Colloidal quantum dots (CQDs) feature a low degeneracy of electronic states at the band edges compared with the corresponding bulk material1, as well as a narrow emission linewidth2, 3. Unfortunately for potential laser applications, this degeneracy is incompletely lifted in the valence band, spreading the hole population among several states at room temperature4, 5, 6. This leads to increased optical gain thresholds, demanding high photoexcitation levels to achieve population inversion (more electrons in excited states than in ground states—the condition for optical gain). This, in turn, increases Auger recombination losses7, limiting the gain lifetime to sub-nanoseconds and preventing steady laser action8, 9. State degeneracy also broadens the photoluminescence linewidth at the single-particle level10. Here we demonstrate a way to decrease the band-edge degeneracy and single-dot photoluminescence linewidth in CQDs by means of uniform biaxial strain. We have developed a synthetic strategy that we term facet-selective epitaxy: we first switch off, and then switch on, shell growth on the (0001) facet of wurtzite CdSe cores, producing asymmetric compressive shells that create built-in biaxial strain, while still maintaining excellent surface passivation (preventing defect formation, which otherwise would cause non-radiative recombination losses). Our synthesis spreads the excitonic fine structure uniformly and sufficiently broadly that it prevents valence-band-edge states from being thermally depopulated. We thereby reduce the optical gain threshold and demonstrate continuous-wave lasing from CQD solids, expanding the library of solution-processed materials11, 12 that may be capable of continuous-wave lasing. The individual CQDs exhibit an ultra-narrow single-dot linewidth, and we successfully propagate this into the ensemble of CQDs.
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Extended data figures and tables
Extended Data Figures
- Extended Data Figure 1: Numerical simulations. (249 KB)
a, b, Poisson distribution of single-exciton (X), biexciton (XX) and multiple excitons in CQD ensembles with different average exciton occupations 〈N〉 under femtosecond (a) and continuous-wave (b) photoexcitations. c, Competition between stimulated emission (blue) and absorption (red) at 〈N〉 = 2.0 exciton population for ensembles. Hydrostatically strained (below the threshold) and biaxially strained (above the threshold) quantum dots. Grey indicates absorption at zero state filling, red indicates absorption of populated dots ensemble, and blue indicates stimulated emission. Black lines indicate excitonic energies and oscillator strengths. d, e, Numerical simulation of absorption bleaching and gain versus exciton occupancy in hydrostatically (d) and biaxially (e) strained CQDs for different hole degeneracies, splitting values and linewidths. f, Numerical simulation showing the dependence of excitation power required to maintain the given occupancy in the continuous-wave regime. A 1.4× gain threshold reduction in terms of excitonic occupancy reduces the required power about 1.7× in the continuous-wave regime. Reducing the gain threshold is critical for realizing continuous-wave lasing. More than 80% of the incident power aimed at achieving population inversion is converted to heat owing to Auger recombination losses.
- Extended Data Figure 2: TEM images and exciton decay dynamics of singly and doubly shelled biaxially strained CQDs. (330 KB)
a, Bright-field TEM and HRTEM characterizations of singly shelled asymmetric CQDs. TEM images unveil the hemispherical shape of asymmetric CQDs, which directly confirms that only (0001) facet growth has been blocked by oleylamine when TOPS was used as a sulfur precursor. b, Bright-field TEM and HRTEM characterizations of doubly shelled asymmetric CQDs. To get an overall morphology characterization, doubly shelled CQDs were deposited on lacey-carbon TEM grids with holes to observe CQDs with different orientations. A thorough analysis reveals that these CQDs (nanocrystals) show hexagonal disk-like shapes with two flat faces: viewing from the  zone axis, they show hexagonal or triangular shapes; observing along the [12 0] axis, they show rectangular shapes with two curved sides. The fast Fourier transform patterns (insets) were obtained from the boxed areas. c, Single- and multiple-exciton lifetimes of asymmetric CQDs with single and double shells, respectively. After the second uniform shell growth, fast non-radiative trap recombination is dramatically eliminated, resulting in greatly lengthened single-exciton lifetime (left) and increased PLQY. The multi-exciton dynamics (right) were investigated by ultrafast transient absorption spectroscopy. To achieve the same exciton population, only the CdSe cores were photoexcited (2.18 eV, 570 nm, 507 μJ cm−2). Owing to improved passivation, the amplitude of the slower decay (t2), which can be attributed to trion Auger recombination, decreases notably in doubly shelled asymmetric CQDs, indicating that photoionization has been partially suppressed. As a result, more excitons were retained in doubly shelled CQDs over the entire time regime investigated (0–8 ns). (In all figures, normalizations were performed as follows: maximum scaled to 1, minimum not rescaled.)
