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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 2, Iss. 5 — May. 1, 2012
  • pp: 496–500
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The dielectric function of PbS quantum dots in a glass matrix

Iwan Moreels, Detlef Kruschke, Peter Glas, and Jens W. Tomm  »View Author Affiliations


Optical Materials Express, Vol. 2, Issue 5, pp. 496-500 (2012)
http://dx.doi.org/10.1364/OME.2.000496


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Abstract

The dielectric function of PbS quantum dots (Qdots) with diameters of 3.5-5.0 nm in glass matrix is determined from transmission measurements by Maxwell-Garnett effective medium theory combined with iterative Kramers-Kronig analysis. The algorithm used provides real and imaginary part of the dielectric function in the 200-1800 nm spectral range, for both Qdot-doped glasses as well as the PbS Qdots alone. The latter data are compared with the results obtained from colloidal PbS quantum dots and, within the limits of the experimental error, agreement is found.

© 2012 OSA

1. Introduction

In recent years lead-salt quantum dots (Qdots), more specifically PbS Qdots, have attracted increasing interest in both basic [1

1. A. Olkhovets, R. C. Hsu, A. Lipovskii, and F. W. Wise, “Size-dependent temperature variation of the energy gap in lead-salt quantum dots,” Phys. Rev. Lett. 81(16), 3539–3542 (1998). [CrossRef]

] and applied research. Their direct band structure promotes optoelectronic applications such as light emitters [2

2. G. Konstantatos, C. J. Huang, L. Levina, Z. H. Lu, and E. H. Sargent, “Efficient infrared electroluminescent devices using solution-processed colloidal quantum dots,” Adv. Funct. Mater. 15(11), 1865–1869 (2005). [CrossRef]

], gain media [3

3. K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 mu m in PbS-doped glasses,” Appl. Phys. Lett. 75(20), 3060–3062 (1999). [CrossRef]

], detectors [4

4. S. A. McDonald, G. Konstantatos, S. G. Zhang, P. W. Cyr, E. J. D. Klem, L. Levina, and E. H. Sargent, “Solution-processed PbS quantum dot infrared photodetectors and photovoltaics,” Nat. Mater. 4(2), 138–142 (2005). [CrossRef] [PubMed]

], solar cells [5

5. S. Günes, K. P. Fritz, H. Neugebauer, N. S. Sariciftci, S. Kumar, and G. D. Scholes, “Hybrid solar cells using PbS nanoparticles,” Sol. Energy Mater. Sol. Cells 91(5), 420–423 (2007). [CrossRef]

], saturable absorbers [6

6. P. T. Guerreiro, S. Ten, N. F. Borrelli, J. Butty, G. E. Jabbour, and N. Peyghambarian, “PbS quantum-dot doped grasses as saturable absorbers for mode locking of a Cr:forsterite laser,” Appl. Phys. Lett. 71(12), 1595–1597 (1997). [CrossRef]

], biomarkers [7

7. L. Levina, W. Sukhovatkin, S. Musikhin, S. Cauchi, R. Nisman, D. P. Bazett-Jones, and E. H. Sargent, “Efficient infrared-emitting PbS quantum dots grown on DNA and stable in aqueous solution and blood plasma,” Adv. Mater. (Deerfield Beach Fla.) 17(15), 1854–1857 (2005). [CrossRef]

], and nanoscopic temperature sensors [8

8. M. Kim and M. Yoda, “Infrared quantum dots for liquid-phase thermometry in silicon,” Meas. Sci. Technol. 22(8), 085401 (2011). [CrossRef]

]. Their narrow (bulk) band gap energy Eg = 0.41 eV offers utmost flexibility for tuning the fundamental resonance of the Qdots by varying their size. In contrast to colloidal Qdots, Qdots in a glass matrix offer an additional practical advantage: The glass almost perfectly protects the semiconductor material against the ambient environment, therefore this type of Qdots can be treated, handled, and machined like pure glass rather than a semiconductor wafer for instance. Moreover, the glass matrix can serve as preform for pulling fibers. This option further widens the range of applications to fiber amplifiers or fiber-based near infrared light sources with customizable spectrum. However, the design of the corresponding devices requires precise knowledge of the spectrum of the dielectric constant (dielectric function) of the Qdots as well as the effective optical constants of the Qdot-doped glasses.

