy level diagram for an oxygen molecule in the ground state. 43

4 In principle, three situations can be distinguished: if the anti-bonding molecular orbital of the oxygen molecule lies higher in energy than the Fermi level of the metallic substrate, no charge transfer will take place, therefore the oxygen molecule will be physisorbed. An incomplete filling of the O 2 anti-bonding molecular orbitals leads to the adsorption of the charged chemisorbed oxygen molecule on the surface. This is the situation when the anti-bonding orbital is situated partially below the substrate Fermi level. A favorable situation for the dissociative chemisorption occurs whenever the anti-bonding orbital is completely filled with electrons; the O 2 anti-bonding orbital lies below the Fermi level of the metal. With increasing number of oxygen adatoms, repulsive lateral interactions between the adsorbates combined with the adsorbate-substrate interaction may lead to the formation of ordered chemisorbed layers. For instance, a quarter of a monolayer of oxygen on Rh(111) forms a (2 x 2) reconstruction (a hexagonal lattice similar to the substrate structure, but with twice the distance between the O atoms as compared to the Rh atoms) [3]. Oxide nucleation and growth Provided that the mobility is high enough, the adsorbates may mix with the substrate atoms and a two-dimensional so-called surface oxide may form. For instance, depending on the partial pressure, temperature and orientation, the oxidation of transition metals (Rh, Pd, Ag) can lead to the formation of surface oxides which may or may not bear a resemblance to the corresponding bulk oxides [4] and ref. herein. The oxide nucleation is an activated process and it was reported that the activation energy should decrease with increasing the oxygen pressure [2]. At low temperatures the thermal activation energy for atomic motion is small. Therefore, at relatively low temperatures and oxygen partial pressures the oxide nucleation is expected to take place mainly at defect sites (e.g. kinks or step edges). The possibility that the oxide would nucleate at any surface site increases with increasing the oxygen pressure. After the formation of oxide islands or clusters, oxidation mostly continues laterally until the first oxide monolayer is closed. Alternatively, a three-dimensional growth may also be observed. A recent study on Cu oxidation [5] has shown the dependence of the oxidation behavior on the crystal orientation and temperature. The kinetic data on the nucleation and growth of oxide islands showed a highly enhanced initial oxidation rate on the Cu(110) surface as compared with Cu(100). It was reported that the 44

5 dominant mechanism for the nucleation and growth on the (100) and (110) oriented crystals is the surface diffusion of oxygen. A markedly different oxidation behavior was observed of Cu(111) shows a dramatically different: the initial stages of oxidation are dominated by the nucleation of threedimensional oxide islands at T < 550 o C and by two-dimensional oxide growth at T > 550 o C. KINETICS OF OXIDE FILM FORMATION As soon as a thin continuous film of oxide has formed on a metal surface, the metal and gaseous reactants are spatially separated by a barrier and the reaction can continue only if cations, anions, or both and electrons diffuse through the oxide layer. The rate-determining step in the oxidation reaction depends on the system in question, the thickness and nature of the oxide film, as well as on the pressure and temperature of the system. As a function of the rate determining processes, two limiting cases may be discussed. On one hand, if the transport through the existing oxide layer is considered to be faster than the processes taking place at the surface (the rate of impingement of the oxygen molecules, oxygen dissociation, chemical reactions), the surface reactions are regarded to be rate limiting. This limiting case is therefore designated as being surface reaction controlled. On the other hand, one can consider the possibility that the transport of defect species through the oxide can be so slow relative to the surface/interfacial reactions that it becomes rate-limiting. This is the case denoted as transport current controlled or diffusion controlled, if the relevant currents are due to diffusion. Based on these assumptions, a number of models have been proposed to explain the kinetics of oxide film growth for different thickness regimes. An arbitrary film-thickness terminology has been proposed by Fromhold [6] which is listed in Table 1.1. L (Ǻ) Terminology < 5 ultra-thin 5-50 very thin thin intermediate thick > very thick Table 1.1: Terminology of oxide films as a function of thickness. 45

