Control of Ge_1−x−ySi_xSn_y layer lattice constant for energy band alignment in Ge_1−xSn_x/Ge_1−x−ySi_xSn_y heterostructures

In this section, we report the investigation of the energy band alignment as estimated from the valence band offset measurement of the Ge_1−xSn_x/Ge_1−x−ySi_xSn_y heterostructure. Figure 1 shows the valence band spectra of the Ge_1−x−ySi_xSn_y, Ge, and Ge_1−xSn_x layers measured using UPS. The binding energy of each spectrum was calibrated with the peak position of the Ge3d core-level spectrum. The mean free pass of the photoelectron was typically estimated to be 0.5–3 nm for 10–2000 eV [20], meaning that the obtained signal of this measurement originated only from the top layer. The position of the valence band edge was estimated from the intersection point of the linear approximation of the valence band spectrum obtained with the least-squares method and the background signal. The intersection points observed in the Ge_1−x−ySi_xSn_y and Ge/Ge samples are lower than that of the Ge_0.902Sn_0.098 sample, indicating that the valence band edges of the Ge_1−x−ySi_xSn_y and Ge layers are lower than that of Ge_0.902Sn_0.098.

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From the valence band spectra shown in figure 1, we evaluated the valence band offset of Ge_1−x−ySi_xSn_y and Ge for Ge_0.902Sn_0.098. Figure 2 shows the valence band offsets of various Ge_1−x−ySi_xSn_y layers for Ge_0.902Sn_0.098 as a function of the Si content. The origin of the energy in figure 2 corresponds to the valence band edge of the Ge_0.902Sn_0.098 layer. The theoretical calculation results of the valence band offsets for the Ge_1−x−ySi_xSn_y layers having strains of −1%, 0%, and 1%, respectively, are also plotted (dashed lines in figure 2), and we show the relationship between the Si and Sn contents (x and y) [21]. Considering another theoretical calculation report [22], the valence band offset in Ge_0.902Sn_0.908/Ge was estimated to be 106 meV, which is 10 meV larger than that evaluated from our experiment. This difference in the valence band offset values may be owing to strain in the Ge_0.902Sn_0.908 layer, where a compressive strain of −1.4% exists the Ge_0.902Sn_0.908 layer prepared in this study while the theoretical calculations do not consider the effect of strain in the Ge_1−xSn_x layer. Herein, as the Si content in Ge_1−x−ySi_xSn_y increases, the valence band offset for Ge_0.902Sn_0.098 increases. This tendency corresponds to theoretically calculated predictions, and can be attributed to a lower valence band edge of Si than that of Ge [23]. However, the valence band offset between Ge_0.902Sn_0.098 and Ge_1−x−ySi_xSn_y with a Si content of 23% was evaluated to be 100 meV and that between Ge_0.902Sn_0.098 and Ge was evaluated to be 96 meV. Considering the theoretical prediction shown in figure 2, this slight difference is related to a small Si content and compressive strain in Ge_1−x−ySi_xSn_y, where the existence of the latter reduces the energy band offset. In contrast, in the sample with a Si content of 42%, the valence band offset was drastically increased compared with the 24%-Si case. We consider that this is not only owing to increasing Si content but also to the tensile strain in the Ge_1−x−ySi_xSn_y layer. From the theoretical calculation [21] and our results, the reason of increasing the valence band offset can be attributed to two effects, one is a higher Si/Sn ratio and another is an effect of a large tensile strain in the Ge_1−x−ySi_xSn_y epitaxial layer. The valence band offset between Ge_0.902Sn_0.098 and Ge_1−x−ySi_xSn_y reaches a maximum with a Si content of 50%, and was evaluated to be 330 meV. This value is 13 times greater than the k_BT value of 26 meV at room temperature and is sufficiently large for the confinement of holes in a Ge_1−xSn_x active layer at room temperature.

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Next, we estimated the conduction band offsets of Ge_1−x−ySi_xSn_y for Ge_0.902Sn_0.098 by calculating the bandgap of each layer based on the report of Ref. [21]. We estimated the conduction band edges of Ge_1−x−ySi_xSn_y and Ge_1−xSn_x by adding the bandgap values calculated without considering the strain to the value of the valence band edge measured in this study. Figure 3 shows the summary of the energy band alignment of the Ge_0.902Sn_0.098/Ge_1−x−ySi_xSn_y heterostructure as a function of the Si content of Ge_1−x−ySi_xSn_y. The origin of the energy in figure 3 corresponds to the valence band edge of Ge_0.902Sn_0.098 and the valence and conduction band edges of Ge_0.902Sn_0.098 are plotted (dashed lines in figure 3). The measured valence band edges of the Ge_1−x−ySi_xSn_y layers are lower than that of the Ge_0.902Sn_0.098 layer, and the estimated conduction band edges of the Ge_1−x−ySi_xSn_y layers are larger than that of the Ge_0.902Sn_0.098 layer in all samples. This result indicates that type-I energy band alignment was achieved in all samples. Comparing the results of Ge_1−x−ySi_xSn_y with a Si content of 23% and that with a Si content of 42%, there is no significant difference in the conduction band edge values. This result is attributed to a lower valence band edge in the Ge_1−x−ySi_xSn_y with a Si content of 42%, as mentioned above, although its bandgap is larger than that of Ge_1−x−ySi_xSn_y with a Si content of 23%. The conduction band offset of Ge_1−x−ySi_xSn_y for Ge_0.902Sn_0.098 approaches its maximum when the Si content is increased to 50%, and was estimated to be 150 meV. This value is 5.7 times greater than the k_BT value at room temperature. From these results of the valence and conduction band offsets, the Ge_1−xSn_x/Ge_1−x−ySi_xSn_y heterostructure is preferable to achieve the type-I energy band alignment for the confinement structure of both holes and electrons in Ge_1−xSn_x active layer at room temperature.

