The fundamental electronic energy bandgap is the most important parameter of a semiconductor, upon which other electronic and optical properties sensitively depend. It is crucial to carefully control the bandgap to optimise the performance of semiconductor devices. Bandgap engineering can be achieved by changing compositions in a semiconductor alloy system^[1]. The field of bandgap engineering was significantly expanded with the introduction of epitaxial growth techniques^[2]. Epitaxy refers to growth of crystalline layer, known as epitaxial layer, on top of a crystalline substrate with the same orientation. In this technique, large stresses in epitaxial layers are generated because of lattice constant mismatch between epitaxial layer and substrate^[3]. The strain in epitaxial layer provides an additional design flexibility for electronic band structure engineering. However, such flexibility is influenced and limited to a critical thickness of epitaxial layer, where strain starts to relieve due to formed defects as a consequence of strain relaxation^[3]. For example, if lattice constant of epitaxial layer significantly depends on its composition, appropriate composition could lead to significant strain energy and so large reduction in h_c into an undesirable value. When growing a material with the same crystal structure with a different lattice constant from the substrate or buffer layer (referred to as a virtual substrate (VS)), the grown material either has a tensile strain or a compressive strain. In the case of Ge_1–ySn_y grown on Ge-VS (or Si substrate), the grown Ge_1–ySn_y epilayer will have a compressive strain because its lattice constant is larger than that of Ge-VS (or Si substrate). If the grown Ge_1–ySn_y has exactly the same inner plane (in-plane) lattice parameter as its Ge-VS (or Si substrate) but a larger outer plane (out-of-plane) lattice parameter, it is referred to as a fully strained Ge_1–ySn_y. Fully strained Ge_1–ySn_y epilayer can be grown up to a certain thickness, so called critical thickness h_c, which mainly depends on Sn concentration (y). Above h_c, Ge_1–ySn_y epilayer gradually begins to relax the compressive strain.

The lattice constant of Ge_1–ySn_y is larger than that of Ge; however, this lattice constant closely depends on the Sn concentration in Ge_1–ySn_y, especially in samples that are not fully strained. As the Sn concentration (y) in the Ge_1–ySn_y binary alloy increases, its lattice volume is expected to increase. The growth of high quality Ge_1–ySn_y, in which segregation and precipitation is controlled, directly on Si substrate using CVD is very challenging due to its large lattice mismatch. To overcome this challenge, a high quality relaxed Ge buffer, which has a larger lattice constant than Si, can be grown on Si substrate and used as an intermediate layer, VS, to reduce the effective lattice mismatch. The strain is a key parameter that influences the physical, optical, and electrical properties of the Ge_1–ySn_y epilayer. For example, it has been suggested that tensile and compressive strain reduce and increase the required Sn concentration to achieve indirect-to-direct bandgap transition, respectively^{[4, 5]}. In addition to Sn concentration, it is possible to adjust carrier mobility^{[6, 7]} and band structure^{[4, 8]} of the epilayer by modifying the strain in the Ge_1–ySn_y epilayer. Therefore, it is essential to fully understand the strain relaxation of Ge_1–ySn_y epilayers.

Theoretically, it should be possible to tune the room temperature energy bandgap of Ge_1–ySn_y alloy from 0.66 eV down to 0.0 eV by modifying the Sn concentration in Ge_1–ySn_y^{[9, 10]}. Ge is a group Ⅳ semiconductor with an indirect bandgap and an energy difference of 0.66 eV between the lowest conduction band minimum, L-point, and the highest valence band maximum, Γ-point, at room temperature^[5]. As y increases in Ge_1–ySn_y, the L-valleys diminishes slower than the Γ-valley as a consequence of E_gΓ,Ge – E_gΓ,αSn ˃ E_gL,Ge – E_gL,αSn, suggesting an indirect-to-direct bandgap transition for a certain^[5]. It has been shown that bandgap energy decreases as a result of tensile biaxial strain in Ge_1–ySn_y, as the effect of strain is significantly higher in direct gap than indirect^{[11, 12]}. The achievement of direct bandgap Ge_1–ySn_y depends strongly on its strain relaxation, for instance, for compressive strained Ge_1–ySn_y, higher Sn concentration is required for an indirect-to-direct bandgap transition than tensile strained Ge_1–ySn_y^[5].