6 The thick and very thick film regime is best described by the theory proposed by Wagner (1933) [7], whereas for the kinetics of thinner oxide the most relevant is the Cabrera-Mott theory (1949) [8] which was further developed by Fromhold and Cook [9, 10]. The above mentioned theories will be briefly presented in the following sections Thin film growth In 1939, Mott [11] proposed a model to explain the limitingthickness behavior of thin oxide films in the low temperature regime. The thermal diffusion of ions was found to limit the oxide growth in the first stage, since the ionic current J i is lower than the current due to tunneling of electrons through the oxide, J e. The growth law in this regime is parabolic. However, as the film thickens the electron current J e drops down considerably and becomes the rate-limiting step. The growth rate in this stage was found to be direct logarithmic. A less restrictive model in terms of temperature and oxide thickness range was proposed in 1949 by Cabrera and Mott [8]. It was based on the electron transport either by tunneling or by thermionic emission from the metal into the oxide conduction band and ionic diffusion. The electrons were considered to be faster than the ions and an equilibrium contact potential is established between the metal and adsorbed oxygen. This contact potential was termed as Mott potential, V M, and is defined as: (1.2) where e is the magnitude of the electronic charge, χ 0 is the metal-oxide work function and χ L is the energy difference between the conduction band in the oxide and O - level of adsorbed oxygen. Figure 1.3 gives a schematic potential energy diagram for the metal/oxide/oxygen system, for which V M is negative in sign. In the absence of space charge, a positive electric field E 0 = V M /L(t) is build-up in the oxide which speeds up the ions and slows down the electrons. The lowering of the energy barrier for ionic motion by large electric fields is termed as non-linear diffusion. 46

7 Figure 1.3: Schematic band structure of the metal-oxide-oxygen system. Further developments have been made by Fromhold and Cook (1967) in a theory that constitutes a synthesis of the Mott and Cabrera-Mott models [9, 10]. The central concept of this theory is that of coupled charge currents. The assumption that the steady state ionic and electronic currents, q i J i and q e J e, respectively, are equal in magnitude, but have opposite signs is made. This is referred to as the coupled-currents condition (or kinetic condition) and mathematically can be written as: (1.3) where q i and q e are the electric charges of single defects of the diffusing ionic and electronic species, respectively, J i is the ion current density and J e is the electron current density. This assumption is valid whenever the spacecharge contribution to the electrostatic potential gradient is negligible relative to the surface-charge contribution. For oxide films thinner than 50 nm, this condition is usually satisfied and a uniform electric field may be considered. The surface-charge field E 0 as a function of oxide thickness is thus determined from the coupled-currents condition (Eq. 1.3) and substituted into one of the two currents Ji and Je to obtain the growth rate: 47 (1.4)

8 J c denotes the rate-limiting particle current and R c represents the volume of oxide formed per particle of the flux J c which is transported across the oxide. The oxide film thickness then is numerically evaluated as a function of time. The main theoretical task is to find suitable expressions for the ion and electron currents. Depending on the oxidation conditions and the properties of the involved materials, either electron or ion transport processes may become the rate-limiting step in the oxidation process. Electron-tunnel current limited growth At low temperatures the thermal energy k B T is insufficient for thermionic emission to occur and the electron transport through the oxide takes place by quantum mechanical tunnel effect. Considering the zero temperature case, if χ L > χ 0, tunneling of electrons from the filled part of the metal conduction band which lies above the O - level takes place (Fig. 1.3). If the metal Fermi level E F and the O - level of adsorbed oxygen are equalized, the current drops to zero and the system is in equilibrium with the potential V M existing across the film. The tunnel electron current during the establishment of this potential is given by: 48 (1.5) where V K = -E 0 L is the kinetic potential. Whenever the kinetic potential equals the Mott potential, the electron tunnel current is zero, corresponding to a current equilibrium of the electronic species. The non-zero temperature situation is more complex, since tunneling in both directions occurs simultaneously. However, it has been shown that the there is a relatively small temperature dependence for tunneling, which implies that the saturation oxide thickness is almost independent of temperature. Numerical calculations shown that in the first stages the oxide growth rate is limited by ionic diffusion and the growth law is inverse logarithmic, as obtained by Cabrera and Mott. In Fig. 1.4 the film thickness versus the logarithm of time for different values of the Mott potential is shown. A sharp transition to a second growth stage occurs at a thickness

