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The drift-diffusion current relations can, amongst
others, be derived from the Boltzmann transport
equation by the method of moments [33] or
from basic principles of irreversible thermodynamics [75]. The
electron and hole current densities are given by
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![$\displaystyle \mathbf{J}_n = \mathrm{q}\cdot\mu_n\cdot n\cdot\left(\mathrm{grad...
...\cdot\mathrm{grad}\left(\frac{n\cdot T_{{\mathrm{L}}}}{N_{C,0}}\right) \right),$](img190.gif) |
(3.4) |
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![$\displaystyle \mathbf{J}_p = \mathrm{q}\cdot\mu_p\cdot p\cdot\left(\mathrm{grad...
...\cdot\mathrm{grad}\left(\frac{p\cdot T_{{\mathrm{L}}}}{N_{V,0}}\right) \right).$](img191.gif) |
(3.5) |
These current relations account for position-dependent
band edge energies,
and
, and for position-dependent effective masses,
which are included in the effective density of states,
and
. The
index
indicates that
and
are evaluated at some (arbitrary)
reference temperature,
, which is constant in real space
regardless of what the local values of the lattice and carrier temperatures
are.
Vassil Palankovski
2001-02-28