Calculating the Dielectric Function of metals - Units trouble

In summary, The conversation discusses calculating the permittivity based on the Lorentz-Drude model mentioned in the paper "Optical properties of metallic films for vertical-cavity optoelectronic devices" by Rakic et al. The paper does not provide information on the units, but the participants have tried different units such as eV and Hz. The units for the formula (1,2,3) in the paper are still unclear and there is confusion about whether to divide by hbar or not. The participant is requesting clarification on the units used in the paper.
  • #1
zellwwf
34
0
Hello everyone here!

See i got my hands on this paper:
Optical properties of metallic films for vertical-cavity optoelectronic devices
by Rakic et al.

A simple google search of the title will give you access to the paper.
Now, i am writing the function in MATLAB to calculate the permittivity based on the Lorentz-Drude model mentioned in the paper.
The paper however doesn't help with the units. It's my fault i know.. i should know my units. But I've tried a lot of stuff and nothing seems to work.. i am getting weird graphs that don't look anything like the ones in the paper. Not even close. I rewrote the MATLAB function a number of times and i don't think it's that. i think its in the units.

Here is what i need help with:
I believe that ε(w) is unitless. Correct me here if i am wrong.
(i will be using silver as an example here)
Plasma Frequency of silver is 9.01 (see ref) eV.
[itex]\omega_p* \hbar = 9.01 eV[/itex]
And if i am not wrong in formulas (1) (2) (3), he references [
itex]\omega_p[/itex], so i automatically divided 9.01 by Hbar (in Ev.S units), but that would give inconsistent results with a Unitless permittivity. It would give units of: [itex]s^{-2}.eV^{-2} [/itex] for the permittivity function he mentions.

so let's check what have i done:
1) Feed 9.01 into the formula where wp is. Wrong Graph.
2) Feed 9.01/Hbar into the formula where wp is. Wrong Graph again.

Can someone tell me what are the units for the formula (1,2,3) in the ref? and what kind of normalizations or unit conversions i have to do in order to put the data from Tables 1, 2 (ref) to make it work?
If i am getting anything wrong, tell me please.
 
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  • #2
Yes, the ##\epsilon_r## he defines is unitless.
Apart from this, I don't understand your problem: both ##\omega## and ##\Gamma## have the same units as ##\Omega_p## so that the whole quotient is unitless, as it should be.
The question is rather: What units are you using for ##\omega##?
 
  • #3
I am using eV, in other words.. i am running a loop from 0.01 ev to 1 ev. Feeding 0.01 to the function.
But [itex]\Omega_p[/itex] is defined as [itex]\sqrt{f}\omega_p[/itex], where omega is in Hz, not eV, as i noted in table 2, in table 2 he says that the value 9.01 is hbar times plasma freq.

Should i divide by hbar? but still that gave me a wrong graph.
I you need, i can send you my results.

If i divided by hbar, that means Omega is not in eV anymore, it's in Hz, which means it the units won't cancel out.
 
Last edited:
  • #4
No matter what you think he may write. If your ##\omega## is in eV, ##\Omega_p## has to be in eV, too.
 
  • #5
I agree... so i shouldnt' divide by hbar?
 

1. What is the dielectric function of metals?

The dielectric function of metals is a measure of how a material responds to an electric field. It describes the relationship between the electric field and the polarization of the material. In metals, the dielectric function is typically complex, with both real and imaginary components.

2. How is the dielectric function of metals calculated?

The dielectric function of metals can be calculated using theoretical models or experimental techniques. The most common theoretical approach is the Drude model, which considers the free electron gas in metals. Experimental techniques such as ellipsometry and spectroscopic measurements can also be used to determine the dielectric function.

3. What units are used to express the dielectric function of metals?

The dielectric function of metals is typically expressed in terms of frequency-dependent complex quantities. The real and imaginary components are often given in units of energy, such as electron volts (eV) or joules (J). The imaginary component is also commonly expressed in units of conductivity, such as siemens per meter (S/m).

4. Why might someone encounter unit troubles when calculating the dielectric function of metals?

Unit troubles may arise when converting between different units of energy or conductivity. It is important to make sure that all components of the dielectric function have consistent units in order to accurately represent the material's response to an electric field.

5. How is the dielectric function of metals used in practical applications?

The dielectric function of metals is important in many practical applications, such as designing and optimizing electronic devices. It can also be used to study the optical properties of metals and to understand how they interact with light. Additionally, the dielectric function is often used in the development of new materials for specific purposes, such as solar cells or sensors.

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