Letter pubs.acs.org/journal/apchd5
Strained Pseudomorphic Ge1−xSnx Multiple Quantum Well Microdisk Using SiNy Stressor Layer
Colleen S. Fenrich,*,† Xiaochi Chen,‡ Robert Chen,‡ Yi-Chiau Huang,§ Hua Chung,§ Ming-Yen Kao,‡,⊥ Yijie Huo,‡ Theodore I. Kamins,‡ and James S. Harris‡ †
Department of Materials Science and Engineering and ‡Department of Electrical Engineering, Stanford University, Stanford, California 94305, United States § Applied Materials Inc., Sunnyvale, California 94085, United States S Supporting Information *
ABSTRACT: We demonstrate tensile-strained pseudomorphic Ge0.934Sn0.066/Ge quantum wells in a microdisk resonator using silicon nitride stressor layers. The hydrostatic and biaxial strain distributions are studied through finite element modeling, while confocal Raman spectroscopy shows local biaxial strain transfers as high as 1.1% at freestanding microdisk edges. These strains are sufficient to overcome the original compressive strain in Ge0.934Sn0.066 epitaxy and reach a direct band gap according to deformation potential theory. A red-shift in microdisk photoluminescence confirms the reduced band gap energies in response to tensile strain and suggests an average biaxial strain transfer of 0.55%. KEYWORDS: germanium−tin, group IV, direct band gap, strain, stressor layer, microdisk resonator
T
he vision of achieving monolithic integration of a light source for silicon photonics has attracted much interest in group IV semiconductors. Despite their indirect nature, which results in poor light-emitting efficiency and high lasing thresholds, there continues to be a wealth of approaches in materials and device engineering to overcome this constraint, especially for pseudodirect band gap germanium (Ge). In particular, alloying 6−9%1−4 α-tin (α-Sn) reduces the energy separation (ΔEΓ−L) between the conduction band minima at the Brillouin zone center (Γ) and ⟨111⟩ directions (L) of Ge, creating a tunable, direct band gap group IV semiconductor capable of exhibiting net modal gain.4,5 In addition to limited solid solubility (less than 1% Sn in Ge)6 the large lattice mismatch between α-Sn and Ge is a persistent challenge for the growth of Ge1−xSnx alloys, particularly on Si substrates and Ge virtual substrates with smaller lattice constants. The accumulation of compressive strain in Ge1−xSnx lattice-matched to Ge (∼0.15% per 1% Sn) increases ΔEΓ−L as well as the fraction of Sn required to achieve a direct band gap crossover.1 While the intrinsic relaxation of an epitaxial film can relieve compressive strain, the subsequent formation of misfit and threading dislocations can contribute to crystal mosaicity or surface roughening undesired in photonic applications.7,8 An alternative approach is to compensate for this compressive strain by applying an opposing tensile strain to avoid defect formation associated with crystal relaxation and further engineer the bandstructure of Ge1−xSnx alloys. In addition to relieving Sn requirements, the application of tensile strain to low Sn alloys (e.g., Ge0.95Sn0.05) is expected to provide more optical gain than fully relaxed direct band gap high Sn alloys (e.g., Ge0.9Sn0.10).9 © XXXX American Chemical Society
Tensile strain in Ge and Ge1−xSnx has been investigated using thermal expansion mismatch10,11 and tunable buffer layers,9,12−15 but these approaches are often limited by the thermal stability of Ge1−xSnx or the additional challenge of CMOS integration in the case of III−V buffer layers. Large uniaxial and biaxial strains have also been achieved using suspended micro- and nanostructured geometries, such as membranes and bridges,16−19 but are difficult to incorporate into optical cavities required for light amplification. Another approach is to utilize high stress layers20−26 known as stressor layers, which can readily be applied to resonator cavities as an extrinsic stressing agent capable of inducing biaxial tensile strains as high as 2%.27 We demonstrate the application of high stress silicon nitride stressor layers to microdisk resonator cavities composed of Ge1−xSnx multiple quantum wells to achieve high strain transfer toward the integration of direct band gap pseudomorphic Ge1−xSnx on Ge-buffered Si.
