1. Introduction

Two-photon-excited fluorescence imaging [1, 2] has been demonstrated to be a powerful technique for biological and medical applications. The success of such a multi-photon microscopy has prompted researchers to explore three-photon processes with hopes of improving spatial resolution, reducing undesirable linear absorption in living organisms, and enhancing signal-to-noise ratio by utilizing a longer excitation wavelength. In that regard, colloidal semiconductor quantum dots (QDs) are promising since they have been reported to possess larger three-photon absorption (3PA) cross-sections compared to organic dyes [3–6]. While 3PA in semiconductor QDs has been investigated [3–6], research on their three-photon-excited luminescence is limited except for CdS QDs and CdSe QDs [3, 4]. CdS QDs and CdSe QDs show efficient three-photon-excited, band-edge emission, but the intrinsic toxicity of cadmium has cast a doubtful future in applications. In addition, the trap states in CdS QDs play an important role in the intensity dependence of luminescence at photon energies below the band edge, which was found to be non-cubic dependence [3]. The cubic dependence on the excitation intensity is crucial in achieving higher spatial resolution in imaging. These two problematic issues may be overcome by using zinc chalcogenide doped with transition metal ions [7, 8]. Here, we report on the synthesis, characterization, Z-scan, and photoluminescence (PL) measurements of aqueous solutions of core/shell structured ZnSe/ZnS QDs with or without copper doping. We demonstrate that the Cu-doped ZnSe/ZnS QDs exhibit high efficiency for below-band-edge PL and nearly cubic dependence on the excitation intensity of femtosecond laser pulses at 1000 nm, which is close to a semi-transparent window for many bio-imaging applications.

2. Synthesis and linear-optical characterization

The synthesis of ZnSe/ZnS QDs was based on the reaction of zinc acetate with sodium hydroselenide in dimethylsulfoxide (DMSO) as solvent. Sodium hydroselenide was prepared by mixing sodium borohydride and selenium powder in methanol under nitrogen. When the selenium powder was completely reduced by NaBH₄, 10 ml of freshly prepared NaHSe solution (0.4 M in methanol) was added into another solution containing 50 ml of 0.2 M of zinc acetate (and 0.002 M copper acetate for 1% Cu doping) with vigorous stirring. Then NaHSe precursor, 6 ml of 1 M of Na2S solution was injected under vigorous stirring. The resulting mixture was precipitated with 10 ml of 1 M of mercaptopropionic acid (MPA) (with pH adjustment to 11 with NaOH). After the centrifuge and washing, the precipitation was re-suspended in water, and then heated to 95°C for 2 h to grow the QDs to a final size of ~4 nm.

The as-prepared QDs in water solution were characterized at room temperature by absorption, PL, and photoluminescence excitation (PLE) spectroscopic techniques under one-photon excitation (see Fig. 1(a)). For comparison, the spectra of ZnSe/ZnS QDs were normalized to those of Zn(Cu)Se/ZnS QDs. The lowest excitonic transition, 1S(e)-1S _3/2(h), in the undoped ZnSe core peaked at 410 nm, from which the core diameter was computed to be ~4.6 nm, according to density functional theory under the corrected local density approximation [9]. It was in agreement with our measurement (4.4±0.5 nm) by transmission electron microscopy (TEM). The 1S(e)-1S _3/2(h) transition in the 1% Cu-doped ZnSe core peaked at 395 nm, and the core diameter was estimated to be 4.1 nm, which agreed well with the TEM finding (4.1±0.5 nm). The PLE spectra showed that copper doping broadens the near-band-edge and higher-energy-level transitions compared with the undoped QDs, which was consistent with the findings on Cu-doped ZnS QDs [10].

 

Fig. 1. (a). One-photon absorption spectra (solid lines), PL spectra (dashed lines) and PLE spectra (dotted lines) of ZnSe/ZnS QDs (black) and Zn(Cu)Se/ZnS QDs (red) in aqueous solution. The PL spectra were measured with an excitation wavelength of 360 nm, and the PLE spectra were obtained with an emission wavelength of 540 nm. (b). Schematic diagram for photodynamics under one-, two-, and three-photon excitation.

