I am trying to find a formula that defines the general shape of the responsivity vs. wavelength curve for semiconductors such as silicon, Ge, GaAs. (See attached picture for examples of responsivity curves). I would like to find a relationship for responsivity based on existing data for the semiconductor, e.g. band diagram, absorption coefficient, refractive index etc...
I am actually more interested in the generation rate of electron-hole pairs in bulk semiconductors which is a more fundamental concept. After going through multiple well known text books the basics of this process is still unclear. The fundamental questions are:
1. Why is the generation rate of semiconductors which have a sharp increase in absorption coefficient (e.g. direct bandgap semiconductors) show a narrow peak in Generation Rate vs. Wavelength, while those with a slow increase of absorption coefficient (e.g. indirect bandgap) show wider bandwidth in generation rate. Is this due to combined effects of the decreasing photon count vs. wavelength and surface recombination? or is there more to it?
2. Why does the quantum efficiency curve deviate from the generation rate curve. For example for silicon the quantum efficiency is nearly 1 right down to the blue (450nm) but the generation rate (or responsivity) drops rapidly after 600nm.
3. What happens when a photon with eV higher than the bandgap gets absorbed into say a direct bandgap material? Does the electron which is generated simply go to a higher energy level. Surely there is a density of states factor coming into this. Would the electron have a higher probability of being re-emitted than an electron closer to the bandgap? (Any text books that might explain this?)
Even though responsivity is based on measurements of DC current flow which involve factors more than the generation rate i think that generation rate is the dominant mechanism (I could be wrong).
I actually have a method for measuring the generation rate of E-H pairs directly using microwave spectrum analysis which is contact free. However this shows a similar shape to the responsivity curves. The only mechanism that should be limiting this measurement is the carrier generation. The carriers are generated and just remain there while being measured. So the only limiting factors should be the bulk and surface recombination and of course the decreasing photon count with wavelength. However if that were the case then this still doesn't explain the deviation of the silicon generation rate at 600nm.
Any references to text books that would explain these effects in detail would be most appreciated. All books I have come across seem to avoid explaining these details.
Hi,
1. This is mostly determined by the width of the bands and their DOS. I'm not sure if it has any relation with the type of the band gap.
2. If you are referring to EQE then I can think of some reasons, such as reflection.
3. The excited electron will indeed go to a higher level if one is available and empty. It will quickly release the excess energy, commonly by thermal means (phonons) but sometimes other routes may be available as well.
Books? I'd start with S.M. Sze Physics of Semiconductor Devices.
In addition, S.O. Kasap, Principles of electronic materials and devices is an easy-to-read textbook
Hi
You may find some of your answers in this book (Dielectric Phenomena in Solids
Author(s): Kwan Chi Kao )
"Fundamentals of semiconductors" by Peter Yu and Manuel Cardona.
Generally, the electron-hole generation process by photon absorption is defined by the detailed band structure. Recombination is trickier, as in indirect band gap semiconductors essentially always requires the participation of a phonon (in the case of band-to-band recombination). Recombination and carrier capture proceses at surfaces and defects further complicate the situation.
Thanks for all the answers and apologies for the late reply.
The Yu and Cardona book is quite useful as it shows explicitly the rate calculations. The "Dielectric Phenomena in Solids" is an interesting one as it explains some of the concepts in a different way. The other books are good also but don't seem to go much beyond the basics.
The book below along with some of the references seems to provide all the foundational material I was looking for:
"SOLID STATE PHYSICS PART II Optical Properties of Solids", M.S. Dresselhaus.
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