1. Introduction

Early theoretical predictions that the electron-hole pair quantum confinement effect in quasi-zero dimensional semiconductor quantum dots [1–4] provides intrinsically lower excitation thresholds compared to bulk crystals for lasers in low-loss media have become a technological reality. Epitaxially grown InGaAs quantum dot diode lasers have achieved ultralow threshold current densities (J_th < 20 A/cm²) [5]. Using low-cost methods of solution-based chemistry [6–8], nanocrystals from the II-VI semiconductors have emerged as technologically viable fluorophores across the red, green and blue (RGB). In addition to CQDs in flat-screen TVs [9] and bio-labels [10, 11], research demonstrations abound from photovoltaics [12, 13] to light-emitting diodes [14–17]. Research has also taken early steps towards laser devices which require exceptionally high-performance optical materials. We note demonstrations of CQD lasers as optically pumped vertical cavity surface emitting lasers (VCSEL) [18], distributed feedback (DFB) lasers across the RGB spectrum [19, 20], and photonic crystal coherent emitters [21, 22]. A newcomer to the field is II-VI colloidal nanocrystalline platelets where very recent work on ASE and lasing has been reported at exceptionally low optical excitation levels [23, 24]. In this manuscript, we focus on the CdSe/ZnCdS and CdSe/ZnS/ZnCdS CQD material system given its relative maturity and investigate the characteristics of those electronic states which can be recruited for optical gain at the lowest possible threshold for prospective practical laser devices.

The basis to optical gain for realistic laser devices is the ability to override competing non-radiative mechanisms. In case of colloidal II-VI nanocrystals there exists important earlier literature where experimental evidence across a vast variety of CQD preparations in solution or solid thin film has led to a number of gain models based on multi-exciton states (per CQD). Invariably, inelastic electronic interactions in multi-exciton systems lead to robust intrinsic non-radiative Auger recombination. What seems beyond dispute is that due to the strong spatial confinement, the many-body Auger processes can lead to profound inhibition and depletion of multi-excitonic gain on a subnanosecond time scale. Experiments have shown directly how e.g. the biexcitonic Auger process is about two orders of magnitude faster than one exciton spontaneous emission rates for typical high quantum yield CdSe-based CQDs [25]. In case of stereotypical biexciton gain models, application of Poisson statistics to CQD ensembles (see below) requires that <N> is greater than 1, where <N> is the number of excitons per CQD on average and <N> = 1 correspond to the condition of an optically transparent state (absorption and induced emission rates are equal) [26]. In such and other related multi-excitonic cases, to avoid premature gain depletion by the Auger processes, prior experiments have focused on study of optical gain under transient excitation in CdSe-based CQDs under femtosecond-pulsed optical pumping. While most valuable for basic research, such transient excitation conditions are impractical for pursuing compact and low-cost CQD-based RGB laser devices as well as other recently emerging solution-growth perovskites [27–29].

One approach to bypassing the Auger impact while lowering the excitation threshold for onset of population inversion has been proposed via using core-shell engineered type-II CQDs with built-in local electric field [30]. Here, the Stark effect is evoked to weaken the spatial overlap of the single particle electron and hole envelope functions [30, 31]. In this case, the optical transparency can be achieved at <N> on the order of 2/3. While now reaching a single-exciton gain regime, the reduced overlap of the electron and hole wave functions imposes a penalty on the optical cross-section leading to significant reduction of luminescence and maximum available optical gain. While not the focus of this paper, we note other nanocrystal structures such as colloidal quantum rods [32] and colloidal nanoplatelets [33] where similar issues on optimizing optical gain are likely present and await for detailed investigation.

In this study, we describe methods and results of the optical gain around 1S(e)-1S_2/3(h) exciton resonance at room temperature via transient spectroscopic techniques, applied to two different sets of type-I core/shell nanocrystals. In terms of structural details, the two core-shell preparations were distinctly different to test whether the single-exciton gain hypothesis might be a general phenomenon which depends only that the optical properties referred to above were satisfied. The thin films of two different sets of CdSe/ZnCdS and CdSe/ZnS/ZnCdS nanocrystals studied here have advanced to a state-of-the-art point where the materials exhibit near unity luminescence efficiency and can tolerate ambient temperatures beyond 150 °C without degradation [9].

