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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23272–23285
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Light absorption in hybrid silicon-on-insulator/quantum dot waveguides

Abdoulghafar Omari, Pieter Geiregat, Dries Van Thourhout, and Zeger Hens  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23272-23285 (2013)
http://dx.doi.org/10.1364/OE.21.023272


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Abstract

We analyze the absorption coefficient of planarized silicon-on-insulator waveguides coated by close packed mono- and multilayers of colloidal PbS/CdS quantum dots (QDs). Experimental data clearly show the influence of the QDs on the waveguide absorbance around 1500 nm, where we find that QDs absorb stronger in thicker layers. To simulate the absorption coefficient of QD functionalized waveguides, the QD layer is replaced by an effective medium with a dielectric function determined by dipolar coupling between neighbouring QDs. Using the host dielectric constant εh as an adjustable parameter, excellent agreement with the experimental results is obtained. In this way, the increase in absorption cross section with layer thickness can be traced back to an increasing εh. We argue that this reflects the decreasing influence of the surroundings on the εh, which therefore evolves from an extrinsic property for monolayers to a more intrinsic film property for multilayers.

© 2013 OSA

1. Introduction

The optical properties of semiconductor nanocrystals show important deviations from their bulk counterparts. Quantum confinement makes the band gap depend on the nanocrystal dimensions, it reduces the quasi continuous energy bands to a set of discrete energy levels [1

1. F. W. Wise, “Lead salt quantum dots: The limit of strong quantum confinement,” Accounts of Chemical Research 3, 773–780 (2000). [CrossRef]

] – especially at the band edges – and it leads to a relaxation of selection rules, thus allowing for example light absorption by transitions within an energy band [2

2. A. Omari, I. Moreels, F. Masia, W. Langbein, P. Borri, D. Van Thourhout, P. Kockaert, and Z. Hens, “Role of interband and photoinduced absorption in the nonlinear refraction and absorption of resonantly excited PbS quantum dots around 1550 nm,” Phys. Rev. B 85, 115318 (2012). [CrossRef]

, 3

3. B. De Geyter, A. J. Houtepen, S. Carrillo, P. Geiregat, Y. Gao, S. ten Cate, J. M. Schins, D. Van Thourhout, C. Delerue, L. D. A. Siebbeles, and Z. Hens, “Broadband and picosecond intraband absorption in lead-based colloidal quantum dots,” ACS Nano 6, 6067–6074 (2012). [CrossRef] [PubMed]

]. As a result, the application of semiconductor nanocrystals in optical or photonic devices is widely investigated, using either self-assembled or colloidal quantum dots (QDs) made by epitaxial growth techniques or wet chemical methods, respectively. Compared to self-assembled QDs, colloidal QDs stand out since they can be synthesized in bulk quantities with low size dispersion and may be combined with various materials technology platforms by straightforward solution-based processing methods. Over the last 5 years, their use has been demonstrated in, e.g., light emitting devices, [4

4. J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 mu m from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-27-26394. [CrossRef]

], amplifiers [5

5. N. Daldosso, D. Navarro-Urrios, A. Pitanti, F. Gourbil-leau, R. Rizk, and L. Pavesi, “Erbium and silicon nanocrystals for light amplification,” in Proceedings of IEEE Conference of Lasers and Electro-Optics Society (LEOS)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 933–934.

], lasers [6

6. S. Hoogland, V. Sukhovatkin, I. Howard, S. Cauchi, L. Levina, and E. H. Sargent, “A solution-processed 1.53 mu m quantum dot laser with temperature-invariant emission wavelength,” Opt. Express 14, 3273–3281 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3273. [CrossRef] [PubMed]

], displays and photodetectors [7

7. J. P. Clifford, G. Konstantatos, K. W. Johnston, S. Hoog- land, L. Levina, and E. H. Sargent, “Fast, sensitive and spectrally tuneable colloidal quantum-dot photodetectors,” Nature Nanotechnology 4, 40–44 (2009). [CrossRef]

] and they have been combined with integrated photonics platforms based on silicon-on-insulator (SOI) or silicon nitride [8

8. I. Moreels, B. De Geyter, D. Van Thourhout, and Z. Hens, “Transmission of a quantum-dot-silicon-on-insulator hybrid notch filter,” J. Opt. Soc. Am. B 26, 1243–1247 (2009). [CrossRef]

12

12. J. F. Young, C. Foell, E. Schelew, and Q. Haijun, “Coupling of nanocrystals and photonic crystals for non-linear applications,” in Proceedings of IEEE Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 129–130.

].

In device applications, colloidal QDs are mostly deposited as close packed nanocrystal thin films, either within a layered stack [13

13. B. De Geyter, K. Komorowska, E. Brainis, P. Em- plit, P. Geiregat, A. Hassinen, Z. Hens, and D. Van Thourhout, “From fabrication to mode mapping in silicon nitride microdisks with embedded colloidal quantum dots,” Appl. Phys. Lett. 101, 161101 (2012). [CrossRef]

] or as a surface coating [8

8. I. Moreels, B. De Geyter, D. Van Thourhout, and Z. Hens, “Transmission of a quantum-dot-silicon-on-insulator hybrid notch filter,” J. Opt. Soc. Am. B 26, 1243–1247 (2009). [CrossRef]

] where they interact with the internal or evanescent optical field, respectively. A typical example here involves QDs embedded in a resonator, where the coupling of the QD light emission to the resonator modes eventually leads to lasing [6

6. S. Hoogland, V. Sukhovatkin, I. Howard, S. Cauchi, L. Levina, and E. H. Sargent, “A solution-processed 1.53 mu m quantum dot laser with temperature-invariant emission wavelength,” Opt. Express 14, 3273–3281 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3273. [CrossRef] [PubMed]

]. Essential to the development and optimization of such QD-based devices is a proper understanding of the optical field in materials with embedded or surface-coated QD films, where the influence of the QD film on the optical field is properly taken into account. In the literature, it is well known that a dilute dispersion of QDs, either in a liquid or a solid host, can be described as an effective optical medium according to the Maxwell-Garnett effective medium theory in the local field approximation [14

14. Z. Hens and I. Moreels, “Light absorption by colloidal semiconductor quantum dots,” Journal of Materials Chemistry 22, 10406–10415 (2012). [CrossRef]

]. On the other hand, far fewer studies have addressed the effective medium description of close packed QD films, let alone the experimental investigation and theoretical simulation of the optical properties of hybrid materials containing close packed QD films.

