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We theoretically investigate a tensile strained GeSn waveguide integrated with Si3N4 liner stressor for the applications in mid-infrared (MIR) detector and modulator. A substantial tensile strain is induced in a 1 × 1 μm2 GeSn waveguide by the expansion of 500 nm Si3N4 liner stressor and the contour plots of strain are simulated by the finite element simulation. Under the tensile strain, the direct bandgap EG,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 Si3N4 liner stressor expands by 1%, the cut-off wavelengths of tensile strained Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 waveguide photodetectors are extended to 2.32, 2.69, and 4.06 μm, respectively. Tensile strained Ge0.90Sn0.10 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 Ge0.90Sn0.10 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 EG,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]. Ge0.91Sn0.09 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 EG,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 Si3N4 tensile liner stressor. The tensile strain induced by the Si3N4 liner leads to the shrinkage of EG,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 Si3N4 liner stressor. Si3N4 stressor has been a common method for introducing tensile strain in Ge devices [27–30]. However, the operating wavelength corresponding to EG,Γ is still limited to about 2 μm. The purpose of this work is to utilize Si3N4 liner stressor and GeSn with smaller EG,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 SiO2 [31, 32]. So SOUP waveguide structure is utilized and a Si3N4 liner stressor wrapping around the waveguide induces tensile strain in the GeSn material. As shown in Fig. 1(b), the Si3N4 expands, and thus stretches the GeSn waveguide.
Fig. 1 (a) 3D schematic of GeSn on SOUP waveguide integrated with the Si3N4 liner stressor. (b) GeSn waveguide is stretched with the expansion of Si3N4 liner stressor.
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 Si3N4 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 Si3N4 was taken as 250.0 GPa [34]. During the simulation, the volume of compressively strained Si3N4 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 Ge0.95Sn0.05 waveguide integrated with Si3N4 liner stressor. Figures 2(b)-2(d) illustrate the contour plots for the strain along [100], [010], and [001] directions in AA’ plane of Ge0.95Sn0.05 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 Ge0.95Sn0.05 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 Ge0.95Sn0.05 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.
Fig. 2 (a) 3D schematic of Si3N4 liner stressor wrapped around GeSn on SOUP waveguide and the key geometric parameters. Coordinate axes are also shown. Contour plots for (b) ε[100], (c) ε[010], and (d) ε[001] in AA’ plane and (e) ε[100], (f) ε[010], and (g) ε[001] in BB’ plane in GeSn waveguide region.
We investigate the impact of tensile strain on the EG,Γ and the indirect band gap at L point EG,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 EG,Г and EG,L values of relaxed GeSn were taken from the recent calculation and experimental results [12–14]. The reduction of EG,Г and EG,L induced by strain is given by [35, 37], where and 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 Si3N4 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 Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10. Compared to relaxed GeSn, the EG,Г and EG,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 Ge0.95Sn0.05 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 EG,Г in tensile strained GeSn devices. Figure 4 compares the EG,Γ and EG,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 EG,Г of relaxed Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 are 0.690, 0.617, and 0.455 eV, respectively. Under the tensile strain that induced by Si3N4 liner stressor, Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 waveguides exhibit the EG,Г of 0.534, 0.461, and 0.306 eV, respectively.
Fig. 3 E-k energy band diagrams of (a) unstrained Ge0.97Sn0.03, (b) tensile strained Ge0.97Sn0.03, (c) unstrained Ge0.95Sn0.05, (d) tensile strained Ge0.95Sn0.05, (e) unstrained Ge0.90Sn0.10, and (f) tensile strained Ge0.90Sn0.10. Decreasing of the energy of Γ and L conduction valleys and splitting of HH and LH bands are observed in the tensile strained GeSn with various compositions. Spin-orbit (SO) split in the valence band is shown.
Fig. 4 Comparison of EG,Γ and EG,L of relaxed GeSn and tensile strained GeSn waveguide wrapped in Si3N4 liner stressor, showing the significant band gap reduction for tensile strained GeSn waveguides over the relaxed GeSn devices.
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.
Fig. 5 Cross-section of tensile strained GeSn on SOUP waveguide, which is butt-coupled to Si waveguide.
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 and EG,Γ of GeSn [41],
where is the Plank constant, 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 equals to the EG,Γ of the materials. The cut-off wavelengths of relaxed Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 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 Si3N4 liner stressor. As the 500 nm Si3N4 liner stressor expands by 1%, the cut-off wavelengths of strained Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 are extended to 2.32, 2.69, and 4.06 μm, respectively.Fig. 6 Calculated absorption spectra for relaxed and tensile strained Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 waveguide photodetectors. The cut-off wavelength of GeSn is significantly extended to MIR due to the tensile strain induced by Si3N4 liner stressor.
3.3 Franz-Keldysh effect in tensile strained Ge0.90Sn0.10 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]
where 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 αb andβ are given byandrespectively. In Eqs. (3) and (4), n is the refractive index, ε0 is the vacuum permittivity, c is the velocity of light, me 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.Figure 7 depicts α versus wavelength plots for the tensile strained Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 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 Ge0.90Sn0.10 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 Ge0.90Sn0.10 waveguide modulator at wavelengths of 4.25, 4.50, and 4.75 μm. The refractive indexes for Ge0.90Sn0.10, Si3N4, and SiO2 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 Ge0.90Sn0.10 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.
Fig. 7 α as a function of wavelength for Ge0.97Sn0.03, Ge0.95Sn0.05, and Ge0.90Sn0.10 waveguides at different electric fields. For all the samples, the shift of cut-off wavelength to MIR is observed with the increase of external electric field.
Fig. 8 Mode profiles of both TE and TM modes at different wavelengths in Ge0.90Sn0.10 waveguide. Single mode transmission is demonstrated.
Fig. 9 Propagation loss of (a) TE mode and (b) TM mode in tensile strained Ge0.90Sn0.10 waveguide at various biases. Propagation loss of GeSn device exhibits the wavelength dependence. Propagation loss increases with the increasing of external electric field due to the FK effect, which will improve the modulation depth of Ge0.90Sn0.10 waveguide electro-absorption modulator.
4. Conclusion
In summary, a tensile strained GeSn waveguide structure integrated with Si3N4 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 Si3N4 liner stressor, which decreases the Γ conduction band energy and lifts the degeneracy of valence bands, thus resulting in the reduction of EG,Γ and extension of cut-off wavelength of the GeSn waveguide detector. Ge0.90Sn0.10 waveguide detector achieves a EG,Γ reduction from 0.455 eV to 0.306 eV caused by the 500 nm Si3N4 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.
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