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In this section, we report the formation of strain-relaxed Ge_1−x−ySi_xSn_y epitaxial layers for more preferable Ge_1−x−ySi_xSn_y/Ge_1−xSn_x structures. First, we show the result of the Ge_1−x−ySi_xSn_y layer grown directly on a p-Si(001) substrate. Figure 4(a) shows the XRD-2DRSM result around the reciprocal lattice point of Ge$\overline{22}4$ for the Ge_0.71Si_0.14Sn_0.15/Si sample. XRD-2DRSM shows contour of the diffraction intensity and the vertical and diagonal lines in the reciprocal space map indicate the trajectories of the reciprocal lattice point of the pseudomorphic and the fully strain-relaxed Ge_1−x−ySi_xSn_y, respectively. The diffraction peak related to the Ge_0.71Si_0.14Sn_0.15 epitaxial layer is weak, which indicates that the crystalline quality of the epitaxial layer is poor. The Si and Sn contents were estimated from the comprehensive results of XRD-2DRSM and Raman scattering spectroscopy (not shown). Figure 4(b) shows an optical microscope image of the sample where a nonuniform surface can be observed, indicating that Sn precipitation takes place. From these results, it is evident that the epitaxial growth of a strain-relaxed Ge_1−x−ySi_xSn_y layer directly on Si is fundamentally difficult. We deduce that the reason for this difficulty is primarily owing to the large lattice mismatch between Si and Ge_0.71Si_0.14Sn_0.15. The lattice constant of Ge, Si, and Sn are 0.566, 0.543, and 0.649 nm [24], respectively, and that of the Ge_0.71Si_0.14Sn_0.15 layer is estimated from Vegard's law to be 0.575 nm. Therefore, the lattice mismatch between Si and the Ge_0.71Si_0.14Sn_0.15 layer is estimated to be 5.9% and this large lattice mismatch causes the degradation of the crystalline quality of the Ge_1−x−ySi_xSn_y epitaxial layer during its growth on Si.

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To improve the crystallinity of the strain-relaxed Ge_1−x−ySi_xSn_y layer, we examined the effect of decreasing the lattice mismatch between the Ge_1−x−ySi_xSn_y layer and the substrate by using a Ge(001) wafer and v-Ge as substrates, whose lattice constants are greater than Si. The XRD-2DRSM results around the reciprocal lattice point of Ge$\overline{22}4$ for the Ge_0.64Si_0.21Sn_0.15/Ge and Ge_0.61Si_0.22Sn_0.17/v-Ge samples are shown in figures 5(a) and (b), respectively. Optical microscope images of the Ge_1−x−ySi_xSn_y layers grown on Ge and v-Ge substrates are shown in figures 5(c) and (d), respectively. The Ge_1−x−ySi_xSn_y layer was prepared on each substrate using conditions similar to those mentioned above, and each element content was estimated comprehensively considering the results of XRD-2DRSM and Raman scattering spectroscopy. The surface morphologies of the Ge_1−x−ySi_xSn_y layers grown on both the Ge and v-Ge substrates were uniform, unlike those grown on the Si substrate; thereby confirming the formation of uniform Ge_1−x−ySi_xSn_y layers without Sn precipitation. The diffraction peak related to the Ge_0.64Si_0.21Sn_0.15 layer grown on the Ge substrate is clearly observed at the same reciprocal-space value to the $[\overline{11}0]$ direction (Q_x) of the diffraction peak related to Ge. This indicates that the Ge_0.64Si_0.21Sn_0.15 layer is pseudomorphically grown on the Ge substrate and that no strain relaxation of the epitaxial layer occurs. In contrast, the diffraction peak related to the Ge_0.61Si_0.22Sn_0.17 layer grown on the v-Ge exhibited a smaller Q_x value than that of v-Ge. This indicates that strain relaxation of the Ge_0.61Si_0.22Sn_0.17 layer occurs, where the degree of strain relaxation (DSR) was estimated from the Q_x value to be 55%. Interestingly, these results mean that the strain relaxation in a Ge_1−x−ySi_xSn_y epitaxial layer preferentially occurs on a v-Ge substrate rather than on a Ge substrate, even with identical growth conditions.

