## Abstract

We theoretically investigate a tensile strained GeSn waveguide integrated with Si_{3}N_{4} liner stressor for the applications in mid-infrared (MIR) detector and modulator. A substantial tensile strain is induced in a 1 × 1 μm^{2} GeSn waveguide by the expansion of 500 nm Si_{3}N_{4} liner stressor and the contour plots of strain are simulated by the finite element simulation. Under the tensile strain, the direct bandgap *E _{G}*

_{,Γ}of GeSn is significantly reduced by lowering the Γ conduction valley in energy and lifting of degeneracy of valence bands. Absorption coefficients of tensile strained GeSn waveguides with different Sn compositions are calculated. As the Si

_{3}N

_{4}liner stressor expands by 1%, the cut-off wavelengths of tensile strained Ge

_{0.97}Sn

_{0.03}, Ge

_{0.95}Sn

_{0.05}, and Ge

_{0.90}Sn

_{0.10}waveguide photodetectors are extended to 2.32, 2.69, and 4.06 μm, respectively. Tensile strained Ge

_{0.90}Sn

_{0.10}waveguide electro-absorption modulator based on Franz-Keldysh (FK) effect is demonstrated in theory. External electric field dependence of cut-off wavelength and propagation loss of tensile strained Ge

_{0.90}Sn

_{0.10}waveguide is observed, due to the FK effect.

© 2015 Optical Society of America

## 1. Introduction

With the fast advances of optical telecommunications and optical interconnects, Si photonics has aroused great interest in recent years [1, 2]. Ge-on-Si photonic devices, such as detectors [3–6], modulators [7, 8], and resonators [9, 10], with cut-off wavelength less than 1.6 μm have been reported. Further extension of the operation wavelength of the devices to mid-infrared range, e.g. 2-5 μm, is highly desired due to the wider applications in medical diagnostics, environmental monitoring, Ladar, free-space laser communications, and so on [11]. A straight-forward approach to extend the spectral range is to utilize a semiconductor with narrower bandgap, e.g. germanium-tin (GeSn).

It has been demonstrated that, by increasing Sn composition, GeSn can be a direct bandgap material with a smaller direct bandgap *E _{G}*

_{,Γ}by lowering the energy of Γ conduction valley [12–14]. Strained and relaxed GeSn films with high crystallinity have been epitaxially grown with molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) at low temperatures [14–16]. Recently, GeSn has been studied for the applications in high mobility metal-oxide-semiconductor field-effect transistors (MOSFETs) [17, 18] and photonic devices [19–25]. Ge

_{0.91}Sn

_{0.09}photodetector with a 2.2 μm absorption wavelength has been realized [22]. But, the Sn composition cannot be increased arbitrarily due to the limited solid solubility of Sn in Ge. Additionally, Sn tends to segregate at surface and cluster, which are the challenges for the GeSn growth and device fabrication. Besides Sn composition, strain also plays a key role in modulating the energy band structure of GeSn [12, 26]. Application of tensile strain to GeSn results in the reduction of direct bandgap

*E*

_{G}_{,Γ}, which offers a possible method for extending the absorption spectrum of GeSn into MIR range and promoting the indirect-to-direct transition without increasing the requirement for Sn composition.

In this letter, we present a design of tensile strained GeSn waveguide used as photodetector and modulator, featuring a Si_{3}N_{4} tensile liner stressor. The tensile strain induced by the Si_{3}N_{4} liner leads to the shrinkage of *E _{G}*

_{,Γ}of GeSn and results in the extension of cut-off wavelength of the waveguide devices. The tensile strained GeSn waveguide modulator based on Franz-Keldysh (FK) effect is analyzed theoretically.

