2.2.1 Kinetics and Growth of Silicon Dioxide

The main ambient parameter used to control oxide growth during silicon oxidation is temperature. However, it is also possible to vary the hydrostatic pressure in the reaction chamber. Whether the oxidation environment is wet (H$_2$O) or dry (O$_2$) also plays a role in determining the growth rate, in addition to the role played by the crystal orientation of the silicon wafer.

2.2.1.1 Dry Oxidation

During dry oxidation, the wafer is placed in a pure oxygen gas (O$_2$) environment and the chemical reaction which ensues is between the solid silicon atoms (Si) on the surface of the wafer and the approaching oxide gas

$$Si+O_{2} \rightarrow SiO_{2}.$$ (29)

Figure 2.7: Oxide thickness versus oxidation time for dry (O$_2$) oxidation of a (100) oriented silicon wafer under various temperatures.

Figure 2.7 shows the oxide thickness as a function of oxidation time for dry oxidation. It can be noted that the oxidation rate does not exceed $\sim$150nm$\slash$h, making it a relatively slow process which can be accurately controled in order to achieve a desired thickness. The oxide films resulting from a dry oxidation process have a better quality than those grown in a wet environment, which makes them more desirable when high quality oxides are needed. Dry oxidation is generally used to grow films not thicker than 100nm or as a second step in the growth of thicker films, after wet oxidation has already been used to obtain a desired thickness. The application of a second step is only meant to improve the quality of the thick oxide.

2.2.1.2 Wet Oxidation

During wet oxidation, the silicon wafer is placed into an atmosphere of water vapor (H$_2$O) and the ensuing chemical reaction is between the water vapor molecules and the solid silicon atoms (Si) on the surface of the wafer, with hydrogen gas (H$_2$) released as a byproduct

$$Si+2H_{2}O \rightarrow SiO_{2}+2H_{2(g)}.$$ (30)

Figure 2.8 shows the oxide thickness as a function of oxidation time for wet oxidation processing.

Figure 2.8: Oxide thickness versus oxidation time for wet (H$_2$O) oxidation of a (100) oriented silicon wafer under various temperatures.

It is evident that wet oxidation operates with much higher oxidation rates than dry oxidation, up to approximately 600nm/h. The reason is the ability of hydroxide (OH$^-$) to diffuse through the already-grown oxide much quicker than O$_2$, effectively widening the oxidation rate bottleneck when growing thick oxides, which is the diffusion of species. Due to the fast growth rate, wet oxidation is generally used where thick oxides are required, such as insulation and passivation layers, masking layers, and for blanket field oxides.

2.2.1.3 Temperature Effects

As the temperature in the oxidation environment is increased, the oxidation rate can increase significantly, both in wet and dry processes. The temperature dependence on the oxidation rate can be observed in Figure 2.7 and Figure 2.8 for dry and wet oxidation, respectively.

Figure 2.9: Oxide thickness versus process temperature for wet (H$_2$O) and dry (O$_2$) oxidation of a (100) oriented silicon wafer at 1000 $^\textrm {o}$C.

In Figure 2.9, the ratio between oxide thickness and temperature is visualized, suggesting the existence of an exponential relationship between the thickness ($x_o$) and inverse negative temperature

$$x_o \propto e^{-1/T}.$$ (31)

The dramatic increase in oxide thickness with increasing temperature is not surprising, since the diffusivity ($D$) of oxygen and water through the oxide depends greatly on temperature,

$$D \propto e^{-c/T},$$ (32)

where $c$ is a parameter independent of temperature $T$. Since the oxidant diffusivity increases exponentially with increasing temperature, so should the oxidation rates, because the diffusivity of oxidants is the rate-limiting step when thicker oxides ($\sim$30nm) are grown. A higher diffusivity rate means that more oxidants will be allowed to penetrate through the already grown oxide to reach the silicon surface.

2.2.1.4 Pressure Effects

The effect of hydrostatic pressure on thermally grown oxides in dry and wet environments is shown in Figure 2.10a and Figure 2.10b, respectively, while Figure 2.10c shows the direct relationship between the oxide thickness and the applied pressure. It is evident that increasing the pressure results in thicker oxides and a faster oxidation rate.

Figure 2.10: Effects of hydrostatic pressure on thermally grown oxide thickness for a (100) oriented silicon wafer in a) dry (O$_2$) and b) wet (H$_2$O) ambients.

(a) Dry oxidation	(b) Wet oxidation
(c) Effect of pressure

A logarithmic relationship appears to exist between the thickness of oxide grown and the applied pressure. The main advantage of increasing the pressure during oxidation is to achieve relatively fast oxidation rates at reduced temperatures [124], [179]. Reducing the processing temperature results in less impurities and minimal movement of the junction during multiple subsequent oxidation steps required for complex IC device manufacturing [125]. Oxides grown in a high pressure ambient have also been found to have significantly reduced stacking faults, leading to an improved device performance [98].

2.2.1.5 Crystal Orientation Effects

Multiple studies have shown that silicon is not oxidized at the same rate in each crystalline direction [122]. Therefore, the crystal orientation of the wafer plays a role in determining the oxide thickness, as can be seen in Figure 2.11. Oxide growth appears to be faster on (111) oriented silicon when compared to (100) oriented silicon. In fact, in [122] it is shown that the (111) and (100) orientations represent the upper and lower bound for oxidation rates, respectively. All other silicon orientations lie between these extrema.

Figure 2.11: Oxide thickness versus oxidation time for (100) and (111) oriented silicon by wet oxidation at various temperatures.

Ligenza [126] argued that the crystal orientation effect on the oxidation rate is due to the differences in the densities of silicon atoms on the various crystal faces. Since silicon atoms are required in order to generate the oxide, having a larger number of bondable Si atoms available on the (111) face meant that the oxide would grow faster in the (111) direction, as is observed experimentally.