Quantification of Free-Carrier Absorption in Silicon ... - ACS Publications

Oct 1, 2008 - We present a highly sensitive and accurate microcavity-based technique to quantify the free-carrier absorption (FCA) cross-section of...
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NANO LETTERS

Quantification of Free-Carrier Absorption in Silicon Nanocrystals with an Optical Microcavity

2008 Vol. 8, No. 11 3787-3793

Rohan D. Kekatpure and Mark L. Brongersma* Geballe Laboratory of AdVanced Materials, Stanford UniVersity, Stanford, California 94305 Received July 15, 2008; Revised Manuscript Received September 11, 2008

ABSTRACT We present a highly sensitive and accurate microcavity-based technique to quantify the free-carrier absorption (FCA) cross-section of semiconductor quantum-dot ensembles. The procedure is based on measuring the pump-intensity-dependent broadening of the whispering gallery modes (WGMs) of microdisk resonators. We have applied this technique to determine the FCA cross-section of Si nanocrystals (Sincs) in the visible-near-infrared wavelength range. Our procedure accounts for the size distribution effects by including the measured wavelength dependence of the excitation cross-section and the decay rate of photoexcited carriers in the analysis. By monitoring the WGM widths at various wavelengths in the 700-900 nm wavelength range, we found that the FCA cross-section follows an approximately quadratic wavelength dependence. The magnitude of the FCA cross-section of Si nanocrystals was determined to be a factor of 7 higher than that in bulk Si. For this reason, these findings have important implications for the design of Si-based lasers and all-optical switching devices in which FCA plays a critical role.

Whereas silicon is the dominant material in todays semiconductor industry, its indirect band gap and weak nonlinear optical effects have hampered the realization of active optical components.1,2 The development of new Si nanocrystal-based light-emitting materials (Si-ncs)2-4 has recently led to the observation of optical gain, and the realization of an electrically pumped laser seemed within reach.4-6 Si-ncs can also serve as broadband sensitizers for rare-earth ions,7,8 opening up the possibility to obtain gain at a variety of other important telecom wavelengths (e.g., Er emits at 1.5 µm). Despite the promising demonstrations of rare-earth sensitization, a laser based on this class of materials has not yet been demonstrated and a deeper understanding of the intrinsic loss processes in these materials is clearly needed. Free-carrier absorption (FCA) of signal photons is one of the main mechanisms known to severely limit (or even preclude) optical gain in semiconductor media.4,9 FCA is a momentum-conserving, phonon-assisted process in which a charge carrier is promoted from one electronic state to another within the same band.10 In confined systems, FCA is sometimes also called confined-carrier absorption (CCA).11 In direct bandgap semiconductors, the absorption losses due to FCA are typically small compared to the optical gain attained in these materials.4,9 In stark contrast, FCA often dominates other weak optical processes in indirect bandgap devices. In fact, Dumke theoretically ruled out the possibility of achieving net optical gain from bulk Si.12 In order to assess * Corresponding author, [email protected]. 10.1021/nl8021016 CCC: $40.75 Published on Web 10/01/2008

 2008 American Chemical Society

the possibility of attaining net gain from Si-nc based materials (potentially with Er), it is important to determine the relevant gain and loss cross-sections for these materials. Since the processes of stimulated emission and FCA both increase in proportion to the number of excess carriers,9 a net gain cannot be achieved by merely increasing the excitation intensity. Eventually, the outcome of the competition between these processes critically depends on the relative magnitude of their cross-sections. Before we continue with a description of a sensitive technique to quantify FCA, it is important to note that the process of FCA is not always undesirable. Although deleterious for lasers, FCA and free-carrier dispersion have enabled gigahertz-speed, all-optical, and electro-optic modulation in bulk crystalline and polycrystalline silicon.13-16 Because of quantum confinement effects and a high surface-to-volume ratio, the momentum-relaxation and scattering mechanisms for the confined charge carriers in nanocrystals differ markedly from those of their bulk counterparts.17 We can thus expect there to be a significant modification in the FCA of carriers in confined nanostructures relative to those in bulk. If stronger FCA in Si nanocrystals can be attained, it could lead to a new generation of compact, low-power Si-compatible all-optical switches. In light of these arguments, the development of a convenient and highly precise way of quantifying FCA in Si-ncs is becoming increasingly important. In the following, we demonstrate a very general microcavity-based procedure to determine the FCA cross-sections

