PN junction: some interesting plots.

Here some plots related to the pn junction we are exploring (for which the total band bending is 0.6 eV...). You can explore this kind of thing as well with Wolfram Alpha. One of the tricks is to strip equations down to their bare essentials to make it easier for W-A to give you what you want. For example, for the 10^17 symmetric junction the band shifts by 0.3 eV on each side, hence the equation 1+.3*(x+1)^2 for E_c(x) (the conduction band edge energy). (In all the plots x_d is scaled to 1, so they all need to be rescaled to correct that.)  In the 2nd plot, for n(x), for the vertical scale, 1 corresponds to 10^17 and the plot shows how n decreases with x. The 12 in the exponential represents 0.3 eV divided by .025 eV (which is unit-less). The third plot shows the charge density vs x (with a simplified vertical scale, i.e., multiply by 1.6*10^-2 to get coulombs). In each plot a 1 on the x axis corresponds to x_d.

This last one shows, I think, the x dependence of the drift current. With x-d set to 1,  (x+1) is proportional to the electric field. The exponential term is proportional to the density of electrons in the conduction band, n(x).