Calculating the Bohr radius or velocity of an excitons

[supercali]

while doing some calculations such as calculating the Bohr radius or velocity of an excitons in semiconductors such as GaAs I didnt understand why is it allowed to use the static permittivity even though the electron and hole aren't as heavy and the spectra is measured at high frequencies such as [tex]\omega=10^{15}Hz[/tex]?

 

[supercali]

anyone ?

 

[charng]

The use of static permittivity in calculating the Bohr radius or velocity of excitons in semiconductors is a common approximation in theoretical models. This is because the exciton is a bound state of an electron and a hole, which are both considered to be relatively heavy particles compared to the surrounding medium. Therefore, their motion can be treated as being slow and the effects of the surrounding medium can be approximated using the static permittivity.

Furthermore, when calculating the Bohr radius or velocity, we are interested in the average behavior of the exciton over a large number of oscillations. At high frequencies such as \omega=10^{15}Hz, the exciton will undergo many oscillations in a short period of time, making it difficult to accurately measure its properties. Using the static permittivity allows us to simplify the calculations and still obtain meaningful results.

However, it is important to note that the use of static permittivity is an approximation and may not fully capture the behavior of excitons at high frequencies. Therefore, experimental measurements at these frequencies are still important to validate theoretical models and improve our understanding of exciton dynamics in semiconductors.