# Strain relief and threading dislocation reduction in GaSb/AlSb/GaSb heterostructures grown on Si(001) substrate

K. Graser, A. Gilbert, J.-B. Rodriguez, Eric Tournié, A. Trampert

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K. Graser, A. Gilbert, J.-B. Rodriguez, Eric Tournié, A. Trampert. Strain relief and threading dislocation reduction in GaSb/AlSb/GaSb heterostructures grown on Si(001) substrate. Journal of Applied Physics, 2025, 137 (20), 10.1063/5.0268051. hal-05457296

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# Strain relief and threading dislocation reduction in GaSb/AlSb/GaSb heterostructures grown on Si(001) substrate EP

Cite as: J. Appl. Phys. 137, 205302 (2025); doi: 10.1063/5.0268051

Submitted: 27 February 2025 · Accepted: 6 May 2025 ·

Published Online: 27 May 2025

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K. Graser,<fnref n="1" />,ª) A. Gilbert,<fnref n="2" />) J.-B. Rodriguez,<fnref n="2" />) E. Tournié,<fnref n="2" />,<fnref n="3" />) and A. Trampert<fnref n="1" />)

## AFFILIATIONS

## ABSTRACT

The monolithic integration of III-Sb materials on Si substrates enables the development of novel functionalities and promising device applications. However, due to the large lattice mismatch to Si, direct heteroepitaxy of III-Sb results in a very large and disadvantageous dislocation density. Here, we report on the effect of strained AlSb interlayers in GaSb as dislocation filters for the epitaxy on Si(001) substrates. The epitaxial stress introduced by the lattice mismatched AlSb layer leads to threading dislocation bending at the interfaces as a strain relieving mechanism, thereby facilitating the reaction and annihilation of dislocations during their lateral glide process. Using comprehensive electron channeling contrast imaging and scanning transmission electron microscopy, we measure the dislocation density at the surface and after filter and cap layers of different thicknesses and analyze the effect of plastic strain relaxation on dislocation reduction. The reduction mechanism is discussed in the context of misfit dislocation networks forming at the respective compressively and tensile strained interfaces. With the new findings, an effective double filter layer structure with adopted layer thicknesses could be realized, which has resulted in a very low threading dislocation density of $1.7 \times 10^7$ cm$^{-2}$.

© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0268051

## I. INTRODUCTION

The increasing demand for data-intensive applications, such as high-speed communications, data centers, and artificial intelligence, requires new approaches for device functionalities and fabrication processes that enhance the speed and capacity of data transfer and storage. Photonic technologies leverage the speed of light, overcoming the limited bandwidth, power consumption, and waste limitations of traditional electronic circuits. Si is the most widely used semiconductor for integrated photonics due to its abundance, optical transparency window (from 1.1 to 7 µm), and high refractive index.<fnref n="1" /> Although Si can efficiently transmit, modulate, and detect light, its indirect bandgap does not allow light emission.<fnref n="2" /> As a result, the integration of III-V lasers on Si substrates has attracted considerable attention in order to combine the optoelectronic properties of III-Vs

with the well-established Si technology to develop photonic integrated circuits.<fnref n="3" />

Group-III-Sb heterostructures offer unrivaled opportunities for designing devices in the whole mid-infrared (MIR) wavelength range from 2 to 12 µm. As a result, a new promising application for Si photonics has emerged: MIR integrated sensing devices. Despite the numerous bonding techniques developed over the years,⁴ monolithic integration or direct epitaxy has emerged as a promising solution for integrating III-V lasers directly onto Si with low cost and high density.⁵ However, epitaxially integrated III-V devices on Si suffer from a severe lack of reliability and degradation of laser performance due to the high crystal defect density generated during growth, after post-growth cooling, and during device operation.⁶⁻¹⁰ Indeed, polar on non-polar heteroepitaxy, a lattice constant mismatch, and a thermal expansion coefficient mismatch between the

<footnote n="1">¹Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e.V., Hausvogteiplatz 5-7, 10117 Berlin, Germany</footnote>

<footnote n="2">²IES, University of Montpellier, CNRS, F34000 Montpellier, France</footnote>

<footnote n="3">³Institut Universitaire de France, F-75005 Paris, France</footnote>

<footnote>ª) Author to whom correspondence should be addressed: graser@pdi-berlin.de</footnote>
III-Vs and Si are responsible for forming antiphase boundaries (APBs),¹¹ dislocations,¹² and cracks. Notably, threading dislocations (TDs) can act as non-radiative recombination centers, which increase the laser threshold current and reduce the devices' performances, such as the operating power and temperatures, the output efficiency, the yield, and reliability.¹³,¹⁴

