B.E. Deal and A.S. Grove have studied the kinetics in detail 1965 (Journal of Applied Physics, Volume 36, number 12, 3770) The assumption is, that molecular O2 and H2O diffuses through the oxide layer. On the silicon surface the oxidant reacts with Si to SiO2. First step is transport of the oxidizing gas from the bulk to the outer surface where it reacts or it is adsorbed. The flux is F1= h(C*-C0) h is the gas phase transport coefficient C0 is the concentration of the oxidant at the outer surface of the oxide at any given time C* ist the equilibrium concentration of the oxidant in the oxide The equilibrium concentration of the oxidant is assumed to be related to the partial pressure of the oxidant in the gas by Henry’s law, C* = Kp The flux of the oxident across the oxide layer is assumed to be given by Fick’s law, F2=Deff(dC/dx). Deff is the effective Diffusion coefficient and dC/dx is the concentration gradient of the oxidizing species in the oxide. Under steady state conditions the flux is at any point within the oxide the same. dF2/ dx = 0 F2=Deff (C0-Ci)/x0 Ci is the concentration of the oxidant near the Oxide- Silicon interface. Finally the flux corresponding to the oxidation reaction is expressed by the first-order relation F3=kCi Steady State: F1=F2=F3 The solution of the rate of growth of the oxide layer is described by dxo / dt = F/N1 N1 is the number of oxidant molecules incorporated into a unit volume of the oxide layer. The solution of the differential equation is x0=A/2 [(1+ (t+tau)/(A²/4B))1/2 –1] where A =2 Deff (1/k + 1/h) B =2 Deff C?/N1 tau = (xi² +Axi)/B tau is a time constant added to the equation to take into account the oxide that preexists on the silicon surface before the oxidation process starts, e.g native oxide. It is interesting to examine two limiting forms of the equation: 1: t >>A²/4B and also t > tau x²0=Bt. This reflects the well known parabolic oxidation law. 2: t << A²/4B x0 = B/A (t+tau) Thus the relationship reduces to a linear law. Temperature dependence of the parabolic or diffusion controllecd rate law: The rate constant B contains the Diffusion coefficient Deff. Deff = D0 exp(-Ed/kT) The Temperature dependence of B yields an Arrhenius activation energy which is called Ed, the activiation energy of diffusion of O2 or H2O through the oxide. This activation energy is about 0,7 eV for wet oxidation and 1,24 eV for dry oxidation. Temperature dependence for the linear region (<100nm). B/A ≈ exp (-Ea/kT) The linear grown law is considered to be associated with the reaction at the oxide-silicon interface. Assuming that the temperature dependence of the rate constant B/A can be described with an Arrhenius equation an activation energy Ea can be defined. Experimental data show a value for Ea around 2 keV. It is interesting to compare this value with energy required to break the Si-Si bond, i.e 1,83 eV. This bond breaking must be one of the fundamental processes in the oxidation reaction and may the rate determining step for oxidation. Inaccuracy of Deal-Grove model in the region below 30nm: It appears that the initial ixidation rate in dry oxygen is very much faster than it is predicted by the model. Massoud et.al. propose an existance of a surface layer in Si substrate which contains additional oxidation sites. This effect enhances the oxidation rate in the region below 30nm. Further effects on Oxidation Kinetics:

Oxidation parameter	Effect on oxidation kinetics	Reference
Wafer orientation	The oxidation rate of (111) planes is greater than that of (100); possible explanation is that there is a lower concentration of Si bonds exposed on the (100) surface.	Ligenza J R 1961 Phys.Chem. 65 2011
Pressure of the oxidising gas	High pressure oxidation can be carried out at much lower temperatures than atmospheric processes. The equilibrium bulk concentration of the oxidizing species in the oxide layer increases, this effect is proportional to the partial pressure This effect is a reason for thickness uniformity variation from run to run caused by atmospheric pressure fluctuations. Absolute pressure control of furnaces may be necessary.	Razouk R R, Lie L N, Deal B E 1981 J.Electrochem. Soc. 128 2214
Effect of HCl on oxidation rate	HCl additions to O2 slightly increase the dry oxidation rate and improve the gettering of metallic impurities by removing them from the surface as volatile chlorides and to neutralize alkali ions at the interface which causes mobile ionic charges	Katz L E 1983 VLSI Technology p 131
Impurities in the oxidising gas	Small concentrations of H20 in O2 may increase the dry oxidation rate
Dopants in the silicon substrate	B solves in the growing oxide nad weakes the SiO2 network. Consequently the Diffusion is enhanced P segregates to the oxide/silicon interface and increases the rate of the interface reaction	Deal B E, Sklar M 1965 J. Elektrochem. Soc. 112 430