Core/shell approach to CM engineering

A recently proposed phenomenological window-of-opportunity model39 relates ε eh to the non-CM (for example, phonon-related) energy-loss rate (k cool ; measured, e.g., in units of eV/ps) and the CM rate (r CM =1/τ CM ; τ CM is the characteristic CM time) by an intuitive expression ε eh =k cool/ r CM =k cool τ CM . In the case of phonon-assisted cooling, k cool =ħω 0 /τ 0 , where ħω 0 and τ 0 are the phonon energy and the phonon emission time, respectively40. This model suggests that one can reduce ε eh by either increasing the CM rate, perhaps by increasing the strength of Coulomb coupling between interacting charges, or by decreasing the rate of cooling. The importance of the cooling factor has been demonstrated by recent comparative studies of PbS, PbSe and PbTe QDs31,39,40, which showed that the observed difference in CM yields can be directly related to the difference in energy-loss rates.

In the present work, we simultaneously manipulate k cool and r CM using appropriately designed core/shell QDs that consist of an infrared-active PbSe core overcoated with an especially thick shell of wider-gap CdSe (Fig. 2a). Available spectroscopic data in conjunction with electronic structure calculations suggest that the conduction band offset at the PbSe/CdSe interface is close to zero41,42. As a result, the wavefunction of the band-edge electron 1S e state in these QDs occupies the entire volume of the core/shell structure, while the band-edge hole wavefunction (1S h ) is closely confined to the core due to a large (~1.48 eV) valence-band offset at the core/shell interface (see Fig. 2a, where we show an approximate structure of electronic states calculated using a simple, single-band effective mass approximation). This regime of confinement, which is characterized by a partial spatial separation between the electron and hole wavefunctions, is typically referred to as quasi-type-II (ref. 43).

Figure 2: Schematic representations of electronic states in core/shell and core-only QDs. (a) Representation of a PbSe/CdSe core/shell QD with a thick shell and the approximate structure of electronic states for a QD with 2 nm core radius and 2 nm shell thickness. The QD energy spectrum features closely spaced electron levels and sparsely distributed hole core levels (with a typical energy separation depicted as ΔE cool ). Red arrows indicate excess energies for the electron and the hole, E e and E h , respectively, demonstrating the asymmetric distribution of the photon excess energy (ħω−E g ) between the two carriers (E h >E e ), which could allow for shifting the CM threshold closer to the fundamental 2E g limit. Relaxation of a hot hole from a shell-based state to a core-localized level can happen either via a CM process (straight black lines) or thermalization (dotted black line). Here, the pre-existing core-localized valence-band electrons interacting in the CM process are spatially separated by the distance d ee , which is much smaller than the overall QD size. The photogenerated and pre-existing carriers are shown by solid and dashed circles, respectively. (b) Band structure and relaxation processes in a core-only PbSe QD of the same overall size. For this structure, the salient differences are mirror-symmetric conduction and valence-band states, which results in a symmetric distribution of the photon excess energy between the electron and the hole, and a larger spatial separation of the carriers interacting in CM. Full size image

The use of quasi-type-II nanostructures can benefit CM for multiple reasons, as schematically illustrated in Fig. 2a,b via a comparison with standard PbSe QDs that are currently among the best CM performers. First, confining the ground-state hole wavefunction to a comparatively small volume increases the energetic gap between the hole states immediately below the band edge of the shell material (ΔE cool , Fig. 2a), slowing down hole relaxation from the higher lying states due to a phonon bottleneck44. Moreover, reduced wavefunction overlap between the higher-lying, shell-based and lower, core-localized hole states will further slow hole relaxation. Finally, the core-localized valence band carriers involved in CM should experience increased Coulomb coupling due to decreased spatial separation between them (d ee in Fig. 2a,b).

Another important aspect of these quasi-type-II structures is a reduced CM threshold compared with standard PbSe QDs. The mirror symmetry between the conduction and valence bands of PbSe45, along with optical selection rules, dictate that the energy of an absorbed photon in excess of E g will be partitioned approximately equally between an electron and a hole, that is, E e =E h =(ħω−E g )/2 (Fig. 2b). Since at the CM threshold either E e or E h must be at least equal to E g , it follows that ħω th is ca. 3E g . In thick-shell PbSe/CdSe QDs, absorption at high CM-relevant energies is dominated by the CdSe shell. Therefore, excitation of one of the optically allowed transitions near the shell band edge leads to a strongly asymmetric case where E h is much greater than E e (see Fig. 2a); as (ħω−E g ) is no longer equally divided between E e and E h , ħω th can more closely approach the fundamental 2E g limit. Furthermore, the large overall size of the QD results in a close energy spacing between electron and hole states of different symmetries near the CdSe band edges, which makes it much easier to simultaneously meet the requirements of both optical and Coulombic selection rules16,46.

