Modeling of a SiGeSn quantum well laser

Bahareh Marzban; Daniela Stange; Denis Rainko; Zoran Ikonic; Dan Buca; Jeremy Witzens

doi:10.1364/PRJ.416505

[1] F. Xia, L. Sekaric, Y. Vlasov. Ultracompact optical buffers on a silicon chip. Nat. Photonics, 1, 65-71(2007).

[2] J. Witzens. High-speed silicon photonics modulators. Proc. IEEE, 106, 2158-2182(2018).

[3] G. Masini, S. Sahni, G. Capellini, J. Witzens, C. Gunn. High-speed near infrared optical receivers based on Ge waveguide photodetectors integrated in a CMOS process. Adv. Opt. Technol., 2008, 196572(2008).

[4] A. Narasimha, S. Abdalla, C. Bradbury, A. Clark, J. Clymore, J. Coyne, A. Dahl, S. Gloekner, A. Gruenberg, D. Guckenberger, S. Gutierrez, M. Harrison, D. Kucharski, K. Leap, R. LeBlanc, Y. Liang, M. Mack, D. Martinez, G. Masini, A. Mekis, R. Menigoz, C. Ogden, M. Peterson, T. Pinguet, J. Redman, J. Rodriguez, S. Sahni, M. Sharp, T. J. Sleboda, D. Song, Y. Wang, B. Welch, J. Witzens, W. Xu, K. Yokoyama, P. De Dobbelaere. An ultra low power CMOS photonics technology platform for H/S optoelectronic transceivers at less than $1 per Gbps. Conference on Optical Fiber Communication (OFC), OMV.4(2010).

[5] H. Yu, P. Doussiere, D. Patel, W. Lin, K. Al-hemyari, J. Park, C. Jan, R. Herrick, I. Hoshino, L. Busselle, M. Bresnehan, A. Bowles, G. A. Ghiurcan, H. Frish, S. Yerkes, R. Venables, P. Seddighian, X. Serey, K. Nguyen, A. Banerjee, S. Amiralizadeh Asl, Q. Zhu, S. Gupta, A. Fuerst, A. Dahal, J. Chen, Y. Malinge, H. Mahalingam, M. Kwon, S. Gupta, A. Agrawal, R. Narayan, M. Favaro, D. Zhu, Y. Akulova. 400 Gbps fully integrated DR4 silicon photonics transmitter for data center applications. Conference on Optical Fiber Communication (OFC), T3H.6(2020).

[6] Y. Wan, D. Jung, J. Norman, C. Shang, I. MacFarlane, Q. Li, M. J. Kennedy, A. C. Gossard, K. M. Lau, J. E. Bowers. O-band electrically injected quantum dot micro-ring lasers on on-axis (001) GaP/Si and V-groove Si. Opt. Express, 25, 26853-26860(2017).

[7] Y. Wang, S. Chen, Y. Yu, L. Zhou, L. Liu, C. Yang, M. Liao, M. Tang, Z. Liu, J. Wu, W. Li, I. Ross, A. J. Seeds, H. Liu, S. Yu. Monolithic quantum-dot distributed feedback laser array on silicon. Optica, 5, 528-533(2018).

[8] Y. Han, Z. Yan, W. K. Ng, Y. Xue, K. S. Wong, K. M. Lau. Bufferless 1.5 μm III-V lasers grown on Si-photonics 220 nm silicon-on-insulator platforms. Optica, 7, 148-153(2020).

[9] Y. Shi, B. Kunert, Y. de Koninck, M. Pantouvaki, J. van Campenhout, D. van Thourhout. Novel adiabatic coupler for III-V nano-ridge laser grown on a Si photonics platform. Opt. Express, 27, 37781-37794(2019).

[10] V. Deshpande, H. Hahn, E. O’Connor, Y. Baumgartner, M. Sousa, D. Caimi, H. Boutry, J. Widiez, L. Brevard, C. Le Royer, M. Vinet, J. Fompeyrine, L. Czornomaz. First demonstration of 3D SRAM through 3D monolithic integration of InGaAs n-FinFETs on FDSOI Si CMOS with inter-layer contacts. Symposium on VLSI Technology, T74-T75(2017).

[11] J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, J. Michel. Ge-on-Si laser operating at room temperature. Opt. Lett., 35, 679-681(2010).

[12] R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, J. Michel. An electrically pumped germanium laser. Opt. Express, 20, 11316-11320(2012).

[13] R. E. Camacho-Aguilera. Ge-on-Si LASER for silicon photonics(2013).

[14] G. He, H. A. Atwater. Interband transitions in Sn_xGe_1−x alloys. Phys. Rev. Lett., 79, 1937-1940(1997).

[15] R. Kitamura, L. Pilon, M. Jonasz. Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature. Appl. Opt., 46, 8118-8133(2007).

[16] R. Soref. The past, present, and future of silicon photonics. IEEE J. Sel. Top. Quantum Electron., 12, 1678-1687(2006).

[17] R. Soref. Mid-infrared photonics in silicon and germanium. Nat. Photonics, 4, 495-497(2010).

[18] S. A. Ghetmiri, W. Du, J. Margetis, A. Mosleh, L. Cousar, B. R. Conley, L. Domulevicz, A. Nazzal, G. Sun, R. A. Soref, J. Tolle, B. Li, H. A. Naseem, S.-Q. Yu. Direct-bandgap GeSn grown on silicon with 2230 nm photoluminescence. Appl. Phys. Lett., 105, 151109(2014).

[19] S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, D. Grützmacher. Lasing in direct-bandgap GeSn alloy grown on Si. Nat. Photonics, 9, 88-92(2015).

[20] D. Stange, S. Wirths, R. Geiger, C. Schulte-Braucks, B. Marzban, N. von den Driesch, G. Mussler, T. Zabel, T. Stoica, J.-M. Hartmann, S. Mantl, Z. Ikonic, D. Grützmacher, H. Sigg, J. Witzens, D. Buca. Optically pumped GeSn microdisk lasers on Si. ACS Photon., 3, 1279-1285(2016).

[21] S. Al-Kabi, S. A. Ghetmiri, J. Margetis, T. Pham, Y. Zhou, W. Dou, B. Collier, R. Quinde, W. Du, A. Mosleh, J. Liu, G. Sun, R. A. Soref, J. Tolle, B. Li, M. Mortazavi, H. A. Naseem, S.-Q. Yu. An optically pumped 2.5 μm GeSn laser on Si operating at 110 K. Appl. Phys. Lett., 109, 171105(2016).

[22] J. Margetis, S. Al-Kabi, W. Du, W. Dou, Y. Zhou, T. Pham, P. Grant, S. Ghetmiri, A. Mosleh, B. Li, J. Liu, G. Sun, R. Soref, J. Tolle, M. Mortazavi, S.-Q. Yu. Si-based GeSn lasers with wavelength coverage of 2–3 μm and operating temperatures up to 180 K. ACS Photon., 5, 827-833(2018).

[23] Q. M. Thai, N. Pauc, J. Aubin, M. Bertrand, J. Chrétien, V. Delaye, A. Chelnokov, J.-M. Hartmann, V. Reboud, V. Calvo. GeSn heterostructure micro-disk laser operating at 230 K. Opt. Express, 26, 32500-32508(2018).

[24] Y. Zhou, W. Dou, W. Du, S. Ojo, H. Tran, S. A. Ghetmiri, J. Liu, G. Sun, R. Soref, J. Margetis, J. Tolle, B. Li, Z. Chen, M. Mortazavi, S.-Q. Yu. Optically pumped GeSn lasers operating at 270 K with broad waveguide structures on Si. ACS Photon., 6, 1434-1441(2019).