In this letter, we analyze the absorption coefficient of SOI planarized waveguides (PWGs) coated with close-packed mono- and multilayers – generally denoted as i-layer with i = 1, 2,... – of PbS/CdS QDs. We retrieve the fingerprint of the QDs in the waveguide absorbance and find that the absorbance per QD increases with the number of QD layers. The experimental data are compared with simulation results, where the QD i-layers are described as an effective medium in which the optical properties depend on dipolar coupling between neighboring QDs [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

]. Close agreement between the experimental values and the simulation results is obtained using the dielectric constant εh of the QD host material as the only adjustable parameter. We find that the increased absorbance in thicker layers makes that a higher value of εh is needed to match the simulated and the experimental data. We interpret this as a transition from a regime where the field lines coupling the QDs mainly pass through the surroundings (monolayer case) to a situation where these field lines are mainly confined within the QD stack (thicker multilayers).

2. Experimental

The PbS/CdS core/shell QDs used in this work were synthesized using an established cationic exchange procedure [16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

, 17

17. J. M. Pietryga, D. J. Werder, D. J. Williams, J. L. Casson, R. D. Schaller, V. I. Klimov, and J. A. Hollingsworth, “Utilizing the lability of lead selenide to produce heterostructured nanocrystals with bright, stable infrared emission,” Journal of the American Chemical Society 130, 4879–4885 (2008). [CrossRef] [PubMed]

]. Core diameter and shell thickness were adjusted to have a band gap absorption at ≈ 1450nm (see Fig. 1(a)). In this way, the long wavelength side of the absorption peak covers the 1500 – 1550nm bandpass window of the SOI grating couplers, which are used to couple light in and out of the waveguides. This will make the QD absorption well discernible in the measurements. Attempts of measuring the QD absorption of only core PbS QDs on the waveguides, showed a blue shift of the QD wavelength spectrum. This has been observed previously for PbS QDs deposited on glass substrates [21

21. Y. Justo, I. Moreels, K. Lambert, and Z. Hens, “Langmuir-Blodgett monolayers of colloidal lead chalcogenide quantum dots: morphology and photoluminescence,” Nanotechnology 21, 295606 (2010). [CrossRef] [PubMed]

]. These optically unstable films will hamper a quantitative study of the QD absorption. The growth of the CdS shell allowed for a better passiviation of the PbS core QDs yielding optically stable PbS/CdS particles, which will enable a quantitative comparison between the experimental and theoretical QD absorption. Using the absorption spectrum of the original PbS QDs and the resulting PbS/CdS QDs, core diameter and shell thickness were estimated to be 5.4 and 0.4 nm, respectively [18

18. Y. Justo, P. Geiregat, K. Van Hoecke, F. Vanhaecke, C.D. Donega, and Z. Hens, “Optical properties of PbS/CdS quantum dots,” Journal of Physical Chemistry C , Just Accepted Manuscript.

, 19

19. B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett. 97, 161908 (2010). [CrossRef]

]. The QDs were locally deposited on the PWGs by combining optical lithography and Langmuir-Blodgett deposition, [20

20. K. Lambert, I. Moreels, D. Van Thourhout, and Z. Hens, “Quantum dot micropatterning on Si,” Langmuir 24, 5961–5966 (2008). [CrossRef] [PubMed]

, 21

21. Y. Justo, I. Moreels, K. Lambert, and Z. Hens, “Langmuir-Blodgett monolayers of colloidal lead chalcogenide quantum dots: morphology and photoluminescence,” Nanotechnology 21, 295606 (2010). [CrossRef] [PubMed]

] forming strips of 200, 500, 1000, 1500μm on otherwise identical waveguides (see Fig. 1(b)). The scanning electron microscopy image shown in Fig. 1(c) is indicative of the close packing and locally hexagonal ordering of the QDs on top of the PWG, while atomic force microscopy imaging reveals that the PWGs are depressed by 5 – 10nm relative to the surrounding silica, with the QD layer conformally following this geometry (see Fig. 1(d)).

Fig. 1 (a) Absorption spectrum of the PbS/CdS QD used here, as recorded on a dilute QD dispersion in tetrachloroethylene. (b) Optical microscopy image of a sample with planarized waveguides coated by a QD monolayer with various strip lengths and a cartoon representation of the opitcal field coupled from the fiber through the grating in the QD coated PWG. (c) Scanning electron microscopy image of a (topview) PWG coated by a QD monolayer. The resolution is such that the individual QDs coating the waveguide can be discerned. (d) Atomic force microscopy image and cross section of a PWG coated by a QD monolayer, clearly showing the offset (l) between the top surface of the (slightly submerged) PWG and its silica cladding.

The use of QD strips with different interaction length on identical waveguides enables us to quantify the light absorption in the QD functionalized sections of the PWGs, regardless of coupling losses (see Fig. 1(b)). Indeed, denoting the absorption coefficient of a bare and QD coated PWG α0 and α, respectively, the net absorption coefficient αQD = αα0 of a QD coated PWG can be derived from the transmitted power Pt through PWGs with different QD strip lengths L. More specifically, using the length of and the power transmitted through one of the QD coated waveguides as a reference, the net waveguide absorbance A reads:
A=lnPtPt,ref=(αα0)(LLref)
(1)
In the determination of A we neglect any contribution of the QD emission to the measured Pt[16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

].

