1. Introduction

Auger recombination (AR) in quantum dots (QDs) is a nonradiative recombination process occurring when one or more extra carriers are introduced into one QD except for the existence of single exciton (electron-hole pair) [1–4]. In this case, the recombination energy rather than releasing as a photon, transfers to a third carrier (an electron or hole) by exciting it to a higher energy level, thereby ineluctably leading to the competition with carrier transfer or radiative recombination processes [5–8]. For example, the photoluminescence (PL) quenching or blinking in QDs is generally attributed to AR, impeding their applications in bio-labeling or QD-lasing [9–12]. Also, for QD LEDs, the light emission efficiency at high current densities is closely related to AR [13,14]. In addition, charge extraction efficiency in photocatalytic system is distinctly limited by AR [15]. For solar energy conversion, ultrafast AR as well impairs the efficiency gains originating from multiexciton generation whereby single QD absorbs one high-energy photon [16,17]. As essential in light-harvesting and emitting devices based on QDs, it is legitimate and significant to study the photophysical underpinnings and scaling laws of AR process, thus modulating the AR rate in corresponding applications. Particularly, bi-exciton recombination, when two excitons exist in one QD and decay nonradiatively [2], is the most frequently studied AR process since the lifetime can be routinely extracted from excitation-density-dependent transient absorption measurement [1].

With broadly tunable fluorescence covering the near-infrared and visible spectral region [18–21], high quantum yield [22,23], long luminescence decay [24,25], large Stokes shift [26,27] and low toxicity, ternary chalcopyrite semiconductor QDs of I-III-VI₂ composition, such as CuInS₂, AgInS₂ or CuGaSe₂, are attracting considerable interest for numerous energy and optoelectronic technologies including photovoltaic [28], luminescent solar concentrators [29], light emitting diodes [30] as well as bioimaging [31]. However, despite high superiority, the basic photophysics of ternary chalcopyrite I-III-VI₂ QDs is still not fully understood due to their chemical complication [26,32–35], giving rise to ambiguous guidelines for their optimization in applications.

Allowing for such situations, in this paper, we specifically study the size-dependent bi-exciton AR lifetime (τ_BX) of CuInS₂ (CIS) QDs as a representative for ternary chalcopyrite I-III-VI₂ QDs. CIS QDs with five different sizes ranging from 2.3 nm to 3.4 nm are prepared by the efficient thermal injection synthesis [24]. Steady-state absorption and PL spectra of the QDs are given for sample characterizations. Simultaneously, X-ray diffraction (XRD) and energy dispersive X-ray (EDX) measurements are performed to determine the structure and chemical composition of the samples, indicating chalcopyrite phase of the samples and verifying the element distributions. Through a well-established process [1], τ_BX of CIS QDs is extracted from excitation power density-dependent transient absorption obtained by pump-probe transient absorption (TA) spectroscopy. It shows τ_BX changes linearly with QD volume (V), conforming to the universal scaling law of τ_BX = γV [1,36,37]. The scaling factor γ is 6.6 ± 0.5 ps·nm⁻³ for CuInS₂ QDs, and the bi-exciton Auger lifetime is 4–5 times slower than typical CdSe QDs [38] with the same volume, suggesting reduced Auger recombination rate in ternary chalcopyrite. The results, facilitating further understanding the photophysics of the AR process in CIS QDs and even ternary chalcopyrite I-III-VI₂ QDs, is significant for practical applications of these QDs.

