I need to optimize a strip loaded slot waveguide based on Silicon cores and to do that I need to set the refractive index of the p-type Silicon I am going to use, in order to understand how much the optical loss increases with doped Silicon cores, as also reported in many papers.
I know that the doping concentration of the Silicon in my SOI wafer is 10E15/cm3. I expect that the refractive index changes, depending on the dopant concentration (B). But I could not find any graph or paper reporting this dependance. Moreover, I found in some forum statements that the refractivity changes are so poor that can be ignored with respect to undoped Silicon. Is it true ?
In general, there is, the only problem is whether the changes in the optical range of frequencies are sufficient for your purpose. The most sensitive method to investigate this type of problem is Electrical Impedance Spectroscopy(EIS), but the usual frequency range (below ~10 GHz) might be too low for your application (optical waveguide ?).
In my experience - the numerical modelling of Si electrical response - the changes are indeed minute, if there are there at all (that is measurable). Within the range of n or p doping between 10^11 and 10^17 cm^-3, the experiment (EIS) shows that the dielectric constant is unchanged (epsr~11.8). Even for the degenerate cases (doping > 10^19 cm^-3), the effect seems to be quite small and fully explainable by the doping dependence of the band gap.
I believe that the answer probably lies in alloying (Si with a bit of Germanium or Carbon ?).
With best regards
Petr
In case of moderate doping at ppm level, the optical band gap in n and p typesetting and doped Silicon is the same as in case of undoped silicon. Refractive index also do not change appreciably on doping. In polycrystalline doped films also refractive index in doped and undoped Si is almost same.
I really thank all of you, guys.
@Petr: yes, my application is for a photonic modulator, so as a basic feature of each photonic device, it is an optical waveguide.
Reading more about the topic and discussing with my boss, it seems that refractive index changes only since the 4th decimal digit on, so for the optical filed optimization it can be considered changes. My boss says that for the RF electrical field (i must optimize the overlap on the same device between the optical and the electrical field) the slight change of n becomes meaningful.
I'm studying more about that.
I thank again all of you !!!
You are welcome Stefano, I am happy that our comments have helped you on the way. If the refr.index changes are taking place on the fourth digit or thereabout (your boss remark), I would not "see" them in EIS measurements, since the absolute accuracy of eps measurement here is given by the geometry accuracy (thickness, the area and edge effects). In our experience this gives us 1% absolute accuracy.
However, you have waken up my interest and I will look into it a bit more (re-analyse some of our old data). If I come with something interesting (academic interest), I let you kno0w.
With regards
Petr
I really thank you Petr.
This is the wonderful concept I have of a scientific community and I really appreciate your help and curiosity.
For me it'll be the same: if I get it, I will input here new findings on the topic.
Bets regards and have a nice new week
Stefano
Hello, refractive index of Si is dependent on temperature, Doping and mechanical Stress. So some data on Doping dependence You can find in following publication:Z.-H.Zhou, B.Choi, M.I. Flik, S.Fan, R.Reif, J.Appl.Phys.76 pp.2448, 1994. Regards. S.
I really thank you Sergey. This publication is extremely useful.
I thank you so much
Best Regards
Stefano
I found also a paper from Soref and Bennett of 1987, IEEE Journal of Quantum Electronics 23, No. 1, showing variations of the refractivity in the order of 10-3 both for free electrons and for free holes when the concentration is in the order of 1017.
So, as a very rough estimation, with a rate in the order of 1015 the index variation should lie in the order of 10-5, that can be considered costant for my aims.
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