3. Results and discussion

Fig. 2 (a) (open squares) Absorbance A – as defined by Eq. (1) – at 1520nm as a function of the strip length difference ΔL for PWG coated with a PbS/CdS QD 2-layer strip 500, 1000, and 1500μm long using the power transmitted through a similar waveguide with a 200μm QD 2-layer as a reference and (full line) best fit of the data to a line passing through the origin with an indication of the thus obtained absorption coefficient αQD. (b) (red, left and bottom axis) αQD thus determined as a function of wavelength for a (filled circles) QD monolayer and a (open squares) QD 2-layer coated PWG. The full lines represent the absorption spectrum of dispersed PbS/CdS QDs normalized to match the respectively measured absorption coefficients. (blue, right and top axis) αQD per QD layer at 1520 nm. The full line is a guide to the eye and the dashed line indicates the average value obtained for a monolayer and a 2-layer.

To compare the experimental αQD with model predictions, we use an approach where the real QD i-layer covering the PWG is replaced by an effective medium with a dielectric function εeff (see Fig. 3(a)). Using the real geometry of the PWG – including the slightly submerged waveguide top surface, coated by a 2 nm thin native silica layer – this enables us to extract a theoretical absorption coefficient αQD,th from the simulated effective refractive index ñeff = neff + eff of the propagating quasi-TE mode:
αQD,th=4πκeffλ
(2)
This approach however requires that the dielectric function of each material or medium involved is known. For silicon and silica, we use typical values at 1520 nm of 3.45 and 1.45, respectively. For εeff, we build on the recent finding that the absorption cross section of QDs in close-packed monolayers similar to the ones used here can be well described by taking dipolar coupling between neighboring QDs explicitly into account [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

]. As shown in the Supplemental Material [16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

], this coupled dipole model (CDM) also applies to all PbS/CdS QD i-layers used in this study. Therefore, the CDM applies for core/shell particles as in [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

] only the absorption cross section of core PbS and CdSe core-QD monolayers deposited on glass was studied. Moreover, the study of imaginary part of εeff through the absorption cross section of QDs in [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

] can be extended to yield a generalised expression for εeff[16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

]:
εeff=εhε0(1+NsLtaQD1aQDS)
(3)
Here, Ns is the QD surface density in the layer, Lt is the thickness of the effective layer, aQD is the polarizability of a single PbS/CdS QD and S is the so-called dipole sum, which sums up the influence of the dipolar field of neighboring QDs on an individual QD in the layer. In general, S is different for fields parallel (S||) or perpendicular (S) to the QD film. However, since the main field component of the quasi-TE modes in the PWG used here lies parallel to the QD film, only S|| – which was analysed experimentally in [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

] – is of relevance here.

Opposite from S, which only depends on the position of the particles relative to each other, aQD is a function of εh and the dielectric function εQD = εQD,R + QD,I of the QDs. While we consider εh as an adjustable parameter in this study, we use calculated values for εQD,R and εQD,I[16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

], taking care that they yield the experimental absorption coefficient spectrum of the QDs in a dilute dispersion while obeying the Kramers-Kronig transformation [22

22. I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Kronig analysis of the absorbance spectrum,” Phys. Rev. B 81, 235319 (2010). [CrossRef]

]. Importantly, in this analysis, we assume that the absorption coefficient of the PbS/CdS core/shell QDs at wavelengths shorter than 400 nm can be derived from the bulk dielectric function of PbS and CdS, respectively – as was demonstrated for PbSe/CdSe QDs [19

19. B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett. 97, 161908 (2010). [CrossRef]

] – and we neglect possible quantization effects in the CdS shell.

Combining the geometry of the PWG cross section and the expression for εeff – based on the coupled dipole model and the self-consistently determined εQD – the electric field of the guided optical mode in the PWG can be calculated, resulting in theoretical values for ñeff and αQD,th. As an example, Fig. 3(b) represents the electric field at a wavelength of 1520 nm for a PWG covered by a QD monolayer as obtained using Fimmwave 3.4 complex mode solver. The figure clearly shows the overlap between the QD film and the evanescent field, which makes that light absorption by the QDs affects κeff and leads to a non-zero αQD,th. The determination of αQD,th would not be possible through a transmission measurement of monolayer coated glass in a spectrophotometer as the absorbance would fall within the noise range. As shown in Fig. 3(c), a close match can be obtained between the simulated and experimental αQD spectrum for a QD monolayer-coated PWG by adjusting εh. It should be noted that the εh value needed to match the experimental and simulated αQD somewhat depends on the geometry of the PWG. Looking at the AFM cross section of the PWG (see Fig. 1(d)), an exact value of the height difference l between the top surface of the PWG and its silica cladding is hard to determine. Varying l between 6 and 10nm as extreme cases, we obtain agreement between experiment and simulation for εh = 1.0 (l = 6nm) to εh = 1.16 (l = 10nm). For QDs capped by oleic acid (ε =2.1 at 2000 nm [23

23. R. Signorell and A. Bertram, “Physical chemistry of aerosols,” Physical chemistry chemical physics : PCCP 11, 7759–7759 (2009). [CrossRef] [PubMed]

]), both figures are relatively low yet they agree with the εh = 1.0 found for PbS and CdSe QD monolayers deposited on glass [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

].

Fig. 3 (a) Cartoon representation of the replacement of the real QD film on top of an SOI planarized waveguide by an effective medium. Indicated are the height difference l between the top surface of the PWG and its silica cladding and the native silica layer in between the PWG top surface and the effective medium representing the QD film. (b) Cross-sectional representation of the simulated electric field for 1520 nm light guided by a PWG coated by a QD monolayer. (c) Comparison of the experimental and simulated αQD absorbance spectrum of a QD coated PWG for two different combinations of l and εh.