In this communication we provide such knowledge via spectroscopic analysis of the optical properties of the glass, either undoped or containing PbS Qdots with a diameter d = 3.5-5.0 nm, confined within the glass matrix. The analysis is based on transmittance measurements leading to spectra of the absorbance A and absorption coefficient α = A/L (L: sample thickness). A newly developed algorithm, which previously has been applied to colloidal Qdots [9

9. 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(23), 235319 (2010). [CrossRef]

], is now used for the Qdot-doped glasses. Based on the Kramers-Kronig (KK) relations, this approach allows for the determination of the real and imaginary part of the dielectric function of the Qdots as well as the Qdot-doped glasses in the 200-1800 nm spectral range. Finally, we provide a brief comparison of our results with the properties of colloidal PbS Qdots. Within the accuracy of our approach, no difference has been detected.

2. Experimental

The samples were grown according to the method of Borrelli and Smith [10

10. N. F. Borrelli and D. W. Smith, “Quantum confinement of PbS microcrystals in glass,” J. Non-Cryst. Solids 180(1), 25–31 (1994). [CrossRef]

]. Glass samples without Qdots and with four different Qdot sizes were synthesized (samples A-D), with following compositions: SiO2: 60.2; Al2O3: 4.2; Na2O: 11.7; NaF: 4.4; ZnO: 12.4; ZnS: 3.1; PbO: 3.0; PbS: 1.0 (A-C) and SiO2: 60.3; Al2O3: 4.3; Na2O: 11.7; NaF: 4.4; ZnO: 13.3; ZnS: 2.0; PbO: 3.0; PbS: 1.0 (D), all percentages by mass. The mixture of the reagent grade materials was molten for 90 min in an alumina crucible at 1380°C (A-C) and 1360°C (D), respectively. Subsequently, it was casted and re-molten for an additional 30 min in order to further improve homogeneity. Glass plates about 3.5 mm thick were obtained, which we then annealed as follows: sample A at 470°C for 22 h and at 523°C for 45min; B at 475°C for 22 h and at 523°C for 70 min; C at 475°C for 22 h and at 523°C for 85 min; D at 470°C for 22h and at 530°C for 105 min. Reference samples have been molten without any sulfur, hence no PbS Qdots were obtained. From each sample, we prepared and carefully polished several coplanar plates ranging from L = 100 µm to 3 mm. The transmittance T was measured in the 200-1800 nm range using a Perkin Elmer Lambda 900 spectrophotometer.

3. Results and discussion

The UV absorption onset of the glass was observed near 350 nm. At longer wavelengths, T, obtained for L = 100 µm, allows to determine the refractive index of the host glass ng by assuming that A is zero and all losses are due to reflections at the air-glass interfaces:
T=16ng2/(1+ng)4
(1)
Measurements on a thicker glass plate (L = 2.9 mm) confirm that A can be neglected in the former case, as we obtain a maximal α of about 0.17 cm−1, with the near-infrared (NIR) absorption caused by d-d transitions in Fe2+ ions [11

11. K. E. Fox, T. Furukawa, and W. B. White, “Transition-metal ions in silicate melts. Part 2. Iron in sodium-silicate glasses,” Phys. Chem. Glasses 23, 169–178 (1982).

