52Handbook of Chemical Vapor Deposition
3.9Mass Transport
When the process is limited by mass-transport phenomena,the controlling factors are the diffusion rate of the reactant through the boundary layer and the diffusion out through this layer of the gaseous by-products. This usually happens when pressure and temperature are high. As a result, the gas velocity is low as was shown above, and the boundary layer is thicker making it more difficult for the reactants to reach the deposition surface. Furthermore, the decomposition reac-tion occurs more rapidly since the temperature is higher and any molecule that reaches the surface reacts instantly. The diffusion rate through the boundary layer then becomes the rate limiting step as shown in Fig. 2.8b.
3.10Control of Limiting Step
To summarize, the surface kinetics (or near surface kinet-ics) is the limiting step at lower temperature and diffusion is the rate limiting step at higher temperature. It is possible to switch from one rate-limiting step to the other by changing the tempera-ture. This is illustrated in Fig. 2.9, where the Arrhenius plot (logarithm of the deposition rate vs. the reciprocal temperature) is shown for several reactions leading to the deposition of silicon,
(b)
Figure 2.8.
(Cont’d.)
Fundamentals of CVD  53
using either SiH4, Sh2Cl2, SiHCl3, or SiCl4 as silicon sources in a hydrogen atmosphere.[15]
Figure 2.9. Arrhenius plot for silicon deposition using various precursors.
In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process a
nd the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased.
3.11Pressure as Rate-Limiting Factor
Pressure is similar to temperature as a rate limiting factor since the diffusibility of a gas is inversely related to its pressure. For instance, lowering the pressure 760 Torr (1 atm) to 1 Torr increases the gas-phase transfer of reactants to the deposition surface and the
54Handbook of Chemical Vapor Deposition
diffusion out of the by-products by more than 100 times. Clearly, at low pressure, the effect of mass-transfer variables is far less critical than at higher pressure.
However, the gain may not be as large if the overall pressure decrease is at the expense of the partial pressure of reactant gas, since the kinetic rate (for first-order reactions) is proportional to the partial pressure of the reactant. Reducing the pressure by reducing the flow of carrier gas (or elimina
ting altogether) is a good alternative and is usually beneficial. At low pressure, surface reaction is the rate determining step and the mass-transfer variables are far less critical than at atmospheric pressure.
It can be now seen that, by proper manipulation of the process parameters and reactor geometry, it is possible to control the reaction and the deposition to a great degree. This is illustrated by the following example. In the deposition of tungsten in a tube mentioned in Sec. 3.2 above, the gas velocity is essentially constant and the boundary layer gradually increases in thickness toward downstream.This means that the thickness of the deposit will decrease as the distance from the tube inlet increases, as shown in Fig. 2.10a. This thickness decrease can be offset and a more constant thickness obtained simply by tilting the susceptor, as shown in Fig. 2.10b. This increases the gas velocity due the flow constriction; the Reynolds number goes up; the boundary layer decreases and the deposition rate is more uniform.[14]
Figure 2.10. Control of deposition uniformity in a tubular reactor (a) susceptor parallel to gas flow, (b) titled susceptor.
(a)
Fundamentals of CVD  55
(b)
Figure 2.10. (Cont’d.)
3.12Mathematical Expressions of the Kinetics of CVD
The flow-dynamics and mass-transport processes can be expressed mathematically and realistic mo
dels obtained to be used in the predictions of a CVD operation and in the design of reactors.[16]–[18] These models are designed to define the complex entrance effects and convection phenomena that occur in a reactor and solve the complete equations of heat, mass balance, and momentum. They can be used to optimize the design parameters of a CVD reactor such as susceptor geometry, tilt angle, flow rates, and others. To obtain a complete and thorough analysis, these models should be complemented with experimental observations, such as the flow patterns mentioned above and in situ diagnostic, such as laser Raman spectroscopy.[19] 4.0GROWTH MECHANISM AND STRUCTURE OF
deposition
DEPOSIT
In the previous sections, it was shown how thermodynamic and kinetic considerations govern a CVD reaction. In this section, the nature of the deposit, i.e., its microstructure and how it is controlled by the deposition conditions, is examined.
56Handbook of Chemical Vapor Deposition
4.1Deposition Mechanism and Epitaxy
The manner in which a film is formed on a surface by CVD is still a matter of controversy and several theories have been advanced to describe the phenomena.[2]  A thermodynamic theory proposes that a solid nucleus is formed from supersaturated vapor as a result of the difference between the surface free energy and the bulk free energy of the nucleus. Another and newer theory is based on atomistic nucle-ation and combines chemical bonding of solid surfaces and statistical mechanics.[20] These theories are certainly valuable in themselves but considered outside the scope of this book.
There are, however, three important factors that control the nature and properties of the deposit to some degree which must be reviewed at this time: epitaxy, gas-phase precipitation, and thermal expansion.
4.2Epitaxy
The nature of the deposit and the rate of nucleation at the very beginning of the deposition are affected, among other factors, by the nature of the substrate. A specific case is that of epitaxy where the structure of the substrate essentially controls the structure of the deposit.[2][15][20] Epitaxy can be defined as the growth of a crystalline film on a crystalline substrate, with the substrate acting as a seed crystal. When both substrate and deposit are of the same material (for instance silicon on silico
n) or when their crystalline structures (lattice parameters) are identical or close, the phenomena is known as homoepitaxy. W hen t he l attice p arameters a re d ifferent, it is h eteroepitaxy. Epitaxial growth cannot occur if these structural differences are too great.
A schematic of epitaxial growth is shown in Fig. 2.11. As an example, it is possible to grow gallium arsenide epitaxially on silicon since the lattice parameters of the two materials are similar. On the other hand, deposition of indium phosphide on silicon is not possible since the lattice mismatch is 8%, which is too high. A solution is to use an intermediate buffer layer of gallium arsenide between the silicon and the indium phosphide. The lattice parameters of common semi-conductor materials are shown in Fig. 2.12.

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