According to the periodic table trend for I.E. Silicon should have a higher 2nd ionization energy than Aluminum so I'm confused.
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Let us look at the electronic configurations of aluminum and silicon and their respective cations.
$\ce{Al}: [\ce{Ne}]\mathrm{3s^2\, 3p^1}$
$\ce{Si}: [\ce{Ne}]\mathrm{3s^2\, 3p^2}$
$\ce{Al^2+}: [\ce{Ne}]\mathrm{3s^1}$ It involves removing from $\mathrm{3s}$ sub shell
$\ce{Si^2+}: [\ce{Ne}]\mathrm{3s^2}$ It involves removing from $\mathrm{3p}$ sub shell
A $\mathrm{3p^1}$ electron has lower binding energy than that of $\mathrm{3s^2}$ electron.
It is due to more screening effect (as the predecessor sub-shells are higher in $\ce{Si}$) and higher stability attained by having a completely filled $\mathrm{3s}$ sub-shell
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1$\begingroup$ Hi and welcome to chemistry.stackexchange.com. Feel free to take a tour of the site. I edited your post to include the
\ce{...}and the\mathrm{...}syntaxes for MathJax. Learn more about them in the help center or this collection of editing hints. Nice first answer. $\endgroup$– JanJan 25 '16 at 13:52