2. Methods

2.1 Spectra measurements

Major instruments used in this section are regeneratively amplified Ti:sapphire laser system (Coherent Legend, 800 nm, 85 fs, 7 mJ/pulse, and 1 kHz repetition rate) and Helios spectrometer (Ultrafast Systems LLC) for the generation and detection, respectively, of ultrafast transient absorption (TA) spectra. Specifically, the 800 nm pulses generated from the regenerative amplifier is split by beam splitters wherein one part is appropriately attenuated and used for the white light continuum (420–800 nm) probe beam generation in a sapphire window, and the other is used to produce the 400 nm pump beam in a frequency-doubling crystal (BBO). Power adjustment of the pump beam is controlled by a series of neutral-density filters. With suitable power, the pump beam is focused at the sample with a beam waist of 300 µm. The white light continuum is split into two parts, with one part used as probe and the other as reference for noise reduction from laser intensity fluctuations. Both the probe and reference beams are focused into a fiber optics coupled multichannel spectrometer, and then detected by complementary metal oxide semiconductor sensors at 1 kHz frequency. The pump beam is chopped by a synchronized chopper to 500 Hz. The probe intensities of the pumped and the unpumped sample are compared to calculate the pump induced absorbance change (ΔA). The delay time between the pump and probe pulses is controlled by a motorized delay stage. The instrument response function of this system is determined to be 120 fs by measuring solvent responses under the same experimental conditions, with the exception of high excitation intensity. The sample is hold in a 2 mm light path length quartz cuvette and stirred constantly by a magnetic stirrer during the measurements to avoid photo degradation.

Besides, UV-Vis and photoluminescence (PL) spectra are measured by a SolidSpec-3700 spectrophotometer (Shimadzu) and FLS980 fluorescence spectrometer (Edinburgh), respectively. XRD and EDX measurements are also implemented using D8 advance X-ray diffractometer (Bruker AXS) and X-ray energy dispersive spectrometer (Hitachi), respectively.

2.2 Synthesis of CIS QDs

CIS QDs are prepared according to an efficient synthesis from a literature by crucially controlling reaction temperature and time [24]. Briefly, indium acetate (0.584 g, 2mmol) is mixed with copper iodide (0.38 g, 2 mmol) and 1-dodecanethiol (DDT, 10 mL) in a three-necked flask. The reaction mixture is degassed under vacuum for 5 minutes and purged with argon three times. The flask is heated to 100 °C for 10 minutes until a clear solution is formed. The temperature is then raised to 230 °C. When the reaction has proceeded for certain periods of time corresponding to desired sample sizes (2.3 nm, 2.8 nm, 2.9 nm, 3.3 nm and 3.4 nm diameter, respectively in our experiments), it is quenched by immersing the flask in an ice-water mixture bath. The product QDs are isolated by precipitating by addition of acetone, centrifuging, and decanting the supernatant. The solid QDs product is redispersible in hexane for spectra measurements.

3. Results

3.1 Sample characterization

We synthesize five different sizes of pyramid CIS QDs with 2.3 nm, 2.8 nm, 2.9 nm, 3.3 nm and 3.4 nm diameter (determined by edge length of pyramid CIS QDs) [39,40], hereafter denoted as CIS_2.3, CIS_2.8, CIS_2.9, CIS_3.3 and CIS_3.4, respectively. Depicted in Fig. 1(a) are the steady state absorption and PL spectra of the samples. It shows undeterminable absorption peaks due to inhomogeneous broadening of the exciton bands originating from heterogeneous distributions of nanocrystal shapes, tetragonal lattice distortions, and compositional off-stoichiometry [19,39,41], which is normal in CIS QDs. Such as it is, the vague exciton peaks roughly present successive red shift with increasing size of CIS QDs, associated with reduced quantum confinement. More accurately, the PL peaks also demonstrate clearer shift to longer wavelength with enlarged size of the QDs, consistent with the changes of absorption spectra. The similar traces of the absorption curves and high symmetry of the PL peaks both imply relatively homogeneous size distribution of the synthesized CIS QDs in spite of the standard issue, (i.e. the size/shape inhomogeneity) for quantum confinement QDs [19]. In order to further validate the exciton peaks, we select a series of TA spectra for the samples. As shown in Fig. 1(b), the first exciton bleaching (XB) signals at ∼1 ps delay time dominated by state filling of CB electron levels [40] clearly display the lowest energy exciton peaks, locating at 523 nm, 579 nm, 589 nm, 614 nm and 622 nm, indicating the optical bandgaps of the five CIS samples as 2.37eV, 2.14eV, 2.11eV, 2.02 eV and 1.99 eV, respectively. Without efficient access to a transmission electron microscope (TEM), the diameters (edge lengths) of pyramid CIS QDs are derived to be 2.3nm, 2.8nm, 2.9nm, 3.3nm and 3.4nm according to the relationship between optical bandgap and diameter of CIS QDs ruled by the finite depth-well EMA theory, which has shown good correspondence with experimental results [39]. Besides, comparing the exciton peaks with PL peaks, large Stokes shift (348 meV, 260 meV, 326 meV, 312 meV, 295 meV) is also observed in these samples, consistent with that reported in literatures [26,42].