Theoretical investigations have shown that biaxial strain can significantly affect the bandgap structure of Ge_1–ySn_y. Specifically, it has been suggested that tensile and compressive strains can respectively decrease and increase the required Sn concentration to achieve an indirect-to-direct bandgap transition in Ge_1–ySn_y^[4]. Tensile strained Ge_1–ySn_y can be grown on partially or fully relaxed Ge_1–ySn_y with a different Sn concentration^[17−20], while compressive strained Ge_1–ySn_y can be grown on Si via Ge-VS^{[21, 22]}. Recent predictions indicate that an indirect-to-direct bandgap transition in Ge_1–ySn_y can be achieved with a Sn concentration ranging from 6 at.% to 11 at.%^{[4, 23−27]}.

Therefore, it is crucial to have a comprehensive understanding of the impact of strain relaxation on the growth rate of Ge_1–ySn_y epilayers, in addition to understanding its critical thickness and Sn concentration, to facilitate the development of optoelectronic devices. As seen in Fig. 1, many studies have been carried out to estimate critical thicknesses and the effect of strain relaxation on Sn concentration as well as quality of epilayers. However, no study has been done to investigate the effect of strain relaxation on growth rate, which is presented in this research.

In this research, all crystalline materials were grown using the ASM Epsilon 2000 system. It is one of the most common epitaxy tools in semiconductor manufacturing, having been used for about three decades to grow Si, Ge, Si_1–xGe_x, Si_1–xC_x and many other group Ⅳ semiconductors. It is a horizontal flow, load-locked, and single wafer reduced-pressure chemical vapour deposition (RP-CVD) tool developed for high-volume semiconductor production in various epitaxy applications. The Si wafer is mounted on a graphite susceptor coated with silicon carbide, which is located in a quartz chamber with a cold wall. During the process, infrared (IR) lamps are responsible for heating the susceptor and the wafer, ones placed on the bottom and the others on the top of the quartz chamber. To control growth at low temperatures, thermocouples embedded in the susceptor are used.

All Ge_1–ySn_y epilayers were grown on 100 mm Si (001) wafers via 0.6 µm thick relaxed Ge virtual substrate. By growing thick enough Ge buffer layer on top of Si (001), strain relaxation within the Ge buffer layer is achieved and so effective lattice mismatch between Si substrate and Ge_1–ySn_y decreases from ~20 % to ~15 %^[5]. Tin-tetrachloride (SnCl₄) was used in combination with germane (GeH₄) with H₂ as a carrier gas and chamber pressure controller. All growth was carried out at 260 °C and 500 Torr.

The Sn concentration of each Ge_1–ySn_y epilayer was measured using high-resolution X-ray diffraction (HR-XRD). HR-XRD ω–2θ coupled scan, symmetric and asymmetric reciprocal space maps (RSMs) were used, alongside with the modified Vegard’s law to measure the Sn concentrations. The Vegard’s law used in this research is:

1a0Ge1−ySny=(1−y)⋅a0Ge+y⋅a0Sn+y(1−y)⋅bGeSn,

where a₀ is the relaxed lattice constant of each crystal, and b^GeSn is the bowing parameter. The bowing parameter (b^GeSn) used in this research is 0.041 Å^[15] according to the latest agreed studies and relaxed lattice constant, a₀ is 5.6579 and 6.4892 Å for Ge and Sn, respectively^[5]. The lattice constant of each epilayer was calculated from the in and out of plane lattice parameters obtained from RSMs.

In this work, the h_c value of Ge_1–ySn_y, which represents the thickness where strain relaxation begins in the epilayer, is initially investigated. The Sn concentration of 11.6 at.% was obtained for the fully strained Ge_1–ySn_y epilayers. The Sn concentration for each sample was measured from RSMs using the modified Vegard’s law. As seen in Fig. 2(a), the thickness fringes around Ge_1–ySn_y peak in HR-XRD ω–2θ coupled scan for the Ge_1–ySn_y epilayer grown for 10 min began to disappear. This indicates the beginning of strain relaxation in the Ge_1–ySn_y epilayer. The thickness of the Ge_1–ySn_y epilayer grown for 10 min was measured using X-TEM to be 95 nm. This shows that the h_c value for Ge_1–ySn_y epilayers grown under the given CVD growth conditions is approximately ~95 nm which agrees with previous studies shown in Fig. 1.