## 2. Key concept and device structure

This section depicts the strain engineering concept and the designed device structure. Figure 1(a) shows the basic structure of the GeSn on Si on oxide undercladding pedestal (SOUP) waveguide wrapped in Si_{3}N_{4} liner stressor. Si_{3}N_{4} stressor has been a common method for introducing tensile strain in Ge devices [27–30]. However, the operating wavelength corresponding to *E _{G}*

_{,Γ}is still limited to about 2 μm. The purpose of this work is to utilize Si

_{3}N

_{4}liner stressor and GeSn with smaller

*E*

_{G}_{,Γ}than Ge to realize waveguide devices operating in the 2-5 μm wavelength range. The transmission window of SOI in the MIR is limited to about 4 μm due to the onset of phonon absorption in SiO

_{2}[31, 32]. So SOUP waveguide structure is utilized and a Si

_{3}N

_{4}liner stressor wrapping around the waveguide induces tensile strain in the GeSn material. As shown in Fig. 1(b), the Si

_{3}N

_{4}expands, and thus stretches the GeSn waveguide.

## 3. Results and discussion

#### 3.1 Simulation of strain profiles and energy band structure in GeSn waveguide

A 3D finite element (FEM) simulation was carried out to analyze the effect of the Si_{3}N_{4} liner stressor on the strain profiles in GeSn waveguide. Figure 2(a) shows the geometric parameters and coordinate axes. *AA*’ plane is cut perpendicular to the GeSn waveguide along [100] direction, and *BB*’ plane is cut through the GeSn waveguide [010] direction. The mechanical parameters, e.g. Young’s modulus and Poisson’s ratio, of GeSn were calculated by linear interpolation method based on the values of Ge and α-Sn. The Young’s modulus values of Ge and α-Sn were taken as 102.9 and 51.5 GPa, respectively, and the Poisson’s ratios were 0.270 and 0.298 for Ge and α-Sn, respectively [33]. The Young’s modulus for Si_{3}N_{4} was taken as 250.0 GPa [34]. During the simulation, the volume of compressively strained Si_{3}N_{4} was set up to expand by 1%. The boundary conditions of the model were set as follows. The bottom surface of Si handle substrate was fixed without any displacement in any direction, and other surfaces were set to be free surfaces. Figure 2 shows the strain profiles in the tensile strained Ge_{0.95}Sn_{0.05} waveguide integrated with Si_{3}N_{4} liner stressor. Figures 2(b)-2(d) illustrate the contour plots for the strain along [100], [010], and [001] directions in *AA*’ plane of Ge_{0.95}Sn_{0.05} waveguide, respectively, which are denoted by *ε*_{[100]}, *ε*_{[010]}, and *ε*_{[001]}, respectively. Figures 2(e)-2(g) illustrate the contour plots for *ε*_{[100]}, *ε*_{[010]}, and *ε*_{[001]} in *BB*’ plane. It is observed that Ge_{0.95}Sn_{0.05} waveguide is under tensile strain along the three principle coordinate directions, and *ε*_{[010]} is much larger than *ε*_{[100]} and *ε*_{[001]}. This indicates that the GeSn waveguide is stretched along [100], [010], and [001] directions and the tensile deformation along [010] direction is the most pronounced. At the center of the strained Ge_{0.95}Sn_{0.05} waveguide, the values of *ε*_{[100]}, *ε*_{[010]}, and *ε*_{[001]} are about 0.25%, 0.75%, and 0.25%, respectively. Calculations show that the difference between strain profiles in GeSn waveguides induced by the various Sn compositions is negligibly small.

We investigate the impact of tensile strain on the *E _{G}*

_{,Γ}and the indirect band gap at L point

*E*

_{G}_{,L}in GeSn with different Sn compositions. The band edge dispersion at the Γ and L points was calculated by multi-band k·p method [35]. The Luttinger-like parameters were calculated based on those in [36], and the

*E*

_{G,}_{Г}and

*E*

_{G}_{,L}values of relaxed GeSn were taken from the recent calculation and experimental results [12–14]. The reduction of

*E*

_{G}_{,Г}and

*E*

_{G}_{,L}induced by strain is given by $\alpha \left({\epsilon}_{\perp}+2{\epsilon}_{\parallel}\right)+b\left({\epsilon}_{\perp}-{\epsilon}_{\parallel}\right)$ [35, 37], where ${\epsilon}_{\parallel}$ and ${\epsilon}_{\perp}$ are the in-plane and out-of-plane strain, respectively, and