During the growth of lattice mismatched III-V layers on Si, elastic strain energy accumulates within the epitaxial layer, and once a critical thickness is reached, plastic (irreversible) relaxation occurs by forming misfit dislocations (MDs) in the interface between the III-V and the substrate. TDs are believed to be directly related to the imperfections of the interfacial MD networks created between the III-V layer and the substrate.¹⁵ Interfacial MD array optimization led to significant lower emerging TD densities in many cases (i.e., for GaSb-on-GaAs epitaxy.¹⁶,¹⁷) However, especially for high mismatched systems (i.e., GaSb/Si with a >12% lattice mismatch), the TD density is still way too high for the realization of photonic applications.¹³,¹⁸ Thus, the massive reduction of the TD density remains one of the key challenges in high-mismatch monolithic integration. Many techniques for TD reduction have been proposed in the literature, such as thermal cycling annealing (TCA)¹⁹,²⁰ or dislocation filtering at a strained layer superlattice (SLS) or dislocation filter layers (DFLs).²¹⁻²³ The dislocation reduction effect of these techniques is attributed to a dislocation reaction and annihilation processes. Stress induced by lattice mismatched DFLs or by TCA based on different thermal expansion coefficients of the materials drives dislocation movements for plastic strain relief. The use of a DFL method has proven to be effective in GaAs and GaSb systems to reduce dislocation densities by one order of magnitude.²⁴⁻²⁸

Addamane et al.²² investigated the TD filter effect of an AlSb DFL for the GaSb/GaAs(001) heteroepitaxy by transmission electron microscopy (TEM). They showed that a single 250 nm-thick AlSb layer is able to reduce the TD density in GaSb from $1.0 \times 10^8 \text{ cm}^{-2}$ down to $3.6 \times 10^7 \text{ cm}^{-2}$. Complex MD networks with primarily 90°-type MDs were observed in both AlSb interfaces. They attributed the TD reduction effect of the AlSb to an interaction of TDs with the interfacial MDs and their consequent pinning in the interface. Despite these observations, the exact interrelation between TD reduction by the DFL and the plastic relaxation process by MDs remains unclear.

In this study, we investigate the dislocation structure in AlSb DFLs embedded in GaSb-on-Si(001) heterostructures by combining electron channeling contrast imaging with scanning transmission electron microscopy. This approach enables a detailed analysis of both TD structures and interfacial MD networks. We determine the spatial arrangement of the interfacial dislocation networks and the various dislocation types as well as the correlation to the density of the resulting TDs. In particular, we analyze the relationship between the TD reduction process and the epitaxial strain relaxation process at the two AlSb interfaces, applying a theoretical model described by Ward et al.²⁶ Based on the findings, an optimized AlSb double filter layer structure is grown and evaluated for its effectiveness in reducing TD density.

## II. EXPERIMENTAL DETAILS

The samples under investigation typically consist of a 1 µm-thick GaSb buffer layer/an AlSb DFL/GaSb cap layer deposited in sequence

on Si(001). They were grown by solid-source molecular beam epitaxy (MBE) at 550 °C (thermocouple) with a Ga growth rate of 0.3 ML/s and an Al growth rate of 0.6 ML/s in a RIBER COMPACT 21 system. Si(001) substrates with residual miscut angles of only 0.5° were used for this study. The substrate surfaces were thermally prepared in situ (above 1000 °C thermocouple) in a dedicated chamber to remove the native oxide.²⁹,³⁰ The growth temperature and the substrate residual miscut were chosen to ensure the overgrowth of anti-phase domains within the 1 µm-thick GaSb buffer.³⁰

For all samples, an in situ thermal cycle annealing inside the MBE chamber was applied after the growth of the AlSb filter layer. The samples were heated up to a temperature of 750 °C (sample deterioration starts at 770 °C) and hold at this temperature for 5 min. Afterward, the temperature was lowered to 100 °C and kept for 5 min again. This process was repeated two times before proceeding with the final growth of the GaSb cap at 550 °C. These heating-cooling cycles were performed to induce thermal stresses on the dislocation structure based on the thermal expansion coefficient mismatch and, thus, to increase dislocation mobility and the associated probability of dislocation annihilation. Despite this additional thermal stress, our previous measurements of the TD density after a 450 nm GaSb cap layer showed no significant difference compared to an unannealed reference sample.³¹ Similarly, no noticeable differences in TD density were found due to variations in the number of heating-cooling cycles or due to longer holding times at high temperatures. To further investigate and understand these unexpected results in more detail, GaSb buffer/AlSb DFL/GaSb-cap dislocation filter structures were grown under the same MBE conditions, whereby the thickness of the GaSb cap layer was varied from 25, 50, and 450 to 1000 nm and the AlSb DFL thickness was kept constant at 150 nm for the series. We investigated the interface structures on the basis of their misfit dislocation network for each GaSb cap layer thickness to estimate the corresponding strain relief. The study serves to identify and better understand the relationship between epitaxial strain relaxation and the simultaneous reduction of the threading dislocation density in the top layer. Finally, the results of the investigation are used to develop a double filter layer consisting of two AlSb layers with thicknesses of 150 and 300 nm and a GaSb intermediate layer of 350 nm. The same annealing process was applied to this structure after each AlSb layer.

