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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 4, JULY/AUGUST 2014 4400306 Modeling the Optical Properties of Low-Cost Colloidal Quantum Dot Functionalized Strip SOI Waveguides Abdoulghafar Omari, Member, IEEE, Weiqiang Xie, Pieter Geiregat, Member, IEEE, Dries Van Thourhout, Member, IEEE, and Zeger Hens Abstract—We studied the optical absorption of silicon-on- insulator strip waveguides functionalized by a monolayer of col- loidal PbS/CdS core/shell quantum dots. The integration is done by Langmuir–Blodgett deposition, which results in a monolayer of quantum dots (QDs) on the waveguides. Experimental absorp- tion coefficients of QD functionalized strip waveguides range from 10–30 cm 1 . These values are about five times larger than the ab- sorption coefficient of QD functionalized planarized waveguides. Using a refractive index as determined from effective medium the- ory including dipolar coupling between the QDs, we obtain simu- lated values for the absorption coefficient that are in quantitative agreement with the experimental values and we find that differ- ence with planarized waveguides results from an increased overlap between the QD layer and the guided optical mode in the case of strip waveguides. The modeling of the absorption coefficients of more complex strip waveguides functionalized by colloidal QDs as demonstrated in this study will enable the development and simu- lation of QD-based photonic devices integrated in silicon. Index Terms—Engineering, optical strip waveguides, nanotech- nology, absorbing media, quantum dots, integrated optoelectron- ics, silicon on insulator (SOI) technology. I. INTRODUCTION C OLLOIDAL lead salt semiconductor nanocrystals or QDs (PbX and PbX/CdX, X=S,Se) are an appealing class of materials, due to the combination of size-tunable optical Manuscript received October 4, 2013; revised December 16, 2013 and Jan- uary 20, 2014; accepted January 22, 2014. The work of A. Omari was sup- ported by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). The work of W. Xie was sup- ported by Ghent University for a BOF scholarship. The work of P. Geire- gat was supported by Ghent University for a BOF scholarship. The work of Z. Hens was supported by the Fund for Scientific Research Flanders (FWO-Vlaanderen) for a research grant (project nr. G.0760.12). The work of Z. Hens and D. V. Thourhout was supported by the Belgian Science Policy Office (IAP 7.35, photonics@be). A. Omari is with the Department of Inorganic and Physical Chemistry and the Department of Information Technology, Photonics Research Group, Ghent University, Ghent 9000, Belgium (e-mail: [email protected]). W. Xie is with the Photonics Research Group, Ghent University, Ghent, Belgium 9000 (e-mail: [email protected]). P. Geiregat is with the Department of Information Technology, Pho- tonics Research Group, Ghent University, Ghent, Belgium 9000 (e-mail: [email protected]). D. Van Thourhout and Z. Hens are with Ghent University, Ghent, Belgium 9000 (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2014.2304180 properties in the NIR range and a suitability for low cost solution-based processing [1], [2]. This implies that their proper- ties can be adjusted to the application and that they can be easily combined with a variety of materials or technology platforms, such as silicon-on-insulator (SOI) and silicon nitride based in- tegrated photonic circuits [3]–[6]. Here, colloidal quantum dots are typically used as close-packed mono- or multilayers for on- chip generation, detection or processing of light [5] and over the years many applications including, e.g., LEDs [7], displays, lasers, and photodetectors [8], [9] have been demonstrated. Regarding the emerging field of colloidal quantum dot tech- nology and with the advent of hybrid colloidal QD/silicon photonics applications, understanding the QD absorption on silicon waveguides will enable engineering these QD devices in a smarter, cost-effective, and more efficient way. In a previous work, we studied the waveguide absorbance of QDs deposited on oxide planarized waveguides (PWGs) [10], which allowed to deduce the host permittivity needed to describe the effective permittivity of the coated layers. In this way, the obtained ef- fective permittivity could be linked with the QD induced WG losses using a complex mode-solver (Fimmwave 6.4). Impor- tantly, the oxide planarization of strip waveguides is a trench isolation process [11] which consist of six post-processing steps, and consequently increases the cost of the PWG fabrication. As strip waveguides (WGs) are the backbone of silicon photonics, a profound knowledge of the properties of these directly coated WGs is essential for device development and a cost-effective fabrication. In this paper, we analyze the absorption coefficient of SOI strip waveguides coated with a monolayer of PbS/CdS core/shell QDs, where we make use of previous reports on the absorption coefficient of dispersed PbS/CdS QDs [12] and of QDs in close-packed monolayers. [13] At wavelengths around the quantum dot bandgap transition, experimental absorption coefficients of 20 cm 1 are found. These values are 5 to 6 times larger then the absorption coefficients for planarized waveguides coated by a QD monolayer [10]. By simulating the QD layer as an effective medium where the dielectric constant is determined by dipolar coupling between neighboring QDs [10], [13] we obtain simulated values for the waveguide loss that are in quantitative agreement with the experimental results. According to the same simulations, the strongly enhanced absorption coefficient in the case of strip waveguides can be attributed to the increased overlap between the guided mode and the QD monolayer, especially at the sides of the strip 1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

