Question 14.7: Production of high-purity silicon, as well as growth of sili...

The reaction of interest can be written as:

SiH_2Cl_2(g) → Si(s) + 2HCl(g)

The equilibrium constant as a function of temperature will be the same for all parts of the problem, so we compute it first. Note that the NIST Chemistry  WebBook adopts the convention that enthalpies of formation are zero for elements in their standard state at 298.15 K, but uses absolute (third-law) values of entropy. Thus, the Gibbs energy of formation not zero for elements in their standard states at 298.15 K. The polynomial used for the temperature dependence of heat capacity also differs from the one we have been using. Fortunately, the NIST WebBook directly provides values of −(G° − H^{°}_{f,298})∕T, which we use along with H^{°}_{f,298})∕T for each species to find G° of each species at several temperatures, as shown in the accompanying table. We then compute \Delta G^{\circ}=2 G^{\circ}(\mathrm{HCl})+G^{\circ}(\mathrm{Si})-G^{\circ}\left(\mathrm{SiH}_2 \mathrm{Cl}_2\right) \text { and } K=\exp \left(-\Delta G^{\circ} /(R T)\right) \text {, } , as also given in the table.

We can now use these values of the equilibrium constant to analyze each of the cases given.

(a) On a basis of 1 mole of SiH_2Cl_2, the gas-phase mole fractions in this case are:

y_{\mathrm{SiH}_2 \mathrm{Cl}_2}=\frac{1-\varepsilon}{1+\varepsilon} \quad \text { and } \quad y_{\mathrm{HCl}}=\frac{2 \varepsilon}{1+\varepsilon}

Note that the solid silicon does not play a role in the gas-phase mole fractions. Moreover, in the general equilibrium expression of Eq. (14.10),

\prod_i\left(\hat{f}_i / f_i^0\right)^{\nu_i}=K     (14.10)

the ratio \hat{f}_i / f_i^0 for pure solid silicon can be taken to be 1.0. The effect of pressure on the fugacity of a solid is negligible, and the standard state for silicon is the pure solid. Thus, it simply does not appear in the equilibrium expression, which assuming that dichlorosilane and HCl are in their ideal-gas state, is simply:

\frac{y_{\mathrm{HCl}}^2}{y_{\mathrm{SiH}_2 \mathrm{Cl}_2}}=K\left(\frac{P^{\circ}}{P}\right)

Using the expressions for the mole fractions:

\frac{4 \varepsilon^2}{(1-\varepsilon)(1+\varepsilon)}=K\left(\frac{P^{\circ}}{P}\right)

From which:

\left(4+K\left(\frac{P^{\circ}}{P}\right)\right) \varepsilon^2=K\left(\frac{P^{\circ}}{P}\right)

And finally:

\varepsilon=\sqrt{^{K\left(\frac{P^{\circ}}{P}\right)} /\left(4+K\left(\frac{P^{\circ}}{P}\right)\right)}=\sqrt{K /(20+K)}

Evaluating this for temperatures from 700 to 1300 K using the corresponding values of equilibrium constant gives the values shown in the following table and in Fig. 14.5.

(b) This is the same as part (a) except with P°/P = 1 instead of P°/P = 1/5, so:

\varepsilon=\sqrt{^{K }/(4+K)}

Results of this expression are shown later in tabular form and plotted in Fig. 14.5.

(c) Here, if we again take 1 mol SiH2Cl2 as our basis, so the extent of reaction is equal to the fraction of dichlorosilane converted to silicon, we also have 19 mol H_2 and the expressions for the mole fractions become:

y_{\mathrm{SiH}_2 \mathrm{Cl}_2}=\frac{1-\varepsilon}{20+\varepsilon} \quad \text { and } \quad y_{\mathrm{HCl}}=\frac{2 \varepsilon}{20+\varepsilon}

Using these expressions for the mole fractions at a pressure of 1 bar:

\frac{4 \varepsilon^2}{(1-\varepsilon)(20+\varepsilon)}=K

And finally:

E=\frac{-19 K+\sqrt{361 K^2+80 K(4+K)}}{2(4+K)}

We have picked the positive sign in the quadratic formula to obtain a positive value of ε. Again, results are shown in the table and in Fig. 14.5.

(d ) This is the same as part (a) except with P°/P = 1000 instead of P°/P = 1/5, so:

\varepsilon=\sqrt{^{1000 K} /(4+1000 K)}

Again, results are presented in the table below and in Fig. 14.5.

This problem illustrates the effect of reduced pressure and dilution on increasing the conversion of this type of reaction at a given temperature. In reality, formation of additional products— including \mathrm{H}_2, \mathrm{SiHCl}_3 \text {, and } \mathrm{SiCl}_4 should be considered under many conditions of relevance to silicon refining. Indeed, SiCl_4 is a major byproduct of solar-grade silicon production.

ε, Fractional Conversion of SiH_2Cl_2 to Si in Ex. 14.7