PhD Thesis: Theoretical Study of Carrier Capture into
Semiconductor Quantum Wells
PhD Thesis: Theoretical Study of
Carrier Capture into Semiconductor Quantum Wells
Karol KALNA
Department of Theory of Semiconductor Microstructures
Institute of Electrical Engineering, Slovak Academy of Sciences
Dubravska cesta 9, 842 39 Bratislava, Slovakia
We have calculated the ambipolar carrier capture time in a separate
confinement heterostructure quantum well (SCHQW) excited by a short
laser pulse. This ambipolar capture time incorporates the semiclassical
hole capture time and the quantum-mechanical electron capture time. The
latter one, calculated for the electron-polar optical phonon
(e-pop) interaction, oscillates as a function of the quantum
well (QW) width. The calculated ambipolar capture time reasonably
agrees with the measured capture time. The analysis of the electron
distribution function in the SCHQW barrier shows that the photoexcited
electrons are nonthermal before they are captured into the QW.
We have also calculated the electron capture times due to the
electron-electron (e-e), electron-hole (e-h) and
e-pop interactions for a model laser regime. The calculated
capture times oscillate as a function of the QW width with the same
period, but with quite different amplitudes. For an electron density
of 1011 cm-2 in the QW, the e-e
capture time is one to three orders larger and the e-h capture time two
to four orders larger than the e-pop capture time. The exceptions are
the QW widths near resonance minima, where the e-e capture time
is only 2-3 times larger and the e-h capture time
10-100 times larger. With increasing density the e-e
capture time decreases and for a high enough density
(1012 cm-2) becomes smaller than the
e-pop capture time. Therefore, in simulations of the QW lasers
the e-e interaction should be taken into account at resonance
for any density 1011 cm-2, while the
e-h interaction should only be considered at densities ~
1012 cm-2.
We have also taken into account effects of exchange and degeneracy on
the e-e capture. The exchange effect increases the e-e
capture time approximately two times while the degeneracy does not
change the capture time except for the QW depths and widths near the
resonance.
Finally, we have shown that the oscillatory behaviour of the e-e
and e-pop capture time has a different physical origin.
In addition, a project to the PhD thesis is also available:
Content of the project:
1 Introduction
2 Liouville-von Neumann Quantum Equation
2.1 Master Equation
3 Boltzmann Transport Equation
3.1 Electron-Electron Hamiltonian in Jellium Model
3.2 Interaction Representation and Distribution Function
3.3 Drift Term
3.4 Scattering Term
3.4.1 Born Approximation for Electron-Phonon Interaction
3.5 Screening and Plasmons
3.6 Interparticle Term
3.6.1 Born Approximation for Electron-Electron Interaction
3.7 Linear Screening
3.7.1 Thomas-Fermi Theory
3.7.2 Random Phase Approximation
3.8 Limitations of Boltzmann Transport Equation
4 Methods for Solution of Boltzmann Transport Equation
4.1 Iterative Technique
4.2 Monte-Carlo Method
4.3 Comparison of Ensemble Monte-Carlo Method with Boltzmann Transport Equation
