Size confinement and origins of two-photon absorption and refraction in CdSe quantum dots

Baohua Zhu; Fangfang Wang; Chen Liao; Huichao Zhang; Jiayu Zhang; Yiping Cui; Yonghong Ye; Yuzong Gu

doi:10.1364/OE.27.001777

1. Introduction

In recent years, third-order nonlinear optical (NLO) properties of semiconductors have aroused substantial research interest due to their applications in electro-optic devices for information processing and telecommunications [1,2]. However, the two-photon absorption (2PA) cross sections in many bulk semiconductors, such as ZnSe [3] and CdSe [4], are not sufficiently large enough for requirement in applications. To improve the NLO properties, some efforts have been denoted in different semiconductor quantum dots (QDs). The 2PA cross sections of CdS QDs [5], CdSe QDs [6–11], CdSe/CdS QDs [12,13], CdSe/ZnTe QDs [4], CdTe QDs [14–16], metal particle-doped CdTe QDs [14,17], ZnTe QDs [18], Mn-doped ZnSe QDs [19], PbSe QDs [20] and Si QDs [21] were reported to be one-five magnitude orders larger than that of their corresponding bulk semiconductors. Nevertheless, the magnitude and the correlation between size and the 2PA cross section and NLO refraction of semiconductor QDs are still not well explored. Some authors have experimentally determined that QDs exhibit NLO enhancement with the QDs’ size decrease [8,13], while other authors have recently reported that the relationship of NLO absorption cross sections with QDs’ size is reversed [6,10,11,15,16,22]. A complete understanding of the correlation between size and QDs’ optical nonlinearities is still lacked. To investigate the QDs’ third-order NLO properties is urgent and important for applications in nonlinear optoelectronic devices.

Recently, in addition to the quantum confinement effect [6,8,23], the mechanism of enhanced optical nonlinearity in semiconductor QDs has also got our attention. The generation of short-lived electron-hole plasma was proposed for the NLO enhancement of CdS_xSe_1-x [24]. The mechanism for NLO improvement in CdS was mainly attributed to the reduction of the exciton absorption strength in the presence of an optically generated trapped electron-hole pair, which was caused by the effect of surface states [25]. The size-dependent optical nonlinearity of Mn-doped ZnSe QDs [19] and CdSe QDs [10] was explained by the modified local field effect. The optical Stark effect was also suggested for the improved NLO performance in CdTe QDs [26]. A comprehensive mechanism of the NLO properties in QDs is less well understood, which is desirable due to its help in determining their suitability for possible applications.

In this paper, the aim is to study the correlation and origins of size confinement on the NLO response of QDs. CdSe QDs with different sizes were successfully synthesized and their third-order NLO properties were investigated. The results showed that the 2PA cross section was increased with size decrease and then decreased with size further decrease. A theoretical correlation of NLO susceptibility with size was deduced to be in agreement with the experimental results. Some NLO origins were discussed.

2. Experiments

The CdSe QDs were synthesized via a well-established organometallic route [27,28]. The QDs with twenty-three various sizes were prepared by controlling the growth time, and the CdSe samples were puriﬁed and labeled as Sample 1 (S1) to Sample 23 (S23). All these colloidal QDs were dissolved in toluene with a concentration of 1.2 × 10⁻⁴ mol/l for measurements, which was adjusted by their absorption spectra.

Figure 1 shows the typical UltraViolet (UV) -Visible optical absorption and photoluminescence (PL) spectra of CdSe QDs at room temperature by using a UV-3600PC ShimadzuCary5000 UV-VIS-NIR spectrophotometer and an Edinburgh F900 fluorescence spectrophotometer, respectively. The absorption peaks are varying from 524 nm to 642 nm with PL peaks from 529 nm to 654 nm. The red shift of absorption and PL peaks indicates the size growth of the QDs. A transmission electron microscopy (TEM, JEM 2000EX, JEOL) is used to image these CdSe QDs. The insets of Fig. 1 show the typical TEM and HRTEM images of CdSe QDs (S6). All the QDs’ average diameters ranging from 2.6 nm to 8.8 nm could be obtained, with the average growth of 0.28 nm.

Fig. 1 The typical absorption (the solid lines) and PL (the dashed lines) spectra of CdSe QDs. The insets show the typical TEM and HRTEM images of S6 with size of 3.8 nm.

