Theory of Semiconductor Quantum-Dot Systems
1st Edition
Published on 22. December 2010
Book
Paperback/Softback
164 pages
978-3-86844-303-5 (ISBN)
Description
The present work "Theory of Semiconductor Quantum-Dot Systems: Applications to slow light and laser gain materials" deals with the theory of the optical properties of semi- conductor quantum dot systems by applying a microscopic treatment of the interaction- induced dynamics of carriers and their coherences. In particular quantum coherence phenomena in different quantum dot models are investigated, in order to assess their suitability for slowing down optical pulses. The difference in the electronic structure of ensembles of quantum dots and quantum dot molecules, consisting of two electronically coupled quantum dots, is also investigated. Based on these results, a new model for op- tical refrigeration using quantum dot molecules is proposed. Finally the performance of quantum dot systems as gain material for intersubband lasers with a resonance frequency in the mid-infrared is studied. These thesis is divided into six parts:
In the first chapter, we discuss how to determine the electronic structure using kp- theory or an "envelope-function"-approximation. The semiconductor Bloch equations and their coupling to the Maxwell's equations are presented. In a first approximation, the interactions that lead to the scattering of carrier and polarization dephasing is treated in relaxation-time approximation.
In chapter 2 we calculate the electronic structure of a quantum dot using kp-theory. The calculated dipole matrix elements suggest a so-called lambda-system for the slow- down of light pulses. The slow-down factors for the group velocity with and without Hartree-Fock contributions are compared. The polarization dynamics induced by the Hartree-Fock contributions change the shape of the spectrum and the maximum attain- able slowdown of the pulse. Furthermore, when Hartree-Fock contributions are neglected, one overestimates the drive pulse intensity required to reach significant pulse slow-down. Finally, propagation effects are included and the slow-down factor is determined directly from the calculated pulse propagation. It turns out, that due to propagation effects, the quantum coherence in a lambda-system do not give rise to a significant pulse delay. As these results depend sensitively on the assumptions for the relaxation times, the descrip- tion of the underlying polarization dephasing will be examined more closely in the next chapters.
Correlation contributions, i. e. scattering and dephasing contributions, to the semi- conductor Bloch equations are presented in chapter three by using a non-equilibrium Green's functions approach (NGF). In that approach, the coupling between spectral and kinetic properties is directly evident. We also recapitulate the derivation of the semicon- ductor Bloch equations in the language of the NGF. Because of the discrete structure of the quantum dot states, a description of polaronic effects is necessary, which give rise to a finite lifetime of single particle states due to the interaction with phonons, and thus lead to an energy uncertainty for electronic transitions. With the additional consideration of continuum states (quantum well) we are able to describe the correlation contributions due to the Coulomb interaction as well as due to the interaction with phonons. Assuming
a particular quantum dot configuration, the contributions can be numerically evaluated. Thus a microscopic calculation of the scattering and dephasing contributions is possible, which replaces the phenomenological relaxation times.
In chapter 4, a semianalytical method for the calculation of the electronic structure of quantum dot molecules is presented, and compared to a kp-calculation. First, the elec- tronic structure and the dipole matrix elements are compared for quantum dot molecules consisting of identical dots and dots of different sizes. Then it is shown that there are im- portant differences in the carrier-phonon scattering between an ensemble of quantum dots and quantum dot molecules. Based on these results, a new model for optical refrigeration is proposed.
Using the theory developed in chapter 3, the assumptions for the polarization dephas- ing in chapter 2 can be replaced by a microscopic calculation. Furthermore its possible to analyze a V -scheme that is more promising for the slowdown of light pulses, which is investigated in chapter 5. We introduce a quantum dot configuration in which such a scheme can be realized. For different quantum dot confinement potentials and lattice temperatures the slow-down factor is calculated to find an optimal quantum dot configu- ration. However, the Coulomb interaction is not significantly affected by this optimization process, so that the attainable slow-down factor remains limited. It is shown that the use of a quantum-dot molecule can overcome this limitation. For this quantum dot molecule also the corrections due to Hartree-Fock contributions are taken into account yielding significantly different results as compared to chapter 2. In the last section, the slow-down factor is directly determined from the pulse propagation and significant improvements compared to the results from chapter 2 are found.
