Abstract

We describe a combined 6 x 6 k · p and one-band effective mass modelling tool to calculate absorption spectra in Ge–SiGe multiple quantum well (MQW) heterostructures. We find good agreement with experimentally measured absorption spectra of Ge–SiGe MQW structures described previously in the literature, proving its predictive capability, and the simulation tool is used for the analysis and design of electroabsorption modulators. We employ strain-engineering in Ge–SiGe MQW systems to design structures for modulation at 1310 nm and 1550 nm.

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  52. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, J. S. Harris, "Quantum-confined stark effect in Ge–SiGe quantum wells on Si for optical modulators," IEEE J. Sel. Topics Quantum Electron. 12, 1503-1513 (2006).
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  54. W. L. Bloss, "Linewidths of quantum well eigenstates with finite barriers," Superlattices Microstruct. 7, 63-67 (1990).
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2010 (1)

L. Lever, Z. Ikonić, A. Valavanis, R. W. Kelsall, "Design of Ge–SiGe quantum-confined Stark effect modulators for CMOS compatible photonics," Proc. SPIE 7606, (2010).

2009 (3)

D. Miller, "Device requirements for optical interconnects to silicon chips," Proc. IEEE 97, 1166-1185 (2009).

V. V. Afanas'ev, A. Stesmans, L. Souriau, R. Loo, M. Meuris, "Valence band energy in confined Si$_{1-x}$Ge$_x$$(0.28 < x < 0.93)$ layers," Appl. Phys. Lett. 94, 172106 (2009).

C. Lange, N. S. Köster, S. Chatterjee, H. Sigg, D. Chrastina, G. Isella, H. von Känel, M. Schäfer, M. Kira, S. W. Koch, "Ultrafast nonlinear optical response of photoexcited Ge–SiGe quantum wells: Evidence for a femtosecond transient population inversion," Phys. Rev. B 79, 201306 (2009).

2008 (4)

M. Virgilio, G. Grosso, "Quantum-confined stark effect in Ge–SiGe quantum wells: A tight-binding description," Phys. Rev. B 77, 165315 (2008).

D. J. Paul, "8-band {\bf k}$\cdot{\bf p}$ modeling of the quantum confined stark effect in Ge quantum wells on Si substrates," Phys. Rev. B 77, 155323 (2008).

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, D. A. Miller, "Material properties of Si-Ge–Ge quantum wells," IEEE J. Sel. Topics Quantum Electron. 14, 1082-1089 (2008).

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, D. A. B. Miller, "C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing," Electron. Lett. 44, (2008).

2007 (1)

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, M. Paniccia, "40 gbit/s silicon optical modulator for high-speed applications," Electron. Lett. 43, (2007).

2006 (2)

K. Driscoll, R. Paiella, "Silicon-based injection lasers using electronic intersubband transitions in the $L$ valleys," Appl. Phys. Lett. 89, 191110 (2006).

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, J. S. Harris, "Quantum-confined stark effect in Ge–SiGe quantum wells on Si for optical modulators," IEEE J. Sel. Topics Quantum Electron. 12, 1503-1513 (2006).

2005 (3)

Y. Ishikawa, K. Wada, J. Liu, D. D. Cannon, H.-C. Luan, J. Michel, L. C. Kimerling, "Strain-induced enhancement of near-infrared absorption in Ge epitaxial layers grown on Si substrate," J. Appl. Phys. 98, 013501 (2005).

M. Rouviere, M. Halbwax, J.-L. Cercus, E. Cassan, L. Vivien, D. Pascal, M. Heitzmann, J.-M. Hartmann, S. Laval, "Integration of germanium waveguide photodetectors for intrachip optical interconnects," Opt. Eng. 44, 075402 (2005).

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, J. S. Harris, "Strong quantum-confined Stark effect in germanium quantum-well structures on silicon," Nature 437, 1334-1336 (2005).

