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Abstract
In the field of silicon photonics, germanium (Ge) is an attractive material for monolithic light sources. Tensile strain is a promising means for Ge based light sources due to enhancing direct band gap recombination. We investigated strain engineering in Ge using silicon nitride (SiNx) stressors. We found that microfabricated Ge greatly improves the tensile strain because SiNx on the Ge sidewalls causes a large tensile strain in the direction perpendicular to the substrate. Tensile strain equivalent to an in-plane biaxial tensile strain of 0.8% at maximum was applied, and the PL emission intensity was improved more than five times at the maximum.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon (Si) photonics has gained widespread interest due to its high-speed, low-energy consumption, low cost, and large-scale integration [1,2]. However, the only missing component to enable full monolithic integration of electronic and photonic devices is a monolithically integrated light source on a Si substrate [3]. Germanium (Ge) is an attractive material for monolithic light sources due to its compatibility with complementary metal oxide semiconductor (CMOS) processes and its pseudo-direct band gap character [4]. Ge is an indirect band gap material with a small splitting between the direct Γ valley and indirect L valley of 140 meV at room temperature. This splitting can be reduced by introducing tensile strain, so that a biaxial tensile strain between 1.7 and 1.9% Ge becomes a direct band gap material [5–8]. A combination of tensile strain induced by thermal expansion mismatch between a Ge and Si substrate [9–12] and heavy n-type doping have been proposed to obtain optical gain through theoretical studies and have achieved enhanced light emission [4,7,13–18]. In recent years, lasing operations pumped by optical and electrical pulses have been observed from tensile-strained and heavily n-type doped Ge [19–21]. However, the threshold current of lasing from Ge is very high [19,21]. The next challenge is reducing the threshold current and increasing the efficiency. Band engineering using a large tensile strain is a promising way to increase the optical gain compared with heavy doping because heavy doping induces large optical loss due to free carrier absorption [16,22] and shortens minority carrier lifetime. In fact, lasing operations of Ge under strong tensile strain by optical pumping have been reported [23–25]. Many methods have been investigated to increase the tensile strain in Ge, for example, a stress concentration method using Ge micro bridges on Ge-on-insulator (GOI) or Si-on-insulator (SOI) substrates [23,24,26–32], mechanical deformation using nano membranes [8,33–40], Ge epitaxial growth on lattice-mismatched buffer layers [41,42], and applying external stressor layers like silicon nitride (SiNx) films [17,25,43–51]. Applying SiNx stressor is a most attractive approach in terms of CMOS compatibility because micro bridges and nano membranes use micro electromechanical systems (MEMS) processes and lattice-mismatched buffer layers are III-V compound semiconductors.
Several structures developed using the SiNx external stressor have been investigated, for example, SiNx deposition only on the top surface of Ge film (top-only-stressor structure) [17,43–45], SiNx deposition on the top and sidewalls of Ge film (delta-shaped-stressor structure) [46–48], and SiNx deposition on the top, bottom, and sidewalls of Ge film (all-around-stressor structure) [25,49–51]. All-around-stressor structure can apply strong tensile strain and achieved lasing operation by optical pumping [25], however, current injection is difficult because whole surface of the Ge film is covered with SiNx layer. Top-only-stressor and delta-shaped-stressor structure are promising in terms of current injection because they have contact points with a Si substrate. Since structural parameters much affect the tensile strain [44], appropriate comparison between the top-only stressor and the delta-shaped stressor, i.e. the effect of SiNx on Ge sidewalls, has not been reported.
In this study, we investigated strain distribution in Ge with the top-only stressor and that with the delta-shaped stressor and the effects of structural parameters using a three-dimensional (3D) finite element model and micro Raman spectroscopy. Also, we investigated the improvement of optical properties by tensile strain by the relation between micro photoluminescence spectra and Raman shifts.