*a*and

*b*are deformation potential constants. In this work, deformation potentials of GeSn alloys are assumed to be the same as those of Ge [36]. The deformation potential constants for direct and indirect conduction bands were taken as −10 and – 4 eV, respectively [38], and that of valence band was - 2.85 eV [39]. The simulated strains at the center of GeSn waveguide were converted into the strain tensor in the k·p Hamiltonian as the input variables. It should be noted that the magnitude of the tensile strain at the interior edge in

*AA*’ plane in GeSn waveguide is much higher than that at the center region. Here, we only use the strains at the center to calculate the energy band diagrams in strained GeSn and actually underestimate the red-shift of cut-off wavelength in devices with Si

_{3}N

_{4}liner stressor. It is also found that the strain distribution in waveguide along [010] direction was also rather nonuniform. Strain is partially relaxed in the regions 1~1.5 μm from the ends of the waveguide, which is attributed to the fact that the two end surfaces are set to be free during the simulation. If the waveguide is shorter than 3 μm in [010] direction, the strain effect will be degraded in the whole waveguide, leading to the blue-shift of cut-off wavelength in device.

Figure 3 shows the *E*-*k* energy band diagrams of relaxed and tensile strained Ge_{0.97}Sn_{0.03}, Ge_{0.95}Sn_{0.05}, and Ge_{0.90}Sn_{0.10}. Compared to relaxed GeSn, the *E _{G}*

_{,Г}and

*E*

_{G}_{,L}are reduced in tensile strained GeSn, due to the decreasing of the energy of Γ and L conduction valleys. Compared to the L conduction valley, the Γ valley demonstrates a more rapid decline of energy due to the large magnitude of deformation potential. The tensile strained Ge

_{0.95}Sn

_{0.05}exhibits a direct band gap structure. Meanwhile, the strain induced splitting of heavy hole (HH) and light hole (LH) bands and shift of HH up further reduce the

*E*

_{G}_{,Г}in tensile strained GeSn devices. Figure 4 compares the

*E*

_{G}_{,Γ}and

*E*

_{G}_{,L}of relaxed and strained GeSn waveguides with different Sn compositions. In this work, the maximum Sn composition in GeSn devices is constrained to be 0.10, which has been demonstrated to withstand annealing temperature of 450 °C without material degradation observed [40]. The

*E*

_{G}_{,Г}of relaxed Ge

_{0.97}Sn

_{0.03}, Ge

_{0.95}Sn

_{0.05}, and Ge

_{0.90}Sn

_{0.10}are 0.690, 0.617, and 0.455 eV, respectively. Under the tensile strain that induced by Si

_{3}N

_{4}liner stressor, Ge

_{0.97}Sn

_{0.03}, Ge

_{0.95}Sn

_{0.05}, and Ge

_{0.90}Sn

_{0.10}waveguides exhibit the

*E*

_{G}_{,Г}of 0.534, 0.461, and 0.306 eV, respectively.

#### 3.2 Absorption coefficient in tensile strained GeSn MIR waveguide photodetector

Figure 5 shows a 3D schematic of tensile strained GeSn on SOUP waveguide butt-coupled to Si waveguide, which can be used as photodetector and electro-absorption modulator.

Absorption coefficient *α* is the most key parameter for determining the electrical and optical performance of a detector. In this work, only the optical transition between Γ conduction valley and HH band is considered and *α* can be obtained calculating the probability of quantum transition from the HH state to Γ conduction band state [41]. The magnitude of *α*, is related to the photon energy $\hslash \omega $ and *E _{G}*

_{,Γ}of GeSn [41],

*ω*is the angular frequency, and

*μ*is the reduced mass, determined by electron and hole effective masses, which can extracted from the band edge dispersion. Figure 6 shows the absorption spectra for relaxed and strained GeSn waveguide photodetectors with Sn compositions of 0.03, 0.05, and 0.10. We define cut-off wavelength as the wavelength

*λ*where $2\pi c\hslash /\lambda $ equals to the

*E*

_{G}_{,Γ}of the materials. The cut-off wavelengths of relaxed Ge

_{0.97}Sn

_{0.03}, Ge

_{0.95}Sn

_{0.05}, and Ge

_{0.90}Sn

_{0.10}waveguide photodetectors are 1.80, 2.01, and 2.72 μm, respectively. Significant red shift of absorption edge is achieved in tensile strained GeSn waveguide photodetectors with the tensile strain induced by Si

_{3}N

_{4}liner stressor. As the 500 nm Si

_{3}N

_{4}liner stressor expands by 1%, the cut-off wavelengths of strained Ge

_{0.97}Sn

_{0.03}, Ge

_{0.95}Sn

_{0.05}, and Ge

_{0.90}Sn

_{0.10}are extended to 2.32, 2.69, and 4.06 μm, respectively.

