Abstract
In this chapter, we assume that a supra-bandgap modulated pump laser and a supra-bandgap constant probe laser shine on a non-homogeneously doped silicon sample with respective irradiances \(\Pi _\text{ pump}(x,y,t)\) and \(\Pi _\text{ probe}(x,y)\). We look at the free electron, free hole and temperature distributions generated in the sample.
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- 1.
The dependence upon time is kept implicit so as to simplify the expressions.
- 2.
The case of an n-type layer can easily be derived by replacing \(P_\text{ doping}\) by \(N_\text{ doping}\) in the final expressions
- 3.
Canceling the Dember field by setting equal electron and hole mobilities results in equally lowered substrate injection for n- and p-type layers.
- 4.
Note that, as we have in Chap. 4, we should also investigate the generation of further harmonics. However, only the constant and fundamental modes of the layer excess carrier concentration contribute to the measured signals (see Chap. 6). The other harmonics are therefore neglected. The reason for the in-depth discussion of the harmonic generation in Chap. 4 is that the existence of further harmonics in the substrate carrier distribution would have modified the layer excess carrier concentration via Eq. (5.9)
- 5.
This equation is easily extended to n-type doped layers by replacing \(P_\text{ doping}\) by \(N_\text{ doping}\)
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© 2012 Springer-Verlag Berlin Heidelberg
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Bogdanowicz, J. (2012). Extension of the Transport Theory to Ultra-Shallow Doped Silicon Layers. In: Photomodulated Optical Reflectance. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30108-7_5
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DOI: https://doi.org/10.1007/978-3-642-30108-7_5
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