The approach as outlined above can be readily extended to simulate αQD for PWG covered by QD i-layers. Using once more εh as an adjustable parameter, correspondence between experimental and simulated values can be obtained as shown by the example of a 7-layer in Fig. 4. Importantly, the increasing QD absorption cross section with thicker layers makes that a larger εh is needed to fit the simulations to the experimental data when the number of layers increases. As shown in Fig. 4(b), an εh in the range of 1.00–1.16 is obtained in the case of a monolayer, whereas values between 1.47 and 1.50 are found for the simulation of the 7-layer using l = 6 and l = 10nm, respectively [16

16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

]. This demonstrates that in the case of a QD i-layer with i close to one, εh is not an intrinsic property of the QD film. Since the field lines that couple neighboring QDs in a monolayer mainly pass through the surroundings, the combined effect of the layers surrounding the QDs – air and native silica on silicon – and the organic ligands separating the QDs will determine εh in this case. For thicker layers however, the larger part of these coupling fields remains within the QD film. In that respect, the trend shown in Fig. 4(b) can be interpreted as the progressive evolution of εh from an extrinsic value, determined by the layer and its surroundings, in the monolayer case to a value that is an intrinsic property of a QD multilayer.

Fig. 4 (a) Comparison of the experimental and simulated αQD spectrum of a PWG coated with (blue) a QD monolayer and (red) a QD seven layer. The respective axis are scaled by a factor of 7 to allow for a direct comparison of the absorbance per number of layers. (b) Evolution of εh values needed to match experimental and simulated absorption coefficient calculated for the extreme case of (red) l = 6 and (blue) l = 10nm.

This results are not only essential for a proper understanding of the optical field in QD mono-layers and the of optical development of QD-based devices, but could have an implication for electronic devices. Thicker QD layers, as outlined above, will allow for more absorption per particle. On the other hand thicker QD layers will hamper charge extraction for photovoltaic or detector devices. In addition, the electric field within a QD layer due to an applied voltage accross the layer will be limited by increasing the layer thickness. This means that the opposing effects of increased absorption and limited electric field will lead to a optimum QD thickness for electronic devices.

4. Conclusion

In conclusion, we have studied light absorption in planarized SOI waveguides functionalized with a top coating of PbS/CdS QD mono- to multilayers. The experimental absorption co-efficients can be simulated using an approach where the QD layer is replaced by an effective medium with an effective dielectric function determined by dipolar coupling between neighboring QDs. This approach leaves the host dielectric constant εh as the only adjustable parameter and provides a generic scheme to model optical properties of composite materials containing close packed QD films. Using εh to match experimental and simulated absorption coefficients, we find that εh systematically increases for thicker films. We interpret this as an evolution of εh from an extrinsic property, both determined by the QD films and the surrounding layers, to a more intrinsic property of the QD layer. To the best of our knowledge, this is the first demonstration of how εh – a typical parameter introduced in effective medium theories – depends on the dimensions of the layer modeled. Our results are essential for the optimization and development of QD-based devices.

5. Appendix

5.1. PbS/CdS synthesis

The PbS QDs were prepared using a procedure as described by [24

24. L. Cademartiri, J. Bertolotti, R. Sapienza, D. S. Wiersma, G. von Freymann, and G. A. Ozin, “Multigram scale, solventless, and diffusion-controlled route to highly monodisperse PbS nanocrystals,” J. Phys. Chem. B 110, 671–673 (2006). [CrossRef] [PubMed]

], where the synthesis conditions were chosen such that oleate capped PbS QDs with a first exciton absorption at 1590 nm – corresponding to a diameter of 6.2 nm – were formed (see blue line in Fig. 5). For the CdS shell growth, a cationic exchange procedure was used, starting from a 5.7μM QD dispersion in toluene. The dispersion was heated to 125°C in a reaction flask placed in an nitrogen atmosphere. Cadmium oleate was added in a 20:1 Cd to Pb ratio. This starts a cationic exchange process in which the outer Pb2+ cations are replaced by Cd2+ cations, leading to a heterostructure with a PbS core and a CdS shell. The reaction was stopped by quenching with a double amount of ethanol as compared to the reaction volume. After centrifugation and decantation the PbS/CdS Qdots were suspended in toluene. The reduction of the PbS core size by cationic exchange leads to a blueshift of the first exciton absorption. For the PbS/CdS used here, the exciton absorption is shifted to 1450 nm (red line in Fig. 5) leading to particles particles with a total size of 6.2 nm, a shell thickness of 0.4 nm and a size dispersion of 8%.

Fig. 5 The QD core shell exciton absorption (red line) shows a blueshift, after cationic exchange procedure, compared with the QD core exciton absorption (blue line).

5.2. Absorption coefficient spectra for one to seven layer coated PWGs

We used the method as outlined in the paper to determine the spectrum of the absorption coefficient of PWGs coated with a QD i-layer with i = 1, 2, 3, 4, 5 and 7. All results are grouped in Fig. 6.

Fig. 6 Experimental αQD, measured as a function of wavelength for a QD monolayer to a QD 7-layer coated PWG. The full lines represent the absorption spectrum of dispersed PbS/CdS QDs normalized to match the respectively measured absorption coefficients.

5.3. Dielectric constant and polarizability of the PbS/CdS core shell Qdots

Fig. 7 (a) The dielectric function of the core (PbS) of PbS/CdS Qdots determined using the IMI method for the KK-analysis. Dotted and full line represent respectively εc,R and εc,I. (b) The real part of the complex effective refractive index ñeff (dotted line) and the extinction coefficient (full line) extracted from applying the coupled dipole model to the PbS/CdS QD layer.