We used electron channeling contrast imaging (ECCI) in a JEOL JSM-IT800 scanning electron microscope (SEM), which is a non-destructive characterization method for observing dislocations.³²⁻³⁴ The advantages of ECCI are its minimal requirements for sample preparation and its ability to generate large-scale area images in a short time, which makes it perfect to image the distribution of TDs close to the sample surface. Furthermore, due to its penetration depth of approximately 150–200 nm, the ECCI beam can reach the interfaces of thin layers to image the MD networks. We also compared our results with (scanning) transmission electron microscopy (STEM), which is by far the most used technique for studying dislocations and other crystal defects in great detail.³⁵ Plan-view investigations of MD structures and cross-sectional high-resolution high-angle annular dark-field (HAADF) STEM observations of the dislocation core structures were performed in a JEOL 2100F field-emission TEM and a spherical aberration corrected JEOL ARM 200F microscope, respectively, both operating at 200 kV. For both plan-view and cross-sectional geometry, sample preparation was performed
conventionally by mechanical thinning followed by Ar-ion polishing and by the preparation of 100–300 nm thin lamellae with a Thermo Fisher Helios 5 UX focused ion beam system.

### III. RESULTS AND DISCUSSION

The TD density reduction effect of a lattice mismatched filter layer relies on the phenomenon that is briefly summarized as follows. The epitaxial stress leads to propagation of the TD arms in the strained layer leaving behind MD segments in the interface of the filter layer that relieve its epitaxial strain. This propagation of TD arms promotes annihilation processes between the TDs, thereby reducing their density. Therefore, the strain state of the layers and the formed MD structures play an important role for the TD reduction mechanisms. In order to analyze this in more detail, the structure of the AlSb DFL and its associated strain state must first be determined. This represents the starting point for the subsequent investigation of the strain relief in the GaSb cap in relation to the TD reduction.

#### A. Misfit dislocation network at the GaSb buffer/AlSb filter layer interface

Figure 1 presents ECCI and STEM observations of a sample with a 100 nm-thick AlSb DFL and a 20 nm-thick GaSb cap layer [cf. schematic drawing in Fig. 1(a)]. The 20 nm-thin GaSb cap is not able to modify the dislocation structure, because its thickness is below the critical layer thickness and is thus not sufficient to bend TDs and allow further plastic relaxation. Consequently, the ECCI image of this sample in Fig. 1(b) reveals the MD network in the bottom AlSb interface between the AlSb layer and the GaSb buffer, located 120 nm below the surface. The network appears disordered and with a complex line arrangement. Some dislocation line segments propagate along the [110] or in the perpendicular [110] direction, as it is to be expected when TDs glide into the interface on the favored {111} planes. On the other hand, the deviations from these preferential line directions are caused by dislocation reactions during the formation of the continuous interfacial dislocation network as discussed by Addamane et al. for the epitaxial GaSb-on-GaAs(001) system,²² where

similar dislocation network structures were observed. The complementary bright-field (BF) STEM plan-view image in Fig. 1(c) confirms the type and arrangement of the disordered network. STEM measurements based on the g·b invisibility criterion demonstrate the presence of Lomer (pure edge or 90°-type) MD resulting from the reaction of two 60° mixed-type dislocations on corresponding (111) and (111) planes or (111) and (111) planes, respectively, according to the following reactions:

$$ \frac{a}{2}[10\bar{1}] + \frac{a}{2}[011] = \frac{a}{2}[110], \\ \frac{a}{2}[101] + \frac{a}{2}[0\bar{1}\bar{1}] = \frac{a}{2}[1\bar{1}0]. $$

These 90°-type MDs are sessile due to their Burgers vectors lying in the (001) plane, but most efficient in epitaxial strain relief. Similar complex misfit dislocation networks were found in the InGaAs/GaAs system after the samples were annealed at 950 °C for 500 s.³⁶ In the present case of the GaSb/AlSb/GaSb filter layer structure, the complex MD network caused by dislocation reactions was also found at the bottom AlSb interface of a sample without the annealing step. Hence, the deviation from the more common 60°-MD cross network cannot be attributed to the thermal cycle annealing during growth. This finding is consistent with the study on AlSb DFLs by Addamane et al.²² where also no annealing was reported.

ECCI investigations additionally facilitate the observation of vertically moving dislocations ascending to the surface, which are equivalent with the definition of TDs in our system. They appear in dot-like bright contrast and are partly disconnected to the network. Several examples are circled in yellow in Fig. 1(b). Counting these contrast features over an area of about 150 µm², a density of TDs around (4.0 ± 0.2) ± 10⁸ cm⁻² is obtained. To achieve such a TD density in a pure GaSb buffer without an AlSb filter layer, a film with thickness of 1.6 µm has to be grown, which corresponds to an approximately 500 nm thicker total structure. This basically illustrates the fundamental effect of the AlSb filter layer. Furthermore, by increasing the thickness of the DFL from 100 to 150 nm, i.e., by 50 nm only, and maintaining a thin cap thickness of 25 nm that still exhibits no significant plastic relaxation, the TD density