in quantum-dot ensembles. Although illustrated here for Sincs, this procedure is applicable to any luminescent bulk or quantum-dot material system. In order to quantify the wavelength-dependent free-carrier absorption cross-sections in Si-ncs, we analyze the photoluminescence (PL) emerging from the microcavity. Such PL exhibits microcavity resonances, whose width is directly linked to the optical losses in the cavity.18 The cross sections for FCA (and potentially other absorption processes that are dependent on the number of excited carriers) can be quantified by monitoring the increase in the cavity linewidth with increasing excitation intensity. This type of microcavity-based measurement offers several advantages over those utilizing planar or ridge/rib waveguides, including the following: (1) The resonance line width of the cavity provides a direct measure of the intrinsic propagation losssi.e., we do not have to infer the FCA loss by subtracting the coupling losses from the total loss. (2) The measurement is differential, implying that the evaluation of FCA relies on measuring a slope rather than absolute values of the optical loss. This ensures that different resonators, which could have different absolute losses, still yield the same value for the FCA cross-section. (3) Compact (micrometer-sized) resonators are more amenable to uniform excitation by circular Gaussian laser spots. In comparison, straight waveguide measurements typically require the use of several-hundred-micrometer-long, highly eccentric elliptical beams for uniform illumination. (4) A microcavity provides a longer length for the interaction between light and the absorbing medium. Therefore the sensitivity of a cavity-based measurement is resonantly enhanced over conventional, nonresonant, straight waveguide-based measurements. (5) By an appropriate choice of size, resonators can be designed to yield a large number of peaks within the Si-nc emission bandwidth, making it possible to obtain the wavelength dependence of the FCA cross-section in a single experiment. The last two aspects clearly highlight the advantages of microcavity-based measurements over the more conventional transient-absorption (TA) technique.19 TA measurements are typically performed using a probe laser which makes a single pass through the sample in a normal direction thereby interacting with the material for a few hundred nanometers. Use of a probe laser in TA measurements also restricts the wavelength range over which the FCA information can be obtained to a few nanometers. In contrast, a cavity-based measurement often allows for resonantly-enhanced interaction lengths and yields FCA parameters over a wavelength range of several hundred nanometers. For our measurements, we fabricated small (5 µm diameter), pedestal-supported microdisks with embedded Si-ncs. The nanocrystal-doped films constituting the microdisks were synthesized by plasma-enhanced chemical vapor deposition (PECVD) with 2% silane (diluted in nitrogen) and nitrous oxide gases on a 〈100〉 oriented crystalline silicon substrate. The deposition temperature and pressure were chosen at 350 °C and 650 mT, respectively. Thereupon, the films were annealed at 1100 °C for 1 h in an ultrapure nitrogen environment to induce Si-nc precipitation. To pattern the 3788