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RESULTS AND DISCUSSION Below the critical thickness of Ge0.934Sn0.066 on Ge-buffered Si, lattice mismatch is accommodated by a strain-induced tetragonal distortion of the Ge0.934Sn0.066 crystal in order to maintain coherence across the interface. The strain state of the as-grown epitaxy in Figure 1a is investigated by (224) highresolution X-ray diffraction (XRD) reciprocal space mapping (RSM) shown in Figure 1b, where the common in-plane scattering vectors (Qx) of Ge and Ge0.934Sn0.066 confirm that the Received: August 3, 2016 Published: November 14, 2016 A
DOI: 10.1021/acsphotonics.6b00562 ACS Photonics XXXX, XXX, XXX−XXX
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Figure 1. (a) As-grown epitaxial stack with 20 nm pseudomorphic Ge0.934Sn0.066 QWs and 20 nm Ge barrier layers (b) High-resolution XRD reciprocal space mapping for an epitaxial stack in (224) orientation. (c) SEM images of 5.7 μm diameter unstressed and stressed microdisks.
Figure 2. (a) Cross-section of the 3D FE model showing hydrostatic strain, 1 (εxx + εyy + εzz), of a microdisk induced by the stressor layer; initial 3
epitaxial strains are not included. (b) Simulated biaxial strain profiles along the microdisk diameter for the top GeSn QW (left) and the top Ge cap layer (right), accounting for initial epitaxial strains.
layers are lattice-matched in real space. The interference fringes visible on the Ge0.934Sn0.066 peak show good interface quality, while the narrow full width at half-maximum of the peak indicates high crystal quality. Ge0.934Sn0.066 is under −0.775% (compressive) strain with respect to the slightly tensile-strained Ge buffer (0.192% thermal mismatch strain), which negates the benefit of Sn alloying and increases the separation of the Γ and L conduction band minima (ΔEΓ−L ≈ 55 meV). As a result, the preferred carrier occupation of the lower energy, 4-fold degenerate indirect L minimum reduces direct radiative recombination and increases lasing thresholds. By intentionally counteracting this compressive strain, it is possible to approach the direct gap condition without intrinsic strain relaxation. High stress silicon nitride (SiNy) is easily integrated to Ge1−xSnx-based microdisk resonators, which have shown strong whispering galley modes attractive for compact, low-threshold lasers,5,28 following resonator fabrication. In addition to straightforward integration on pre-existing device structures, SiNy has advantages of CMOS compatibility and lowtemperature deposition methods, such as plasma-enhanced chemical vapor deposition (PECVD), suitable for the metastable Ge1−xSnx system. Figure 1c shows scanning electron microscope (SEM) images of two microdisks (5.7 μm diameter) composed of three pseudomorphic Ge0.934Sn0.066 quantum wells (QWs) supported by Ge posts on Si. For the stressed microdisk, 150 nm of compressively stressed SiNy
(−1.9 GPa) is additionally deposited on the top of the resonator with thinner coverage on the back side and sidewall, which subsequently expands and relaxes to impart tensile strain to the underlying microdisk. Compared to top-only stressor layers, a fully encapsulating layer induces higher strains;25 however, slight deflections (∼65 nm) at the disk edges are still visible due to a vertical strain gradient from nonuniform stressor layer deposition on the top and back side of the microdisk, as well as the reduced compressive stress in the back-side stressor layer that is shielded from the low frequency plasma. Stressor Layer-Induced Strain Distribution. Following the geometry of Figure 1c, a 3D finite element (FE) simulation is conducted for a microdisk with a fully encapsulating stressor layer (150 nm on top and edges, 80 nm on back side) with an undercut width of 1 μm. A cross-section of the resulting hydrostatic strain, 1 (εxx + εyy + εzz), induced by the stressor 3
layer is shown in Figure 2a, excluding initial epitaxial strains. Regions of highest hydrostatic strain are concentrated at the freestanding microdisk edges with reduced resistance to deformation. A 35 nm deflection at the microdisk edge is predicted, which is less than the bending observed in SEM since the FE model assumes a constant stress throughout the entire stressor layer where the back-side stressor contributes an opposing bending moment to reduce curvature. B
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Figure 3. Raman strain distributions for Ge0.934Sn0.066 and Ge along the diameter of the unstressed (blue squares) and stressed microdisk (red diamonds) and net strain transferred (black triangles).
