Opt Quant Electron (2018) 50:115 https://doi.org/10.1007/s11082-018-1375-6

Spectroscopic study of oscillator strength and radiative decay time of colloidal CdSe quantum dots Abdelnasser Aboulfotouh1 • Mohamed Fikry1,2 • Mona Mohamed3 Magdy Omar1 • Hossam Rady2,4 • Yahia Elbashar2,5

•

Received: 17 August 2017 / Accepted: 7 February 2018  Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract Characterization of samples of cadmium selenide quantum dots (CdSe) QDs dissolved in toluene colloidal solutions at a concentration of 1.4 mg/ml was carried out through UV–Vis absorption and photoluminescence (PL) spectroscopy. The size-dependent absorption and red-shifted PL emission peak wavelengths could be tuned between 510–576 and 545–606 nm respectively. Optical absorption spectral measurements yielded CdSe QDs having diameters about * 2.44–3.69 nm with energy gaps 2.32–2.08 eV which are higher than the bulk CdSe (1.74 eV) reminiscent of quantum confinement. This is found to be in good agreement with the semi-empirical pseudopotential model. In addition, the first excitonic absorption transition 1S(e)1S3/2(h) oscillator strength and the corresponding fluorescence radiative decay time of CdSe QDs are assessed using relevant Einstein relations for absorption and emission in a two-level system. The elaborated calculations would anticipate that the transition oscillator scale with the CdSe QD radius as * R2.54. Correspondingly, the calculated radiative decay times decrease from 56.4 to 23.2 ns which scale with CdSe QDs radius as * R-2.155 in fairly good agreement with experimental values reported in the literature. Keywords Spectroscopic analysis  Quantum dots  Photoluminescence radiative decay time

& Yahia Elbashar [email protected] 1

Department of Physics, Faculty of Science, Cairo University, Giza, Egypt

2

Egypt Nanotechnology Center (EGNC), Cairo University, Giza, Egypt

3

National Institute of Laser Enhanced Sciences, Cairo University, Giza, Egypt

4

Institute of Nanoscience and NanoTechnology, Kafrelsheikh University, Kafrelsheikh, Egypt

5

Department of Physics, Faculty of Science, Aswan University, Aswaˆn, Egypt

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1 Introduction Photoluminescence semiconductor quantum dots (QDs) have a variety of potential applications in optoelectronics including LEDs, lasers and solar cells (Rogach et al. 2008; Eisler et al. 2002; Hoogland et al. 2006; Huang et al. 2014) as well as biomedical analysis and imaging (Li et al. 2014; Frecker et al. 2016; Petryayeva et al. 2013). Colloidal CdSe QDs have developed remarkably in the last two decades (Konstantatos and Sargent 2013). Such novel nanoparticles exhibit size-dependent optical properties because of the inherent quantum confinement effect (Murray et al. 1993; Klimov 2010). Optical absorption and photoluminescence in these QDs are essentially described in terms of the formation of electron–hole exciton and its annihilation by radiative recombination. Because the particle size directly relates to the QD’s bandgap energy, these nanoparticles have size and composition dependent absorption and emission tunability. Chemical synthesis routes have been established to obtain high-quality QDs with various shapes and sizes. These chemical reactions involve capping ligands to passivate the QD surface trap states and prevent dissolution of smaller sized QDs to form aggregates. Bifunctional organic molecules with both thiol and carboxylic acid, amine or alcohol functional groups have been widely adopted as capping molecules for CdSe and other II– VI group semiconductor nanoparticles (Deng et al. 2006). The organometallic route is carried out in standard airless conditions at relatively high temperatures in the presence of stabilizing agents such as trioctylphosphine, trioctylphosphine oxide and hexadecylamine (Pan et al. 2007; Kim et al. 2005; Jha and Sionnest 2007). The resulting monodispersed nanoparticle QDs stability and optical properties are influenced by growth kinetics, capping ligands and pH of the environment (Ayelea et al. 2014; Mi et al. 2012). In the present work, the size-dependent absorption and fluorescence spectra have been studied. Characterization of the optical properties of CdSe QDs capped with (TOP, TOPO, HDA) dispersed in toluene have been explored and theoretical calculations of inherent excitonic absorption band edge transition oscillator strengths, as well as fluorescence radiative decay times, assessed.

