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Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si

Jifeng Liu, Xiaochen Sun, Dong Pan, Xiaoxin Wang, Lionel C. Kimerling, Thomas L. Koch, and Jurgen Michel

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Abstract

We analyze the optical gain of tensile-strained, n-type Ge material for Si-compatible laser applications. The band structure of unstrained Ge exhibits indirect conduction band valleys (L) lower than the direct valley (Γ) by 136 meV. Adequate strain and n-type doping engineering can effectively provide population inversion in the direct bandgap of Ge. The tensile strain decreases the difference between the L valleys and the Γ valley, while the extrinsic electrons from n-type doping fill the L valleys to the level of the Γ valley to compensate for the remaining energy difference. Our modeling shows that with a combination of 0.25% tensile strain and an extrinsic electron density of 7.6×1019/cm3 by n-type doping, a net material gain of ~400 cm-1 can be obtained from the direct gap transition of Ge despite of the free carrier absorption loss. The threshold current density for lasing is estimated to be ~6kA cm-2 for a typical edge-emitting double heterojunction structure. These results indicate that tensile strained n-type Ge is a good candidate for Si integrated lasers.

©2007 Optical Society of America

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Figures (2)
Fig. 1.
Fig. 1. (a) Schematic band structure of bulk Ge, showing a 136 meV difference between the direct gap and the indirect gap, (b) the difference between the direct and the indirect gaps can be decreased by tensile strain, and (c) the rest of the difference between direct and indirect gaps in tensile strained Ge can be compensated by filling electrons into the L valleys.

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Fig. 2.
Fig. 2. (a) Band-to-band absorption measurement of the direct transition in unstrained [22] and tensile strained Ge (this work); (b) gain spectra from the direct transition in 0.25% tensile-strained n+ Ge with N=7.6×1019 cm-3 at different injected carrier densities; and gain from the direct transition, free carrier loss and net gain as a function of injected carrier density in (c) 0.25% tensile strained n+ Ge, and (d) n+ bulk Ge

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Equations (5)

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γ Γ ( h ν ) = ∣ α Γ ( h ν ) ∣ ( f c − f ν ) ,
∣ α Γ ( h ν ) ∣ = A ( h ν − E g Γ ) ⁄ h ν ,
∣ α Γ ( h ν ) ∣ = A ( h ν − E g Γ ( lh ) + h ν − E g Γ ( hh ) ) ⁄ h ν ,
α f ( λ ) = AN λ a + BP λ b ,
α f ( λ ) = − 3.4 × 10 − 25 N λ 2.25 − 3.2 × 10 − 25 P λ 2.43 ,
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