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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 8 — Apr. 12, 2010
  • pp: 8466–8481
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Silicon nanocrystals on bottle resonators: Mode structure, loss mechanisms and emission dynamics

P. Bianucci, X. Wang, J. G. C. Veinot, and A. Meldrum  »View Author Affiliations


Optics Express, Vol. 18, Issue 8, pp. 8466-8481 (2010)
http://dx.doi.org/10.1364/OE.18.008466


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Abstract

Bottle resonators can support high Q-factor whispering gallery modes (WGMs) and demonstrate a rich mode spectrum. Resonators were fabricated using a fiber tapering apparatus and were coated with a thin, smooth layer of luminescent silicon nanocrystals. The photoluminescence spectrum showed WGM peaks with Q-factors near 2,500; however, evanescent measurements showed that these modes are a composite of many modes with Q-factors exceeding 106, the highest yet seen for a silicon-nanocrystal-coated microresonators. The mode structure showed strong polarization and sensitivity to position within the bottle resonator. An analysis of loss mechanisms establishes surface roughness scattering as the limiting factor in these nanocrystal-coated bottle resonators in the absence of excited carriers.

© 2010 Optical Society of America

1. Introduction

Silicon nanocrystals (Si-NCs) hold high promise as light emitters in future microphotonic devices [1

1. L. Pavesi, “Silicon-Based light sources for silicon integrated circuits,” Adv. Opt. Technol. 2008, 416926 (2008).

]. Ensembles of oxide-embedded silicon nanocrystals display a broad, spectrally featureless luminescence band centered near 800 nm, with the possibility of quantum efficiencies above 50% [2

2. D. Jurbergs, E. Rogojina, L. Mangolini, and U. Kortshagen, “Silicon nanocrystals with ensemble quantum yields exceeding 60%,” Appl. Phys. Lett. 88, 233116 (2006). [CrossRef]

]. One of the greatest hopes in microphotonics is to develop a Si-NC laser; numerous research groups are currently pursuing this objective and there have been several reports of optical gain or stimulated emission [3–5

3. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000). [CrossRef] [PubMed]

], although it is not entirely clear what conditions are required to produce it [5

5. A. Polman and R. G. Elliman, Towards the first silicon laser, vol. 93 of NATO Science Series (Kluwer Academic Publishers, The Netherlands, 2003).

, 6

6. P. Fauchet, J. Ruan, H. Chen, L. Pavesi, L. Dal Negro, M. Cazzaneli, R. Elliman, N. Smith, M. Samoc, and B. Luther-Davies, “Optical gain in different silicon nanocrystal systems,” Opt. Mater. 27, 745–749 (2005). [CrossRef]

]. Coupling Si-NC luminescence into high-quality microcavities can provide fine control over its spectrum, may be one of the best avenues toward lasing, and could also lead to new applications including silicon-nanocrystal-based luminescence sensors [7

7. P. Bianucci, J. R. Rodríguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105, 023108 (2009). [CrossRef]

]. There is one report of stimulated emission in a nanocrystal-coated microsphere, although there was no clear evidence of cavity modes in the emission spectrum. The photoluminescence peak reported as possible stimulated emission was weak, blueshifted from the normal emission peak near 800 nm, and broad (full-width half-maximum ≈ 40 nm) [8

8. H. Chen, J. Sung, A. Tewary, M. Brongersma, J. Shin, and P. Fauchet, “Evidence for stimulated emission in silicon nanocrystal microspheres,” in “Group IV Photonics, 2005. 2nd IEEE International Conference on,” (2005), pp. 99–101.

]. For this article we fabricate Si-NC-coated high-Q bottle resonators, explore their mode structure in photoluminescence (PL) and transmission configurations, analyze possible loss mechanisms to estimate an upper bound on the achievable Q-factors, and study the time-resolved behavior of the PL.

In the present work, we investigate bottle resonators coated with a layer of oxide-embedded silicon NCs. Bottle resonators are attracting interest [13

13. C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101, 127403 (2008). [CrossRef] [PubMed]

, 14

14. S. Vicknesh, F. Li, and Z. Mi, “Optical microcavities on si formed by self-assembled InGaAs/GaAs quantum dot microtubes,” Appl. Phys. Lett. 94, 081101 (2009). [CrossRef]

] for several reasons: they support high Q-factors and small mode volumes; the guided modes (a major source of loss in cylindrical cavities) can be strongly suppressed; bottle resonators combine azimuthal and axial modes that can provide enhanced tunability of the resonant frequencies [15

15. M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultra-high-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

]; and they are not especially difficult to fabricate or handle. For example, bottle resonators can be made by “pinching” adjacent regions of an optical fiber to form a central bulged region [16

16. G. Kakarantzas, T. E. Dimmick, T. A. Birks, R. L. Roux, and P. S. J. Russell, “Miniature all-fiber devices based on CO2 laser microstructuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

] [Fig. 1(a)].

