Demonstration of a Ge/GeSn/Ge Quantum-Well Microdisk Resonatoron Silicon: Enabling High-Quality Ge(Sn) Materials for Micro- andNanophotonicsRobert Chen,*,† Suyog Gupta,† Yi-Chiau Huang,‡ Yijie Huo,† Charles W. Rudy,† Errol Sanchez,‡

Yihwan Kim,‡ Theodore I. Kamins,† Krishna C. Saraswat,† and James S. Harris†

†Department of Electrical Engineering, Stanford University, Stanford, California 94305, United States‡Applied Materials Inc., Sunnyvale, California 94085, United States

*S Supporting Information

ABSTRACT: We theoretically study and experimentally demon-strate a pseudomorphic Ge/Ge0.92Sn0.08/Ge quantum-well microdiskresonator on Ge/Si (001) as a route toward a compact GeSn-basedlaser on silicon. The structure theoretically exhibits many electronicand optical advantages in laser design, and microdisk resonators usingthese structures can be precisely fabricated away from highly defectiveregions in the Ge buffer using a novel etch-stop process.Photoluminescence measurements on 2.7 μm diameter microdisksreveal sharp whispering-gallery-mode resonances (Q > 340) withstrong luminescence.

KEYWORDS: Germanium tin, silicon photonics, nanophotonics, microdisk resonators, lasers

The effort toward developing an efficient group-IV laser hasbeen driven by a motivation to monolithically integrate a

full family of photonic devices on a silicon (Si) platform for on-chip optical communication. High-performance active devices,such as photodetectors1 and optical modulators,2 have alreadybeen developed to help reach this goal; however, the integratedlight source has been challenging to develop due to theindirect-bandgap nature of group-IV semiconductors. Recentefforts have utilized germanium (Ge), which is a nearly direct-bandgap material with its lowest indirect L-valley just 136 meVbelow the direct Γ-valley in the conduction band (CB).Theoretical and experimental works have shown that the Gebandstructure can be modified to make direct-gap emissionmore favorable by using in-plane tensile strain3−6 or uniaxialstrain,7 and other efforts to create carrier inversion for lasingcan be achieved by donor doping.8,9 Recently, the combinationof slight strain and high doping yielded the first electricallyinjected, Ge-based laser using an indirect-bandgap gainmedium.10 However, the high lasing threshold of ∼280 kA/cm2 and short operational lifetime limit its practicality. Newtechnologies and designs must be developed to reduce thethreshold of Ge-based lasers.The germanium−tin (GeSn) alloy has the ability to greatly

improve the performance of Ge-based lasers by offering atunable bandstructure. Many theoretical investigations of thealloy bandstructure11−16 predict a direct-bandgap material withthe substitutional incorporation of Sn in Ge with a crossoverpoint ranging from 2 to 25% Sn. More recently, experimental

investigations17−21 have determined this crossover point tooccur between 6.5 and 11%. This addresses the prominent issueof quantum efficiency for light emission with indirect-bandgapGe, which has a 4-fold degenerate, indirect L-valley. Any efforttoward reducing the energy difference between the direct Γ-valley and the indirect L-valley provides vast improvements inquantum efficiency. Theoretical investigations of Ge-basedlasers with Ge or GeSn as the gain medium, either in bulk8,22 orin quantum wells (QW) with SiGeSn barriers23−27 suggest thatreduced laser thresholds can be achieved. These systems,however, require strain-relaxed GeSn, which is difficult toachieve due to the lack of lattice-matched buffer templates.Recent efforts in developing relaxed GeSn films would be usefulfor realizing such structures. However, these techniquesrecrystallize amorphous materials28 or require post-growththermal annealing,29−31 which are likely to result in defects andnonuniformity or Sn precipitation leading to reducedefficiencies for optical emission. High-temperature annealingto reduce defects may have limited benefits in the thermallymetastable GeSn alloy with a solid solubility of less than 1% Snin Ge.32 It is expected that the highest-quality GeSn materialwould be grown pseudomorphic (fully strained) to its templateor buffer layer with thickness below the critical thickness (40

Received: July 29, 2013Revised: November 22, 2013

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nm for 8% Sn in Ge on a Ge template33,34) to preventrelaxation from misfit or threading dislocations.In this Letter, we demonstrate that pseudomorphic Ge/