 

Fig. 1. Static absorption, emission and selected TA absorption signals for sample characterization at room temperature. (a) Absorption (solid lines) and PL (dashed lines, 400 nm excitation wavelength) of the five CIS QDs. (b) TA spectra of the five samples with 400 nm, 280 µJ cm⁻² excitation at ∼1 ps delay time showing the lowest energy exciton peak (corresponding to the maximum of the exciton bleach signal).

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For further validating the structure and chemical composition of the samples, we carry out XRD and EDX measurements. Figure 2(a) shows the XRD patterns of the samples with different sizes. The three peaks corresponding to the (112), (204)/(220) and (116)/(312) reflections of the crystal structure, well consist with related research and tentatively implies chalcopyrite phase of the QDs [39]. To confirm the information about chemical composition, the synthesized CIS_3.4 QDs are deposited on a quartz glass tank. EDX spectrum in Fig. 2(b) verifies the existence of Cu, In and S. The ratio of the elements derived from Fig. 2(h) is 1.38(Cu):1(In):2.30(S), signifying a Cu-rich composition. The appearance of C element owes to the hexane solution for dispersing the QDs before deposited on the quartz glass tank. Figure 2(c) gives a topography of the deposited QDs and a small area denoted by a red square is selected to obtain element distributions. Figure 2(d)–(h) exhibits an overlaid distribution of Cu, In, S and C elements, and the spatial distributions of each element.

 

Fig. 2. (a) XRD patterns of the samples with different sizes, (b) EDX spectrum of the CIS_3.4 QDs, (c) The topography of deposited CIS_3.4 QDs on a quartz glass tank, (d) The overlaid distribution of Cu, In, S and C elements, and (e-h) the spatial distributions of each element.

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3.2 Bi-exciton lifetime of CIS QD

In this part, we perform excitation (400 nm) power density dependent TA measurement to determine bi-exciton AR lifetime of CIS QDs. The TA spectrum of CIS_3.4 with 280 µJ cm⁻² exciton power density is given in Fig. 3(a) as a representative (other spectra with different exciton power densities of CIS_3.4, CIS_3.3, CIS_2.9, CIS_2.8 and CIS_2.3 see Fig. S1-S5 in Supplement 1). As the spectrums show, except for the dominant exciton bleach (XB), there is an extra weak, broadband photo-induced absorption (PA) signal (corresponding to positive ΔA) for all the QDs, whose amplitude increases with excitation power densities. With the hypothesis that PA amplitude is constant over the whole investigated spectral range [5,6,43], we subtract PA signal from the global TA spectrum and extract the XB kinetics. In Fig. 3(b), we plot the power density dependent XB kinetics of CIS_3.4 (other XB kinetics for CIS_3.3, CIS_2.9, CIS_2.8 and CIS_2.3 see Supplement 1, Fig. S6). As it shows, at low excitation power densities (especially below 560 µJ cm⁻²), when the photo-excited QDs are dominated by single exciton states, the XB signal is generally long-lived for all the QDs. At higher excitation power densities, a new fast decay component arises and becomes progressively conspicuous with increasing power densities, consistent with AR process of multiple exciton states [1,44].