2. Properties of dense CQD films

Figures 1(a) and 1(b) show transmission electron microscope (TEM) images of pyramidal-shaped CdSe/Zn_0.5Cd_0.5S (~6.2 nm in diameter) and spherical-shaped CdSe/ZnS/Zn_0.65Cd_0.35S (~13.6 nm in diameter) CQDs, respectively. For our laser device goals, reaching high optical density thin film was particularly important. Thus, the two sets of CQDs were synthesized in solution to high concentrations (~150 mg/ml) while ensuring minimal (unwanted) aggregation and maintaining high quantum yield. Subsequent formation of ~300 nm-thick solid films was enabled with optically smooth surface flatness (Fig. 1(c), as measured by atomic force microscopy [18]) and the effective refractive indices (n = 1.75 and 1.90 for pyramidal and spherical CQDs, respectively) by ellipsometry. These values correspond to a packing density of the films about 50% and 65% which approach the theoretical maximum for identical hard spheres (~74%), even without accounting for the finite thickness effects of the organic ligands. This tightly bound ligands in the high packing density of CQD films give rise to electronic isolation of individual CQDs. This implies that nearest neighbor interactions remain weak between the individual CQDs via direct electronic wave function overlap, or due to dipole-dipole interaction (thereby preventing propagation of excitation to e.g. defect sites on the macroscale). As a result, luminescence efficiency retained approximately 90% of its solution value in the self-assembled dense films.

 

Fig. 1 Structural characteristics of CQDs and their spin-cast, densely packed films. (a) TEM images of individual CdSe/ZnCdS CQDs showing pyramidal-type shape anisotropy, and (b) more spherical CdSe/ZnS/ZnCdS CQDs. Insets are cartoons of each type of CQD internal structure with red, green and yellow representing CdSe, ZnS, and ZnCdS layers, respectively; (c) SEM cross-sectional image of a close-packed CQD film on a silicon substrate (chosen for ease of cleaving and conducting). Individual CQDs within the close-packed assembly are somewhat visible with the films possessing an optically smooth top surface. XRD patterns for (d) CdSe/ZnCdS and (e) CdSe/ZnS/ZnCdS CQDs, indicative of a wurtzite crystal structure for both cases. For reference, the red “ticks” represent the well-known diffraction peak positions for bulk wurtzite CdSe.

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Figures 1(d) and 1(e) show X-ray diffraction (XRD) patterns of the CdSe/ZnCdS and CdSe/ZnS/ZnCdS CQDs. Although the geometrical shapes of the two classes of CQDs were quite different in symmetry, they possessed the same underlying wurtzite nanocrystal structure. The peaks in XRD patterns are resolved well enough for this conclusion, in spite of the relatively small sizes of the individual CQDs for XRD measurements, further underscoring the well-ordered crystalline quality of these nanocrystal preparations.

Figure 2 shows the absorption and spontaneous emission spectra from the two classes of dense CQD films at room temperature (PL acquired using a Xenon flash lamp filtered at 400 nm). Both sets of films display a corresponding clear and isolated lowest 1S(e)-1S_3/2(h) exciton absorption peak (n = 1), accompanied by higher order quantum dot interband transitions at least up to n = 3. While the spectral linewidths and the associated Stokes shifts are somewhat different for the two preparations, they maintain, importantly, an approximate commensurate relationship between these two critical parameters (i.e. a comparable relative spectral overlap between 1S exciton absorption and emission). This, we argue, is one key for achieving single-exciton-driven optical gain without necessity of multi-excitonic processes. For the pyramidal CdSe/ZnCdS CQDs the Stokes shift is as large as 52 meV but is of the same order as the half-width at half-maximum (HWHM, 43 meV) of the PL emission. For the spherical CdSe/ZnS/ZnCdS CQDs, the corresponding values are 17 meV for the Stokes shift and 27 meV for narrower luminescence linewidth.

 

Fig. 2 Absorption (dashed) and PL (solid) spectra from close-packed CQD films at room temperature. The PL spectra are red-shifted with respect to their lowest (and distinct) 1S(e)-1S_3/2(h) exciton absorption peaks by 17 and 52 meV, respectively. Note that while the CdSe/ZnCdS CQD films have a larger Stoke shift, their PL linewidth is broader whereas the CdSe/ZnS/ZnCdS CQDs show a narrow PL linewidth (27 meV of HWHM).

