root/trunk/matml/transport/problems/cvd/cvd.tex

\documentclass{article}
\usepackage{fullpage}
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\begin{document}
\begin{enumerate}
\item Chemical vapor deposition

  \begin{center}
    \input{cvdbox}
  \end{center}
  
  A CVD reactor, pictured above, pases a dilute mixture of silane gas (SiH$_4$)
  in argon over heated substrates to deposit a layer of silicon.  The screen at
  the entrance distributes the flow evenly over the entrance, so the velocity
  profile there is uniform.  Assume the deposition is diffusion-limited, so the
  equilibrium SiH$_4$ concentration at the substrates is zero, and ignore
  exit conditions and natural convection instabilities (due to the placement of
  hot substrates below the cooler gas).

  Data:
  \begin{itemize}
  \item chamber dimensions: 0.75m high $\times$ 2m wide $\times$ 2m long
  \item argon viscosity $\rm\eta=3\times10^{-5}\frac{N\cdot s}{m^2}$
  \item silane diffusivity in argon $D_{\rm SiH_4}=2\times10^{-4}\frac{\rm
      m^2}{\rm s}$
  \item silicon density $\rm\rho_{Si}=2500\frac{kg}{m^3}$
  \end{itemize}

  \begin{enumerate}
  \item Calculate the mass transfer Prandtl number in the (mostly argon) gas at
    an operating temperature of 500K and pressure of 0.1 atm (you may need the
    ideal gas law for the argon density).

  \item Given a flow rate of $0.3\rm\frac{m^3}{s}$, calculate the Reynolds
    number Re$_H$.  Is the flow likely to be laminar or turbulent?

  \item Treating the entire bottom of the chamber as a substrate, sketch the
    velocity and concentration boundary layers over the region as accurately as
    you can.

  \item Using a concentration of 1 mol\% silane in the gas, calculate the
    diffusive flux of silane to the substrates at distances of 10 cm and 30 cm
    from the entrance.

  \item Calculate the deposition rate in $\rm\frac{nm}{sec}$ at a location 10
    cm from the entrance, and another 30 cm from the entrance.  If a wafer is
    placed near the entrance, how uniform will the deposited layer be
    (qualitatively)?

  \item How would you change the design to make the deposited layer more
    uniform?
  \end{enumerate}
\end{enumerate}
\end{document}