Synthesis and optical spectroscopy of PbSe/CdSe QDs

The PbSe/CdSe QDs studied in this work were synthesized via a modified version of a previously reported method (see Methods)47. Briefly, we first fabricate large PbSe QDs with radii from 3.5 to 5 nm, and then apply partial cation exchange to create an outer CdSe shell of controlled thickness by exchanging ions of Pb2+ with Cd2+. Using a moderate reaction temperature (130 °C), we can achieve a wide range of shell thicknesses while avoiding the formation of homogeneous CdSe particles. This procedure preserves the overall diameter of the QDs and allows us to gradually tune the aspect ratio of the resulting core/shell structure (ρ), defined as the ratio of the shell thickness (H) to the total radius (R): ρ=H/R. Both the starting PbSe QDs and the final PbSe/CdSe structures exhibit a nearly spherical shape and fairly narrow size dispersity (s.d. of the overall size is ~7%; see transmission electron microscopy (TEM) images, in Fig. 3a). The core and shell sizes within a given sample appear less uniform, exhibiting ca. 15% dispersion.

Figure 3: Structural and spectroscopic characterization of core/shell QDs. (a) TEM images showing typical core/shell QDs with aspect ratios of 0.27, 0.4 and 0.52, and a constant overall radius of 4 nm. Scale bars, 10 nm. Insets are higher resolution images (scale bars, 2 nm) of individual QDs. (b) Absorption spectra for the same QDs, indicating a blue shift and a decrease in amplitude of the first excitonic peak associated with the 1S e −1S h transition with increasing shell thickness. Spectra are shifted vertically for clarity. (c) PL spectra for the same QDs, showing progressive blue shifts with increasing shell size and the emergence of visible emission for the QDs with the thickest shell (shaded spectra). Inset shows a schematic representation of the band structure, indicating the transitions associated with the infrared and visible emission. All infrared spectra are normalized, whereas for the thick-shell structure the visible emission amplitude is multiplied by a factor of 60 for the purpose of comparison. (d) Infrared PL traces (core emission) are characterized by microsecond time constants and indicate a progressive increase in single-exciton lifetime (from 0.42 to 1.2 μs, and then 2.6 μs for the plotted traces) for structures with larger shell thicknesses, which is a typical signature of a quasi-type-II regime. (e) The PL quantum yield of the infrared band increases with increasing aspect ratio. Full size image

Spectroscopic measurements of these QDs conducted as a function of increasing ρ reveal typical signatures of a transition to a quasi-type-II localization regime. As H increases, the band-edge 1S absorption peak shifts to the blue due to increased spatial confinement of the band-edge hole state (Fig. 3b) and becomes progressively weaker until it completely vanishes for QDs with the thickest shells. The band-edge photoluminescence (PL) also shifts to higher energy (Fig. 3c) and its decay becomes progressively longer (Fig. 3d), which is accompanied by an increase in the emission quantum yield (up to 5.5% for ρ=0.62; Fig. 3e). The apparent reduction in 1S-absorption oscillator strength and increase in PL lifetime are both consistent with expectations for a quasi-type-II system exhibiting progressively increased electron-hole separation.

The most striking effect of increasing shell thickness is the development of measureable emission in the visible, which occurs for ρ>~0.45. This new band is observed simultaneously with infrared emission (Fig. 3c, shaded spectra, and Fig. 4a). Although initially observed as a broad, weak band consistent with some contribution from emission associated with localized traps within the band gap of the CdSe shell, the emission grows stronger and progressively narrower with shell thickness, while also shifting to lower energy, approaching, yet remaining above, the bulk band gap of CdSe. Simultaneously, we observe a sharp increase in the quantum yield of the visible band (Fig. 4b). Together, these characteristics strongly support emission involving an electron in the conduction band-edge state and an unrelaxed (hot) valence band hole residing in the CdSe shell. Normally, because of extremely fast intraband relaxation, hot emission from QDs is only observed in ultrafast spectroscopic measurements; the fact that in these structures it is seen under low-intensity continuous-wave excitation suggests a dramatic slowing of intraband thermalization compared with standard QDs, similar to other heterostructures exhibiting dual-band emission48,49.