5.4. Coupled Dipole Model: Derivation of εeff

In the coupled dipole model, we consider a collection of polarizable point particles embedded with a volume density N in a host with permittivity εh[15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

]. We can define an effective dielectric constant εeff for this composite medium by relating the average dielectric displacement to the average electric field:
D=εeffE=ε0E+P=ε0E+ε0(εh1)E+Np0
(6)

In the latter sum, the polarization is split into the contribution of the host and the additional contribution of the dipoles p0 induced on the point particles. The latter term can be rewritten in terms of the polarizability (a0) of the point particles and the local electric field EL that polarizes them:
Np0=Nε0a0EL
(7)
Using the expression derived by [27

27. A. V. Goncharenko, “Optical properties of core-shell particle composites. I. Linear response,” Chem. Phys. Lett. 386, 25–31 (2004). [CrossRef]

] for spherically symmetrical core/shell particles, a0 can be expressed as:
a0=εhV(εshεh)[εsh+(εcεsh)13(1p)]+pεsh(εcεsh)[εsh+(εcεsh)13(1p)][εh+13(εshεh)]+p13εsh(εcεsh)
(8)
Here, p denotes the ratio of the volume of the core and the volume of the whole core/shell particle.

In the case of a close packed layer, the local field that drives an individual dipole i is the sum of the external field and the field of the neighboring dipoles j:
EL,i=E+jiβi,jEL,j
(9)
A crucial element in writing down equation 9 is the assumption that because of symmetry reasons, EL is the same for all particles:
EL=E+Sε0a0εhEL
(10)
Here, S is the dipole sum which contains all contributions from the neighboring particles on the local field driving a central particle. For an applied field parallel to the QD film (S||), the dipole sum is given by:
S||=14πji(1ikdij)(3cos2(θij1))eikdijdij3+k2sin2(θij)eikdijdij
(11)

To obtain a consistent expression for N in the case of QD i-layers, we determine it as the ratio between the QD surface density in the layer Ns – which is the total number of QDs in the i-layer per unit of surface area – and the thickness Lt attributed to the i-layer. In this study, we take Lt as the product of the number of layers i and the spacing between close-packed planes in an fcc stacking of QDs. With d the QD diameter (6.2 nm) and llig the thickness of the ligand shell (taken as 1.8 nm), we thus have:
Lt=0.82(d+2llig)×i8×inm
(12)

Using this definition of N and Lt, εeff is obtained as:
εeff=εhε0(1+NsLtaQD1aQDS)
(13)
In Fig. 7(b), we plot the spectrum of the real and imaginary part of the refractive index as derived from εeff for a PbS/CdS QD monolayer with a surface density Ns =1.2 1012 1cm2 and taking εh =1 and Lt =8 nm.

5.5. Coupled Dipole Model: Multi-layers

The use of the coupled dipole model to analyze the effective permittivity of nanocrystal composites was elaborated by [15

15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

] for the case of a single component monolayer. Their analysis showed a remarkable absorption enhancement effect absent in other effective medium models for dilute systems, such as the Maxwell-Garnett mixing rule. However, the experimental and theoretical analysis was limited to monolayers of QDs. As shown in Fig. 8(a), the ratio between the absorbance of a QD i-layer and the number of layers is in a good approximation constant, which means that the same absorption enhancement as for monolayers holds for i-layers. We can thus extend the expression of εeff that follows from the coupled dipole model to the analysis of QD i-layers.

Fig. 8 (a) Monolayer of PbS nanocrystals deposited on TEM grid. Inset : The Fourier image of the monolayer yields a hexagonal diffraction pattern clearly illustrating the strong hexagonal order within the monolayer. (b) The absorbance Ai per layer of i-layers of PbS and PbS/CdS QDs normalized relative to the absorbance of a monolayer as a function of the number of layers i.

5.6. Simulated αQD spectrum of the PbS/CdS core shell Qdots

To simulate the absorption coefficient of the QD functionalized waveguides, the QD layer is replaced by an effective medium with a dielectric function determined by dipolar coupling between neighbouring QDs as outlined above. Using the host dielectric constant εh as an adjustable parameter we match the simulated absorption coefficient to the experimental spectrum. As shown in Fig. 9, a good match between both is obtained for all i-layers, provided that a larger εh is used when the number of layers increases.

Fig. 9 The full lines represent the absorption spectrum of the simulated αQD spectrum with the needed εh values for l = 6nm to match the experimental and simulated absorption coefficient. Similar curves where obtained for l = 10nm.

5.7. Contribution of the QD PbS/CdS core shell emission to the measured A and Pt

In dispersion, the PbS/CdS QDs used here have a photoluminescence peaking at 1520 nm (see Fig. 10) and a quantum yield of 37%, as determined using an integrating sphere [28

28. J. C. De Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photo-luminescence quantum efficiency,” Adv. Mat. 9, 230232 (1997). [CrossRef]

]. When deposited on waveguides, part of this luminescence may be coupled to the waveguides, thus raising the transmitted power and lowering the resulting absorption coefficient. In general, the fraction of the absorbed light entering the waveguide in the direction of the detector is determined by the product QY × ηcoupling of the photoluminescence QY and a coupling factor ηcoupling, which is the ratio between the power emitted in the waveguide in one of the two directions to the total power emitted by the QDs. By comparing the transmitted power through waveguides with and without QDs, the net QD absorption coefficient αα0 is obtained. Clearly, when each QD covering the WGs would re-emit each absorbed photon in the waveguide in the direction of the detector (QY = 1, ηcoupling = 1), then the QD-emission will fully compensate the QD-absorption and αα0 would amount to zero. Otherwise, if QY ×ηcoupling ≪ 1, the QD-emission contribution to the measured absorbance will be very low and the measured additional waveguide loss can be directly linked to light absorption by the QDs. As mentioned above, the QY of the PbS/CdS QDs in tetrachloroethylene dispersions used here was determined at 0.37. In general, this QY goes down after Langmuir-Blodgett deposition on silicon [29

