### Abstract

In recent years, the study of exciton dynamics in semiconductor heterostructures has advanced considerably due to its important applications in electronic industries. As excitons have larger binding energies in quantum wells, they can be observed easily at room temperature absorption spectra. However the theoretical study of excitons in quantum wells is a difficult area as the space quantization in a quantum well destroys the translational symmetry of the crystal in the direction perpendicular to the quantum well plane.In this project, processes like the generation, scattering and decay of excitons are theoretically examined. First, we extend the theory of excitons developed in 3D systems to Quasi-2D systems. Then we present an approach to calculate the generation rate of heavy hole exciton at various quantum well widths and depths. A Quasi 2D exciton-phonon interaction operator applicable in quantum wells is derived and is used to calculate the transition rate of an electron hole pair to an exciton. We obtain an expression for the transition rate as a function of the quantum well width and binding energy. To obtain the binding energies of exciton at various well widths, we follow a method which uses the model of an exciton in a fractional-dimensional space.

The rate of exciton generation is plotted as a function of the well width for different values of aluminium concentration, x, in GaAs-A1

_{x}Ga

_{1-x}As quantum wells. The rate of exciton generation increases from 5 x 10

_{8 s-1}to 1 x 10

_{10}

_{s-1}when quantum well widths decreases from 200Å to 25Å, which agrees well with recent experimental results. Results indicate that the rate of exciton generation decreases sharply with quantum well width for the case of an infinite well, but the decrease becomes gradual for finite potential wells.

Next we study the scattering of delocalised excitons due to acoustic phonons in quantum wells. We assume that the exciton scattering takes place due to exciton-phonon interactions. The rates of HH exciton scattering are obtained in the range of about 2 x 10

_{11 s-1}to 20 x 10

_{12 s-1}at temperatures ranging from 10K to 100K and for well widths varying from 25Å to 200Å. These results compare well with the experimental rates. At a given temperature our results indicate that the excitonic linewidths from wider wells are smaller than those from narrower wells. The results also predict scattering of the heavy hole (HH) exciton to be greater than the light hole (LH) exciton.

We have also extended the study of scattering of an exciton to include its decay into an electron-hole pair by absorbing an acoustic phonon. Our results show that at small well widths, the rate of LH exciton decay is apparently larger than that of HH decay, but the difference diminishes at large well widths. This is consistent with recent experimental measurements which show that the decay time for the LH excitons is twice that for the HH exciton.

Next, we present the theory of Quasi-2D polarons in semiconductor quantum wells. We have derived analytical expressions for the energy gap shift and effective polaron mass in the small well width limit. The analytical results agree exactly with those obtained for an ideal 2D system in the limit of zero well width. For larger quantum well widths, we have numerically evaluated the values for the energy gap shift and effective mass of a polaron.

The theory used for electrons interacting with phonons in quasi-2D systems is extended to study excitonic polarons in quantum wells. Numerical values for the energy gap shift and effective mass of an excitonic polaron in a GaAs-A1

_{x}Ga

_{1-x}As system are obtained. We find that the polaronic effect is more pronounced for excitonic polarons, particularly in the case of the LH exciton in quantum wells of small widths. Our results also show the importance of the inclusion of the exciton-phonon interaction in the calculation of the exciton ground state energy in semiconductor quantum wells.

In conclusion, we have presented a study of the dynamics of excitons due to their interaction with acoustic and optical phonons in this thesis. All theories put forward here have been supported by known experimental results. This agreement validates the theory while offering an explanation for recent experiments. Hence we expect our results to have importance in the quantitative understanding of the present and future experimental work on semiconductor devices.

Date of Award | 1993 |
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Original language | English |

Supervisor | Jai Singh (Supervisor) |