In the chemical vapor deposition of silane (SiH4) on a silicon wafer, a process gas stream rich in an inert nitrogen (N2) carrier gas has the following composition: ySIH4 = 0.0075, yH2 = 0.015, yN2 = 0.9775 The gas mixture is maintained at 900 K and 100 Pa total system pressure. Determine the

Question

In the chemical vapor deposition of silane [latex]\left(\mathrm{SiH}_{4}\right)[/latex] on a silicon wafer, a process gas stream rich in an inert nitrogen [latex]\left(\mathrm{N}_{2}\right)[/latex] carrier gas has the following composition:

[latex]y_{\mathrm{SIH}_{4}}=0.0075, \quad y_{\mathrm{H}_{2}}=0.015, \quad y_{\mathrm{N}_{2}}=0.9775[/latex]

The gas mixture is maintained at 900 K and 100 Pa total system pressure. Determine the diffusivity of silane through the gas mixture. The Lennard–Jones constants for silane are [latex]\varepsilon_{A} / \kappa=207.6 \mathrm{~K}[/latex] and [latex]\sigma_{A}=4.08 Å[/latex]

Accepted Answer

The binary diffusion coefficients at 900 K and 100 Pa total system pressure estimated by the Hirschfelder equation (24-33) are

[latex]D_{A B}=\frac{0.001858 T^{3 / 2}\left[\frac{1}{M_{A}}+\frac{1}{M_{B}} ight]^{1 / 2}}{P \sigma_{A B}^{2} \Omega_{D}}[/latex] (24-33)

[latex]D_{\mathrm{SiH}_{4}-\mathrm{N}_{2}}=1.09 imes 10^{3} \mathrm{~cm}^{2} / \mathrm{s} \quad ext { and } \quad D_{\mathrm{SiH}_{4}-\mathrm{H}_{2}}=4.06 imes 10^{3} \mathrm{~cm}^{2} / \mathrm{s}[/latex]

The binary diffusion coefficients are relatively high because the temperature is high and the total system pressure is low. The composition of nitrogen and hydrogen on a silane-free basis are

[latex]y_{N_{2}}^{\prime}=\frac{0.9775}{1-0.0075}=0.9849 \quad ext { and } \quad y_{H_{2}}^{\prime}=\frac{0.015}{1-0.0075}=0.0151[/latex]

Upon substituting these values into the Wilke equation (24-49), we obtain

[latex]D_{1- ext { mixture }}=\frac{1}{y_{2}^{\prime} / D_{1-2}+y_{3}^{\prime} / D_{1-3}+\cdots+y_{n}^{\prime} / D_{1-n}}[/latex] (24-49)

[latex]D_{\mathrm{SiH}_{4} ext {-mixture }}=\frac{1}{\frac{y_{\mathrm{N}_{2}}^{\prime}}{D_{\mathrm{SiH}_{4}-\mathrm{N}_{2}}}+\frac{y_{\mathrm{H}_{2}}^{\prime}}{D_{\mathrm{SiH}_{4}-\mathrm{H}_{2}}}}=\frac{1}{\frac{0.9849}{1.09 imes 10^{3}}+\frac{0.0151}{4.06 imes 10^{3}}}=1.10 imes 10^{3} \frac{\mathrm{cm}^{2}}{\mathrm{~s}}[/latex]

This example verifies that for a dilute multicomponent gas mixture, the diffusion coefficient of the diffusing species in the gas mixture is approximated by the binary diffusion coefficient of the diffusing species in the carrier gas.

Question 24.4: In the chemical vapor deposition of silane (SiH4) on a silic...

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