2004 (4)

R. Lewén, S. Irmscher, U. Westergren, L. Thylén, U. Eriksson, "Segmented transmission-line electroabsorption modulators," J. Lightw. Technol. 22, 172-179 (2004).

J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, L. C. Kimerling, "Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si(100)," Phys. Rev. B 70, 155309 (2004).

J. M. Hartmann, A. Abbadie, A. M. Papon, P. Holliger, G. Rolland, T. Billon, J. M. Fédéli, M. Rouvière, L. Vivien, S. Laval, "Reduced pressure–chemical vapor deposition of Ge thick layers on Si(001) for 1.3–1.55-$\mu$m photodetection," J. Appl. Phys. 95, 5905-5913 (2004).

D. J. Paul, "Si/SiGe heterostructures: From material and physics to devices and circuits," Semicond. Sci. Technol. 19, R75R108 (2004).

2003 (1)

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, L. C. Kimerling, "Strain-induced bandgap shrinkage in Ge grown on Si substrate," Appl. Phys. Lett. 82, 2044-2046 (2003).

2002 (1)

E. Peiner, A. Guttzeit, H.-H. Wehmann, "The effect of threading dislocations on optical absorption and electron scattering in strongly mismatched heteroepitaxial IIIV compound semiconductors on silicon," J. Phys.: Conden. Matt. 14, 13195 (2002).

2000 (1)

F. Tekia, M. Ferhat, A. Zaoui, "Band-gap bowing in ${\rm Si}_x{\rm Ge}_{1-x}$ alloy," Phys. B: Cond. Matt. 293, 183-186 (2000).

1999 (1)

S.-H. Wei, A. Zunger, "Predicted bandgap pressure coefficients of all diamond and zinc-blende semiconductors: Chemical trends," Phys. Rev. B 60, 5404-5411 (1999).

1998 (1)

T. H. Wood, "Multiple quantum well (MQW) waveguide modulators," J. Lightw. Technol. 6, 743-757 (1998).

1997 (2)

D. J. Dunstan, "Strain and strain relaxation in semiconductors," J. Materi. Sci.: Mater. Electron. 8, 337-375 (1997).

M. E. Brenchley, M. Hopkinson, A. Kelly, P. Kidd, D. J. Dunstan, "Coherency strain as an athermal strengthening mechanism," Phys. Rev. Lett. 78, 3912-3914 (1997).

1996 (3)

A. Ramdane, F. Devaux, N. Souli, D. Delprat, A. Ougazzaden, "Monolithic integration of multiple-quantum-well lasers and modulators for high-speed transmission," IEEE J. Sel. Top. Quantum Electron. 2, 326-335 (1996).

M. V. Fischetti, S. E. Laux, "Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys," J. Appl. Phys. 80, 2234-2252 (1996).

E. Li, B. Weiss, K.-S. Chan, "Eigenstates and absorption spectra of interdiffused AlGaAs-GaAs multiple-quantum-well structures," IEEE J. Quantum Electron. 32, 1399-1416 (1996).

1995 (1)

T. Ido, S. Tanaka, M. Suzuki, H. Inoue, "MQW electroabsorption optical modulator for 40 Gbit/s modulation," Electron. Lett. 31, 2124-2125 (1995).

1994 (3)

M. Kahan, M. Chi, L. Friedman, "Infrared transitions in strained-layer Ge$_x$Si$_{1-x}$/Si," J. Appl. Phys. 75, 8012-8021 (1994).

X. Q. Zhou, H. M. van Driel, G. Mak, "Femtosecond kinetics of photoexcited carriers in germanium," Phys. Rev. B 50, 5226-5230 (1994).

A. McLean, C. Mitchell, D. Swanston, "Implementation of an efficient analytical approximation to the voigt function for photoemission lineshape analysis," J. Electron. Spectr. Related Phenom. 69, 125-132 (1994).

1993 (3)

N. Susa, "Improvement in electroabsorption and the effects of parameter variations in the three-step asymmetric coupled quantum well," J. Appl. Phys. 73, 932-942 (1993).