2 Experimental Preparation of mono-dispersed organically passivated semiconductor nanocrystals is essential to achieve novel nano-sized particles in contrast with the bulk materials. Nanocrystals (NCs) of Trioctyl phosphine-oxide-Hexadecyl amine capped CdSe (TOP/ TOPO/HDA) QDs in this work are prepared by the pyrolysis of organometallic reagents through injection into a hot coordinating solvent after Yu et al. (2003). UV–Vis absorption spectra of samples in cuvettes of 1 cm diameter were recorded using Thorlabs SPLICCO spectrometer CCS series in the 300–800 nm wavelength range. Laser-induced photoluminescence spectra of CdSe QDs is carried out using a multi-power (10–80 mW) SpectraPhysics Ar Laser (488 nm) model 183-C0201 with amplifier model AD110 as an excitation source.

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3 Results and discussion 3.1 Optical absorption and photoluminescence A series of spherical shaped CdSe QDs of different sizes were taken from the reaction mixture at different intervals during the growth of the particles and dissolved in toluene. It is worth noting that, CdSe QDs colloidal solutions at a concentration of 1.8 mg/ml were found to manifest optimal optical absorption as well as PL emission intensities as shown in Fig. 1a, b. The absorption spectra in Fig. 1a reveal a broad rising absorption whose peak tends to shift to smaller wavelengths as the CdSe QDs size decreases reminiscent of quantum confinement effect. On the other hand, as shown in Fig. 1b, the PL emission peaks tend to shift towards longer wavelengths as the CdSe QDs size diameter as well. In addition, each PL emission profile retraces a Gaussian distribution reminiscent of polydispersity of QDs sizes.

Fig. 1 CdSe QDs a absorption and b PL spectra

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At the absorption edge peak, photoexcitation induces an electron–hole 1Se1/21Sh3/2 transition coupling leading to hydrogen-like bound state quasiparticle (exciton) formation that was confined to and delocalized over the volume of the nanocrystal. The sizes of CdSe QDs samples were calculated from the first absorbance excitonic absorption peak wavelength k (nm) using Yu et al. (2003) empirical equation.   DðnmÞ ¼ ð1:6122  109 Þk4  2:6575  106 k3 ð1Þ     þ 1:6242  103 k2  4:277  101 k þ 41:57 The selected CdSe nanoparticles sizes are listed in Table 1. Considering the absorption edge peak as a band-to-band transition, the effective bandgap energy could be estimated using Tauc and Davis-Mott models (Tauc 1973).   ðahmÞm ¼ b hm  Ug ð2Þ where m is a constant and b denotes an exponent constant index. The absorption coefficient a for CdSe QDs of different sizes at a concentration of 1.4 mg/ml (A * 0.8) was calculated using Eq. (3). 1 Io 2:303 Io 2:303 log ¼ A a ¼ ln ¼ d I d d I

ð3Þ

where A is the absorbance and d is the sample thickness. Thereupon, plots of (ahm)2 versus hm for the different CdSe QDs colloidal solutions at a concentration of 1.4 mg/ml were extrapolated to intercept the hm axis at the bandgap energy Ug as shown in Fig. 2. In this context, Urbach’s rule (Eq. 4) was applied to calculate the Urbach energy U (energy width of the absorption edge) as well as the usual convergence energy point ( hxo) (band gap at 0K) for CdSe QDs (Tauc and Menth 1972).   ð hx  hxo Þ ð4Þ að hxÞ ¼ ao ðT Þ exp U ðT Þ where ao is a temperature dependent normalized transition strength. The linear relation between the logarithm of absorption coefficient a and the incident photon energy ⁄x at the tail of the absorption edge yielded the Urbach energy and convergence energy point values listed in Table 1. Interestingly, the usual convergence energy point turns out to coincide with the calculated bandgap energy of CdSe QDs according to Tauc’s plot method with less than * 1.7% deviation. The calculated energy gap values were contrasted with others against rigorous theoretical models that describe electron properties of passivated semiconductor Table 1 Absorption band edge size dependent energy gap and Urbach energy of CdSe QDs

