OSA / IPR/PS 2010 a209_1.pdf IMA5.pdf
Spontaneous emission dynamics and Purcell enhancement in Si-nc-based microdisk resonators Mher Ghulinyan1*, Alessandro Pitanti2, Daniel Navarro-Urrios3, Georg Pucker1 and Lorenzo Pavesi2 1
Advanced Photonics & Photovoltaics, Fondazione Bruno Kessler, Trento, Italy 2
Nanoscience Lab., Department of Physics, University of Trento, Trento, Italy 3
Departament d'Electrònica, Universitat de Barcelona, Barcelona, Spain *
[email protected]
Unlike to III-V quantum dots, Si-nanocrystals (Si-ncs), because of their large intrinsic linewidths are not considered to be suitable emitters for emission rate enhancement observations (Purcell effect). Here, we report on direct measurements of spontaneous emission rate enhancement of Sincs embedded in a whispering-gallery mode (WGM) resonator at room temperature [1]. Optically active microdisk resonators have been fabricated and characterized through single-disk timeresolved micro-photoluminescence (PL) experiments. We demonstrate experimentally that the emission lifetime of Si-ncs coupled to WGM cavity resonances is reduced by up to ~70% with respect to uncoupled ones. Comparing our experimental results with theoretically predicted Purcell enhancement in a bad emitter regime, we estimate effective linewidths of 10meV through which Si-nc emitters are coupled to WGM cavity photons. Finally, our study provides an alternative method for the estimation of sub-natural linewidths of quantum dots at room temperature. © 2010 Optical Society of America OCIS codes: 140.4780 Optical resonators; 160.4236 Nanomaterials; 250.5230 Photoluminescence; 300.3700 Linewidth
1.
Introduction
The demonstration of optical gain at optical wavelengths [2] in nanocrystalline silicon (Si-nc) has triggered a huge scientific interest for its potential use in CMOS-compatible optoelectronic devices. Integrated resonator devices containing Si-ncs have been realized and studied [3]. Key optical properties of single nanocrystals yet remain unaddressed, on one side, because of the difficulty to perform single-nanocrystal spectroscopic experiments; different fabrication techniques likely produce nanocrystal ensembles with broad size distrubutions. On the other side, the quantum-confined electronic structure of Si-ncs is far more complex than those of III-V compound quantum dots, due to the indirect band gap nature of the bulk silicon material itself. As proposed for nanostructured porous silicon, quantum exchange interaction splits excitonic states into few meV separated singlet (upper level) and triplet states (lower level). Low-temperature PL experiments allow probing only the triplet recombination rate, while at room temperature (RT) singlet transitions are dominant. For this last, at high temperatures no information can be extracted due to important non-radiative recombinations. Field-matter interactions can deeply modify the spontaneous emission rate (Γr) of Si-ncs, when these are coupled to optical cavity modes; the presence of large photonic density of states shortens the radiative lifetime, τr (~Γr−1 ), of emitters due to Purcell effect [4]. From a general point of view, Si-ncs are not ideal candidates for studying the Purcell effect, the possibility to measure emission rate enhancement, ϵ, would provide useful information on the effective average linewidths through which Si-nc emitters are coupled to resonator modes. In this contribution we report on direct estimation of Purcell enhancement for Si-ncs coupled to WG modes of a microdisk resonator through RT time-resolved measurements. The emission lifetimes (τ) of Si-ncs are measured to be up to 70% shorter at wavelengths resonant with the WGMs (coupled) with respect to τ’s probed at out-ofresonance wavelengths (uncoupled). Such a difference in τ leads to fairly modest Purcell factors as expected in the bad emitter regime, when the emitter homogeneous linewidth Δωem is larger than that of the cavity (Δωcav). We show that such estimated linewidths imply upper limits for cavity quality factors, Q, that could be utilized for efficient Purcell enhancement in Si-ncs. Moreover, we predict that larger Purcell factors can be still probed using resonators with ultra-small cavity mode volumes. Finally, the used method can be easily applied to other systems where fundamental linewidths are unknown or which are in the bad-coupling regime.
OSA / IPR/PS 2010 a209_1.pdf IMA5.pdf
2.
Results and Discussion
Different active WGM resonators (flat μ-disks, Fig. 1(a), right) and bent (μ-kylix, Fig. 1(a), left)) with embedded Sinc emitters have been fabricated and tested in both static and time-resolved micro-PL experiments.
Fig.1 Panel (a) Scanning electron micrographs (SEM) of Si-nc-based WGM resonators: (left) micro-kylix and (right) flat disk. (b) The respective WGM emission spectra and extracted quality factors.