#### 3.3 Franz-Keldysh effect in tensile strained Ge_{0.90}Sn_{0.10} MIR electro-absorption modulator

In this section, tensile strained GeSn electro-absorption modulator based on the FK effect is studied. The *α* as a function of wavelength with various external electric fields due to FK effect is expressed as [42]

*F*is the external electric field,

*μ*is the reduced mass at Γ point, Ai and Ai’ are the Airy function and derivative Airy function, respectively, and

*α*and

_{b}*β*are given by

*n*is the refractive index,

*ε*

_{0}is the vacuum permittivity,

*c*is the velocity of light,

*m*is electron effective mass at Γ point and Δ is the spin-orbit splitting. In both the relaxed and strained GeSn, only the optical transition between Γ conduction valley and HH band was taken into account.

_{e}Figure 7 depicts *α* versus wavelength plots for the tensile strained Ge_{0.97}Sn_{0.03}, Ge_{0.95}Sn_{0.05}, and Ge_{0.90}Sn_{0.10} waveguide modulators under various external electric fields. The strength of electric field varies from 0 to 10 MV/m in steps of 2 MV/m. For all materials, the cut-off wavelength is shifted to MIR spectra range with the increasing of external electric filed due to the FK effect. With the external electric field, the absorption spectra demonstrate the oscillatory behavior with change in wavelength, which is a typical characteristic of FK effect. The optical transmission properties of Ge_{0.90}Sn_{0.10} waveguide modulator were characterized with a 2D finite-different time-domain (FDTD) method. Figure 8 shows the waveguide mode profiles of transverse electric (TE) and transverse magnetic (TM) modes in tensile strained Ge_{0.90}Sn_{0.10} waveguide modulator at wavelengths of 4.25, 4.50, and 4.75 μm. The refractive indexes for Ge_{0.90}Sn_{0.10}, Si_{3}N_{4}, and SiO_{2} are 4.02, 1.98, and 1.35, respectively, in the range of wavelength in this wok [43]. For all the cases, single mode transmission in GeSn waveguide is observed. Figures 9(a) and 9(b) plot the propagation loss versus wavelength for TE and TM modes, respectively, of tensile strained Ge_{0.90}Sn_{0.10} waveguide under different electric fields. Propagation loss of GeSn exhibits significant dependence on wavelength. At a fixed wavelength, the propagation loss increases with the increasing of applied electric field due to the FK effect, which will improve the modulation depth of GeSn waveguide electro-absorption modulator. Without the external electric field, the intrinsic *α* is zero at these wavelengths, and the propagation loss increases with the increasing of wavelength since the optical field becomes less confined in the waveguide.

## 4. Conclusion

In summary, a tensile strained GeSn waveguide structure integrated with Si_{3}N_{4} liner stressor used as MIR detector and modulator is investigated by simulation. FEM, k･p method and FDTD were utilized to calculate the strain distribution, energy band structure, and optical transmission properties in GeSn waveguide, respectively. A large tensile strain is induced by the Si_{3}N_{4} liner stressor, which decreases the Γ conduction band energy and lifts the degeneracy of valence bands, thus resulting in the reduction of *E _{G}*

_{,Γ}and extension of cut-off wavelength of the GeSn waveguide detector. Ge

_{0.90}Sn

_{0.10}waveguide detector achieves a

*E*

_{G}_{,Γ}reduction from 0.455 eV to 0.306 eV caused by the 500 nm Si

_{3}N

_{4}stressor liner with 1% expansion, extending the cut-off wavelength beyond 4 μm. FK effect in tensile strained GeSn is theoretically studied and the absorption coefficient can be modulated effectively by external electric field.

## Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 106112013CDJZR120015, 106112013CDJZR120017). G. Han acknowledges the start-up fund of one-hundred talent program from Chongqing University, China.

## References and links

**1. **R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1678–1687 (2006). [CrossRef]

**2. **L. Tsybeskov, D. J. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE **97**(7), 1161–1165 (2009). [CrossRef]

**3. **L. Colace, G. Masini, G. Assanto, H. C. Luan, K. Wada, and L. C. Kimerling, “Efficient high-speed near-infrared Ge photodetectors integrated on Si substrates,” Appl. Phys. Lett. **76**(10), 1231–1233 (2000). [CrossRef]

**4. **T. Yin, R. Cohen, M. M. Morse, G. Sarid, Y. Chetrit, D. Rubin, and M. J. Paniccia, “31 GHz Ge n-i-p waveguide photodetectors on Silicon-on-Insulator substrate,” Opt. Express **15**(21), 13965–13971 (2007). [CrossRef] [PubMed]

**5. **D. Ahn, C. Y. Hong, J. Liu, W. Giziewicz, M. Beals, L. C. Kimerling, J. Michel, J. Chen, and F. X. Kärtner, “High performance, waveguide integrated Ge photodetectors,” Opt. Express **15**(7), 3916–3921 (2007). [CrossRef] [PubMed]

**6. **J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics **4**(8), 527–534 (2010). [CrossRef]

**7. **N.-N. Feng, D. Feng, S. Liao, X. Wang, P. Dong, H. Liang, C.-C. Kung, W. Qian, J. Fong, R. Shafiiha, Y. Luo, J. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “30GHz Ge electro-absorption modulator integrated with 3 μm silicon-on-insulator waveguide,” Opt. Express **19**(8), 7062–7067 (2011). [CrossRef] [PubMed]

**8. **A. E. J. Lim, T.-Y. Liow, N. Duan, L. Ding, M. Yu, G. Q. Lo, and D. L. Kwong, “Germanium electro-absorption modulator for power efficient optical links,” In Proceedings of IEEE International Topical Meeting on Microwave Photonics Conference. (IEEE, 2011), pp. 105–108. [CrossRef]

**9. **P. H. Lim, Y. Kobayashi, S. Takita, Y. Ishikaw, and K. Wad, “Enhanced photoluminescence from germanium-based ring resonators,” Appl. Phys. Lett. **93**(4), 041103 (2008). [CrossRef]

**10. **P. Wang, T. Lee, M. Ding, A. Dhar, T. Hawkins, P. Foy, Y. Semenova, Q. Wu, J. Sahu, G. Farrell, J. Ballato, and G. Brambilla, “Germanium microsphere high-Q resonator,” Opt. Lett. **37**(4), 728–730 (2012). [CrossRef] [PubMed]

**11. **R. Soref, “Group IV photonics for the mid infrared,” Proc. SPIE **8629**, 862902 (2013). [CrossRef]

**12. **S. Gupta, B. Magyari-Köpe, Y. Nishi, and K. C. Saraswat, “Achieving direct band gap in germanium through integration of Sn alloying and external strain,” J. Appl. Phys. **113**(7), 073707 (2013). [CrossRef]

**13. **G. Grzybowski, R. T. Beeler, L. Jiang, D. J. Smith, J. Kouvetakis, and J. Menendez, “Next generation of Ge_{1-}* _{y}*Sn

*(*

_{y}*y*= 0.01-0.09) alloys grown on Si(100) via Ge

_{3}H

_{8}and SnD

_{4}: reaction kinetics and tunable emission,” Appl. Phys. Lett.