2. Experimental

The resonators were made from standard optical fibers using a hydrogen torch to heat the fibers and a motorized apparatus to pull them into the required prolate spheroidal shape. They were subsequently dipped into a solution of hydrogen silsesquioxane (HSQ) dissolved in methyl isobutyl keytone that formed a thin layer on the fiber surface [17

17. C. M. Hessel, M. A. Summers, A. Meldrum, M. Malac, and J. G. C. Veinot, “Direct patterning, conformal coating, and erbium doping of luminescent nc-si/sio2 thin films from solution processable hydrogen silsesquioxane,” Adv. Mater. 19, 3513–3516 (2007). [CrossRef]

]. Subsequent thermal processing at 1100°C for 1 hour under 95% N2 +5% H2 drove off excess solvent, collapsed the HSQ cage structures, and induced disproportionation that results in silicon nanocrystals ≈ 3 nm in diameter embedded in a silicon oxide matrix [17

17. C. M. Hessel, M. A. Summers, A. Meldrum, M. Malac, and J. G. C. Veinot, “Direct patterning, conformal coating, and erbium doping of luminescent nc-si/sio2 thin films from solution processable hydrogen silsesquioxane,” Adv. Mater. 19, 3513–3516 (2007). [CrossRef]

]. The nanocrystal containing film is thin (on the order of 100 nm [7

7. P. Bianucci, J. R. Rodríguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105, 023108 (2009). [CrossRef]

]), and smoother than typical results obtained using lithography and etching [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

] or evaporated thin films [9

9. A. Beltaos and A. Meldrum, “Whispering gallery modes in silicon-nanocrystal-coated silica microspheres,” J. Lumin. 126, 607–613 (2007). [CrossRef]

]. We used an atomic force microscope (AFM) in contact mode to estimate a root-mean-square surface roughness. The dimensions of the resonator were measured from an image taken with an optical microscope.

The luminescence was excited in one of two ways: (i) bringing the beam of an Ar+ laser directly onto the resonator (free-space pumping), or (ii) by coupling the laser into a tapered fiber that was brought into contact with the bottler resonator (evanescent pumping). The mode structure was also measured in two ways: by using a microscope objective to collect the luminescence and deliver it to a grating spectrometer, or by coupling a tunable diode laser (centered around 828 nm, bandwidth 4 MHz) and measuring the transmission through the tapered fiber as a function of wavelength. When evanescently pumping the resonator with the the Ar+ laser, we tuned the resonant mode (to enhance the pumping efficiency) using a mounting fork with a piezoelectric stack to apply small strains to the bottle resonator, in a way similar to that in Ref. [15

15. M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultra-high-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

].

Fig. 1. (a) Optical image of a bottle resonator. The scale bar represents 100 μm. (b) Photoluminescence (PL) emitted by the same resonator under evanescent excitation. (c, d) PL spectra collected at different resonator positions and different detection polarizations, after removing a constant background.

For the time-resolved studies, the excitation Ar+ laser was chopped into 500 μs square pulses using an acousto-optic modulator and delivered either through free-space or evanescently. The PL was collected by the microscope after filtering to remove the scattered excitation laser light and was finally routed to a photomultiplier tube (PMT). The PMT was connected to a multi-scale analyzer (MSA) with a maximum temporal resolution of 5 ns.

3. Results

Fig. 2. (a) Transmission spectrum of the optical resonator from Fig. 1 (black) compared to a magnified section of the PL spectrum (red). (b) Detail of the transmission spectrum, showing a rich structure with many resonant modes. (c) Detail of the marked box, including lorentzian fits to the transmission dips. The measured Q-factors are, from left to right, 1.1×106, 1.2×106, 9.9×105, 9.2×105 and 8.3×105.

Fig. 3. (a) Pictorial representation of the ray trajectory of a spiral mode in a bottle resonator. The curvature of the surface is exaggerated for a clearer presentation. (b) PL spectrum (black) compared to the mode structure calculated from Eq. (2) and the parameters given in the text (red). The numbers in the graph represent selected m, q pairs. The calculation includes values of q up to 20 for clarity. The slight mismatch in the free spectral range between the PL spectrum and the theoretical peak positions may be due to the effect of the film coating, as well as any errors in the determination of the resonator profile

4. Mode structure

The prolate geometry of the bottle resonators results in a distinctive mode structure. Using a geometrical optics description, it can be seen that these resonators support standard WGMs (where the ray path closes on itself after just one round-trip around the resonator axis or, equivalently with kz = 0) and spiral WGMs (with kz ≠ 0 and a ray trajectory that not only bounces just below the resonator surface but also moves back and forth along the axis between two turning points). Figure 3(a) shows a pictorial representation of one of these spiral trajectories.

The resonator profile is approximated (far from the pinched regions) by a parabola:

R(z)R0(112(Δkz)2),
(1)

where R0 = 38.1μm is the maximum radius (where is arbitrarily located at z = 0) and Δk = 0.002μm-1 is the profile curvature. These values were obtained by capturing an image using an optical microscope and a color charge-coupled-device (CCD) camera, tracing the resonator profile from the image and fitting Eq. (1) to the trace.

Due to the optical confinement on the resonator boundary, there is a discrete set of allowed eigenmodes [22

22. Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72, 031801 (2005). [CrossRef]

], with wavenumbers

kmq2=m2R02+(q+12)ΔEm,
(2)

where m is the usual azimuthal order number (corresponding to the number of nodes in the field along the azimuthal direction), q is an axial order number representing the number of nodes along the resonator axis and ΔE = 2mΔk/R0 (only the lowest radial mode is considered in the analysis, so there is no radial order number). The axial number q will also influence the z positions of the peak field since there are two symmetric positions, the caustics, on the axis where the field peaks: the larger q is, these peaks will be farther away from the center.

Using these equation with n = 1.453 for silica at room temperature, we can quantify the mode spacings (while the model does not account for the thin nanocrystal film, we can assume that the latter will cause a minor red shift of the mode resonant wavelengths [23

23. I. Teraoka and S. Arnold, “Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer,” J. Opt. Soc. Am. B 23, 1434–1441 (2006). [CrossRef]

]). For example, there is an upper limit of m = 420 for the mode wavelengths to fall within the scanned range (827.95–828.07 nm). The spacing between two modes with the same q number and consecutive m numbers is Δvmc/2πnR0 ≈ 862 GHz ≈ 2 nm, as can be appreciated in Fig. 2(a). The spacing between two modes with the same m number but consecutive q numbers, would then be ΔvqcΔk/2π ≈ 95 MHz ≈ 0.2 nm, which is larger than the scanned range of approximately 0.11 nm. Thus we can safely infer that the multitude of modes observed in the transmission spectrum in Fig. 2(b) possess different m and q numbers. Since the tapered fiber was located close to the center of the resonator, modes with lower q numbers will be more efficiently excited so the measured modes should have values near the upper limit in m. A comparison showing qualitative agreement between the calculated spectra and the measured PL at a given position is given in Fig. 3(b).

