Problem

One of the procedures in the production of integrated circuits is the formation of a thin...

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 m2/h) is as follows:
where k is Boltzmann’s constant (8.62 × 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 100 nm thick at both 700°C and 1000°C.
(b) In an atmosphere of H2O (1 atm pressure), the expression for B (again, in units of m2/h) is
Calculate the time required to grow an oxide layer that is 100 nm thick (in an atmosphere of H2O) at both 700°C and 1000°C, and compare these times with those computed in part (a).