By Chambadal L., Ovaert J.-L.
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Extra info for Cours de mathematiques. Analyse II
Within a momentum expansion of Boltzmann’s transport equations, the charge conservation represents only the lowest order contribution. The hydrodynamic and energy balance models include diﬀerential equations describing the conservation of momentum and energy [5, 6]. From this system of equations, the drift-diﬀusion equations can be obtained by assuming constant and equal temperatures for electrons, holes, and the crystal lattice. The thermodynamic model applies principles of irreversible thermodynamics and linear transport theory to derive a system of equations describing carrier concentrations as well as carrier and lattice temperatures [9, 11].
In other words, only for one inhomogeneous broadening and one association between theoretical and experimental densities can a very good match be achieved. The experimental densities can then be deduced from the comparison with the theory. Once the actual material parameters and the inhomogeneous broadening are known, the theory has no free parameters left. Then, the optical spectra for the running device can be predicted [Fig. 8(d)]. On this basis, variations of other parameters, like the temperature, polarization of the light ﬁeld, or external electric ﬁelds, can then be studied realistically.
It is very satisfying to see that the agreement between experiment and theoretical prediction is very good. The procedure described here could be automated and integrated into software used in diagnostic tools that measure the luminescence of devices while still on the wafer. The ideal spectra could be precalculated and tabulated for several inhomogeneous broadenings. The comparison between experimental and theoretical luminescence spectra would then be done by scanning through the data sets for diﬀerent broadenings while shifting the spectra according to the mismatch in the peak position.
Cours de mathematiques. Analyse II by Chambadal L., Ovaert J.-L.