The eigenmode distribution from Eq. (2) also explains why the resonant peaks in Fig. 1 seem to shift when measured at different axial positions. Mode PL emission will be strongest at the caustics, so the higher q numbers imply that the strongest emission will be located farther away from the resonator midpoint. As we collect emission from locations away from the center, the predominant PL comes from modes with higher q values (and lower m values) which will certainly show a different resonant wavelength. This also provides an explanation for the fine structure observed in Fig. 2(a), as the spectrometer slit (1.8 μm accounting for the 10X magnification of the microscope) collects emission from modes with different values for q.

5. Loss mechanisms

The addition of the coating decreases the Q-factor in the resonators by one or two orders of magnitude. The ability to maintain high Q-factors in coated resonators matters in different contexts: it is critical to minimize the threshold in a laser and it enhances the interaction between light and matter in a way that could make cavity phenomena like the Purcell effect or strong coupling easier to achieve. It is also important for low-power operation of resonator-based optical filters. We can analyze the contribution of different loss mechanisms to the degradation of Q-factors to see if it would be possible in principle to improve them still further. The main loss mechanisms in Si-NC-containing resonators when the excitation power is kept low and the wavelength is in the near-infrared range are radiation losses in the modes, surface roughness scattering, Mie scattering and inter-band absorption by the nanocrystals [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

]. The final Q-factor is then given by

Qf1=QRad1+QRough1+QMie1+QIB1.
(3)

When the resonator is excited by the blue light emitted by the Ar+ laser, a population of carriers builds up in the Si-NCs. These excited carriers can absorb the light circulating within the cavity [24

24. R. Kekatpure and M. Brongersma, “Quantification of free-carrier absorption in silicon nanocrystals with an optical microcavity,” Nano. Lett. 8, 3787–3793 (2008). [CrossRef] [PubMed]

], and thus introduce a new loss channel. This additional loss mechanism is normally called confined-carrier-absorption (CCA), and we will consider it separately.

5.1. Radiation loss

Since we have measured Q-factors close to 108 in uncoated cavities, we can assume QRad ≥ 108, and the loss due to radiation is negligible. This is not surprising, given the relatively large diameter of 76 μm.

5.2. Surface roughness

αRough=φ2(r)(nfilm21)k028nfilmσ2πneff21,
(4)

Using these numbers in Eq. (4), we obtain αRough = 0.05 cm-1, and from that we estimate QRough as follows:

QRough=2πneffλαRough=2.1×106.
(5)

5.3. Inter-band absorption

The estimated losses caused by inter-band absorption by Si-NC can be estimated by following the procedure outlined in Ref. [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

] from the absorption cross-section, the nanocrystal size distribution and the mode field profile. We obtained the nanocrystal size distribution ρ(R) from energy-filtered transmission electron microscopy (see the appendix for details). Then, the absorption is given by [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

]

αIB=Γ(λ)R=R(λ)R=Rmaxσabs(R)ρ(R)dR,
(6)

where σabs(R) is the absorption cross-section (as a function of the nanocrystal radius), R(λ) is the radius for a nanocrystal with an emission of wavelength λ and Rmax is the radius of the largest nanocrystal in the sample and Γ(λ) ≈ 0.01 is the confinement factor calculated from the mode profile. Using the values reported in Ref. [27

27. N. Daldosso, M. Melchiorri, L. Pavesi, G. Pucker, F. Gourbilleau, S. Chausserie, A. Belarouci, X. Portier, and C. Dufour, “Optical losses and absorption cross-section of silicon nanocrystals,” J. Lumin. 121, 344 (2006). [CrossRef]

], we find αIB = 2.24 × 10-3 cm-1 and QIB = 4.7 × 107.

5.4. Mie scattering

Finally, the Mie scattering losses can be estimated by adding the contribution for each nanocrystal size weighted by the size distribution,

αMie=Γ(λ)R=RminR=RmaxσMie(R,λ)ρ(R)dR,
(7)

with the scattering cross-section given by the Rayleigh formula [28

28. J. D. Jackson, Classical electrodynamics; 3rd ed. (Wiley, New York, NY, 1998). [PubMed]

]

σMie=8π3(2πnSiO2λ)4R6(nSi2nSiO22nSi2+2nSiO22)2.
(8)

Taking nSiO2 = 1.46 and nSi = 3.69, we find σMie = 9.25 × 10−4 cm−1 and QMie = 1.2 × 108.

The final estimated Q-factor results Qf= 1.9 × 106, comparable to what we observed in the transmission spectra. From this analysis, surface roughness scattering is the dominant loss factor, followed by interband absorption. Mie scattering does not seem to contribute significantly to the scattering, just like radiation losses. The films produced by the dip-coating method are already very smooth (as compared, for instance, to lithographically fabricated microdisks which have a much higher root-mean-square roughness [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

] or evaporated thin films. However, the experimental Q-factors could be increased (up to a factor of 6) by further improving their surface properties. It is worthwhile to note that Mie scattering and interband absorption are greatly reduced because of the thinness of the nanocrystal-containing film (expressed by the small confinement factor Γ). Thicker films would increase the losses due to these intrinsic mechanisms, and correspondingly decrease the maximum achievable Q-factors. Our fabrication method then becomes attractive for applications requiring resonators with high Q-factors.

