# Lorentzian lineshape, uncertainty principle and AlGaAs conduction band offset

1. Apr 20, 2010

### daffoddill

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

2. Apr 21, 2010

### Rajini

Hi,
1) In general, Lorentzian profiles are related to lifetime and and not Gaussian. Gaussian rapidly touches the x-axis and Lorentzian dont behave like that. I suggest you to plot and see the difference..(if you want i can upload two plots).
3)I have no idea

3. Apr 27, 2010

### 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

4. Apr 27, 2010

### 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!

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Last edited: Apr 27, 2010