Introduction

Metamorphic buffers (MB) have been extensively used in the last couple of decades to design novel photonic and optoelectronic devices. Of particular interest has been the use of metamorphic buffers in strained InxGa1-xAs, lasers on GaAs substrates for telecommunications purposes [1,2,3,4,5,6]. Compared to the current InP substrates, GaAs is less brittle [7], less sensitive to temperature changes [2] and is more readily available in large wafer sizes [8]. InGaAs quantum wells (QWs) have been successfully introduced as the active region and used to tune specific wavelengths, e.g. 1.3 µm and 1.5 µm, and are thought to have less potential performance reproducibility issues when compared to their quantum dot laser counterparts [8]. However, due to constraints around the In concentration and thickness of the QW [9], commercial InGaAs QW on GaAs lasers performance is usually limited to 1.2 µm. A potential solution to this is to reduce the difference between the lattice constant of the substrate and the subsequent layers which can be achieved using a MB layer.

MBs are layers in which the composition of the alloy is gradually changed, serving as a bridge between the substrate and the subsequent layers, and hence allowing to tailor the in-plane lattice parameter of the subsequent layers. This effectively reduces the defect density, such as misfit (MD) and threading dislocations (TD) that arise at the buffer/substrate interface and is known to greatly affect the bandgap [10, 11], optical [12] and electronic [13, 14] properties of the laser.

MBs has proven to be an effective approach to decrease the defect density and relax the strain in a controlled manner, presenting an opportunity to control how the strain is distributed to the next layers and thus, offers exciting possibilities for band structure engineering. There are different chemical grading types of MB including uniform [15,16,17], step graded [18,19,20] and continuously graded [21,22,23]. The continuously graded approach could be linear [20, 24] or parabolic [25, 26], and generally speaking it allows more flexibility in the growth, tailoring the strain relaxation. Importantly, the parabolic profile has been shown to be less sensitive to variations in the MB thickness [22] and it has been shown to confine the defects further away from the active region [27, 28] thus, making it a more promising approach for strain tuneability.

Parabolic-graded MBs for metamorphic InGaAs QW on GaAs lasers have been recently explored for telecommunication applications at 1.3 µm. Gocalinska et al., found that for a series of different parabolic InGaAs MBs on GaAs or ‘stack designs’, the management of strain in the MB under different stack designs, with some of the findings being rather unexpected [26]. For a full GaAs metamorphic structure, several different stack designs were tried with the optimal design giving an operating laser with low lasing threshold and emission extending up to 1.36 µm [29]. Parabolic-graded MBs have also been used for InP substrate-based devices. Ye et al., fabricated a photodiode operating at 2 µm with a low bit error rate which would be suitable for “laser imaging, detection, and ranging” (LIDAR) applications [30].

Indeed, MBs represent a unique opportunity for the design of novel semiconductor devices. However, the number of reports on the defect and strain distribution as a function of the architecture is limited. Typically, reports focus on the device performance or surface roughness in the metamorphic buffer and often these do not evaluate the strain levels in subsequent layers and distribution of dislocations in the MB. Strain is known to have a significant impact on the bandgap [31], which can in turn affect device performance. Therefore, establishing a connection between the strain distribution across the layers can facilitate the optimisation of metamorphic laser performance. In this paper we present a systematic study into the MB of several architectures on GaAs (001) substrate for metamorphic lasers, and a full GaAs metamorphic laser recently reported [29], via transmission electron microscopy techniques. We map the distribution and density of dislocations in the MB, with respect to In concentration. Furthermore, we present an overview on the localised strain in subsequent layers, comparing the overall strain profile of the different layers that would be used as cladding in a full laser structure. This provides an insight into the difference strain management while changing architecture/stacking for the GaAs-based metamorphic InxGa1-xAs QW lasers.

Experimental

Sample growth and preparation

The sample here investigated were grown using metal organic vapour phase epitaxy (MOVPE) with full growth conditions presented elsewhere [29, 32]. All precursors had purity grades at the highest of what is commercially available, for example Arsine is used at a commercial grade called Megabit III, and metalorganics were acquired by different producer, with similar quality and commercial grade availability (e.g. Optoelectronic Grade, EpiPure, and EpiGrade). Further details and discussion can be found in previous work [33,34,35]. Cross-sectional TEM lamellae were prepared using a TESCAN Lyra 3 dual beam FIB/SEM by standard in situ lift out procedure [36].

