Applet: A graphical illustration of the formation of a PN junction diode and its band diagram.  It shows both the band diagram and a schematic cross-section of the device as the junction approaches its thermal equilibrium. 

See also the non applet: Energy Diagrams of p-type and n-type semiconductors

and the two non applet graphs of carrier concentration vs.electron energy: linear plot and logarithmic plot

Barrier height        V_BH = (kT/q) ln(N_aN_d/n_i²)   { "built-in voltage" }
 
Overview slide (source)

 
Applet: PN junction diode, space charge profile and electric field which shows a cross-section of the sample, space charge and the electric field in depletion layer 

 
Points to note: (see Math. Analysis) about the depletion width

Note how the electric field varies with position in the depletion layer.

•   x_n N_d = x_p N_a    {  q A x_n N_d = q Ax_p N_a charge-equality condition}

Applet: Space charge and electric field in biased PN junction.

Note, in particular, how depletion layer stretches with increasing back bias.

Applet: Biased PN Junction: band diagram, diffusion and drift currents, etc.  It shows both the energy band under bias and the animated carriers flowing across the junction.

Note, in particular, the importance of accounting for the recombination of carriers.

See also the non applet: Energy diagrams of biased pn homojunctions

Applet: Current flow in forward-biased pn junction  An applet that shows an animated flow of carriers in a simplified band model.