29. R. Quintero-Torres, C. A. Foell, J. Pichaandi, F. C. J. M. van Veggel, and J. F. Young, “Photoluminescence dynamics in solid formulations of colloidal PbSe quantum dots: Three-dimensional versus two-dimensional films,” Appl. Phys. Lett. 101, 121904 (2012). [CrossRef]

,30

30. C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M. van Veggel, and J. F. Young, “Saturation behaviour of colloidal PbSe quantum dot exciton emission coupled into silicon photonic circuits,” Opt. Express 20, 10453–10469 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10453. [CrossRef] [PubMed]

], such that the value of 0.37 should be seen as an upper limit. For determining ηcoupling, we use an FDTD numerical solver to determine the fraction of the power emitted by a dipole oscillator that is coupled to the waveguide modes. The oscillator is located at a distance of 20 nm from the surface, which should be regarded as an average position of the QD-monolayers relative to the waveguide surface. Along the light propagation direction, the oscillator is put at the center of the waveguide and we find that ηcoupling amounts to 0.15. Here, we accounted for the fact that only half of the emitted light will be collected at one of the waveguide ends and we averaged over the three spatial directions in which the dipole can oscillate. This shows that the emitted light will amounts to, at its best, 5.6% of the absorbed light. This number falls within the ≈10% error of our αQD measurements, and the contribution is therefore discarded.

Fig. 10 Photoluminescence spectrum of the PbS/CdS QDs used in this work after excitation at 750 nm. The QDs are dispersed in tetrachloroethylene. The emission peak is at 1520 nm.

Acknowledgments

A.O. acknowledges the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) for a scholarship. P.G. acknowledges Ghent University for a BOF scholarship. Weiqiang Xie is acknowledged for the FDTD simulations. Z.H. acknowledges the Fund for Scientific Research Flanders (FWO-Vlaanderen) for a research grant (project nr. G.0760.12). Z.H. and D.V.T. acknowledge the Belgian Science Policy Office for funding this research (IAP 7.35, photonics@be).

References and links

1.

F. W. Wise, “Lead salt quantum dots: The limit of strong quantum confinement,” Accounts of Chemical Research 3, 773–780 (2000). [CrossRef]

2.

A. Omari, I. Moreels, F. Masia, W. Langbein, P. Borri, D. Van Thourhout, P. Kockaert, and Z. Hens, “Role of interband and photoinduced absorption in the nonlinear refraction and absorption of resonantly excited PbS quantum dots around 1550 nm,” Phys. Rev. B 85, 115318 (2012). [CrossRef]

3.

B. De Geyter, A. J. Houtepen, S. Carrillo, P. Geiregat, Y. Gao, S. ten Cate, J. M. Schins, D. Van Thourhout, C. Delerue, L. D. A. Siebbeles, and Z. Hens, “Broadband and picosecond intraband absorption in lead-based colloidal quantum dots,” ACS Nano 6, 6067–6074 (2012). [CrossRef] [PubMed]

4.

J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 mu m from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express 19, 26394–26398 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-27-26394. [CrossRef]

5.

N. Daldosso, D. Navarro-Urrios, A. Pitanti, F. Gourbil-leau, R. Rizk, and L. Pavesi, “Erbium and silicon nanocrystals for light amplification,” in Proceedings of IEEE Conference of Lasers and Electro-Optics Society (LEOS)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 933–934.

6.

S. Hoogland, V. Sukhovatkin, I. Howard, S. Cauchi, L. Levina, and E. H. Sargent, “A solution-processed 1.53 mu m quantum dot laser with temperature-invariant emission wavelength,” Opt. Express 14, 3273–3281 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3273. [CrossRef] [PubMed]

7.

J. P. Clifford, G. Konstantatos, K. W. Johnston, S. Hoog- land, L. Levina, and E. H. Sargent, “Fast, sensitive and spectrally tuneable colloidal quantum-dot photodetectors,” Nature Nanotechnology 4, 40–44 (2009). [CrossRef]

8.

I. Moreels, B. De Geyter, D. Van Thourhout, and Z. Hens, “Transmission of a quantum-dot-silicon-on-insulator hybrid notch filter,” J. Opt. Soc. Am. B 26, 1243–1247 (2009). [CrossRef]

9.

A. G. Pattantyus-Abraham, H. Qiao, J. Shan, K. A. Abel, T.-S. Wang, F. C. J. M. van Veggel, and J. F. Young, “Site-selective optical coupling of PbSe nanocrystals to Si-based photonic crystal microcavities,” Nano Letters 9, 2849–2854 (2009). [CrossRef] [PubMed]

10.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia- Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Letters 10, 1506–1511 (2010). [CrossRef] [PubMed]

11.

D. V. Talapin, J.-S. Lee, M. V. Kovalenko, and E. V. Shevchenko, “Prospects of colloidal nanocrystals for electronic and optoelectronic applications,” Chemical Reviews 110, 389–458 (2010). [CrossRef]

12.

J. F. Young, C. Foell, E. Schelew, and Q. Haijun, “Coupling of nanocrystals and photonic crystals for non-linear applications,” in Proceedings of IEEE Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 129–130.

13.

B. De Geyter, K. Komorowska, E. Brainis, P. Em- plit, P. Geiregat, A. Hassinen, Z. Hens, and D. Van Thourhout, “From fabrication to mode mapping in silicon nitride microdisks with embedded colloidal quantum dots,” Appl. Phys. Lett. 101, 161101 (2012). [CrossRef]

14.

Z. Hens and I. Moreels, “Light absorption by colloidal semiconductor quantum dots,” Journal of Materials Chemistry 22, 10406–10415 (2012). [CrossRef]

15.

P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano 7, 987–993 (2013). [CrossRef] [PubMed]

16.

