Question

(Regarding chemical vapour deposition)

Describe the dependency of reaction limited deposition rate in relation to free energy change in a reaction. State the relevant equation which shows these dependencies.

Answer 1

In this solution some basic concepts of Chemical - Thermodynamics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.

4.1 Introduction Thermodynamic studies of a CVD process are undertaken to provide a basic understanding of chemical reactions under equilibrium conditions. To ensure a high quality of a CVD coating it is essential to determine the feasibility of a particular CVD reaction first, then select the suitable precursors for the CVD processes. CVD phase diagrams are derived based on the minimisation of Gibbs free energy and are useful in predicting theequilibrium phases present in the chemical reaction system under given processing conditions determined by the deposition temperature, pressure and reactant concentration. A CVD process is also a non-equilibrium process and typically consists of complex chemical reactions. The kinetics of a CVD system involves many steps which determine the rate of the deposition process. Among them, three important steps are: (1) homogeneous reactions taking place among the gases in a reaction chamber, (2) heterogeneous reactions occurring on the surface of a substrate and (3) mass transportation of the gaseous precursors. The overall deposition rate of the CVD process is limited by the slowest step in the three aforementioned steps. This chapter covers these topics and gives details on these processes.

Thermodynamics of Chemical Vapour Deposition 4.2.1 Chemical Reaction Feasibility When a CVD system is proposed for consideration, the first task is to evaluate the feasibility of its underlying chemical reaction. If this reaction is infeasible, an alternative system should be selected and considered. This feasibility can be determined by calculating the Gibbs free energy, AGr, of the reaction under given conditions. A negative AG, implies that the reaction may occur, whereas a positive AGr indicates that the reaction would not take place. If several possible reactions are proposed and all are thermodynamically feasible, the reaction with the most negative AGr should be ideally selected since it leads to the most stable products. The next selection is to determine the other processing parameters, such as depositing temperature, pressure, concentration and so forth In order to calculate the Gibbs free energy of a chemical reaction, it is necessary to work out the Gibbs free energy of each reactant and product. The Gibbs free energy AG(T) for a given species can be calculated using the following equation [1]

298 P where (298) is the enthalpy of formation, AS0 (298) is standard entropy and Cp(T) is the heat capacity The heat capacity of a gas has a close relationship with the temperature, and the expression is given by [2] с,-@tbT+cT-+dT 2 (kJ.mol-l,K-ı) (4.2) where a, b, c and d are four different constants. These coefficient values for some ses are listed in Table 4.1,

Table 4.1. Data for the heat capacity of some gaseous species [2] Substance SiH4 SiH Cl SiHCl, SiCl4 SiC, 5x10 68.23 36.91 20.77 4.80 1.68 1.37 8.48 dx106 0.989 1.546 1.488 1.345 -0.531 0.0438 0.217 CX10 34.39 68.77 86.18 103.91 56.80 28.00 24.43 17.79 -9.73 5.51 1.43 -0.515 0.927 1.445 HCl

The thermodynamic data (G, Cp, S, H) for a number of substances are available from some standard sources such as JANAF tables. Entropy and heat capacity are relatively accurate because they can be calculated theoretically and measured by experiments. By contrast, the standard enthalpies of formation are less well known and sometimes must be estimated. When the free energy of al species is known, the Gibbs free energy of chemical reaction, AG, can be calculated from the following expression [3]: ΔGr Σ Gf (products)--SAG, (reactants) (4.3) For a given chemical reaction, the equilibrium constant Kr is related to the Gibbs free energy (AG) by the following expression: AG RT (4.4) where R and T are the perfect gas constant and temperature respectively. With the equilibrium constant (KT) of a chemical reaction the partial pressure of each reactant and product can be calculated. The partial pressures of the gaseous species involved in a reaction in equilibrium conditions are related to KT by the law

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