Electron Microscopy techniques: Transmission electron microscopy (TEM) and scanning TEM (STEM) were conducted using a Thermofishcher Talos F200-X at 200 kV fitted with a field emission gun (FEG) and four in-column Super-X energy dispersive X-ray spectrometer (EDX) detectors having a total collection angle of ∼0.9 sr. Dislocations in the MB were analysed using weak-beam dark field (WBDF) imaging mode [37]. Determination of g vectors was done by comparing experimental diffraction patterns to simulated using data from Giesecke and Pfister [38] in Single Crystal™ Software [39]. The number of MDs and TDs was assigned based on previous work [40, 41]. Dislocation density in the MB was measured using the line-length method [42]. The length was extracted from the annular dark field (ADF)-STEM images, using a stamp filtering process similar to the method reported elsewhere [43] with density calculated from the derived length, assumed thickness of the lamella and total area of the STEM image using an in house MATLAB script of the line-length method. The atomic fraction (at.%) profile was calculated from the EDX data, using the Kα peaks of Al, As and Ga, with Lα peaks used for In. Background correction was done with a multipolynomial function modelled as parabolic function with a Brown-Powell Ionization cross-sectional model [44]. Quantitative strain mapping was calculated using geometric phase analysis (GPA) on the ADF-STEM images using a Gatan script from Rouvière [45] and Strain +  + [46], both of which are based on theory from Hÿtch et al. [47]. The g-vectors tested were g = 002 and g = \(\mathbf{2\overline{2 }0}\) with a comparison of g = 004 and g = \(\mathbf{2\overline{2 }0}\) also investigated. Theoretical strains were calculated with lattice parameters derived from Vegard’s law [48].

Results and discussion

Sample overview

All samples here investigated consist of a GaAs (001) substrate misoriented towards [1 1 1]A (or also referred to as the (1 1 1) plane which terminates ideally with Ga atoms [49]) by either 0.2° or 6° on a parabolic-graded InxGa1-xAs MB with an In concentration varying from 0 < x < 0.18 and a nominal thickness of 1 µm. The profile of the MB is similar to the design described by Müller et al. [25]. After the MB, the samples have different stacking, as described schematically in Fig. 1. From bottom to top, the first sample has a GaAs substrate, the 1 µm InxGa1-xAs MB and 1.4 µm In0.66Ga0.34P film (Fig. 1a). This sample is referred to as A2168 and two variations in this are investigated, 0.2° and 6° misorientation of the GaAs substrate towards [1 1 1]A.

Figure 1
figure 1

Schematic overview of five samples, with nominal thickness. a A2168 0.2° & 6° b A2192 0.2°, c A2229 0.2° and d A2248 6°. 0.2° and 6° represent misorientation towards [1 1 1]A GaAs plane. The layers are colour coded: grey represents the GaAs substrate, purple represents the InxGa1-xAs MB layer, blue is the In0.13Ga0.87As SBL, light green is the 1.4 µm In0.66Ga0.34P film, green/orange in c and d is the latticed matched/tensile strained InGaP layer in the SL samples, respectively, and dark red the Al.31In0.15GaAs layer in the SL samples. × 5 indicates the SL repetition

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The second sample contains a strain balancing layer (SBL) of 0.3 µm In0.13Ga0.87As placed between the InxGa1-xAs MB and the 1.4 µm In0.66Ga0.34P film. The sample also has a 0.2° GaAs substrate misorientation, here referred as A2192 0.2°. SBLs have been reported to aid reducing surface roughness, improving film quality [26].

