zeus_the_almighty
Oct28-04, 05:54 AM
Hi Everybody,
Does anybody know how to solve, analytically or numerically, the following differential equation :
\frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2})
The unknown function is \Phi.
a and b are some strictly positive constants.
q\Phi is the energy band bending of a P-type substrate MOS capacitor versus the distance to the silicon dioxide/silicon interface.
Uth is the thermal voltage and BExp(-(\frac{x-x_{m}}{\sigma})^2}) the (non-uniform) dopant concentration in the substrate versus the distance to the silicon dioxide/silicon interface.
THANX.
Does anybody know how to solve, analytically or numerically, the following differential equation :
\frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2})
The unknown function is \Phi.
a and b are some strictly positive constants.
q\Phi is the energy band bending of a P-type substrate MOS capacitor versus the distance to the silicon dioxide/silicon interface.
Uth is the thermal voltage and BExp(-(\frac{x-x_{m}}{\sigma})^2}) the (non-uniform) dopant concentration in the substrate versus the distance to the silicon dioxide/silicon interface.
THANX.