PN diode example (1D)

This is an example of a diode. The value of its built-in voltage that is numerically found is compared to an value solved analytically.

Setting constants and equations

set eps [expr 11.8 * 8.854e-14 / 1.619e-19]
term name=qfn add eqn = "DevPsi - 0.025*log(Elec/1.0e10)"
term name=qfp add eqn = "0.025*log(Hole/1.0e10) + DevPsi" 

set Emob 200.0; 
set Hmob 100.0; 

set eqnP "$eps * grad(DevPsi) + Doping - Elec + Hole"
set eqnE "ddt(Elec) - $Emob * 0.025 * sgrad(Elec, DevPsi/0.025)"
set eqnH "ddt(Hole) - $Hmob * 0.025 * sgrad(Hole, -DevPsi/0.025)"