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Page 1: Modeling the Optical Properties of Low-Cost Colloidal Quantum Dot Functionalized Strip SOI Waveguides

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 4, JULY/AUGUST 2014 4400306

Modeling the Optical Properties of Low-CostColloidal Quantum Dot Functionalized

Strip SOI WaveguidesAbdoulghafar Omari, Member, IEEE, Weiqiang Xie, Pieter Geiregat, Member, IEEE,

Dries Van Thourhout, Member, IEEE, and Zeger Hens

Abstract—We studied the optical absorption of silicon-on-insulator strip waveguides functionalized by a monolayer of col-loidal PbS/CdS core/shell quantum dots. The integration is doneby Langmuir–Blodgett deposition, which results in a monolayerof quantum dots (QDs) on the waveguides. Experimental absorp-tion coefficients of QD functionalized strip waveguides range from10–30 cm−1 . These values are about five times larger than the ab-sorption coefficient of QD functionalized planarized waveguides.Using a refractive index as determined from effective medium the-ory including dipolar coupling between the QDs, we obtain simu-lated values for the absorption coefficient that are in quantitativeagreement with the experimental values and we find that differ-ence with planarized waveguides results from an increased overlapbetween the QD layer and the guided optical mode in the case ofstrip waveguides. The modeling of the absorption coefficients ofmore complex strip waveguides functionalized by colloidal QDs asdemonstrated in this study will enable the development and simu-lation of QD-based photonic devices integrated in silicon.

Index Terms—Engineering, optical strip waveguides, nanotech-nology, absorbing media, quantum dots, integrated optoelectron-ics, silicon on insulator (SOI) technology.

I. INTRODUCTION

COLLOIDAL lead salt semiconductor nanocrystals or QDs(PbX and PbX/CdX, X=S,Se) are an appealing class

of materials, due to the combination of size-tunable optical

Manuscript received October 4, 2013; revised December 16, 2013 and Jan-uary 20, 2014; accepted January 22, 2014. The work of A. Omari was sup-ported by the Institute for the Promotion of Innovation through Science andTechnology in Flanders (IWT-Vlaanderen). The work of W. Xie was sup-ported by Ghent University for a BOF scholarship. The work of P. Geire-gat was supported by Ghent University for a BOF scholarship. The workof Z. Hens was supported by the Fund for Scientific Research Flanders(FWO-Vlaanderen) for a research grant (project nr. G.0760.12). The work ofZ. Hens and D. V. Thourhout was supported by the Belgian Science PolicyOffice (IAP 7.35, photonics@be).

A. Omari is with the Department of Inorganic and Physical Chemistry andthe Department of Information Technology, Photonics Research Group, GhentUniversity, Ghent 9000, Belgium (e-mail: [email protected]).

W. Xie is with the Photonics Research Group, Ghent University, Ghent,Belgium 9000 (e-mail: [email protected]).

P. Geiregat is with the Department of Information Technology, Pho-tonics Research Group, Ghent University, Ghent, Belgium 9000 (e-mail:[email protected]).

D. Van Thourhout and Z. Hens are with Ghent University, Ghent, Belgium9000 (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTQE.2014.2304180

properties in the NIR range and a suitability for low costsolution-based processing [1], [2]. This implies that their proper-ties can be adjusted to the application and that they can be easilycombined with a variety of materials or technology platforms,such as silicon-on-insulator (SOI) and silicon nitride based in-tegrated photonic circuits [3]–[6]. Here, colloidal quantum dotsare typically used as close-packed mono- or multilayers for on-chip generation, detection or processing of light [5] and overthe years many applications including, e.g., LEDs [7], displays,lasers, and photodetectors [8], [9] have been demonstrated.

Regarding the emerging field of colloidal quantum dot tech-nology and with the advent of hybrid colloidal QD/siliconphotonics applications, understanding the QD absorption onsilicon waveguides will enable engineering these QD devices ina smarter, cost-effective, and more efficient way. In a previouswork, we studied the waveguide absorbance of QDs depositedon oxide planarized waveguides (PWGs) [10], which allowedto deduce the host permittivity needed to describe the effectivepermittivity of the coated layers. In this way, the obtained ef-fective permittivity could be linked with the QD induced WGlosses using a complex mode-solver (Fimmwave 6.4). Impor-tantly, the oxide planarization of strip waveguides is a trenchisolation process [11] which consist of six post-processing steps,and consequently increases the cost of the PWG fabrication. Asstrip waveguides (WGs) are the backbone of silicon photonics,a profound knowledge of the properties of these directly coatedWGs is essential for device development and a cost-effectivefabrication.

