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2.2.1 Balance Equations

By applying the divergence operator to eqn. (2.3)

$\displaystyle \ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}... ...athrm{\nabla}}}}\ensuremath{\times}\ensuremath{\boldsymbol{\mathrm{H}}}}\bigr)}$ $\displaystyle = \ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}... ...ath{\cdot}\ensuremath{\partial_{t} \, \ensuremath{\boldsymbol{\mathrm{D}}}}}\ ,$ (2.16)
0 $\displaystyle = \ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}... ...l{\mathrm{\nabla}}}}\ensuremath{\cdot}\ensuremath{\boldsymbol{\mathrm{D}}}}}\ ,$ (2.17)

and using eqn. (2.4) a continuity equation for the conduction current density is formed

$\displaystyle \boxed{\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\n... ...suremath{\boldsymbol{\mathrm{J}}}}+ \ensuremath{\partial_{t} \, \varrho}= 0}\ .$ (2.18)

This result states that the sources and sinks of the conduction current density are compensated by the time variation of the space charge density.


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M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF