Germanium-tin alloys: applications for optoelectronics in mid-infrared spectra

Cizhe Fang; Yan Liu; Qingfang Zhang; Genquan Han; Xi Gao; Yao Shao; Jincheng Zhang; Yue Hao

doi:10.29026/oea.2018.180004

Abstract

We summarize our work of the optoelectronic devices based on Germanium-tin (GeSn) alloys assisted with the Si3N4 liner stressor in mid-infrared (MIR) domains. The device characteristics are thoroughly analyzed by the strain distribution, band structure, and absorption characteristics. Numerical and analytical methods show that with optimal structural parameters, the device performance can be further improved and the wavelength application range can be extended to 2~5 μm in the mid-infrared spectra. It is demonstrated that this proposed strategy provides an effective technique for the strained-GeSn devices in future optical designs, which will be competitive for the optoelectronics applications in mid-infrared wavelength.

Keywords

Genquan Han|optoelectronics germanium-tin alloys mid-infrared spectra

Introduction

It is known to all that Group Ⅳ semiconductors have been widely applied in electronic devices due to their compatibility with mature complementary metal-oxide- semiconductor (CMOS) technologies and excellent electronic transport properties. However, low luminous efficiency caused by their indirect-bandgap limits their applications in photonic functional devices. Recently, a new technology based on incorporating Sn into Ge has triggered a tremendous interest for the accessibility of the direct bandgap material^1-6. The pioneering work has been made by R. Soref and C. H. Perry in ref. ⁷. After that, subsequent theoretical studies^8-11 revealed that an indirect- bandgap material can be tuned to be a direct-bandgap one by increasing the substitutional Sn concentration in the Ge lattice. Moreover, the incorporation of Sn in the Ge lattice not only yields significant red shifts in the band gap energies but also makes it a possible candidate as the gain medium^{12, 13}, which indicates the potential applications of photonics in the mid-infrared (MIR) regions^14-17. Up to now, different kinds of efficient devices based on GeSn have been fabricated^{13, 18}, including photodetectors and lasers with a response up to 2 μm.

However, there is a trade-off between high Sn composition and direct bandgap in GeSn based devices due to the fact that solid solubility resulting from high Sn composition would be destructive to the overall function of the optoelectronic device¹⁹. Furthermore, the thermal stability of GeSn film caused by high Sn content becomes an obstacle to device fabrication^20-24. By inducing a tensile strain into GeSn alloys, the Sn composition can be reduced to achieve direct bandgap compared with the relaxed one^{2, 25, 26}, benefiting their light emission efficiency^{27, 28}. Therefore, silicon nitride (SiN_x) films are used as an external stressor to induce tensile or compressive strain into semiconductor^29-32, which poses a strategy to improve the optical performance of the strained GeSn-based structures.

We sum up the work of different kinds of optoelectronic devices based on GeSn alloys with the assistance of the Si₃N₄ liner stressor. Analytical calculations show that the tensile strain induced by Si₃N₄ liner in GeSn contributes to both device performance and the extension of optical absorption spectrum. It is demonstrated that the proposed strategy could expand the application spectrum of group Ⅳ based devices, which will find important applications in the novel optoelectronic applications.

Device design and characteristic

Photodetector

It is worth noting that employing the tensile strained GeSn alloys achieves a material with improved absorption coefficient α in MIR ranging, which provides an effective technique for extending the absorption edge of GeSn to mid-infrared wavelength. Here, we discuss three photodetectors based on different strained GeSn architectures. Figure 1(a) shows a conceptual illustration of the GeSn on Si on oxide undercladding pedestal (SOUP) waveguide. The 3-D schematics of GeSn pillar and fin array detectors are shown in Fig. 1(b) and 1(c), respectively. The tensile strain is introduced in the GeSn material by the Si₃N₄ liner stressor.

Figure 1.3D schematics of the designed GeSn photodetectors based on different architectures. (a) GeSn on SOUP waveguide integrated with the Si₃N₄ liner stressor. Three-dimensional schematics of GeSn detectors with (b) pillar and (c) fin array integrated with the Si₃N₄ liner stressor on Si platform. Figure reproduced from: (a) ref. ²⁶, Optical Society of America; (b, c) ref. ³³, IEEE.