9 around Ǻ. In this latter growth stage ionic current equilibrium exists. The rate is limited by electron tunnelling and a direct logarithmic growth law results. Figure 1.4: Film thickness versus the logarithm of time for different values of Mott potential. Curves 1-4: V M = 0, V M = -0.25, V M = -0.5 and V M = V, respectively. Dashed curve, V M = +0.1 V [9]. Thermal electron emission current limited growth At sufficiently high temperatures ( o C) thermionic emission of electrons over the metal-oxide work function χ 0 becomes a likely transport mechanism. The region in film thickness where electron tunneling and electron thermal emission occur simultaneously to an appreciable extent is very limited, since the electron tunneling becomes increasingly difficult as the oxide film thickness exceeds Ǻ. The ion diffusion current J i is produced by the concentration gradient of ionic defects in the oxide which is due to the differing chemical reactions at the metal-oxide x = 0 and the oxide-oxygen x = L interface and can be expressed mathematically by equation 1.8. A negative electric field E 0 is established which opposes the ionic diffusion, but has the proper polarity to facilitate the emission of electrons from the metal into the oxide conduction band (Schottky emission): 49 (1.6) The equation for the electron current due to thermionic emission Je is given by [2]: (1.7)

10 where A is a constant equal to 4πmk B 2 =h 3 = 7.5 x electron/cm 2 sec K 2. It is important to notice that the electron current J e is independent on the oxide thickness, as opposed to the previously discussed case of electron tunneling. The ionic diffusion potential V D = -E 0 L(t) is also independent of the film thickness. Therefore, at low oxide thicknesses a high electric field is established which leads to a rapid initial growth. As the film thickens, the magnitude of the electric field decreases and a linear growth rate is observed. The slope of the curves is found to increase with temperature. This can be observed also in Fig. 1.5 [10] which illustrates the temperature dependence of aluminium oxide thickness versus time during the oxidation of molten aluminium. Figure 1.5: Calculated thickness evolution as a function of time at different temperatures. The symbols represent experimental data measured for liquid Al oxidation [10]. The overall agreement between the experimental data and theoretical predictions is good. However, the data taken at 973 K are more scattered around the theoretical values, due to the fact that in this thickness regime (< 50 Ǻ) the electron tunneling is modifying the growth kinetics. Ion diffusion current limited growth Thermally activated ionic motion in the presence of an electric field is considered to be the primary mechanism for ion transport in coherent oxides. The ionic current is expected to be the rate limiting process for 50

11 semiconducting oxides or for oxides which manifest large defect electron conductivity. In the steady-state approximation and in the absence of space-charge effects, the ionic diffusion current density is given by: (1.8) where 2a is the ionic jump distance, ν i is the frequency at which each ion attempts to surmount the energy barrier W i for diffusion, k B is the Boltzmann constant, T is the temperature, Z i e is represents effective charge per particle of ionic species, E 0 is the surface-charge field, L is the thickness of the oxide layer, C i (0) and C i (L) are the defect concentrations of the diffusing ionic species at the metal-oxide interface (x = 0) and the oxideoxygen interface (x = L), respectively. A logarithmic growth rate with a limiting thickness behavior is predicted and the limiting thickness is expected to increase considerably upon increasing the oxidation temperature. Kinetics of Cr 2 O 3 growth during Cr(110) oxidation are following the above mentioned behavior [12]. In Fig. 1.6 the thickness of Cr 2 O 3 on Cr(110) is plotted as a function of the oxidation time and for different oxidation temperatures. Figure 1.6: The thickness of Cr 2 O 3 on Cr(110) plotted as a function of the oxidation time and for different oxidation temperatures [12]. 51