5.5. Confined carrier absorption

To estimate the degree of confined carrier absorption, we measured the linewidth of a resonant mode under free-space excitation of the resonator with the Ar+ laser. Then, comparing this linewidth with the one in the absence of an external excitation we can obtain an estimate of the extra loss induced by the free carrier absorption. At an excitation intensity of 34 kW/cm2 (the maximum we could safely route through our microscope), the linewidth increased by 0.42 pm. Following Ref. [24

24. R. Kekatpure and M. Brongersma, “Quantification of free-carrier absorption in silicon nanocrystals with an optical microcavity,” Nano. Lett. 8, 3787–3793 (2008). [CrossRef] [PubMed]

], this results in αCCA = 2πneff/(λ2Γ) = 0.054 cm-1 and QCCA = 2.0 × 106. Combined with the near-infrared Q-factor calculated above, the Ar+ -excited Q-factor would be

QAr+=(Qf+QCCA)1=9.7×105.
(9)

The evolution of the transmission spectra as the pump power increases [Fig. 4(a)] shows the gradual increase in the full-width half-maximum (FWHM) of the modes as the pump intensity increases. There is also a red-shift associated with the pumping, which is due to thermal effects on the resonator (we verified this by corroborating that the time scale of the shift is in the order of a tens of milliseconds). Figure 4(b) displays the fitted mode FWHM as a function of incident power. At the lower intensities the mode linewidth stays roughly constant while it increases for pump intensities larger than 19 kW/cm2, the point where the confined carrier absorption becomes the dominant loss mechanism.

5.6. Losses and PL linewidth

Fig. 4. (a) Transmission spectra of a resonator excited by a focused free-space Ar+ pump laser at different pump excitation intensities. (b) Intensity dependence of the FWHM of the resonant mode indicated with an arrow in the top panel. The error bars indicate the error from fitting the mode dip to a lorentzian function and the dashed lines show the trend.

6. High-power excitation

Steady-state spectral measurements at increasing pump powers (up to an estimated 380 μW transferred from the waveguide into the resonator, corresponding to 9 mW of circulating power for a Q-factor of 105) did not show qualitative changes beyond an increase in PL intensity (in particular, there was no clear trend of an increasing PL linewidth as the pump power increased). The upper inset in Fig. 5 shows a representative spectrum, together with ones from the free-space configuration and a flat film. The WGMs are not observable in this spectra because light was collected from the whole resonator so as not to miss possible lasing modes. The free-space-excited resonator PL peak was blue shifted compared to that from the flat film, while the evanescently excited PL no longer had a well defined peak, instead gradually rising into the blue part of the spectrum and was eventually cut off by the longpass filter that blocked the laser. This blue shift is consistent with the high excitation power density inside the resonators, especially for evanescent pumping, which increases the contribution of fast processes.

7. Time-resolved behavior

Since there have been reports of short-lived gain in Si-NCs [30

30. L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franzo, F. Priolo, and F. Iacona, “Dynamics of stimulated emission in silicon nanocrystals,” Appl. Phys. Lett. 82, 4636–4638 (2003). [CrossRef]

], we also performed time-resolved studies of the PL. As a baseline, we measured the time-resolved PL from a flat film of oxide-embedded Si-NCs (Fig. 5). This showed a typical stretched exponential decay, I(t)=I(0)exp((tτ)β) with τ = 21 μs and β = 0.77. The emission from a coated resonator using free-space excitation gave a similar curve (τ = 16 μs, β = 0.55). The trace from the evanescently excited resonator showed a fast rise (rise time ≈ 200 ns, close to the AOM modulator limit) followed by a slower decay to a steady state. The decay of this steady state was also on the order of 200 ns and was followed by a much weaker decay with a time constant on the order of microseconds.

The lifetime decreases and the spectrum blueshifts on going from a flat film to a free-space-pumped cavity and finally to an evanescently pumped cavity (Fig. 5). In fact, the evanescently coupled resonator is somewhat reminiscent of the gain reported in Si-NCs [30

30. L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franzo, F. Priolo, and F. Iacona, “Dynamics of stimulated emission in silicon nanocrystals,” Appl. Phys. Lett. 82, 4636–4638 (2003). [CrossRef]

] but with a much longer decay to the steady state, which is inconsistent with Auger-induced gain quenching [6

6. P. Fauchet, J. Ruan, H. Chen, L. Pavesi, L. Dal Negro, M. Cazzaneli, R. Elliman, N. Smith, M. Samoc, and B. Luther-Davies, “Optical gain in different silicon nanocrystal systems,” Opt. Mater. 27, 745–749 (2005). [CrossRef]

]. No spectral narrowing or threshold behavior was observed when changing the pump power (see the lower inset of Fig. 5), only saturation at high pump powers. The fast (nanosecond) component of the rise and decay times are consistent with the so-called F-band emission [31

31. L. T. Canham, “Luminescence bands and their proposed origins in highly porous silicon,” Phys. Status Solidi B 190, 9–14 (1995). [CrossRef]

], likely due to luminescent defects in silicon-rich oxide [32

32. L. Tsybeskov, J. Vandyshev, and P. Fauchet, “Blue emission in porous silicon - oxygen-related photoluminescence,” Phys. Rev. B 49, 7821–7824 (1994). [CrossRef]

] which are not saturated in the evanescently-pumped configuration (the nanocrystals themselves contributing only to the low-amplitude slow dynamics). The initial decay to a steady state just after the pulse onset was unexpected, and it may be due to a reversible photobleaching of luminescent centers caused by the high excitation power density coupled into the cavity. It was only observed for evanescent pumping. Despite the small time constants and bluer emission, the lack of sharp peaks in the spectrum coupled with the absence of a threshold behavior leads us to conclude the Si-NCs do not show stimulated emission in these excitation and measurement configurations.