GeSn/Ge QWs (GeSn-QW) can improve the performance ofGe-based lasers in several ways. In this design, we considermaterials and stacks that can be achieved to high quality bycombining state-of-the-art GeSn-growth technology withrelaxed-Ge growth technology. First, we show how reducedcarrier densities for transparency can be realized by using 8% Sn(from this point forward, [x*100]% Sn refers to Ge1−xSnx)grown pseudomorphic to Ge in GeSn-QW structures. Next, weexperimentally explore the pseudomorphic GeSn-QW designon a Si substrate with a thick Ge buffer layer (Ge-on-Si) inbetween. The GeSn-QW is fabricated into a compact microdiskresonator using a recently developed selective etch of Ge thatallows for precise control in defining a single-transverse-modemicrodisk away from highly defective regions in the Ge buffer

for improved material quality in the active region. Thefabrication method presented in this work exemplifies howthis etch technology can be used to create Ge(Sn)-basedmicro/nanophotonic structures. Using microphotolumines-cence (μPL) in a surface-normal pump/collection configu-ration, we demonstrate for the first time a single-transverse-mode GeSn-based microdisk resonator on Si with greatlyenhanced luminescence efficiency in whispering-gallery-mode(WGM) resonances.

Predicted Advantages in Pseudomorphic GeSn on Geand 20 nm GeSn Quantum Wells Compared to Bulk Gein Laser Design. The motivation behind strain-relaxed GeSnis that strain plays an important role in the bandstructure andaffects the quantum efficiency of the alloy. Figure 1 illustratesthe effects of both Sn alloying and strain on the bandstructureof bulk Ge. With sufficient amounts of Sn (roughly 7%according to recent experimental results19−21), the alloy

Figure 1. A schematic of Sn alloying on the bandstructure of Ge. (a) Bulk Ge is an indirect-bandgap material with its L-valley 136 meV below the Γ-valley. (b) Adding substitutional Sn to the Ge lattice lowers the Γ- and L-valleys in energy, with Γ lowering faster than L. Furthermore, theapplication of strain can also change the bandstructure. (c) Tensile strain brings Γ down even further while lifting the LH band. (d) Compressivestrain has the opposite effect of tensile strain and makes the alloy indirect bandgap again while lifting the HH band. The latter is the case forpseudomorphic GeSn grown on Ge.

Figure 2. Results from deformation-potential and gain calculations for GeSn grown pseudomorphic on Ge. (a) The four critical bandedges of GeSncompressively strained to Ge are shown as a function of Sn content. GeSn does not become direct bandgap due to the compressive strain, but type-Iconfinement with respective bands in Ge (energy level in Ge denoted by dashed lines) is predicted. (b) A reduction in ΔEΓ‑L is also predicted, whichfavors increased population in the direct Γ-valley and improved quantum efficiency. Additionally, HH−LH splitting occurs due to biaxial strain. Theenergy differences shown are for 8% Sn. (c) The threshold carrier density for transparency (gain minus free-carrier absorption equal to zero) for a 20nm GeSn-QW is shown to reduce by a factor of ∼5 with 8% Sn. (d) With 8% Sn, extremely high net material gain (gain minus free carrierabsorption) can be achieved for the TE mode while providing no gain for the TM mode for the two lowest bound-to-bound state (Γ1-HH1, Γ2-HH2)transitions in a 20 nm GeSn-QW. The four curves show carrier densities in GeSn ranging from 2 × 1019 to 5 × 1019 cm−3.

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becomes direct bandgap, as shown in Figure 1b. If the alloy isgrown on a lattice-mismatched buffer or substrate, the alloy willbe under biaxial tensile (Figure 1c) or biaxial compressive(Figure 1d) strain, further changing the bandstructure.Additionally, strain splits the light hole (LH) and heavy hole(HH) degeneracy in the valence band (VB). In the case ofGeSn grown pseudomorphic on Ge, the alloy is undercompressive strain (approximately 0.15% strain per percentSn added) and will not yield a direct bandgap withtechnologically interesting Sn contents (less than 15% Sn).While an unstrained or tensile-strained, direct-bandgap GeSnfilm is desired for high quantum efficiency, pseudomorphic,compressively strained GeSn has several advantages fordeveloping and engineering photonic devices. In this section,we illustrate these advantages using experimentally determinedbandgap values for GeSn and deformation-potential theory forpseudomorphic GeSn grown on a relaxed Ge buffer.The results of the deformation-potential calculations are