To better analyze the influence of the strain on the energy band, the E-k energy band diagrams of the relaxed and tensile strained Ge_0.90Sn_0.10 in three different detectors are plotted and compared in Fig. 2. It is observed that in contrast to relaxed GeSn, the E_{G, Г} is obviously reduced in tensile strained GeSn because there is a decline in the energy of Г conduction valleys. It is clear that the E_{G, Г} of tensile strained GeSn in pillar detector exhibits a larger attenuation than that of fin detector. The impacts of geometric parameters on the energy band structure in fin and pillar detectors are discussed in detail in ref. ³³. What's more, the impact of Sn content on the E-k energy band for relaxed and tensile strained GeSn is analyzed in ref. ²⁶. It is concluded that by utilizing the Si₃N₄ liner stressor, the E_{G, Г} of GeSn alloy can be reduced, which is potential to extend the cutoff wavelength of various photonic devices into the MIR region.

Figure 2.E-k energy band diagrams of relaxed and strained GeSn devices. (a) Relaxed Ge_0.90Sn_0.10. (b) Tensile strained Ge_0.90Sn_0.10 in fin array detector with the L_pillar of 200 nm. (c) Tensile strained Ge_0.90Sn_0.10 in pillar array detector with the L_pillar of 200 nm. (d) Tensile strained Ge_0.90Sn_0.10 on SOUP waveguide. Figure reproduced from: (a, b, c) ref. ³³, IEEE; (d) ref. ²⁶, Optical Society of America.

In order to evaluate the performance of the proposed photodetectors, we calculate the absorption coefficient α, a key parameter for determining the detection spectrum of the detector, by equation (1) ³⁴:

1 $ \alpha \left( \hbar \omega \right)=\frac{\alpha \text{b}}{{{\left( 2\pi \right)}^{2}}}\frac{2{{\mu }^{\frac{3}{2}}}}{{{\hbar }^{2}}}{{\left( \hbar \omega-{{E}_{G, \Gamma }} \right)}^{\frac{1}{2}}}, $

where $\hbar$ is the reduced Plank constant $h/2{\rm{ \mathit{ π} }}$, $\omega $ is the angular frequency, and μ is the reduced mass, which can be calculated by $m_{\rm{e}}^ * m_{\rm{h}}^ * /(m_{\rm{e}}^ * + m_{\rm{h}}^ *)$. The electron and hole effective masses ($m_{\rm{e}}^ * $ and $m_{\rm{h}}^ * $) are extracted from E-k energy band diagrams based on

$ {m^ * } = {(\frac{1}{{{\hbar ^2}}} \cdot \frac{{{{\rm{d}}^2}E}}{{{\rm{d}}{k^2}}})^{-1}}. $

The ${\alpha _{\rm{b}}}$ is given by

2 $ {\alpha _{\rm{b}}} = \frac{{2{\rm{ \mathit{ π} }}{{\rm{e}}^2}{E_{G, \Gamma }}({E_{G, \Gamma }} + \Delta )}}{{3n{\varepsilon _0}\omega c{m_{\rm{e}}}({E_{G, \Gamma }} + \frac{{2\Delta }}{3})}}. $

In equation (2), n is the refractive index, ε₀ is the vacuum permittivity, c is the velocity of light, m_e is the electron mass, and $\Delta $ is the spin-orbit splitting.

Figure 3(a) shows that the calculated absorption coefficient α is modeled as a function of optical wavelength for relaxed and strained Ge_0.90Sn_0.10 in fin and pillar array detectors with different geometric parameters. It can be clearly seen that the optical response spectra of both strained Ge_0.90Sn_0.10 fin and pillar detectors are wider than that of relaxed detector. Besides, the pillar detector exhibits a larger cutoff frequency than fin detector when L_pillar and T_fin are equal. With the decrease in fin and pillar dimensions, the cut-off wavelengths display an obvious redshift. It should also be noted that the cut-off wavelengths are extended to be 4.35 μm with the L_pillar of 100 nm. As shown in Fig. 3(b), we investigate the impact of the Sn content on the cut-off wavelengths of both the relaxed and strained devices. A significant redshift of absorption edge can be obtained in the strained devices. Furthermore, the cut-off wavelength performs a greater improvement with a larger Sn composition. All the enhancements in the cut-off wavelength can be speculated that there is an attenuation in the E_{G, Г} of GeSn.

Figure 3.(a) Comparisons of the absorption spectra of relaxed and strained GeSn in fin and pillar array detectors at the Sn content of 0.1. L_pillar and T_fin feature size varys from 100 nm to 500 nm in a step of 100 nm. (b) Calculated absorption spectra for relaxed and tensile strained GeSn waveguide photodetectors at different Sn content. Figure reproduced from: (a) ref. ³³, IEEE; (b) ref. ²⁶, Optical Society of America.