M. M. Rieger, P. Vogl, "Electronic-band parameters in strained $si1-xgex$ alloys on $si1-ygey$ substrates," Phys. Rev. B 48, 14 276-14 287 (1993).

M. E. Chin, W. S. C. Chang, "Theoretical design optimization of multiple-quantum-well electroabsorption waveguide modulators," IEEE J. Quantum Electron. 29, 2476-2488 (1993).

1991 (2)

A. M. Fox, D. A. B. Miller, G. Livescu, J. E. Cunningham, W. Y. Jan, "Excitonic effects in coupled quantum wells," Phys. Rev. B 44, 6231-6242 (1991).

M. Fischetti, "Monte Carlo simulation of transport in technologically significant semiconductors of the diamond and zinc-blende structures. I. Homogeneous transport," IEEE Trans. Electron. Devices 38, 634-649 (1991).

1990 (2)

S. Schmitt-Rink, D. S. Chemla, W. H. Knox, D. A. B. Miller, "How fast is excitonic electroabsorption?," Opt. Lett. 15, 60-62 (1990).

W. L. Bloss, "Linewidths of quantum well eigenstates with finite barriers," Superlattices Microstruct. 7, 63-67 (1990).

1989 (2)

C. G. Van de Walle, "Band lineups and deformation potentials in the model-solid theory," Phys. Rev. B 39, 1871-1883 (1989).

J. Weber, M. I. Alonso, "Near-band-gap photoluminescence of Si-Ge alloys," Phys. Rev. B 40, 5683-5693 (1989).

1988 (1)

D. Y. K. Ko, J. C. Inkson, "Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems," Phys. Rev. B 38, 9945-9951 (1988).

1987 (1)

D. F. Nelson, R. C. Miller, D. A. Kleinman, "Band nonparabolicity effects in semiconductor quantum wells," Phys. Rev. B 35, 7770-7773 (1987).

1986 (1)

C. G. Van de Walle, R. M. Martin, "Theoretical calculations of heterojunction discontinuities in the Si/Ge system," Phys. Rev. B 34, 5621-5634 (1986).

1985 (1)

1984 (2)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, "Band-edge electroabsorption in quantum well structures: The quantum-confined Stark effect," Phys. Rev. Lett. 53, 2173-2176 (1984).

D. Chemla, D. Miller, P. Smith, A. Gossard, W. Wiegmann, "Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures," IEEE J. Quantum Electron. QE-20, 265-275 (1984).

1971 (1)

L. D. Laude, F. H. Pollak, M. Cardona, "Effects of uniaxial stress on the indirect exciton spectrum of silicon," Phys. Rev. B 3, 2623-2636 (1971).

1966 (2)

A. Frova, P. Handler, F. A. Germano, D. E. Aspnes, "Electro-absorption effects at the band edges of silicon and germanium," Phys. Rev. 145, 575-583 (1966).

M. Cardona, F. H. Pollak, "Energy-band structure of germanium and silicon: The ${\bf k}\cdot{\bf p}$ method," Phys. Rev. 142, 530-543 (1966).

1958 (1)

R. Braunstein, A. R. Moore, F. Herman, "Intrinsic optical absorption in germanium-silicon alloys," Phys. Rev. 109, 695-710 (1958).

1955 (1)

B. Lax, J. G. Mavroides, "Statistics and galvanomagnetic effects in germanium and silicon with warped energy surfaces," Phys. Rev. 100, 1650-1657 (1955).

Appl. Opt. (1)

Appl. Phys. Lett. (3)

Y. Ishikawa, K. Wada, D. D. Cannon, J. Liu, H.-C. Luan, L. C. Kimerling, "Strain-induced bandgap shrinkage in Ge grown on Si substrate," Appl. Phys. Lett. 82, 2044-2046 (2003).