<figure><img src="image_5.png" /><figcaption>FIG. 1. (a) Illustration of the sample structure (100 nm AlSb). (b) and (c) ECCI and zone-axis BF-STEM plan-view image of the interface between AlSb DFL and the GaSb buffer layer, both showing the complex MD network in the interface. Some TDs are marked with orange circles in the ECCI image.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>FIG. 2. BF-STEM images of the MD network of the AlSb/GaSb interface for 100 nm (a) and 150 nm AlSb thickness (b). (c) An enlarged part showing a square network of 90° MDs for the sample with 150 nm AlSb.</figcaption></figure>

is further reduced by a factor of two to (2.0 ± 0.2) × 10⁸ cm⁻². Figure 2 shows related STEM images of the lower interface of the filter layer for both samples. The comparison of these two images documents that, with increasing filter layer thickness, the overall arrangement of the MDs becomes denser and more regular due to higher degree of strain relaxation in the thicker layer, whereby areas with hexagonal or rectangular dislocation meshes simultaneously expand considerably. The rectangular dislocation pattern [see enlargement in Fig. 2(c)] consists of pure 90° edge-type MDs, which are the most efficient type for misfit strain relief. The result also suggests that a more homogeneous dislocation network not only reduces strain more efficiently, but can also reduce the number of TDs.

Assuming a rectangular array of MDs, it is possible to determine the strain state in the filter layer. The plastic strain relief by MDs with effective Burgers vector parallel to the (001) interface plane is given by

$$ \epsilon_p = b_{\parallel} \cdot \rho_{MD\langle110\rangle}, \quad (1) $$

with $\rho_{MD}$ being the average MD density in the $\langle 110 \rangle$-direction. Line scans can be used to measure the mean dislocation distance $d_{MD}$, which then gives

$$ \rho_{MD\langle110\rangle} = 1/d_{MD\langle110\rangle}. \quad (2) $$

Considering the presence of 90°-type dislocations with Burgers vector $b_{\parallel} = a/\sqrt{2}$, the plastic strain relaxation of the 150 nm-thick AlSb layer is about (0.39 ± 0.03)%. The uncertainty of this value primarily arises from the spatial inhomogeneity of the MD networks, leading to significant statistical variations in the measured mean dislocation distance. In relation to the lattice mismatch between completely relaxed bulk-like GaSb and AlSb of 0.65% at room temperature, this means that the filter layer still has a residual strain of about 0.26%. However, it needs to be noted that, because of the larger coefficient of thermal expansion of GaSb compared to AlSb, the lattice mismatch

between the two materials is smaller at growth temperature compared to room temperature. Assuming that the MD network does not change during the cool-down, the plastic relaxation remains constant, whereas the residual strain of the layer is reduced by about 0.1% at growth temperature. This strain state of the filter layer has to be taken into account when discussing the epitaxial growth of the GaSb cap layer on top and the effect of strain relief on the TD density reduction.

## B. Development of the TD density as a function of GaSb cap layer thickness and strain relaxation

In order to investigate the relationship between the dislocation network forming at the upper AlSb/GaSb interface and the density of TDs in more detail, we increased the thickness of the GaSb cap layer and analyzed the corresponding microstructure. Three samples were studied having a GaSb cap thickness of 25, 50, and 450 nm, while the AlSb DFL thickness was kept at 150 nm. Figure 3 displays the results of the MD generation at the upper interface by STEM and the number and distribution of TDs in the cap layer by ECCI measurements.

The BF-STEM plan-view image in Fig. 3(a) and the ECCI image in Fig. 3(d) of the 25 nm-thin cap reveal the existence of short dislocation segments at the interface between the cap and filter layer visible as dark and bright lines, respectively, which are nucleated from preexisting TD by dislocation bending. This demonstrates experimentally that the critical layer thickness for plastic strain relaxation of GaSb on 150 nm-thick AlSb DFL has been reached. This value is close to the critical layer thickness that can be calculated by the Matthews–Blakeslee model,²⁴

$$ h_c = \frac{b(1 - \nu \cos^2(\alpha))}{8\pi\epsilon(1 + \nu)\cos(\lambda)} \left[ \ln\left(\frac{h_c}{b}\right) + 1 \right]. \quad (3) $$

