2.1 Silicon Dioxide Properties

The growth of silicon dioxide is one of the most important processes in the fabrication of MOS transistors [175]. The attributes of SiO$_2$ which make it appealing for the semiconductor industry are [80,175]:

- It is easily deposited on various materials and grown thermally on silicon wafers.

- It is resistant to many chemicals used during the etching of other materials, while allowing itself to be selectively etched with certain chemicals or dry-etched with plasmas.

- It can be used as a blocking material for ion implantation or diffusion of many unwanted impurities.

- The interface between silicon and silicon dioxide has relatively few mechanical and electrical defects, although with newer technology nodes and reduced geometries, even slight defects must be addressed.

- It has a high dielectric strength and a relatively wide band gap, making it an excellent insulator.

- It has high a temperature stability of up to 1600 $^\textrm {o}$C, making it a useful material for process and device integration.

Table 2.1 shows some important properties of silicon dioxide [47]. It can be noted that oxides grown in a dry atmosphere have a higher density, which implies less impurities and a better quality oxide than when grown in a wet atmosphere. Thermal expansion refers to the oxide's volume expansion or shrinkage, when exposed to a range of temperatures. For oxides, the thermal expansion coefficient is very low, meaning it does not exert much stress and strain on other materials which are in contact with it. Young's modulus and Poisson's ratio measure the oxide's stiffness and its negative ratio of transverse to axial strain, respectively, which are important measures of a material's mechanical stability. The thermal conductivity, which varies for thin sputtered (1.1W$\slash$m-K), thin thermally grown (1.3W$\slash$m-K), and bulk (1.4W$\slash$m-K) oxides is an important parameter which affects power during operation [25]. It is also found that the thermal conductivity of oxides changes depending on the oxide thickness [25]. The high dielectric strength shows the stability of SiO$_2$ under high electric fields, suggesting that the oxide film is very suitable for dielectric isolation.

Table 2.1: Important properties of SiO$_2$ (silicon dioxide).

Crystal structure	Amorphous
Atomic weight	60.08g/mole
Density (thermal, dry/wet)	2.27/2.18g/cm$^{3}$
Molecules	2.3$\cdot$10$^{22}$/cm$^{3}$
Specific heat	1.0J/g-K
Melting point	1700 $^{\textrm {o}}$C
Thermal expansion coefficient	5.6$\cdot$10$^{-7}$/K
Young's modulus	6.6$\cdot$10$^{10}$N/m$^{2}$
Poisson's ratio	0.17
Thermal conductivity	1.1W/m-K - 1.4W/m-K
Relative dielectric constant	3.7 - 3.9
Dielectric strength	10$^{7}$V/cm
Energy bandgap	8.9eV
DC resistivity	$\simeq$10 $^{17}\Omega$cm

The silicon dioxide molecule can be described as a three-dimensional network of tetrahedra cells, with four oxygen atoms surrounding each silicon ion, shown in Figure 2.2a. The length of a Si-O bond is 0.162nm, while the normal distance between two oxide bonds is 0.262nm. The Si-Si bond distance depends on the SiO$_2$ arrangement, but is approximately 0.31nm and the bond angle O-Si-O is approximately 109 $^\textrm {o}$. The bond angle Si-O-Si is ideally approximately 145 $^\textrm {o}$, but it can vary between 100 $^\textrm {o}$ and 170 $^\textrm {o}$ with minimal change in bond energy. The tetrahedral form is the basic unit from which a SiO$_2$ structure is formed, even though SiO$_2$ can exist in a crystalline structure. The reason for the amorphous oxide structure is the absence of any crystalline form of SiO$_2$ whose lattice size closely matches the silicon lattice [175]. The tetrahedra bond together by sharing oxygen atoms as illustrated in Figure 2.2b in a sample six-membered ring.

Figure 2.2: (a) Structure of fused silica glass along with (b) a six-membered ring structure of SiO$_2$.

(a) Si-O bond structure	(b) Six-membered ring

From the above analysis, it can be concluded that, as the oxide grows, it consumes the silicon atoms at the surface of the wafer. This causes the silicon-silicon dioxide interface to move into the wafer while the oxide grows. The equation which governs the amount of consumed silicon is

$$X_{Si}=X_{SiO_2}\cdot \cfrac{N_{SiO_2}}{N_{Si}},$$ (27)

where $N_{SiO_2}$ is the molecular density of the oxide, $N_{Si}$ is the atomic density of the silicon wafer, and $X_{SiO_2}$ and $X_{Si}$ are represented in Figure 2.3. These values are known, resulting in the amount of silicon consumed with respect to the oxide thickness

$$X_{Si}=X_{SiO_{2}}\cdot\cfrac{2.3\times10^{22}molecules\slash cm^{3}}{5\times10^{22}atoms\slash cm^{3}}=0.46\, X_{SiO_2},$$ (28)

Therefore approximately 46% of the silicon dioxide which is grown on a silicon wafer is found within the bounds of the original silicon, while approximately 54% is new volume, which grows into the ambient. Figure 2.3 shows the location of the original silicon surface followed by the oxide-silicon and oxide-ambient interfaces after an oxidation step.

Figure 2.3: Moving interfaces and volume expansion after silicon oxidation.