1. Introduction

Recently, germanium-tin (GeSn) alloy has attracted tremendous interests as a photonic material due to the fact that it has the ability to improve the performance of germanium (Ge) photodetectors [1,2], enhance the quantum efficiency in Ge light-emitting devices [3–6] and expand the spectral window for Si-based photonics into the mid-infrared (MIR) range [7–12]. Ge photodetectors fabricated on silicon (Si) with an upper absorption wavelength of 1.6 μm have been widely reported [13–15]. Further extension of the spectral range of Si photonics from Ge-on-Si into the MIR range (e.g. 2 - 5 μm) utilizing GeSn is highly desired for many applications, such as chemical-biological-physical sensing, medical diagnostics, environmental monitoring, active imaging, and free-space laser communications [16, 17].

Theoretical and experimental investigations have demonstrated that, by tuning the Sn composition, GeSn can be a direct band gap material with smaller direct band gap E_G,Γ than Ge with lowering Γ conduction valley in energy [18–20]. High quality GeSn with a few percent of Sn can be pseudomorphically grown on Ge with non-equilibrium low temperature techniques by molecular beam epitaxy (MBE) and chemical vapor deposition (CVD). GeSn photodetector with a Sn composition of 9% has been realized and the device extended the cut-off absorption wavelength beyond 2.2 μm [8]. Nevertheless, Sn composition cannot be increased arbitrarily due to the lattice mismatch between GeSn and Ge and the limited solid solubility of Sn in Ge. Moreover, Sn atoms tend to segregate at surface and cluster which presents challenges during the material growth and device fabrication.

It should be noted that, besides the Sn composition, the strain plays an important role in modulating the band structure of GeSn [18]. GeSn grown pseudomorphically on Ge is under compressive strain. The compressive strain, leading to the increase of E_G,Γ of GeSn, is against indirect-to-direct transition and unfavorable for extension of absorption wavelength. It is encouraging that high quality relaxed GeSn can been epitaxially grown on Si by CVD [21, 22]. Application of tensile strain to GeSn results in the further reduction in energy at both Γ and L conduction band valleys. This offers an interesting possibility of employing tensile strained GeSn alloys for achieving a material with absorption spectrum in MIR ranging. Furthermore, the introduction of tensile strain into GeSn promotes the indirect-to-direct transition, improving the light emission efficiency of the material.

In this letter, we propose and design a novel strained GeSn photodetector with Si₃N₄ tensile liner stressor wrapped around fins. The expansion of Si₃N₄ liner generates a larger biaxial tensile strain in fins for the reduction of E_G,Γ of GeSn, which leads to the extension of cut-off wavelength of the device. Comparison studies of energy band structures and absorption wavelength of relaxed and tensile strained GeSn photodetectors with various Sn compositions are carried out.

2. Key concept and device structure

This section illustrates the strain engineering concept investigated in this paper. The design of strained GeSn fin photodetector is based on the fact that tensile strain plays an active role in reducing the E_G,Г, which results in red shift of the cut-off wavelength for absorption spectra.

Figure 1(a) shows the basic structure of the device, a relaxed GeSn p⁺-i-n⁺ structure formed on Si(001) substrate. The GeSn layers of p⁺ and intrinsic regions are processed into fins, as shown in Fig. 1(b). GeSn fins are along [010] direction. Figure 1(c) depicts GeSn fin photodetector integrated with the Si₃N₄ liner stressor. The metallic contacts are formed on uncovered n⁺ and p⁺ GeSn regions. Figure 1(d) shows the 3D zoomed-in view of a GeSn fin wrapped in Si₃N₄. The width, height and thickness of fin are represented by W_fin, H_fin, and T_fin, respectively. The thickness of Si₃N₄ liner is denoted by T_liner. Si₃N₄ deposited by CVD is widely used as liner stressor in metal-oxide-semiconductor field-effect transistors [23] as well as Ge photonic devices [24–27]. The strain type in Si₃N₄ can be controlled by modulating the deposition conditions, especially the temperature. In the simulation, we use compressively strained Si₃N₄ as the tensile liner stressor on GeSn fins. As shown in Fig. 1(e), the Si₃N₄ expands, and thus stretches the GeSn fin. Large biaxial tensile strain in (100)-plane is induced in GeSn fin.

 

Fig. 1 3D schematics of (a) GeSn p⁺-i-n⁺ structure formed on Si(001), (b) GeSn fins, and (c) GeSn fin photodetector integrated with the Si₃N₄ liner stressor. (d) 3D zoomed-in view of Si₃N₄ wrapped around GeSn fin. (e) GeSn fin is stretched along [010] and [001] directions. GeSn fins are along [010] direction.

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3. Results and discussion

3.1 Simulation of strain profiles in GeSn fin

A 3D finite element (FEM) simulation was performed to analyze the effect of the Si₃N₄ liner stressor on the strain profiles in GeSn fins. The geometric parameters and material properties used in simulations are list in Table 1. The Young’s modulus of GeSn was calculated by linear interpolation method based on the values of Ge and α-Sn. We assumed that the Young’s modulus of the materials is isotropic, and the [100]-directed values were utilized. During the simulation, we set up the Si₃N₄ volume to expand by 1%. The boundary conditions of the model were set as follows. The bottom surface of the Si(001) substrate was fixed with the zero displacement in any direction, and other surfaces were set to be free surfaces. Figure 2 shows the strain profiles in the GeSn fin with a T_fin of 200 nm. As shown in Fig. 2(a), AA’ plane is cut through the GeSn fin along [010] direction and BB’ plane is cut perpendicular to the fin along [100] direction. Coordinate axes are also shown. Figure 2(b), 2(c), and 2(d) illustrate the contour plots for the strain along [100], [010], and [001] directions in AA’ plane, respectively, which are denoted by ε_[100], ε_[010], and ε_[001], respectively. Figure 2(e), 2(f), and 2(g) depict the strain profiles of ε_[100], ε_[010], and ε_[001] in BB’ plane in the central fin, respectively. It is observed that in the GeSn fins, ε_[010] and ε_[001] are tensile, while ε_[100] is compressive, i.e. the fins are under a biaxial tensile strain in (100)-plane. ε_[010] and ε_[001] increase as the point moves up along Z[001] axis. At the center of the GeSn fin, the values of ε_[100], ε_[010], and ε_[001] are - 0.3%, 0.3% and 0.4%, respectively. There is almost no difference in strain profiles between the fins.

Table 1. Geometric parameters and materials properties used in simulation of strain profiles

View Table

 

Fig. 2 (a) AA’ plane cutting through the GeSn fin along [010] direction and BB’ plane cutting perpendicular to the fin. Coordinate axes are also shown. Contour plots for (b) ε_[100], (c) ε_[010], and (d) ε_[001] in plan AA’ and (e) ε_[100], (f) ε_[010], and (g) ε_[001] in plan BB’. The strain contour lines are plotted with an interval of 0.1%.

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3.2 Calculations of energy band structure and absorption coefficient in GeSn fin photodetectors

To analyze the strain effect of Si₃N₄ liner stressor on the energy band structure of GeSn, an 8 × 8 k·p method was used to calculate the E-k energy band diagrams for both the relaxed and strained GeSn. The E_G,Г values of relaxed GeSn were taken from the recent experimental and calculation results in [18–20]. The Luttinger parameters of GeSn were evaluated by linear interpolation based on the values of Ge and Sn given in [30]. According to the deformation potential theory, the E_G,Г reduction induced by tensile strain can be expressed as $a({\epsilon }_{\perp }+2{\epsilon }_{\left|\right|})+b({\epsilon }_{\perp }-{\epsilon }_{\left|\right|})$, where ${\epsilon }_{\left|\right|}$ is the in-plane tensile strain, related ε_[010] and ε_[001], ${\epsilon }_{\perp }$is the out-of-plane strain, i.e. ε_[100], and a and b are deformation potential constants [31]. Deformation potentials of GeSn were the same as those of Ge [30, 32]. The simulated strains at the center of GeSn fin were converted into the strain tensors in the k·p Hamiltonian as the input variables.

Figure 3(a) shows the E-k energy band diagram of relaxed Ge_0.92Sn_0.08 alloy. Figure 3(b) and 3(c) illustrate the E-k energy band diagrams of strained GeSn fin photodetector with T_fin of 200 and 100 nm, respectively. The performance of GeSn photodetector is determined by the direct interband optical absorption, so the conduction L and Δ valleys are not shown. It is observed that under the biaxial tensile strain, the energy of the Γ conduction valley decreases. Meanwhile, the degeneracy of heavy hole (HH) and light hole (LH) bands at zone center is lifted. Strain induced shift of Γ conduction valley down and HH band up leads to a reduction of E_G,Г of GeSn. The band gap reduction is more pronounced in GeSn fin with 100 nm T_fin compared to the fin structure with 200 nm T_fin, which is attributed to the higher strain induced by Si₃N₄ liner stressor at smaller T_fin. It should be noted that the strain caused by Si₃N₄ liner stressor has a great impact on the carrier effective masses near the Γ point. The values of effective mass are extracted from the E-k curves shown in Fig. 3, and expressed as $1/[(1/{\hslash }^2)(d^{2}E/d{k}^2)]$, where $\hslash$ is the Planck constant. The effective masses of the HH band and Γ conduction band are significantly reduced along the tensile strain directions. The effective masses of Γ conduction band and HH band of strained Ge_0.92Sn_0.08 photodetector with T_fin of 200 nm are 0.03m₀ and 0.34 m₀, respectively, which are smaller than those of the relaxed device, 0.032 m₀ and 0.385m₀.