shown in Figure 2a and illustrate several benefits that can beachieved using pseudomorphic GeSn on Ge. The first benefit isthat the energy difference between the Γ-valley and the L-valley(ΔEΓ‑L) decreases as the Sn content increases, as seen in Figure2a,b. Under the conditions studied, GeSn never becomes directbandgap (defined as ΔEΓ‑L < 0), but ΔEΓ‑L does decrease as theSn content increases (a 74 meV decrease with 8% Sn). Thisreduction of ΔEΓ‑L is extremely important in obtaining a higherfraction of carriers in the Γ valley, reducing the threshold for aGeSn laser. Additionally, the compressive strain applied by theGe buffer helps to split the HH−LH degeneracy, furtherreducing threshold carrier densities needed for inversion. TheHH is the dominant band for hole population, which favorstransverse-electric (TE) gain strongly over transverse-magnetic(TM) gain, greatly improving efficiency in the TE lasingmode.35

Another benefit is the possibility of carrier confinement inthe GeSn region, which is ideal for developing low-thresholdlasers in double-heterostructure or QW designs. With 8% Sn,both the L- and Γ-valley minima in GeSn should be lower inenergy than their corresponding minima in Ge, and a type-Ialignment is predicted. Because of the smaller bandgap inGeSn, there will be little CB-to-VB absorption loss in Ge. Ifintegrated into a pseudomorphic GeSn double heterostructureor QW, the Ge regions can act as cladding layers in a waveguideor resonator for lasers while the center GeSn region providesgain to a guided optical mode. Furthermore, the Ge barriersmight be useful in isolating the GeSn active region from topand bottom surface states, which can be detrimental to carriernonradiative lifetimes.We extend these results by calculating the optical gain that

can be achieved with a pseudomorphic GeSn-QW on Ge with a20 nm thick GeSn well. Figure 2c demonstrates how thethreshold carrier density (equal electron and hole populations)for transparency decreases as the Sn content is increased. Thiscalculation includes free-carrier absorption (FCA) to definetransparency (material gain minus FCA equal to zero) but doesnot include any resonator loss. Presumably, this would be lowfor a high-Q resonator (loss <50 cm−1). For indirect-bandgaplasers, FCA is an important loss mechanism to consider due tothe high carrier densities needed to reach threshold. At 8% Sn,a ∼5× reduction in the threshold carrier density is predictedwhen compared to bulk Ge, which would correlate to reducedinjection current density threshold for lasers. The kink inFigure 2c at 2−3% Sn is due to a transition of peak gain to

bound-to-bound transitions. Figure 2d shows the TE and TMnet-gain spectra for pseudomorphic 8% Sn with large net TEgain from the Γ-HH transition.

Stack Design and Fabrication of Precisely DefinedGeSn Quantum Well Microdisk Resonators Using aNovel Selective Etch and Etch-Stop Layer. We explore theadvantages predicted in the previous section by considering aGeSn-QW microdisk resonator with 8% Sn and Ge barriers onSi(001). In this design, we wish to have a GeSn gain regionbetween Ge barriers all inside of a microdisk resonator, astructure that has been shown to display high Q-factorsexceeding 104 in other material systems36,37 and mimics otherextremely high-Q structures.38,39 Ideal placement of the GeSnregion is in the center of the microdisk where the confined fieldintensity will be largest for a single-transverse optical mode. Tomaintain high quality, we keep the GeSn thickness below theaforementioned critical thickness. In addition, a high-qualitygrowth template is desired for epitaxial growth of the GeSn-QW. If the GeSn-QW is grown directly on Si, it is expected thatthe GeSn gain region will be highly defective, which isdetrimental to long nonradiative carrier lifetimes and deviceperformance. To reduce defects in the GeSn active region, athick and relaxed Ge buffer can be used where multiplehydrogen anneals and continued Ge-epitaxy cycles in the bufferare performed to reduce threading dislocations (<107

cm−2);40−43 systematic improvements in the dislocation densityare seen even as total Ge thicknesses exceed 2 μm.42 Whilehigh-quality GeSn can be grown on a thick Ge buf-fer,30,33,32,44,45 the formation of a single-transverse-modemicrodisk at 2 μm wavelength requires a thickness less than∼250 nm for Ge or GeSn.46 Current Ge-based microdiskdesigns rely on a non-Ge substrate or buffer material that canbe used as a sacrificial layer to selectively undercut, such as Si47