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D (nm)

U (meV)

ao (cm-1)

⁄x0 (eV)

Ug (eV)

2.445

43.64

1.824

2.36

2.311

2.696

35.03

1.824

2.28

2.242

3.167

34.30

1.824

2.18

2.15

3.357

33.41

1.824

2.15

2.11

3.573

46.63

1.824

2.11

2.087

3.692

41.46

1.824

2.10

2.074

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Fig. 2 Tauc plot of CdSe QDs absorption spectra

nanostructures. Figure 3 displays relevant previous experimental data reported by others and theoretical calculations based on tight binding model (TBM) as well as semi empirical pseudo potential model (SEPPM) reported by Viswanatha et al. (2005) and Wang and Zunger (1994) respectively. The experimental data were in good agreement with reported experimental findings (Hamizi and Johan 2012; Nazzal and Fu 2009) in accordance with the SEPPM calculations. Yet, experimental data of Li and Wang (2003) appear to be in accordance with the predictions of the tight binding model (TBM). Optical properties of CdSe QDs colloidal suspensions in toluene at a common concentration of about 1.4 mg/ml were investigated through calculations of reflectance R and

Fig. 3 Variation of CdSe QDs band gap with radius

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transmittance T within the absorption band of CdSe nanoparticles. The refractive index n could be estimated using the relation, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þR 4R þ  K2 ð5Þ n¼ 1R ð1  RÞ2 The extinction coefficient K is directly related to the absorption coefficient of the medium (a) whereas the reflectivity R correlates with the medium absorbance and transmittance (Hamizi and Johan 2012). Thereupon, the linear refractive index n(k) dispersion of CdSe QDs is displayed in Fig. 4. Obviously, the refractive index typically changed from anomalous to normal dispersion accompanied by the optical absorption at the band edge gap of each of the CdSe QDs (Schdffner et al. 1992). In addition, the photoluminescence quantum yield of the colloidal CdSe nanocrystal solutions was determined using a comparative method which involves the use of wellcharacterized standard Rhodamine 6G (Rh6G) having a high PL quantum yield about 0.95. The obtained experimental PL Q.Y values amount to 0.4882, 0.460, 0.443, 0.375, 0.393 and 0.378 for CdSe QDs with sizes 2.44, 2.696, 3.167, 3.357, 3.573 and 3.692 nm respectively. The decrease of PL Q.Y values with CdSe QDs size is correlated with charge carrier trapping of QDs in favor of non-radiative recombination (Streka 2014).

3.2 Oscillator strength and radiative decay time One of the most important optical properties of a presumably two-level system is the transition oscillator strength (f) and radiative decay time (srad). The calculation of the transition oscillator strength and radiative decay times of the first excitonic emission transition of colloidal CdSe QDs dispersed in toluene have been elaborated. Having a Gaussian spectral profile, the first excitonic band edge absorption peaks of different CdSe QDs have been simulated using Origin nonlinear fit software. Consequently, the individual spectrally integrated absorption cross sections per CdSe nanoparticle were computed. The

Fig. 4 Refractive index spectra of CdSe QDs

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first absorption excitonic peak spectra of CdSe QDs colloidal suspensions are displayed in Fig. 5. The spectrally integrated absorption coefficient was subsequently used to estimate the associated oscillator strength of the absorption transition using the relation (Henderson and Imbusch 1989), ! Z n 3mo c m2 raik ðmÞdm ð6Þ fik ¼ e2 jFloc j2 m1 The absorption cross section per CdSe nanoparticle raik is calculated using the relation (Yu et al. 2005), raik ¼

aik 43 pR3 qaik ¼ N C

ð7Þ

where, a, C, R, and q are the CdSe QDs absorbance coefficient, concentration, radius and density (qCdSe = 5.68 g cm-3) and N is the number of CdSe QDs per unit volume. In dense dielectric media such as semiconductor inorganic–organic composites, a suitable correction |Floc|2 (Henderson and Imbusch 1989) must be introduced to take into account the actual local electric field acting on the valence electrons due to the electromagnetic incoming wave. In addition, the refractive index (n) of the absorber medium (CdSe QDs) was estimated from the refractive index dispersion (Fig. 4). The logarithmic scaling of the calculated oscillator strength per nanoparticle with the CdSe nanoparticle radius is shown in Fig. 6. The oscillator strength per nanoparticle associated with the 1Se1/21Sh3/2 absorption peak turns out to increase as the CdSe nanoparticle radius R (nm) increases according to the power law, fik  0:278R2:54

ð8Þ

This trend is compatible with the relatively higher electric dipole moment of the larger CdSe QDs (Rabani 2001; Sole et al. 2005) in good agreement with reported empirical findings (Leatherdale et al. 2002; Langevin et al. 2013).

