Lorentzian lineshape, uncertainty principle and AlGaAs conduction band offset

[daffoddill]

Homework Statement

1) I try to understand the lorentzian lineshape and relate to the gaussian graph but i don't know what is the difference.

2) Uncertainty principle- if it's related to the lorentzian lineshape it will give the information about the lifetime in the well and the width of the transmission peak. This has to be applied for one dimensional two barrier of AlGaAs material to find the transmission probability.

3) For AlGaAs conduction band offset-find how the conduction band offset varies with Al concentration and why Al increases the conduction band offset.

Homework Equations

The Attempt at a Solution

 

[Rajini]

Hi,
1) In general, Lorentzian profiles are related to lifetime and and not Gaussian. Gaussian rapidly touches the x-axis and Lorentzian don't behave like that. I suggest you to plot and see the difference..(if you want i can upload two plots).
2)the FWHM of Lorentzian is equal to the lifetime (please write more information)
3)I have no idea

 

[daffoddill]

thx rajini..
yes if you can upload the two plots it will be great..because it's quit few information that i found through the internet..could you please upload if you have any other information about it?
thanks

 

[Rajini]

Hi,
Loretzian function:
$$f(x)=\frac{I_0(\Gamma/2)^2}{(x-x_0)^2+(\Gamma/2)^2}$$
$$\Gamma$$=FWHM.

Gaussian function:
$$f(x)=I_0\exp\left(\frac{-(x-x_0)^2}{2\Gamma^2}\right)$$
$$\Gamma2\sqrt{2\ln2}$$=FWHM.
For both function:
I₀=height of peak.
x₀=position of peak.
You will find 2 pictures with same height, fullwidth=1 for lorentzian and position =0. For Gaussian fullwidth=1.1774 (=$$0.5\times2\sqrt{2\ln2}$$).
Note how the Gaussian function rapidly touches the x-axis and for Lorentzian it is not!