A well established model for thermal oxide growth has been proposed by Deal and Grove  in the middle of the 60's and because of its simplicity it is still applied frequently. One reason for this simplicity is that the whole physics of the oxidation process is contained in two so-called Deal-Grove parameters, which must be extracted from experiments. Furthermore, it is assumed that the structure is one-dimensional. Therefore, the model can only be applied to oxide films grown on plane substrates.
(1) It is transported from the bulk of the oxidizing gas to the outer surface of oxide, where it is adsorbed.
(2) It is transported across the oxide film towards silicon.
(3) It reacts at the interface with silicon and form a new layer of SiO.
Each of these steps can be described as independent flux equation. The adsorption of oxidants is written as
It was found experimentally that wide changes in gas flow rates in the oxidation furnaces, changes in the spacing between wafers on the carrier in the furnace, and a change in wafer orientation (standing up or lying down) cause only little difference in oxidation rates. These results imply that is very large, or that only a small difference between and is required to provide the necessary oxidant flux.
is also the solubility limit in the oxide, which is assumed to be related to the partial pressure of the oxidant in the gas atmosphere by Henry's law
The flux represents the diffusion of the oxidants through the oxide layer to the Si-SiO-interface, which can be expressed as
The third part of the oxidation process is the flux of oxidants consumed by the oxidation reaction at the oxide-silicon interface given by
Deal and Grove assumed that in the steady state condition these three fluxes are equal, which allows to express them as
The differential equation can be simplified as
In order to get an analytical relationship between oxide thickness and oxidation time the first order differential equation (2.14) must be solved. For this purpose in the first step (2.14) can be rewritten in the form
At first with (2.18) the oxidation time for a specific desired oxide thickness can be estimated by
On the other side solving the quadratic equation (2.18) in regard of x leads to the following explicit expression for the oxide thickness in terms of oxidation time:
The formulas (2.44) and (2.20) are a real strength of the Deal-Grove model, because the oxide thickness for any oxidation time or the needed time for a specific thickness can be determined in an uncomplicated and fast way. Of course the thickness can be only estimated in one direction on planar structures, but in practice this fast approach is indeed helpful.
It is interesting to examine two limiting forms of the linear-parabolic relationship (2.44). One limiting case occurs for long oxidation times when and
The rate constants and are also termed as Deal-Grove-parameters. In most publications which use the Deal-Grove model the oxide growth is described with and . The parameters and are normally determined experimentally by extracting them from growth data. The reason for taking this approach is simply that all parameters in (2.23) and (2.25) are not known. in particular contains a lot of hidden physics associated with the interface reaction.
In order to model the corresponding growth rate for different temperatures, the values for and must change with temperature. As explained in Section 2.4.2, the oxidation rate increases with higher temperature, and so the values of and must also increase. It was found experimentally that both and are well described by Arrhenius expressions of the form
For the parabolic rate constant the activation energy is quite different for O and HO ambients. (2.23) suggests that the physical mechanism responsible for might be the oxidant diffusion through SiO, because is a constant and is not expected to increase exponentially with temperature. In fact, independent measurements of the diffusion coefficients of O and HO in SiO show that these parameters vary with temperature in the same way as (2.26) and with values close to those shown in Table 2.2. The clear implication is that in the linear parabolic model really represents the oxidant diffusion process.
The values for in the table are all quite close to 2 eV. (2.25) suggests that the physical origin of is likely connected with the interface reaction rate . Traditionally, the 2 eV activation energy has been associated with the Si-O bound formation process because of measurements by Pauling  that suggested that the Si-O bond energy was in the correct range to explain the values. However, the interface reaction is very complex and it is likely that other effects also affect the experimental values. An additional observation supports the idea that it is somehow associated with the silicon substrate which determines , because is essentially independent of the oxidation ambient. It is also essentially independent of the substrate crystal orientation, which suggests that represents a fundamental part of the oxidation process, not something only associated with the substrate.
The linear parabolic model predicts that the oxide growth rate should be directly proportional to the oxidant pressure as shown in (2.9). If Henry's law  holds and the concentration of oxidants on the gas/SiO interface is proportional to the pressure , then both and are proportional to from (2.23) and (2.25), and the oxide growth rate should therefore be proportional to .
Experimental measurements have shown that for wet oxidation this prediction is correct, and for HO ambients the pressure dependence of the parabolic and linear rate constants are 
If is not linearly proportional to , from (2.25) must depend on in a non-linear fashion. Considering the pressure dependence of and above, the chemical surface reaction must depend on pressure in the way .
Even before the development of the Deal-Grove model, it has been observed that crystal orientation affects the oxidation rate . The crystal effects can be incorporated in the following way: Except perhaps in the region very near the Si/SiO interface, the oxide grows on silicon in an amorphous way. So it does not incorporate any information about the underlying silicon crystal structure. Therefore, the parabolic rate constant B should not be orientation dependent, since B represents the oxidant diffusion through the SiO. If the oxide structure is unrelated to the underlying substrate, there should be no crystal orientation effect on B. In fact it was found experimentally by extracting growth data , that in context of the model there is no crystal effect on the rate constant B. The B values are the same for all orientations.
On the other hand B/A should be orientation dependent, because it involves the reaction at the Si/SiO interface. This reaction surely involves silicon atoms and should be affected by the number of available reaction sites. It was found experimentally , that there are two extremes of the linear rate constant B/A. The minimum was found for (100) oriented silicon whereas the maximum is at (111) orientation, and all other orientation are normally between these two extremes. In the context of the model the orientation effect must be incorporated for the rate constant B/A in the following way :
It has been observed in many experiments that there is a rapid and non-linear oxide growth in the initial stage of dry oxidation , as presented in Fig. 2.18. One weakness of the model is the impossibility to predict the initial stage of the oxidation growth. As shown in Fig. 2.18, even with the best fit, the approximately first 30 nm of the oxide thickness can not be forecasted with the linear parabolic model, because the oxide growth is fast and non-linear but the model offers only a linear fit for such thin thicknesses  .