# complex permittivity and dielectric function

Discussion in 'Physics' started by kj4g09, Dec 5, 2011.

1. ### kj4g09 Thread Starter New Member

Dec 4, 2011
29
0
Hi guys, hope someone can help me out.

I wanted to calculate the conductivity of a semiconductor by using the optical constant of that semiconductor. Then I'm having 2 doubts below.
1.Can dielectric function works on semiconductor?
2.From equation of complex permittivity and conversion of dielectric function we have: ε" = σ/ω and ε" = 2nk
σ static conductivity,
n refractive index,
k extinction coefficient.
The question is that can I say σ/ω = 2nk ? I tried to calculate this using optical constant of silicon at 632.8nm. which gives a conductivity of 10 to power of 14 which seems not quite right, also the unit of both sides are not the same.

2. ### polychromeuganda New Member

Dec 12, 2011
8
0
Yes, that's supposed to work, but I'm not sure why you're using an extinction rate (which I'm assuming is the recombination rate given your numerical answer). (Hint: if you did this for a block of vacuum, you should get the permitivity of free space.)

This works for simple material assumptions, like a block of glass or quartz crystal. The prop velocity reduction is proportional to the root of the relative permitivity, which you are assuming is all in the relative dielectric constant in your case. Since that's what gives rise to the index of refraction in the first place a single measurement of the critical angle tells all.

if you're invoking semiconductor physics and you're really looking for a frequency dependent complex permitivity, i.e. including the loss tangent and dielectric absorbtion (dielectric polarization can have time constants), then I don't think you can use a simple measurement of the refractive index. The reason I don't think that would work is that you can't get a complex permitivity, which is two scalar answers, from a single scalar measurement, and that's only 2 out of 3. I've never looked into it, but I tend to expect you can seperate some of that better if you also measure the change in the polarization angle. Still, that polarizaion change isn't all due to the loss tangent, part of it is the dielectric absorbtion, So, you'd have to measure the bulk material in transmission to extract a loss tangent independently of the dielectrc absorbtion. I don't know if this covers all the bases, but at least its 3 measurements for 3 unknowns.