[25] J. Chrétien, N. Pauc, F. A. Pilon, M. Bertrand, Q.-M. Thai, L. Casiez, N. Bernier, H. Dansas, P. Gergaud, E. Delamadeleine, R. Khazaka, H. Sigg, J. Faist, A. Chelnokov, V. Reboud, J.-M. Hartmann, V. Calvo. GeSn lasers covering a wide wavelength range thanks to uniaxial tensile strain. ACS Photon., 6, 2462-2469(2019).

[26] Z. Alferov. Double heterostructure lasers: early days and future perspectives. IEEE J. Sel. Top. Quantum Electron., 6, 832-840(2000).

[27] R. Chen, S. Gupta, Y.-C. Huang, Y. Huo, C. W. Rudy, E. Sanchez, Y. Kim, T. I. Kamins, K. C. Saraswat, J. S. Harris. Demonstration of a Ge/GeSn/Ge quantum-well microdisk resonator on silicon: enabling high-quality Ge(Sn) materials for micro- and nanophotonics. Nano Lett., 14, 37-43(2014).

[28] D. Stange, N. von den Driesch, D. Rainko, S. Roesgaard, I. Povstugar, J.-M. Hartmann, T. Stoica, Z. Ikonic, S. Mantl, D. Grützmacher, D. Buca. Short-wave infrared LEDs from GeSn/SiGeSn multiple quantum wells. Optica, 4, 185-188(2017).

[29] D. Stange, N. von den Driesch, T. Zabel, F. Armand-Pilon, D. Rainko, B. Marzban, P. Zaumseil, J.-M. Hartmann, Z. Ikonic, G. Capellini, S. Mantl, H. Sigg, J. Witzens, D. Grützmacher, D. Buca. GeSn/SiGeSn heterostructure and multi quantum well lasers. ACS Photon., 5, 4628-4636(2018).

[30] N. von den Driesch, D. Stange, D. Rainko, I. Povstugar, P. Zaumseil, G. Capellini, T. Schröder, T. Denneulin, Z. Ikonic, J.-M. Hartmann, H. Sigg, S. Mantl, D. Grützmacher, D. Buca. Advanced GeSn/SiGeSn group IV heterostructure lasers. Adv. Sci., 5, 1700955(2018).

[31] S. Wirths, D. Buca, Z. Ikonic, P. Harrison, A. T. Tiedemann, B. Holländer, T. Stoica, G. Mussler, U. Breuer, J. M. Hartmann. SiGeSn growth studies using reduced pressure chemical vapor deposition towards optoelectronic applications. Thin Solid Films, 557, 183-187(2014).

[32] A. Elbaz, D. Buca, N. von den Driesch, K. Pantzas, G. Patriarche, N. Zerounian, E. Herth, X. Checoury, S. Sauvage, I. Sagnes, A. Foti, R. Ossikovski, J.-M. Hartmann, F. Boeuf, Z. Ikonic, P. Boucaud, D. Grützmacher, M. El Kurdi. Ultra-low-threshold continuous-wave and pulsed lasing in tensile-strained GeSn alloys. Nat. Photonics, 14, 375-382(2020).

[33] Y. Zhou, Y. Miao, S. Ojo, H. Tran, G. Abernathy, J. M. Grant, S. Amoah, G. Salamo, W. Du, J. Liu, J. Margetis, J. Tolle, Y.-H. Zhang, G. Sun, R. A. Soref, B. Li, S.-Q. Yu. Electrically injected GeSn lasers on Si operating up to 100 K. Optica, 7, 924-928(2020).

[34] B. Marzban, J. Nojic, D. Stange, D. Buca, J. Witzens. Design of a waveguide-coupled GeSn disk laser. IEEE Photonics Society Summer Topicals, 1-2(2020).

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

[36] G. Sun, R. A. Soref, H. H. Cheng. Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode. Opt. Express, 18, 19957-19965(2010).

[37] D. Rainko, Z. Ikonic, N. Vukmirović, D. Stange, N. von den Driesch, D. Grützmacher, D. Buca. Investigation of carrier confinement in direct bandgap GeSn/SiGeSn 2D and 0D heterostructures. Sci. Rep., 8, 15557(2018).