See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.

17.

J. M. Pietryga, D. J. Werder, D. J. Williams, J. L. Casson, R. D. Schaller, V. I. Klimov, and J. A. Hollingsworth, “Utilizing the lability of lead selenide to produce heterostructured nanocrystals with bright, stable infrared emission,” Journal of the American Chemical Society 130, 4879–4885 (2008). [CrossRef] [PubMed]

18.

Y. Justo, P. Geiregat, K. Van Hoecke, F. Vanhaecke, C.D. Donega, and Z. Hens, “Optical properties of PbS/CdS quantum dots,” Journal of Physical Chemistry C , Just Accepted Manuscript.

19.

B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett. 97, 161908 (2010). [CrossRef]

20.

K. Lambert, I. Moreels, D. Van Thourhout, and Z. Hens, “Quantum dot micropatterning on Si,” Langmuir 24, 5961–5966 (2008). [CrossRef] [PubMed]

21.

Y. Justo, I. Moreels, K. Lambert, and Z. Hens, “Langmuir-Blodgett monolayers of colloidal lead chalcogenide quantum dots: morphology and photoluminescence,” Nanotechnology 21, 295606 (2010). [CrossRef] [PubMed]

22.

I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Kronig analysis of the absorbance spectrum,” Phys. Rev. B 81, 235319 (2010). [CrossRef]

23.

R. Signorell and A. Bertram, “Physical chemistry of aerosols,” Physical chemistry chemical physics : PCCP 11, 7759–7759 (2009). [CrossRef] [PubMed]

24.

L. Cademartiri, J. Bertolotti, R. Sapienza, D. S. Wiersma, G. von Freymann, and G. A. Ozin, “Multigram scale, solventless, and diffusion-controlled route to highly monodisperse PbS nanocrystals,” J. Phys. Chem. B 110, 671–673 (2006). [CrossRef] [PubMed]

25.

A. Neeves and M. Birnboim, “Composite structures for the enhancement of nonlinear-opitcal susceptibility,” J. Opt. Soc. Am. B 6, 787–796 (1989). [CrossRef]

26.

S. Ninomiya and S. Adachi, “Optical-properties of wurtzite CdS,” J. Appl. Phys. 78, 1183–1190 (1995). [CrossRef]

27.

A. V. Goncharenko, “Optical properties of core-shell particle composites. I. Linear response,” Chem. Phys. Lett. 386, 25–31 (2004). [CrossRef]

28.

J. C. De Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photo-luminescence quantum efficiency,” Adv. Mat. 9, 230232 (1997). [CrossRef]

29.

R. Quintero-Torres, C. A. Foell, J. Pichaandi, F. C. J. M. van Veggel, and J. F. Young, “Photoluminescence dynamics in solid formulations of colloidal PbSe quantum dots: Three-dimensional versus two-dimensional films,” Appl. Phys. Lett. 101, 121904 (2012). [CrossRef]

30.

C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M. van Veggel, and J. F. Young, “Saturation behaviour of colloidal PbSe quantum dot exciton emission coupled into silicon photonic circuits,” Opt. Express 20, 10453–10469 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10453. [CrossRef] [PubMed]

31.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 14, 949 (2002). [CrossRef]

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(160.4760) Materials : Optical properties
(230.7370) Optical devices : Waveguides
(230.7390) Optical devices : Waveguides, planar
(240.0310) Optics at surfaces : Thin films
(300.1030) Spectroscopy : Absorption
(310.6860) Thin films : Thin films, optical properties
(260.2065) Physical optics : Effective medium theory
(160.4236) Materials : Nanomaterials

ToC Category:
Optical Devices

History
Original Manuscript: June 6, 2013
Revised Manuscript: August 25, 2013
Manuscript Accepted: August 29, 2013
Published: September 24, 2013

Citation
Abdoulghafar Omari, Pieter Geiregat, Dries Van Thourhout, and Zeger Hens, "Light absorption in hybrid silicon-on-insulator/quantum dot waveguides," Opt. Express 21, 23272-23285 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23272


