One of the procedures in the production of integrated circuits

One of the procedures in the production of integrated circuits is the formation of a thin insulating layer of SiO2 on the surface of chips (see Figure 18.26). This is accomplished by oxidizing the surface of the silicon by subjecting it to an oxidizing atmosphere (i.e., gaseous oxygen or water vapor) at an elevated temperature. The rate of growth of the oxide film is parabolic—that is, the thickness of the oxide layer (x) is a function of time (t) according to the following equation:

Here the parameter B is dependent on both temperature and the oxidizing atmosphere.
(a) For an atmosphere of O2 at a pressure of 1 atm, the temperature dependence of B (in units of µm2/h) is as follows:

where k is Boltmann’s constant (8.62 A? 10–5 eV/atom) and T is in K. Calculate the time required to grow an oxide layer (in an atmosphere of O2) that is 75 nm thick at both 750°C and 900°C.
(b) In an atmosphere of H2O (1 atm pressure), the expression for B (again in units of µm2/h) is

Now calculate the time required to grow an oxide layer that is 75 nm thick (in an atmosphere of H2O) at both 750°C and 900°C, and compare these times with those computed in part (a).