8. Conclusion

In summary, we studied Si-NC-coated bottle resonators under evanescent excitation. The tuning range and high Q- factors of bottle resonators allow for efficient pumping of the Si-NCs, leading to the emission of luminescence coupled to resonator modes. The PL modes approach 2,500; however, they were found to be composed by many modes with Q-factors on the order of 106, the highest yet reported in Si-NC-coated resonators. The measured spectra can be qualitatively explained by means of a mode analysis of the resonator geometry. We found no clear-cut evidence of either steady-state or short-time (5 ns time resolution) stimulated emission when pumping the Si-NC-coated resonator either in free space or evanescently despite the high Q-factors. These Q-factors correspond to the ones estimated when considering the most likely loss mechanisms. Even though the films as fabricated are very smooth (root-mean-square roughness σ = 3.40 nm) surface roughness scattering is still the dominant loss mechanism in the absence of excited carriers; when carriers are excited into the nanocrystals by a suitable excitation source, absorption by these confined carriers becomes the main limiting loss mechanism and the transition point between these two regimes has been found at an pump excitation power of 19 kW/cm2). Thus, it should be possible to decrease the losses and increase the Q-factors by careful optimization of the film surface properties and avoiding the buildup of large carrier populations. If such high Q-factors could be measured in PL using, for example, a chip-scale tapered slab spectrometer [33

33. O. Schmidt, P. Kiesel, S. Mohta, and N. Johnson, “Resolving pm wavelength shifts in optical sensing,” Appl. Phys. B 86, 593–600 (2007). [CrossRef]

], the resolution of refractometric fiber sensors such as those developed in Ref. [7

7. P. Bianucci, J. R. Rodríguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105, 023108 (2009). [CrossRef]

] would increase by several orders of magnitude. Considering a Q-factor of 106 and a shift of 33 nm/RIU the estimated detection limit would be 2.5×10-5 RIU, competitive with other sensing technologies such as surface plamon resonance [34

34. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 429–493 (2008). [CrossRef]

], although the emitter bandwidth may play a limiting role in the case of Si-NCs [29

29. A. Meldrum, P. Bianucci, and F. Marsiglio, “Purcell effect in inhomogenously broadened ensembles of quantum dots coupled to optical microcavities,” (2010).

]. Future work will investigate the gain dynamics at short timescales (ps) where Auger-induced quenching may not limit the gain mechanisms in high-Q nanocrystal-coated resonators.

Fig. 5. Time-resolved PL traces. Upper inset: Unfiltered PL spectra of the flat film and the resonator under free space and evanescent excitation. The bottle spectra have been multiplied by 3. Lower inset: Pump power dependence of time-resolved signal, at the peak (open circles) and the steady state (filled circles), showing saturation in both cases.
Fig. 6. Atomic force microscope image of the surface of a coated resonator. The measured root-mean-squared roughness from the image is 3.40 nm.

A. Measuring the surface roughness

We measured the surface roughness of a coated resonator using an atomic force microscope. The captured AFM image of the resonator surface can be seen in Fig.6). We used the Roughness analysis feature of the software package Nanoscope 6.11r1 to calculate the root-mean-squared surface roughness from the captured data, with a resulting σ = 3.40 nm.

B. Calculating the nanocrystal size-dependent density

In order to estimate the losses due to some of the analyzed mechanisms (Mie scattering, interband absorption) we need the nanocrystal size-dependent density ρ(R), defined as the number of nanocrystals per unit volume with radius between R and R+ dR and measured in units of cm-3 nm-1 [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

]. We obtain this function from transmission electron microscope (TEM) analysis of a flat film prepared under the same conditions as the bottle resonators with proper normalization.

B.1. Measurement of the nanocrystal size distribution

Imaging Si-NCs embedded in an oxide matrix by conventional TEM methods is somewhat difficult due to the low contrast between Si and SiO2. Although high resolution TEM (HRTEM) is able to image Si-NCs [Fig. 7(a)], the appearance of the nanocrystals in the HRTEM image requires a zone-axis orientation, limiting the application of the technique for determining size distributions (while not directly relevant to our sample, it is worth noting that amorphous Si-NCs can’t be imaged by HRTEM either). Instead, we used energy filtered TEM (EFTEM) to detect Si-NCs. This method works because the plasmon losses for Si and SiO2 are different (centered at 17 eV and 23 eV respectively). In this work, the spectrometer slit was centered at the silicon plasmon loss peak at 17 eV, with a slit width of 4 eV, permitting the Si-NCs to be imaged without significant interference from the oxide matrix [Fig. 7(b)]. We can then measure the diameter of the Si-NCs which appear bright in the image. Sampling a number of different nanocrystals (200 in our case), we can reconstruct the the size distribution of the Si-NCs in our sample as shown in Fig. 8. The nanocrystal diameters were estimated by visual inspection of the intensity profile of each nanocrystal in the image (the software package Digital Micrograph was used to obtain the intensity profiles). It should be pointed out that delocalization of the plasmon scattering process can result in a size distribution that represents a slight overestimate of the true particle sizes [35

35. R. F. Egerton, “New techniques in electron energy-loss spectroscopy,” Micron 34, 127–129 (2003). [CrossRef] [PubMed]

]. Finally, we fit a log-normal distribution,

Fig. 7. (a) HRTEM image showing the presence of crystalline Si nanoparticles. (b) EFTEM image showing the Si-NCs (white) on the oxide background (grey).
ρTEM(R)=12πeln(R/R0)22σ2
(10)

to the experimental data, obtaining a good agreement with R0 = 1.57 nm and σ= 0.18.