microdisks, 5 µm diameter circular areas were exposed using electron-beam lithography. The resist patterns were then transferred onto the nanocrystal-doped films by reactive-ion etching in NF3 plasma using the resist as masking layer. The silicon underneath the disks was etched in a 25% tetramethylammonium hydroxide (TMAH) solution to form the pedestal. The devices were finally cleaned in a 4:1 solution of sulfuric acid and hydrogen peroxide prior to optical testing. Figure 1a shows the scanning electron microscope (SEM) image of a typical microdisk used in our study and a highresolution transmission electron microscopy (HR-TEM) image of the Si-ncs inside the disk. When embedded in a microdisk, the emission of the nanocrystals is enhanced at wavelengths that fit an integer number of wavelengths along the disk circumference. At these wavelengths, light circulates around the circumference of the disk similar to the whispering gallery modes (WGMs) of circular acoustic cavities that have brought about this nomenclature. Figure 1b shows the calculated electric field profile of a typical transverse electric (TE) mode supported by these microdisks in the visible/nearinfrared wavelength range. For optical testing, the microdisk devices were mounted on a fine-travel XYZ translation stage and were uniformly illuminated by the 488 nm line of an argon-ion laser through a 10× microscope objective. The laser excitation spot was aligned to the microdisk by imaging the latter with a CCD camera. Our numerical calculations indicate that the leakage radiation from the resonant modes is primarily directed along the plane of the microdisk.18 Therefore, the collection optics were placed at right angles to the excitation optics and aligned to collect the resonant emission from the microdisk edge. Figure 1c depicts the schematic of our measurement setup used to optically pump the disks from the top and to collect the nanocrystal emission from the side. The emitted light from the disk diverges rapidly and is collimated by a 2-in. diameter plano-convex lens and then routed to a spectrometer for spectral analysis. A polarization filter placed in the light collection path can selectively suppress the TE or transverse magnetic (TM) mode emission and makes closely spaced resonant peaks more easily resolvable for data analysis. Unpatterned films with Si-ncs display a broad PL spectrum in the visible and near-infrared (NIR) wavelength range (Figure 1d). In a microdisk, the smooth spectrum of the nanocrystals transforms into a set of discrete, sharp peaks at wavelength obeying the WGM resonance condition. The widths of these resonant peaks provides a direct measure of the optical losses experienced by the circulating light (see Supporting Information section 2 and ref 18) and can be utilized for direct quantification of the FCA cross-section, as shown below. Figure 2a shows the excitation-intensity-dependent resonant PL spectra of two selected peaks. An increase in the excitation intensity brings about a broadening of the resonance peaks along with a shift in their center wavelengths. We will show that the broadening is simply explained by an increase in the populations of the excited electrons and holes that can give rise to a FCA that exceeds the intrinsic propagation losses at low excitation intensity. The observed wavelength shift can be attributed to the thermo-optic effect. Nano Lett., Vol. 8, No. 11, 2008

Figure 1. (a) A high-resolution transmission electron microscope image of a Si nanocrystal inside the 5 µm diameter silicon-rich oxide (SRO) microdisk resonator structure shown in the accompanying scanning electron microscope image. The nanocrystals are uniformly distributed throughout the volume of the disk. (b) Finite-element-method calculations showing the electric field intensity |E|2 of a whispering gallery mode (λ ) 750 nm) of the microdisk shown in (a). The arrow indicates the polarization direction of the dominant electric field. (c) The microphotoluminescence measurement setup used for optical measurements. (d) Photoluminescence spectrum of Si nanocrystals taken from an unpatterned film (red spectrum) and a 5 µm diameter microdisk (blue spectrum).

Using the known value for the thermo-optic coefficient of SiO2, the temperature increase at the highest excitation intensities was found to be ∼50 °C (see Supporting Information section 3). To quantify the optical losses, we extracted the FWHM of the resonance peaks by fitting them with a Lorentzian function. Three different regimes of excitation-intensitydependent optical loss can be seen in Figure 2b, which plots the peak width (FWHM) at 895 nm versus the pump intensity, Ip. The FWHM initially remains constant with increasing Ip until Ip ) 0.3 kW/cm2 after which it increases following a I1/3 p dependence. The increase in FWHM finally saturates for Ip > 40 kW/cm2. The FWHM at low excitation intensities is indicative of the optical loss in an unexcited cavity. This loss arises from excitation-intensity-independent loss processes, including band-to-band absorption in nanocrystals, Mie scattering, and roughness scattering by the microcavity sidewall imperfections.18 As we further increase Ip, FCA increases and becomes a significant fraction of the total loss. The cube-root dependence of the FWHM on the excitation intensity is consistent with the emergence of fast, three-particle Auger recombination processes, which limit the number of carriers that may be excited in the nanocrystals.19,20 For Ip ∼ 40 kW/cm2, Auger processes start to dominate the carrier recombination rate as the excited electron-hole-pair concentration is about one per nanocrystal (based on a rate equation model presented below and detailed in the Supporting Information section 3). These fast Auger Nano Lett., Vol. 8, No. 11, 2008