2. Experimental procedure
2.1 Sample structure
In this study, we prepared samples with different Ge and SiNx structures to investigate the effect of structures of Ge and SiNx stressor on tensile strain. Figure 1 shows a cross section of the SiNx structures and a top view of the Ge structures. The thickness of the Ge is 200 nm, and 300-nm-thick SiNx stressors were deposited on the Ge in two ways. One is SiNx deposition on the top surface of the Ge (top-only-stressor structure), and the other is SiNx deposition over the entire surface except for the bottom of the Ge (delta-shaped-stressor structure). We can evaluate the effect of the SiNx stressors on the sidewalls of the Ge by comparing the two SiNx structures. Two structures of Ge were used, waveguides and micro disks, to compare the effects of uniaxial in-plane stress and biaxial stress. Also, the waveguide width and micro disk diameter (W) were varied from 600 nm to 10 µm to investigate the effect of miniaturization on tensile strain.
Fig. 1. Schematic image of (a) cross section of the SiNx structures and (b) top view of Ge structures
2.2 Fabrication process
A 200-nm-thick Ge layer was epitaxially grown on a Si wafer with a two-step growth technique including post growth annealing and high temperature regrowth, using a cold-wall rapid thermal chemical vapor deposition (CVD) system [12]. The Ge was kept undoped to eliminate the band gap narrowing effect caused by high-level doping to analyze the band modulation caused by strain [14,52]. After the Ge growth, different fabrication processes were performed for the top-only-stressor and delta-shaped-stressor structures. To fabricate the top-only-stressor structure, a 300-nm thick SiNx layer with a compressive stress of 1 GPa was directly deposited on the Ge layer using inductively coupled plasma enhanced CVD (ICP-CVD). The SiNx and Ge layers were then patterned by electron beam lithography and dry etching. To fabricate the delta-shaped-stressor structure, the Ge layer was patterned by electron beam lithography and dry etching, and a 300-nm-thick SiNx layer with a compressive stress of 1 GPa was then deposited using ICP-CVD. Figure 2 shows a cross-sectional scanning electron microscope image of the delta-shaped-stressor structure with a 1-µm-W waveguide shape.
2.3 Measurement
Strain in the tensile-stressed Ge was evaluated by micro-Raman spectroscopy [Tokyo Instruments, Nanofinder]. The spectroscopy was carried out with an Ar laser in which the pumping wavelength was 457.9 nm, and the excited area was a 1-µm-diameter circle area located in the center of the devices. In this study, we only evaluated the center regions of the devices, so contribution of the edge part was not included in the measurement of devices with a W higher than 1 µm. Optical properties were also evaluated by micro photoluminescence (PL) spectroscopy. Optical excitation was carried out with a laser in which the pumping wavelength was 740 nm and pumping power was 20 mW. The excited area was same as that for the micro-Raman spectroscopy, and light emissions from the Ge were detected by an InGaAs photo detector with a cut off wavelength of 2.2 µm.
2.4 Stress field analysis
We performed 3D finite element modeling (FEM) of the stress field in the Ge to analyze stress distribution in the devices using CoventorWare. The properties of the materials used in this study are shown in Table 1. The Young’s modulus and Poisson coefficients were set on the basis of previous reports [53–59]. We simplified the Young’s modulus of the materials to be isotropic, and the [100]-directed values were utilized. In the mechanical analysis of the microstructures, it is necessary to consider the size effect. According to the previous reports [57–59], the size effect on the mechanical properties is remarkable at sizes of several tens of nanometers for SiNx and single crystal Si, but the size effect to the Young’s modulus is not significant at size of several hundred nanometers. Therefore, it was estimated that the size effect was small in this study. An initial tensile strain in the Ge induced by the Ge epitaxial growth process [12] was not included because the purpose of this study is to analyze the tensile strain induced by stressors. Also, it was assumed that the adhesion between the materials is high and the stress was not relaxed at the interface. In this study, a brick-shaped finite element mesh was used to study in each direction of X, Y, and Z. The element size was uniform throughout the model, and the dimensions in both the X and Y directions were 500 nm. Moreover, since the film thickness of Ge and SiNx was as thin as 200 and 300 nm, respectively, the dimension in the Z direction was made as fine as 100 nm. The value of W in the waveguide-shaped Ge varied from 1 to 10 µm in the X direction and the length (L) was 10 µm in the Y direction.
Table 1. Properties of materials used in stress simulation.