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The NLO measurements were carried out at room temperature using a mode-locked 80 fs Ti:sapphire (Mira900-F, Legend-F from Coherent Inc.) laser and an amplifier system operating at a repetition rate of 1 kHz with the light source at 800 nm wavelength, corresponding to an energy lower than the bandgap of CdSe (hν/E₀<1). The NLO absorption and refraction of samples were measured by open-aperture (OA) and closed-aperture (CA) Z-scan method, from which the magnitudes and signs of samples' imaginary part (Imχ⁽³⁾) and real part (Reχ⁽³⁾) of the third-order NLO susceptibility (χ⁽³⁾) could be determined, respectively [2,29]. The input light was focused by a convex lens with the focal length of 100 mm, and all the Z-scans were performed with excitation irradiance of 14.1 GW/cm². The light path was testified to be correct by using a liquid-CS₂ cell as a calibration standard.

3. Results and discussion

Figure 2 shows the typical OA, CA and CA/OA Z-scan curves of CdSe with size of 2.6, 4.9, and 5.5 nm, respectively. The CA/OA Z-scan curves show peak-to-valley profile, suggesting a self-focusing and positive nonlinear refractive index (n₂) in QDs. The OA curves exhibit a valley, indicating the two-photon absorption (2PA) process and negative nonlinear absorption coefficient β. The Z-scan curves are fitted according to the equations in [26] and Reχ⁽³⁾ and Imχ⁽³⁾ values could be calculated accordingly. Note that, the χ⁽³⁾ value of toluene is measured to be too small to be negligible compared with that of QDs, which is shown in OA, CA and CA/OA Z-scan curves.

Fig. 2 Typical OA (a), CA (b), and CA/OA Z-scan (c) curves of CdSe QDs. The blue solid lines are the fitting curves by theoretical formulae of [26].

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Figure 3 shows the plots of χ⁽³⁾, Reχ⁽³⁾ and Imχ⁽³⁾ versus the QDs size. It can be seen that Imχ⁽³⁾ and χ⁽³⁾ values are 10⁻¹² esu, which are one order magnitude larger than that of Reχ⁽³⁾, indicating that NLO absorption dominates the NLO performance. The Imχ⁽³⁾ value increases from 0.96 × 10⁻¹² esu to 7.8 × 10⁻¹² esu with size increasing, and then decreases to 1.94 × 10⁻¹² esu with the size further increasing. A maximum value of 7.8 × 10⁻¹² esu is obtained for CdSe QDs with size of 4.9 nm.

Fig. 3 2χ⁽³⁾, 10Reχ⁽³⁾ and Imχ⁽³⁾ versus the size of CdSe QDs.

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To testify the experimental results obtained by Z-scan method, NLO transmittance method was used [30]. Figure 4 shows the typical NLO transmission plots, by fitting which the 2PA cross section can be obtained. The 2PA cross sections are 0.9 × 10⁻¹⁸ cm⁴/GW (2.6 nm), 3.5 × 10⁻¹⁸ cm⁴/GW (4.9 nm), and 1.3 × 10⁻¹⁸ cm⁴/GW (5.5 nm), respectively. Compared with the values of 1.2 × 10⁻¹⁸ cm⁴/GW (2.6 nm), 5.1 × 10⁻¹⁸ cm⁴/GW (4.9 nm), and 2.0 × 10⁻¹⁸ cm⁴/GW (5.5 nm) by Z-scan experiments, the magnitude and trend of the QDs’ values are consistent. The magnitude of 2PA cross section is comparable with that reported in [15] and [11]. The trend of the NLO enhancement with the QDs’ size increase from 2.1 nm to 4.9 nm is comparable with that of semiconductor QDs in some reports [6,10,15,16]. And the trend of the NLO weakness with QDs’ size increase from 4.9 nm to 8.8 nm is similar to that of QDs in other studies [8,13].

Fig. 4 Plots of output intensity versus input intensity. The blue solid lines are fitting curves.

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A two-band approximation model was used to analyze the third-order NLO susceptibility of semiconductor QDs with different sizes [31]. In this model, the interaction between the system and the external field was treated with photoinduced dipole approximation. The total effective NLO susceptibility of the QDs is given by [31]

χ^{(3)} = - \frac{3 i}{16 R ε_{0}} {\begin{cases} \frac{4 A^{2}}{(i ω_{1} + γ) (ω_{1}^{2} + γ^{2})} - \sum_{σ} B_{σ}^{2} \times \dots \\ \times [\frac{2}{[i (ω_{2 σ} - ω_{1}) + γ] (ω_{1}^{2} + γ^{2})} + \frac{1}{(i ω_{1} + γ) (i ω_{2 σ} + γ)} [\frac{1}{i (ω_{2 σ} - ω_{1}) + γ} - \frac{1}{i ω_{1} + γ}]] \end{cases}}

where A and B are the photoinduced transition dipole moments for the one-pair and two-pair exciton states, respectively.