**101**(7), 072105 (2012). [CrossRef]

**14. **R. Chen, H. Lin, Y. Huo, C. Hitzman, T. I. Kamins, and J. S. Harris, “Increased photoluminescence of strain-reduced, high-Sn composition Ge_{1-}* _{x}*Sn

*alloys grown by molecular beam epitaxy,” Appl. Phys. Lett.*

_{x}**99**(18), 181125 (2011). [CrossRef]

**15. **J. Tolle, R. Roucka, A. V. G. Chizmeshya, J. Kouvetakis, V. R. D’Costa, and J. Menéndez, “Compliant tin-based buffers for the growth of defect-free strained heterostructures on silicon,” Appl. Phys. Lett. **88**(25), 252112 (2006). [CrossRef]

**16. **R. T. Beeler, J. Gallagher, C. Xu, L. Jiang, C. L. Senaratne, D. J. Smith, J. Menéndez, A. V. G. Chizmeshya, and J. Kouvetakis, “Band gap-engineered group-IV optoelectronic semiconductors, photodiodes and prototype photovoltaic devices,” ECS J. Solid State Sci. and Technol. **2**(9), Q172–Q177 (2013). [CrossRef]

**17. **G. Han, S. Su, C. Zhan, Q. Zhou, Y. Yang, L. Wang, P. Guo, W. Wei, C. P. Wong, Z. X. Shen, B. Cheng, and Y.-C. Yeo, “High-mobility germanium-tin (GeSn) p-channel MOSFETs featuring metallic source/drain and sub-370 °C process modules,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2011), pp. 402–404.

**18. **M. Liu, G. Han, Y. Liu, C. Zhang, H. Wang, X. Li, J. Zhang, B. Cheng, and Y. Hao, “Undoped Ge_{0.92}Sn_{0.08} quantum well pMOSFETs on (001), (011) and (111) substrates with in situ Si_{2}H_{6} passivation: high hole mobility and dependence of performance on orientation,” in Symposium on VLSI Technology Digest of Technical Papers (IEEE, 2014), pp. 1–2.

**19. **S. Su, B. Cheng, C. Xue, W. Wang, Q. Cao, H. Xue, W. Hu, G. Zhang, Y. Zuo, and Q. Wang, “GeSn p-i-n photodetector for all telecommunication bands detection,” Opt. Express **19**(7), 6400–6405 (2011). [CrossRef] [PubMed]

**20. **G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure midinfrared laser,” J. Appl. Phys. **108**(3), 033107 (2010). [CrossRef]

**21. **G.-E. Chang, S.-W. Chang, and S. L. Chuang, “Strain-balanced Ge* _{z}*Sn

_{1-}

*-Si*

_{z}*Ge*

_{x}*Sn*

_{y}_{1-}

_{x}_{-}

*multiple-quantum-well lasers,” IEEE J. Quantum Electron.*

_{y}**46**(12), 1813–1820 (2010). [CrossRef]

**22. **A. Gassenq, F. Gencarelli, J. Van Campenhout, Y. Shimura, R. Loo, G. Narcy, B. Vincent, and G. Roelkens, “GeSn/Ge heterostructure short-wave infrared photodetectors on silicon,” Opt. Express **20**(25), 27297–27303 (2012). [CrossRef] [PubMed]

**23. **H. Li, J. Brouillet, A. Salas, X. Wang, and J. Liu, “Low temperature growth of high crystallinity GeSn on amorphous layers for advanced optoelectronics,” Opt. Mater. Express **3**(9), 1385–1396 (2013). [CrossRef]

**24. **M. Oehme, K. Kostecki, M. Schmid, M. Kaschel, M. Gollhofer, K. Ye, D. Widmann, R. Koerner, S. Bechler, E. Kasper, and J. Schulze, “Franz-Keldysh effect in GeSn pin photodetectors,” Appl. Phys. Lett. **104**(16), 161115 (2014). [CrossRef]

**25. **R. Roucka, J. Mathews, R. T. Beeler, J. Tolle, J. Kouvetakis, and J. Menéndez, “Direct gap electroluminescence from Si/Ge_{1-}* _{y}*Sn

*p-i-n heterostructure diodes,” Appl. Phys. Lett.*

_{y}**98**(6), 061109 (2011). [CrossRef]

**26. **R. Kotlyar, U. E. Avci, S. Cea, R. Rios, T. D. Linton, K. J. Kuhn, and I. A. Young, “Bandgap engineering of group IV materials for complementary n and p tunneling field effect transistors,” Appl. Phys. Lett. **102**(11), 113106 (2013). [CrossRef]