- Extended Data Figure 3: Band and exciton fine structures simulations. (343 KB)
a, Core-shell structures following the strain relaxation procedure. The left panel shows a tetrahedron shape, with the 4 nm CdSe core exactly at the centre, leading to hydrostatic strain. the right panel shows a disk shape, with the 4 nm CdSe off-centre by 2 nm, leading to biaxial strain. The local lattice constant mapping of the simulated biaxially strained core–shell structure is plotted here for comparison with experimental results in Fig. 2c. b, Wavefunctions of the topmost electron (E1) and hole states (H1, H2, H3, H4) in the biaxially strained CQDs. c, Single-particle states of hydrostatically and biaxially strained CdSe-CdSe core–shell quantum dots calculated with the tight-binding method (h is the manifold of four hole states). d, Exciton fine structures from tight-binding atomistic simulations. The lowest dark state originates from the spin-forbidden configuration based on the heavy hole. The lowest dark–bright splitting depends on the electron–hole exchange interaction, which remains on the order of 1 meV in thick-shell dots and is not affected by the splitting between the heavy-hole and light-hole states; that is, it is insensitive to biaxial strain.
- Extended Data Figure 4: Full absorbance spectra and absorption cross-sections of hydrostatically and biaxially strained CQDs. (177 KB)
a, b, Full-scale spectra. c, d, Spectra with exciton peaks zoomed in. See Methods for absorption cross-section measurement details.
- Extended Data Figure 5: Absorbance spectra, their second derivatives and photoluminescence spectra of CQDs with varying degrees of splitting. (316 KB)
a–c, Samples named asymmetric CQD1, CQD2 and CQD3; see synthetic details in the Methods. Asymmetric CQD3 is the single-shell CQD mentioned in the main text. Blue and red arrows highlight the peak positions. d, Photoluminescence spectrum of asymmetric CQD2. e–i, Absorbance and photoluminescence spectra evolution during first-shell growth; the resulting product is asymmetric CQD3. e, f, During the growth of the first asymmetric shell, the first exciton peak gradually broadens and then splits into two peaks with increasing reaction time, reaching a maximum splitting of 62 meV. At the same time, the band-edge exciton peak continuously redshifts as a result of increased electron wave function delocalization. g, The progressive splitting is more obvious in the second-derivative absorbance spectra. h, i, The photoluminescence linewidths dramatically decrease after shell growth and photoluminescence peaks redshift as the band-edge exciton peaks shift. j, A summary of data from e–f.
- Extended Data Figure 6: Single-dot photoluminescence linewidth measurement. (201 KB)
a, b, Typical single-dot spectra of hydrostatically (a) and biaxially (b) strained CQDs, with FWHMs of 60 meV and 32 meV, respectively. c, 24 hydrostatically strained CQDs show average photoluminescence linewidth of 63 meV and peak position of 1.96 eV, with standard deviations of 11.8% and 0.67%, respectively. d, The average photoluminescence linewidth and peak position of 20 biaxially strained single dots are 36 meV and 1.95 eV, with standard deviations of 7.2% and 0.5%, respectively. The binning time of the single-dot photoluminescence linewidth measurement is 50 ms.
