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By definition the potential
fulfills
![$\displaystyle {\mathbf{E}} = -\nabla V .$](img28.png) |
(2.7) |
By Maxwell's equations we have
![$\displaystyle {\mathbf{D}} = \varepsilon \varepsilon_0 {\mathbf{E}} .$](img29.png) |
(2.8) |
and
Here
is the electrical permittivity of free
space and
the dimensionless dielectric constant
is a material
dependent parameter.
In our case the charge density
is given by
![$\displaystyle \rho = q(M_0 - C) ,$](img33.png) |
(2.10) |
with
the (negative) elementary charge,
the
zeroth moment, that is, the particle density, and
the net doping.
Previous: 2.1.1 The Boltzmann Equation
Up: 2.1 The Boltzmann Poisson
Next: 2.1.3 Dimensional Reduction
R. Kosik: Numerical Challenges on the Road to NanoTCAD