12 After a very rapid increase during the first 10 s, the oxide thickness changes very slowly on a linear time scale, indicating a limiting thickness behavior. The solid lines are model calculations for the time dependence assuming that Cr-ion diffusion is rate limiting. This assumption is well justified by the large electron defect conductivity existing in Cr 2 O 3. Thick film growth Thick oxide films are usually formed at elevated temperatures and as the oxide grows out of the thin film regime previously discussed the growth law most commonly observed is parabolic. Summaries of much of this work are available in the book by Kubaschewski and Hopkins [13] and in the review articles by Lawless [2] and Atkinson [14]. The mechanism of oxidation at elevated temperatures must depend primarily on the detailed nature of the oxide formed. A solid oxide will normally contain a varied array of defects. These defects may take the form of point defects (vacancies or interstitials), line defects (dislocations) and planar defects (stacking faults or grain-boundaries). These defects are responsible for material transport through the oxide and thus play a critical role in the oxidation process. Macroscopic defects in the form of pores or cracks are frequently found in oxide scales and material transport is no longer rate limiting. The best known and most thoroughly tested theory of parabolic growth of oxide films at elevated temperatures was developed by Wagner [7], based on the idea of ambipolar diffusion of the reactants through the volume of compact oxide as the rate controlling process. It was assumed that cations, anions and electrons are the diffusing species with the ions moving through the oxide via lattice defects under the influence of an electrochemical potential gradient. Thermodynamic equilibrium is assumed to exist between metal and oxide at the metal-oxide interface, and between oxide and oxygen gas at the oxide-oxygen interface. The ions and electrons are presumed to migrate independently of one another, and the effects of electric field transport are considered to be negligible. The assumptions of charge-neutrality for each volume element of the oxide and a zero net charge transport through the oxide are also made.wagner's theory shows that the growth of the oxide films obeys parabolic time dependence: (1.9) 52

13 where x is the film thickness and k p is the parabolic rate constant. Wagner's theory is based upon diffusion across the film being the slowest, and therefore, the rate-limiting step in the overall sequence of reactions. Phase boundary reactions are considered to be rapid with respect to the ratedetermining diffusion processes. Oxidation of metals vs. alloys oxidation It should be noted that the although the previously discussed theories have been proven to successfully describe the kinetics of oxide growth on different systems, they are still rather restrictive as concerning the conditions of validity. It was suggested that in practice these conditions are often not observed. The case of alloy oxidation is far more complex, since additional factors come into play. For instance, concurrent processes of oxidation-induced chemical segregation and selective oxidation induce compositional changes in the alloy subsurface during oxidation must be accounted for. Depletion of the active species in the near-surface region of the metallic alloy may yield departure from the rate law otherwise expected. A review of the oxidation of alloys was written by Wallwork [15]. REFERENCES: [1] E. T. M. Atalla and E. J. Scheibner, Bell Syst. Tech. J. 38, 749 (1959). [2] K. R. Lawless, Rep. Prog. Phys. 37, 231 (1974). [3] J. Gustafson, Ph.D. thesis, Lund University, [4] E. Lundgren, A. Mikkelsen and P. Varga, J. Phys.: Condens. Matter. 18, 481 (2006). [5] G. Zhou and J. C. Yang, J. Mater. Res. 20, 1684 (2005). [6] J. A. T. Fromhold, Theory of Metal Oxidation, Vol. I - Fundamentals of Defects in Crystalline Solids (North-Holland Publishing Company, Amsterdam - New York - Oxford, 1976). [7] C. Wagner, Z. Physik. Chem. B 21, 25 (1933). [8] N. Cabrera and N. F. Mott, Rep. Prog. Phys. 12, 163 (1949). [9] A. T. Fromhold and E. L. Cook, Phys. Rev. Lett. 158, 600 (1967). [10] A. T. Fromhold and E. L. Cook, Phys. Rev. Lett. 17, 1212 (1966) [11] N. F. Mott, Rep. Prog. Phys. 35, 1175 (1939). [12] A. Stierle and H. Zabel, Europhys. Lett. 37, 365 (1997). 53

14 [13] O. Kubaschewski and B. E. Hopkins, Oxidation of Metals and Alloys (Butterworths, London, 1962). [14] A. Atkinson, Rev. Mod. Phys. 57, 437 (1985). [15] G. R. Wallwork, Rep. Prog. Phys. 39, 401 (1976). 54