- #1
zeus_the_almighty
- 7
- 0
Hi Everybody,
Does anybody know how to solve, analytically or numerically, the following differential equation :
[tex] \frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2})[/tex]
The unknown function is [tex]\Phi[/tex].
a and b are some strictly positive constants.
q[tex]\Phi[/tex] 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 [tex]BExp(-(\frac{x-x_{m}}{\sigma})^2})[/tex] 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 :
[tex] \frac{d^2\Phi}{dx^2}-a.Sinh(\frac{\Phi}{U_{th}})=-b.Exp(-(\frac{x-x_{m}}{\sigma})^2})[/tex]
The unknown function is [tex]\Phi[/tex].
a and b are some strictly positive constants.
q[tex]\Phi[/tex] 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 [tex]BExp(-(\frac{x-x_{m}}{\sigma})^2})[/tex] the (non-uniform) dopant concentration in the substrate versus the distance to the silicon dioxide/silicon interface.
THANX.