An alternative approach to control the strain and reduce dislocation formation in the active region is the growth of superlattices (SL) [50, 51]. Two SL structures investigated in this study consist of a GaAs substrate with the InxGa1-xAs MB (identical to all previous samples), along with a 0.02 µm thick layer of In0.18Ga0.82As on top of the MB. The two alloys used for the SLs here investigated are InGaP and Al0.31In0.15GaAs repeated five times (Fig. 1c and d). The first SL structure is lattice matched (LM) with a 0.2° misorientation towards [1 1 1]A and a 0.05 µm In0.66Ga0.34P layer on top of the In0.18Ga0.82As layer, followed by a 0.25 µm Al0.31In0.15GaAs layer which is the basis the for the SL, with 5 repetitions of the In0.66Ga0.34P and Al0.31In0.15GaAs. The top of the structure has a 0.05 µm In0.66Ga0.34P layer. This sample is referred as A2229 0.2°.

The second SL sample is intentionally strained. The sample denoted as A2248 6° follows the same MB structure as sample A2229 0.2° (Fig. 1c) with the difference that after the MB, the SL consists of a 0.25 µm Al0.31In0.15GaAs and 0.05 µm In0.62Ga0.38P repeated 5 times (Fig. 1d). In this design, the In0.62Ga0.38P is under tensile strain (TS) with respect to the Al0.31In0.15GaAs. For comparison, we also refer to a full GaAs-based parabolic-graded InxGa1-xAs MB laser structure previously investigated by Mura et al. [29], referred here as A2398 6° and further described in SI (see Fig. S1). Apart from being a full laser structure, the lower cladding consists of a Al0.31In0.15GaAs/TS In0.62Ga0.38P SL, similar to A2248 6° (Fig. 1d). It should be noted that the measured thickness of layers such as the MB, can deviate from the nominal thickness (see Table S1).

Figure 2 displays a representative cross-sectional ADF-STEM image of the Al0.31In0.15GaAs/TS In0.66Ga0.34P SL sample (A2248 6°). ADF-STEM images for all samples here investigated are presented in the SI (see Fig. S2). The most striking characteristic is the presence of dislocations within the MB layer, apparent by their bright contrast. Given that one main purpose of the parabolic MB layer is to control strain relaxation and contain dislocations, it is then reasonable and relevant to investigate the relationship between the In concentration across the MB and the position, and density, of dislocations.

Figure 2
figure 2

ADF-STEM overview of sample A2248 6° viewed down [1 1 0] zone axis. The blue arrow refers to the distance here referred as t0 (distance between InxGa1-xAs MB/GaAs interface and last observed MD), and the orange box represents the area from which the EDX profile shown in Fig. 2 was acquired. The white dotted line represents the interface between layers before and after the MB

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Dislocations analysis

The MB here studied is InxGa1-xAs, in which as mentioned before, the concentration of In will vary as function of thickness, in a parabolic manner. As the In concentration changes so does the lattice parameters and thus, the strain is intimately linked to In concentration. This means that the dislocation density and their spatial distribution within the MB can be considered as a direct result of the changes in the In concentration. Therefore, it is of interest to investigate the relationship between In concentration and dislocations distribution in the MB.

The atomic concentration was measured by EDX as described in the experimental section. The area around the dislocation area, at the bottom of the MB, analysed for all samples is highlighted in Fig. 2. As expected, the higher dislocation density is located near the InxGa1-xAs MB/GaAs interface. However, an interesting aspect is to evaluate how far into the thickness of the MB (towards the top of the structure) dislocations can be found. In this work, we measured the distance at which the last dislocation is observed, for each sample, from the InxGa1-xAs MB/GaAs interface and refer to this distance as t0. This was measured using a combination of ADF-STEM and EDX (detailed in SI). Next, the measured In concentration is compared to the nominal In concentration to see if the In at.% is reasonable for the t0 measured. It is documented in literature that for the parabolic InxGa1-xAs-graded MB used [25, 26], the general expression for the nominal mole fraction or concentration of In at any thickness (x(t)) can be expressed in terms of the total thickness of the MB (T), initial concentration (xin) and the desired final In concentration (xf):

$$x\left(t\right)= {(x}_{f}-{x}_{\mathrm{in}})\left[1-{\left(1-\frac{t}{T}\right)}^{2}\right]+{x}_{\mathrm{in}}$$
(1)

The MB is InxGa1-xAs with a concentration of 0 < x < 0.18, and total nominal thickness of 1 µm. Thus, xin takes the value of 0 and xf is assumed to be ~ 0.18 and T = 1000 nm.

