One- and two-photon photoluminescence excitation spectra of CdTe quantum dots in a cryogenic confocal microscopy platform

Diogo B. Almeida; André A. de Thomaz; Hernandes F. Carvalho; Carlos L. Cesar

doi:10.1364/OE.23.019715

1. Introduction

The Nonlinear optical (NLO) properties of Quantum Dots (QDs) are important for a number of applications such as 2-photon excited fluorescence (TPEF) in confocal microscopy [1, 2], quantum computing, optical switches and others [3, 4]. Since the first reports on QDs, it has been shown that their optical properties were controllable by their size [5–7], an effect attributed to the confinement of charge carriers in the dot. A series of theoretical models for the confinement energy levels [8–12] have been published since then, but with some controversy [8–10] about the best confinement models, even today. Experimental measurements have not been completely capable of selecting the best model, mostly because there is a large interval of accepted parameters that can explain the optical transitions observed. This shows the necessity of further measurements capable to discriminate different theoretical approaches.

An experimental measurement capable to discriminate the models should observe not only the energy levels closest to the gap, but a more complete set of levels within the same band, to diminish the degree of freedom in the choice of the parameters. An optical characterization robust enough to put to test these models would be the spectroscopy of the intersubband transitions [13–15], using the same parameters chosen for the intraband transitions. The direct observation of the intersubband transitions, however, is very hard because the lines fall at the mid-infrared range, above the hydrogen vibrations at 2.5 µm, where several molecular vibrations of the solvent for the QDs will completely hide these absorption lines.

An alternative to intersubband transitions is to measure one and two photon absorption, because the selection rules for these transitions are different, especially for different parities. This way, 1-photon (1P) forbidden transitions can be observed by 2-photon (2P) absorption, or photoluminescence excitation (PLE) spectra, performed in the visible region. Our group have already proved the ability of performing 2PA of quantum dots [16]. These measurements were performed at ambient conditions and with QDs in glass matrix and now we enhance the capability of obtaining information concerning 1P forbidden transition energies by working with low temperatures and switching the spectroscopy technique to 2-PLE. PLE have a much higher sensitivity than direct absorption because it is a background free measurement and one can detect only one single quantum dot emission. Moreover, in PLE it is possible to collect only a smaller window of a broad size distribution of quantum dots. In this paper we show the 1-P and 2P-PLE of the same CdTe QDs performed at 40 K in a confocal microscope system.

Schmidt et al. [17] and Baranov et al. [18] performed 2P-PLE of quantum dots at low temperature. They focused the pulsed beams with long focal length lenses (several centimeters), using high laser powers to reach the nonlinear regime, and normalized the spectra by dividing the signal by the square of the incident laser intensity. This procedure neglects any pulse duration or spot size differences when varying the pulsed laser wavelength. Advances in the measurement of 2-photon absorption (2PA) cross-sections with a proper normalization procedure were made [19–21] but mostly using organic fluorophores and through normalization methods dependent on other nonlinear properties, besides the 2PA, of the sample. In this work, we managed to overcome all these issues performing the measurements in a higher numerical aperture confocal microscope system and using a normalization signal independent of the original sample, acquired simultaneously with the luminescence signal.

TPE requires high intensity, which can be easily obtained with tunable femtosecond pulsed lasers in high numerical aperture microscopes. Besides, the high numerical aperture also implies in a large solid angle collection of optical signals enhancing the NLO spectroscopy sensitivity. Actually, the present high numerical aperture optical microscopes became more than just a microscope, but an analytical instrument capable to acquire several kinds of linear and NLO spectra in a focal volume as small as 10⁻¹⁶ L. Moreover, the spectroscopy in laser scanning confocal systems is quite convenient because one can stop the laser focus at any position in the sample, or even scan one Region of Interest (ROI), without losing the alignment to external monochromators or detectors.

To implement PLE in the scanning confocal system one needs to lower the temperature to a few degrees to increase the optical signals and diminish the linewidth. The vast majority of PLE spectroscopy in the literature is performed below temperatures corresponding to the material’s LO phonon energy, to make sure that the phonon population and, thus, the homogeneous broadening, is cut to a minimum. Only the inhomogeneous broadening remains at such low temperatures. The narrowing of the excitation/emission lines, correspondingly, increases the intensity of the signals.