or lattice-matched III−V materials.48,49 The former is moreinteresting for integration on Si, but growing the GeSn-QWdirectly on Si would result in a highly defective GeSn gainregion.To solve this issue, we leverage a recently developed

isotropic dry etch that has extremely high etch selectivity ofGe over GeSn using CF4 chemistry and tuned processconditions.50 In ref 50, we show that 8% Sn is not etched byCF4 chemistry (see Supporting Information Figure S1),implying that it can be used as an effective etch-stop layerwhen etching Ge. In addition, this dry etch enables bettercontrol of etch rates and etch thicknesses when compared tothe alternative wet-etch option, which has around 8:1selectivity.51 This technology allows for the growth of a thick,high-quality and relaxed Ge buffer on Si with the GeSn-QW ontop. Between the Ge buffer and GeSn-QW, a thin 8% Sn etch-stop layer can be inserted, as shown in Figure 3a. The Ge buffercan be etched to form the microdisk post while the entireGeSn-QW is protected. With dimensions and layers of themicrodisk defined epitaxially, the GeSn gain region can beprecisely placed in the center of the microdisk. A WGM nearthe edge of the microdisk will experience tight opticalconfinement due to the strong index contrast of GeSn/Geand air, and the mode will be centered on the GeSn gain foroptimized modal overlap.The material stack in Figure 3a was grown using an Applied

Materials Centura Epi reduced-pressure chemical vapordeposition (RPCVD) system with digermane (Ge2H6) andtin tetrachloride (SnCl4) precursors at reduced growthtemperatures of less than 350 °C for layers above the Ge

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buffer. All layers in the stack are nominally undoped. The initial4-μm-thick Ge buffer shown in Figure 3a provides a smooth,high-quality template for subsequent Ge and GeSn growthusing multiple hydrogen-anneal and Ge-growth steps.32,53 Aftergrowing a thin 10-nm GeSn etch-stop layer, we grow the GeSn-QW that forms the entire microdisk region. The 220-nm totalthickness of the microdisk region was designed to have a singlemode in the transverse direction for 2-μm-wavelength lightemission. A 20-nm GeSn layer is located in the center of themicrodisk to act as the gain region for this study. The materialstack was examined using X-ray diffraction (XRD) for structuralanalysis. An XRD 1D ω-2θ scan around the (004) reflectionwas used to determine that the Ge buffer layer is under 0.16%tensile strain (see Supporting Information Figure S2), which isexpected for relaxed Ge-on-Si growth.54 The reciprocal spacemap around the (224) reflection (Figure 3b) confirms that theGeSn layer is pseudomorphic to the Ge buffer. Analysis oflattice parameters extracted from XRD results in an 8% Sn layerthat is under 1.0% biaxial compressive strain on a slightly

tensile-strained Ge buffer, which are approximately the materialconditions studied in Figure 2d. We note that the GeSn etch-stop layer has the same Sn content as the GeSn gain region.Fabrication of GeSn-QW microdisks was achieved using

optical lithography to define circular patterns, anisotropic Cl2-based dry etching to form circular mesas, a silicon nitride (SiN)sidewall spacer to protect the microdisk sidewalls, and thehighly selective, isotropic CF4 etch for microdisk undercuttingand Ge-post formation. A schematic of the process steps isshown in Figure 4a. During the undercut and Ge-post-formation step with the CF4 selective etch, Ge regions in theGeSn-QW are protected by SiN (top and sides) and the 10 nmGeSn etch-stop layer (bottom). A scanning electron micro-graph (SEM) of a completed 2.7 μm GeSn-QW microdisk isshown in Figure 4b. The measured thickness of the microdisk isvery close to the designed thickness (including the etch-stoplayer). As seen in the SEM image, this process yields regionsprecisely defined by the GeSn etch-stop layer, demonstratinghow robust this selective etch and etch-stop combination is increating micro- and nanostructures in a Ge(Sn) system.Extended details of the entire fabrication process can befound in Supporting Information.