The micro disk-shaped Ge, which was simulated by replacing the circle shape with a square shape due to the limitation of the finite element mesh type, had its value of W varied from 1 to 10 µm and its L equal to W. An example of the entire model is shown in Fig. 3. Since the device structure is symmetrical, only one quarter is shown. A Ge waveguide with a SiNx stressor is placed on a Si substrate with a thickness of 5 µm and a blank space of 5 µm each in the X and Y directions. Since the actual Si substrate, which was an 8-inch wafer with a thickness of 700 µm or more, was much larger than the model, the substrate is hardly warped by the SiNx stressor. The warpage of the Si substrate in the simulation is estimated to be larger than it actually is, because the Si substrate in the model is thin and easy to warp. Therefore, in the model, the bottom and sidewalls of the Si substrate were fixed with the zero displacement in any direction to reduce the warpage of the Si substrate, and other surfaces were set to be free surfaces. In this study, we discuss the change of stress depending on the shape and the size of the devices to avoid effects of the warpage of the Si substrate.
3. Analysis of stress distribution
We investigated structure dependence on tensile strain in the top-only-stressor and delta-shaped-stressor structures by micro-Raman spectroscopy. Figures 4(a) and (b) show the Raman spectra of the top-only-stressor and delta-shaped-stressor structures respectively, which have a waveguide shape and varied W from 1 to 10 µm. The dots show experimental data and solid lines show Lorentzian fitting. Changes in peak wave numbers of devices with various W were not large in the top-only-stressor structure. On the other hand, peak wave numbers decreased with narrowing W, and the maximum shift was -2.4 cm-1 in the 1-µm-W delta-shaped-stressor structure compared with the 10-µm-W delta-shaped-stressor structure. A Raman shift of -2.4 cm-1 corresponds to 0.48% of in-plane biaxial tensile strain [12,60]. The reason for the large Raman shifts in the delta-shaped-stressor structure with a narrow W was considered to be the difference in strain distribution at the edge part of the devices due to the existence of SiNx on the Ge sidewalls.
Fig. 4. Raman spectra of (a) top-only-stressor structure and (b) delta-shaped-stressor structure with waveguide shapes and varied W from 1 to 10 µm. Dots show experimental data and solid lines show Lorentzian fitting.
To clarify the cause of the difference in tensile strain of the top-only-stressor structure and the delta-shaped-stressor structure, stress distribution in the top-only-stressor and delta-shaped-stressor structures were carried out using 3D FEM. In micrometer-scale microstructures, local strain on the top surface, sidewalls, and structure edges interfere with each other, so stress analysis for each direction is important to analyze the effects of the SiNx structure. Figure 5 shows a bird’s-eye view of the 3D FEM and simulated distributions of σxx, σyy, and σzz in cross sections of the waveguide-shaped top-only-stressor and delta-shaped-stressor structures. Since the device structure is symmetrical, only one quarter is shown. The L and W of the model were 10 and 2 µm, respectively. The edge curvature of the SiNx was not taken into account in this analysis, but it did not significantly affect the stress distribution because the stress at the edge of the SiNx was easily relieved. In the top-only-stressor structure, σxx (Fig. 5(b)) was high at the top part of the Ge, and it decreases sharply as the height decreases. Discontinuity of stress at the Ge/Si interface is due to the difference in Young’s moduluses of Ge and Si. In addition, the stress at the end of the Ge was reduced because the stress of the SiNx was relaxed at the end [61]. σxx was larger than σyy (Fig. 5(c)) because the tensile stress in the X direction increased due to the film-edge-induced stress effect [62,63]. Since the built-in stress of the SiNx in the Z direction is completely relaxed, σzz (Fig. 5(d)) was low except for the compressive stress at the edge caused by σxx compensation. In the delta-shaped-stressor structure, σxx (Fig. 5(f)) was lower than that in top-only-stressor structure because the film-edge-induced stress effect was suppressed by the compressive stress of the SiNx around Ge. Also, σxx at the edge of the Ge waveguide was redced by SiNx on th Si substrate (see trapezoidal yellow-green region in the Ge waveguide in Fig. 5(f)), whereas σxx was applied to the Si substrate under the SiNx. σyy (Fig. 5(g)) was higher than that in the top-only-stressor structure due to the warpage of the Si substrate, which was estimated to be larger than it actually was, because the delta-shaped-stressor structure had SiNx on the Si substrate. σzz (Fig. 5(h)) was especially strong at the edge of the Ge because relaxation of built-in stress along Z direction in SiNx was suppressed by Ge sidewalls [64]. In the delta-shaped-stressor structure, the tensile stress was particularly large at the edge, so the contribution of the tensile stress in the Z direction at the edge increased in the devices with narrow W, and it is thought that the reason of increased Raman shift in the delta-shaped-stressor structure with a narrow W.