There is a problem, however, in combining high numerical aperture microscopy system with cryogenics. High numerical aperture usually means short working distances and immersion liquids to match the refraction index, while cryogenics requires a vacuum chamber isolating the sample to avoid heat dissipation and water condensation at the windows. The separation between sample and vacuum seal windows is of orders of mm. In this paper we show that we could couple an external small cryogenic system to a commercial microscope maintaining all microscopes capabilities, especially to move the sample with respect to the objective in “z”, to get the focus, and “x-y” to find a ROI, or to scan a 3D focal volume. We demonstrate this system capability and functionality by the acquisition of fluorescence spectra, sample images, as well as Second Harmonic Generation (SHG), from room temperature down to 10 K.

Once we solved the problem of coupling the cryostat to the confocal microscope, we have to face the most important issue to perform two photons excited spectroscopy, namely, the spectral normalization. The 1P-PLE require only the normalization by the intensity of excitation beam as a function of the wavelength [22]. For 2P, however, the excitation depends upon the square of the incident power, the spot size and the pulse duration at the sample, which are all parameters that change with the wavelength. The solution we proposed in this work is to use another NLO phenomenon subjected to the same optical parameters, such as the urea microcrystals second harmonic generation, and used its emission line area for the spectral normalization. Urea SHG signal is intense and it has a fairly linear response in the spectral interval of interest [23]. The fact that the SHG source was mixed with the sample assured that the normalization signal follows the same optical path as the sample luminescence and both signals, SHG and PL (photoluminescence) can be acquired simultaneously. Moreover, the phase matching condition is loosened in the higher NA and fine powder like SHG sources we used [24]. Using this experimental setup we succeed to acquire 2P-PLE and to compare it with 1P-PLE of the same CdTe QD sample at the same conditions. We also show that a parabolic effective mass model can explain the different transition selection rules we observed for 1P and 2P-PLE.

2. Experimental setup

Figure 1 illustrates our system assembly, composed by a confocal laser scanning microscope, the cryostat, a femtosecond laser and a spectrometer. The confocal microscope was an upright LSM 780 NLO equipped with a 32 channels APD array from Zeiss, and a 405 nm, 66 ps pulse duration diode laser (BDL-405-SMC, Becker&Hickl). The cryostat was an open cycle Cryovac Konti microcryostat and the femtosecond laser was a MaiTai HP DeepSee (Spectra Physics) Ti:sapphire, with a pulse duration of ∼ 100 fs (before entering the microscope) and a spectral bandwidth of ∼ 10 nm FWHM. A SP2300i 30 cm monochromator with a PIXIS 100BR silicon CCD peltier cooled to −80°C, from Princeton Instruments composed the spectrometer.

Fig. 1 Representation of the whole experimental setup design. The cryostat is placed just below the objective and the optical pump and detection are also external to the microscope.

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The first adaptation needed for this assembly was to open space to fit the cryostat in the gap between its objectives and plate, which was done by removing the microscope plate and condenser. The cryostat was held in a small aluminum platform with its feet directly attached to the optical table to ensure mechanical stability. The sample movement was performed with a “x-y” translation stage between the cryostat and platform. Another aluminum piece was machined to ensure the perfect fit of the cryostat into the translation stage. To avoid the mechanical vibrations generated by the vacuum system, the hard vacuum hoses where clamped to the optical table and the mechanical pump, seated over a foam, was put aside of the system. The Helium flow was generated by an auxiliary pump localized after the He exit. The soft rubber hoses for Helium recovery at higher pressure do not couple acoustic vibrations to the microscope system, making it easier to isolate this vibration source.