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References

  1. F. W. Wise, “Lead salt quantum dots: The limit of strong quantum confinement,” Accounts of Chemical Research3, 773–780 (2000). [CrossRef]
  2. A. Omari, I. Moreels, F. Masia, W. Langbein, P. Borri, D. Van Thourhout, P. Kockaert, and Z. Hens, “Role of interband and photoinduced absorption in the nonlinear refraction and absorption of resonantly excited PbS quantum dots around 1550 nm,” Phys. Rev. B85, 115318 (2012). [CrossRef]
  3. B. De Geyter, A. J. Houtepen, S. Carrillo, P. Geiregat, Y. Gao, S. ten Cate, J. M. Schins, D. Van Thourhout, C. Delerue, L. D. A. Siebbeles, and Z. Hens, “Broadband and picosecond intraband absorption in lead-based colloidal quantum dots,” ACS Nano6, 6067–6074 (2012). [CrossRef] [PubMed]
  4. J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directional emission at 1.55 mu m from PbSe colloidal quantum dot electroluminescent device on silicon,” Opt. Express19, 26394–26398 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-27-26394 . [CrossRef]
  5. N. Daldosso, D. Navarro-Urrios, A. Pitanti, F. Gourbil-leau, R. Rizk, and L. Pavesi, “Erbium and silicon nanocrystals for light amplification,” in Proceedings of IEEE Conference of Lasers and Electro-Optics Society (LEOS)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 933–934.
  6. S. Hoogland, V. Sukhovatkin, I. Howard, S. Cauchi, L. Levina, and E. H. Sargent, “A solution-processed 1.53 mu m quantum dot laser with temperature-invariant emission wavelength,” Opt. Express14, 3273–3281 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3273 . [CrossRef] [PubMed]
  7. J. P. Clifford, G. Konstantatos, K. W. Johnston, S. Hoog- land, L. Levina, and E. H. Sargent, “Fast, sensitive and spectrally tuneable colloidal quantum-dot photodetectors,” Nature Nanotechnology4, 40–44 (2009). [CrossRef]
  8. I. Moreels, B. De Geyter, D. Van Thourhout, and Z. Hens, “Transmission of a quantum-dot-silicon-on-insulator hybrid notch filter,” J. Opt. Soc. Am. B26, 1243–1247 (2009). [CrossRef]
  9. A. G. Pattantyus-Abraham, H. Qiao, J. Shan, K. A. Abel, T.-S. Wang, F. C. J. M. van Veggel, and J. F. Young, “Site-selective optical coupling of PbSe nanocrystals to Si-based photonic crystal microcavities,” Nano Letters9, 2849–2854 (2009). [CrossRef] [PubMed]
  10. A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia- Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Letters10, 1506–1511 (2010). [CrossRef] [PubMed]
  11. D. V. Talapin, J.-S. Lee, M. V. Kovalenko, and E. V. Shevchenko, “Prospects of colloidal nanocrystals for electronic and optoelectronic applications,” Chemical Reviews110, 389–458 (2010). [CrossRef]
  12. J. F. Young, C. Foell, E. Schelew, and Q. Haijun, “Coupling of nanocrystals and photonic crystals for non-linear applications,” in Proceedings of IEEE Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)(Institute of Electrical and Electronics Engineers, Lake Buena Vista, FL, 2007), 129–130.
  13. B. De Geyter, K. Komorowska, E. Brainis, P. Em- plit, P. Geiregat, A. Hassinen, Z. Hens, and D. Van Thourhout, “From fabrication to mode mapping in silicon nitride microdisks with embedded colloidal quantum dots,” Appl. Phys. Lett.101, 161101 (2012). [CrossRef]
  14. Z. Hens and I. Moreels, “Light absorption by colloidal semiconductor quantum dots,” Journal of Materials Chemistry22, 10406–10415 (2012). [CrossRef]
  15. P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant and broad-band absorption enhancement in colloidal quantum dot monolayers through dipolar coupling,” ACS Nano7, 987–993 (2013). [CrossRef] [PubMed]
  16. See the Appendix section for a thorough discussion of the synthesis, dielectric function, coupled dipole model, experimental and simulated results.
  17. J. M. Pietryga, D. J. Werder, D. J. Williams, J. L. Casson, R. D. Schaller, V. I. Klimov, and J. A. Hollingsworth, “Utilizing the lability of lead selenide to produce heterostructured nanocrystals with bright, stable infrared emission,” Journal of the American Chemical Society130, 4879–4885 (2008). [CrossRef] [PubMed]
  18. Y. Justo, P. Geiregat, K. Van Hoecke, F. Vanhaecke, C.D. Donega, and Z. Hens, “Optical properties of PbS/CdS quantum dots,” Journal of Physical Chemistry C, Just Accepted Manuscript.
  19. B. De Geyter and Z. Hens, “The absorption coefficient of PbSe/CdSe core/shell colloidal quantum dots,” Appl. Phys. Lett.97, 161908 (2010). [CrossRef]
  20. K. Lambert, I. Moreels, D. Van Thourhout, and Z. Hens, “Quantum dot micropatterning on Si,” Langmuir24, 5961–5966 (2008). [CrossRef] [PubMed]
  21. Y. Justo, I. Moreels, K. Lambert, and Z. Hens, “Langmuir-Blodgett monolayers of colloidal lead chalcogenide quantum dots: morphology and photoluminescence,” Nanotechnology21, 295606 (2010). [CrossRef] [PubMed]
  22. I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens, “Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Kronig analysis of the absorbance spectrum,” Phys. Rev. B81, 235319 (2010). [CrossRef]
  23. R. Signorell and A. Bertram, “Physical chemistry of aerosols,” Physical chemistry chemical physics : PCCP11, 7759–7759 (2009). [CrossRef] [PubMed]
  24. L. Cademartiri, J. Bertolotti, R. Sapienza, D. S. Wiersma, G. von Freymann, and G. A. Ozin, “Multigram scale, solventless, and diffusion-controlled route to highly monodisperse PbS nanocrystals,” J. Phys. Chem. B110, 671–673 (2006). [CrossRef] [PubMed]
  25. A. Neeves and M. Birnboim, “Composite structures for the enhancement of nonlinear-opitcal susceptibility,” J. Opt. Soc. Am. B6, 787–796 (1989). [CrossRef]
  26. S. Ninomiya and S. Adachi, “Optical-properties of wurtzite CdS,” J. Appl. Phys.78, 1183–1190 (1995). [CrossRef]
  27. A. V. Goncharenko, “Optical properties of core-shell particle composites. I. Linear response,” Chem. Phys. Lett.386, 25–31 (2004). [CrossRef]
  28. J. C. De Mello, H. F. Wittmann, and R. H. Friend, “An improved experimental determination of external photo-luminescence quantum efficiency,” Adv. Mat.9, 230232 (1997). [CrossRef]
  29. R. Quintero-Torres, C. A. Foell, J. Pichaandi, F. C. J. M. van Veggel, and J. F. Young, “Photoluminescence dynamics in solid formulations of colloidal PbSe quantum dots: Three-dimensional versus two-dimensional films,” Appl. Phys. Lett.101, 121904 (2012). [CrossRef]
  30. C. A. Foell, E. Schelew, H. Qiao, K. A. Abel, S. Hughes, F. C. J. M. van Veggel, and J. F. Young, “Saturation behaviour of colloidal PbSe quantum dot exciton emission coupled into silicon photonic circuits,” Opt. Express20, 10453–10469 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-10453 . [CrossRef] [PubMed]
  31. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron.14, 949 (2002). [CrossRef]

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