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Here, we deduce the reason for this difference of the strain relaxation. Previously, our group has reported the enhancement of the strain relaxation of a Ge_1−xSn_x epitaxial layer on a v-Ge substrate owing to the threading dislocations that inherently exist in the Ge buffer layer [25]. The density of threading dislocations in the v-Ge substrate was typically estimated to be 10¹¹ cm⁻² in our previous case. We consider that a similar mechanism exists for the strain relaxation of the Ge_1−x−ySi_xSn_y epitaxial layer on a v-Ge substrate in this study. The high-density threading dislocations in the v-Ge continuously propagate in the Ge_1−x−ySi_xSn_y layer grown on a v-Ge substrate, and these threading dislocations should play the role of a nucleus generating the misfit dislocations at the Ge_1−x−ySi_xSn_y/v-Ge interface. However, the crystallinity of the Ge substrate used in this study is very high and the density of threading dislocations on the Ge surface is negligible. In our case, the Ge_1−x−ySi_xSn_y epitaxial layer pseudomorphically grown on the Ge substrate also exhibits high crystallinity and no threading dislocations are introduced in the growth of a thin epitaxial layer below the critical thickness of strain relaxation. As a result, it is considered that the strain relaxation in the Ge_1−x−ySi_xSn_y epitaxial layer is enhanced with the propagation of misfit dislocations rather than that on Ge, even with the same growth conditions.

In addition, we examined the effects of enhancing the strain relaxation of Ge_1−x−ySi_xSn_y layers by PDA to raise the in-plane lattice constant of the Ge_1−x−ySi_xSn_y layer. Figure 6 shows the annealing temperature dependence of the in-plane lattice constant, the DSR of the Ge_0.61Si_0.22Sn_0.17 layer, and the strain in the Ge_0.94Sn_0.06 layer, which would be formed on the Ge_0.61Si_0.22Sn_0.17 layer as-grown or annealed at 300 and 400 °C for 10 min in N₂ ambient. In figure 6, we estimated the strain in a Ge_0.94Sn_0.06 layer because the indirect-direct transition crossover of Ge_1−xSn_x is predicted with a low Sn content of 6% and a low tensile strain of 0.2% [19]. For comparison, we also show the results for the Ge_0.64Si_0.21Sn_0.15 epitaxial layer grown on a Ge substrate. The DSR of the Ge_0.64Si_0.21Sn_0.15 layer grown on a Ge substrate does not increase after 300 °C-PDA. After 400 °C-PDA, the DSR of the Ge_0.64Si_0.21Sn_0.15 layer grown on a Ge substrate increases slightly, but the DSR value is as low as 7.5%. On the other hand, the DSR of the Ge_0.61Si_0.22Sn_0.17 layer grown on v-Ge increases after PDA at 300 and 400 °C, and were estimated to be 64% and 70%, respectively. Notably, after 400 °C-PDA, the lattice constant of the Ge_0.61Si_0.22Sn_0.17 layer was estimated to be 0.571 nm. This result indicates the possibility of the formation of a 0.14%-tensile-strained Ge_0.94Sn_0.06 layer on this Ge_0.61Si_0.22Sn_0.17 layer, and a direct transition Ge_1−xSn_x layer could be obtained by increasing the strain relaxation slightly. Here, we deduce the reason for the enhancement of strain relaxation after PDA. In the Ge/Si case, there is a thermal expansion mismatch [26] whose influence on the strain should be considered. However, in the Ge_1−x−ySi_xSn_y/Ge case, it is reported that the mismatch of the thermal expansion coefficient is negligibly small [27]. Also, in this study, the highest process temperature of 400 °C is not so high, therefore, we do not consider the effect of a thermal expansion mismatch upon the strain in epitaxial layer. From this reason, we think that the enhancement of strain relaxation only occurs due to the propagation of threading dislocations in the Ge_1−x−ySi_xSn_y/Ge and v-Ge samples.

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We also investigated the surface morphology of strain-relaxed Ge_1−x−ySi_xSn_y layers using AFM observation, and figures 7(a) and (b) show the AFM images and surface profiles of the Ge_0.64Si_0.21Sn_0.15/Ge and the Ge_0.61Si_0.22Sn_0.17/v-Ge samples, respectively, after PDA at 400 °C. Scarcely any agglomeration can be observed on the surfaces of both samples, indicating that no Sn precipitation occurs after 400 °C-PDA. The root mean square (RMS) roughnesses of the Ge_0.61Si_0.22Sn_0.17/v-Ge and the Ge_0.64Si_0.21Sn_0.15/Ge samples were evaluated to be 2.7 and 4.7 nm, respectively, indicating that using v-Ge is an effective way to suppress the surface roughness.

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