The tradeoff between the objective numerical aperture and working distance was resolved using a Plan-Nofluar 40× 0.6 NA Korr long WD (2–3 mm) objective from Zeiss, which collects efficiently the emitted photons from a surface 2 mm away. However, we still needed to insert a copper lump, see Fig. 2(a), in the sample holder to increase its height to let the sample surface rest very close (∼ 2 mm) to the cryostat window, but still far enough to assure no water condensation at the optical window. In this geometry the only access to optical signals is through the back-reflected light. We placed the sample on top of an aluminum coated microscopy cover slip mirror as shown in the inset of Fig. 2(b). This mirrored sample holder brings two advantages: collection of a good fraction of the transmitted optical signals, and isolation of any spurious signal coming from the cryostat copper cold finger or the glue used to hold the sample with good thermal contact.

Fig. 2 Detail of the cryostat with the sample placed in the copper lump. (b): representation of the cover slip mirror with a film of QD+urea in it. (c): microscope scan head scheme, along with the coupling of the lasers and external detectors.

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The excitation for both, Mai Tai and 405 nm solid state lasers, were performed through the scan unit of the multiphoton platform. The descanned detection to perform spectroscopy is almost mandatory. Although nonlinear optical signals can be detected with non descanned detectors (NDD), it is hard to align NLO moving beam to the slit of the monochromator in the NDD geometry. Figure 2(c) shows the detection geometry of our setup. A filter wheel inside the scan unit can divert the collected light to the internal grating/APD array of the LSM 780, or redirect it as a collimated beam out of the microscope to the external monochromator. The monochromator was equipped with two grating carrousels carrying 300, 600 and 1200 g/mm gratings, one set for 750 nm and the other for 300 nm blaze wavelengths. The spectral resolution with the 1200 g/mm grating was 0.14 nm. The PIXIS CCD array is composed by 1340×100 pixels and we chose a ROI with the 50 central vertical pixels to eliminated noise from the non illuminated part of the CCD.

The optical response of the system was obtained with an absolute spectral calibration, consisting in irradiating the system with a black body radiator, in our case a tungsten filament halogen lamp, and comparing with an ideal black body spectrum at the same temperature. The filament temperature was calculated by the fact that its resistivity is temperature dependent in a well known fashion [25]. The value of the resistivity is found measuring the filament’s resistance at room temperature and at the working temperature. Assuming an ohmic behavior, the resistances’ ratio is the same as the resistivities’. The signal acquired is compared with the ideal black body at the calculated temperature and the ratio gives the calibration values for each wavelength.

3. Sample preparation

We prepared CdTe QDs using an aqueous method and thiol capping, based in the synthesis of Zhang et al. [26,27] In a sealed flask, under argon atmosphere and magnetic agitation, 40 mL of water and 38 mg of Tellurium powder (Aldrich; 99.997%; >40 mesh) were heated up to 80°C. In parallel, 66.8 mg of NaBH₄ (Aldrich; > 96%) was dissolved in ∼5 mL of water and then added to the previous 80°C solution to reduce the Te into Te⁻², maintaining the conditions for 2h.

To prepare the Cadmium and thiol mixed solution we added 0.52 mL of a 0.1 mol/L solution of Cd(ClO₄)₂ (Aldrich; > 99.9%, hidrataded) into 0.24 mL of a 5% in mass aqueous solution of mercaptoacetic acid (MAA, Sigma-Aldrich, > 99%) at atmospheric conditions. This solution was quickly added to the reduced tellurium by injection through a rubber sept, after which the temperature was increased to ∼ 100°C and kept under stirring for 30 min. Figure 3 shows the sample’s primary characterization. On the left, the PL spectrum (solid red line) with an 405nm excitation is shown. Along with it there is the absorbance spectrum (green dashed line), taken with a Perkin-Elmer Lambda 9 Spectrometer. Both spectra were performed with the as prepared solution at room temperature and in aqueous solution. On the right, we show a typical Transmission Electron Microscopy (TEM) image, taken with a JEOL JEM-3010 microscope. Altogether, this characterization shows a typical behavior of a good quality CdTe QDs sample, supporting the results obtained with the 1P and 2P PLE.

Fig. 3 PL (red, solid, excited with a 405nm laser) and absorption (green, dashed) spectra of the QDs at room temperature (left). TEM image of the sample (right).

