Stacked layers of submonolayer InAs in GaAs: Zero- or two-dimensional? S. Harrison*, M. Young, M. Hayne, P. D. Hodgson, R. J. Young A. Schliwa, A. Strittmatter, A. Lenz, H. Eisele, U. W. Pohl, D. Bimberg Department of Physics, Lancaster University Institut für Festkörperphysik, TU Berlin *s.harrison5@lancaster.ac.uk
Low-dimensional nanostructures bulk low-dimensional structure single atom Conduction band E C E g E g E g E V E Valence band lowering dimensionality
Low-dimensional nanostructures bulk quantum well quantum wire quantum dot 3D 2D 1D 0D
Low-dimensional nanostructures E C width large QD bulk medium QD bulk small QD bulk E e1 e smaller bandgap, Eg large bandgap E h1 h + E V
Our samples: stacked sub-monolayer growth Deposit 0.5 MLs of InAs on GaAs InAs GaAs Cap with GaAs (1.5, 2.0 and 2.5 MLs in our samples) ~1 ML Repeat another 9 times
Actual structure 1 X-STM reveals QDs and quantum wells (QWs): Growth direction SML stack GaAs cladding In-rich agglomerations A zero- or two-dimensional system? 1 A. Lenz et al, J. Vac. Sci. Technol. B 29 1071 (2011)
counts Photoluminescence (PL) in a magnetic field electron E C photon PL emission at a energy tuneable by the size of QD E V hole Gives us an idea of how charge carriers are confined E
1 A. Lenz et al, J. Vac. Sci. Technol. B 29 1071 (2011) 2 B. Bansal et al, Appl. Phys. Lett. 91, 251108 (2007) 2D system? Large Bohr radius (i.e. small confinement) 9.42 mev 7.39 mev 6.87 mev 2D system Narrow line-widths (more akin to an InGaAs QW 1 ). Spacer layer thickness (ML) Stack height (nm) Lateral geometry (B//z) a B (nm) μ (m 0 ) 2.5 15.5 16.1 0.085 2.0 13.0 15.6 0.091 1.5 10.5 15.0 0.097
0D system? Excited-state peaks visible at 400K. Fitted by Fock-Darwin spectrum. For our samples, confinement energy ~ 9 mev. Counts (/s) 1500 1000 500 0 17T spectrum 1.2 1.3 1.4 1.5 Energy (ev) 2.5 ML spacers 400 K 0D system!
0D and 2D? Different dimensionalities of confinement for electrons and holes. Heterodimensional system In-rich agglomerations too small to confine the light electrons, so they see an InGaAs QW. GaAs matrix QW e - QD h + Heaver holes confined in the agglomerations
Use of COMSOL Adapted the Conical Quantum Dot model for a QD in a QW. Solves the 1-band Schrodinger equation in the effective mass approximation. Gives us energy levels in the system, telling us whether they lie in the QD or QW. ħ2 8π 2 1 m e r wave function Ψ r energy level + V r Ψ r = EΨ(r) effective mass potential well
Effective mass modelling Simple model to solve 1-band Schrödinger equation in the effective mass approximation used to give energy eigenvalues for both electron and hole states. 300nm GaAs In 0.15 Ga 0.85 As 5nm 13nm Electrons confined in QW: GaAs matrix QW e - QD 0.43 ev E e1 = 0.25 ev 0.22 ev 0 ev In 0.5 Ga 0.5 As Holes confined in QDs: h + E h1 = 0.10 ev 0 ev 0.22 ev 0.43 ev
Effective mass modelling Simple, single-band (effective mass) calculation supports this interpretation Electrons and holes confined in QW GaAs 0.30 300nm In y Ga 1-y As 5nm 13nm In x Ga 1-x As Phase diagram of electron and hole confinement for differing In content QW indium content, y 0.25 0.20 0.15 0.10 0.05 Electrons confined in QW, holes confined in QD Electrons and holes confined in QD 0.00 0.2 0.4 0.6 0.8 1.0 QD indium content, x
Summary Introduced the concept of heterodimensional system. Electrons confined in 2D, holes in 0D. Practical investigation backed up by use of COMSOL. Paper submitted to PRL: For more details: s.harrison5@lancaster.ac.uk