Optical modulators

In this section, we theoretically investigate tensile strained GeSn electro-absorption modulator based on the Franz-Keldysh (FK) effect. As depicted in Fig. 4, α is modeled as a function of wavelength for tensile strained GeSn waveguide modulators with different Sn content, which is calculated by ref. ²⁶. During simulation, the intensity of electric field varies from 0 to 10 MV/m at a step of 2 MV/m. Although Sn composition is different, the cut-off wavelength of all materials redshifts to MIR spectra range with the increase in the magnitude of electric filed. Furthermore, it is found that the cut-off wavelength increases along with Sn content. To explore the optical transmission properties, here we employ the 2D finite-different time-domain (FDTD) method to model the Ge_0.90Sn_0.10 waveguide modulator. Mode profiles of transverse electric (TE) and transverse magnetic (TM) modes in the tensile strained Ge_0.90Sn_0.10 waveguide modulator are plotted at different wavelengths in Fig. 5. The refractive indexes for Ge_0.90Sn_0.10, Si₃N₄ and SiO₂ are all extracted from ref. ³⁵. Remarkably, single mode transmission can be observed in the waveguide for all the cases. Importantly, there is a leakage of light from waveguide with the increase in wavelength. In order to gain a deeper understanding on the optical transmission characteristics, the propagation loss versus wavelength is calculated for the tensile strained Ge_0.90Sn_0.10 waveguide under different electric fields in Fig. 6. For both TE and TM modes, it shows a strong dependence of propagation loss on wavelength. The propagation loss increases along with the wavelength since the optical field becomes weakly confined in the waveguide, which corresponds to the mode profiles in Fig. 5. Moreover, for a fixed wavelength, the propagation loss increases with the increase of applied electric field due to the FK effect, which results in an enhancement in the modulation depth of GeSn waveguide electro-absorption modulator.

Figure 4.Modeled α as a function of wavelength at different electric fields at (a) Ge_0.97Sn_0.03, (b) Ge_0.95Sn_0.05, and (c) Ge_0.9Sn_0.1, respectively. Figure reproduced from ref. ²⁶, Optical Society of America.

Figure 5.Mode profiles of both TE and TM modes at different wavelengths in Ge_0.90Sn_0.10 waveguide. Figure reproduced from ref. ²⁶, Optical Society of America.

Figure 6.Propagation loss of (a) TE mode and (b) TM mode in tensile strained Ge_0.90Sn_0.10 waveguide at various biases. Figure reproduced from ref. ²⁶, Optical Society of America.

Lasers

Accessibility of the direct bandgap material makes GeSn a decent alternative to Si in the functional photonic platform, which helps to realize a monolithically integrated laser. A GeSn/SiGeSn multiple quantum well (MQW) laser wrapped in Si₃N₄ liner stressor is proposed and investigated, as described in Fig. 7. The laser performances are thoroughly analyzed by Sn composition, injected carrier density n_injected, and quantum well number n_well. It is demonstrated that the threshold current density J_th reduces from 476 to 168 A/cm² and the optical gain is improved obviously, by introducing the Si₃N₄ liner stressor.

Figure 7.3D schematic of the Ge_1-xSn_x/Si_1-y-zGe_ySn_z MQW laser wrapped in a Si₃N₄ liner stressor. Figure reproduced from ref. ³⁶, IEEE.

To analyze the impact of the Si₃N₄ liner stressor on the GeSn/SiGeSn MQW laser, strain distributions on the normal and radial cross section planes are plotted in Fig. 8. The strain along [100], [010], and [001] directions in the normal cross section plane are denoted by ε_[100], ε_[010], and ε_[001], respectively. The strain contour plots indicate that [100] and [010] directions are under a tensile strain while ε_[001] is compressive. At the center of the GeSn layer of GeSn/SiGeSn MQW laser, it can be seen that the values of ε_[100], ε_[010], and ε_[001] are 0.85%, 0.85%, and -0.77%, respectively.

Figure 8.Contour plots for (a) ε_[100], (b) ε_[010], and (c) ε_[001] in the normal cross section plane and (d) ε_[100], (e) ε_[010], and (f) ε_[001] in the radial cross section plane in GeSn well for the Ge_0.90Sn_0.10/Si_0.161Ge_0.695Sn_0.144 MQW laser wrapped in a 500 nm Si₃N₄ liner stressor. Figure reproduced from ref. ³⁶, IEEE.