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To obtain the mixture of the QD film with urea microcrystals we used the following procedure: 100 µL of CdTe QDs solution was deposited in an aluminum coated microscope coverslip heated to ∼ 50°C and dried for 1h until a film of the sample was formed. This procedure also helped the evaporation of some of the organic residues of the QDs synthesis. After this 1 hour, 50 µL of an aqueous saturated solution of urea was dropped over the QD film and the resulting system was dried out for another hour at the same temperature. Figure 4 shows a TPEF of the QD image in green together with the urea SHG image in magenta, displaying a fairly homogeneous QD film speckled with small urea crystals.

Fig. 4 2PA confocal fluorescence image of a QDs film (green) region speckled with urea small crystals (magenta).

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4. Photoluminescence spectra

Using the microscope in the imaging mode, we found a concentrated region of the QD film. The spectroscopy was performed with the laser scanning a ROI to avoid photobleaching due to the long exposition times required by the experiment, which includes at least 8 spectra at different temperatures. With this system we acquired a series of cw 405 nm laser excited photoluminescence spectra varying the temperature between 10–300 K continuously scanning the same sample region (200×200 µm field) for 30s. The temperature was measured using a standard built-in thermocouple that seated close to the sample holder. Figure 5(a) shows the spectra obtained and Fig. 5(b) shows a plot of the photoluminescence (PL) intensity peak as a function of temperature. The red curve is the Varnish relation [28], E (T) = E_T₌₀ + αT²/(T + β) for the CdTe band gap as function of temperature. The expected results demonstrate the quality of our PL vs temperature microscopy & spectroscopy setup. The QDs synthesis used was similar to the one described and characterized by Kapitonov et al. [29], and their sample also showed a asymmetric spectrum, that had a low energy band strongly temperature dependent, similar as ours. This band is attributed to trap states, that lose efficiency with higher temperature as the carriers have more energy to escape from them. For that reason, the lower energy tail of the spectra were discarded when the data fittings were performed. To find the values of the peaks used in Fig. 5(b), only the higher energy band of the PL peaks (to avoid the QDs surface contributions to the spectra) were fitted with Gaussian curves.

Fig. 5 (a): several PLs spectra of the same sample, excited by a 405 nm laser, in a temperature series. The “red shift” behavior is consistent with the literature. (b): Energy of the PLs’ peaks plotted against the temperature, showing that the peak shift follows the Varnish relation.

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4.1. 2P-PLE

The 2P-PLE spectra were acquired at 40 K in a highly concentrated film area found in image mode. For each excitation wavelength we collect the whole PL+SHG spectrum at once with the CCD by scanning a 200×200 µm area continuously (avoiding the irradiation of a fixed point) for 40s. Figure 6 shows a typical QDs+urea sample spectrum excited with the pulsed laser tunned at 800 nm. It is worth noticing the fluorescence from de QDs and the SHG from urea are spectrally well separated. The sample area chosen for the measurements was the one displayed in Fig. 6, and it is near de edge of the QD film because the ratio between the SHG and PL signal intensities have the same order of magnitude in this kind of region.

Fig. 6 Typical two-photon excited spectrum obtained from the QDs+urea sample. In this case the sample was excited with 800nm.

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The ∼100 fs pulse duration and 10 nm bandwidth excitation laser wavelength was scanned from 750 nm to 1000 nm in 5 nm steps to assure an oversampling ratio of 2. The normalization procedure was performed by fitting the SHG peak with a Gaussian function. The area under the curve was calculated with fitted parameters and the whole spectrum was divided by this value. To construct the PLE spectrum we integrated the signals in a 5 nm window centered at 530 nm of the PL signal, repeating the procedure for all spectra for each excitation wavelength.

4.2. 1P-PLE

The 1P-PLEs were performed in a commercial Xe lamp spectroscopy system (ISS PC1) with a Photomultiplier (PMT) detection. To reach the low temperatures (40 K), a closed-cycle He cryostat (DISPLEX DE-204SL from APD Cryogenics) was adapted in the sample holder’s place. The bandwidth of the PMT’s optical collection window was set to 5 nm and centered at 530nm to match the 2P measurement. The lamp excitation window was set to 1 nm in order to reach a PLE spectrum as close as possible of the collection window. The sample preparation was performed in the same fashion of the 2P-PLE measurement ones. The only differences were the absence of urea and the coverslip was not mirror coated, to avoid the influence of the excitation signal, which is now much closer to the collection spectral region.