Here, b is the magnitude of the Burgers vector, $\nu$ is Poisson's ratio, $\alpha$ is the angle between the dislocation line and its Burgers vector,
<figure><img src="image_7.png" /><figcaption>FIG. 3. (a)–(c) Plan-view BF-STEM images of MDs in the upper AlSb interface for samples with 25, 50, and 450 nm GaSb cap thickness, respectively. (d)–(f) Corresponding ECCI images at the sample surface. The insets show the individual black-and-white contrast of TDs emerging at the sample surface.</figcaption></figure>

and $\lambda$ is the angle between the slip direction (i.e., the Burgers vector direction) and the normal in the interface to the dislocation line direction. Taking into account the strain state of the AlSb layer defined by the MD network at the lower interface and assuming that this strain state does not change during the GaSb cap growth, i.e., the DFL can be regarded as a rigid substrate, then the misfit strain is given by $\epsilon = \epsilon_{p,AlSb} = 0.39\%$, and Eq. (3) results in a value for $h_c$ of about 28 nm for the bending of 60°-type dislocations, a value that is indeed very close to that found experimentally. It is known that the Matthews-Blakeslee model is a standard approach predicting the equilibrium critical thickness neglecting kinematical restrictions and metastable strained layer growth. We attribute the good agreement with the model to the initial conditions for plastic relaxation in the GaSb/AlSb/GaSb-on Si layer system, namely, the high TD density and the relatively high growth temperature of the GaSb (550 °C) compared to its melting point (712 °C), which promotes high dislocation mobility.

At this early stage of plastic strain relaxation, the GaSb cap layer is still highly strained and far away being fully relaxed. Since the misfit segments are short isolated lines connected with threading

segments both below and above the interface, there is still no reduction in the overall TD density at this point. The related ECCI image in Fig. 3(d) indicates a high density of isolated bright-dark spots, which are identified as TDs near the sample surface. The inset highlights the characteristic black-and-white contrast produced by TDs emerging at the surface.<sup>37,38</sup> A TD density of $(2.0 \pm 0.2) \times 10^8 \text{ cm}^{-2}$ is determined. It is moreover obvious from the micrograph that MD segments form preferentially in one $\langle 110 \rangle$ direction only. This observation is consistent with the results obtained for the growth of compressively strained (In,Ga)As on GaAs(001) substrates (see, e.g., Ref. 39). The anisotropy is attributed to differences in the onset of plastic relaxation by $\alpha$ and $\beta$ dislocations (V-atom core dislocation and III-atom core dislocation), leading to the asymmetry in the MD densities along the $[110]$ and $[1\bar{1}0]$ directions.<sup>40</sup>

As the GaSb cap thickness increases to 50 nm, the strain relaxation of the lattice mismatch rapidly continues as additional MD segments form at the interface and/or existing segments continue to expand in the respective glide planes. Generally, the thicker the layer, the longer the misfit segment lengths and the greater the number of MDs per unit area, i.e., the MD density.
**Figure 3(b)** shows a BF-STEM image in plan-view that represents an incomplete dislocation line network consisting of perpendicular misfit line segments along the [110] and [110] directions resulting in a cross-grid pattern. The average MD distance corresponds to a strain relief of (0.05 ± 0.01)% based on Burgers vectors belonging to 60°-type dislocations. In fact, STEM images taken under different two-beam diffraction conditions indicate that almost all MDs of the upper interface are of 60°-type. However, cross-sectional high-resolution HAADF-STEM demonstrates the presence of about 5 nm short stacking faults lying at the middle of the interface or just below and expanding predominantly into the AlSb layer. The HAADF-STEM image in Fig. 4(a) shows a 60° dislocation dissociated into a 90°- and a 30°-partial dislocation, respectively, with the stacking fault in between. In contrast, in Fig. 4(b), the undissociated core structure of a 90° pure edge MD in the bottom AlSb interface can be seen. The different core structures of the dislocations (dissociated and undissociated) can be attributed to the inverse sign of the epitaxial stress acting at the two interfaces. While the AlSb layer on top of the GaSb buffer is compressively strained, the GaSb cap is tensile strained. It has been proposed by Maree *et al.*<sup>41</sup> that a dissociation of 60° dislocations into partial dislocations is preferably expected in the presence of tensile strain, a finding that was later also confirmed experimentally.<sup>42</sup> Maree *et al.* additionally argued that a dissociation increases dislocation mobility due to the extended core structure and should enhance the misfit strain relaxation process. In this sense, the annihilation process of the TDs in the upper interface should be enhanced as well. On the other hand, it can be seen in our experiments that some dislocations intersect easily, whereas others are blocked by transverse dislocations and pressed into the overlying layer as it is demonstrated by the magnified ECCI image in Fig. 4(c). This process known as TD blocking was originally introduced by Freund.<sup>43</sup> It can happen, for example, when one dislocation type moves faster into the interface (α or β) and creates dislocation segments, which then become a blocking obstacle for intersecting dislocations of the later arriving one, because the stress field of the dislocations counteracts the progress of the threading segment [see the scheme in Fig. 4(d)]. Such repulsive dislocation interactions delay the relaxation process. Nevertheless, the dislocation

interactions and annihilations lead to an overall reduction in the TD density. The respective ECCI image in Fig. 3(e) accordingly proves the very similar network structure and measures the TD density near the surface to be about (1.14 ± 0.16) × 10⁸ cm⁻².

