root/trunk/matml/transport/problems/cvdreact/cvdreact-solution.tex

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\item Chemical vapor deposition reactor design

  \begin{enumerate}
  \item The streamlines should have looked something like:
    \begin{center}
      \PSbox{cvdcylines.ps}{200pt}{90pt}
    \end{center}

  \item The problem given was to make the deposition more uniform from wafer to
    wafer, but not necessarily across each wafer.  Based on this, several
    people suggested simply rotating the wafers so the gas would blow across
    them, which would make each wafer the same but would not help uniformity
    across the wafer.  Likewise, a couple of people suggested blowing the gas
    faster, which would lead to more uniform concentration from wafer to wafer
    but higher concentration of the depositing gas species in the outflowing
    gas (based on the plug flow equation), though the improved quality could
    well be worth the extra cost.

    One design change which would help both inter- and intra-wafer uniformity
    is to lower the temperature, increasing the probability of reaction
    limitation, which would promote very uniform deposition.  Unfortunately, it
    would also be very slow.  So this illustrates the various cost vs. quality
    tradeoffs which can be made in this type of design problem.

    My favorite student answer to this problem was called ``Rotisserie CVD,''
    which had the wafers hanging on a rotating scaffold to periodically expose
    each to more and less concentrated gas.  That might work in principle,
    though having a lot of moving parts in this environment could complicate
    matters...
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