B = \sqrt{2} A = 2 \sqrt{2} P_{c v}^{2}

, where

P_{c v} = ℏ e / \sqrt{4 μ E_{R}}

is the photoinduced transition dipole matrix element [31],

E_{R} = E_{g} + ℏ^{2} π^{2} / 2 R^{2} (1 / m_{e}^{*} + 1 / m_{h}^{*}) - 1.8 e^{2} / ε R

is the bandgap of CdSe QDs [32], R is the radius of CdSe QDs, E_g is bandgap of bulk CdSe, and m_e* and m_h* are the effective mass of electron and hole, respectively.

ω_{1} = E_{1} - ω

,

ω_{2 σ} = E_{2} - 2 ω

, ω is photon energy (1.55 eV (800 nm) in our experiments),

2 E_{1} ≃ E_{R} (α_{B} / R) [1.8 {(α_{h} / R)}^{1 / 2} - 0.4] - E_{2}

is one-pair exciton energy,

E_{2} = 2 π^{2} E_{R} {(α_{e} / R)}^{2} + E_{R} (α_{B} / R) [13.2 {(α_{h} / R)}^{1 / 2} - 9.2]

is two-pair exciton energy [31], α_B, α_h and α_e is the exciton Bohr radius, hole Bohr radius and electron Bohr radius of CdSe, respectively. γ is dissipation factor. The effective NLO susceptibility is affected by the regimes quantization of the CdSe exciton, R>α_B (4.2 nm), quantization of the electron, α_B>R>α_h (1.1 nm), and quantization of electron and hole, α_h >R, respectively [33]. Our QDs’ radius ranging from 1.05 nm (smaller than the CdSe hole Bohr radius) to 4.4 nm (larger than the CdSe exciton Bohr radius) is across the strong, moderate and weak confinement regimes. With this understanding, the coulomb energy of two-pair exciton is strengthened with QDs radius decrease, and the two-pair exciton energy is smaller than the plus of two exciton energy [31]. Figure 5 presents the comparison between the theoretical results based on Eq. (1) and the experimental data. The trend of the theoretical NLO susceptibility is coincident with the experimental results.

Fig. 5 The experimental data (the dots) and theoretical fitting curves (the blue dash line) of χ⁽³⁾ of CdSe QDs.

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The photoinduced transition dipole moment, which dominates the NLO performance in CdSe QDs, results from the exciton oscillator strength (f_cv) as $P_{c v}^{2} = f_{c v} ℏ e^{2} / 2 m_{0} ω_{c v}$ [31,34]. The exciton oscillator strength is related to the overlap of electron and hole wave functions [25]. In the weak confinement regime, the electron and hole wave functions of the two excitons are suggested to have few overlap since the movement of electron and hole is free, and thus the photoinduced dipole moment is small. In the moderate regime, the electron is localized by the QDs size, and the wave functions of electron and hole in two-pair exciton become increasingly overlappled with size decrease. This enhances the two-pair exciton oscillator strength and accordingly improves the photoinduced dipole moment and optical nonlinearity of QDs [31,34]. However, in the strong regime, both the hole and the electron in two-pair exciton are localized by NCs size [34]. The coulomb interaction repulsion force between two electrons and two holes in two-pair exciton becomes stronger with size further decrease. This causes the overlap of elctron and hole wave functions in two-pair exciton reduced, and accordingly makes the two-pair exciton oscillator strength weakened and the NLO response of CdSe decreased [25,31,34]. One-pair exciton-related photoinduced dipole moments might contribute to this difference, because they monotonically increased the overlap between elctron and hole wave functions with size decrease and accordingly monotonically improve the NLO performance of CdSe [34].

We have also observed that the maximum χ⁽³⁾ value is obtained with QDs size 7.6 nm, which is different from the experimental results. The difference between the experimental results and the theoretical ones might be caused by local field effect. According to the Maxwell Garnet model [35], the local field effect, has been used to explore the NLO behavior in Mn:ZnSe [19] and CdSe/CdS [12]. In the case of CdSe dispersed in toluene, the effective nonlinear susceptibility of QDs can be given by $χ_{e f f}^{(3)} = p {(\frac{3 ε_{0 s}}{2 ε_{0 s} + ε_{e f f}})}^{4} χ_{m}^{(3)}$ [35], where χ_m⁽³⁾ is the NLO susceptibility of CdSe QDs, p is the volume fraction of the QDs and ε_0s is the dielectric constant of the solution. Given CdSe dielectric constant (4.8), the effective dielectric constant ε_eff can be calculated by the formula in [35]. Meanwhile, since the CdSe concentrations used in our experiments are the same, the volume fraction p is increased with QDs size increase. The theoretical results from local field effect could improve the NLO susceptibility of CdSe QDs with size increase, which accordingly contributes to the shift from 4.9 nm to 7.6 nm size in Fig. 5.

