# Plasma Frequency of Bulk Silver in Terahertz Range

• luke

#### luke

Does anyone know where I can find measured values for the plasma frequency of bulk silver? I would like them to be for light in the Terahertz range. I have looked in all type of book of optical constants and I have searched many different articles. Just a suggestion of where to look would be nice. Thanks

## Answers and Replies

do a google search under silver plasma frequency...

Yeah I have searched google. My only problem is that I have seen values that range from 1300 THz to 24 THz. To just have a value that is within an order of magnitude would be good. Thanks for the reply

thank you for your help since the suggestion to do a google search lead me to an article which states "For bulk silver a value of 1 / τ = 2.4 × 10^13 s− 1, is the common textbook value used to fit the plasmons resonance near 400 nm." Well this reminded me that the plasma frequency depends on the wavelength but for what I am doing I do not need the plasma frequency for any wavelength I just need it for a single wavelength. So I think this problem is solved since I was searching for something I didn't need.

Thanks again

plasma frequency of silver

The plasma frequency of silver is 2.17 *10^15 Hz or 138 nm. This is calculated from the equation plasma frequency = sqrt(4*pi*N*e^2/m_0), where N is the number of electrons per cm^3, e = 4.8E-10 esu, m_0 is the electron mass m_o=9.11E-28 grams. The plasma frequency will be in Hertz or 1/sec.

Tau is the momentum scattering time. A good explanation is in Mark Fox's book "Optical Properties of Solids".

do a google search under silver plasma frequency...

Brilliant! A simple yet effective way to find the answer to everything!

Plasma frequency for silver : 3.75(eV)-3.80(eV)

reference:
1. Phys. Rev. 132, 1599 - 1602 (1963)
2. Phys. Rev. Lett. 5, 470 - 472 (1960)

I try to use the formula suggested by Marcie, using n=5.86*10^22 (cm^-3) (from the book by Ashcroft) and I get 8.99(eV).

Well, I hope someone can tell me why the formula doesn't work. I found an article saying that there is a reflection minimum at 9.2(eV). See :Phys. Rev. 121, 1100 - 1103 (1961). I am not sure if the 9.2 eV has anything to do with the calculated 8.99eV.

The equation in Ashcroft & Mermin is for the case of a free electron gas in the presence of a uniform positive background (i.e. the jellium model). It is only an approximation of the real system, so it will never give you the "correct" answer. It does a pretty good job though, especially for simple metals at STP.

for quantasham,
For pure SIlver it will be the value you calculated. But for doped Silver which is a semiconductor its value is nearly 9 ev.

I need plasma frequency for all the doped semiconductor for my research. My question is
1) Is there a range for maximum and minimum doping of a semiconductor?
2) Plasma fy= sqrt(4piNe^2/m0); Is N the doping concentration in case of doped semiconductor?
3) how to convert frequency in Hertz to ev?