]; see Fig. 1(a)
Fig. 1 (a) Absorption coefficient of the host glass without PbS Qdots. (b) Absorbance spectra of PbS-doped glasses obtained from samples A-D.
. A fit to the ng-data using a Sellmeier equation,
ng2=1+b1λ2/(λ2c12)+b2λ2/(λ2c22)
(2)
yields b1 = 1.39, c1 = 193.6 nm, b2 = 9.91 and c2 = 10000 nm (fixed value). For the Qdot-doped glasses, we compiled absorbance spectra using the data from those plates, where the condition A ~1 is best fulfilled [Fig. 1(b), spectra normalized to one at 400 nm]. In the NIR spectral region, the first absorption peak yields the ground-state transition, from which we calculate d using an empirical sizing curve; see Table 1

Table 1. Physical Properties of Qdot-Doped Glass

table-icon
View This Table
[12

12. 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 3(10), 3023–3030 (2009). [CrossRef] [PubMed]

]. In the visible, spectra almost match. This is in line with results obtained for colloidal PbS Qdots and other II-VI, IV-VI and III-V material systems (see the discussion in [12

12. 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 3(10), 3023–3030 (2009). [CrossRef] [PubMed]

]) and it implies that optical transitions in this range are no longer influenced by quantum confinement. At 400 nm a theoretical intrinsic Qdot absorption coefficient αi = 2.19 × 105 cm−1 is calculated from bulk PbS optical constants (ε = 4.53 + i·26.4) and ng = 1.67 according to the Maxwell-Garnett (MG) effective medium theory [12

12. 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 3(10), 3023–3030 (2009). [CrossRef] [PubMed]

,13

13. A. Sihvola, “Two main avenues leading to the Maxwell Garnett mixing rule,” J. Electromagn. Waves Appl. 15(6), 715–725 (2001). [CrossRef]

]. The experimental α of the Qdot-doped glasses then yields the Qdot volume fraction f = α/αi; see Table 1.

The absorbance spectra, together with the refractive index spectrum of the glass, now allow to calculate the Qdot dielectric function εQD = εR + i·εI via KK-analysis of α [9

9. 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(23), 235319 (2010). [CrossRef]

]. Experimental data are used for λ>400 nm, while below this wavelength bulk properties are assumed. Hence α is known over the entire spectral range, a prerequisite for the KK-analysis. However, MG theory implies that α is determined by both real and imaginary part of εQD, therefore a straightforward calculation of the optical constants as for bulk materials, is not possible. We circumvented this issue by applying an iterative scheme to calculate εQD [9

9. 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(23), 235319 (2010). [CrossRef]

]. Starting from an initial guess for the imaginary part of the dielectric function, εI,0 (the bulk PbS εI makes a good approximation), we calculate εR,0 via the KK-relations. Both then yield an initial guess α0 for the absorption coefficient. From a linearization of the ratio α0/α, we calculate a first-order correction to εI,0 and obtain εI,1 = εI,0 + ΔεI . This scheme is repeated until the calculated αk is converged to the experimental α.

From the intrinsic Qdot optical constants we now come to the effective optical constants neff and keff of the Qdot-doped glasses, i.e. to the properties of our actual samples. They are obtained from the complex effective dielectric function (MG-theory, low-f limit [13

13. A. Sihvola, “Two main avenues leading to the Maxwell Garnett mixing rule,” J. Electromagn. Waves Appl. 15(6), 715–725 (2001). [CrossRef]

]):
εeff=ng2+ffLF(εQDng2)
(3)
The local field factor fLF, describing the electric field ratio inside and outside the Qdots, is calculated from the optical constants of Qdots and the pure glass [12

12. 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 3(10), 3023–3030 (2009). [CrossRef] [PubMed]

]. Figure 3(a)
Fig. 3 (a) Spectra of the effective extinction coefficient as obtained from samples A-D. Notice that the number of keff data points is reduced for display purposes. (b) Spectra of the refractive index of the undoped reference sample and the effective refractive index of sample A. (c) Difference between neff of Qdot-doped glasses A-D and reference.
shows the keff-spectra of the four samples. Interestingly, the resulting keff, see full circles in Fig. 3(a),agrees well with values directly calculated from the absorption coefficient α = (4π/λ)keff, see full black lines. This provides further justification to our approach. Figure 3(b) displays the neff-spectra of sample A and of the pure glass. Due to the incorporation of Qdots, with a higher dielectric constant than the glass, neff of samples A-D exceeds ng of the undoped reference sample by 0.5-3.5∙10−3; see Fig. 3(c). Notice that the enhancement of neff calculated for sample A-D follows exactly the volume fractions f given in Table 1.