In this paper, we analyze the absorption coefficient ofSOI strip waveguides coated with a monolayer of PbS/CdScore/shell QDs, where we make use of previous reports on theabsorption coefficient of dispersed PbS/CdS QDs [12] and ofQDs in close-packed monolayers. [13] At wavelengths aroundthe quantum dot bandgap transition, experimental absorptioncoefficients of ≈ 20 cm−1 are found. These values are 5 to6 times larger then the absorption coefficients for planarizedwaveguides coated by a QD monolayer [10]. By simulating theQD layer as an effective medium where the dielectric constantis determined by dipolar coupling between neighboringQDs [10], [13] we obtain simulated values for the waveguideloss that are in quantitative agreement with the experimentalresults. According to the same simulations, the stronglyenhanced absorption coefficient in the case of strip waveguidescan be attributed to the increased overlap between the guidedmode and the QD monolayer, especially at the sides of the strip

1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

Page 2: Modeling the Optical Properties of Low-Cost Colloidal Quantum Dot Functionalized Strip SOI Waveguides

4400306 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 4, JULY/AUGUST 2014

TABLE ITHE PROPERTIES OF PBS/CDS CORE/SHELL SAMPLES AS DETERMINED FROM

THE OPTICAL ABSORBANCE SPECTRUM OF THE QDS DISPERSED IN TCE

The emission peak of sample A could not be determined due to the low sensitivity of the InGaAs detector around 1600 nm.

waveguide. The extension of experimental absorption coeffi-cient measurements and device modeling to the technologicallyrelevant strip waveguides as demonstrated here is an importantstep in the direction of the simulation-supported developmentof integrated photonic devices based on colloidal QDs.

II. EXPERIMENTAL DETAILS

In this study, we make use of two different PbS/CdS QD sam-ples, denoted by A and B, with a first exciton peak at 1520 and1450 nm, respectively. The initial PbS core QDs are preparedusing a procedure as described by [14]–[16]. For the CdS shellgrowth, a cationic exchange procedure was used .1 The samplesare chosen such that the peak wavelength (sample A) or thelong wavelength side (sample B) of their first exciton transi-tion falls within the bandpass window of the grating couplers,thus enabling a clear observation of the QD losses through thewaveguide absorbance. The waveguide absorbance is monitoredusing a laser which is wavelength tunable around 1520 nm. Thelaser light is injected into a polarization controller to maxi-mize the coupled light in the TE-mode grating couplers of thewaveguide. Core size, shell thickness and the basic optical char-acteristics of the PbS/CdS QDs used are summarized in Table I.The QDs are deposited locally on the WGs using optical lithog-raphy combined with Langmuir-Blodgett deposition [10], [17],yielding strips of hexagonally close-packed monolayers of QDson the waveguide [see Fig. 1(a) and (b)]. The strip lengths arevaried from 100, to 200, 500, 1000, 1500 and 1750 μm. Inthis way, the QD absorption coefficient αQD can be determined,which is the QD induced loss due to absorption in the WG,excluding any coupling losses. As part of the QDs can re-emitthe absorbed photon back into the WGs, the induced absorptionloss may be partly lifted leading to a decrease of αQD and a netQD absorption coefficient α∗

QD will be measured. If we define αas the total loss of the QD coated waveguide and α0 as the lossof a bare waveguide then α∗

QD is given by α − α0 . Denoting byL and Pt the length of the QD covered part of a strip waveguideand the power transmitted through that waveguide and by Lrefand Pt,ref the same, yet for a reference waveguide, α∗

QD can bedetermined from the waveguide absorbance A according to

A = − lnPt

Pt,ref= (α − α0) (L − Lref ) (1)

Fig. 1(b) illustrates A as a function of strip length differ-ence ΔL = L − Lref for a WG coated with a PbS/CdS QD

1See appendix for a discussion of synthesis, coupling efficiency, and thedipole sum.

Fig. 1. (a) Optical microscopy image of a sample with strip waveguides coatedby a QD monolayer with various strip lengths and a representation of the opticalfield coupled from the fiber through the grating in the QD coated WG. (b) SEMpicture illustrating a close-packed QD-monolayer coating the strip waveguide.(Inset) Zoom of the SEM image showing clearly discernable quantum dots onthe sidewall of the strip waveguide. (c) Absorbance A of sample A—as deter-mined according to (1) at 1520 nm as a function of the strip length difference.(d) Representation of (full red line) absorption spectrum of sample B as recordedin tetrachloroethylene (TCE) and (markers) the measured αQD spectrum forstrip waveguides coated by a monolayer of sample B QDs. The absorptionspectrum in TCE has been rescaled to stress the correspondence between bothquantities.

monolayer, using the 100 μm strip as a reference. The full linerepresents the best fit of the data, yielding α∗

QD as the slope of

ln Pt

Pt , r e fversus L − Lref . As we will show below, the QD emis-

sion contribution can be discarded, such that α∗QD equals αQD .