B.2. Normalization

Once we have the size distribution as measured from the TEM (which we call ρTEM(R)) we can compute ρ(R), following closely the procedure in Ref. [11

11. R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

]. We begin by assuming that:

ρ(R)=AρTEM(R).
(11)

We can calculate the number of Si atoms in the nanocrystals by integrating the volume of a spherical nanocrystal times the nanocrystal density distribution, and dividing by the volume occupied by 1 atom (≈ 1/(8a3), where a is the lattice constant of silicon):

NSi=A0ρTEM(R)4πR33dR18a3.
(12)
Fig. 8. Unnormalized size distribution measured from EFTEM images (black dots). The dotted line is a fit using a lognormal function.

On the other hand, if we assume that all the excess silicon is in the form of nanocrystals and then take a unit volume, we can see that

NSi=ρSi/ASi1+VSiO2VSi,
(13)

using that NSi = ρSi VSi/ASi, where ρSi is the density of silicon and ASi its atomic mass.

Moreover, we can define a filling fraction f as

f=NSiNSi+NSiO2
(14)

or, equivalently,

VSiO2VSi=1ffASiO2ρSiASiρSiO2,
(15)

where ρSiO2 and ASiO2 are the density and molecular mass of SiO2, respectively.

We can then insert Eq. (15) into Eq. (13) to obtain then the number of silicon atoms as a function of the filling fraction f. Equating that to the one calculated from Eq. (12), we can calculate the value of the proportionality constant A. In our case, the filling fraction (measured using TEM) is f = 0.12, resulting in A = 1.94×1018cm-3nm-1. Integrating this density distribution over all possible nanocrystal sizes results in a number density NNC = 2.4×1018 cm-3.

Acknowledgements

References and links

1.

L. Pavesi, “Silicon-Based light sources for silicon integrated circuits,” Adv. Opt. Technol. 2008, 416926 (2008).

2.

D. Jurbergs, E. Rogojina, L. Mangolini, and U. Kortshagen, “Silicon nanocrystals with ensemble quantum yields exceeding 60%,” Appl. Phys. Lett. 88, 233116 (2006). [CrossRef]

3.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000). [CrossRef] [PubMed]

4.

M. Cazzanelli, D. Navarro-Urríos, F. Riboli, N. Daldosso, L. Pavesi, J. Heitmann, L. X. Yi, R. Scholz, M. Zacharias, and U. Gosele, “Optical gain in monodispersed silicon nanocrystals,” J. Appl. Phys. 96, 3164–3171 (2004). [CrossRef]

5.

A. Polman and R. G. Elliman, Towards the first silicon laser, vol. 93 of NATO Science Series (Kluwer Academic Publishers, The Netherlands, 2003).

6.

P. Fauchet, J. Ruan, H. Chen, L. Pavesi, L. Dal Negro, M. Cazzaneli, R. Elliman, N. Smith, M. Samoc, and B. Luther-Davies, “Optical gain in different silicon nanocrystal systems,” Opt. Mater. 27, 745–749 (2005). [CrossRef]

7.

P. Bianucci, J. R. Rodríguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, “Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers,” J. Appl. Phys. 105, 023108 (2009). [CrossRef]

8.

H. Chen, J. Sung, A. Tewary, M. Brongersma, J. Shin, and P. Fauchet, “Evidence for stimulated emission in silicon nanocrystal microspheres,” in “Group IV Photonics, 2005. 2nd IEEE International Conference on,” (2005), pp. 99–101.

9.

A. Beltaos and A. Meldrum, “Whispering gallery modes in silicon-nanocrystal-coated silica microspheres,” J. Lumin. 126, 607–613 (2007). [CrossRef]

10.

A. Tewary, M. J. F. Digonnet, J. Sung, J. H. Shin, and M. L. Brongersma, “Silicon-Nanocrystal-Coated silica microsphere thermooptical switch,” IEEE J. Sel. Top. Quantum Electron. 12, 1476–1479 (2006). [CrossRef]

11.

R. D. Kekatpure and M. L. Brongersma, “Fundamental photophysics and optical loss processes in si-nanocrystal-doped microdisk resonators,” Phys. Rev. A 78, 023829 (2008). [CrossRef]

12.

M. Ghulinyan, D. Navarro-Urríos, A. Pitanti, A. Lui, G. Pucker, and L. Pavesi, “Whispering-gallery modes and light emission from a si-nanocrystal-based single microdisk resonator,” Opt. Express 16, 13218–13224 (2008). [CrossRef] [PubMed]

13.

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101, 127403 (2008). [CrossRef] [PubMed]

14.

S. Vicknesh, F. Li, and Z. Mi, “Optical microcavities on si formed by self-assembled InGaAs/GaAs quantum dot microtubes,” Appl. Phys. Lett. 94, 081101 (2009). [CrossRef]

15.

M. Pöllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultra-high-Q tunable whispering-gallery-mode microresonator,” Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]

16.

G. Kakarantzas, T. E. Dimmick, T. A. Birks, R. L. Roux, and P. S. J. Russell, “Miniature all-fiber devices based on CO2 laser microstructuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

17.

C. M. Hessel, M. A. Summers, A. Meldrum, M. Malac, and J. G. C. Veinot, “Direct patterning, conformal coating, and erbium doping of luminescent nc-si/sio2 thin films from solution processable hydrogen silsesquioxane,” Adv. Mater. 19, 3513–3516 (2007). [CrossRef]

18.

T. Kipp, H. Welsch, C. Strelow, C. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96, 077403 (2006). [CrossRef] [PubMed]

19.

Y. Rakovich, S. Balakrishnan, J. Donegan, T. Perova, R. Moore, and Y. Gun’ko, “The fabrication, fluorescence dynamics, and whispering gallery modes of aluminosilicate microtube resonators,” Adv. Funct. Mater. 17, 1106 (2007). [CrossRef]

20.

