I think that it would be conceptually clearer to present the n(E) and p(E) mouseover data in the form of n(E) @ E and p(E) @ E instead of E @ n(E).

My reasoning is that n(E) and p(E) (as well as f(E) and g(E)) are all FUNCTIONS of E. We generally graph functions as dependent variable on the y-axis and independent variable on the x-axis, but in the case of band diagrams E is the independent variable and is plotted on the y- axis. This does not change the dependency relationship between the quantities plotted, and for my students the interpretation would probably be simpler if the mouse-over values were given in the order I suggest: Dependent variable value @ independent variable value.

I think this would be a quick and easy fix, just a rearranging of the script to display the two values.

Also, change e to E for the power of 10, and remove the [ ] brackets around the energy units.
Is there a way to simplify the units for the density? can superscripts be used? [eV cm3] (sup) -1 or
/[eV cm3] instead of /eV/cm3, which is hard to interpret unless you already know what the units are.

For example, show:
Electrons T = 300K
6.2794 E 14 /[eV cm3] @ 1.1858 eV

instead of

Electrons T = 300K
1.1858[eV] @ 6.27943e+14/eV/cm3