**Figure 3(c)** displays a BF-STEM image of the upper dislocation network in plan-view for the GaSb cap layer thickness of 450 nm. The dislocation network appears coherent over the entire observed interface, and the dislocation lines still run along the perpendicular 〈110〉 directions. It is obvious that the average MD density has further increased accompanied by an increase in the strain relaxation level of the lattice misfit given by $\epsilon_{p,GaSb} \approx (0.18 \pm 0.01)\%$. In the network, the vast majority of MDs is still of (dissociated) 60°-type and glides in the {111} planes along the 〈110〉 directions, but their distribution is rather inhomogeneous and the density slightly differs in both directions. These results are in strong contrast to the lower GaSb/AlSb interface in terms of the proportion of 60°- to 90°-type dislocations and the crystallographic alignment of the network. Nevertheless, the number of TDs further decreases to (5.8 ± 1.2) × 10⁷ cm⁻², as determined from the corresponding ECCI image in Fig. 3(f).

**Figure 5(a)** summarizes the results obtained from the sample series with varying GaSb cap layer thicknesses. Both the TD density measured by ECCI (black) and the plastic relaxation of the GaSb cap layers estimated from the interfacial MD networks (orange) are shown, including a measuring point of the TD density at the large thickness value of 1 µm. The exponential decrease in the dislocation density is clearly visible over the entire thickness range. The required mobility of the TDs for the annihilation process results from the epitaxial stress caused by the lattice mismatch to the DFL and its strain relaxation process. In fact, as the TD density decreases, the degree of plastic relaxation increases with the cap layer thickness as indicated by the orange data points. Efficient TD reduction through plastic relaxation requires that the plastic relaxation is caused only by the bending of TDs, rather than through MD multiplication or half-loop nucleation at the sample surface. The observed MD networks show no indication of a high degree of dislocation multiplication or half-loop formation. These mechanisms are, therefore, neglected.

<figure><img src="image_8.png" /><figcaption>**FIG. 4.** (a) and (b) (110)-cross-sectional HAADF-STEM images of MDs in the upper and lower AlSb interface. (a) Dissociated 60° MD in the upper AlSb interface that generates a stacking fault. (b) Complete 90° MD in the bottom AlSb interface. Dotted white lines highlight the disrupted stacking sequence and the ending atomic half planes, respectively. Burgers circuits around the dislocations are indicated in yellow. (c) ECCI enlargement of regions in the 50 nm GaSb cap sample depicting a group of misfit dislocations being blocked and repelled by the perpendicular set of MDs and giving rise to threading dislocations. A schematic of the blocking process is shown in (d).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>FIG. 5. (a) Threading dislocation density $\rho_{TD}$ measured by ECCI as a function of the GaSb cap layer thickness (black squares) and the plastic relaxation $\epsilon_p$ of the layer (orange circles). The trends are indicated by dotted lines as a guide for the eye. A dashed orange line is included showing the plastic relaxation assuming a constant excess stress of $\sigma_{exc} = 10^{-3}\mu$ of the layer. (b) TD density depending on the plastic relaxation for the AlSb layer (teal squares) and the GaSb cap (orange circles) with exponential fits based on Eq. (4).</figcaption></figure>

In Fig. 5(b), the TD density measured with ECCI is plotted against the total strain relieved as determined by the average MD distance. It shows measurements for both the GaSb cap layer and the AlSb filter layer. The plastic relaxation of the AlSb was calculated using the two samples with 100 and 150 nm thick AlSb layers (see Fig. 2) and a third sample with an AlSb layer thickness of 18 nm, i.e., below the critical thickness. For all three samples, the thickness of the GaSb cap is below $h_c$ to ensure that the decrease in TDs is only due to the plastic relaxation of the AlSb and is not influenced by the GaSb cap. Both data sets follow a linear trend in the logarithmic plot in Fig. 5(b).

Previous work on modeling of the interaction of mobile dislocations in an epitaxially strained layer establishes that the TD density decreases exponentially with the relaxed strain as given by the following equation:²⁶

$$\rho_{TD}(\epsilon_p) = \rho_{TD}^0 \exp\left(\frac{-2Rq\epsilon_p}{Db_{\parallel}}\right), \quad (4)$$

where $\rho_{TD}^0$ defines the TD density just below the interface to the strained filter layer. The parameter $D$ is a geometrical factor that considers the symmetry of the MD network ($D = 1/2$ for a square network) and $b_{\parallel}$ is the Burgers vector component parallel to the interface (here for a 60°-type: $b_{\parallel} = a/(2\sqrt{2})$) depending only on the crystallography of the cubic system. The fractional change in the TD density is mainly determined by the product $R \cdot q$, defined by the interaction radius $R$ capturing mobile dislocations and the probability that two randomly picked dislocations can annihilate (e.g., $q = 1/4$, if assuming four Burgers vectors with the same incidence). Therefore, the product $R \cdot q$ can be seen as an efficiency of the TD reduction process. A higher value leads to a more efficient TD reduction for the same plastic relaxation of the layer. According to