L. Guimarães and J. De Mendonça, “Analysis of the resonant scattering of light by cylinders at oblique incidence,” Appl. Opt. 36, 8010–8019 (1997). [CrossRef]

21.

P. Bianucci, J. Rodríguez, F. Lenz, J. G. C. Veinot, and A. Meldrum, “Mode structure in the luminescence of si-nc in cylindrical microcavities,” Physica E 41, 1107 (2009). [CrossRef]

22.

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72, 031801 (2005). [CrossRef]

23.

I. Teraoka and S. Arnold, “Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer,” J. Opt. Soc. Am. B 23, 1434–1441 (2006). [CrossRef]

24.

R. Kekatpure and M. Brongersma, “Quantification of free-carrier absorption in silicon nanocrystals with an optical microcavity,” Nano. Lett. 8, 3787–3793 (2008). [CrossRef] [PubMed]

25.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26, 977–986 (1994). [CrossRef]

26.

J. R. Rodríguez, P. Bianucci, A. Meldrum, and J. G. C. Veinot, “Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals,” Appl. Phys. Lett. 92, 131119 (2008). [CrossRef]

27.

N. Daldosso, M. Melchiorri, L. Pavesi, G. Pucker, F. Gourbilleau, S. Chausserie, A. Belarouci, X. Portier, and C. Dufour, “Optical losses and absorption cross-section of silicon nanocrystals,” J. Lumin. 121, 344 (2006). [CrossRef]

28.

J. D. Jackson, Classical electrodynamics; 3rd ed. (Wiley, New York, NY, 1998). [PubMed]

29.

A. Meldrum, P. Bianucci, and F. Marsiglio, “Purcell effect in inhomogenously broadened ensembles of quantum dots coupled to optical microcavities,” (2010).

30.

L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franzo, F. Priolo, and F. Iacona, “Dynamics of stimulated emission in silicon nanocrystals,” Appl. Phys. Lett. 82, 4636–4638 (2003). [CrossRef]

31.

L. T. Canham, “Luminescence bands and their proposed origins in highly porous silicon,” Phys. Status Solidi B 190, 9–14 (1995). [CrossRef]

32.

L. Tsybeskov, J. Vandyshev, and P. Fauchet, “Blue emission in porous silicon - oxygen-related photoluminescence,” Phys. Rev. B 49, 7821–7824 (1994). [CrossRef]

33.

O. Schmidt, P. Kiesel, S. Mohta, and N. Johnson, “Resolving pm wavelength shifts in optical sensing,” Appl. Phys. B 86, 593–600 (2007). [CrossRef]

34.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 429–493 (2008). [CrossRef]

35.

R. F. Egerton, “New techniques in electron energy-loss spectroscopy,” Micron 34, 127–129 (2003). [CrossRef] [PubMed]

OCIS Codes
(230.5750) Optical devices : Resonators
(250.5230) Optoelectronics : Photoluminescence
(140.3948) Lasers and laser optics : Microcavity devices

ToC Category:
Optical Devices

History
Original Manuscript: February 12, 2010
Revised Manuscript: April 1, 2010
Manuscript Accepted: April 2, 2010
Published: April 7, 2010

Citation
P. Bianucci, X. Wang, J. G. Veinot, and A. Meldrum, "Silicon nanocrystals on bottle resonators: Mode structure, loss mechanisms and emission dynamics," Opt. Express 18, 8466-8481 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8466