Fig. 5. (a) Bird’s-eye view of 3D FEM and simulated distribution of (b) σxx, (c) σyy, and (d) σzz in cross section of waveguide-shaped top-only-stressor structure. (e) Bird’s-eye view of 3D FEM and simulated distribution of (f) σxx, (g) σyy, and (h) σzz in cross section of waveguide-shaped delta-shaped-stressor structure.
Next, we investigated size dependence of the distribution of tensile stress. To compare the uniaxial miniaturization effect and the biaxial miniaturization effect, the W dependence of stress profile in the waveguide and micro disk shapes was analyzed. Figures 6(a)–(f) show stress profiles from the center to the edge along the X direction of the top-only-stressor and delta-shaped-stressor structures with waveguide and micro disk shapes with various W from 1 to 10 µm. The Y and Z coordinates were the center of the Ge. The blue lines show the profiles of the waveguide shape and the red lines show those of micro disk shape. In the top-only-stressor structure, σxx was distributed in accordance with the film-edge-induced stress effect [62,63], and the tensile stress became maximum at a position about 1 µm from the edge. Therefore, when the W was narrowed to 2 µm, the ratio of the region where the tensile stress was large increased, and the average value of σxx in the Ge became maximum. In the delta-shaped-stressor structure, σxx is distributed more uniformly than that in the top-only-stressor structure because the film-edge-induced stress effect was suppressed by the compressive stress of SiNx around Ge. Therefore, the W dependence of average σxx in the devices was lower than those in the top-only-stressor structure. In addition, the σxx distributions of the waveguide and micro disk shapes were the same in both the top-only-stressor and delta-shaped-stressor structures, and it was found that miniaturization in the Y direction does not affect σxx. For the same reason, the distribution of σyy in the X direction was uniform, and the W dependence of the waveguide shape was low in both the top-only-stressor and delta-shaped-stressor structures. σyy was improved by reducing W in the micro disk shape in both the top-only-stressor and delta-shaped-stressor structures, since miniaturization in the Y direction influences σyy. In the micro disk shape, σxx and σyy are equal at the center of the devices, so the average value of the σyy in the top-only-stressor and delta-shaped-stressor structures was maximum when the W was 2 and 1 µm, respectively, as in σxx. As shown in Figs. 6(c) and (f), the σzz of the SiNx on the Ge upper surface was completely relaxed, so σzz in the top-only-stressor structure was low except for compressive stress at the end due to σxx compensation. Since the compressive stress at the end was high in both the waveguide and the micro disk, the average value of the compressive stress in the Z direction of the devices increased as the W decreased. On the other hand, in the delta-shaped-stressor structure, σzz rapidly increased as it approached the edge due to the pulling-up effect by the SiNx on the Ge sidewall. The peak value of σzz was very high at nearly 300 MPa at the Ge edge, so the effect of increasing the average value of the tensile stress in the Z direction in the devices with narrow W is significant.
Fig. 6. Stress profiles from the center to the edge along the X direction. (a) σxx, (b) σyy, and (c) σzz of top-only-stressor structure, and (d) σxx, (e) σyy, and (f) σzz of delta-shaped stressor structure. Blue lines show stress in waveguide shape and red lines show micro disk shape.