4. Conclusions

In summary we present spectra of the dielectric function of PbS Qdots in glass matrix in the 200-1800 nm range. The transmittance data are processed by a newly developed algorithm, which previously has been applied to colloidal Qdots. Based on the KK-analysis, this approach allows for the determination of the real and imaginary part of the dielectric function of the Qdots. A comparison of Qdots in glass matrix and colloidal Qdots reveals that optical properties are comparable. By calculating both the intrinsic Qdot refractive index and extinction coefficient and data on the effective optical constants of the synthesized Qdot-doped glasses, we provide important input for the modeling of photonic devices employing these novel materials.

References and links

1.

A. Olkhovets, R. C. Hsu, A. Lipovskii, and F. W. Wise, “Size-dependent temperature variation of the energy gap in lead-salt quantum dots,” Phys. Rev. Lett. 81(16), 3539–3542 (1998). [CrossRef]

2.

G. Konstantatos, C. J. Huang, L. Levina, Z. H. Lu, and E. H. Sargent, “Efficient infrared electroluminescent devices using solution-processed colloidal quantum dots,” Adv. Funct. Mater. 15(11), 1865–1869 (2005). [CrossRef]

3.

K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 mu m in PbS-doped glasses,” Appl. Phys. Lett. 75(20), 3060–3062 (1999). [CrossRef]

4.

S. A. McDonald, G. Konstantatos, S. G. Zhang, P. W. Cyr, E. J. D. Klem, L. Levina, and E. H. Sargent, “Solution-processed PbS quantum dot infrared photodetectors and photovoltaics,” Nat. Mater. 4(2), 138–142 (2005). [CrossRef] [PubMed]

5.

S. Günes, K. P. Fritz, H. Neugebauer, N. S. Sariciftci, S. Kumar, and G. D. Scholes, “Hybrid solar cells using PbS nanoparticles,” Sol. Energy Mater. Sol. Cells 91(5), 420–423 (2007). [CrossRef]

6.

P. T. Guerreiro, S. Ten, N. F. Borrelli, J. Butty, G. E. Jabbour, and N. Peyghambarian, “PbS quantum-dot doped grasses as saturable absorbers for mode locking of a Cr:forsterite laser,” Appl. Phys. Lett. 71(12), 1595–1597 (1997). [CrossRef]

7.

L. Levina, W. Sukhovatkin, S. Musikhin, S. Cauchi, R. Nisman, D. P. Bazett-Jones, and E. H. Sargent, “Efficient infrared-emitting PbS quantum dots grown on DNA and stable in aqueous solution and blood plasma,” Adv. Mater. (Deerfield Beach Fla.) 17(15), 1854–1857 (2005). [CrossRef]

8.

M. Kim and M. Yoda, “Infrared quantum dots for liquid-phase thermometry in silicon,” Meas. Sci. Technol. 22(8), 085401 (2011). [CrossRef]

9.

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(23), 235319 (2010). [CrossRef]

10.

N. F. Borrelli and D. W. Smith, “Quantum confinement of PbS microcrystals in glass,” J. Non-Cryst. Solids 180(1), 25–31 (1994). [CrossRef]

11.

K. E. Fox, T. Furukawa, and W. B. White, “Transition-metal ions in silicate melts. Part 2. Iron in sodium-silicate glasses,” Phys. Chem. Glasses 23, 169–178 (1982).

12.

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 3(10), 3023–3030 (2009). [CrossRef] [PubMed]

13.

