Crow, G.C. (1994) *The transport and relaxation of holes in quantum wells.* Doctoral thesis, Durham University.

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## Abstract

Two properties of holes in InGaAs quantum wells have been investigated and are reported in the thesis - their in-plane mobility at low electric fields, and their capture by a potential well. Monte Carlo simulations of hole transport in InGaAs-AlGaAs quantum wells of different widths and alloy compositions have been carried out at 77 K, and for field strengths less than 10(^5) Vm(^-1) Valence bandstructure has been generated using a k.p method in the infinite well approximation, which accounts for mixing between heavy and light hole states. Although less accurate than more detailed k.p calculations which include mixing with the conduction, spin split-off and remote bands, it provides an adequate description of states lying close to the valence band edge, simplifies the calculation of scattering rates and is computationally efficient. The effects of alloy, impurity and phonon scattering have been included. A study of hole transport in 90 Å In(_z) Ga(_1-z)As wells (0.10 < x < 0.25) predicted that the hole mobility should increase with indium concentration, since the reduction in the effective mass of the highest HHl subband more than compensates for the greater alloy scattering rate. An analysis of wells with 18% indium content and widths in the range 50-150 Å indicated a general increase in the hole mobility with well width but with a local minimum around 120 Å due to intersubband scattering from the HHl subband to the heavier HH2 subband. A model for the 'quantum' capture of holes into a square well potential is developed in part two of the thesis. This involves the calculation of transition rates from unbound barrier states above the continuum edge to quasi-two dimensional bound states that form the quantum well subbands. The physical mechanisms and rates for the quantum capture of holes into a 30 Å In(_0.7)Ga(_0.3)As-InGaAsP quantum well (suitable for use in lasers operating at 1.55 µm) are discussed. In particular, the role of polar and non-polar optical phonon scattering, acoustic phonon and alloy scattering are considered. Bound and unbound states have been calculated using an eight band k.p band- structure model which describes mixing between the heavy and light hole, spin split-off and conduction bands. The quantum well has three subbands which derive from the HHl, HH2 and LHl zone centre states. By treating quantum capture in a similar way to a barrier transmission problem, the hole capture rate into the well can be expressed in terms of the incident particle flux density. Such local information can be readily incorporated into classical device models, for example those based on Monte Carlo simulation. Heavy and light holes of a particular energy and momentum (both transverse and parallel to the plane of the quantum well) are represented by their appropriate barrier plane wave states. The fraction of the incident amplitude which is transmitted into the well region oscillates as a function of the wavevector normal to the well, and capture is induced by a scattering process, due to phonons or alloy disorder for example. The transition rate is determined by the matrix element between the transmitted wave and the final bound state, hence the capture probability varies as a function of the in-plane wavevector and energy of the unbound state. Peaks in the capture probability are associated with transmission resonances into the well (virtual bound states), but subband mixing is also found to be an important influence.

Item Type: | Thesis (Doctoral) |
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Award: | Doctor of Philosophy |

Thesis Date: | 1994 |

Copyright: | Copyright of this thesis is held by the author |

Deposited On: | 16 Nov 2012 11:01 |