Fig. 5 Excitonic absorption transition of CdSe colloidal suspensions Gaussian profile simulation

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Fig. 6 Logarithmic scaling of 1Se–1S3/2h absorption transition oscillator strength per CdSe QDs

On the other hand, the radiative decay time (sr) can be obtained from the relation, #1   2 "m 2 gk k 1 srad ¼ Aki ¼ r rðmÞdm ð9Þ gi 8pn2 m1 where Aki is the spontaneous emission rate. The PL emission wavelength (k) is taken as the absorption band edge peak wavelength plus the observed Stoke’s shift. The k2 dependence in Eq. 9 indicates that the radiative decay time would increase with particle size. However, according to the observed excitonic spectra, this dependence introduces a minor effect.

Fig. 7 Logarithmic scaling of PL radiative decay time of CdSe QDs

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Fig. 8 CdSe first excitonic state 1Se1/21Sh3/2 fine structure (Klimov 2010)

Figure 7 illustrates the logarithmic scaling of the first excitonic transition radiative decay time with CdSe QDs radius. The radiative decay times revealed a decreasing function with CdSe QDs radius in agreement with those extracted from a bi-exponential fit reported by Gong et al. (2013) and Gyori et al. (2010). In particular, the calculated radiative times predict fairly well the experimental findings of Gyori et al. (2010). The calculated radiative decay time tends to decrease as CdSe QD radius R (nm) increases and satisfies the power law, srad  87R2:155

ð10Þ

The observed increase of PL radiative decay time, as well as PL quantum yield increase as the CdSe nanoparticle size decreases, is a manifestation of quantum confinement (Chukwuocha and Onyeaju 2012; Norris et al. 1996). The estimated radiative times in this work are compatible with the literature (Mahajan et al. 2013; Donega et al. 2003; Califano et al. 2005). It’s worth noting that, the first excitonic absorption transition, creates an electron–hole pair occupying the lowest 1S(e)1S(h)3/2 exciton state. The eightfold degeneracy of this state is partially lifted by the combined effects of crystal field asymmetry, shape anisotropy, and electron–hole exchange interaction, yielding five levels, two of which are optically passive in the electric dipole approximation. The absorption transition involves all of the five levels as depicted in Fig. 8. On the other hand, the emission transition involves only the lowest two levels belonging to the ‘‘dark (F = ± 2L)’’ and the ‘‘bright (F = ± 1L)’’ excitons (Klimov 2010).

4 Conclusion Cadmium selenide (CdSe) QDs nanoparticles of different sizes (2.4–3.69 nm) have been prepared via established conventional chemical methods. An optimum concentration of 1.4 mg/ml of CdSe QDs in toluene colloidal solutions were adopted in favor of UV–Vis absorption and PL emission higher intensities. The CdSe QDs size related excitonic band gap energies were in good agreement with theoretical calculations based on a semi-empirical pseudopotential model (SEPPM). In addition, Urbach rule could be applied to determine the convergence energy point ( hx0) of CdSe QDs of high quality and reproduced the same values of the energy gap estimated using Tauc plots method with less than * 1.7% deviation. In addition, theoretical calculations based on Einstein relations for absorption and emission taking into account CdSe QDs fine structure and local field effects successfully predict the values and trend of reported empirical CdSe size dependent first

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excitonic absorption transition oscillator strengths and radiative decay times under similar experimental conditions. Acknowledgements Authors are deeply grateful to members of the Nanotechnology Lab. at the National Institute of Laser Enhanced Sciences (NILES) and the esteemed staff of the solid-state Lab. at physics department, faculty of science, Cairo University.

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