processes result in the saturation of the ∆FWHM for excitation intensities exceeding 40 kW/cm2. In order to analyze the losses from just FCA at the different wavelengths, the FWHM at the lowest excitation intensity is subtracted from the measured FWHM at each pump intensity. Figure 2c shows the increase in the FWHM (∆FWHM) as a function of the excitation intensity for three selected wavelengths. At all wavelengths, a fast initial rise is observed, followed by a slower increase at high excitation intensities. In order to extract the FCA cross-section from the broadening of the resonant PL spectra, one requires knowledge of the total number of the excited electrons and holes in the entire nanocrystal ensemble as a function of the excitation intensity. We obtain this information in three steps. First, we determine the nanocrystal size distribution (density of nanocrystals as a function of their diameter) from the measured the chemical composition of our films21 and the relationship between the nanocrystal diameter and its PL emission wavelength. This calculation and its underlying assumptions are reported in ref 18 and also reproduced in the Supporting Information, section 2. In particular, we note that our calculated nanocrystal distribution shows good agreement with the detailed materials studies employing energy-filtered TEM techniques.22-25 The calculated nanocrystal diameter at the PL peak wavelength also matches well with the average nanocrystal size measured from our TEM images (Figure 1a). In the second step, we calculate the occupancy f(λ, Ip) of an excited nanocrystal as a function of the pump intensity. 3789

Figure 2. (a) PL spectrum exhibiting a shift and broadening of the resonant peaks in the photoluminescence spectrum of Si-nanocrystaldoped microdisk resonator with increasing excitation intensity. Only a selected wavelength range between 850 and 900 nm is displayed for clarity. (b) The full width at half-maximum (FWHM) of the 895 nm peak as a function of the excitation intensity, Ip, on a log x-scale. (c) The increase in the FWHM (∆FWHM) with increasing excitation intensity for three different resonant peaks across the photoluminescence spectrum of Si nanocrystals. (d) Calculated total free-carrier density as a function of the excitation intensity. The error bars in (b) and (c) indicate the uncertainty in fitting the resonant peaks with a Lorentzian function.

The occupancy of a nanocrystal is defined as the average number of electron-hole pairs present in a nanocrystal (having an emission wavelength λ) as a result of continuouswave pumping with an intensity Ip. The occupancy is obtained by solving the steady-state rate equation for an indiVidual nanocrystal: 0)

df(λ, Ip) σex(λ)Ip f(λ, Ip) f(λ, Ip)3 ) dt pωp τ1(λ) τA(λ)

(1)

Here, pωp ) 2.54 eV is the excitation energy (488 nm line of an Ar-ion laser), σex(λ), τ1(λ), and τA(λ) are, respectively, the excitation cross section, the first-order decay time, and the Auger recombination time of a nanocrystal having an emission wavelength λ. If the ensemble was comprised of identically sized nanocrystals, the knowledge of these parameters at a single wavelength would have been sufficient to determine the excited carrier population. However, a typical CVD-synthesized Si nanocrystal ensemble has a broad size distribution.22,23 An accurate estimation of the occupancy therefore needs the dependence of σex and τ1 on the emission wavelength of the nanocrystal. We have obtained the wavelength dependence of σex and τ1 by the well-known technique of measuring the rise and fall times of the transient photoluminescence.26 The measurement was carried out at five wavelengths between 700 and 900 nm and a straight line interpolation was used for the intermediate points. The measurement procedure and the results are reported in detail 3790

in Supporting Information section 1. The third term in eq 1 models Auger recombination in which an excited electron-hole pair recombines and gives off its energy to another excited carrier in the same nanocrystal. This is process occurs more frequently at high excitation intensities, where it limits the carrier density. As mentioned before, it is the Auger process that causes the saturation behavior in the plot of the FWHM versus the excitation intensity shown in Figure 2c. Owing to the Ip1/3 dependence of the saturation of the FWHM, we model the Auger recombination by a three-particle process by assuming that τA-1 ) CA(2/V)2 where CA is the Auger recombination coefficient and V ) 4πR3/3 is the volume of the nanocrystal with a radius R.27 Because of a tight overlap of electron and hole wave functions and relaxed momentum conservation requirements,17,19 the magnitude of CA in nanocrystals can exceed the bulk value. However, since recent transient absorption measurements in Si nanocrystal films have yielded CA values similar to bulk Si, we have used the bulk Si CA values for analysis of our data.19 In the final step, the total free-carrier density, nFC, at a given pump intensity Ip is determined by summing of the occupancies of all the nanocrystals present in the ensemble nFC(Ip) )