Figure 4: Spectral and temporal characteristics of shell-related visible PL. (a) Absorption (blue line) and two-band PL (red and green lines) spectra of a thick-shell PbSe/CdSe QD sample with ρ=0.64. (b) Visible PL quantum yields plotted as a function of aspect ratio show a sharp growth of the emission efficiency for ρ>0.5, suggesting a significant reduction in the intraband cooling rate for shell-localized holes; horizontal and vertical error bars are defined by, respectively, the QD sample size dispersion (s.d. of aspect ratios based on TEM studies) and the noise level (evaluated in terms of s.d.) of the measurements factoring into the PL quantum yield determination. (c) Dynamics of visible PL originating from the CdSe shell is controlled by relaxation of shell-localized holes. Relaxation time constants for samples with ρ=0.52 and 0.59 are 6 ps (blue traces) and 10 ps (black traces), respectively (solid lines are the measurements, dashes are the exponential fits); red line is the measured pump pulse, which defines the width of the instrument response function. All spectroscopic measurements were conducted using low excitation powers for which the average per-dot excitonic occupancy did not exceed 0.1. Full size image

Using a streak camera we were able to time-resolve shell emission for the samples with the thickest shell (ρ>0.5), which yielded PL lifetimes of 6–10 ps (Fig. 4c). Based on these measurements, we estimate the shell emission quantum yield of 0.03 to 0.05%, if we assume that the radiative time constant of the transition involving the shell-localized hole is close to that of standard CdSe QDs (~20 ns50). This estimation is in line with direct quantum yield measurements, which produced values of 0.01 to 0.07% for samples with ρ>0.5 (Fig. 4b).

Although both core and shell PL bands involve the same band-edge electron state (inset of Fig. 3c), their dynamics are dramatically different (compare Figs 3d and 4c). This implies that the shell emission lifetime is controlled by relaxation of a shell-localized hole and further suggests that the hole residence time in the shell region is at least 6–10 ps. As in these thick-shell structures CM might also contribute to relaxation of shell-localized holes (Fig. 2a), the characteristic time of hole cooling via non-CM processes is likely to be even longer than that extracted from the visible PL dynamics.

Although being short compared with typical radiative dynamics, the measured relaxation of hot, shell-localized holes is considerably longer than intraband relaxation in core-only PbSe QDs, in which 1P-to-1S relaxation occurs in 0.25–2.6 ps (depending on the QD size)51. The relaxation constants at higher, CM-relevant energies are expected to be even shorter due to decreased spacing between electronic states. Thus, the measured hot hole lifetimes of at least 6–10 ps indicate a significant slowing of intraband cooling, which should translate into increased multiexciton yields.

Auger recombination lifetimes

In these PbSe/CdSe core/shell structures, CM is also expected to benefit from enhanced carrier–carrier Coulomb interactions compared with PbSe QDs of the same overall size. This enhancement is evident from the ρ-dependence of lifetimes of biexciton Auger recombination (τ 2A ), a Coulombic process in which the energy released during recombination of an electron-hole pair is transferred to a third charge (an electron or a hole). In quasi-type-II structures with more strongly confined holes, Auger recombination is dominated by the hole excitation pathway49 (Fig. 5a), and thus involves scattering processes very similar to those of CM initiated by a hot hole (Fig. 2a). Therefore, as was proposed in our earlier work31,39,52, the biexciton Auger lifetimes can be a surrogate for evaluating relative changes in the CM time constant, τ CM , as a function of changes in the QD structure. Indeed, we find that for PbSe/CdSe QDs with large aspect ratios, that is, small core radii (1.42–2.35 nm), the biexciton Auger lifetime is approximately three times shorter than that for standard PbSe QDs of the same total size (Fig. 5b). This is consistent with our expectation that Coulomb coupling between the valence-band charges becomes enhanced in thick-shell PbSe/CdSe QD samples, which should also enhance the CM channel involving a hot hole (Fig. 2a).