In what follows, we will therefore denote the measured net QDabsorption coefficient by αQD .

III. RESULTS AND DISCUSSION

Fig. 1(c) shows that αQD is determined as 20.2 cm−1

(9 dB/mm) for sample A at 1520 nm. As the typical lossesof uncoated waveguides are 0.45 cm−1(0.2 dB/mm) [10], thispronounced increase in loss indicates the presence of QDs on thestrip waveguide. Similar αQD values are observed for sample B[see Fig. 1(d)], where the wavelength dependence resembles thespectrum of the QDs dispersed in tetracholoroethylene (TCE).This clearly shows the interaction of the quantum dots withthe optical field in the WGs. To compare the experimental QDabsorption with model predictions, we use an approach wherethe real QD layer covering the WG is replaced by an effectivemedium with a dielectric function εeff . Using the waveguidegeometry as shown in Fig. 2(a) this enables us to extract a the-oretical absorption coefficient αth from the simulated effectiverefractive index neff = neff + iκeff of the propagating quasi-TEmode:

αth =4πκeff

λ. (2)

This approach however requires that the permittivity of eachmaterial or medium involved is known. For silicon and silica,we use typical values for the refractive index at 1520 nm of 3.45

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OMARI et al.: MODELING THE OPTICAL PROPERTIES OF LOW-COST COLLOIDAL QUANTUM DOT FUNCTIONALIZED STRIP SOI WAVEGUIDES 4400306

Fig. 2. (a) Schematic view illustrating a perfect monolayer of PbS/CdS QDsconformally covering the SOI strip waveguide surface. (b) The model structureused to simulate the surface morphology with uncovered parts at the waveguideedges (t1 ) and trenches (t2 ). (c) The calculated TE field component |Ex | ofthe quasi-TE mode, for a perfect monolayer showing the clear interaction ofthe optical mode with the QD top and edge interface layers. The field strengthincreases from light to dark blue. (d) (lines) the simulated αth spectrum fordifferent values of t1 and t2 as indicated (t1 = t2 for all simulations). Theexperimental values (blue markers) coincide with the simulated values for t1 =t2 = 0 nm.

and 1.45, respectively. For εeff , we use the expression based onthe coupled dipole model studied before [10]:

εeff = εhε0

(1 +

Ns

δ

aQD

1 − aQDS

). (3)

Here, δ denotes the assumed thickness of the effective layer (seeTable I), which amounts to the nanocrystal diameter increasedby 3.6 nm to account for the thickness of the oleate ligandshell [14]. Importantly, the dipole sum S is in general differentfor fields parallel (S‖) or perpendicular (S⊥) to the QD film.1

Consequently, S will be different for QDs on top or at the edgeof the quasi-TE mode excited WGs. In contrary to S, which onlydepends on the position of the particles relative to each other,aQD is a function of the host permittivity εh and the dielectricfunction εQD = εQD ,Re + iεQD ,Im of the QDs. εh was shownto be an extrinsic property depending on the layer thickness andthe surrounding environment of the QDs [10], where a valueof εh in the range 1–1.16 was determined for a QD monolayer.εQD ,Re and εQD ,Im are calculated values taking care that theyyield the experimental absorption coefficient spectrum of theQDs in a dilute dispersion while obeying the Kramers–Kronigtransformation [18]. Importantly, in this analysis, we assumethat the absorption coefficient of the PbS/CdS core/shell QDsat wavelengths shorter than 400 nm can be derived from thebulk dielectric function of PbS and CdS, respectively as wasdemonstrated for PbS/CdS QDs [12] and we neglect possiblequantization effects in the CdS shell. For the numerical values ofεeff , we refer to [10] as the samples used there for the planarizedwaveguides are similar to the ones here in strip waveguidesand this will allow for a comparison of αQD for both types ofwaveguides.

Given the WG cross section and the expression for εeff thatresults from the coupled dipole model and the self-consistentlydetermined aQD , the electric field of the guided optical mode

Fig. 3. (a) Coupling efficiency η and η Q Y2 as a function of the wavelength

for a dipole oscillator located 5 nm away from the top waveguide surface.(b) Wavelength dependence of η and η Q Y

2 for a dipole oscillator located 5 nmfrom the edge WG-surface, which is the distance from the QD center positionand the WG-surface. The difference between the curves in Fig. 3 (a) and (b) isalmost negligible.

in the WG can be calculated, resulting in theoretical values forneff and αth . As an example, Fig. 2(c) represents the electricfield along the TE direction at a wavelength of 1520 nm for aWG covered by a QD monolayer as obtained using Fimmwave6.4 complex mode solver. The figure clearly shows the overlapbetween the QD film and the evanescent field, which makes thatlight absorption by the QDs affects εeff and leads to a non-zeroαth .