As shown in Fig. 9(a) and 9(b), the threshold current density J_th and optical gain α in GeSn/SiGeSn lasers are modeled as a function of Sn composition in GeSn wells and injected current density, respectively. Here, L_z is the thickness of the potential well. By introducing the tensile strain, there is an obvious attenuation in the J_th in Ge_0.90Sn_0.10/Si_0.161Ge_0.695Sn_0.144 MQW laser. It can be clearly seen that the J_th decreases from 476 to 168 A/cm² at a Sn content of 0.1. For comparison, the values of Γ_{MQW, TE}·g_Г-HH and Γ_{MQW, TM}·g_Г-LH are calculated as a function of injected current density J for the relaxed and tensile strained Ge_0.90Sn_0.10/Si_0.161Ge_0.695Sn_0.144 MQW lasers, as shown in Fig. 9(b). The calculation results indicate that J decreases significantly to achieve a same α for the strained Ge_0.90Sn_0.10 device. It should also be noted that compared to the Ge_0.90Sn_0.10/Si_0.161Ge_0.695Sn_0.144 laser, Ge_0.96Sn_0.04/ Si_0.274Ge_0.611Sn_0.115 device performs an improved J under the same tensile strain, indicating the influence of the Sn component.

Figure 9.(a) Modeled J_th as a function of the Sn composition in GeSn wells for relaxed and tensile strained GeSn/SiGeSn MQW lasers wrapped in a 500 nm Si₃N₄ liner stressor. L_z is 7 nm and n_well is 20. (b) Modeled optical gain α as a function of injected current density J for the relaxed and tensile strained MQW lasers. Figure reproduced from ref. ³⁶, IEEE.

To better understand the impact of the gain medium on photoluminescence inside the cavity, a brief introduction is presented from the energy band structure. The subband energy difference between E_Γ and E_L is defined as ΔE. Here, E_Γ and E_L are the energies of the ground sub-band levels of Γ and L valleys, respectively. Large density of the states concentrates in L-bandedge due to the fact that the effective mass is large. It is recognized that injected carriers occupy firstly lower energy states. Consequently, there is a larger carrier leakage for large ΔE and a small value of ΔE of the material is preferable to increase the gain. Energy band structure and carrier distribution in GeSn/SiGeSn MQW are discussed in detail in ref. ³⁶. According to the discussion above, under tensile strain, the band structure is changed. During the injection of carriers, the population inversion between the sub-bandgap E_sub-G in GeSn wells occurs for the increase of electron occupation probability in Γ conduction valley, which contributes to the improvement of light emission performance in lasers. It is believed that the Sn compositions at well layers and the strain should be carefully designed to achieve a large optical gain.

Light-emitting diode

In consideration of few experimental studies on the tensile strained GeSn light emitters up to date, we theoretically design and analyze a GeSn/SiGeSn double heterostructure (DH) light emitting diode (LED) with a microdisk structure wrapped in Si₃N₄. The impacts of Sn content on strain distributions and energy band structure are thoroughly analyzed. Moreover, the analysis of simulation results shows that the spontaneous emission rate r_sp and the internal quantum efficiency η_IQE can be improved by increasing Sn composition, carrier injection density n_injected, and n-type doping concentration n_doping in the GeSn active layer. The 3D schematic of a GeSn/SiGeSn DH LED with a microdisk device architecture is shown in Fig. 10.

Figure 10.3D schematic of lattice-matched GeSn/SiGeSn DH LED wrapped in a Si₃N₄ liner stressor. Figure reproduced from ref. ³⁷, Optical Society of America.

The values of ε_[100], ε_[010], and ε_[001], and volume strains in the central region for intrinsic GeSn layers are determined by the finite element method (FEM), which are extracted and compared in Fig. 11(a). One can see that there is no more change in the strain distribution. Figure 11(b) gives the E_{G, Γ} and E_{G, L} of the relaxed and strained GeSn with different Sn compositions. It can be observed that under the tensile strain, the energy of the Γ conduction valley and L conduction valley declines with the increase in Sn content. It should also be noted that the energy of the Γ conduction valley decreases more significantly than that of the L conduction valley, which leads to a decline of Sn content required for achieving the direct bandgap.

Figure 11.(a) Modeled strain components as a function of Sn composition in the intrinsic GeSn layer. (b) Comparison of E_{G, Γ} and E_{G, L} in relaxed and strained GeSn with various Sn compositions. Figure reproduced from ref. ³⁷, Optical Society of America.