Purcell factor,
FP , represents the cavity figure-of-merit and for an ideal emitter [5] reads as
3
Q ⎛λ⎞ ⎜ ⎟ with Q being the cavity quality factor, Vm the mode volume and n the refractive index of the V 4π m ⎝n⎠ dielectric [6]. The FP is estimated through the ratio of measured PL intensities from a cavity resonance and the bulk material. Though the PL intensity is proportional to the radiative recombination rate, such an approach, however, results in overestimated FP ’s; geometrical corrections have to be seriously taken into account when the WGM cavity emission (within a small solid angle in the resonator plane) and the bulk emission (isotropic) are compared. The degree of uncertainty by which the correction factors can be estimated, allows to extract Purcell enhancement only by comparing lifetimes for coupled and uncoupled to cavity modes emitters, as previously done for III-V quantum dots. We measured PL lifetimes through time-resolved experiments using the 488 nm pump line of a kHz-modulated CW laser source. First, we measured lifetimes in spectral dips between neighboring WGM resonances, for which excitons are considered to be uncoupled to any cavity mode. The lifetimes have been extracted from fitting parameters of single stretched exponential decay functions (see the original manuscript for details, [1]). FP =
3
2
Fig.2 Left panel: Si-ncs provide isotropic emission of visible light from a WGM resonator under a laser pump. At resonant wavelengths photons emitted from close vicinity of the WGM mode (ii) can experience Purcell enhancement, while the total PL emission will include background Sinc emission from the rest of the microdisk volume as well (i). Right panel: The fitting parameter A in Eq. (1) has been defined as the PL intensity ratio of the mode, Imode, and the background, Ibase.
Next, we measured PL lifetimes at cavity peak wavelengths. Since our emitters are uniformly distributed in the resonator, the PL emission from peaks results from a contribution of (i) photons coupled to the cavity mode and (ii) a background signal of emitters uncoupled to the WGMs (leaky contribution) (Fig.2, left panel). In this scheme, the decays were fitted using a sum of two exponential functions:
[(
I (t ) I 0 = A exp − (t − t 0 ) / τ peak
)β ]+ exp[− ((t − t0 ) /τ dip )],
(1)
OSA / IPR/PS 2010 a209_1.pdf IMA5.pdf
where the term A stands for the intensity ratio of coupled/uncoupled emitters and has been determined from static PL measurements (see the explanations in Fig. 2). In Eq.(1) τ peak is the lifetime of mode-coupled emitters, while
τ dip is the average lifetime at the peak wavelength extracted from interpolated τ PL data for dips (and, thus, represents the uncoupled emitters lifetime). Figure 3 (left panel) reports an example of measured peak and dip lifetimes, where important differences can be appreciated. The extracted lifetimes at various resonances and dips, the estimated lifetime shortening and Si-nc effective linewidths at RT in a wide spectral range are summarized in Fig. 3(a), (b) and (c) respectively (refer to the original manuscript, Ref. [1], for details on estimation procedures).
Fig. 3 Left panel: An example of measured out-of-resonance (full squares, λ = 853 nm) and on-resonance (empty circles, λ = 846 nm) PL signals form the WGM resonator. The data have been fitted using single and double stretched exponential decays, respectively. Right panel: (a) Measured PL lifetimes for the emission peaks (●, ▼) and dips (○, ∇) of the WGM spectra. (b) Calculated lifetime shortening ϵ = τdip / τpeak and (c) the estimated effective linewidth of Si-ncs at room temperature.
While the difference between peak and dip lifetimes is appreciable, the resulting ratio ϵ is slightly larger than unity (Fig. 3(b)), with a maximum relative shortening (1 − ϵ) of about 70 %. Note that ϵ represents the lower limit of Purcell enhancement when non-radiative recombination rates are non-negligible, as in our case. A measured linewidth of 10 meV corresponds to emitter Q factors, Qem = ωem/Δωem, of ~200. Such low Q’s impose an upper limit to the cavity linewidth which can be efficiently exploited to couple Si-ncs to resonator modes. Larger Q-factor does not affect the radiative lifetime but simply filter out the emission. However, the Purcell enhancement can be still favored by a small mode volume of the cavity (in our resonators, for example, Vm ~ 25(λ n) 3 ). Utilizing ultra-small mode volumes up to 25-fold Purcell enhancements can be expected. 3.
References
[1] A. Pitanti, M. Ghulinyan, D. Navarro-Urrios, G. Pucker, and L. Pavesi, “Probing the spontaneous emission dynamics in Si-nc based microdisk resonators,” Phys. Rev. Lett. (in production, March 2010). [2]
L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzò and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440-444 (2000).
[3] M. Ghulinyan et al., “Whispering-gallery modes and light emission from a Si-nanocrystal-based single microdisk resonator,” Opt. Express 16, 13218 (2008); R.-J. Zhang, S.-Y. Seo, A.P. Milenin, M. Zacharias and U. Gösele, “Visible range whispering-gallery mode in microdisk array based on size-controlled Si nanocrystals,” Appl. Phys. Lett. 88, 153120 (2006); T. J. Kippenberg, A. L. Tchebotareva, J. Kalkman, A. Polman, and K. J. Vahala, “Purcell-factor-enhanced scattering from Si nanocrystals in an optical microcavity,” Phys. Rev. Lett. 103, 027406 (2009). [4]
E.M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
[5] The ideality condition implies that: (i) the emitter and the cavity resonances are spectrally tuned and Δωem «Δωcav, (ii) the emitted field is aligned with that of the cavity and placed in a cavity-field anti-node, (iii) non-radiative recombination rate is negligible. [6] J.M. Gérard et al., “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81, 1110 (1998). [7] We note, that the stretched exponential decay is a peculiarity of the bad emitter regime, whereas in the limit of Δωem « Δωcav, such as in the case of III-V quantum dots, usually single exponentials are observed.