Strong Whispering-Gallery-Mode Resonances fromSurface-Normal Microphotoluminescence. The fabricatedGeSn-QW microdisks were probed using μPL with a 980 nmdiode laser focused to a ∼3 μm diameter spot size in a surface-normal pump/collection geometry. The μPL data for a 2.7 μmGeSn-QW microdisk is shown in Figure 5. Figure 5a showsclear WGM resonances in the low-energy regime, whichoverlap the broadband GeSn emission region as shown in the7.4 mW-pumped bulk (as-grown) spectra. The broadband PLcorrelates well with the bandgap predicted using thedeformation-potential calculations in Figure 2 with only slightdeviations (less than 50 meV from the lowest bound state ofthe QW, see Supporting Information). Under equivalent pumpconditions at 1.4 mW, there is strong enhancement of theluminescence from the microdisk when compared to the bulk.The sizable increase from the noise floor in the broadband PLis attributed to enhanced surface-normal scattering from themicrodisk edges, while the appearance of strong WGM peaks isattributed to stimulated emission. We estimate that the in-planeazimuthal mode number (m) is less than or equal to 12 for theresonances seen based on solutions to the Helmholtz equationin the effective refractive index (neff) approximation andassuming the index of GeSn is similar to Ge.55 The fourmarked peaks have an energy spacing of Δ1,2 = 0.0274 eV, Δ2,3

Figure 3. The material stack and its XRD reciprocal space map. (a)The GeSn-QW microdisk region is grown on a Si(001) substrate witha thick, relaxed Ge buffer in between. The thickness of the Ge bufferallows for multiple hydrogen anneal steps to enable high-qualityGeSn/Ge epitaxy on top. The GeSn-QW region is defined by insertinga 10 nm GeSn etch-stop layer which allows precise definition of themicrodisk region. (b) An XRD reciprocal space map was used toexamine the strain of the GeSn with respect to the Ge layer. Asexpected, the map around the (224) reflection shows that the GeSnlayer is fully strained to Ge, as evidenced by alignment along thepseudomorphic line. By using the well-known elastic deformation ofGe, the pseudomorphic nature of GeSn, and Vegard’s Law,52 wedetermine that the GeSn layer has around 8% Sn and is under 1.0%biaxial compressive strain.

Figure 4. The process flow for forming the GeSn-QW microdisks. (a) Microdisk formation is completed through standard optical lithography withthe use of the CF4 selective etch, which does not etch the GeSn in our samples. After the microdisk mesa is formed, a protective SiN layer is requiredto prevent etching of the Ge layers in the GeSn-QW structure during the CF4 etch. The orange layers (dark and light) represent GeSn regions. Note:These dimensions are not to scale. (b) A scanning electron micrograph of a completed 2.7 μm GeSn-QW microdisk on a Ge post.

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= 0.0267 eV, and Δ3,4 = 0.0240 eV, which we attribute toconsecutive-m TE modes. The decrease in energy spacing withincreasing energy (or decreasing wavelength) is expected sinceneff increases with increasing energy due to both the greatermode confinement and the increasing refractive index at shorterwavelengths.Power-dependent spectra are shown in Figure 5b with pump

power ranging from 0.4 to 1.4 mW. These spectra arecharacterized by an increase in the broadband and WGM PLsignal without any clear signature of lasing or dominance from asingle mode. The inset in Figure 5b analyzes the dominant peaknear 0.6 eV (∼2240 nm), showing an increase in the line widthor decrease in Q-factor under intense pumping. The Q-factorfor this particular peak reaches a maximum value of ∼340 whenpumped with 0.6 mW, then drops as the pump power isincreased. A similar trend was seen in ref 36 (attributed to FCAand sample heating). The measured Q-factor is likely to belimited by the resolution of our setup (Qmax ≈ 500 for aninfinitesimally narrow peak) due to a trade-off between signaland resolution. However, the trend in the Q-factor decrease isnot affected by this.The steady-state carrier densities based on pump power and

pump absorption calculations are high enough to reachthreshold with net material gain exceeding resonator losses (1mW of pump power corresponds to a steady-state carrierdensity of around 2 × 1019 cm−3 in a 20 nm GeSn-QW for ourmodel described in the Supporting Information and Figure S3,and a Q of 340 corresponds to an absorption loss of roughly380 cm−1 55). Despite this prediction, lasing characteristics arenot observed. Additional analysis suggests that FCA in the Gelayer (FCAGe) may provide an additional loss mechanism sincea large number of carriers are still generated in the Ge barriers.In the GeSn-QW studied here, the confined optical modeoverlaps only 10% with the GeSn layer while overlapping nearly70% with the Ge barriers. Considering the 7× difference in the

mode overlap, FCAGe dominates the GeSn gain with increasedcarrier densities (see Supporting Information Figure S4).Additional GeSn gain regions in a multiple QW structure can

