Diamagnetism as a probe of exciton localization in quantum wells

Abstract

Exciton photoluminescence (PL) is an important technique for the characterization of quantum wells (QW's). We discuss the etfect of localization on the diamagnetic energy shift of an exciton in a QW. It is shown how the diamagnetism of an electron in the ground state, with arbitrary geometry, depends on the dimensions of its wave packet. We consider the properties of free excitons in QW s, introducing an effective electron-hole interaction. We use dimensional analysis to relate the finitebarrier problem to the simpler case of perfect confinement. For a bound exciton, localization in the plane of the QW causes the diamagnetism to be smaller than for a free exciton. The efFect of localization is not important if the range is much larger than the free-exciton Bohr radius. The exciton diamagnetic shift is reduced by localization in 10 and 20 A (In, Ga)As/InP QW s grown by solidsource molecular-beam epitaxy. Uncertainty about the value of the free-exciton diamagnetic shift limits the sensitivity of the diamagnetism as a probe of exciton localization. Despite this, the method still provides valuable information on exciton localization, particularly when combined with studies of the phonon sideband of PL.

Magnetism as a probe for wave function localization in GaSb/AlGaSb quantum wells

“…The barrier material has a larger effective mass than the well, and this effects the in-plane motion because the electron and hole wave functions penetrate into the barrier. We consider the in-plane mass m~ (i = e, h), of electron and hole separately, given by [6]: according to ref. [7], assuming an energy-dependent electron effective mass me (Lz) = = meo ( 1 + A/Lz ), where me0 is the bulk effective mass of the electron at k = 0 and A is the non-parabolicity parameter (A = 1.5 nm).…”

“…On the other hand, a quadratic shift occurs when 1 > ~. In this case the magnetic field interacts with the exciton particle as a whole, resulting in a diamagnetic shift [5,6] …”

An evaluation of exciton diamagnetic shift as a function of magnetic field for InAs/InP and self-assembled quantum wires and evaluation of electron energy levels of quantum wire in a transverse magnetic field

“…Moreover the application of external magnetic field can give important information of carrier confinement. The charge confinement can be studied with the help of exciton diamagnetic shift [12][13][14][15] . One measures wave function radii of the electron, heavy hole and exciton along the growth direction of QW and [001] direction of QWR.…”

An exciton in a quantum well in the presence of crossed electric and magnetic fields

“…Their calculations are strictly valid for weak and intermediate magnetic fields. An alternative procedure was adopted by Nash et al [9] who treated the magnetic field as a perturbation valid for fields of up to moderate strength. Hou et al [10] included some theory with their experimental results for excitons in InGaAs/GaAs strained QWs in which a variational method was employed using hydrogenic wavefunctions as the basis sets for low magnetic fields but with harmonic oscillator wavefunctions for high magnetic fields.…”