[Tex/LaTex] Bracket size and sqrt problem

Question

How can I make the top line of the sqrt display correctly as well the last right bracket in appropriate size?

    \documentclass[a4paper,12pt]{article}
\begin{document}
\begin{equation}\label{eq:teh}
T (w,V_{bias},E)
\propto
\exp\left[{-2w
\enspace
\sqrt{
\frac{2m}{\hbar^2}
\left(
\frac{\phi_{tip}-\phi_{sample}}{2}
+
\frac{eV_{bias}}{2}
-
E
\right)
}}\right]
\end{equation}
\end{document}

Answer 1

I would not make the square bracket taller than the horizontal line produced by the \sqrt directive. To create a bit of whitespace between the end of the square root's horizontal bar and the closing ], insert a \, (thinspace) instruction immediately before the closing square bracket.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath} 
\begin{document}
\begin{equation}\label{eq:teh}
T (w,V_{\mathrm{bias}},E)
\propto \exp
\Biggl[
-2w
\,
\sqrt{
\frac{2m}{\hbar^2}
\biggl(
\frac{\phi_{\mathrm{tip}}-\phi_{\mathrm{sample}}}{2}
+ \frac{eV_{\mathrm{bias}}}{2}
- E
\biggr) 
}\, 
\Biggr]
\end{equation}
\end{document}