When comparing the HR-XRD ω–2θ coupled scans of the Ge_1–ySn_y epilayers shown in Fig. 2(a), it becomes evident that as more strain relaxation is achieved, the Ge_1–ySn_y peak in the HR-XRD ω–2θ coupled scan begins to shift to the right. This shift is solely due to strain relaxation within the layers of Ge_1–ySn_y and not to a reduction in Sn concentration. This is demonstrated when measuring the Sn concentration using XRD RSMs.

As shown in Fig. 2(b), the Ge_1–ySn_y grown for 8 min is fully strained, and its peak appeared exactly under the relaxed Ge-VS in the asymmetric RSM. However, for the Ge_1–ySn_y grown for 10 min, as shown in Fig. 2(c), the Ge_1–ySn_y peak in the asymmetric RSM is slightly shifted to the left, indicating the appearance of strain relaxation in the Ge_1–ySn_y layers. In addition, for the Ge_1–ySn_y grown for 15 min, as shown in Fig. 2(d), the Ge_1–ySn_y peak in the asymmetric RSM is significantly shifted to the left, indicating a greater degree of strain relaxation in the Ge_1–ySn_y layers compared to the previous epilayer, which was grown for only 10 min. As shown in Fig. 2(d), the Sn concentration of the Ge_1–ySn_y epilayer grown under the same CVD growth conditions has indeed increased due to strain relaxation. The Ge_1–ySn_y epilayer grown for 15 min has 0.2 at.% more Sn concentration than the fully strained Ge_1–ySn_y epilayer grown for 8 min. For the Ge_1–ySn_y epilayer grown for 10 min, no change in Sn concentration was observed as the epilayer has just begun to relax at the h_c of ~95 nm.

An additional Ge_1–ySn_y epilayer was also grown for 15 min under the same growth conditions, indicating a relaxation of strain in the epilayer. The thickness of this epilayer is also measured using X-TEM. As seen in Fig. 2(a), an additional peak is observed next to each of the HR-XRD ω–2θ coupled scans of Ge_1–ySn_y epilayers (with apparent strain relaxation), which were grown for 10 and 15 min. It should be noted that shoulders on the left side of the Ge peak in HR-XRD ω–2θ coupled scans are normally considered to be due to polycrystalline Ge_1–ySn_y or Ge_1–ySn_y with very low Sn concentration (around Sn solubility in Ge). Nevertheless, as can be seen in Fig. 2(a), such peaks or shoulders are not present in HR-XRD ω–2θ coupled scans of fully strained Ge_1–ySn_y epilayers grown under the same CVD conditions. The apparent shoulders are presumably due to Sn segregation, especially considering they are not evident for fully strained Ge_1–ySn_y epilayers. As such, the shoulder does not appear in the HR-XRD ω–2θ coupled scan of the 150 nm thick Ge_0.878Sn_0.122. It may depend on the area of the epilayer scanned; thus, some areas on the wafers have no Sn segregation.

A thicker Ge_1–ySn_y epilayer was grown for 20 min under the same growth conditions. Symmetric and asymmetric RSMs of the heterostructure are shown in Fig. 2(e). At first glance, two Ge_1–ySn_y peaks in the asymmetric RSM can be noticed. Before discussing the double Ge_1–ySn_y peaks, it is important to note that both Ge_1–ySn_y peaks are more relaxed (shifted more to the left in asymmetric RSM) than the Ge_1–ySn_y peak in asymmetric RSM of thinner Ge_1–ySn_y epilayers. In addition, both Ge_1–ySn_y peaks indicate higher Sn concentrations than thinner Ge_1–ySn_y, as shown in Fig. 2, confirming an increase in Sn concentration due to strain relaxation. In Fig. 3(a), high resolution X-TEM of Ge_0.878Sn_0.122 is given which shows thickness and smooth surface of the epilayer.

A summary of the relationship between thickness, Sn concentration and total growth rate of Ge_1–ySn_y epilayers is shown in Fig. 3(b). For the Ge_1–ySn_y epilayer with growth time of 20 min (150 nm thick Ge_1–ySn_y epilayer), only one peak is included (the one with lower Sn concentration). It should be noted that this summary is only valid for Ge_1–ySn_y epilayers grown under the same CVD conditions using the same precursors and respective partial pressures. This is because each of these CVD conditions can influence lattice diffusion and thus h_c. For example, as the growth temperature decreases, lattice diffusion is minimised which may increases the h_c. Another example is the Sn concentration itself: as the Sn concentration in the Ge_1–ySn_y epilayer increases, the h_c decreases, so the epilayer strain relaxation is achieved more quickly.