5. Results

Figure 7 shows the 1P-PLE (blue) and half of excitation wavelength of the 2P-PLE (red) spectra of the same sample of CdTe quantum dots, normalized to coincide in the 2.8 eV region, to stress the first peak excitation differences. Both spectra were taken at 40K and the optical collection windows were centered at 530nm (2.34 eV). The clear spectral differences can only be explained by the different selection rules for one and two-photon absorption.

Fig. 7 One (blue) and two (red) photon PLE spectra of the same sample of CdTe quantum dots put together. Both spectra were taken integrating the intensity of an optical window 5 nm, centered at 530 nm. The comparison clearly shows access to different electronic transitions.

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5.1. Selection rules and oscillator strength

The probability for 1P and 2P transition between the initial (i) and final (f) states with wave-functions Ψ_i and Ψ_f, respectively, in the dipole approximation, using first and second order perturbation theory are given by:

\begin{array}{l} W_{i \to f}^{1 p} \propto \frac{1}{ω^{2}} {| 〈 Ψ_{f} | e_{z} \cdot \nabla | Ψ_{i} 〉 |}^{2} δ (E_{f} - E_{i} - ℏ ω) \\ W_{i \to f}^{2 p} \propto \frac{1}{ω^{4}} {| \sum_{p} \frac{〈 Ψ_{f} | e_{z} \cdot \nabla | Ψ_{p} 〉 〈 Ψ_{p} | e_{z} \cdot \nabla | Ψ_{i} 〉}{Δ E_{p}} |}^{2} δ (E_{f} - E_{i} - 2 ℏ ω) \end{array}

where ΔE_p = (E_f + E_i)/2−E_p. In the parabolic envelope function model, neglecting band mixing, the wavefunctions of the QD problem are written as a product of functions in two subspaces, of the |Ψ_j〉 = |u_j〉 ⊗ |ξ_i〉, Bloch functions |u_n〉, where n = c, v for conduction/valence band, that takes into account the crystalline potential of the QD’s material, and the envelope function space |ξ_n〉. The distributive application of the operator e_z · ∇ in the 1p selection rule:

〈 Ψ_{f} | e_{z} \cdot \nabla | Ψ_{i} 〉 = 〈 ξ_{f} | ξ_{i} 〉 〈 u_{f} | e_{z} \cdot \nabla | u_{i} 〉 + 〈 u_{f} | u_{i} 〉 〈 ξ_{f} | e_{z} \cdot \nabla | ξ_{i} 〉

leads to the first term corresponding to an intraband transition, and a second corresponding to an intersubband transition. For two different bands 〈u_f|u_i〉 = 0, and the intraband transition between valence and conduction bands is given by:

〈 Ψ_{c} | e_{z} \cdot \nabla | Ψ_{v} 〉 = 〈 ξ_{f} | ξ_{i} 〉 〈 u_{c} | e_{z} \cdot \nabla | u_{v} 〉

\begin{array}{l} W_{i \to f}^{2 p} \propto \frac{1}{ω^{4}} {| 〈 u_{v a l} | e_{z} \cdot \nabla | u_{c o n d} 〉 |}^{2} \\ {| \sum_{p} \frac{〈 ξ_{v a l} | \vec{e} \cdot \nabla | ξ_{p} 〉 〈 ξ_{p} | ξ_{c o n d} 〉}{Δ E_{p}} + \sum_{b} \frac{〈 ξ_{v a l} | ξ_{p} 〉 〈 ξ_{p} | \vec{e} \cdot \nabla | ξ_{c o n d} 〉}{Δ E_{p}} |}^{2} δ (E_{f} - E_{i} - 2 ℏ ω) \end{array}

