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}

Answer 2

After some vertical and horizontal correction (we are cheating that the square root is a bit higher):

\documentclass[a4paper,12pt]{article}
\begin{document}
\begin{equation}\label{eq:teh}
T (w,V_{\mathrm{bias}},E)
\propto
\exp\left[{-2w
\enspace
\sqrt{
\frac{2m}{\hbar^2}
\left(
\frac{\phi_{\mathrm{tip}}-\phi_{\mathrm{sample}}}{2}
+
\frac{eV_{\mathrm{bias}}}{2}
-
E
\right)
}}^{\rule{0mm}{2mm}}\,\right] %as much height as you need - PS
\end{equation}
\end{document}

Answer 3

Why not a simplebmatrix environment instead of a \left[ … \right] pair? The top of the brackets is exactly at the height of the horizontal line of the square root symbol?

\documentclass[a4paper,12pt]{article}

\usepackage{mathtools}%

 \begin{document}

\begin{equation}\label{eq:teh}
  T (w,V_\text{bias},E)
  \propto
  \exp \begin{bmatrix}
  {-2w
    \enspace
    √{
      \frac{2m}{\hbar²}
      \left(
      \frac{\phi_\text{tip}-\phi_\text{sample}}{2}
      +
      \frac{eV_\text{bias}}{2}
      -
      E
      \right)
      }\:}
  \end{bmatrix}
\end{equation}

\end{document} 

Answer 4

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath} 
\begin{document}
    \begin{equation}\label{eq:teh}\delimitershortfall=-1pt
    T (w,V_{\mathrm{bias}},E)
    \propto \exp
    \left[
    -2w
    \,
    \sqrt{
        \frac{2m}{\hbar^2}
        \left(
        \frac{\phi_{\mathrm{tip}}-\phi_{\mathrm{sample}}}{2}
        + \frac{eV_{\mathrm{bias}}}{2}
        - E
        \right) 
    }\, 
    \right]
    \end{equation}
\end{document}