Since the light-emitting performance of the devices is dependent on r_sp and η_IQE, we first focus on r_sp. Detailed calculation of r_sp per unit volume in the energy and η_IQE can be seen in the ref. ³⁷. As depicted in Fig. 12, the total spontaneous emission spectra of the proposed device are plotted under different conditions. Considering that there are two valence bands (e.g. a light hole (LH) band and a heavy hole (HH) band), r_{sp, LH} and r_{sp, HH} are calculated, respectively, corresponding to two peaks in the spontaneous emission spectrum. Compared to the relaxed one, r_sp can be improved markedly in the strained device. Figure 12(b) compares the total spontaneous emission spectra with different Sn compositions. It can be clearly seen that with the same n_injected, the spontaneous emission spectra of the strained GeSn increase with the Sn content. With the same doping condition, a rapid increase in the intensity can be observed in Fig. 12(c), suggesting the similar impact of Sn content and n_injected on the strength of spontaneous emission rate. Besides, it is worth noting that the increases of Sn composition and n_injected bring about an opposite shift of peak position. That is, the redshift is caused by increasing Sn composition while the blueshift results from improved n_injected. Figure 12(d) describes the impact of n_doping on r_sp, which shows that r_sp can exhibit an enhancement with the increase in the n-type doping concentration n_doping.

Figure 12.Calculated spontaneous emission spectra for the direct transition of GeSn in the lattice-matched GeSn/SiGeSn DHLEDs (a) under different strain status, (b) with different Sn compositions, (c) with different n_injected, and (d) with various n_doping. For all the curves, the stronger and weaker peaks represent r_{sp, HH} and r_{sp, LH}, respectively. Figure reproduced from ref. ³⁷, Optical Society of America.

As another key factor to evaluate the light-emitting performance of the devices, the η_IQE is calculated as a function of Sn composition in Fig. 13. The defect-limited carrier lifetime is denoted by τ_SRH, which can be increased by improving the material quality of GeSn. It seems that η_IQE can be improved along with Sn content in GeSn layer and the devices with a large τ_SRH achieve an enhancement in η_IQE compared to those with a small τ_SRH. It can be seen from Fig. 13(a) that η_IQE of DH LEDs is enhanced significantly after introducing tensile strain for the increase of n_{e, Γ}/n_{e, total} in the tensile strained GeSn. Here, the total electron concentration n_{e, total} is the sum of those in Γ and L valleys (n_{e, Γ}+n_{e, L}). The impacts of n_injected and n_doping on η_IQE are investigated and shown in Fig. 13(b) and 13(c). It seems that η_IQE shows similar n_injected-depengence and n_doping-dependence like r_sp. That is, the increase of n_injected and n_doping can also improve η_IQE of the devices.

Figure 13.η_IQE versus Sn composition characteristics of lattice-matched GeSn/SiGeSn DH LEDs with the τ_SRH of 100 and 50 ns. (a) Relaxed and tensile strained GeSn devices. (b) Strained GeSn devices wrapped in a Si₃N₄ liner stressor with different values of n_injected. (c) Strained devices with different n_doping. Figure reproduced from ref. ³⁷, Optical Society of America.

Outlook and summary

In the last part of this section, we will briefly discuss the possible future avenues in GeSn material. Considering that band gap can be adjusted by adding Sn content, GeSn material can be applied for light emitting devices, including laser and LED. It has been reported that the related work is underway in laser^38-40 and light emission^41-43. However, most of work is just focused on optical pumping at low temperature and the luminous efficiency is low. GeSn material with direct bandgap leads to a small band gap (i.e., ~0.56 eV), which limits its applications in optical communication⁴⁴. Besides, the existence of solid solubility and limitation of strain engineering also influence the performance of GeSn based devices. Above all, the photodetector with GeSn is potential for the feasibility of practical applications. It is demonstrated that there are already some achievements in photodetection^45-46. Due to the tremendous research attention to this material, the growth of GeSn film is correspondingly explored to improve the stability and quality of GeSn film for the development of GeSn-based photonic applications^47-49. Owing to the fast growing rate of the research on this material, the author is confident that more breakthroughs in practical applications will be achieved.

Conclusion

In summary, we discuss the recent achievements in the applications of GeSn based devices wrapped by the Si₃N₄ liner stressor. Their strain distribution is analyzed in detail by numerical simulation tools, which is introduced by the Si₃N₄ liner stressor. The calculations show that the performance can be improved by optimizing the geometric parameters. Importantly, the operating wavelength can be extended to the whole mid-infrared (2~5 μm) region, which paves the way for the monolithic and CMOS- compatible mid-infrared integrated optics applications like image sensors and optical receivers.

Acknowledgements

The authors thank National Natural Science Foundation of China (Grant No. 61534004, 61604112 and 61622405).

Competing interests

The authors declare no competing financial interests.

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