∫

λ)λmax

λ)λmin

f(λ, Ip)F(R)

dR dλ dλ

(2)

where λmin and λmax are the wavelength limits of the PL spectrum and F(R) is the size distribution as calculated in Nano Lett., Vol. 8, No. 11, 2008

∆FWHM )

Figure 3. (a) Increase in the full width at half-maximum (∆FWHM) plotted against the total free-carrier density for the three wavelengths shown in Figure 2. The dotted lines indicate the straight-line fits expected according to eq 1. The error bars represent the uncertainty in fitting the resonant peaks with the Lorentzian function. (b) FCA cross-section for an electron-hole pair in a nanocrystal, as extracted from the slopes of the straight lines in (a) (blue diamonds) and the power-law fit (blue dotted line). The other lines are the bulk FCA cross-section for electrons (green, dotted), holes (yellow, dotted), and their sum (red, solid).

Supporting Information section 2.18 The total free-carrier concentration calculated according to eqs 1 and 2 using the experimentally measured, wavelength-dependent values of σex(λ) and τ1(λ) is plotted in Figure 2d as a function of Ip. It is observed that the calculated nFC shows the same trend with the excitation intensity as ∆FWHM in Figure 1c providing strong evidence that the pump-induced resonant peak broadening is indeed due to the free-carrier absorption. The determination of the total electron-hole pair (EHP) concentration directly impacts the calculation of the FCA cross-section. Most studies on determination of the FCA cross-section estimate this to the first order by making assumptions like one EHP per nanocrystal or one EHP per absorbed photon. Our calculation shows a possible way to refine the estimate of the EHP concentration to the second order by taking into account information on the Si-nc size distribution. The FCA loss per unit length, RFCA, can be related to nFC through the FCA cross-section: RFCA ) σFCAnFC. At a wavelength λ, the increment in the FWHM is proportional to the pump-induced FCA loss and is given by Nano Lett., Vol. 8, No. 11, 2008

λ2Γconf(λ) λ2Γconf(λ) RFCA(λ) ) σ (λ)nFC(λ) (3) 2πneff(λ) 2πneff(λ) FCA

where Γconf and neff are the confinement factor and the effective index of the resonant mode, respectively (see Supporting Information section 2). The latter quantities were obtained as a function of wavelength from full-vectorial field calculations of the microdisk resonator modes such as shown in Figure 1b. The linear relationship between ∆FWHM and nFC suggested by eq 3 is indeed observed experimentally. Figure 3a shows the linear fits to the ∆FWHM data from Figure 2c plotted against the nFC data from Figure 2d. According to eq 3, the slope of these straight lines is proportional to the FCA cross-section σFCA at the different wavelengths. The wavelength dependence of the FCA cross-sections between 700 and 900 nm was obtained by analyzing the pumpinduced broadening of the several resonant peaks in that wavelength range. Figure 3b shows the FCA cross-sections extracted from Figure 3a in this fashion. In the measured wavelength range, the FCA cross-section follows a quadratic dependence on the wavelength: σFCA(λ) ) (5 ( 2) × 10-9λ2.0(0.3 cm2. The quadratic dependence of the FCA crosssection between 700 and 900 nm is similar to bulk crystalline Si28 and to porous Si nanocrystals observed by Maly et al.29 For comparison, Figure 3b also shows electron, hole, and the total FCA cross-section in bulk silicon according to ref 13. The FCA cross-section for an electron-hole pair in a nanocrystal is seen to be approximately 7 times higher than that for individual electrons and holes in bulk crystalline silicon over the measured wavelength range. The enhanced FCA in nanocrystals can be explained qualitatively by the Drude model, which yields the following expression for the FCA cross-section:30 σFCA(λ) )

1 e2λ2 2 3 τ 4π ε0c m*n s

(4)