the result of our linear fits, the product is $(24.1 \pm 0.5)$ nm and $(39.6 \pm 9.9)$ nm for the AlSb filter and the GaSb cap layer, respectively. Assuming $q = 1/4$, the capturing radius would be $(96.4 \pm 2.0)$ nm for AlSb and $(158 \pm 40)$ nm for GaSb. Consequently, the resulting interaction radii are large compared to typical values for $R$ of 40 nm determined for the GaAs system,²⁶ pointing to a highly effective dislocation reduction in the III-Sb filter layer system. On the other hand, the two distinct values for $R$ indicate a more efficient TD reduction by the plastic relaxation of the GaSb cap compared to that of the AlSb layer. In addition to the fact that dislocation mobility differs in different materials, the dissimilar dislocation reduction efficiencies can be attributed to the distinct MD arrangements in the two AlSb interfaces. The dissociated 60°-MDs in the interface to the GaSb cap are known to be highly mobile, whereas the dislocation reactions forming a dense network of sessile 90°-MDs in the bottom AlSb interface can result in a pinning of TD arms at the AlSb interface impeding their ability of movement and annihilation.

Dislocation pinning and blocking in the dense interfacial MD networks also impede the plastic relaxation process of the layers resulting in a saturation of the TD reduction process for larger layer thicknesses, a mechanism known as strain hardening. It can be seen in the figure that even for large GaSb cap layer thicknesses, the plastic relaxation $\epsilon_p$ is much smaller than the initial strain of the layer of 0.36%, meaning that high residual strain is still present in the layer. The expected progress of plastic relaxation can be estimated using a model by Dodson and Tsao, which introduces the concept of an “excess stress,” an additional stress exceeding the equilibrium stress that balances the dislocation line tension, and is required to drive plastic relaxation.⁴⁴,⁴⁵ Applying the approach of Dodson and Tsao to the present situation for GaSb growth at 550 °C, which is equivalent to about 80% of the melting temperature of the GaSb, a reasonable value of excess stress is in the range
of $\sigma_{exc} = 10^{-3}\mu$ with $\mu$ as the materials shear modulus.⁴⁴ Assuming that the strain is homogeneous throughout the layer thickness and that, independent of the layer thickness, a constant excess stress of $10^{-3}\mu$ is required for further plastic relaxation, results in the plastic relaxation curve added as a dashed orange line in Fig. 5(a). It can be seen that the model can match reasonably well the measurements at small layer thicknesses, but the plastic relaxation of the 450 nm-thick GaSb layer is significantly smaller than that prediction. The deviation to the constant excess stress curve at larger layer thickness indicates a reduction of dislocation mobility, or, in other words, an increase of the excess stress at high film thicknesses caused by strain hardening. Therefore, multiple filter layers are needed to attain further TD reduction. They offer additional strained layers, where the TD arms can move to form interfacial MDs despite the TD pinning in the lower interfaces.

### C. Threading dislocation reduction in a double GaSb/AlSb filter layer structure

To investigate the effect of multiple filter layers, a double AlSb filter layer structure was realized accordingly. After a first 150 nm-thick AlSb filter layer, a GaSb interlayer with a thickness of 350 nm was grown based on the optimal thickness range found from Fig. 5(a). Indeed, a large plastic relaxation of the interlayer is required to achieve sufficient strain in the second filter layer and ultimately to apply sufficient epitaxial stress, which, in turn, leads to effective TD reduction, as observed here for the GaSb cap. The interlayer was followed by a second AlSb filter layer of 300 nm thickness. The larger layer thickness of the second AlSb layer was

chosen to achieve a similar plastic relaxation degree than for the first one, despite the residual strain of the GaSb interlayer. The sample was completed with a 450 nm thick GaSb cap layer. A cross-sectional STEM image of the complete structure is shown in Fig. 6(a).

ECCI measurements at a sample surface give a TD density of $(1.7 \pm 0.2) \times 10^7 \text{ cm}^{-2}$. Thus, the double filter layer structure is actually able to further reduce the TD density significantly compared to a single AlSb layer. The TD density is three times lower than that of the structure with a single 150 nm AlSb filter layer and a 1000 nm-thick GaSb cap, despite having a similar overall thickness (cf. Fig. 5). To analyze the TD reduction process inside the layer structure in more detail, depth-resolved STEM images of targeted plan-view samples of 100–300 nm thickness were used to determine the dislocation density in the second AlSb filter layer and the deeper GaSb interlayer. The results of the STEM observation and the ECCI measurement at a sample surface are shown in Fig. 6(b) as orange data points, indicating the reduction of the TD number related to each layer of the structure. Similar to the samples with only one filter layer, in the second pair consisting of an AlSb filter and a GaSb cap layer, GaSb shows a more efficient TD reduction than AlSb despite its lower plastic relaxation. This goes along with the observation of the same two different types of MD networks (90°/60°-type mixed vs 60°-type MD network) in the compressive GaSb/AlSb and tensile AlSb/GaSb interface. Plan-view STEM images of the MD networks in the upper interface of the second AlSb layer, the bottom interface of the second AlSb layer, and the upper interface of the first AlSb layer are shown in Figs. 6(c)–6(e). The MD network in the upper interface of the first AlSb layer still exhibits a 60°-type MD cross