Figure 4. Bandstructure calculated by deformation potentials using Raman strain distribution, including Γ and L conduction band minima and heavy hole (HH) and light hole (LH) valence band maxima for an unstressed (dashed lines) and stressed (solid lines) microdisk.
measured by Raman (−0.745% and 0.122% for Ge0.934Sn0.066 and Ge, respectively) are consistent with the as-grown epitaxial strains measured by XRD (−0.775% and 0.192%). The stressor layer increases biaxial strain at this position by 0.36%, which is comparable to 0.35% from FE modeling, fully compensates the initial compressive strain in Ge0.934Sn0.066 at the microdisk edges, and provides a maximum additional 1.1% biaxial strain to Ge0.934Sn0.066. The net strain transfer obtained from Raman studies is slightly greater than FE modeling due to assumptions in elastic constants, and the distribution line shape appears broader as a result of the limited spatial resolution of the Raman system compared to FE discretization. Furthermore, the Raman analysis provides an upper limit of the strain distribution due to the smaller and more localized volume of material probed. At a laser wavelength of 633 nm, the penetration depth is approximately 50 nm such that only the top Ge cap layer and the top Ge0.934Sn0.066 QW dominate the Raman signal; these layers are expected to be more highly strained since they are closest to the top SiNy interface. Stressed Microdisk Bandstructure and Photoluminescence. Although biaxial strain in the (001) plane does not affect the 4-fold degeneracy of the L minima in Ge0.934Sn0.066 and Ge, the nonhydrostatic strain lifts the valence band degeneracy in addition to shifting band energy levels. From the Raman strain distributions, Figure 4 shows the corresponding spatial energy distribution of the conduction band minima and valence band maxima in Ge0.934Sn0.066 and Ge for an unstressed (dashed lines) and stressed (solid lines) microdisk as calculated
In Figure 2b, the average simulated (001) biaxial strain (εxx = εyy) along the diameter of the microdisk is shown for the top Ge0.934Sn0.066 QW and Ge cap layer, accounting for initial epitaxial strains. In the unstressed microdisk, Ge0.934Sn0.066 exhibits slight strain relaxation at radial distances approaching the undercut, resulting from removal of the constraining underlying buffer. In the initial strain state of the epitaxy, the Ge0.934Sn0.066 layers are compressively strained with respect to the Ge buffer, while the Ge barrier layers are unstrained with respect to the Ge buffer. Once the buffer is etched away, expansion of Ge0.934Sn0.066 both reduces its compressive strain and imparts additional tensile strain to Ge. Relaxation of compressively strained quantum wells in III−V microdisk resonators has similarly been noted by Fujita et al., where it was found that carrier diffusion toward relaxed microdisk edges can also provide reduced lasing thresholds.29 With the added stressor layer, the average strain transferred to the top Ge0.934Sn0.066 QW is 0.54%. The minimum biaxial strain at the microdisk center, where radius (r) is 0 μm, increases by 0.35%, while absolute strains as high as 0.33% and 1.30% for Ge0.934Sn0.066 and Ge occur at the onset of the microdisk undercut (r ≈ 2 μm) as a result of its freedom to deform. However, the sidewall stressor also limits the in-plane deformation of the microdisk and results in an abrupt decrease of in-plane strain at microdisk edges near the SiNy interface. One-dimensional Raman spectroscopy line scans in Figure 3 produce similar strain distributions as predicted by FE modeling. The initial strains at the microdisk center as C
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scattering during surface normal collection, no WGMs are detected in this work. While it is difficult to assign specific transitions of Ge0.934Sn0.066 and Ge contributing to the overall PL signal under such varied strain distributions, especially overlapping emission energies of highly tensile-strained Ge and compressive-strained Ge0.934Sn0.066, the overall PL shift is assumed to be comparable to the energy shift in Ge0.934Sn0.066, suggesting a strain transfer of 0.55% by the stressor layer. This agrees well with the average strain transfer from FE modeling (0.54%) and is within the range of strains observed from Raman studies (0.36−1.1%). The lower strain transfer obtained from PL compared to Raman is due to an averaging effect. Since the pump laser spot size is comparable to the microdisk area and the penetration depth is over 10× deeper at 980 nm, the collected signal reflects an average strain over the entire volume of material in the microdisk and post, including the low-strain regions far from the freestanding edges. In summary, we demonstrate the application of high stress SiNy stressor layers to impart tensile strain to pseudomorphic Ge0.934Sn0.066/Ge in microdisk resonator cavities. PL characterization indicates an average addition of 0.55% biaxial tensile strain, while Raman spectroscopy shows local strain transfers as high as 1.1%, sufficient to overcome the initial compressive strain in the original Ge0.934Sn0.066 epitaxy. The ability to strainengineer Ge1−xSnx reduces the requirements of Sn alloying toward achieving a direct band gap, avoids the formation of defects associated with the strain relaxation process, and provides an avenue for using pseudomorphic direct band gap Ge1−xSnx as a gain medium for on-chip light sources in Si photonics.