Moreover, if the thickness of the Ge_1–ySn_y epilayer is greater than h_c, misfit dislocations can form at the two ends^[28]. These dislocations could create a loop so that the two ends can join or thread onto the surface, which could potentially restrict applications of relaxed Ge_1–ySn_y^{[6, 29]}. Examples of AFM scans of the epilayers with various thicknesses are provided in Figs. 3(c)–3(e). The surface roughness in terms of RMS for all Ge_1–ySn_y epilayers grown in this study is shown in Fig. 3(f). It is evident that the surface roughness remained low for all fully strained Ge_1–ySn_y, and as soon as a h_c of ~95 nm was reached (at growth time of ~10 min), the surface roughness began to increase. This could be due to Sn segregation, which may be a consequence of strain relaxation^[30].

It is important to discuss the reasons for the appearance of two Ge_1–ySn_y peaks (as can be seen in Fig. 2(e)) in asymmetric RSM of Ge_1–ySn_y epilayer grown for 20 min. The justification for this behaviour is as follows: the second peak, which indicates that Ge_1–ySn_y layers with a slightly higher Sn concentration can be grown when a certain strain relaxation is achieved. The Sn concentration increases gradually and steadily as the layers relax (as the thickness of the epilayer increases) until a certain point. After this certain point, there is a sudden transition to Sn concentration, because the top layers (which now act as an intermediate substrate) allow Ge_1–ySn_y to grow with such a higher Sn concentration.

In this section, the effect of strain relaxation on the growth rate of Ge_1–ySn_y epilayers is investigated. As shown in Fig. 3(b), the growth rate of Ge_1–ySn_y epilayers decreases with increasing thickness. The growth rates shown in Fig. 3(b) are the growth rates for the entire Ge_1–ySn_y epilayers. To understand the effect of strain relaxation on growth rate, it is therefore necessary to investigate the relationship between growth rate and thickness of Ge_1–ySn_y epilayers.

As shown in Fig. 4(a), the average growth rate for fully strain Ge_1–ySn_y grown up to 10 min under the given CVD conditions was 9.8 nm/min. We assumed that for partially relaxed Ge_1–ySn_y epilayers, which were grown for 15 and 20 min, the growth rate for the initial 10 min was the same as the growth rate for fully strained Ge_1–ySn_y epilayers. Based on this assumption, the average growth rate from 10 to 15 min was measured at 6.1 nm/min and the average growth rate from 15 to 20 min was measured at 4.4 nm/min. These growth rates were calculated by growing Ge_1–ySn_y with different growth times.

Considering the average growth rates of the epilayers depending on their thickness as shown in Fig. 4(a), it is possible to understand the effect of strain relaxation on growth rates. As shown in Fig. 4(b), a straight line (orange colour) is fitted to the data, representing the average growth rate at the given thickness of the Ge_1–ySn_y epilayer. For thicknesses below the h_c, in which all Ge_1–ySn_y epilayers are fully strained, the growth rate is assumed to remain constant. Therefore, a straight horizontal line was fitted to those epilayers with thickness of up to h_c. The epilayers with thickness of above h_c are partially relaxed and their degree of relaxation is discussed in the next Section. It is also evident that the rate of suppression in the average growth rate is at its highest level just after the Ge_1–ySn_y epilayer passes the h_c, and the rate of reduction in the average growth rate gradually decreases as the thickness of the epilayer increases.

The in-plane and out-of-plane strain of Ge_1–ySn_y epilayers grown were estimated using the following equations:

2Strainin−plane=a∥GeSn−a0GeSna0GeSn,

3Strainout−of−plane=a⊥GeSn−a0GeSna0GeSn,

where a∥ and a⊥ are in-plane and out-of-plane of the lattice respectively. Additionally, a0GeSn refers to the relaxed lattice constant for Ge_1–ySn_y at a given Sn concentration, and GeSn refers to the actual Ge_1–ySn_y epilayer grown and its HR-XRD ω–2θ coupled scan and RSMs were collected.

In-plane and out-of-plane strain of grown Ge_1–ySn_y epilayers were calculated using Eqs. (1) and (2) and presented in Table 1. It is evident that the thickness of the Ge_1–ySn_y epilayer does not affect the in-plane or out-of-plane strain if the thickness is less than the h_c (~0.10 µm). However, when the thickness of the Ge_1–ySn_y epilayer exceeds h_c, the strain relaxation begins, and both the in-plane and out-of-plane strains of the epilayer converge towards relaxed lattice constant, a0GeSn.

