Source: http://aoot.osa.org/ome/abstract.cfm?uri=ome-9-3-1257
Timestamp: 2019-04-21 20:07:00+00:00

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We theoretically compare the energies and wave functions of the electron/hole states between InP- and CdSe-based core/shell/shell colloidal quantum dots (QDs) and investigate how the bandgap energy of the core material affects the light emission characteristics such as the photoluminescence quantum yield and linewidth. The band diagrams and electron/hole energies of InP/ZnSe/ZnS and CdSe/ZnSe/ZnS QDs, having the same emission wavelength, are calculated on the basis of strain-modified effective mass approximation (EMA). The QD strain distribution, caused by the lattice mismatch, is considered based on the continuum elasticity theory. The energies and wave functions of all the electron and hole states in the InP- and CdSe-based core/shell/shell QDs are obtained through the analytical solution of the Schrödinger equation under the EMA. Then, the emission spectra of the two QDs are calculated while considering the homogeneous and inhomogeneous broadening. Finally, we elucidate why the emission characteristics of InP-based QDs, such as the quantum efficiency and emission linewidth, are inferior to those of CdSe-based QDs, and how these can be improved by using the III-V ternary core materials with a bandgap energy comparable to or larger than that of CdSe.
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Fig. 1 Layer structures of InP/ZnSe/ZnS and CdSe/ZnSe/ZnS QDs along with the schematics of their energy diagrams. The thicknesses of all layers are determined to make the emission wavelengths of the two QDs equal. The InP QD, having a smaller bandgap energy than that of the CdSe QD, should have the smaller layer thickness to enhance the energies of QD electron and hole states caused by the quantum confinement of the three-dimensional QD electric potential.
Fig. 2 Calculated strain distributions of (a) InP/ZnSe/ZnS and (b) CdSe/ZnSe/ZnS QDs. The positive and negative strain values represent tensile and compressive strains, respectively. The hydrostatic strains, inducing the change in the band-edge energy of conduction and valence bands, are compressive in the core and ZnSe inner shell regions and tensile in the ZnS outer shell region.
Fig. 3 Calculated band diagrams without and with the consideration of the strain-induced band-edge energy change in (a) InP/ZnSe/ZnS and (b) CdSe/ZnSe/ZnS QDs. The strain-modified bandgaps of the core and ZnSe shell increase owing to the applied compressive strain. In the ZnS shell, the strain-modified bandgap decreases owing to the applied tensile strain.
Fig. 4 Calculated energy levels of the electron and hole states for (a) InP/ZnSe/ZnS and (b) CdSe/ZnSe/ZnS QDs. The terms C and HH represent the electron and heavy hole, respectively. Because of the deep potential barrier and large radius, the ground states (C1 and HH1) of the CdSe/ZnSe/ZnS QD are closer to the band edge and more confined to the QD potential than those of the InP/ZnSe/ZnS QD.
Fig. 5 Calculated radial probabilities of the electron and hole ground-state wave functions in (a) InP/ZnSe/ZnS and (b) CdSe/ZnSe/ZnS QDs. The wave functions of the electron and HH states in the CdSe QD are more confined to the core region than those in the InP QD. Therefore, the CdSe QD has a stronger overlap of the wave functions between the electron and hole states than that of the InP QD. The strong confinement of the wave functions to the ground state in the CdSe QD results in less carrier scattering and a smaller broadening linewidth of the CdSe QD than that of the InP QD.
Fig. 6 Comparison of the calculated emission spectra of InP/ZnSe/ZnS and CdSe/ZnSe/ZnS QDs. The standard deviation of the inhomogeneous broadening is assumed to be σ = 40 meV for both QD ensembles because the degree of the fluctuation in the size or material composition of InP and CdSe QDs is assumed to be the same. The linewidth of the homogeneous broadening is assumed to be γ = 30 meV for the CdSe QD and γ = 40 meV for the InP QD on the basis that the ground-state carrier of the CdSe QD is more strongly confined than that of the InP QD. The CdSe QD shows larger emission intensity than that of the InP QD.
Fig. 7 Bandgap energy versus lattice constant of III-V and II-VI materials . The bandgap energy of InP is smaller than that of CdSe. The bandgap energy of InGaP increases with respect to the fraction of GaP and becomes comparable to or larger than the bandgap energy of CdSe. In this case, the optical characteristics of the Cd-free InGaP QD could be better than those of the CdSe QD.
Fig. 8 Calculation results of the (a) strain distribution and (b) band diagram of In0.43Ga0.57P/ZnSe/ZnS QDs. The amount of the strain applied to the In0.43Ga0.57P QD decreases owing to the reduced lattice mismatch between the In0.43Ga0.57P core and ZnSe/ZnS shell materials.
Fig. 9 (a) Calculated energy levels of the electron and HH states for the In0.43Ga0.57P/ZnSe/ZnS QD. (b) Calculated radial probabilities of the electron and HH ground-state wave functions in the In0.43Ga0.57P/ZnSe/ZnS QD. The wave-function overlap of 0.83 in the In0.43Ga0.57P/ZnSe/ZnS QD is very close to that of 0.861 in the CdSe/ZnSe/ZnS QD.
Fig. 10 Comparison of the calculated emission spectra of InP/ZnSe/ZnS, CdSe/ZnSe/ZnS, and In0.43Ga0.57P/ZnSe/ZnS QDs. The standard deviation of the inhomogeneous broadening is assumed to be σ = 40 meV for all QD ensembles. The linewidth of the homogeneous broadening for InGaP QD is set to be γ = 30 meV because the degree of the ground-state carrier confinement in the InGaP, related to the wave-function overlap, is close to that in the CdSe QD.
Table 1 Simulation parameters used in calculation [17,19].
(2) Δ E v = a v ε hyd = a v ( ε rr + ε θθ + ε ϕϕ ).
(7) κ nl q = 2 m q * ( V q − E nl )/ ℏ 2 .
(8) R nl q ( r q )= R nl q+1 ( r q ) 1 m q * d R nl q ( r ) dr | r= r q = 1 m q+1 * d R nl q+1 ( r ) dr | r= r q+1 .
(9) det[ M( E nl ) ]=0.
(13) | M env | 2 =| ∫ 0 ∞ dr R nl e (r) R n ′ l ′ h (r) r 2 |.
(15) D( E ′ )= 1 2π σ Exp[ − ( E ′ − E QD,nl max ) 2 2 σ 2 ].
Simulation parameters used in calculation [17,19].

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