 

Fig. 3. (a) TA spectra of CIS_3.4 with 400 nm, 280 µJ cm⁻² excitation as a representative, (b) XB kinetics of CIS_3.4 with 400 nm, various excitation power densities (56 µJ cm⁻², 112 µJ cm⁻², 140 µJ cm⁻², 168 µJ cm⁻², 224 µJ cm⁻², 420 µJ cm⁻², 560 µJ cm⁻², 840 µJ cm⁻², 1120 µJ cm⁻², 1400 µJ cm⁻², 1680 µJ cm⁻², 2240 µJ cm⁻², 2800 µJ cm⁻²) as a representative.

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To determine τ_BX of the samples, w, the initial average number of excitons per QD, is necessary for efficiently taking the different between kinetics at two lowest power densities with w<1 and 1<w<2, respectively. Acquisition of w values with different excitation power densities is routinely made by analyzing the power density dependence of the XB signal amplitude [24]. In short, at long delay time, t_L=200 ps, when AR is completed and only single exciton states remain, the transient XB signal amplitude is proportional to the number of excited QDs. We can define a normalized transient signal at t_L [5,6,45,46]:

At early delay time t₀∼1 ps, prior to AR, the initial normalized transient bleach signal is given by [5,6,45,46]:

We fit the normalized transient XB signals ΔS (t₀=1 ps) and ΔS (t_L=200 ps) in CIS as a function of excitation densities according to Eq. (1) and (2). Since the parameter w is proportional to the excitation density (I): w = CI, C is the only fitting parameter. As shown in Fig. 4(a), the experimental data can be well fitted with the model governed by Eq. (1) and (2), and from the fitting we obtain w values with any given excitation power density. On the basis of determination of w, we perform subtraction between the XB kinetics of CIS_3.4 with w<1 (56µJ/cm²; w=0.17) and 1<w<2 (420µJ/cm²; w=1.2), respectively, corresponding to the two lowest excitation power densities. It should be pointed out that it is reasonable to choose 420µJ/cm² and 56µJ/cm² during the kinetics subtraction because, when w<<1 (56µJ/cm²; w=0.17), there is very low probability for us to find a QD with more than one exciton, in other words, the kinetics corresponds to a single exciton process. In contrast, when 1<w<2 (420µJ/cm², 560µJ/cm²), we can find considerable QDs occupied by two excitons, leading to kinetics including both single exciton process and bi-exciton Auger recombination. Thus we can obtain a single exponential bi-exciton Auger process by kinetics subtraction. However, we didn’t choose the kinetics for 560µJ/cm² (w=1.6), because w is essentially a statistical average, that is, the higher the excitation power density is, the more probability we may find more than two excitons in one QD. In this case, the subtracted kinetics won’t be a pure bi-exciton Auger process but mixed with multi-exciton Auger process (Supplement 1, Fig. S7 indeed shows the fitted bi-exciton Auger lifetime decreases with increased excitation power density chosen in the range of 1<w<2, although they don’t deviate much obviously). Thus we choose the kinetics for 420µJ/cm² to ensure a pure single exponential bi-exciton Auger process after kinetics subtraction. The subtraction is plotted in Fig. 4(b) and fitted by single exponential curve. The consequent τ_BX is 23 ± 2 ps. For CIS_3.3, CIS_2.9, CIS_2.8 and CIS_2.3 QDs, corresponding normalized transient XB signals and w are plotted and fitted in Supplement 1, Fig. S8, which also show good agreement with the model mentioned above. τ_BX values of CIS_3.3, CIS_2.9 and CIS_2.8 are extracted as 21 ± 2 ps, 12 ± 2 ps and 10 ± 3 ps, as shown in Supplement 1, Fig. S9. Note that τ_BX of CIS_2.3 is not given in Supplement 1, Fig. S9 due to failure of single-exponential fit for subtracted kinetics. We speculate that it is too short to be derived from the literature method [1].

 

Fig. 4. (a) Normalized transient XB signals ΔS (t₀=1 ps) (black squares) and ΔS (t_L=200 ps) (red circles) in CIS_3.4 QD as a function of excitation density. The black solid lines are fits according to the model described in Eq. (1) and (2). The red dashed lines are fitted initial average exciton numbers per QD as a function of excitation density, (b) Bi-exciton Auger recombination process in CIS_3.4 QD obtained by kinetics subtraction (black dashed lines). The red solid line are single-exponential fit to it. (Corresponding data for other CIS QDs see Supplement 1, Figs. S8 and S9 for details).