from deformation potential theory (see Methods). The valence band maximum in unstrained Ge is used as the zero energy reference. Without applied stress, the compressive strain in Ge0.934Sn0.066 raises the energy of the heavy hole (HH) valence band, while the slight tensile strain in Ge raises the light hole (LH) valence band. An indirect band gap is still observed for Ge0.934Sn0.066 with ΔEΓ−L ≈ 55 meV at the microdisk center and ∼49 meV at the edge (r ≈ 2 μm). Upon adding high stress SiNy, regions of tensile strain near microdisk edges lift the LH band in Ge0.934Sn0.066 just as in Ge. These strains, in addition to Sn alloying, are sufficient to approach the direct band gap transition where ΔEΓ−L is reduced to ∼27 meV at the microdisk center but ∼−38 meV near the edges (r ≈ 2 μm) under maximum strain. This results from the larger reduction in energy for the Γ valley compared to the L and X valleys in response to tensile strain applied within the (001) plane.2 Although the added tensile strain simultaneously decreases the Γ and L conduction band energies in Ge, as well as lifts the LH energies, the reduced band gap energy is still sufficient to form a type I heterostructure in Ge0.934Sn0.066 for carrier confinement. The spatially varying band structure also provides carrier confinement in the lateral direction, forming a pseudoheterostructure within the Ge0.934Sn0.066 QW as a result of localized high-strain regions. For a 6 μm diameter microdisk, the electric field maximum of first-order whispering gallery modes (WGM) resides approximately 0.5 μm from the sidewall, which overlaps direct band gap regions with greater electron population in comparison to the microdisk center or the unstressed microdisk. The reduced band gap energies are also observed by a corresponding red shift in room-temperature photoluminescence (PL) shown in Figure 5. The broad resonances visible in
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METHODS Material Growth and Stressor Layer Deposition. Ge/ Ge1−xSnx epitaxy is grown below 350 °C in an Applied Materials Centura Epi reduced-pressure chemical vapor deposition (RPCVD) system using digermane (Ge2H6) and tin tetrachloride (SnCl4) precursors. A strain-relaxed 1 μm Ge buffer (threading dislocation density ∼3 × 107 cm−2) is grown on (001) Si followed by a 10 nm Ge0.934Sn0.066 etch stop layer, three 20 nm Ge0.934Sn0.066 quantum wells separated by 20 nm Ge barrier layers, and a 30 nm Ge cap layer. A PANalytical X’Pert PRO X-ray diffractometer is used for high-resolution (224) reciprocal space mapping of the as-grown epitaxy. Details of microdisk fabrication are described by Chen et al.28 and Shang et al.30 The SiNy stressor layer is deposited in an STS plasma-enhanced chemical vapor deposition chamber at 350 °C using silane (SiH4) and ammonia (NH3) precursors. Deposition conditions are optimized to achieve maximum compressive stress using low chamber pressure (460 mTorr), low RF power (10 W), and a low frequency power source (187.5 kHz). To determine film stress, 260 nm of SiNy was deposited on an unpatterned 100 mm (001) Si substrate to measure wafer curvature using a Tencor FLX-2320 system. The radius of curvature was −18.4 m, corresponding to a film stress of −1.9 GPa using the Stoney formula. Strain Modeling and Characterization. FE strain simulations are performed using the solid mechanics module in COMSOL Multiphysics for a 3D model with a fully encapsulating stressor layer (see Supporting Information). Confocal Raman spectroscopy is carried out using a Horiba Labram HR Evolution Raman system in a backscattering geometry. A 633 nm laser is focused through a 100× objective (∼0.5 μm spot size), and the collected signal is dispersed using
Figure 5. Photoluminescence spectra show a clear red shift in PL emission for the stressed microdisk (red) compared to the unstressed microdisk (blue). FP resonances associated with the microdisk diameter agree with the calculated FP resonance spectrum using the transfer matrix method (black).