A. Sihvola, “Two main avenues leading to the Maxwell Garnett mixing rule,” J. Electromagn. Waves Appl. 15(6), 715–725 (2001). [CrossRef]

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(300.1030) Spectroscopy : Absorption
(260.2065) Physical optics : Effective medium theory
(160.4236) Materials : Nanomaterials

ToC Category:
Nanomaterials

History
Original Manuscript: December 12, 2011
Revised Manuscript: March 12, 2012
Manuscript Accepted: March 12, 2012
Published: April 2, 2012

Virtual Issues
Quantum Dots for Photonic Applications (2012) Optical Materials Express

Citation
Iwan Moreels, Detlef Kruschke, Peter Glas, and Jens W. Tomm, "The dielectric function of PbS quantum dots in a glass matrix," Opt. Mater. Express 2, 496-500 (2012)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-2-5-496


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References

  1. A. Olkhovets, R. C. Hsu, A. Lipovskii, and F. W. Wise, “Size-dependent temperature variation of the energy gap in lead-salt quantum dots,” Phys. Rev. Lett.81(16), 3539–3542 (1998). [CrossRef]
  2. G. Konstantatos, C. J. Huang, L. Levina, Z. H. Lu, and E. H. Sargent, “Efficient infrared electroluminescent devices using solution-processed colloidal quantum dots,” Adv. Funct. Mater.15(11), 1865–1869 (2005). [CrossRef]
  3. K. Wundke, J. Auxier, A. Schulzgen, N. Peyghambarian, and N. F. Borrelli, “Room-temperature gain at 1.3 mu m in PbS-doped glasses,” Appl. Phys. Lett.75(20), 3060–3062 (1999). [CrossRef]
  4. S. A. McDonald, G. Konstantatos, S. G. Zhang, P. W. Cyr, E. J. D. Klem, L. Levina, and E. H. Sargent, “Solution-processed PbS quantum dot infrared photodetectors and photovoltaics,” Nat. Mater.4(2), 138–142 (2005). [CrossRef] [PubMed]
  5. S. Günes, K. P. Fritz, H. Neugebauer, N. S. Sariciftci, S. Kumar, and G. D. Scholes, “Hybrid solar cells using PbS nanoparticles,” Sol. Energy Mater. Sol. Cells91(5), 420–423 (2007). [CrossRef]
  6. P. T. Guerreiro, S. Ten, N. F. Borrelli, J. Butty, G. E. Jabbour, and N. Peyghambarian, “PbS quantum-dot doped grasses as saturable absorbers for mode locking of a Cr:forsterite laser,” Appl. Phys. Lett.71(12), 1595–1597 (1997). [CrossRef]
  7. L. Levina, W. Sukhovatkin, S. Musikhin, S. Cauchi, R. Nisman, D. P. Bazett-Jones, and E. H. Sargent, “Efficient infrared-emitting PbS quantum dots grown on DNA and stable in aqueous solution and blood plasma,” Adv. Mater. (Deerfield Beach Fla.)17(15), 1854–1857 (2005). [CrossRef]
  8. M. Kim and M. Yoda, “Infrared quantum dots for liquid-phase thermometry in silicon,” Meas. Sci. Technol.22(8), 085401 (2011). [CrossRef]
  9. 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(23), 235319 (2010). [CrossRef]
  10. N. F. Borrelli and D. W. Smith, “Quantum confinement of PbS microcrystals in glass,” J. Non-Cryst. Solids180(1), 25–31 (1994). [CrossRef]
  11. K. E. Fox, T. Furukawa, and W. B. White, “Transition-metal ions in silicate melts. Part 2. Iron in sodium-silicate glasses,” Phys. Chem. Glasses23, 169–178 (1982).
  12. 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 Nano3(10), 3023–3030 (2009). [CrossRef] [PubMed]
  13. A. Sihvola, “Two main avenues leading to the Maxwell Garnett mixing rule,” J. Electromagn. Waves Appl.15(6), 715–725 (2001). [CrossRef]

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