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In the latter case, we performed additional PL spectroscopy on single individual CQDs to show how in these preparations it was possible to reach a high degree of monodispersity in nanocrystal size which yields a 1S exciton linewidth at room temperature near the homogeneously broadened limit as seen in Fig. 3. Obviously, the PL peaks for the individual pyramidal shaped CQDs are more widely distributed than for the spherical shaped dual-shell CQDs. In addition, the HWHM values of PL show larger difference when compared between the single and ensemble CQD for pyramidal shaped CQDs. Note that the HWHM of PL for the ensemble of CdSe/ZnCdS CQDs is 43 meV, while it is just 30 meV for the single CQD case. However, this difference for CdSe/ZnS/ZnCdS CQDs is just 3 meV (27 meV for the ensemble and 24 meV for the single CQDs). These results suggest that the spherical shaped dual-shell CQDs are highly monodispersive to yield low inhomogeneous broadening.

 

Fig. 3 PL spectra from 10 single (a) CdSe/ZnCdS and (b) CdSe/ZnS/ZnCds CQDs at room temperature.

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We note the extensive literature on the widely varying, preparation-dependent Stokes shifts in II-VI CQDs [34–37] with values ranging from few meVs to hundreds of meVs. Below we suggest that there is an optimal range for a ground state exciton Stokes shift in emission (and gain spectrum) where single exciton inversion can overcome one-photon self-absorption, yet possess sufficient and useful optical gain.

With attributes such as outlined above, optically pumped lasers embedding closed-packed CQD films in monolithically integrated optical cavity structures have been demonstrated, such as CQD VCSELs in the red and green operating at modest excitation levels which empirically pointed to a dominant role of single-exciton gain [18]. Further, surface-emitting DFB lasers from the materials discussed here were achieved with high spatial coherence and good power conversion efficiency across the RGB colors using a compact optical pumping source [20].

3. Optical gain with CQD films

As the main method for metrology of optical gain, we applied time-resolved spectroscopy techniques to the two sets of CQD films focusing attention near the lowest exciton resonance. A series of ultrafast pump-probe experiments were performed. The output from an amplified Ti-Sapphire laser was frequency-doubled and used for pump pulses (400 nm, 100 fs, 100 kHz). The probe pulses were acquired by using a fraction of the Ti-Sapphire laser output for continuum white light generation. The pump and probe pulses were focused to circular spots (75 and 30 µm in diameter, respectively) near the center area of the close-packed CQD films. The CQD films were self-assembled by spin-casting the CQD solutions on glass substrates at optimized spinning speed (~2000 rpm) for one minute. Such small spot sizes were necessary to avoid any confounding effects from unwanted ASE and backscattering effects.

Key experimental results by gain spectroscopy are shown in Fig. 4 where the (non-linear) transient probe absorption spectrum is expressed as the sum of the low intensity linear absorption α(ω) and the pump induced photomodulation Δα(ω,t) for the two types of the solid close-packed CQD films. The spectral summaries of Figs. 4(a) and 4(b) are particular snapshots measured at 2 ps after the ultrashort pulse excitation, by which thermalization of the internal exciton bath has taken place, but prior to onset of any population decay by exciton recombination, including potential Auger processes. Thus the negative values of α(ω) + Δα(ω,t) provide a direct measure of the presence of optical gain through the 300 nm optical paths (film thicknesses). For the CdSe/ZnCdS CQDs, the optical gain is seen to onset on the red-shifted flank of the PL spectrum when the pump fluence reaches the level corresponding to creating the average number of e-h pairs per CQD of <N> = 0.6, that is at level of excitation which is well within the single-exciton gain regime. Similarly, for the CdSe/ZnS/ZnCdS CQDs, the optical gain emerges at <N> = 0.7. Though slightly higher than the case of CdSe/ZnCdS CQD films it adds support to empirical evidence that these nearly monodisperse CQD films also provide ready access to optical gain in the single-exciton regime. We note the importance of our calculation on average number per CQD. We used independent experimental data sets to do conversion from excitation energy to <N> by three calculation methods [18]: direct absorption measurement (i.e. absorption cross-section), multi-exciton contribution in time-resolved PL, and linear dependence of PL intensity on excitation energy at threshold levels. The calculated <N> values obtained from three different methods agree well to each other and confirm our single-exciton gain.

 

Fig. 4 Transient absorption spectra of (a) CdSe/ZnCdS and (b) CdSe/ZnS/ZnCdS CQD films at various excitation levels at room temperature [38]. The onset for optical gain occurs at α + Δα < 0 (black arrows). Corresponding e-h pair occupancy values at gain threshold are approximately <N> ~0.6 and 0.7, respectively. (As shown elsewhere [18–20], stimulated emission for both types of CQD films in laser resonator devices also occur well within the single-exciton gain regime). Time-resolved transient absorption measured at 2.02 and 1.93 eV (where optical gain first onsets) for (c) CdSe/ZnCdS and (d) CdSe/ZnS/ZnCdS CQD films at various excitation levels. Under sufficiently high optical excitation (<N> ~2.0), the optical gain decay lasts more than 1 ns, two orders of magnitude longer than the Auger process although there is a fast decaying multi-excitonic component at the beginning. At optical excitation below the gain threshold levels, the decay curves exhibit just slow exponential behavior (~10 ns).