A meaningful comparison of the simulated αth and experi-mental α∗

QD is possible only if the re-emission of light absorbedby the QDs in the WGs can be neglected. This depends on theproduct QY η

2 of the photoluminescence quantum yield QY andthe coupling efficiency η of the QD emitted light in the WG. Toaccount for the waveguide geometry, the fraction of the emit-ted light in the waveguide (QY η

2 ) is calculated for two dipoleoscillator locations (see Fig. 3). At best, it amounts to 4.6% ofthe absorbed light (see Fig. 3) (for a detailed discussion, seeAppendices A–C for a discussion of synthesis, coupling effi-ciency, and the dipole sum). This number falls within the ≈10%error on the αQD measurements, and the contribution of the QDemission is therefore discarded.

In Fig. 1(b), the SEM picture clearly shows a close-packedQD monolayer covering the strip waveguide. Note that someparts of the waveguide may remain uncovered by QDs. Theseparts are typically located at the corner between the waveguideedge and the trench and might affect the measured waveguideabsorbance. To account for these possible deposition anomaliesin the calculated αth , we start from the schematic geometries asshown in Fig. 2(a) and (b), where the waveguides are, respec-tively, coated by a QD monolayer covering the whole waveguidesurface and a waveguide showing a gap at the WG corners. Here,t1 and t2 denote the width of this gap at the waveguide-edgesand trenches, respectively. Using a value of εh = 1.16, the sim-ulated αth is calculated for sample B [see Fig. 2(d)]. Here, wehave set t1 equal to t2 and have varied these parameters from0 nm (a perfect layer) to 220 nm (completely sparse WG edgesand trenches). In this case, a good match between the experi-mental αQD and the simulated αth is obtained when both t1 andt2 equal zero. This indicates that for sample B, the depositionanomalies are minor and the strip waveguide is well covered.

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4400306 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 4, JULY/AUGUST 2014

Fig. 4. Simulated αth for sample A for different combinations of t1 and t2 .The crossing of the experimental αQD (the green dashed line) with differentαth curves yields allowed values for t1 and t2 .

Note that for sample B, αQD is 21 cm−1 around 1520 nm.This value is about 6 times larger than the 3.6 cm−1 (1.6 dB/mm)measured for a monolayer of QDs deposited on a planarizedwaveguide [10]. A first look at the simulated field [Fig. 2(c)]already indicates that this is most likely due to the strong field atthe edges of the waveguide. From these simulations, we can cal-culate the confinement factor CF , which yields the fraction ofthe power in the guided mode that passes through the QD-layer.In the case of a strip waveguide, a CF of 3.6% is calculated.This number is composed of contributions for the QDs cover-ing the WG-edge, top and trench, amounting to 2.1%, 0.96%,and 0.55%, respectively. Hence, almost 60% of the total powerpassing through the QD monolayer on the WG is attributed tothe QDs at the edge. A similar calculation for QDs depositedon a planarized waveguide yields a total CF of about 0.8%, anumber similar to what is obtained for the top surface of the stripwaveguide. Since the increase in confinement factor agrees withthe increase in absorption coefficient, the strongly enhanced ab-sorption in strip waveguides as compared to planarized waveg-uides mainly reflects an enhanced CF , especially due to thewaveguide edges being covered by QDs.

For sample A, a value of αQD = 20.2 cm−1 is experimentallydetermined at 1520 nm. Here, if we set t1 = t2 = 0 a valueof 26 cm−1 is calculated, overestimating the 20.2 cm−1 value.Fig. 4 shows the simulations for different values of t1 and t2 .Although, we have two degrees of freedom t1 and t2 , we candetermine possible ranges for t1 and t2 , given the conditionthat αth needs to match αQD as indicated by the dashed greenline in Fig. 4. First of all, we notice an exponential decrease inαth with increasing t2 , which is due to the removal of QDs inthe x direction along which the TE-mode decays exponentially.The typical 1/2e decay constant along the x-direction for allthe αth curves at the different t1 values is ≈100 nm. Second,from the figure we can determine a lower and upper boundfor t1 , which we will denote as t1,min and t1,max . For t1,min ,which corresponds to t2 = ∞, a value of 20 nm is found. Thissituation would represents a totally uncovered waveguide trenchand a gap of 20 nm at the WG-edge. t1,max is determined as90 nm and corresponds to t2 = 0 nm. This case correspondsto a completely filled trench, while a large gap is present at thewaveguide edge. As these values show the extreme cases and

given that in practice 0 nm < t2 < 200 nm one can expect a t1value in between 20 and 90 nm.