Figure 3 plots t0 (the distance furthest from the InxGa1-xAs MB/GaAs interface at which dislocations can be observed) as a function of the In concentration for all samples, as well as the nominal/theoretical concentration. We can observe that the samples fit broadly within the theoretical In concentration value from Eq. 1. From this plot we can directly compare the different samples and make some interesting observations:

  1. a.

    The samples with the lowest t0 are the 0.2° and 6° misoriented samples consisting of the InxGa1-xAs MB and 1.4 µm In0.66Ga0.34P film (A2168). From these, the dislocations are found slightly higher up the MB in the sample with the larger misorientation A2168 6° (599 ± 10 nm) vs A2168 0.2° (558 ± 10 nm). A larger t0 means that the dislocation appear over a wider area, hence providing greater strain relaxation and in turn less strain in layers following the MB [25]. Considering the thickness of InxGa1-xAs MB (1.11 ± 0.01 µm for A2168 0.2° and 1.14 ± 0.01 µm A2168 6°), the larger thickness in A2168 6° could also account for the higher t0 of this sample compared to that of A2168 0.2°. This can be significant as it has been stated that increasing the MB thickness could increase t0 and vice versa [25].

  2. b.

    The next sample is that with the SBL layer (sample A2192 0.2°) for which the t0 (686 ± 10 nm) is higher compared those without the SBL (558 ± 10 nm for A2168 0.2° and 599 ± 10 nm for A2168 6°). In this case, the measured MB thickness for A2192 0.2° is 1.08 ± 0.01 µm, 0.3 µm thinner than A2168 0.2° (1.11 ± 0.01 µm) and 0.6 µm thinner than A2168 6° (1.14 ± 0.01 µm).

  3. c.

    The SL samples exhibit a greater t0 compared to all of the other samples. The LM sample (A2229 0.2°) has a t0 = 711 ± 10 nm, while the TS samples (A2248 6° and A2398 6°) have t0 values of 703 ± 10 nm and 798 ± 10 nm, respectively. Comparing the measured MB thickness of A2229 0.2° (1.16 ± 0.01 µm) and A2248 6° (1.11 ± 0.01 µm), we can see that despite the noticeable differences in thickness, the values of t0 are very close to each other, which would mean that greater MB thickness leading to higher t0 is not applicable here. However, it is clear that the full metamorphic laser structure (A2398 6°) has a significantly larger MB thickness (1.22 ± 0.01 µm) not only with to the other SL samples but also the In0.66Ga0.34P samples (A2168 and A2192 0.2°). Thus, possible explaining the reasons for the highest t0 observed in A2398 6°.

Figure 3
figure 3

In concentration as a function of distance from the InxGa1-xAs MB/GaAs interface t0. The blue solid represents the theoretical In concentration values using Eq. 1. Six points are measured for the In at.% (left y axis), the corresponding x in InxGa1-xAs (right y axis) and t0, for samples A2168 0.2° (red point), A2168 6° (magenta point), A2192 0.2° (black point), A2229 0.2° (green point), A2248 6° (blue point) and A2398 6° (orange point). Tabulated values of t0 and In at.% provided in Table S2

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The large variation in t0 amongst the samples is perhaps surprising, given that the MB for all samples can be considered nominally similar. The measured thickness of the MB layer for all samples differ slightly from the nominal 1 µm (see Table S1) and this could be related to small differences in the associated MOVPE growth [52]. However, it is not clear to the authors why t0 varies by ~ 200 nm. The MB thickness for A2192 0.2° (1.08 ± 0.01 µm) is ~ 30 nm lower than both A2168 samples; however, the t0 is much higher. Similarly, the increasing t0 cannot explain the observations of A2192 0.2° as the MB thickness for A2192 0.2° is lower in comparison with both A2168 samples. In summary, the t0 values are higher in the SL and the measured In concentration is very close to the expected In concentration at the measured t0 value.

