Below is a graph of the Intensity of the Infrared Emission vs. Energy (in eV).

After initially measuring this data, our job was to identify and make sense of all the peaks. 

Through research, we were able to find out that the band gap energy of GaAs is 1.5114eV at 77 Kelvin. Knowing this, we could confidently identify the peak corresponding to the bottom of the well. It should be mentioned that there are several prominent peaks at lower energies than that of the GaAs substrate. We attribute these peaks to impurity energy levels in the band gap, which would obviously have slightly lower energies. 

We found equations giving us the band gap energy of AlGaAs at varying temperatures. At room temperature the band gap is 1.425+1.155x + 0.37x^2 where x is the concentration of the Aluminum (in our case, .33). We scaled this value to 77 K by using the temperature coefficient (-3.95 - 1.15x).  Doing these calculations, we found the theoretical value for AlGaAs band gap to be 1.753eV. Exactly where we see a peak!!! Therefore, we could confidently label the peak corresponding to the top of the well.

With these two values, we could then calculate the quantum well height, 241.4 meV, and find the energy levels for both an infinite and finite quantum well. Our data is seen in the table below.

Infinite Well Calculations of Confinement Energies.

Experimental Value Theoretical Value Percent Error
QW 2 (2.9 nm) 0.20456 eV 0.667 eV 69.3%
QW 3 (5.9 nm)  0.09131 eV 0.16 eV 42.9%
Qw 4 (9.8 nm) 0.04164 eV 0.058 eV 28.2%

As expected, the infinite well modeling gave much better results for the wider wells. However, finite well modeling will be much better!

Finite Well Calculations of Confinement Energies.

Experimental Value Theoretical Value Percent Error
QW 2 (2.9 nm) 0.20456 eV 0.2259 eV 9.4 %
QW 3 (5.9 nm)  0.09131 eV 0.09810 eV 6.9 %
Qw 4 (9.8 nm) 0.04164 eV 0.0433 eV 3.8 %

Our theoretical and experimental results coincide! From this data were were able to label all the peaks on the graph above! The sharp rise in intensity at the low energy end of the spectrum is attributed to the top (InGaAs) quantum well. 

It is interesting to notice that the most intense signal comes from the well closest to the top of the sample, and the least intense comes from the bottom. We hypothesized that this occurs because the wells near the top are stimulated by more intense laser light, therefore, the emission is more greater. Also, there is a greater chance that emission from the lower wells will be reabsorbed in the sample.


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