**27. **R. Kuroyanagi, L. M. Nguyen, T. Tsuchizawa, Y. Ishikawa, K. Yamada, and K. Wada, “Local bandgap control of germanium by silicon nitride stressor,” Opt. Express **21**(15), 18553–18557 (2013). [CrossRef] [PubMed]

**28. **G. Capellini, C. Reich, S. Guha, Y. Yamamoto, M. Lisker, M. Virgilio, A. Ghrib, M. El Kurdi, P. Boucaud, B. Tillack, and T. Schroeder, “Tensile Ge microstructures for lasing fabricated by means of a silicon complementary metal-oxide-semiconductor process,” Opt. Express **22**(1), 399–410 (2014). [CrossRef] [PubMed]

**29. **A. Ghrib, M. El Kurdi, M. de Kersauson, M. Prost, S. Sauvage, X. Checoury, G. Beaudoin, I. Sagnes, and P. Boucaud, “Tensile-strained germanium microdisks,” Appl. Phys. Lett. **102**(22), 221112 (2013). [CrossRef]

**30. **L. Ding, T.-Y. Liow, A. E.-J. Lim, N. Duan, M.-B. Yu, and G.-Q. Lo, “Ge waveguide photodetectors with responsivity roll-off beyond 1620 nm using localized stressor,” in Proceedings of OFC/NFOEC Tech. Digest, (2012), paper OW3G. [CrossRef]

**31. **R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics **4**(8), 495–497 (2010). [CrossRef]

**32. **V. Singh, P. T. Lin, N. Patel, H. Lin, L. Li, Y. Zou, F. Deng, C. Ni, J. Hu, J. Giammarco, A. P. Soliani, B. Zdyrko, I. Luzinov, S. Novak, J. Novak, P. Wachtel, S. Danto, J. D. Musgraves, K. Richardson, L. C. Kimerling, and A. M. Agarwal, “Mid-infrared materials and devices on a Si platform for optical sensing,” Sci. Technol. Adv. Mater. **15**(1), 014603 (2014). [CrossRef]

**33. **S. Adachi, *Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors* (John Wiley & Sons, 2009).

**34. **N. Lobontiu and E. Garcia, *Mechanics of Microelectromechanical Systems* (Kluwer Academic Publishers, 2005).

**35. **S. Ridene, K. Boujdaria, H. Bouchriha, and G. Fishman, “Infrared absorption in Si/Si_{1-}* _{x}*Ge

*/Si quantum wells,” Phys. Rev. B*

_{x}**64**(8), 085329 (2001). [CrossRef]

**36. **S. Gupta, V. Moroz, L. Smith, Q. Lu, and K. C. Saraswat, “7-nm FinFET CMOS design enabled by stress engineering using Si, Ge and Sn,” IEEE Trans. Electron. Dev. **61**(5), 1222–1230 (2014). [CrossRef]

**37. **J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, “Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si(100),” Phys. Rev. B **70**(15), 155309 (2004). [CrossRef]

**38. **S.-H. Wei and A. Zunger, “Predicted band-gap pressure coefficients of all diamond and zinc-blende semiconductors: chemical trends,” Phys. Rev. B **60**(8), 5404–5411 (1999). [CrossRef]

**39. **M. Chandrasekhar and F. H. Pollak, “Effects of uniaxial stress on the electroreflectance spectrum of Ge and GaAs,” Phys. Rev. B **15**(4), 2127–2144 (1977). [CrossRef]

**40. **R. Chen, Y.-C. Huang, S. Gupta, A. C. Lin, E. Sanchez, Y. Kim, K. C. Saraswat, T. I. Kamins, and J. S. Harris, “Material characterization of high Sn-content, compressively-strained GeSn epitaxial films after rapid thermal processing,” J. Cryst. Growth **365**, 29–34 (2013). [CrossRef]

**41. **M. J. Deen and P. K. Basu, *Silicon Photonics: Fundamental and Devices* (John Wiley & Sons, 2012).

**42. **P. K. Basu, *Theory of Optical Processes in Semiconductors Bulk and Microstructures* (Clarendon, 1997).

**43. **E. D. Palik, *Handbook of Optical Constants of Solids* (Academic, 1998)