Having measured the maximum distance at which dislocations can be found in the MB layer (t0), we now consider the dislocation density. Table 1 shows the measured dislocation density observed in the InxGa1-xAs MB up to t0. Four different areas were looked at in the MB region with lowest and highest dislocation density referring to lowest/highest dislocation density recorded. It should be noted that in all samples the MDs seem to be mainly contained within two regions, evoking reports showing that MDs occur in two waves [53, 54]. The first wave is considered to occur at the point where MDs become energetically favourable and provide minimal strain relief, known as critical thickness [55]. The second wave could be formed significantly further away from this critical thickness after which the layer relaxes completely [53].

Table 1 Dislocation density in MB region, between InxGa1-xAs MB/GaAs substrate interface and t0 for A2168 0.2°, A2168 6°, A2192 0.2°, A2229 0.2°, A2248 6° and A2398 6°
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From this it can be seen that all samples have a dislocation density between ~ 108 and 1010 cm−2 in agreement with previous reports for similar systems [26, 56]. Comparing the samples with the simpler design, those with the In0.66Ga0.34P film after the MB (samples A2168 and A2192 0.2°), an immediate observation is that the sample containing the SBL layer (A2192 0.2°) exhibits a dislocation density one order of magnitude higher when compared to the samples without the SBL. A reason for the difference in density could be explained by the inclusion of the SBL itself. Previous work has shown for two parabolic-graded MB (one MB below and one MB above the SBL) that the dislocation density decreases with the inclusion of the SBL [26]. Conversely, the dislocation density with a single parabolic-graded MB with an SBL was shown to have similar density compared without the SBL [26]. An alternative consideration is that the thickness of the SBL (in the case of being too thick) can have a detrimental effect. For this buffer a thickness above 0.30 µm was considered to lead to roughening [8].

Similarly, the dislocation density is higher for the SL samples (A2248 6° and A2229 0.2°) compared to the A2168 samples. To the authors knowledge while no specific densities have been quoted for this SL system in a parabolic-graded InGaAs MB, it has been established that both the TS and LM SL in InGaAs/GaAs can reduce dislocation density by one order of magnitude [51] and there is no consensus in the literature that one type of SL would lead to significantly lower density than the other. In other words, it is not surprising that both samples A2229 0.2° and A2248 6° have similar dislocation densities. This however do not explain why the SL samples have a higher density compared to the A2168 samples. Regarding the full metamorphic laser structure (A2398 6°) we observe that the dislocation density is one order of magnitude lower than both A2229 0.2° and A2248 6° despite using a similar TS SL design based off A2248 6°. These could be explained by the fact that the SL in A2398 6° was further optimised by using linear ramping (gradually increasing the Al concentration in each AlInGaAs layer in the SL) and reducing the number of units in the SL [29].

For dislocation measurements, it is important to consider the lamella thickness and the method used. Looking at Figs. 1 and S1, we can clearly see that dislocations are more visible in the SL samples and the In0.66Ga0.34P film with the SBL (A2192 0.2°) but not as clear in the In0.66Ga0.34P film samples without the SBL (A2168). This could mean an underestimation of the true density in the A2168 samples, as a thicker lamella might exhibit more dislocations than a thinner lamella. A second point to consider is the method which uses stamp filtering on identifying dislocations using contrast (i.e. white lines observed in Figs. 1 and S2) across the image. The risk here is that parts of the image that are not dislocations may be included and conversely, dislocations may not be identified and in turn be omitted. The filtering procedure included manual selection of dislocations regions to help exclude areas that were not dislocations.