[38] S. Cho, R. Chen, S. Koo, G. Shambat, H. Lin, N. Park, J. Vuckovic, T. I. Kamins, B.-G. Park, J. S. Harris. Fabrication and analysis of epitaxially grown Ge_1-xSn_x microdisk resonator with 20-nm free-spectral range. IEEE Photon. Technol. Lett., 23, 1535-1537(2011).

[39] H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, Y.-H. Lee. Electrically driven single-cell photonic crystal laser. Science, 305, 1444-1447(2004).

[40] O. Moutanabbir, S. Assali, X. Gong, E. O’Reilly, C. A. Broderick, B. Marzban, J. Witzens, W. Du, S.-Q. Yu, A. Chelnokov, D. Buca, D. Nam. Monolithic infrared silicon photonics: the rise of (Si)GeSn semiconductors. Appl. Phys. Lett., 118, 110502(2021).

[41] R. Geiger. Direct band gap germanium for Si-compatible lasing(2016).

[42] B. Julsgaard, N. von den Driesch, P. Tidemand-Lichtenberg, C. Pedersen, Z. Ikonic, D. Buca. Carrier lifetime of GeSn measured by spectrally resolved picosecond photoluminescence spectroscopy. Photon. Res., 8, 788-798(2020).

[43] S. N. Khatami, Z. Aksamija. Lattice thermal conductivity of the binary and ternary group-IV alloys Si-Sn, Ge-Sn, and Si-Ge-Sn. Phys. Rev. Appl., 6, 014015(2016).

[44] U. Piesbergen. The mean atomic heats of the III-V semiconductors: AlSb, GaAs, InP, GaSb, InAs, InSb and the atomic heats of the element Ge between 12 and 273 K. Z. Naturforsch., 18, 141-147(1963).

[45] H. Tran, W. Du, S. A. Ghetmiri, A. Mosleh, G. Sun, R. A. Soref, J. Margetis, J. Tolle, B. Li, H. A. Naseem, S.-Q. Yu. Systematic study of Ge_1−xSn_x absorption coefficient and refractive index for the device applications of Si-based optoelectronics. J. Appl. Phys., 119, 103106(2016).

[46] T. B. Bahder. Eight-band k·p model of strained zinc-blende crystals. Phys. Rev. B, 41, 11992-12001(1990).

[47] K. L. Low, Y. Yang, G. Han, W. Fan, Y.-C. Yeo. Electronic band structure and effective mass parameters of Ge_1-xSn_x alloys. J. Appl. Phys., 112, 103715(2012).

[48] M. Jaros. Simple analytic model for heterojunction band offsets. Phys. Rev. B, 37, 7112-7114(1988).

[49] I. Synopsys. Sentaurus™ Device User Guide, Version N-2017.09(2017).

[50] C. R. Crowell. The Richardson constant for thermionic emission in Schottky barrier diodes. Solid-State Electron., 8, 395-399(1965).

[51] D. Tammaro, K. Hess, F. Capasso. Γ- X phonon-assisted thermionic currents in the GaAs/Al_xGa_1-x As interface system. J. Appl. Phys., 73, 8536-8543(1993).

[52] N. K. Dutta, R. J. Nelson. The case for Auger recombination in In_1–xGa_xAs_yP_1-y. J. Appl. Phys., 53, 74-92(1982).

[53] N. F. Massé, A. R. Adams, S. J. Sweeney. Experimental determination of the band gap dependence of Auger recombination in InGaAs/InP multiple quantum well lasers at room temperature. Appl. Phys. Lett., 90, 161113(2007).

[54] R. Geiger, T. Zabel, H. Sigg. Group IV direct band gap photonics: methods, challenges, and opportunities. Front. Mater., 2, 52(2015).

[55] A. Sugimura. Band-to-band Auger recombination effect on InGaAsP laser threshold. IEEE J. Quantum Electron., 17, 627-635(1981).

[56] W. W. Lui, T. Yamanaka, Y. Yoshikuni, K. Yokoyama, S. Seki. Suppression of Auger recombination effects in compressively strained quantum-well lasers. IEEE J. Quantum Electron., 29, 1544-1552(1993).