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Figures 4(c) and 4(d) show time-resolved transient absorption under various excitation levels, now at fixed wavelengths corresponding to the onset of optical gain in Figs. 4(a) and 4(b) (i.e. the likely spectral location of peak gain). The probe pulses were tuned to 2.02 and 1.93 eV and for ease of viewing, the vertical axes in Figs. 4(c) and 4(d) are inverted so that optical gain occurs when -Δα/α > 1 in these plots. For both types of CQD films, the transient absorption curves show a single exponential decay rate at low excitation levels as expected for a single-exciton recombination process (i.e. <N> = 0.45 and 0.52 in Figs. 4(c) and 4(d), respectively). However, as the excitation levels increase, a faster decay process emerges which we assign to the multi-excitonic Auger process. The Auger decay time constants extracted from fits to the experimental transient absorption data are 125 ± 3 (CdSe/ZnCdS) and 257 ± 16 (CdSe/ZnS/ZnCdS) ps. While not studied in more detail here, we note that the extensive theoretical and experimental studies in CdSe-based CQDs have suggested how the Auger recombination process is influenced by the spatial shape (abruptness) of the electronic confinement potential of the CQD core/shell structure [39–41]. We surmise that the CdSe/ZnS/ZnCdS CQDs may benefit from some “smoothing” out the electronic confinement potential across the core/shell interface, appears to reduce the Auger recombination rate in comparison with cases of an abrupt boundary [40].

Useful information is also embedded in the time-resolved transient absorption data. In particular, we see the gain persists beyond 1 ns at sufficient excitation levels. From Figs. 4(c) and 4(d), starting at moderate level of excitation, the optical gain turns off after ≈220 and 380 ps at pumping level of <N> = 1.00 and 1.15 for the CdSe/ZnCdS and CdSe/ZnS/ZnCdS CQDs, respectively. As the excitation is increased, the optical gain persists up to one order of magnitude longer than predicted from the presumed Auger recombination rate in both cases. Statistically, of course, with ultrashort pump pulses, there exists finite probability of multi-exciton presence even at relatively low excitation levels. In the simplest description, the Poisson distribution of various excitons per CQD is given by:

In order to observe clearly the roles of Stokes shift in the optical gain of CQD materials, we measured and analyzed ASE signals at various temperatures (Fig. 5). By decreasing the temperature, we observed an increase of the Stokes shift while reducing the linewidths of optical transitions (PL and absorption) for the CdSe/ZnCdS CQDs as shown in Fig. 6(b). However for the CdSe/ZnS/ZnCdS CQDs, only the linewidths reduce and the Stokes shift remains the same as lowering the temperature (Fig. 6(e)). The linewidth narrowing per se is most likely due to reduced exciton-phonon coupling. Overall, the reduction in the spectral overlap of spontaneous emission and absorption spectra appeared to benefit formation of optical gain as seen from the lowering of the ASE thresholds. Spectral relationships in Figs. 5(a)-5(c) further show that the emergence of the ASE peaks (gain maxima) from the parent PL peak is curiously temperature dependent for the CdSe/ZnCdS CQDs. Whereas at room temperature the ASE peak is slightly red-shifted from the PL peak (Fig. 5(a)), at T = 175 K it locates at the center of the PL peak (Fig. 5(b)), while at T = 5 K where the magnitude of the Stokes shift (~72 meV) is almost comparable to the PL linewidth (~74 meV), the ASE peak occurs on the higher energy side of the PL (Fig. 5(c)). Correspondingly, across the entire temperature range, the ASE thresholds decrease monotonically from <N> = 0.78 and 0.87 at room temperature to <N> = 0.30 and 0.44 at T = 5 K (Fig. 6(a)) for the CdSe/ZnCdS and CdSe/ZnS/ZnCdS, respectively. Note that the ASE thresholds are higher than the gain threshold measured by pump-probe experiments due to losses of photons in the stripe excitation. The spectral results show that the ASE peak follows the tail of absorption peak rather than stays red-shifted from the PL peak with biexciton binding energy offset as a signature of conventional biexciton gain mechanism.