It is known that dislocations appear as a strain relief mechanism, and their distribution provides a starting point to further understand strain relaxation mechanisms in strained layers. It has been theoretically shown that in compositionally graded layers pinning can be greatly reduced, and there is a much larger residual strain at the surface with reduced strain deep inside the graded layer [27]. The classification and multiplication of dislocations has been extensively studied for GaAs-based systems. Mainly, there are MDs which lie parallel to the interface and can be classified as 60° and 90°. 60° MDs glide on {111} type of planes [57, 58], and lie on the \(\left[1 1 0\right]\) or \(\left[1 0 \overline{1 }\right]\) (for α and type β dislocations, respectively, with distinct mobility which results in asymmetric distribution of dislocations [57]). Their Burgers vectors are of the type \(\frac{a}{2}\left[1 0 1\right]\), \(\frac{a}{2}\left[0 1 \overline{1 }\right]\), \(\frac{a}{2}\left[1 0 \overline{1 }\right]\), \(\frac{a}{2}\left[0 1 1\right]\) where \(a\) is the lattice constant of InGaAs [58,59,60]. Edge dislocations, or 90° MDs, lie on the (001) plane and can have Burgers vector of either \(\frac{a}{2}[1 \overline{1 } 0]\) or \(\frac{a}{2}[1 1 0\)] and can be formed by two 60° MDs interacting with one another [40]. Additionally TDs can form as a result of MDs which do not terminate at the surface of a crystal [41]. TDs can act as non-radiative recombination centres [56] where the recombination of the electron and hole during the electron transition leads to formation of a phonon. This results in unwanted generation of heat energy, an undesired effect in a laser. It should be noted that previous reports have also suggested that edge dislocations can act as non-radiative recombination centres [61]. The classification as such of the dislocations is not the scope of this work and we investigate the distribution of MDs and TDs within the MB layer, to gain a better understand how the strain is relaxed towards the next interface.

WBDF analysis was performed, using the invisibility criterion g.(b × u), where g is the diffraction vector, b is the Burgers vector of the dislocation and u is the line direction of the dislocation [62]. Figure 4 shows a representative WBDF analysis for sample A2192 0.2° where most dislocations lie parallel to the [2 2 0] direction, in agreement to previous reports [63, 64]. Considering that the same nominal recipe for MB is used for all samples, similar results can be expected from the samples studied here (see Figs. 1 and S2).

Figure 4
figure 4

WBDF analysis for sample A2192 0.2°. Bright field TEM image of A2192 0.2° a and corresponding WBDF field image with g220 b. Images viewed down [1 1 0] zone axis

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Using the g220 vector, all of the dislocations become invisible, both 60° and 90° MDs, which is in agreement with previous results [58, 65]. WBDF using g002 (see SI) suggests asymmetry within the dislocations which could be a consequence of the mistilt of the GaAs (001) towards the [1 1 1] A plane that leads to a change in the shear strain on the glide plane of the MDs, favouring certain MD formation [66] or can be indicative of the asymmetry previously discussed in 60° MDs. Thus, we can confirm that within the limitations of a cross-sectional analysis, most of the dislocations here observed are MDs with a few TDs. It should be noted that it is possible that both TD/MD components could be present such as a TD with MD [67] or two TDs that originate from a half loop of a MD [41]. Figure 5 summarises the distribution of all dislocations in the MB up to t0. The number of data points used for each sample and the total number assigned as MD and TD is outlined in SI.

Figure 5
figure 5

Distribution of MDs (red points) and TDs (green points) in the MB for all samples up to t0. for A2192 0.2° a, A2229 0.2° b, A2248 6° c and A2398 6° d. The distance is measured from the InGaAs MB/GaAs substrate interface. The dotted line represented t0. Full details on the data points used for each plot can be found in Table S3

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Except for the TS SL sample (A2248 6°), it can be observed that the MDs tend to be closer to t0 compared to TDs and TDs appear to stop between 200 nm and 300 nm away from t0. This suggests that the MDs are pinning the TDs in the lower region of the MB where a lower strain level can be expected. Considering the In concentration shown in Fig. 3, we can identify approximately the In mole fraction (x) at which TD stop in the MB. From the plots, it suggests that: (i) for the 1.4 µm In0.66Ga0.34P sample with the SBL (A2192 0.2°) is x ~ 0.12, (ii) for the LM SL sample and full metamorphic laser structure (A2398 6°), x ~ 0.14 and (iii) for A2248 6°, x ~ 0.16. Comparing the points for the MDs, we have a strong indication that two waves of MDs are present, one starting near the GaAs/InGaAs MB interface and the other starting higher up, as documented in the literature [40, 53].