[57] S. Assali, M. Elsayed, J. Nicolas, M. O. Liedke, A. Wagner, M. Butterling, R. Krause-Rehberg, O. Moutanabbir. Vacancy complexes in nonequilibrium germanium-tin semiconductors. Appl. Phys. Lett., 114, 251907(2019).

[58] E. Gaubas, J. Vanhellemont. Dependence of carrier lifetime in germanium on resisitivity and carrier injection level. Appl. Phys. Lett., 89, 142106(2006).

[59] S. Gupta, R. Chen, J. S. Harris, K. C. Saraswat. Atomic layer deposition of Al₂O₃ on germanium-tin (GeSn) and impact of wet chemical surface pre-treatment. Appl. Phys. Lett., 103, 241601(2013).

[60] S. Park, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, H. Nishi, R. Kou, S.-I. Itabashi. Influence of carrier lifetime on performance of silicon p-i-n variable optical attenuators fabricated on submicrometer rib waveguides. Opt. Express, 18, 11282-11291(2010).

[61] N. von den Driesch. Epitaxy of group IV Si-Ge-Sn alloys for advanced heterostructure light emitters(2017).

[62] C. Schulte-Braucks. Investigation of GeSn as novel group IV semiconductor for electronic applications(2017).

[63] O. A. Golikova, B. Y. Moizhes, L. S. Stilbans. Hole mobility of germanium as a function of concentration and temperature. Sov. Phys. Solid State, 3, 2259-2265(1962).

[64] N. D. Arora, J. R. Hauser, D. J. Roulston. Electron and hole mobilities in silicon as a function of concentration and temperature. IEEE Trans. Electron. Devices, 29, 292-295(1982).

[65] http://www.doi.org/10.6084/m9.figshare.14115407. http://www.doi.org/10.6084/m9.figshare.14115407

[66] L. A. Coldren, S. W. Corzine, M. Mashanovitch. Diode Lasers and Photonic Integrated Circuits(2012).

[67] L. A. Coldren, S. W. Corzine, M. Mashanovitch. Diode Lasers and Photonic Integrated Circuits(2012).

[68] D. V. Karasyov, V. K. Kononenko. Broadening of gain spectra of quantum-well lasers. J. Appl. Spectrosc., 61, 739-743(1994).

[69] R. Nagarajan, T. Kamiya, A. Kurobe. Band filling in GaAs/AlGaAs multiquantum well lasers and its effect on the threshold current. IEEE J. Quantum Electron., 25, 1161-1170(1989).

[70] A. A. Afonenko, V. K. Kononenko, A. Joullié. On spectral line broadening in quantum-well heterostructure lasers. Proc. SPIE, 6184, 618428(2006).

[71] M. Prost, M. El Kurdi, F. Aniel, N. Zerounian, S. Sauvage, X. Checoury, F. Bœuf, P. Boucaud. Analysis of optical gain threshold in n-doped and tensile-strained germanium heterostructure diodes. J. Appl. Phys., 118, 125704(2015).

[72] J. I. Pankove, P. Aigrain. Optical absorption of arsenic-doped degenerate germanium. Phys. Rev., 126, 956-962(1962).

[73] R. Camacho-Aguilera, Z. Han, Y. Cai, L. C. Kimerling, J. Michel. Direct band gap narrowing in highly doped Ge. Appl. Phys. Lett., 102, 152106(2013).

[74] S. C. Jain, D. J. Roulston. A simple expression for band gap narrowing (BGN) in heavily doped Si, Ge, GaAs and Ge_xSi_1−x strained layers. Solid State Electron., 34, 453-465(1991).

[75] J. T. Robinson, K. Preston, O. Painter, M. Lipson. First-principle derivation of gain in high-index-contrast waveguides. Opt. Express, 16, 16659-16669(2008).

[76] M. Heiblum, J. Harris. Analysis of curved optical waveguides by conformal transformation. IEEE J. Quantum Electron., 11, 75-83(1975).