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3.3 Size dependent bi-exciton lifetime of CIS QDs

To further understand the scaling law for Auger recombination in CIS QDs, we plot τ_BX as the function of the sample volume ($V = \sqrt 2 {d^3}/12$) in Fig. 5. As it shows, τ_BX linearly increases with sample volume, conforming to reduced quantum confinement effect with larger size and the universal V-scaling law [1,36,37]. According to the fitting parameters, τ_BX corresponding to d=2.3 nm is determined to be ∼2 ps. It is very close to 1 ps and the literature method [1] no longer works, thus leading to the deficiency of τ_BX of CIS_2.3 in Supplement 1, Fig. S9, as we have discussed above. Compared with typical CdSe and PbSe QDs [38], τ_BX of CIS is much longer (about 4-5 times that of CdSe and PbSe with the same volume) and the scaling factor, γ is fitted to be 6.6 ± 0.5 ps·nm⁻³). The 4-5 times difference in the Auger recombination between CdSe (or PbSe) and CIS QDs probably originates from the difference between their surface effect and carrier-carrier Coulomb coupling responsible for Auger decay [36]. For spherical CdSe (or PdSe) QDs and pyramid CIS QDs with the same volume, the surface area of CIS is much larger than that of CdSe (or PbSe). With larger surface-to-volume ratio in CIS QDs, carriers are easier trapped on the quantum dot surface, then the AR process should slow down [41,47]. In addition, carrier-carrier Coulomb coupling tend to weaken due to less compact pyramid structure compared to spherical structure, which also reduces the AR effect in CIS QDs. These two factors taken together generate slower Auger recombination observed in CIS QDs than that in CdSe (or PbSe) QDs.

 

Fig. 5. Bi-exciton lifetime as a function of the volume of CIS QDs. Bottom right table: τ_BX of each sample.

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4. Discussion

To the best of our knowledge, systematical study of the bi-exciton AR lifetime for CIS QDs is still rare and the scaling law remains unclear [35]. It should be mentioned that the results reported by Nagamine et al. [35] manifested longer bi-exciton AR process of CIS QDs (∼7 times slower than CdSe QDs with the same volume) against our samples. However, their CIS samples virtually referred to the Type-I core/shell CIS/ZnS QDs. The extension of the AR lifetime in core/shell CIS/ZnS QDs can be attributed to surface-related traps in such structure according to literatures [24,40], legitimately differing with core-only CIS QDs in our experiment. Moreover, they reported Auger lifetime as the function of the absorption cross sections instead of the volume, which also contributes to the imparity. In fact, the size dependent XB peaks and τ_BX in our results, specifically for CIS_2.9 (λ=589 nm, τ_BX= 12 ± 2 ps) and CIS_2.8 (λ=579 nm, τ_BX= 10 ± 3 ps), consist well with that reported by Wu et al. (CIS with 3.34 ± 0.95 nm size, λ= ∼580 nm, τ_BX= 9 ± 3 ps) [40] within an acceptable margin of error, indicating the rationality of the experimental data for all CIS sizes in this paper.

In summary, by detailedly analyzing the ultrafast time resolved absorption spectra of CIS QDs with various sizes, we demonstrate that bi-exciton Auger recombination of CIS QDs complies with the universal volume-scaling law: τ_BX= γV. The bi-exciton lifetime of CIS is 4-5 times that of typical CdSe and PbSe QDs with identical sizes, implying much slower Auger recombination process in ternary chalcopyrite. Consequently, it is important to take advantage of the positive effect of slow Auger recombination in scenario of exploiting light-harvesting and emitting applications based on ternary chalcopyrite QDs. Meanwhile, our results may provide useful information for further understanding the physical mechanism of Auger recombination process in ternary chalcopyrite QDs.