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Department of Physics and Astronomy   1

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Department of Physics and Astronomy

 

1.   Calculate the number of bound states and the lowest energy level for electrons and light and heavy holes in a GaAs well 6 nm wide sandwiched between layers of A1_0.35Ga_0.65 As. How good an approximation is an infinitely deep well?

     Hence recalculate the energy of the optical transition in the 6 nm well in the sample whose photoluminescence was shown in Figure 1.4. How much difference does the finite depth make? Does it improve agreement with experiment, or are there any signs of error (in the model or the growth)? How large a shift would occur if the thickness of the well were to fluctuate by a monolayer?

 

2.    Calculate the probability of finding an electron in the lowest bound state inside the 4 nm well, using equation (4.21). This requires the ratio of coefficients DIC, which can be calculated from equation (4.7) or (4.8) after E  (and hence k and K ) has been found. Explain qualitatively how this fraction depends on the width of the well. (equation refer to the book Physics of Low dimensional).

 

3.      Plot a graph of the energy of the bound states in a GaAs well 0.3 eV deep as a function of width from 0 to 20 nm.

 

4.      Estimate the spacing of the energy levels for electrons and holes (both light and heavy), and the optical transition energies, for the sample shown in Figure 4.5. Make the obvious approximation that the parabolic potential continues upwards, rather than stopping when it reaches the maximum imposed by the bands of the AlGaAs; this should be adequate for the lowest levels. Ignore also the variation in effective mass through the heterostructure.