 

Fig. 3 (a) E-k energy band diagrams of unstrained Ge_0.92Sn_0.08. (b) and (c) show the E-k energy band diagrams of strained Ge_0.92Sn_0.08 with T_fin of 200 and 100 nm, respectively.

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Figure 4 compares the E_G,Г of relaxed and strained GeSn fin photodetectors (T_fin = 200 and 100 nm) with different Sn compositions. To ensure that the proposed design can be implemented in practice, we constrain the maximum Sn composition in GeSn devices to be 10%, which has been demonstrated to withstand temperatures up to 450 °C without any degradation in material quality observed [33]. The E_G,Г of relaxed Ge_0.96Sn_0.04, Ge_0.92Sn_0.08, and Ge_0.90Sn_0.10 are 0.65, 0.52, and 0.45 eV, respectively. Under the biaxial tensile strain induced by Si₃N₄ liner stressor, Ge_0.96Sn_0.04, Ge_0.92Sn_0.08, and Ge_0.90Sn_0.10 fin photodetectors with a 200 nm T_fin exhibit the E_G,Г of 0.55, 0.41, and 0.34 eV, respectively. As T_fin decreases to be 100 nm, the E_G,Г of GeSn fin is further reduced by ~0.03 eV.

 

Fig. 4 Comparison of E_G,Γ of relaxed GeSn and strained GeSn fin photodetectors with different T_fin, showing the band gap reduction for strained GeSn fin photodetector over the relaxed GeSn devices.

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Finally, the absorption coefficient α as a function of wavelength for relaxed and strained GeSn fin photodetector was calculated. In both the relaxed and strained GeSn photodetectors, only the optical transition between Γ conduction valley and HH band was taken into account. α can be obtained by calculating quantum mechanically the probability of transition from the HH state to Γ conduction band state. The magnitude of α is proportional to $m_r{}^{3/2}{(\hslash \omega -E_{G,\Gamma })}^{1/2}$, where m_r is reduced mass, determined by electron and hole effective masses, and $\hslash \omega$ is the incident photon energy [34]. The cut-off wavelength of the device is directly determined by E_G,Г of the material. Figure 5 shows the simulated optical absorption spectra for relaxed and strained GeSn fin photodetectors with Sn compositions of 0.04, 0.08, and 0.10. Relaxed Ge_0.96Sn_0.04, Ge_0.92Sn_0.08, and Ge_0.90Sn_0.10 fin photodetectors demonstrate the cut-off wavelengths of 1.91, 2.38, and 2.76 μm, respectively. Significant red shift of absorption edge is achieved in tensile strained GeSn devices with Si₃N₄ stress liner due to the biaxial tensile strain. The cut-off wavelengths of strained Ge_0.92Sn_0.08 devices with T_fin of 200 and 100 nm are 3.01 and 3.27 μm, respectively. The cut-off wavelength of strained Ge_0.90Sn_0.10 fin photodetector with 100 nm T_fin is even extended to ~4 μm. The absorption wavelength can be further extended to long wavelength as T_fin continues to scale down, although which will reduce the effective absorption area of the device. The magnitude of α decreases in strained GeSn fin photodetector compared to the relaxed device, which is resulted from the reduction of carrier effective masses caused by the tensile strain.

 

Fig. 5 Calculated absorption spectra for relaxed and strained Ge_0.96Sn_0.04, Ge_0.92Sn_0.08, and Ge_0.90Sn_0.10 fin photodetectors with T_fin of 100 and 200 nm. The cut-off wavelength of GeSn fin photodetector is significantly extended to MIR due to the biaxial tensile strain induced by Si₃N₄ liner stressor.

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4. Conclusion

In summary, tensile strained GeSn fin photodetectors with various Sn compositions integrated with Si₃N₄ stressor liner were investigate by simulation. FEM and k·p method were utilized to calculate the strain distribution and energy band structure in GeSn devices, respectively. The biaxial tensile strain induced by the Si₃N₄ liner stressor decreases the Γ conduction band energy and lifts the degeneracy of valence bands, both of which result in the reduction of E_G,Γ, and extension of cut-off wavelength of the GeSn fin photodetector. Ge_0.90Sn_0.10 with a 100 nm T_fin achieves a E_G,Γ reduction from 0.45 eV to 0.31 eV caused by the Si₃N₄ stressor liner with 1% expansion, leading to the extension of cut-off wavelength up to 4 μm. This demonstrates that utilizing the technique of Si₃N₄ stressor liner, GeSn fin photodetectors with a Sn composition less than 10% cover the spectrum of MIR, up to 4 μm wavelength.