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References

  1. L. Pavesi, "Silicon-Based light sources for silicon integrated circuits," Adv. Opt. Technol. 2008, 416926 (2008).
  2. D. Jurbergs, E. Rogojina, L. Mangolini, and U. Kortshagen, "Silicon nanocrystals with ensemble quantum yields exceeding 60%," Appl. Phys. Lett. 88, 233116 (2006). [CrossRef]
  3. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, "Optical gain in silicon nanocrystals," Nature 408, 440-444 (2000). [CrossRef] [PubMed]
  4. M. Cazzanelli, D. Navarro-Urr’ıos, F. Riboli, N. Daldosso, L. Pavesi, J. Heitmann, L. X. Yi, R. Scholz, M. Zacharias, and U. Gosele, "Optical gain in monodispersed silicon nanocrystals," J. Appl. Phys. 96, 3164-3171 (2004). [CrossRef]
  5. A. Polman and R. G. Elliman, Towards the first silicon laser, vol. 93 of NATO Science Series (Kluwer Academic Publishers, The Netherlands, 2003).
  6. P. Fauchet, J. Ruan, H. Chen, L. Pavesi, L. Dal Negro, M. Cazzaneli, R. Elliman, N. Smith, M. Samoc, and B. Luther-Davies, "Optical gain in different silicon nanocrystal systems," Opt. Mater. 27, 745-749 (2005). [CrossRef]
  7. P. Bianucci, J. R. Rodr’ıguez, C. M. Clements, J. G. C. Veinot, and A. Meldrum, "Silicon nanocrystal luminescence coupled to whispering gallery modes in optical fibers," J. Appl. Phys. 105, 023108 (2009). [CrossRef]
  8. H. Chen, J. Sung, A. Tewary, M. Brongersma, J. Shin, and P. Fauchet, "Evidence for stimulated emission in silicon nanocrystal microspheres," in "Group IV Photonics, 2005. 2nd IEEE International Conference on," (2005), pp. 99-101.
  9. A. Beltaos and A. Meldrum, "Whispering gallery modes in silicon-nanocrystal-coated silica microspheres," J. Lumin. 126, 607-613 (2007). [CrossRef]
  10. A. Tewary, M. J. F. Digonnet, J. Sung, J. H. Shin, and M. L. Brongersma, "Silicon-Nanocrystal-Coated silica microsphere thermooptical switch," IEEE J. Sel. Top. Quantum Electron. 12, 1476-1479 (2006). [CrossRef]
  11. R. D. Kekatpure and M. L. Brongersma, "Fundamental photophysics and optical loss processes in si-nanocrystaldoped microdisk resonators," Phys. Rev. A 78, 023829 (2008). [CrossRef]
  12. M. Ghulinyan, D. Navarro-Urrıos, A. Pitanti, A. Lui, G. Pucker, and L. Pavesi, "Whispering-gallery modes and light emission from a si-nanocrystal-based single microdisk resonator," Opt. Express 16, 13218-13224 (2008). [CrossRef] [PubMed]
  13. C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, "Optical microcavities formed by semiconductor microtubes using a bottlelike geometry," Phys. Rev. Lett. 101, 127403 (2008). [CrossRef] [PubMed]
  14. S. Vicknesh, F. Li, and Z. Mi, "Optical microcavities on si formed by self-assembled InGaAs/GaAs quantum dot microtubes," Appl. Phys. Lett. 94, 081101 (2009). [CrossRef]
  15. M. P¨ollinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, "Ultra-high-Q tunable whispering-gallery-mode microresonator," Phys. Rev. Lett. 103, 053901 (2009). [CrossRef] [PubMed]
  16. G. Kakarantzas, T. E. Dimmick, T. A. Birks, R. L. Roux, and P. S. J. Russell, "Miniature all-fiber devices based on CO2 laser microstructuring of tapered fibers," Opt. Lett. 26, 1137-1139 (2001). [CrossRef]
  17. C. M. Hessel, M. A. Summers, A. Meldrum, M. Malac, and J. G. C. Veinot, "Direct patterning, conformal coating, and erbium doping of luminescent nc-si/sio2 thin films from solution processable hydrogen silsesquioxane," Adv. Mater. 19, 3513-3516 (2007). [CrossRef]
  18. T. Kipp, H. Welsch, C. Strelow, C. Heyn, and D. Heitmann, "Optical modes in semiconductor microtube ring resonators," Phys. Rev. Lett. 96, 077403 (2006). [CrossRef] [PubMed]
  19. Y. Rakovich, S. Balakrishnan, J. Donegan, T. Perova, R. Moore, and Y. Gun’ko, "The fabrication, fluorescence dynamics, and whispering gallery modes of aluminosilicate microtube resonators," Adv. Funct. Mater. 17, 1106 (2007). [CrossRef]
  20. L. Guimaraes and J. De Mendonca, "Analysis of the resonant scattering of light by cylinders at oblique incidence," Appl. Opt. 36, 8010-8019 (1997). [CrossRef]
  21. P. Bianucci, J. Rodr’ıguez, F. Lenz, J. G. C. Veinot, and A. Meldrum, "Mode structure in the luminescence of si-nc in cylindrical microcavities," Physica E 41, 1107 (2009). [CrossRef]
  22. Y. Louyer, D. Meschede, and A. Rauschenbeutel, "Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics," Phys. Rev. A 72, 031801 (2005). [CrossRef]
  23. I. Teraoka and S. Arnold, "Enhancing the sensitivity of a whispering-gallery mode microsphere sensor by a high-refractive-index surface layer," J. Opt. Soc. Am. B 23, 1434-1441 (2006). [CrossRef]
  24. R. Kekatpure and M. Brongersma, "Quantification of free-carrier absorption in silicon nanocrystals with an optical microcavity," Nano. Lett. 8, 3787-3793 (2008). [CrossRef] [PubMed]
  25. F. P. Payne and J. P. R. Lacey, "A theoretical analysis of scattering loss from planar optical waveguides," Opt. Quantum Electron. 26, 977-986 (1994). [CrossRef]
  26. J. R. Rodr’ıguez, P. Bianucci, A. Meldrum, and J. G. C. Veinot, "Whispering gallery modes in hollow cylindrical microcavities containing silicon nanocrystals," Appl. Phys. Lett. 92, 131119 (2008). [CrossRef]
  27. N. Daldosso, M. Melchiorri, L. Pavesi, G. Pucker, F. Gourbilleau, S. Chausserie, A. Belarouci, X. Portier, and C. Dufour, "Optical losses and absorption cross-section of silicon nanocrystals," J. Lumin. 121, 344 (2006). [CrossRef]
  28. J. D. Jackson, Classical electrodynamics; 3rd ed. (Wiley, New York, NY, 1998). [PubMed]
  29. A. Meldrum, P. Bianucci, and F. Marsiglio, "Purcell effect in inhomogenously broadened ensembles of quantum dots coupled to optical microcavities," (2010).
  30. L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franzo, F. Priolo, and F. Iacona, "Dynamics of stimulated emission in silicon nanocrystals," Appl. Phys. Lett. 82, 4636-4638 (2003). [CrossRef]
  31. L. T. Canham, "Luminescence bands and their proposed origins in highly porous silicon," Phys. Status Solidi B 190, 9-14 (1995). [CrossRef]
  32. L. Tsybeskov, J. Vandyshev, and P. Fauchet, "Blue emission in porous silicon - oxygen-related photoluminescence," Phys. Rev. B 49, 7821-7824 (1994). [CrossRef]
  33. O. Schmidt, P. Kiesel, S. Mohta, and N. Johnson, "Resolving pm wavelength shifts in optical sensing," Appl. Phys. B 86, 593-600 (2007). [CrossRef]
  34. J. Homola, "Surface plasmon resonance sensors for detection of chemical and biological species," Chem. Rev. 108, 429-493 (2008). [CrossRef]
  35. R. F. Egerton, "New techniques in electron energy-loss spectroscopy," Micron 34, 127-129 (2003). [CrossRef] [PubMed]

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