Under exposure to oxygen, a silicon surface oxidizes to form silicon dioxide (SiO2). Native silicon dioxide is a high-quality electrical insulator and can be used as a barrier material during impurity implants or diffusion, for electrical isolation of semiconductor devices, as a component in MOS transistors, or as an interlayer dielectric in multilevel metallization structures such as multichip modules. The ability to form a native oxide was one of the primary processing considerations which led to silicon becoming the dominant semiconductor material used in integrated circuits today.
Thermal oxidation of silicon is easily achieved by heating the substrate to temperatures typically in the range of 900-1200 degrees C. The atmosphere in the furnace where oxidation takes place can either contain pure oxygen or water vapor. Both of these molecules diffuse easily through the growing SiO2 layer at these high temperatures. Oxygen arriving at the silicon surface can then combine with silicon to form silicon dioxide. The chemical reactions that take place are either
for so-called "dry oxidation" or
for "wet oxidation". Due to the stoichiometric relationships in these reactions and the difference between the densities of Si and SiO2, about 46% of the silicon surface is "consumed" during oxidation. That is, for every 1 um of SiO2 grown, about 0.46 um of silicon is consumed (see Figure 1).
Initially, the growth of silicon dioxide is a surface reaction only. However, after the SiO2 thickness begins to build up, the arriving oxygen molecules must diffuse through the growing SiO2 layer to get to the silicon surface in order to react.
A popular model for the oxide growth kinetics is the "Deal/Grove" model. This model is generally valid for temperatures between 700 and 1300 C, partial pressures between 0.2 and 1.0 atmospheres, and oxide thicknesses between 0.03 and 2 microns for both wet and dry oxidation. To understand this model, consider Figure 2, and let:
Cg = concentration of oxidant molecules in the bulk gas Cs = concentration of oxidant molecules immediately adjacent to the oxide surface Co = equilibrium concentration of oxidant molecules at the oxide surface Ci = concentration of oxidant molecules at the Si/SiO2 interface
Note that: 1) Cg > Cs (due to depletion of the oxidant at the surface) 2) Cs > Co (due to the solubility limits of SiO2)
The oxidizing species are transported from the bulk gas to the gas/oxide interface with flux F1 (where flux is the number of molecules crossing a unit area per unit time). The species are transported across the growing oxide toward the silicon surface with flux F2, and react at the Si/SiO2 interface with flux F3. Mathematically:
F1 = flux of oxidant from gas -> surface
(where Hg = the gas phase mass transfer coefficient) F2 = flux through the oxide layer
(where D is the diffusivity of the oxidant molecule in SiO2)
If we asume a linear concentration gradient inside the oxide layer, then:
(where d is the current value of the oxide thickness)
(where Ks = the rate constant for the surface chemical reaction)
Now let's look at F1 more closely. By Henry's Law:
where H is Henry's Law constant, C* is the equilibrium concentration of oxidant molecules in the bulk SiO2, and Ps and Pg are the partial pressures of the oxidant molecules adjacent to the SiO2 surface and in the bulk gas, respectively. From the Ideal Gas Law, we have:
where k is Boltzman's constant and T is the temperature in degrees K. Therefore, F1 can be re-written as:
where h = Hg/HkT. At steady-state, all three fluxes should be equal. In other words,
If the oxidation growth rate depends only on the supply of oxidant to the Si/SiO2 interface, it is said to be "diffusion controlled. Under this condition, D is close to zero. Therefore:
If, on the other hand, there is plenty of oxidant at the interface, the growth rate depends only on the reaction rate. This situation is called "reaction-controlled." In this case, D appoaches infinity, and:
Now, we are finally ready to compute the growth rate itself. Let N1 be the number of oxidant molecules per cubic cm incorporated into the oxide layer. Then, we can write the following differential equation:
Under the boundary condition that d = 0 when t = 0, we can solve the first order differential equation to obtain:
and di is the initial oxide thickness. For short times, the growth rate is reaction limited, and the oxide thickness is approximately:
For longer times, growth is diffusion-limited, and the approximation used is:
A and B are constants which correspond to the oxidation conditions (i.e. - temperature and wet or dry). They can typically be looked up in tables.