V. V. Afanas'ev, A. Stesmans, L. Souriau, R. Loo, M. Meuris, "Valence band energy in confined Si$_{1-x}$Ge$_x$$(0.28 < x < 0.93)$ layers," Appl. Phys. Lett. 94, 172106 (2009).

K. Driscoll, R. Paiella, "Silicon-based injection lasers using electronic intersubband transitions in the $L$ valleys," Appl. Phys. Lett. 89, 191110 (2006).

Electron. Lett. (3)

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, M. Paniccia, "40 gbit/s silicon optical modulator for high-speed applications," Electron. Lett. 43, (2007).

T. Ido, S. Tanaka, M. Suzuki, H. Inoue, "MQW electroabsorption optical modulator for 40 Gbit/s modulation," Electron. Lett. 31, 2124-2125 (1995).

J. E. Roth, O. Fidaner, E. H. Edwards, R. K. Schaevitz, Y.-H. Kuo, N. C. Helman, T. I. Kamins, J. S. Harris, D. A. B. Miller, "C-band side-entry Ge quantum-well electroabsorption modulator on SOI operating at 1 V swing," Electron. Lett. 44, (2008).

IEEE J. Quantum Electron. (3)

M. E. Chin, W. S. C. Chang, "Theoretical design optimization of multiple-quantum-well electroabsorption waveguide modulators," IEEE J. Quantum Electron. 29, 2476-2488 (1993).

E. Li, B. Weiss, K.-S. Chan, "Eigenstates and absorption spectra of interdiffused AlGaAs-GaAs multiple-quantum-well structures," IEEE J. Quantum Electron. 32, 1399-1416 (1996).

D. Chemla, D. Miller, P. Smith, A. Gossard, W. Wiegmann, "Room temperature excitonic nonlinear absorption and refraction in GaAs/AlGaAs multiple quantum well structures," IEEE J. Quantum Electron. QE-20, 265-275 (1984).

IEEE J. Sel. Top. Quantum Electron. (1)

A. Ramdane, F. Devaux, N. Souli, D. Delprat, A. Ougazzaden, "Monolithic integration of multiple-quantum-well lasers and modulators for high-speed transmission," IEEE J. Sel. Top. Quantum Electron. 2, 326-335 (1996).

IEEE J. Sel. Topics Quantum Electron. (2)

R. K. Schaevitz, J. E. Roth, S. Ren, O. Fidaner, D. A. Miller, "Material properties of Si-Ge–Ge quantum wells," IEEE J. Sel. Topics Quantum Electron. 14, 1082-1089 (2008).

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, J. S. Harris, "Quantum-confined stark effect in Ge–SiGe quantum wells on Si for optical modulators," IEEE J. Sel. Topics Quantum Electron. 12, 1503-1513 (2006).

IEEE Trans. Electron. Devices (1)

M. Fischetti, "Monte Carlo simulation of transport in technologically significant semiconductors of the diamond and zinc-blende structures. I. Homogeneous transport," IEEE Trans. Electron. Devices 38, 634-649 (1991).

J. Appl. Phys. (5)

M. Kahan, M. Chi, L. Friedman, "Infrared transitions in strained-layer Ge$_x$Si$_{1-x}$/Si," J. Appl. Phys. 75, 8012-8021 (1994).

M. V. Fischetti, S. E. Laux, "Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys," J. Appl. Phys. 80, 2234-2252 (1996).

N. Susa, "Improvement in electroabsorption and the effects of parameter variations in the three-step asymmetric coupled quantum well," J. Appl. Phys. 73, 932-942 (1993).

J. M. Hartmann, A. Abbadie, A. M. Papon, P. Holliger, G. Rolland, T. Billon, J. M. Fédéli, M. Rouvière, L. Vivien, S. Laval, "Reduced pressure–chemical vapor deposition of Ge thick layers on Si(001) for 1.3–1.55-$\mu$m photodetection," J. Appl. Phys. 95, 5905-5913 (2004).

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