So far, the variation in the t0 is perhaps a surprising finding that could be explained by the possible variations in the nominal recipe used to grow the MB layers. However, a common aspect is that the MDs appear in two waves, with close proximity of each other and that these waves are very close to the measured t0. It is now important to evaluate how the strain is distributed to the layers above the MB, as the strain greatly influences the laser properties. Here, the main emphasis will be given to the growth direction [0 0 2], as this is the strain that propagates up the structure from the MB towards a lower cladding layer which comes before the active region in a metamorphic laser or any other semiconductor device.

Strain mapping

The strain profile in the AlInGaAs and InGaP layers, immediately after the InxGa1-xAs MB, was measured by applying GPA on high-resolution ADF-STEM micrographs. It should be noted that a positive value represents compressive strain and negative values indicate tensile strain [68]. For consistency, all micrographs were analysed with the same magnification and procedure as outlined in SI. As indicated in the experimental section, the STEM micrographs used for the strain analysis are non-corrected and thus, the focus will be on the strain trend and variations between the different sample designs. The full details on the analysis and considerations for this are detailed in the SI.

The full strain maps for all samples are detailed in SI and Fig. 7 summarises the strain along the growth direction [0 0 2] (εyy). Figure 6 displays representative relative strain maps for the samples with the simpler 1.4 µm In0.66Ga0.34P film after the MB design (A2168 0.2° and A2168 0.6°) as differences in misorientation are one of the main factors influencing the strain [69, 70]. In A2168 0.2°, the strain is highest in εyy and more relaxed in the in-plane direction [220] (εxx). In comparison, A2168 6° has a lower magnitude of strain in εyy (− 0.16 ± 0.42%) and higher strain in εxx (− 0.25 ± 0.04%) compared to the sample with lower 0.2° misorientation towards [1 1 1]A. Based on Vegard’s Law (see SI) and the proposed chemical composition of the sample, the theoretical strain between an In0.66Ga0.34P layer and the In0.18Ga0.82As MB would be − 0.07%. Comparing the theoretical strain values to the experimental strain, the In0.66Ga0.34P εyy component is in agreement with the predicted theoretical strain for A2168 6°. Furthermore, the tensile strain in A2168 0.2° (− 2.35 ± 1.72%) is outside the expected − 0.02% strain. The addition of the SBL layer (A2192 0.2°) has changed the strain from tensile (− 2.35 ± 1.72%) to under compressive (0.43 ± 0.29%). This is not unexpected given that the theoretical strain between In0.66Ga0.34P film layer grow on In0.13Ga0.87As is 0.36% (see SI). A further point that should be noted is the surface at the very top of the In0.66Ga0.34P layer in A2192 0.2° displays peaks and valleys (see Fig. S2C.) which were also observed in the bulk of the sample during FIB milling. This could be indicative of build-up of strain in the system and the strain relaxation not happening as effectively in sample A2192 0.2° [26]. From Fig. 3, it can be seen that A2192 0.2° has the lowest t0, which as discussed by Tersoff [27] would mean that more strain is present in the system at the end of the metamorphic buffer. Thus, a build-up of strain after the metamorphic buffer would be expected as reported by Romanato et al. [71].

Figure 6
figure 6

High-resolution STEM of In0.66Ga0.34P/InxGa1-xAs MB interface in A2168 0.2° used for GPA a with εyy strain b and εxx strain c. HRSTEM of In0.66Ga0.34P/InxGa1-xAs MB interface in A2168 6° used for GPA d with εyy strain e and εxx strain f. All images viewed down [1 1 0] zone axis

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As expected, the εyy value for the LM SL sample (A2229 0.2°) is minimum (0.01 ± 1.01%). This is reasonable given that Al0.31In0.15GaAs and In0.66Ga0.34P in the SL are lattice matched to each other. With regards to the sample with the TS SL (A2248 6°) the In0.62Ga0.38P layer is under tensile strain (− 1.04 ± 0.75%) in εyy relative to the Al0.31In0.15GaAs, Fig. 7. This is expected as the lattice constant of Al0.31In0.15GaAs (0.5727 nm) will be the same as In0.66Ga0.34P (as Al0.31In0.15GaAs /In0.66Ga0.34P are LM) and in turn the lattice constant of In0.62Ga0.38P (0.5710 nm) is smaller relative to that of Al0.31In0.15GaAs. This leads to tensile strain in the In0.66Ga0.34P layer (see SI). It should be stated that the measured strain (− 1.04 ± 0.75%) does not fall within predicted strain (− 0.06%). Possible reasons for discrepancy could include local differences in the chemical composition (i.e. not being the exact same as the theoretical concentrations used in the calculation), thickness variations in the sample [72], differences in size/location of the reference region [45, 73], and the mask size used during GPA analysis which has been demonstrated to influence accuracy [74] (as discussed in the SI).

