Surface kinetics control

Gypsum growth rates show a square law dependence on supersaturation with an activation energy of 64 kJ/mol. Growth appears to be surface kinetics controlled. 

There is a variety of fundamental physical and chemical principles lhat can control the deposition rate and quality of a film resulting from a CVD process. We briefly introduce them here, but refer the reader to Chapter 2 and other books on CVD for more detailed discussions. The basic processes underlying CVD can be subdivided into mass transport effects and chemical effects, each of which can occur in both the gas and solid phases. Chemical effects can be further subdivided into thermodynamic effects and kinetic effects. In some cases, a particular effect can be separated out as rate limiting, and a CVD process can be said to be mass-transport controlled or surface-kinetics controlled. In reality, transport and chemical reactions are closely coupled, with their relative importance varying with the details of the operating conditions. 

Numerous studies on the kinetics and mechanisms of CVD reactions have been made. These studies provide useful information such as activation energy and limiting steps of deposition reactions which are important for the understanding of deposition processes. The main problem in the CVD kinetics studies is the complexity of the deposition process. The difficulty arises not only from the various steps of the CVD process but also from the temperature and concentration gradient, geometric effects, and gas flow patterns in the reaction zones. Exact kinetic analysis is therefore usually not possible as the kinetic data are reactor dependent. There are several possible rate-limiting factors but mass transport and surface kinetics control are the most... 

When the observed deposition rate is lower than both the mass input rate into the reactor, and the mass transport rate present in the vapor phase in the reactor (to or from the substrate), a surface kinetic control pathway exists. Surface kinetic control is demanded for uniform coatings on odd-shaped substrates. 

Since mass transport in the vapor phase, or surface kinetics, usually control the deposition rate, most CVD discussions are limited to these two cases. Surface kinetic control normally is desirable and means a maximum in step coverage. In surface kinetic control, a fast diffusion in the vapor is combined with a slow surface reaction. For mass transport control, the surface kinetics are fast while the mass transport in the vapor phase is slow. 

The temperature region of surface kinetic control expands at lower pressures. Surface kinetics also can be attained by increasing the gas flow velocity. At low gas flow velocities, the deposition is fully thermodynamically controlled. A substantial increase of the gas flow will push the operation to enter the mass transport controlled regime. Finally, surface kinetic control is reached at yet still higher gas flow velocities. In ultra-high vacuum OMMBE processes the molecules entering the reactor from the source behave ballistically, i. e., they travel to the substrate without collisions either with other molecules or the reactor walls. This is termed the molecular flow regime. In this unique case, neither convection, either forced or natural, nor diffusion, plays a role in... 

The fourth possibility to reach the surface kinetically controlled region is to use different precursors possessing higher thermochemical stabilities. For example, the movement to higher substrate temperatures in ALE may demand more thermally robust compounds as vapor phase sources. 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

Students of professor R. G. Anthony at College Station, TX used a mechanism identical (by chance) to that in UCKRON for derivation of the kinetics. Yet they assumed a model in which the surface reaction controls, and had two temperature dependent terms in the denominator as 13,723 and 18,3 16 cal/mol. Multiplying both the numerator and the denominator with exp(-15,000) would come close to the Ea,/R about 15,000 cal/mol, with a negative sign, and a denominator similar to that in the previously discussed models. 

Figures 1.27a to d show how the Evans diagram can be used to illustrate how the rate may be controlled by either the polarisation of one or both of the partial reactions (cathodic, anodic or mixed control) constituting corrosion reaction, or by the resistivity of the solution or films on the metal surface (resistance control). Figures 1. lie and/illustrate how kinetic factors may be more significant than the thermodynamic tendency ( , u) and how provides no information on the corrosion rate.

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

Two general models can describe the kinetics of adsorption. The first involves fast adsorption with mass transport control, while the other involves kinetic control of die system. Under the latter (and Langmuirian) conditions, the surface coverage of tlie adsorbate at time t, Tt, is given by. 

Figure 2.8. Rate-limiting steps in a CVD reaction (a) surface reaction kinetics control, (b) diffusion control.

Pressure controls the thickness of the boundary layer and consequently the degree of diffusion as was shown above. By operating at low pressure, the diffusion process can be minimized and surface kinetics becomes rate controlling. Under these conditions, deposited structures tend to be fine-grained, which is usually a desirable condition (Fig. 2.13c). Fine-grained structures can also be obtained at low temperature and high supersaturation as well as low pressure. 

In general, a preparation of mixed monolayer can be realized by either a kinetic control or a thermodynamic control (Figure 1, left). Kinetic control is based on a suggestion that for an initial deposition step the desorption rate is ignorable in comparison with the adsorption rate. In this case, the concentration ratio of the adsorbed species A and B on the surface corresponds to the ratio of products of their adsorption rate constant ( a or b) and concentration (Ca or Cb) A aCa/A bC b. The validity of the initial assumption on low desorption rate means that the total surface coverage obtained under kinetic control is essentially lower than 100%. This non-complete coverage does not disturb most of optical applications of the... 

If we assume that t0= 10 13 s (vibrational frequency)-1, then for a heat of adsorption AH of 40 kJ mol-1 and a surface temperature of 295 K the residence time zsurf is 3 x 10-6 s and for 80 kJ mol-1 it is 102 s as T decreases the value of the surface residence time increases rapidly for a given value of AH. Decreasing the temperature is one possible approach to simulating a high-pressure study in that surface coverage increases in both cases the reaction, however, must not be kinetically controlled. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

A more detailed picture of the temperature dependence of the growth is given in Figure 2.4, where the island density is plotted as a function of temperature. It can be seen that only in the temperature range from 207 to 288 K the growth is perfectly template controlled and the number of islands matches the number of available nucleation sites. This illustrates the importance of kinetic control for the creation of ordered model catalysts by a template-controlled process. Obviously, there has to be a subtle balance between the adatom mobility on the surface and the density of template sites (traps) to allow a template-controlled growth. We will show more examples of this phenomenon below. 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

---