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From the PL spectra for the two types of QDs, one can conclude that band-to-band PL signals were completely quenched by defect states and/or copper-related states, respectively, in agreement with the observations by Pradhan, et al., [8, 11]. The peak of the copper-related PL in the Zn(Cu)Se/ZnS QDs was red-shifted, compared with the PL signal of ZnSe/ZnS QDs that peaked at 498 nm originating mainly from the defect states. These spectroscopic results could be understood by photodynamics (see Fig. 1(b)). Shortly after electrons were excited from the valence band to the conduction band in pure ZnSe, they relaxed to the defect states, from which they recombined with holes in the valence band, emitting photons in the green spectral region. If copper ions were present in ZnSe, however, radiative recombination between electrons in the defect states and holes in d-orbital of copper-ions would become dominant, with a 25-nm red-shift compared to pure ZnSe QDs. More significantly, we have found that the quantum efficiency of the copper-related PL was greatly enhanced by ~20 fold, in agreement with the findings by Pradhan, et al., [8, 11].

3. Three-photon absorption and three-photon excited photoluminescence

Similar to one-photon excitation, the above photodynamics could also be realized with three-photon processes. In order to determine the 3PA cross-sections, open-aperture Z-scans were employed. The experimental set-up was similar to the standard one [12]. The 1000-nm laser pulses were provided by a Coherent Legend (seeded by Mira) pumped TOPAS-C operating at 1 kHz repetition rate, which minimized or eliminated any possible thermal effects. The full-width- at-half-maximum of the laser pulses was 200 fs. The QD solutions were contained in 1 mm-thick quartz cells for the Z-scans, which were depicted in Fig. 2. Following the Z-scan theory for 3PA [13], we plotted the absorbance (1-T _OA) (where T _OA is the open-aperture transmittance) as a function of the maximum laser intensity on the Z-axis. The slopes of ~2 were indicative of the presence of 3PA. To calibrate our set-up, we also conducted open-aperture Z-scans on ZnSe bulk crystal (Semiconductor Wafer, Inc. 0.9 mm-thick), from which we determined that the 3PA coefficient γ to be 0.044 cm³/GW², which was in the same order of magnitude as the theoretical predication by Brandi, et al., [14] (0.018 cm³/GW²).

 

Fig. 2. Open-aperture Z-scans with 200-fs, 1000-nm laser pulses at different excitation irradiances (I₀₀) for the aqueous solutions of (a) ZnSe/ZnS QDs and (b) Zn(Cu)Se/ZnS QDs. The symbols denote the experiment data, while the solid lines are the theoretical curves. The insets show the plots of Ln(1-T _OA) vs. Ln(I₀), and the solid lines represent the linear fits.

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Table 1. QD density, diameter, band-gap energy and 3PA of bulk and QD semiconductors.

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The 3PA coefficients are 1.1×10^-4 and 2.3×10^-4cm³/GW², respectively, for the aqueous solutions of ZnSe/ZnS QDs and Zn(Cu)Se/ZnS QDs. The 3PA cross-sections were then derived as 2.0×10^-77 and 3.5×10^-77 cm⁶ s²/photon² from σ ₃=(ћω)² γ/N, where N is the QD density. As shown in Table 1, such values were comparable with the reported values for CdS QDs [3], CdSe QDs [4] and ZnS QDs [5]. These cross-sections, however, were two orders of magnitude smaller than the findings by Lad, et al., for ZnSe/ZnS QDs [6]. It should be pointed out that the measurements of Lad et al. were performed with 35-ps laser pulses at an intensity of 6 GW/cm². Under their experimental conditions, the electron-hole pairs per QD, N _e-h/N, for ZnSe-II QDs might be estimated by

where τ_G is the pulse duration. It was much greater than unity and, hence, the three-photon-excited intraband absorption could become significant in their experiment [15]. Under our experimental condition, and using the 3PA coefficients listed in Table 1, the three-photonexcited electron-hole pairs per QD were computed to be less than unity. As such, threephoton- excited intraband absorption should be insignificant [15].

The three-photon-excited PL measurements were performed at room temperature with the same laser used in the Z-scans. To determine the PL efficiency precisely, a standard sample (Rhodamine 6G, 10^-4M in methanol) was measured with the same experimental set-up as described in the following. The incident pulses were focused by a 10× objective lens onto a 1 cm-thick quartz cell containing the QD or Rhodamine 6G solution, and the focal spot size was ~9 µm. The PL signal was collected by the same objective lens, refocused by another 10× objective lens, and then coupled into an optical fiber that was connected to a spectrometer (Avaspec-2048-SPU), with 1000-nm excitation wavelength filtered away.