Next, the above analysis results were compared with the Raman shifts. Due to the measurement area of micro-Raman spectroscopy being a circular region with a 1-µm diameter at the center of the devices, the average value of the tensile stress in the region of the devices shown in Fig. 6(a)–(f) were calculated and compared with the Raman shifts. Raman shift is related to strain [12,60]. Also, Raman shift is related to stress via Hooke’s law. We adopted stress as a parameter of Raman shift due to consistency with Fig. 6. We use the sum of the stress since stress in each X, Y, and Z direction contributes to Raman shift. Figures 7(a) and (b) show the W dependence of average value of simulated tensile stress (σxx + σyy + σzz) and measured Raman shifts of the top-only-stressor and delta-shaped-stressor structures. The data of the waveguide and micro disk shapes are outlined in blue and red, respectively, with the dots indicating the Raman shift and the dashed lines indicating the calculated values of the tensile stress. The Raman shift was calculated on the basis of the peak wave number of the device with a W of 10 µm to eliminate the variation of the strain caused by the Ge epitaxial growth process, and we could then evaluate changes in strain due to W dependence. In Fig. 7(a), both tensile stress and Raman shifts have a gentle W dependence with a peak at a W of 2 µm, and the Raman shift due to W dependence was -2 cm-1 at maximum. The measured Raman shift agrees with the trend of the calculated values, the top-only-stressor structure has low controllability of strain by miniaturization and the compressive strain of SiNx needs to be changed for strain control in the top-only-stressor structure. In Fig. 7(b), both tensile stress and Raman shifts increase with narrowing W. Stress increases rapidly especially with W below 1 µm, and the Raman shift was -5 cm-1 at maximum. The main factor for those rapid increases was the σzz at the edge region induced by the SiNx on the sidewalls, and the average tensile stress of the delta-shaped-stressor structure increases with narrowing W since σzz reaches peak value at the end of the Ge as shown in Fig. 6(f). From these results, the delta-shaped-stressor structure has high controllability of tensile strain due to the SiNx on Ge sidewalls and it is clear that tensile strain can be made stronger by further miniaturization. Application of Ge nanowires [23,29,31] and Ge fins [65,66] are promising candidate for further enhancement of tensile strain.
Fig. 7. W dependence of average value of simulated tensile stress (σxx + σyy + σzz) and measured Raman shifts for waveguide (blue) and micro disk (red) shapes of the (a) top-only-stressor and (b) delta-shaped-stressor structures. Dots indicate the Raman shift and dashed lines indicate the calculated values of the tensile stress.
4. Band modulation and light emission enhancement by tensile stress
We investigated the relationship between the tensile strain and shrinkage of the direct band gap energy from the Raman shifts and PL spectra. The PL spectra of the top-only-stressor structure had a strong optical interference due to the large refractive index difference between the Ge sidewalls and air, making it difficult to estimate the direct band gap energies of the top-only-stressor structure [27]. Therefore, the PL spectra of the top-only-stressor structure were not applied to the analysis. Figures 8(a) and (b) show the PL spectra of the waveguide-shaped and micro disk with delta-shaped-stressor structure with various W. Dashed lines show Gaussian fitting. In both figures, since the peak wavelength red shifted and the PL intensity increased with narrowing W, it is thought that the direct band gap energy decreased due to the increase in tensile strain caused by reducing W, and the proportion of electrons excited at the Γ point increased. In addition, the PL spectra of W of 1 and 2 µm in Fig. 8(b) are broader than others. Dispersion of PL spectra of 1-µm-W micro disk was 200 nm whereas that of 10-µm-W micro disk was 65 nm. PL spectra of micro disks with narrow W have contribution from strongly tensile strained Ge edges, so that the strong dispersion of PL spectra indicates strong dispersion of strain in edges of the Ge microdisks.
Fig. 8. PL spectra of (a) waveguide-shaped and (b) micro-disk-shaped delta-shaped-stressor structure with various W. Dashed lines show Gaussian fitting.