On the other hand, defects in CdSe QDs might depress their optical nonlinearities and result for the shift to small size in the experimental results in comparation with theoretical ones. It is suggested that large ground-state dipole moment, which is a kind of the intrinsic internal field and is linked with defects of QDs, will strongly affect the selection rule and the electronic structure by means of excitonic transitions [36,37]. The ground state dipole moment induced intrinsic 2PA coefficient of CdSe QDs (γ) is determined by $γ = β n_{0 s}^{2} / (n_{0}^{2} p {| f |}^{4})$ [38], where $β = 4 π Im χ^{(3)} / (λ n_{0}^{2} c ε_{0})$ [2], n_0s and $n_{0} = {[1 + (ε_{0} - 1) / (1 + 0.308 / \sqrt{R})]}^{1 / 2}$ are the linear refractive index of solution and QDs, respectively, and ε₀ is dielectric constant of QDs. p is the volume fraction of CdSe QDs in the solution and $f = 3 ε_{0 s} / (2 ε_{0 s} + ε_{e f f})$ is the local field correction depending on the dielectric constants of solvent ε_0s and the QDs’ ε_eff [12]. The trend of intrinsic 2PA coefficient γ is evaluated to coincide with that of β by Z-scan measurements, confirming that the NLO performance is related with defects in QDs. It is also demonstrated that the nonradiative defect states in QDs could rapidly quench electrons and lessen the spatial overlap of electron and hole wave functions [7,25]. This decreases the photoinduced dipole moment and thus weakens the QDs’ NLO response.

The role of defects can be confirmed by X-ray diffraction (XRD) spectra. Figure 6 shows the typical XRD spectra of the CdSe QDs by a Rigaku D/max 2500 VL/PC diffractometer. The crystalline domain could be calculated from Sherrer equation according to the width of the (110) peaks. For S13, the calculated crystalline domain is similar with the average size obtained from TEM image (0.98:1), and in other two sizes, the ratio of the crystalline domain from XRD spectra to the average size from TEM images is 0.95:1 and 0.96:1, respectively. This indicates that the QDs with size of 4.9 nm has less defects than the other two samples, which arises from surface optimization/reconstruction during the size growth of QDs [28,39]. Furthermore, for QDs with size of 2.6 nm, the intensities of the (103) and (102) diffraction peaks (2θ around 46° and 35°, respectively) are reduced compared to those of the (110) and (112) peaks, which is possibly caused by lattice contraction occurring when the size of the NCs becomes smaller, and hence defects are increased [39]. The role of surface defects is also illustrated by PL quantum yield (QY) of CdSe QDs, as exhibited in the inset of Fig. 6. The PL QY is increased from 8% to 46% with the QDs’ size increase, which is attributed to the lower possibility of capturing excitons by surface defect traps induced by surface reconstruction. The PL QY is then decreased from 46% to 6% with the QDs’ size further increase, which is due to a higher possibility of capturing excitons by surface defect nonradiative traps [28,39].

Fig. 6 Typical XRD spectrum of CdSe QDs. The inset represents the PL QY versus QDs’ size.

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4. Summary

In summary, CdSe QDs with size ranging from 2.6 nm to 8.8 nm were successfully synthetized and the size-dependent third-order NLO response and its origins have been investigated. As the diameter of the QDs was decreased, the 2PA cross section and NLO refraction index were found to be improved. The enhancement can be attributed to the increase of two-pair exciton-related photoinduced dipole moment and intrinsic dipole moment in CdSe, as well as the local field effect surrounding the QDs. When the QDs size was further decreased, the 2PA cross section and NLO refraction were depressed. The NLO reduction mainly origins from the defects in QDs and surface reconstruction. Theoretical approaches are in accordance with experimental results. The CdSe QDs, which possess a large 2PA cross section due to size-confined dipole moment and local field, is a potential nanomaterial used to improve the NLO performance of photoelectric devices in the near-infrared field.

Funding

National Natural Science Foundation of China (NSFC) (61404045, U1404624, 61875053, 61505237); Natural Science Foundation of Henan Province (144300510018); Scientific Research Funds of Henan University (CX0000A40680).

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Size confinement and origins of two-photon absorption and refraction in CdSe quantum dots

Abstract

1. Introduction

2. Experiments

3. Results and discussion

4. Summary

Funding

References

Cited By

Figures (6)

Equations (1)

Optics Express