 

Fig. 3. Three-photon-excited PL spectra of ZnSe/ZnS () and Zn(Cu)Se/ZnS () QDs in water are compared with that of Rhodamine 6G in methanol (). The PL spectra are obtained with 1000-nm excitation wavelength at 77 GW/cm². The inset shows log-log plots for the PL signals as a function of the excitation intensity.

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As shown by Fig. 3, band-edge PL of the QDs is entirely quenched, consistent with the one-photon-excited PL discussed previously. It is interesting to note that there is a red-shift between the one- and three-photon excited PL signals (Fig. 4), in agreement with several reports [16–18]. The red-shift was more pronounced for the Zn(Cu)Se/ZnS QDs than the undoped ZnSe/ZnS QDs. Due to the weak overlapping of the localized defect states electron wave with the valence band, such defect-state-related emission efficiency usually was very low. The strong green PL from copper-doped QDs was due to transitions from the defect states to the copper ions [7].

Inset of Fig. 3 shows the power dependence of the PL signals on the excitation intensity. Rhodamine 6G clearly possessed a quadratic dependence, indicating that the PL was induced by two-photon absorption (2PA). It was consistent with the observation of Albota, et al., who reported the two-photon-excited PL from Rhodamin 6G with femtosecond laser pulses at 960 nm [19]. The slopes are 2.8 and ~2.7 for the ZnSe/ZnS QDs and the Zn(Cu)Se/ZnS QDs, respectively. These slopes were different from that measured for CdS QDs by Chon, et al. [3], who observed that the slope was less than 2 for defect-state-related PL excited with laser wavelengths of 900–1000 nm. The slopes of 2.7–2.8 suggested that the two-photon transitions between the defect states and the valence band (or copper ions) played a less important role in ZnSe QDs than CdS QDs [3].

To extract the fluorescence quantum efficiency (η ₃) of the QDs, one may compare their PL photon counts with Rhodamine 6G under the same excitation intensity. Two- and threephoton excited fluorescence counts (f ₂ and f ₃) are given by [20, 21],

where φ is the fluorescence collection efficiency of the experimental set-up, σ_n is the n-photon absorption cross-section, ρ is the sample concentration, d_s·d_z is the small volume of the focused laser beam considered, and I_r is the nearly-constant laser intensity at this small volume. With the assumption that the temporal and spatial profiles of the laser pulse are Gaussian functions, one can integrate both Eq. (2) and Eq. (3) over the entire laser-focused volume and time, and obtain their ratio as follows:

For Rhodamine 6G, the quantum efficiency η ₂ was known as 0.895 and the 2PA cross-section σ ₂~15×10^-48 cm⁴ s/photon [19]. Substituting these two known values into Eq. (4), we computed the quantum efficiency to be 27% and 1.4%, for the Zn(Cu)Se/ZnS QDs and the ZnSe/ZnS QDs, respectively, and their 3PA action cross-sections (σ ₃η₃) were 9.5×10^-78 and 2.8×10^-79 cm⁶ s² photon^-2.

 

Fig. 4. One-photon-excited (-) (excitation wavelength=360 nm) and three-photon-excited (excitation wavelength=1000 nm) PL spectra of the Zn(Cu)Se/ZnS QDs (top) and ZnSe/ZnS QDs (bottom) in aqueous solution. For comparison purpose, all the spectra are normalized.

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4. Conclusion

In conclusion, 3PA and three-photon-excited PL of ZnSe/ZnS and Zn(Cu)Se/ZnS QDs in aqueous solutions have been unambiguously determined by Z-scan and PL measurements with femtosecond laser pulses at 1000 nm, which is close to a semi-transparent window for many biological specimens. The 3PA cross-section is as high as 3.5×10^-77 cm⁶ s² photon^-2 for the 4.1 nm-sized, Zn(Cu)Se/ZnS QDs, while their below-band-edge PL has a nearly cubic dependence on excitation intensity, with a quantum efficiency enhanced by ~20 fold compared to the undoped ZnSe/ZnS QDs.