Figure 7
figure 7

εyy strain in layers with respect to (wrt) reference regions. Strain in In0.66Ga0.34P layer in A2168 0.2° and A2168 6° measured with respect to InxGa1-xAs MB (green point), In0.66Ga0.34P layer in A2192 0.2° with respect to In0.13Ga0.87As SBL (magenta point), Al0.31In0.15GaAs layer in A2229 0.2° with respect to In0.66Ga0.34P (blue point) and In0.62Ga0.38P layer in A2248 6° (red point) with respect to Al0.31In0.15GaAs. Tabulated values of εyy can be found in Table S5

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In general, this strain analysis provides a good indication of the type of strain present in subsequent layers and clearly demonstrates the differences in the strain distribution in In0.66Ga0.34P film or AlInGaAs/InGaP SL after the MB for each architecture. That is, changing the misorientation and the inclusion of SBL affects the strain in the In0.66Ga0.34P film.

Finally, as an additional test on the strain calculations here obtained, the strain in a full metamorphic laser structure (A2398 6°) was measured to compare the GPA analysis between non-Cs and Cs corrected STEM images. In both cases the Al0.31In0.15GaAs layer was calculated to be tensile strained with respect to the InGaAs MB and both values were within the same order of magnitude (− 1.03 ± 0.03% for the non-Cs image vs − 0.92 ± 0.71% for the Cs corrected image). A further comparison between GPA scripts and reflections was carried out, and detailed in SI, supporting the conditions here used.

Conclusions

We investigated InGaAs MB on GaAs substrate samples with different architectures and looked at the distribution of dislocation in the MB and subsequent strain in preceding layers. In general, the dislocation density was found to be one order of magnitude higher in samples with Al0.31In0.15GaAs/InGaP SL (109–1010 cm−2) compared to samples with an In0.66Ga0.34P film (108–109 cm−2) after the InxGa1-xAs MB.

We have correlated the In concentration to the dislocations propagation, and identified the region above the GaAs buffer where the dislocations would relax (stop). Depending upon the sample, this was found to vary from 550 nm to 800 nm from the InxGa1-xAs MB/GaAs interface. We propose that this large variation can be partially explained by variations in the MB thickness across the samples. Importantly, it was found that there is good agreement between the theoretical predicted and the measured In concentration values at t0. In the InxGa1-xAs MB, it was seen that MDs are concentrated near the value of t0 and depending upon the architecture, it was common for TDs to end approx. 200–300 nm before the last MD. The dislocation density showed that the sample with the In0.13Ga0.87As SBL between the In0.66Ga0.34P film and InxGa1-xAs MB displayed the highest dislocation density.

The strain mapping between the MB and the subsequent layers provides a systematic insight into the local strain levels across different architectures (AlInGaAs/InGaP or in InGaP film after the MB). The common aspect is that generally the strain is largest in the growth direction whilst the system is relaxed in the out of the plane direction. And the change in misorientation towards [1 1 1]A (0.2° vs 6°) has shown to greatly reduce the strain, from tensile to no overall strain. Furthermore, the addition of an SBL changed the strain from tensile to compressive, matching theoretical predictions. As expected, there was no overall strain in the LM Al0.31In0.15GaAs/In0.66Ga0.34P SL while there was tensile strain in the In0.62Ga0.38P layer in the Al0.31In0.15GaAs/In0.62Ga0.38P SL.

Overall, these findings provide further insight into how the dislocations are distributed in the MB and the effects this has on the strain distribution across the system. Knowledge of the strain and the dislocation distribution provides a key understanding on different approaches to tailor the strain in semiconductor devices, especially metamorphic lasers.