both spectra are associated with Fabry−Perot (FP)-type modes since the free spectral range (FSR) matches well with the FP spectrum calculated by the transfer matrix method with cavity lengths equivalent to the microdisk diameter (in black). No difference in FSR is observed between the two microdisks, which suggests that the stressor layer does not significantly alter microdisk dimensions or effective index. Similar FP resonances have also been reported in stressed Ge microdisks by Millar et al.27 Although WGM can be coupled out-of-plane from edge D
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(3) Chen, R.; Lin, H.; Huo, Y.; Hitzman, C.; Kamins, T. I.; Harris, J. S. Increased photoluminescence of strain-reduced, high-Sn composition Ge1−xSnx alloys grown by molecular beam epitaxy. Appl. Phys. Lett. 2011, 99, 181125. (4) Wirths, S.; Geiger, R.; von den Driesch, N.; Mussler, G.; Stoica, T.; Mantl, S.; Ikonic, Z.; Luysberg, M.; Chiussi, S.; Hartmann, J. M.; Sigg, H.; Faist, J.; Buca, D.; Grützmacher, D. Lasing in direct-bandgap GeSn alloy grown on Si. Nat. Photonics 2015, 9, 1−5. (5) Stange, D.; et al. Optically pumped GeSn Microdisk Lasers on Si. ACS Photonics 2016, 9, 1279−1285. (6) Baldé, L.; Legendre, B.; Balkhi, A. Etude du diagramme d’équilibre entre phases du système ternaire germanium-étain-tellure. J. Alloys Compd. 1995, 216, 285−293. (7) Gencarelli, F.; Vincent, B.; Demeulemeester, J.; Vantomme, A.; Moussa, A.; Franquet, A.; Kumar, A.; Bender, H.; Meersschaut, J.; Vandervorst, W.; Loo, R.; Caymax, M.; Temst, K.; Heyns, M. Crystalline Properties and Strain Relaxation Mechanism of CVD Grown GeSn. ECS J. Solid State Sci. Technol. 2013, 2, P134−P137. (8) Wang, W.; Zhou, Q.; Dong, Y.; Tok, E. S.; Yeo, Y.-C. Critical thickness for strain relaxation of Ge1−xSnx (x ≤ 0.17) grown by molecular beam epitaxy on Ge(001). Appl. Phys. Lett. 2015, 106, 232106. (9) Wirths, S.; Ikonic, Z.; Tiedemann, A. T.; Holländer, B.; Stoica, T.; Mussler, G.; Breuer, U.; Hartmann, J. M.; Benedetti, A.; Chiussi, S.; Grützmacher, D.; Mantl, S.; Buca, D. Tensely strained GeSn alloys as optical gain media. Appl. Phys. Lett. 2013, 103, 192110. (10) Harris, T. R.; Yeo, Y. K.; Ryu, M.-Y.; Beeler, R. T.; Kouvetakis, J. Observation of heavy- and light-hole split direct bandgap photoluminescence from tensile-strained GeSn (0.03% Sn). J. Appl. Phys. 2014, 103502, 0−7. (11) Lieten, R. R.; Seo, J. W.; Decoster, S.; Vantomme, A.; Peters, S.; Bustillo, K. C.; Haller, E. E.; Menghini, M.; Locquet, J. P. Tensile strained GeSn on Si by solid phase epitaxy. Appl. Phys. Lett. 2013, 102, 2−7. (12) Huo, Y.; Lin, H.; Chen, R.; Makarova, M.; Rong, Y.; Li, M.; Kamins, T. I.; Vuckovic, J.; Harris, J. S. Strong enhancement of direct transition photoluminescence with highly tensile-strained Ge grown by molecular beam epitaxy. Appl. Phys. Lett. 2011, 98, 3−5. (13) Wirths, S.; Tiedemann, A. T.; Ikonic, Z.; Harrison, P.; Holländer, B.; Stoica, T.; Mussler, G.; Myronov, M.; Hartmann, J. M.; Grützmacher, D.; Buca, D.; Mantl, S. Band engineering and growth of tensile strained Ge/(Si)GeSn heterostructures for tunnel field effect transistors. Appl. Phys. Lett. 2013, 102, 192103. (14) de Kersauson, M.; Prost, M.; Ghrib, A.; El Kurdi, M.; Sauvage, S.; Beaudoin, G.; Largeau, L.; Mauguin, O.; Jakomin, R.; Sagnes, I.; Ndong, G.; Chaigneau, M.; Ossikovski, R.; Boucaud, P. Effect of increasing thickness on tensile-strained germanium grown on InGaAs buffer layers. J. Appl. Phys. 2013, 113, 183508. (15) Wang, W.; Loke, W. K.; Yin, T.; Zhang, Z.; D’Costa, V. R.; Dong, Y.; Liang, G.; Pan, J.; Shen, Z.; Yoon, S. F.; Tok, E. S.; Yeo, Y.C. Growth and characterization of highly tensile strained Ge1−xSnx formed on relaxed InyGa1−yP buffer layers. J. Appl. Phys. 2016, 119, 125303. (16) Sánchez-Pérez, J. R.; Boztug, C.; Chen, F.; Sudradjat, F. F.; Paskiewicz, D. M.; Jacobson, R. B.; Lagally, M. G.; Paiella, R. Directbandgap light-emitting germanium in tensilely strained nanomembranes. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 18893−8. (17) Al-Attili, A. Z.; Kako, S.; Husain, M. K.; Gardes, F. Y.; Higashitarumizu, N.; Iwamoto, S.; Arakawa, Y.; Ishikawa, Y.; Arimoto, H.; Oda, K.; Ido, T.; Saito, S. Whispering Gallery Mode Resonances from Ge Micro-Disks on Suspended Beams. Front. Mater. 2015, 2, 1− 9. (18) Gassenq, A.; Guilloy, K.; Pauc, N.; Hartmann, J. M.; OsvaldoDias, G.; Rouchon, D.; Tardif, S.; Escalante, J.; Duchemin, I.; Niquet, Y. M.; Chelnokov, A.; Reboud, V.; Calvo, V. Study of the light emission in Ge layers and strained membranes on Si substrates. Thin Solid Films 2015, 613, 0−3. (19) Al-Attili, A. Z.; Kako, S.; Husain, M. K.; Gardes, F. Y.; Iwamoto, S.; Arakawa, Y.; Saito, S. Tensile strain engineering of germanium
a grating spectrometer (1800 l/mm). To minimize thermal effects, only 1% of the maximum laser power (13.7 mW) is used. Ge1−xSnx and Ge Raman shifts (Δω) are obtained using Lorentz fitting of the Ge−Ge LO mode with reference to an unstrained (001) Ge substrate and correlated to biaxial in-plane strain (ε||) by the relationship Δω = ax + bε||, where a = (−75.4 ± 4.5) cm−1,31 x is the Sn fraction, bGe = −415 cm−1,31 and bGeSn = −485 cm−1 (measured from similar composition and growth conditions).32 Bandstructure and PL Characterization. Strain effects on bandstructure are calculated using deformation potentials in model−solid theory (see Supporting Information) as described by Van de Walle.33 Micro-PL measurements are taken in a surface-normal pump and collection configuration using a 980 nm diode laser focused through an objective (NA = 0.4, laser spot size ∼8 μm), phase-sensitive lock-in detection, and an extended-InGaAs detector (2.4 μm cutoff). Sufficient out-ofplane coupling of WGM from edge scattering can still occur in the surface-normal arrangement. Spectra for the stressed and unstressed microdisks are both measured at 11 mW pump power, where heating-induced changes to the band gap are not observed, and are corrected for system response calibrated by a tungsten halogen lamp at 2960 K.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.6b00562. Strain simulation details and material parameters for bandstructure calculations (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Colleen S. Fenrich: 0000-0001-7635-3556 Present Address ⊥
Department of Electrical Engineering, National Taiwan University, Taipei 10617, Taiwan.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank APIC Corporation and Innovation Core SEI, Inc. for funding support. C.F. is supported in part by the Natural Sciences and Engineering Research Council of Canada. The authors thank Dr. William Nix for discussions on strain modeling. Work was performed in the Stanford Nano Shared Facilities supported by the National Science Foundation under award ECCS-1542152 and the Stanford Nanofabrication Facility.
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REFERENCES
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