Here, c and ε0 are, respectively, the velocity of light in vacuum and the permittivity of the free space, e is the electron charge, n is the refractive index, m* is the carrier effective mass, and τs is the average scattering time of charge carriers in the semiconductor medium. According to eq 4, σFCA is expected to scale inversely with τs. The mean scattering time for carriers in bulk silicon can be estimated from their mobility µ as τsbulk ) µm*/e and is 2 × 10-13 s for electrons. Since the nanocrystal diameter is much smaller than the carrier mean-free-path, the field-driven motion of the carriers confined in a nanocrystal is constrained by its interface with the host matrix. The scattering time in a nanocrystal can therefore be estimated by calculating the time it takes for a carrier traveling at a thermal velocity to traverse the diameter of the nanocrystal. The thermal velocity, Vth, of electrons at a temperature T is Vth ) (3kBT/m*)1/2, where kB is the Boltzmann constant. This yields a scattering time τsnc in a nanocrystal to be 2 × 10-14 s for electrons, about an order of magnitude less than that in the bulk. The ratio τsbulk/τsnc thus provides a good qualitative explanation for the enhancement in the FCA cross-section in nanocrystals over that in bulk Si. Any further refinement of this estimate will have to account for the size distribution of the nanocrystals in addition to a full quantum-mechanical calculation of the 3791

phonon-assisted intraband transitions in Si nanocrystals surrounded by an amorphous oxide host matrix. The increased magnitude of FCA in Si nanocrystals has important implications for several Si-based active photonic devices, including electrically pumped lasers employing Si nanostructures and all-optical switches. One of the most promising and widely studied gain mediums for an electrically pumped, Si-based, telecom wavelength laser is Si-nc sensitized, erbium-doped silica. In this system, the Er ions provide gain at 1550 nm when excited via an energy transfer from the Si-ncs. Excitation of Er ions via Si-ncs thus necessarily requires the presence of excited carriers in the Si-nc. Through detailed experiments and modeling, Pacifici et al.7 have predicted the maximum allowable total FCA cross-section for observation of optical gain at 1550 nm from the Si-nanocrystal-erbium system to be 10-18 cm2. On the basis of the magnitude and the quadratic trend in our experiments, the value of σFCA at 1550 nm is predicted to be 8 × 10-17shigher by almost 2 orders of magnitude than the allowed maximum. This necessitates a serious reconsideration of various schemes aimed at utilizing the charge injection into Si nanocrystals and subsequent energy transfer to erbium atoms for a Si-based telecom-wavelength laser. Electrically pumped lasers based on just Si-ncs (and no Er) will suffer from the same free-carrier absorption losses. New approaches should be pursued aimed at reducing the modal overlap with Si nanostructure containing regions or increasing the transfer rate from the nanostructures to Er.7 Pulsed charge injection may provide another way to reduce losses associated with the excited carrier concentration.5 Although a serious concern for lasers, the stronger freecarrier effect in silicon nanocrystals can be used advantageously to lower the switching energies and to increase the operating speed in all-optical switching devices.15 The power efficiency can be increased as fewer excited carriers are needed for switching. Moreover, the speed of Si-based alloptical switches may be increased as well by using Si-ncs as these devices are limited by carrier diffusion/recombination. This process can be faster in nanocrystals owing to a higher surface-to-volume ratio and a potentially faster Auger recombination of excited carriers. A nanocrystal-based alloptical switch also offers several design and processing advantages. The low refractive index of Si-rich oxide results in longer evanescent tails of the optical mode out of the resonators, which puts less stringent fabrication constraints on all-optical switching/modulation devices (e.g., disk/ring resonator, Bragg reflectors). Additionally, the nanocrystalbased devices are fabricated on deposited thin films, i.e., they do not require crystalline Si on oxide. This aspect will allow more freedom in the choice of substrates and can potentially reduce the fabrication costs of Si-based all-optical switches. In conclusion, we have demonstrated the use and benefits of optical microcavities to quantify free-carrier absorption in quantum dot ensembles. It was found that the magnitude of the FCA cross-section in Si-ncs is significantly higher than that in bulk Si, having important consequences for the design of Si-based lasers, modulators, and switches. Most generally, this work demonstrates the usefulness of microcavities as 3792