- Extended Data Figure 7: ASE threshold, and modal gain measurements of CQDs films. (235 KB)
a, b, Spectra of hydrostatically (a) and biaxially (b) strained CQDs, respectively, with increasing photoexciting power, showing ASE peaks rising above the photoluminescence background. c, Emission as a function of photoexciting peak power density and pulse energy for both hydrostatically and biaxially strained CQDs. A 2 mm × 10 μm stripe with 3.49 eV (355 nm) photoexcitation energy and 1 ns pulse duration was used. The ASE thresholds are 36 μJ cm−2 and 26 μJ cm−2 for hydrostatically and biaxially strained CQDs, respectively. d, Variable stripe length measurements for both hydrostatically and biaxially strained CQDs. Measurements were carried out using a photoexciting energy of four times the threshold value, obtained using a 2 mm × 10 μm stripe. The gain values g are 200 cm−1 and 150 cm−1 for hydrostatically and biaxially strained CQDs, respectively. The lower gain value from biaxially strained CQDs can be explained by the fact that fewer emission states are participating in the optical gain. e, f, ASE threshold measurements of CQD films with 250 fs and 3.49 eV (355 nm) photoexcitation. Thresholds of 22 μJ cm−2 and 14 μJ cm−2 were determined from hydrostatically (e) and biaxially (f) strained CQD films used for measuring the 1 ns ASE threshold.
- Extended Data Figure 8: Single- and multiple-exciton lifetimes of hydrostatically and biaxially strained CQDs, respectively. (326 KB)
a, Owing to the similar total shell volume, both types of core–shell CQDs show similar single-exciton lifetimes. b, The multiple exciton decays with core-only photoexcitation (2.18 eV, 570 nm, 507 μJ cm−2) can be fitted as bi-exponential decays (c): in the fast decay regime, hydrostatically strained core–shell CQDs show slightly longer lifetime than the biaxially strained CQDs, but the opposite is true in the slower decay regime. Since multiple exciton decays are dominated by Auger recombination, the decay rates and amplitudes measured from transient absorption are much higher than those of the single-exciton radiative recombination measured using the TCSPC system. d, e, Multiple exciton decays under different photoexcitation intensities. The bleach signals time traces of hydrostatically strained and biaxially strained CQDs show clear dependence upon photoexcitation power, confirming that Auger recombination is the main decay path.
- Extended Data Figure 9: Continuous-wave PC-DFB CQD lasers with biaxially strained and hydrostatically strained CQDs. (486 KB)
a, Normalized integration of the emitted signal (shown in Extended Data Fig. 9c) as a function of power under optical photoexcitation at 2.81 eV using a continuous-wave laser. b, Spectra at varying pump powers. c, Time traces of normalized emission intensity of the PC-DFB laser as a function of input excitation power with continuous-wave excitation. d, Emission spectra at powers above and below the threshold for 50 ms pulses and 10 Hz repetition rate, constituting a 50% duty cycle; e, Emission spectra at powers above and below the threshold for 75 ms pulses and 10 Hz repetition rate, constituting a 75% duty cycle. These data were collected by applying a delay to the spectrometer acquisition and measuring the spectra of the last ten microseconds of the pulse. f, HeNe laser (633 nm) signal with electrical interference induced by the acousto-optic modulator driver in the photodiode signal with alternating-current coupling (the measured HeNe laser signal is continuous wave with steady output). g, Electrical signal in the photodiode with no input radiation, showing electrical interference. The oscillation (102 Hz) in these traces and in lasing experiments is consistent, and caused by electrical interference, rather than changes in intensity. h, Emission spectra of PC-DFB lasers made from hydrostatically strained CQDs at powers above and below the threshold for 30 μs pulses and 10 Hz repetition rate, i, Transient behaviour of the lasing intensity for 30 μs at 20 kW cm−2.
Extended Data Tables
- Supplementary Information (1.5 MB)
This file contains Supplementary Figures 1-5, Supplementary Table 1 and additional references.
- Supplementary Data 1 (326 KB)
This file contains the Source Data for Supplementary Figure 1
- Supplementary Data 2 (778 KB)
This file contains the Source Data for Supplementary Figure 2
- Supplementary Data 3 (171 KB)
This file contains the Source Data for Supplementary Figure 3
- Supplementary Data 4 (17 KB)
This file contains the Source Data for Supplementary Figure 5