This expression could be seen as the sum of two terms: the first one as a valence intersubband transition followed by an intraband transition, and the second one as an intraband transition followed by a conduction intersubband transition. Now, the envelope functions for the parabolic model in a QD with radius a are given by

| ξ_{b n p} (r) 〉 = | j_{n} (π χ_{b p} \frac{r}{a}) Y_{n}^{m} (θ, φ) |

and the confinement levels by

E_{b n p} = \frac{h^{2} χ_{n p}^{2}}{8 m_{b} a^{2}}

where j_n (r)and

Y_{n}^{m} (θ, φ)

are the spherical Bessel functions and the spherical harmonics, respectively, and χ_np is related with the p-th root of j_n (r) by the relation j_n (πχ_np) = 0. All the terms in 1p and 2p can now be easily calculated using the fact that:

〈 j_{f} (π χ_{f β} \frac{r}{a}) | j_{f} (π χ_{f p} \frac{r}{a}) 〉 = \frac{a^{3}}{2 π^{3}} j_{f + 1}^{2} (χ_{f β}) δ_{p β}

and

\begin{array}{l} 〈 j_{f} (π χ_{f β} \frac{r}{a}) Y_{f}^{m} (θ, φ) | e_{z} \cdot \nabla | j_{i} (π χ_{i α} \frac{r}{a}) Y_{i}^{m}^{'} (θ, φ) 〉 = \\ π δ_{m, m^{'}} [\begin{array}{l} + \sqrt{\frac{(f + 1 - m) (f + 1 + m)}{(2 f + 3) (2 f + 1)}} \frac{χ_{f + 1, α}}{a} 〈 j_{f} (π χ_{f β} \frac{R}{a}) | j_{f} (π χ_{f + 1, α} \frac{R}{a}) 〉 δ_{f, i - 1} + \\ - \sqrt{\frac{(f - m) (f + m)}{(2 f - 1) (2 f + 1)}} \frac{χ_{f - 1, α}}{a} 〈 j_{f} (π χ_{f β} \frac{R}{a}) | j_{f} (π χ_{f - 1, α} \frac{R}{a}) 〉 δ_{f, i + 1} \end{array}] \end{array}

The final result for 1p is:

W_{v \to c, 1 p h} \propto {| 〈 u_{v} | e_{z} \cdot \nabla | u_{c} 〉 |}^{2} {| \frac{a^{3}}{ω} j_{n + 1}^{2} (χ_{n p}) |}^{2} δ (E_{c n p} - E_{v n p} - ℏ ω)

The 2p transition probability, however, is given by:

\begin{array}{l} W_{v i α \to c f β, 2 p h} \propto \frac{χ_{i α}^{2} a^{4}}{ω^{4}} \times \\ \times [\begin{array}{l} \frac{(i - m) (i + m)}{(2 i + 1) (2 i - 1)} {| 〈 j_{i - 1} (π χ_{i - 1, β} \frac{r}{a}) | j_{i - 1} (π χ_{i, α} \frac{r}{a}) |}^{2} \times \\ \times {| \frac{j_{i + 2}^{2} (χ_{i α})}{(\frac{E_{c (i - 1) β} + E_{v i α}}{2}) - E_{c i α}} + \frac{j_{i}^{2} (χ_{i - 1, β})}{(\frac{E_{c (i - 1) β} + E_{v i α}}{2}) - E_{v (i - 1) β}} |}^{2} δ (E_{c (i - 1) β} - E_{v i α} - 2 ℏ ω) δ_{f, i - 1} + \\ + \frac{(i - m + 1) (i + m + 1)}{(2 i + 1) (2 i + 3)} | 〈 j_{i + 1} ((π χ_{i + 1, β} \frac{r}{a}) | j_{i + 1} {((π χ_{i, α} \frac{r}{a}) 〉}^{2} \times \\ {| \frac{j_{i + 2}^{2} (χ_{i α})}{(\frac{E_{c (i + 1) β} + E_{v i α}}{2}) - E_{c i α}} + \frac{j_{i + 2}^{2} (χ_{i + 1, β})}{(\frac{E_{c (i + 1) β} + E_{v i α}}{2}) - E_{v (i + 1) β}} |}^{2} δ (E_{c (i + 1) β} - E_{v i α} - 2 ℏ ω) δ_{f, i + 1} \end{array}] \end{array}

The m index will always have definite values due to their relation with the i index and the Kronecker delta restrictions. With eqs. (9) and (10) it is possible to calculate the oscillator strengths of the energy levels for QDs of any material and size.