In the previous paragraph the ranges of t1 and t2 were ob-tained without taking into account the ≈10% error on αQD .Moreover, εh was determined in the range 1-1.16 and we used avalue of 1.16 in the simulations and we have neglected possiblescattering losses as these layers will become inhomogeneousaround the gaps. All these effects are expected to have verysmall consequences on the obtained results for t1 and t2 . Insummary, using an εh value determined from a previous re-sult [10], where εh is obtained from a simple planar geometry,we are able to model the QD absorption coefficient in morecomplex strip waveguides. Part of these coated WGs may notbe covered. To account for these possible deposition anomalies,we take into account the morphology of the QD-layer in thesimulated absorption coefficients, as discussed in the previousparagraphes.

IV. CONCLUSION

We have studied light absorption of colloidal PbS/CdS QDsin SOI strip waveguides. Using Langmuir-Blodgett deposition,close-packed monolayers are formed on the strip waveguides.By analyzing the waveguide absorbance, we show a clear in-teraction of the QDs with the quasi-TE optical mode. The ex-perimental absorption coefficients due to the presence of theQDs can be simulated using an approach where the QD layeris replaced by an effective medium with an effective dielectricfunction determined by dipolar coupling between neighboringQDs. The strong presence of the electric field at the strip wave-guide edges yields experimental losses that are more than fivetimes larger as compared to QDs deposited on planarized waveg-uides. In addition, the morphology of the deposited layers mayneed to be taken into account to explain the experimental QDabsorption coefficients. Therefore, these results form the basisfor a complete simulation of absorption (and possibly emis-sion) of light by colloidal QDs deposited on strip waveguides.Since colloidal QDs are easily deposited using wet chemicalprocedures, these results pave the way for the development ofcost-effective silicon photonic devices.

APPENDIX A

SYNTHESIS OF PBS/CDS QUANTUM DOTS

The PbS core QDs are prepared using a procedure as de-scribed by [16]. For the CdS shell growth, a cationic exchangeprocedure was used, starting from a 5.7 μM QD dispersion intoluene. The dispersion is heated to 125 ◦C in a reaction flaskplaced in an nitrogen atmosphere. Cadmium oleate is added ina 20:1 Cd to Pb ratio. This starts a cationic exchange processin which the outer Pb2+ cations are replaced by Cd2+ cations,leading to a heterostructure with a PbS core and a CdS shell.The reaction is stopped by quenching with a double amount ofethanol as compared to the reaction volume. After centrifugationand decantation, the PbS/CdS QDs are suspended in toluene.The typical size dispersion of these QDs is 8%. The QD basicoptical properties are summarized in Table I and the absorption

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OMARI et al.: MODELING THE OPTICAL PROPERTIES OF LOW-COST COLLOIDAL QUANTUM DOT FUNCTIONALIZED STRIP SOI WAVEGUIDES 4400306

Fig. 5. (a) Absorption spectra of sample A and sample B recorded in a diluteTCE solution. (b) Emission spectrum for sample B.

spectra for sample A and sample B are given in Fig. 5(a)–(b) to-gether with the photoluminescence spectrum of sample B. Theemission spectrum of sample A could not be determined due tothe low sensitivity of the InGaAs detector around 1600 nm.

APPENDIX B

DERIVATION OF NETTO ABSORPTION COEFFICIENT α∗QD

Each QD will re-emit the absorbed photon with a probabilityof QY × η

2 , with QY the photoluminescence quantum yield andη denoting the photon coupling coefficient from the QD layerto the propagating mode in the waveguide. If we define N(z)as the amount of photons per unit area per unit time at a certainposition z along the propagation direction of the waveguide,then the amount of lost photons dNabs due to QDs within asmall section z, z + dz is

dNabs = −αQDNdz (4)

From the absorbed photons wihtin the section dz, there will bea fraction QY η

2 re-emitted in the positve z-direction, which willlead to an re-increase of the photon population. Therefore theamount of emitted photons dNem within the section dz will be

dNem = −dNabsQY η

2. (5)

To simplify, we regarded the QDs as all absorbing and emittingaround the same wavelength and neglecting any reduce of theemitted power due to broadening of the QD emission spectrum.In this way, the dNem can be seen as an upperlimit of the emittedphotons around the wavelength of study. The total change of thephotonflux dN reads

dN = dNabs + dNem = −αQD

(1 − QY η

2

)N. (6)

Integration of the above equation and multiplying the photon-flux with the photon-energy yields for the power at the end ofthe waveguide:

P (L) = P0e−αQ D (1− Q Y η

2 )L . (7)

Therefore, the QD-absorption coefficient αQD will be loweredby a factor 1 − QY η

2 yielding a netto loss coefficient

α∗QD = αQD

(1 − QY

η

2

). (8)

The factor 2 in the denominator, denotes that only half of thespontaneously emitted photons will be collected at one of of the

waveguide ends. Clearly, if QY = 1 and η = 1, then for eachtwo absorbing QDs, one photon will be emitted with a directionto the waveguide-end, and thus the netto loss coefficient will behalf the QD absorption coefficient. Otherwise, if QY × η � 1,the contribution of the emission to the waveguide loss can beneglected.

APPENDIX C

DIPOLE SUM S

The dipole sum S relates the local field driving the particlesto the applied electric field [10] and contains all contributionsfrom the neighboring particles (j) on the local field driving acentral particle i. For an applied field parallel to the QD film(S‖), the dipole sum is given by

S‖ =14π

∑j =i

(1 − ikdij )(3 cos2(θij − 1))eikdi j

d3ij

+k2 sin2(θij )eikdi j

dij(9)

and for a field perpendicular to the QD film (S⊥), the dipolesum reads

S⊥ =14π

∑j =i

(1 − ikdij )ei(kdi j +π )d3

ij

+k2eikdi j

dij(10)

ACKNOWLEDGMENT

L. Van Landschoot is acknowledged for the SEMimaging.

REFERENCES

[1] F. W. Wise, “Lead salt quantum dots: The limit of strong quantum con-finement,” Accounts Chem. Res., vol. 33, no. 11, pp. 773–780, 2000.

[2] Y. Justo, I. Moreels, K. Lambert, and Z. Hens, “Langmuir-blodgett mono-layers of colloidal lead chalcogenide quantum dots: Morphology and pho-toluminescence,” Nanotechnology, vol. 21, no. 29, 2010.

[3] B. De Geyter, K. Komorowska, E. Brainis, P. Emplit, P. Geiregat, A.Hassinen, Z. Hens, and D. Van Thourhout, “From fabrication to modemapping in silicon nitride microdisks with embedded colloidal quantumdots,” Appl. Phys. Lett., vol. 101, no. 16, 2012.

[4] 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 ofpbse nanocrystals to si-based photonic crystal microcavities,” Nano Lett.,vol. 9, no. 8, pp. 2849–2854, 2009.

[5] 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-opticalswitching in a silicon-nanocrystal-based silicon slot waveguide at telecomwavelengths,” Nano Lett., vol. 10, no. 4, pp. 1506–1511, 2010.

[6] D. V. Talapin, J.-S. Lee, M. V. Kovalenko, and E. V. Shevchenko,“Prospects of colloidal nanocrystals for electronic and optoelectronic ap-plications,” Chem. Rev., vol. 110, no. 1, pp. 389–458, 2010.

[7] J. Heo, Z. Jiang, J. Xu, and P. Bhattacharya, “Coherent and directionalemission at 1.55 mu m from PbSe colloidal quantum dot electrolumines-cent device on silicon,” Opt. Exp., vol. 19, no. 27, pp. 26 394–26 398,2011.

[8] S. Hoogland, V. Sukhovatkin, I. Howard, S. Cauchi, L. Levina, andE. H. Sargent, “A solution-processed 1.53 μm quantum dot laser withtemperature-invariant emission wavelength,” Opt. Exp., vol. 14, no. 8,2006.

[9] J. P. Clifford, G. Konstantatos, K. W. Johnston, S. Hoogland, L. Levina,and E. H. Sargent, “Fast, sensitive and spectrally tuneable colloidal

Page 6: Modeling the Optical Properties of Low-Cost Colloidal Quantum Dot Functionalized Strip SOI Waveguides

4400306 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 4, JULY/AUGUST 2014

quantum-dot photodetectors,” Nat. Nanotechnol., vol. 4, no. 1, pp. 40–44, 2009.

[10] A. Omari, P. Geiregat, D. Van Thourhout, and Z. Hens, “Light absorptionin hybrid silicon-on-insulator/quantum dot waveguides,” Opt. Expr., vol.21, no. 20, pp. 23 272–23 285, 2013.

[11] C. Baum and S. Gaddam, “An improved process, metrology and method-ology for shallow trench isolation etch,” in Proc. Adv. Semicond. Manuf.,2004.

[12] Y. Justo, K. Geiregat, Pieter Van Hoecke, D. C. Vanhaecke, Frank, and Z.Hens, “Optical properties of PbS/CdS quantum dots,” J. Phys. Chem. C,vol. 117, no. 39, pp. 20 171–20 177, 2013.

