mobility of the drude model in index perturbation material

fdtd

#1

For the mobility values for holes and electrons to be entered in their respective fields in the Drude model used in an index perturbation material based on Si. Should their values be the mobility values after the doping or excess charge existence in the material or should it be the values in intrinsic Si (which are the default entered already) ?


#2

Hi @hmekawey,
The drude model derivation assumed the carriers are moving freely in the optical field according to Newton’s second law. This means the mobility in the equation compensates for this quite wrong assumption. So regarding your question, I think the value of the mobility should be the one of the new doping state.


#3

I agree with @aya_zaki. Since the mobility of a semiconductor is very sensitive to doping (specially in degenerately doped semiconductors), I believe that the equation should use the modified mobility of the doped semiconductor that accounts for the effect of increased scattering due to the impurities

One thing to note here is that the mobility will depend on the doping concentration since this also corresponds to the density of scattering points in the material. However, any change in the carrier concentration due to applied bias (i.e. due to depletion or carrier injection in a pn junction) should not affect the mobility. So for a p-i-n diode, even if the carrier concentration changes due to applied bias (carrier injection), the mobility values for intrinsic silicon should be used.


#4

Thanks @aalam, So when there is no doping but only different excess carrier concentrations at different regions of the structure, which is the scenario I actually care about, we should use a single material for all of them with the intrinsic Si mobility used in it. correct ?


#5

Hi @aalam
I would like also to clarify that in the doping case the objective of my question is not whether we should depend the mobility of the doped material as this is clear from the equations point of view. the aim is to know whether lumerical FDTD index perturbation material user interface require us to enter the mobility after the doping or should we enter the base material mobility and then FDTD solution would calculate internally the mobility for different doping/charge concentrations returned from Device results imported in FDTD solutions.

Thanks for your help


#6

correct!

You will need to manually input the correct mobility (including the effect of doping). FDTD does not adjust the mobility value based on the charge variation since it does not know where the charge variation is coming from (whether from doping or depletion or injection).


#7

@hmekawey, @aya_zaki Regarding your question that we should select the mobility corresponds to certain doping concentration.
Now, I used N-type doping,I selected certain dopant concentration and i got the mobility of electron from here http://www.cleanroom.byu.edu/ResistivityCal.phtml.
My question is how can you determine the mobility of the minority carrier?

Another question.
https://kb.lumerical.com/en/ref_sim_obj_charge_to_index_conversion.html
the epsilon in the refractive index equation is the epsilon the dielectric constant of Si 11.7 ?? is that is correct ?


#8

Hi. You can use the mobility correction models in DEVICE to calculate the mobility of the minority carriers for different doping values. You don’t even need to run a simulation. Simply get the mobility value from the material database. In the screenshot below I have used the Masetti model the calculate the mobility for holes for different donor (ND) concentration.

The epsilon (11.7) that you see for silicon in DEVICE is the DC permittivity. You should use the permittivity at the frequency/wavelength of operation. For example at 1.55 um the permittivity is approximately 12.