Figure 5: Auger decay in core/shell PbSe/CdSe QDs compared with core-only samples. (a) Schematic representation of biexciton Auger decay in a thick-shell PbSe/CdSe QD. In these structures, it is dominated by Coulomb scattering between the two core-localized holes whereby one hole is transferred to the conduction band and the other is excited within the valence band. For the structures with enhanced CM (ρ=0.6–0.7), the excess energy is not sufficiently high to promote the hole above the CdSe valence-band edge. (b) The measured biexciton lifetimes as a function of aspect ratio for the PbSe/CdSe structures with the same overall radius of 4 nm and ρ from 0.42 to 0.64 (blue symbols). The black and red symbols correspond to core-only PbSe and CdSe QDs, respectively; for both samples the QD radius is ca. 4 nm, that is, similar to the total radius of the core/shell structures. The τ 2A constants measured for the PbSe/CdSe core/shell QDs are considerably shorter compared with those for either core-only PbSe or CdSe QDs, indicating an increase in CM-relevant Coulomb coupling between core-localized charges. Horizontal and vertical error bars are defined by, respectively, the QD samples’ size dispersion (from TEM measurements) and the quality of the exponential fits (least squares method, using a global fit across all fluences) to the measured biexciton dynamics. Full size image

CM measurements

Experimental measurements indeed indicate a considerable increase in the CM efficiency in PbSe/CdSe heterostructures compared with standard PbSe QDs. In Fig. 6a, we show multiexciton yields (η=q−1, where q is the number of electron-hole pairs generated per absorbed photon) measured using transient PL for PbSe/CdSe core/shell structures (squares) of various aspect ratios but similar band gaps (0.87±0.02 eV), compared with measurements of same-E g core-only PbSe QDs (red line) and nanorods (blue line; interpolated from the data of ref. 34); in all measurements the excitation energy is 3.1 eV, which corresponds to ħω/E g of ca. 3.5. For the thinnest-shell sample (ρ=0.15), the multiexciton yield is only slightly higher than that for the core-only QDs but still lower than that for the nanorods. The value of η increases with ρ, and this growth is especially fast when the aspect ratio exceeds 0.4–0.5. This corresponds to the range of slowed cooling where the core/shell structures exhibit dual infrared and visible emission. For ρ of 0.68, the multiexciton yield reaches the value of 0.75, which is almost four times that in the core-only QDs and twice as large as in the nanorods.

Figure 6: CM efficiency for core/shell QDs of varying aspect ratios. (a) Multiexciton yields measured for PbSe/CdSe core/shell structures with progressively increasing shell thicknesses (3.1 eV excitation). The QDs have different total sizes but similar band gaps (~0.87 eV) for proper comparison and are represented by different colour squares on the plot (black dashed line is a guide to the eye). The region where energy conservation is met and, simultaneously, slow cooling is observed (green shading) corresponds to the highest CM yields. The CM yields for PbSe QDs and PbSe nanorods (as interpolated from ref. 34) of similar band gaps are shown by red and blue dashed lines, respectively. Horizontal and vertical error bars are defined by, respectively, the QD samples’ size dispersion (from TEM studies) and the quality of the modified Poissonian fits (according to a previously reported method52) to the measured exciton multiplicities plotted as a function of pump fluence. (b) CM threshold measurements for a core/shell sample with E g =0.8 eV (red squares) and PbSe nanorods with E g =0.81 eV (blue circles) using the output of a tunable parametric amplifier, as well as the fundamental-frequency and the second-harmonic outputs of a Ti:sapphire laser (vertical error bars are determined in same way as in a). These data indicate a significant reduction of the CM threshold in the core/shell QDs, approaching the fundamental 2E g limit. The CM threshold in the nanorods is ca. 2.5E g . Full size image

For the considered shell-hole initiated CM pathway, energy conservation is only met within the range of aspect ratios up to a certain critical value (ρ c ) defined by the condition that the energy released during hole relaxation from the shell- to the core-localized state is greater than or equal to the QD band gap (Fig. 2a). Our estimations show that for the QDs with R=4 nm, ρ c is ca. 0.7. This suggest that the range of the optimal aspect ratios where both conditions, slowed cooling and energy conservation, are met corresponds to ρ from ~0.45 to ~0.7 (shown as a shaded area in Fig. 6a).