By considering the measured in-plane and out-of-plan strain, it is possible to investigate the effect of strain relaxation on both the growth rate and Sn concentration of Ge_1–ySn_y epilayers. As shown in Table 1, the average growth rate decreases as more strain relaxation are achieved. These average growth rates represent the growth rate for the entire Ge_1–ySn_y epilayers, not at a given in-plane or out-of-plane strain (or simply at a given thickness). To determine the true growth rate at a given thickness, the fitted line to the actual data shown in Fig. 4(b) can be used. Using this approach, the growth rate at a thickness of 128 nm was estimated to be ~5 nm/min and at a thickness of 150 nm was estimated to be ~4 nm/min. Based on these estimates, the effect of strain relaxation on the growth rate at given thicknesses can be explored. As shown in Fig. 5, the growth rate at the given thickness of the Ge_1–ySn_y epilayer is (almost) linearly dependent on the in-plane and out-of-plane strain. Since only two data points are available for partially relaxed Ge_1–ySn_y, more studies are required to investigate further the effect of strain relaxation on the growth rate of the Ge_1–ySn_y epilayer at a given thickness.

As explained previously, the growth rate of Ge_1–ySn_y mainly depends on the Ge incorporation in the growing layers. Since all growth conditions such as temperature, pressure and partial pressures of precursors remained constant over the growth of all Ge_1–ySn_y epilayers, the production of Ge and Sn atoms remained constant. Therefore, the suppression of the Ge incorporation in growing layers cannot be due to the lack of Ge adatoms produced in the chamber. It seems that the strain relaxation directly influences the incorporation of Ge. As Ge_1–ySn_y relaxes more, a lower percentage of available Ge adatoms on the growing layers can be incorporated into the growing layers, resulting in a reduction in the growth rate.

Finally, the effect of strain relaxation on average Sn concentration can be examined. Here, we are discussing only the average Sn concentration across the entire Ge_1–ySn_y epilayer, rather than the Sn concentration at a specific thickness of the Ge_1–ySn_y epilayer. As shown in Table 1, the average Sn concentration increases as a result of strain relaxation. This can be explained by taking into account the effect of the growth rate on the average Sn concentration of Ge_1–ySn_y epilayers. Like Ge production, as CVD growth conditions remained the same, the production of Sn adatoms remained the same during the growth of Ge_1–ySn_y epilayer. Therefore, as the growth rate decreases, more of supplied Sn adatoms have the chance to incorporate into Ge_1–ySn_y growing layers, leading to an increase in Sn concentration.

It should be noted that even though the average growth rate decreases by ~55 % due decrease in incorporation of Ge into growing layers as a result of strain relaxation, the average Sn concentration in Ge_1–ySn_y has increased only by ~8 % from 11.6 at.% to 12.5 at.%. It is important to consider that this is the average Sn concentration of the whole epilayer and not just the top layers grown with lower growth rates. This result shows that the total Sn concentration does not significantly increase as a result of the reduction in growth rate, and the relationship could be nonlinear. This suggests that the incorporation rate of Sn into the growing Ge_1–ySn_y layers during the total growth time has indeed decreased, and the reason why the total Sn concentration is increased is because of the reduction in growth rate itself.

In this research, the effect of strain relaxation in compressive strained Ge_1–ySn_y, which were grown at 260 °C, on growth rate is investigated. It is experimentally shown that strain relaxation within Ge_1–ySn_y decreases the growth rate of the epilayer. We also examined how Sn concentration and surface morphology of Ge_1–ySn_y epilayers may be influenced as a result of strain relaxation. It is important to note that strain relaxation could be potentially different in Ge_1–ySn_y epilayers with the same Sn concentration but grown under different CVD growth conditions. More experiments should be carried out to investigate strain relaxation for Ge_1–ySn_y epilayers grown under different CVD growth conditions. Furthermore, since the strain relaxation in Ge_1–ySn_y epilayers affects the electrical, for example indirect-to-direct bandgap transition^{[4, 23−27]}, and the physical properties of epilayers, it is therefore essential to consider further investigations in order to fully understand the mechanism of strain relaxation of Ge_1–ySn_y epilayers. This could pave the way for the widespread adoption of Ge_1–ySn_y based semiconductor devices and applications in the near future.