I need best references of analytical solution of rate of spontaneous emission of indirect semiconductors like Silicon,and I want to simulate that in Matlab for extract the PL signal.
(I'm new in Matlab).
Ali,
Assuming that the excess electrons is equal to the excess of holes such that dn=dp, This is because the incident photons generate electron hole pairs.
These electrons and hole recombine with each other by radiative recombination radiating photons with the rate phio= rate of recombination U, since every electron-hole pairs when recombining gives on photon. Then phio= U=dp/ Trad,
Assuming the thickness of the specimen= d and the dp is independent of the position in he specimen which is a simplifying assumption since normally dp changes in the depth of the specimen. Then phiot= phio x d. This will be the radiating photons/cm^2?s or the radiated photon flux.
The other part of the problem is to obtain dp due to the incident photon flux phi
The incident photons affects photo generation with a rate G= alpha x phi,
At steady state G= net recombination rate = dp /Tau where Tau is the net lifetime.
The net lifetime can be expressed by:
1/Tau= 1/Trad + 1/ Tnonrad,
Tnonrad is nonradiated lifetime .
In silicon Tnonrad
Ali,
Assuming that the excess electrons is equal to the excess of holes such that dn=dp, This is because the incident photons generate electron hole pairs.
These electrons and hole recombine with each other by radiative recombination radiating photons with the rate phio= rate of recombination U, since every electron-hole pairs when recombining gives on photon. Then phio= U=dp/ Trad,
Assuming the thickness of the specimen= d and the dp is independent of the position in he specimen which is a simplifying assumption since normally dp changes in the depth of the specimen. Then phiot= phio x d. This will be the radiating photons/cm^2?s or the radiated photon flux.
The other part of the problem is to obtain dp due to the incident photon flux phi
The incident photons affects photo generation with a rate G= alpha x phi,
At steady state G= net recombination rate = dp /Tau where Tau is the net lifetime.
The net lifetime can be expressed by:
1/Tau= 1/Trad + 1/ Tnonrad,
Tnonrad is nonradiated lifetime .
In silicon Tnonrad
It might be that you need to consider hot-carrier (bremsstrahlung) type of radiation e.g.
"On the bremsstrahlung origin of hot-carrier-induced photons in silicon devices"
AL Lacaita, F Zappa, S Bigliardi…
http://risorse.dei.polimi.it/spad/1993/On%20the%20bremsstrahlung.pdf
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