In Fig. 9, PL peak energies of the delta-shaped-stressor structure were plotted with the Raman shifts shown in Fig. 7(b) to investigate the relationship between the tensile strain in the Ge and direct band gap modulation. The relationship between the in-plane tensile strain and direct band gap energy [6] is also shown by the dashed line. However, weak Fabry-Pérot interference appeared in the PL spectra of W of 5 and 10 µm in Fig. 8(b), so it was difficult to identify the peak wavelength accurately in those devices. It can be seen from Fig. 9 that PL peak energy decreases up to 0.1 eV and the tensile strain corresponding to the in-plane tensile strain of up to 0.8% was applied in the micro disk with delta-shaped-stressor structure. Stronger tensile strain in Ge can be expected with appropriate process condition of SiNx deposition, because compressive stress of SiNx in this study is relatively weaker (-1 GPa) than previously reported (-1.8 to -4.5 GPa) [25,43,44,47,48,51]. The direct band gap energy and in-plane tensile strain have an almost linear relationship [6]. The relationship between biaxial tensile strain corresponding to the PL peak energy and Raman shift was linearly approximated with a linearity of 0.836 and a regression coefficient of -7.5 cm-1. The regression coefficient is higher than those of previous reports [12,60]. One possible reason is the difference in measured depth due to the difference in pumping wavelength in Raman and PL spectroscopy. This indicates strong dispersion of strain in Ge as discussed above. Therefore, the band structure of Ge can be controlled by controlling the tensile strain by refining the structure.
Fig. 9. PL peak energies of delta-shaped-stressor structure plotted with Raman shifts. Dashed line shows the relationship between in-plane tensile strain and direct band gap energy.
Next, we investigated the effect of enhancing light emission by direct band gap modulation using tensile strain. Integrated PL intensities and PL peak energies of the delta-shaped-stressor structure are shown in Fig. 10. The dashed line shows the change due to direct band gap modulation by tensile strain of the proportion of electrons at the Γ valley among the electrons in the conduction band (ne(Γ)/ne(L)). In the calculation, total electron density was set to 2×1017 cm-3. For devices with a W narrower than 1 µm, the excitation light could not be irradiated sufficiently due to the device’s small size. Therefore, data of devices with a W smaller than 1 µm were not adopted. The PL intensity increased as PL peak energy decreased, and a light emission intensity improvement of more than five times was confirmed. The change of PL intensity for PL peak energy agrees with the increasing trend of electron density at the Γ valley by direct band gap modulation. Therefore, the emission efficiency can be controlled by increasing the direct transition rate due to direct band gap modulation. The micro disk-shaped devices with a W of 4 µm or more have higher PL peak energies over 0.77 eV because of the small tensile strain, but the emission intensities tended to be higher than those of the waveguide-shaped devices. One possible reason is an error of PL peak energies or integrated PL intensities induced by Fabry-Pérot interference in the spectra [27].
Fig. 10. PL peak energy dependence of integrated PL intensity of delta-shaped-stressor structure. Dotted line shows ne(Γ)/ne(L).
5. Conclusions
We investigated external-stressor structure suitable for applying to current-injection devices and effect of miniaturization of Ge on the tensile strain and light emission properties. Micro-Raman spectroscopy and stress distribution analysis in each direction revealed that SiNx on Ge sidewalls causes large tensile strain in the Z direction at the edge. Therefore, miniaturization of Ge (i. e. reducing W) greatly increased tensile strain due to increase of volume ratio of the edges. As a result, the delta-shaped-stressor structure had a maximum Raman shift of -5 cm-1 by reducing W, whereas the top-only-stressor structure had a maximum Raman shift of -2 cm-1. The Raman shift showed a linear correlation with PL peak energy, and a peak energy shift due to miniaturization was larger than -0.1 eV at maximum. In addition, the integrated PL intensity improved by more than five times with the PL peak shift. The degree of improvement in PL intensity agrees with the correlation between the direct band gap shrinkage and electron density at the Γ valley in the conduction band. From these results, the microfabricated delta-shaped-stressor structure is a promising candidate for reducing the threshold current of Ge lasers because of its high tensile strain controllability.
Funding
Japan Society for the Promotion of Science.
Acknowledgments
We thank Professor Yasuhiko Arakawa, Professor Satoshi Iwamoto, Dr. Satoshi Kako, Professor Yukihiro Shimogaki, and Assistant Professor Momoko Deura for their enlightening discussions.
Disclosures
The authors declare no conflicts of interest.
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