enable positive net modal gain due to improved overlap withGeSn gain regions. We predict that a modal overlap greaterthan 1:2 between GeSn/Ge in similar QW structures canenable positive net modal gain using a moderate resonator (loss<150 cm−1) under moderate carrier densities (<4 × 1019 cm−3)for pseudomorphic 8% Sn. However, this may require a totalGeSn thickness greater than the critical thickness to reach the1:2 ratio and maintain a relatively thick disk for reasonableresonator Q. Tseng et al.56 and Ragan et al.57 have shown thatGeSn films with thicknesses far exceeding the theoretical criticalthickness can be grown using low-temperature molecular beamepitaxy, and thick, relaxed layers of GeSn/Ge heterostructureshave also been developed for other devices;45,58−60 whether thequality of these materials is sufficient for lasers has not beendetermined. These materials can leverage the same process flowdescribed here to enable strain-relaxed GeSn microdisks withreduced FCAGe through removal of the Ge layer completely.Additionally, it has been shown that strained layers with totalthickness beyond the critical thickness in the SiGe/Ge systemcan be achieved using superlattice or multiple QW layers,61

where the addition of Ge between strained SiGe layers canreduce the maximum relaxation energy to increase the effectivecritical thickness. This method could also be applied to theGeSn/Ge system.In summary, we have shown that pseudomorphic GeSn on

Ge has several advantages in improving the performance of Ge-based lasers, and incorporation of 8% Sn in a 20 nm GeSn-QWresults in a ∼5× reduction in the carrier density needed for netgain. We investigated pseudomorphic GeSn on Ge by designinga GeSn-QW microdisk resonator on a thick Ge buffer forimproved material quality. Microdisks were formed using arecently developed selective etch and etch-stop layer, andfabricated devices showed strong WGM resonances and greatly

Figure 5. μPL data from a 2.7 μm GeSn-QW microdisk. (a) Extremely large enhancement of the luminescence is seen for the GeSn-QW in amicrodisk, as evidenced by the comparison between the microdisk spectra and the bulk (as-grown) spectra shown for the 1.4 mW excitation (thebulk spectra is almost entirely at the noise floor). The 1.4 mW conditions are denoted by solid lines, and the 7.4 mW conditions are denoted bydotted lines. “Base” represents recorded spectra when pumping the etched Ge buffer region next to the microdisk. Strong WGM resonances are seenin the microdisk spectra, which show great luminescence enhancement. The resonances marked by red dots show relatively close energy spacings of∼0.026 eV. b) Increased pump power increases the emission intensity for both the background luminescence and the WGM luminescence. The insetshows extracted peak information for the strong peak near 0.6 eV (∼2240 nm). The integrated peak luminescence increases only linearly, and the Q-factor falls as the pump power is increased, indicating additional loss with increased pump.

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enhanced luminescence in surface-normal PL studies. Lasing inthese structures was inhibited by parasitic FCA in the Gebarriers, and improving the GeSn:Ge ratio with varioustechnologies could overcome this issue. A combination ofthese technologies with the fabrication process described hereto create microphotonic resonators might enable the firstGeSn-based laser on Si.

■ ASSOCIATED CONTENT*S Supporting InformationExtended details on the bandedge, gain, and pump-carriercalculations. Additionally, the fabrication process and μPLmeasurement setup are explained in detail. Also included areadditional gain calculations with FCAGe and data from an XRD1D ω-2θ scan. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: robert.chen@stanford.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported in part by the U.S. Government andthe Naval Air Systems Command through the AdvancedPhotonic Integrated Circuits (APIC) Corporation, the AirForce Office of Scientific Research (AFOSR), and the StanfordInitiative for Nanoscale Materials and Processes (INMP). R.C.would like to acknowledge financial support from the NationalScience Foundation Graduate Research Fellowship (NSF-GRFP Grant DGE-0645962). S.G. would like to acknowledgefinancial support from the Stanford Graduate Fellowship.C.W.R. would like to acknowledge financial support from theJoint Technologies Office (JTO Grant FA9550-10-1-0560).The authors would also like to thank Edward Fei, ColleenShang, and Dr. Hai Lin for technical discussions leading up tothis work, in addition to the Byer group for use of equipment.Work was performed in part at the Stanford NanofabricationFacility of National Nanotechnology Infrastructure Network(NNIN), supported by the National Science Foundation.

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