[77] R. Soref, B. Bennett. Electrooptical effects in silicon. IEEE J. Quantum Electron., 23, 123-129(1987).

[78] A. Afzali-Kushaa, G. I. Haddad. Effects of biaxial strain on the intervalence-band absorption spectra of InGaAs/InP systems. J. Appl. Phys., 77, 6549-6556(1995).

[79] C.-Y. Tsai, C.-Y. Tsai, C.-H. Chen, T.-L. Sung, T.-Y. Wu, F.-P. Shih. Theoretical model for intravalley and intervalley free-carrier absorption in semiconductor lasers: beyond the classical Drude model. IEEE J. Quantum Electron., 34, 552-559(1998).

[80] M. Nedeljkovic, R. Soref, G. Z. Mashanovich. Predictions of free-carrier electroabsorption and electrorefraction in germanium. IEEE Photon. J., 7, 2600214(2015).

[81] R. Newman, W. W. Tyler. Effect of impurities on free-hole infrared absorption in p-type germanium. Phys. Rev., 105, 885-886(1957).

[82] E. Jaberansary, T. M. B. Masaud, M. M. Milosevic, M. Nedeljkovic, G. Z. Mashanovich, H. M. H. Chong. Scattering loss estimation using 2-D Fourier analysis and modeling of sidewall roughness on optical waveguides. IEEE Photon. J., 5, 6601010(2013).

[83] V. R. D’Costa, C. S. Cook, A. G. Birdwell, C. L. Littler, M. Canonico, S. Zollner, J. Kouvetakis, J. Menéndez. Optical critical points of thin-film Ge_1−ySn_y alloys: a comparative Ge_1−ySn_y/Ge_1−xSi_x study. Phys. Rev. B, 73, 125207(2006).

[84] W.-J. Yin, X.-G. Gong, S.-H. Wei. Origin of the unusually large band-gap bowing and the breakdown of the band-edge distribution rule in the Sn_xGe_1-x alloys. Phys. Rev. B, 78, 161203(2008).

[85] A. Kurobe, H. Furuyama, S. Naritsuka, N. Sugiyama, Y. Kokubun, M. Nakamura. Effects of well number, cavity length, and facet reflectivity on the reduction of threshold current of GaAs/AlGaAs multiquantum well lasers. IEEE J. Quantum Electron., 24, 635-640(1988).

[86] P. C. Grant, J. Margetis, W. Du, Y. Zhou, W. Dou, G. Abernathy, A. Kuchuk, B. Li, J. Tolle, J. Liu, G. Sun, R. A. Soref, M. Mortazavi, S.-Q. Yu. Study of direct bandgap type-I GeSn/GeSn double quantum well with improved carrier confinement. Nanotechnology, 29, 465201(2018).

[87] S. Assali, A. Dijkstra, A. Attiaoui, É. Bouthillier, J. E. M. Haverkort, O. Moutanabbir. Midinfrared emission and absorption in strained and relaxed direct band-Gap Ge_1-xSn_x semiconductors. Phys. Rev. Appl., 15, 024031(2021).

[88] Y. C. Chang, R. B. James. Saturation of intersubband transitions in p-type semiconductor quantum wells. Phys. Rev. B, 39, 12672-12681(1989).

[89] S. L. Chuang. Chapter 4: theory of electronic band structures in semiconductors. Physics of Optoelectronic Devices(1995).

[90] Y.-M. Mu, S. S. Pei. Effects of anisotropic k·p interactions on energy bands and optical properties of type-II interband cascade lasers. J. Appl. Phys., 96, 1866-1879(2004).

[91] M.-Y. Ryu, T. R. Harris, Y. K. Yeo, R. T. Beeler, J. Kouvetakis. Temperature-dependent photoluminescence of Ge/Si and Ge_1-ySn_y/Si, indicating possible indirect-to-direct bandgap transition at lower Sn content. Appl. Phys. Lett., 102, 171908(2013).