Figure 8 illustrates the results along with peak position and oscillator strength, obtained using eqs. (9) for one (blue) and (10) for two (red) photons excitation and the literature [31] data for a 2.1 nm radius CdTe QD, up to the fourth electronic transition only. The traced lines represent the convolution between the peaks and Gaussian size distribution, in which the standard deviation has 12% of the value of the average QD size. It is clear that the higher absorption peak lies in the 2.4 eV region for 1P, and 2.9 eV for the 2P absorption. Results above 3 eV differs from experimental curves because the consideration of higher transiton levels would be necessary to a better agreement in this region.

Fig. 8 Energy transitions for one (blue) and two (red) photons with its respective oscillator strengths for a 2.1 nm radius CdTe QD. The traced lines take into account the broadening due a 12% Gaussian size distribution.

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The first transitions peaks for both, 1p and 2p, are in great accordance with the experimental results of 1P and 2P-PLEs as shown in Fig. 9, where the solid lines are the theoretical predictions and the dots are the experimental points.

Fig. 9 One (blue) and two (red) photon PLE spectra (dots) compared with their respective theoretical oscillator strengths (solid lines).

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The experimental data (dots) of the sample, aquired at the same spectral window (2.30 eV) and temperature (40 K), are put togeghter to observe more clearly the differences between the absorption peaks profile. Moreover, the theoretical oscilator strenghts (solid lines) for both measurements were also plotted in the same chart. For the calculations, we used a 2.1 nm radius and a size distribution of 12% of the CdTe QDs. It is well known that parabolic models overestimate the confinement energy, but the wavefunctions, neglecting band mixing, must be similar to the ones obtained with other models. One way to correct this overestimation is to increase the quantum dot size, until a good agreement with the observed peaks is obtained. For the samples under sutdy, this value was obtained with 2.1 nm radius, larger than experimental measurement, but able to explain both, 1p and 2p first absorption peaks and their relative oscillator strength.

6. Conclusion

In this work we proposed and performed a method for measuring 2P-PLE and 1P-PLE of CdTe QDs. The results can be explained with a parabolic model, also described in this paper. This clearly shows that we were able to reach different optical transitions, through the change in the selection rules, enabling the construction of a more complete panorama of the nanostructure’s energy levels.

We have been able to transform a confocal microscope platform into an analytical tool capable to acquire linear and non-linear spectra from 10 K to room temperature, without losing any of the microscope capabilities. That is a platform capable to resolve features in space, in time and spectrally with temperature control. We also solved the most important problem to perform non linear optics spectroscopy, which is the spectrum normalization that takes into account the exciting power, pulse duration and spot size at the sample, after the objective, without any assumptions about the beam shape. The sample preparation mixing with urea micro/nano crystals method allowed the acquisition of the nonlinear normalization signal simultaneously with the luminescence to assure both signals and reference optical paths are the same. This means that this procedure is possible of taking into account all the inhomogeneities of the system, without any complex calculation or signal manipulation.

Acknowledgments

D. B. Almeida was recipient of a fellowship of Coordenaçãode Aperfeiçoamento de Pessoal de Nível Superior (CAPES). This work was developed with resources from Instituto Nacional de Fotônica Aplicada à Biologia Celular-INFABIC (CNPq grant 573913/2008-0, FAPESP grant 08/57906-3) and also Centro de Óptica e Fotônica - CEPOF (FAPESP grant 05/51689-2). The author would also would like to thank the Brazilian Synchrotron Light Laboratory (LNLS) and its nanotechnology center (LNNano) for the help in obtaining the HRTEM images.

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One- and two-photon photoluminescence excitation spectra of CdTe quantum dots in a cryogenic confocal microscopy platform

Abstract

1. Introduction

2. Experimental setup

3. Sample preparation

4. Photoluminescence spectra

4.1. 2P-PLE

4.2. 1P-PLE

5. Results

5.1. Selection rules and oscillator strength

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (9)

Equations (10)

Optics Express