convenient experimental platforms to accurately quantify fundamental optical loss processes. Acknowledgment. Authors thank A. Hryciw, A. Guichard, and R. Shenoy for helpful discussions. This work was sponsored by the Si-based Laser Initiative of the Multidisciplinary University Research Initiative (MURI) under the Air Force Aerospace Research OSR Award Number FA955006-1-0470 and supervised by LTC Gernot Pomrenke. The authors acknowledge the support of the Interconnect Focus Center, one of five research centers funded under the Focus Center Research Program, a Semiconductor Research Corporation and DARPA program. Supporting Information Available: (1) Calculation of the size distribution F(R) of the nanocrystals from the stoichiometric composition of the silicon-rich oxide films and the PL spectrum, (2) derivation of the relationship between the carrier density and the FWHM of the cavity resonances, (3) analysis of the possible mechanisms that can potentially contribute to spectral shifting of cavity resonances, and (4) estimation of the maximum temperature reached during the measurements and analysis of the thermal effects such as temperature-induced bandgap narrowing on the broadening of cavity resonances.This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Miller, D. Proc. IEEE 2000, 88, 728–749. (2) Polman, A. Nat. Mater. 2002, 1, 10–12. (3) Godefroo, S.; Hayne, M.; Jivanescu, M.; Stesmans, A.; Zacharias, M.; Lebedev, O. I.; Van Tendeloo, G.; Moshchalkov, V. V. Nat. Nano 2008, 3, 174–178. (4) Pavesi, L.; Dal Negro, L.; Mazzoleni, C.; Franzo`, G.; Priolo, F. Nature 2000, 408, 440. (5) Walters, R. J.; Bourianoff, G. I.; Atwater, H. A. Nat. Mater. 2005, 4, 143. (6) Presti, C. D.; Irrera, A.; Franzo`, G.; Crupi, I.; Priolo, F.; Iacona, F.; Stefano, G.; Piana, A.; Sanfilippo, D.; Fallica, P. G. Appl. Phys. Lett. 2006, 88, 033501. (7) Pacifici, D.; Franzo`, G.; Priolo, F.; Iacona, F.; Dal Negro, L. Phys. ReV. B 2003, 67, 245301. (8) Izeddin, I.; Moskalenko, A. S.; Yassievich, I. N.; Fujii, M.; Gregorkiewicz, T. Phys. ReV. Lett. 2006, 97, 207401. (9) Bhattacharya, P. Semiconductor optoelectronic devices, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1996. (10) Ridley, B. K. Quantum processes in semiconductors, 4th ed.; Oxford Science Publications: New York, 2000. (11) Elliman, R. G.; Forcales, M.; Wilkinson, A. R.; Smith, N. J. Nucl. Instrum. Methods Phys. Res., Sect. B 2007, 257, 11–14. (12) Dumke, W. P. Phys. ReV. 1962, 127, 1559–1563. (13) Soref, R.; Bennett, B. IEEE J. Quantum Electron. 1987, 23, 123– 129. (14) Xu, Q.; Schmidt, B.; Pradhan, S.; Lipson, M. Nature 2005, 435, 325– 327. (15) Almeida, V. R.; Barrios, C. A.; Panepucci, R. R.; Lipson, M. Nature 2004, 431, 1081–1084. (16) Liu, A.; Jones, R.; Liao, L.; Samara-Rubio, D.; Rubin, D.; Cohen, O.; Nicolaescu, R.; Paniccia, M. Nature 2004, 427, 615. (17) Kovalev, D.; Heckler, H.; Ben-Chorin, M.; Polisski, G.; Schwartzkopff, M.; Koch, F. Phys. ReV. Lett. 1998, 81, 2803–2806. (18) Kekatpure, R. D.; Brongersma, M. L. Phys. ReV. A 2008, 78, 023829. (19) Troja´nek, F.; Neudert, K.; Bittner, M.; Maly´, P. Phys. ReV. B 2005, 72, 075365. (20) Klimov, V. I.; Mikhailovsky, A. A.; Leatherdale, C. A.; Bawendi, M. G. Science 2000, 287, 1011. (21) Tewary, A.; Kekatpure, R. D.; Brongersma, M. L. Appl. Phys. Lett. 2006, 88, 093114. (22) Iacona, F.; Franzo`, G.; Spinella, C. J. Appl. Phys. 2000, 87, 1295– 1303. Nano Lett., Vol. 8, No. 11, 2008

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