 

Fig. 5 ASE spectra at various temperatures for the (a-c) CdSe/ZnCdS and (d-f) CdSe/ZnS/ZnCdS CQD films.

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Fig. 6 Threshold characteristics of edge emitted ASE signals as a function of <N> at various temperatures for the (a) CdSe/ZnCdS and (d) CdSe/ZnS/ZnCdS CQDs. The Stokes shift and the linewidth of the PL as a function of temperature for the (b) CdSe/ZnCdS and (e) CdSe/ZnS/ZnCdS CQDs. The location of the spectral peaks of the PL, ASE and the first absorption spectra at the 1S(e)-1S_3/2(h) exciton resonance for the (c) CdSe/ZnCdS and (f) CdSe/ZnS/ZnCdS CQDs.

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The above experimental results, coupled to our parallel applied demonstrations of low-threshold lasing in optical resonator structures of both types of CQDs [20] underscore that the putative single-exciton mechanism is not a “single sample effect”, a point of some relevance given the challenges in precisely controlling the reproducibility in the growth chemistry of various colloidal nanocrystals in this field. We, therefore, suggest that single-exciton optical gain mechanism can be a rather general, and perhaps dominant electronic source of gain for appropriately tailoring of nanocrystals for II-VI CQD lasers - if certain conditions are satisfied as discussed next.

In contrast to very well established epitaxially grown single crystal planar heterostructures (e.g. GaAs/AlGaAs and Ge/Si), accurate quantitative modeling of the electronic structure in the solution-synthesized nanocrystals remains problematic, in part due to extrinsic reasons (including variations in the CQD preparations from one laboratory to another). The heterojunction discontinuities in the II-VI core-shell CQDs can be roughly estimated from bulk crystal parameters (such as work functions) though the effects of the ligands on the shell electronic energies is a challenge. Here we make an empirical argument for the single-exciton gain while drawing from published theoretical work as follows. It is well appreciated how a significant enhancement of the electron-hole Coulomb interaction impacts optical properties in low dimensional semiconductors such as quasi-two dimensional quantum wells, related quantum nanoplatelets, and quasi-zero dimensional quantum dots. In principle, a further enhancement may ensue from dielectric confinement effect by a lower index surrounding medium [42, 43]. Experimentally, it is evident from e.g. Fig. 2, the ground state exciton is very robust at room temperature in the CdSe-based CQDs considered here and the specific optical resonance we are interested in, specifically in the range of magnitudes of the Stokes shift between the 1S(e)-1S_3/2(h) exciton absorption peak (n = 1) and its corresponding spontaneous emission (PL).

Apart from extrinsic (i.e. growth specific effects), fundamentals of the purely electronic origins for the Stoke shift are known in principle. In terms of the microscopics of the e-h interaction, the exchange portion of the (indirect Coulomb) interaction results an enhancement to the energy difference between the spin-singlet and -triplet excitons, providing one specific mechanism for the Stokes shift [44]. In addition, for CdSe-based CQDs in the strong confinement regime, the intrinsic asymmetry of the wurtzite structure and the effect of spin-orbit coupling are additional factors for contributing to the Stokes shift. These effects split the exciton energy levels further to form optically forbidden ground exciton states [34, 45]. Thus, the combination of energy difference between the optically active and forbidden states as well as the energy gap between the singlet and triplet exciton states caused by the electron-hole exchange interaction form a baseline for the intrinsic Stokes shift, further compounded by the nanocrystal shape asymmetry and internal crystal field effects [46]. For the spherical dual-shell CQDs, their high degree of monodispersity benefits the single-exciton gain from the narrow transition linewidths which are already present in conjunction with the relatively small Stokes shifts in the CQD films.

4. Conclusion

In conclusion, we measure the non-linear absorption spectra from two different sets of type-I CQD films with high packing density and robust 1S exciton state to verify the single-exciton state as a dominant optical gain mechanism at room temperature. We find out that the optical gain occurs for both CQDs when the average occupancy of the electron-hole pair is less than 1 (single-exciton gain regime, i.e. <N> < 1). Time-resolved transient absorption results show the long decay characteristic of the optical gain attributed by effective circumventing of the non-radiative Auger process. High volume fraction of the CQDs in gain media, precise spectral balance in the absorption and emission spectra and high monodispersity of the CQD ensemble are the key parameters for achieving the single-exciton gain state. This study can be an important issue for opening a universal access toward single-exciton optical gain regime in colloidal quantum nanostructures for practical device design.