2.4.1 Chemical Vapor Deposition

One of the most effective methods to deposit material in microelectronics is to use a chemical reaction at the surface and of the underlying materials by reactant diffusion into the target material. This method is called chemical vapor deposition (CVD) and requires the underlying materials to act as catalytic materials. If a material does not, that material should at least do not react with the deposited material. However, some materials do not provide one of these mandatory requirements and therefore demand an additional barrier or seed layer, which provides the needed properties to both material layers.

Figure 2.14: Deposition rate as a function of temperature.

The type of the deposition can be classified into three major categories: a mass transport limited regime, a surface reaction limited regime, and a reactant concentration limited regime. As Figure 2.14 and Figure 2.15 depict, the mass transport and the surface reaction are influenced by the temperature, where all three limitations depend on the geometry. These regimes have different constraining factors which reduce the maximum deposition rate and thus the growth rate of the material in the reactor [127,25,165].

• In the mass transport limited regime, the maximal support of masses is given by the chemical reactor and constrained by the external settings of the reactor; for instance the gas flux density is set by the engineers to control the growth rate in the reactor and the constellation between the reactor size, the set pressure, and the flux through the reactor determine the mass supported by the particular reactor system.
• In the surface reaction limited regime enough reactants are available but the reaction at the surface (and sometimes in the bulk) is limited mostly by the temperature or the available catalytic particles, for instance elements at the surface area. Hence, the amount of reaction which can be performed is decreased either due to decreasing reaction coefficients [24] or by the surface area on which the reaction can take place [127].
  
• The reactant concentration limited regime has to be considered if the shape of the surface changes the gas fluxes, for instance inside deep trenches. In that case, the gas exchange can only be performed at regions close to the surface. Hence, in deeper regions of the trench a depletion of active reactants can be observed which yields exponentially decreasing reaction rates. However, the impact of this effect can be reduced if the deposition is performed at lower pressures (LPCVD). In that case, the by-products of the reaction in the trench have to be considered because they cannot be easily transported from the surface to the exit of the reactor. Therefore, they cause a considerable decrease of the growth rate due to collisions of the by-products with active reactants coming form the material source.

Figure 2.15: Sticking probability as a function of the aspect ratio.

Once the materials are deposited, the possibilities to change the microstructure of the material are very limited because the internal material structure has mainly been defined by the deposition process. However, there are different methods, e.g. rapid thermal annealing (RTA) [127], dopant implantations [166,167], and mechanical and chemical methods like CMP (chemo-mechanical polishing) [168,169,170], which can slightly modify the microstructure. However, all these a-posteriori methods affect the regions at the surface or a limited region underneath the surface of the material only. For instance, if the ${\mathrm{Si}}$ surface is oxidized by O$_2$ or H$_2$ O to obtain $\mathrm{SiO_2}$ , the corresponding chemical reactions use ${\mathrm{Si}}$ from the surface. Therefore, the thickness of the ${\mathrm{Si}}$ layer is reduced, which is often not desired for certain applications [25]. Hence, for this case, the material has to come from an external gas source to preserve the previous deposited layers. However, these chemical reactions follow mostly complex pyrolytically reactions and produce a lot of highly reactive byproducts [171].

Huge efforts have been made to describe the result of the material deposition in advance. However, due to the different and highly complex chemical reactions inside a reactor, the predictability is still limited. Several approaches have been proposed to deal with these problems. There are two main approaches for the simulation of material deposition. One approach is cell-based [167,172] and has been introduced to describe etching of ${\mathrm{Si}}$ and the deposition of Tungsten and Silicon [172]. For the ${\mathrm{Si}}$ deposition, a CVD process of Silan has been considered in [173,172]. Since the description for two and three-dimensional structures increases in complexity and memory consumption, a level-set approach has been proposed as a second approach [174,175], which is presented in Chapter 5.