[13] P. Geiregat, Y. Justo, S. Abe, S. Flamee, and Z. Hens, “Giant andbroad-band absorption enhancement in colloidal quantum dot monolayersthrough dipolar coupling,” ACS Nano, vol. 7, no. 2, pp. 987–993, 2013.

[14] I. Moreels, K. Lambert, D. Smeets, D. De Muynck, T. Nollet, J. C. Martins,F. Vanhaecke, A. Vantomme, C. Delerue, G. Allan, and Z. Hens, “Size-dependent optical properties of colloidal PbS quantum dots,” Acs Nano,vol. 3, pp. 3023–3030, 2009.

[15] L. Cademartiri, J. Bertolotti, R. Sapienza, D. S. Wiersma, G. vonFreymann, and G. A. Ozin, “Multigram scale, solventless, and diffusion-controlled route to highly monodisperse PbS nanocrystals,” J. Phys. Chem.B, vol. 110, no. 2, pp. 671–673, 2006.

[16] 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 se-lenide to produce heterostructured nanocrystals with bright, stable infraredemission,” J. Amer. Chem. Soc., vol. 130, no. 14, pp. 4879–4885, 2008.

[17] K. Lambert, I. Moreels, D. Van Thourhout, and Z. Hens, “Quantum dotmicropatterning on si,” Langmuir, vol. 24, no. 11, pp. 5961–5966, 2008.

[18] I. Moreels, G. Allan, B. De Geyter, L. Wirtz, C. Delerue, and Z. Hens,“Dielectric function of colloidal lead chalcogenide quantum dots obtainedby a kramers-kronig analysis of the absorbance spectrum,” Phys. Rev. B,vol. 81, no. 23, 2010.

Abdoulghafar Omari (M’09) received the M.Eng. degree in applied physicsat Ghent University in 2009. He is currently a Ph.D. student at the Departmentof Inorganic and Physical Chemistry and the Department of Information Tech-nology, Photonics Research Group, Ghent University. His research interestsinclude the synthesis, processing, characterization of colloidal quantum dotsand on-chip integration and simulation of quantum dots for photonic applica-tions.

Weiqiang Xie received the B.S. degree in applied physics from Xi’an JiaotongUniversity, China, in 2008, and the M.S. degree in condensed matter physicsfrom Shanghai Jiaotong University, China in 2011. He is currently workingtoward the Ph.D. degree in Photonics Research Group, Ghent University andIMEC. His research interests include the integration of colloidal quantum dotswith silicon and silicon nitride photonics for on-chip visible and infrared lightsources.

Pieter Geiregat (M’10) received the Bachelor’s and Master’s degree in en-gineering physics at Ghent University in 2008 and 2010, respectively. He iscurrently working toward the Ph.D. degree in the Photonics Research Group(University of Ghent) and the Physics and Chemistry of Nanostructures Group,University of Ghent under a BOF personal grant specializing in (ultrafast) op-tical spectroscopy of nanostructures for use in integrated photonics.

Dries Van Thourhout (M’98) received the Masters degree in applied physicsand the Ph.D. degree in electrical engineering from Ghent University, Ghent,Belgium, in 1995 and 2000, respectively. From October 2000 to September2002, he was with Lucent Technologies, Bell Laboratories, New Providence,NJ, USA, where he was engaged in the design, processing, and characteriza-tion of InP/InGaAsP monolithically integrated devices. In October 2002, hejoined the Department of Information Technology (INTEC), Ghent Univer-sity, where he is currently a member of the permanent staff of the PhotonicsGroup and is also a Lecturer or a Colecturer for four courses within the GhentUniversity Master in Photonics Program (Microphotonics, Advanced Photon-ics Laboratory, Photonic Semiconductor Components and Technology). He isalso engaged in coordinating the cleanroom activities of the research group.His research interests include the design, fabrication, and characterization ofintegrated photonic devices, including silicon nanophotonic devices, heteroge-neous integration of InP-on-silicon, and integrated InP-based optical isolators.He is also engaged in research on the development of new fabrication processesfor photonic devices, e.g., based on focused ion beam etching and die-to-waferbonding. He has authored or coauthored more than 160 journal papers, andhas presented invited papers at several major conferences. Dr. Thourhout is amember of the IEEE Photonics Society [formerly known as IEEE Laser andElectro-Optics Society (LEOS)] and an Associate Editor for the IEEE PHOTON-ICS TECHNOLOGY LETTERS.

Zeger Hens received the Ph.D. degree from Ghent University in 2000, whichwas followed by a Postdoctoral Reserch at the University of Utrecht. In 2002,he returned to Ghent University as a Professor and started a research group oncolloidal nanocrystals. His work covers the synthesis, processing, and charac-terization of colloidal quantum dots and their application in photonic devices.