In the last chapter, we investigate the performance of quantum dot intersubband transitions for optical gain. For typical GaAs-based quantum dots, this leads to a fre- quency in the mid-infrared. We investigate a structure, where a thin layer of quantum dots is sandwiched by two quantum wells. For the case of carrier injection into one of the quantum wells we calculate the achievable population inversion of the optically active states, as an important parameter for laser performance. The main contribution to the carrier dynamics, which leads to optical gain, is the interaction of carriers with phonons, and for this interaction we calculate the population inversion for different injection rates. The population inversion is higher at lower lattice temperatures, but a room temperature operation is feasible. Additionally, the small signal gain is determined from the popula- tion inversion. The numerical calculation is extended for stronger fields and scattering contributions due to Coulomb interaction are taken into account. Promising results are obtained for the realization of midinfrared lasers using quantum dots as gain material.
In the first chapter, we discuss how to determine the electronic structure using kp- theory or an "envelope-function"-approximation. The semiconductor Bloch equations and their coupling to the Maxwell's equations are presented. In a first approximation, the interactions that lead to the scattering of carrier and polarization dephasing is treated in relaxation-time approximation.
In chapter 2 we calculate the electronic structure of a quantum dot using kp-theory. The calculated dipole matrix elements suggest a so-called lambda-system for the slow- down of light pulses. The slow-down factors for the group velocity with and without Hartree-Fock contributions are compared. The polarization dynamics induced by the Hartree-Fock contributions change the shape of the spectrum and the maximum attain- able slowdown of the pulse. Furthermore, when Hartree-Fock contributions are neglected, one overestimates the drive pulse intensity required to reach significant pulse slow-down. Finally, propagation effects are included and the slow-down factor is determined directly from the calculated pulse propagation. It turns out, that due to propagation effects, the quantum coherence in a lambda-system do not give rise to a significant pulse delay. As these results depend sensitively on the assumptions for the relaxation times, the descrip- tion of the underlying polarization dephasing will be examined more closely in the next chapters.
Correlation contributions, i. e. scattering and dephasing contributions, to the semi- conductor Bloch equations are presented in chapter three by using a non-equilibrium Green's functions approach (NGF). In that approach, the coupling between spectral and kinetic properties is directly evident. We also recapitulate the derivation of the semicon- ductor Bloch equations in the language of the NGF. Because of the discrete structure of the quantum dot states, a description of polaronic effects is necessary, which give rise to a finite lifetime of single particle states due to the interaction with phonons, and thus lead to an energy uncertainty for electronic transitions. With the additional consideration of continuum states (quantum well) we are able to describe the correlation contributions due to the Coulomb interaction as well as due to the interaction with phonons. Assuming
a particular quantum dot configuration, the contributions can be numerically evaluated. Thus a microscopic calculation of the scattering and dephasing contributions is possible, which replaces the phenomenological relaxation times.
In chapter 4, a semianalytical method for the calculation of the electronic structure of quantum dot molecules is presented, and compared to a kp-calculation. First, the elec- tronic structure and the dipole matrix elements are compared for quantum dot molecules consisting of identical dots and dots of different sizes. Then it is shown that there are im- portant differences in the carrier-phonon scattering between an ensemble of quantum dots and quantum dot molecules. Based on these results, a new model for optical refrigeration is proposed.
Using the theory developed in chapter 3, the assumptions for the polarization dephas- ing in chapter 2 can be replaced by a microscopic calculation. Furthermore its possible to analyze a V -scheme that is more promising for the slowdown of light pulses, which is investigated in chapter 5. We introduce a quantum dot configuration in which such a scheme can be realized. For different quantum dot confinement potentials and lattice temperatures the slow-down factor is calculated to find an optimal quantum dot configu- ration. However, the Coulomb interaction is not significantly affected by this optimization process, so that the attainable slow-down factor remains limited. It is shown that the use of a quantum-dot molecule can overcome this limitation. For this quantum dot molecule also the corrections due to Hartree-Fock contributions are taken into account yielding significantly different results as compared to chapter 2. In the last section, the slow-down factor is directly determined from the pulse propagation and significant improvements compared to the results from chapter 2 are found.
In the last chapter, we investigate the performance of quantum dot intersubband transitions for optical gain. For typical GaAs-based quantum dots, this leads to a fre- quency in the mid-infrared. We investigate a structure, where a thin layer of quantum dots is sandwiched by two quantum wells. For the case of carrier injection into one of the quantum wells we calculate the achievable population inversion of the optically active states, as an important parameter for laser performance. The main contribution to the carrier dynamics, which leads to optical gain, is the interaction of carriers with phonons, and for this interaction we calculate the population inversion for different injection rates. The population inversion is higher at lower lattice temperatures, but a room temperature operation is feasible. Additionally, the small signal gain is determined from the popula- tion inversion. The numerical calculation is extended for stronger fields and scattering contributions due to Coulomb interaction are taken into account. Promising results are obtained for the realization of midinfrared lasers using quantum dots as gain material.