<figure><img src="image_10.png" /><figcaption>FIG. 6. (a) STEM image of the cross section of the double filter layer structure. (b) Calculation of the TD density in the structure based on Eq. (4). The calculated values based on the plastic relaxation of each layer are depicted as teal squares. Comparison measurements of the TD density with ECCI and STEM are shown as orange circles. White and gray areas of the chart indicate the positions of AlSb and GaSb layers, respectively. (c)–(e) Plan-view STEM images taken at the top three interfaces labeled 1–3 in (a).</figcaption></figure>
network, although it experienced annealing of the second AlSb layer. It confirms that the fundamental nature of the two different MD networks depends on the sign of the strain (tensile vs compressive) and is not a consequence of the thermal cycle annealing.

In order to correlate the TD reduction with the lattice strain relief, the dislocation networks at the interfaces were measured as before and the plastic strain relaxation was determined using Eq. (2), resulting in a value of (0.18 ± 0.01)% for the GaSb interlayer, (0.29 ± 0.03)% for the second AlSb layer, and (0.24 ± 0.01)% for the GaSb cap. Assuming that the same mechanism describes the dependency between strain relief and dislocation annihilation in the double filter layer as well as in the single layer case, Eq. (4) can be used to calculate the respective dislocation density in the individual layers. Using the measured TD density in the first AlSb layer, $\rho_{TD}^0 = 4.5 \times 10^8 \text{ cm}^{-2}$, a plastic relaxation of the GaSb interlayer of $\epsilon_p = 0.18\%$, and a $R \cdot q$-value of 39.6 nm as determined from Fig. 6(b) for GaSb results in a calculated TD density of $1.2 \times 10^8 \text{ cm}^{-2}$. This is the theoretical value expected for the GaSb interlayer if the TD reduction efficiency due to plastic relaxation in the GaSb interlayer is the same as that found for the GaSb cap in the case of a single filter layer structure. In a similar manner, the TD density measured by STEM in the GaSb interlayer ($1.3 \times 10^8 \text{ cm}^{-2}$) and in the second AlSb layer ($6.4 \times 10^7 \text{ cm}^{-2}$) can be used as $\rho_{TD}^0$ to calculate the theoretically expected TD density in the second AlSb layer and in the GaSb cap, respectively. These three calculated values are shown in Fig. 6(b) as teal data points. Comparison of these values with the measured values shows that the model also gives a good estimate of the TD reduction effect for the double filter structure, but somewhat underestimates the TD density for the second AlSb layer and the GaSb cap.

These deviations can be attributed to limitations of the model when applying to the present case. Based on the model used to derive Eq. (4), it is assumed that *R* and *q* are constant and independent of other parameters, which may not be the case here. In fact, with a smaller TD density, the ECCI measurement at the surface of the filter layer structure reveals clustering of TDs and lateral irregular distributions, respectively [cf. Fig. 3(f)]. It is likely that such clustering leads to a locally non-uniform distribution of dislocations with the same Burgers vector, which significantly affects the TD annihilation process [smaller value of *q* in Eq. (4)]. In addition, an uneven distribution of Burgers vectors could already be present at the interface to the Si substrate at the beginning of TD generation.

## IV. CONCLUSION

The monolithic integration of GaSb on Si substrates introduces a high density of dislocations, resulting from the large lattice mismatch between the two materials. A 150 nm-thick AlSb dislocation filter layer inserted into GaSb buffer layers grown on Si was found to reduce the TD density from about $10^9$ to mid-$10^7 \text{ cm}^{-2}$. STEM and ECCI were employed as complementary techniques to investigate the MD networks formed at the two interfaces of the AlSb layer and the TDs emerging at the sample surface. Analyzing the MD networks at the bottom and top AlSb interfaces allowed for the determination of the strain relaxation of the AlSb layer and the GaSb cap, respectively. Samples with varying thicknesses of the AlSb layer and of the GaSb cap were used to investigate the

relationship between plastic relaxation and the TD density reduction. An exponential decrease of the TD density with the plastic relaxation for both layers was found, consistent with theoretical models presented in the literature.²⁶

Fitting the data to the model indicates an efficient TD reduction with plastic relaxation of both layers. However, a higher efficiency of the TD reduction process was evidenced for the GaSb cap. Fundamentally different MD networks were observed in the two interfaces of the AlSb and are proposed as the reason for these different TD reduction efficiencies. A complex MD network formed by dislocation reactions in the bottom AlSb interface results in dislocation pinning with significantly reduced dislocation mobility and a smaller capture radius *R* for dislocation reactions in the AlSb layer compared to the glissile 60° MDs found in the top interface with the GaSb cap. The nature of the MD networks also affects the plastic relaxation responsible for TD reduction. Dislocation pinning and blocking mechanisms within the MD network are the origin of strain hardening, resulting in high residual strain of the layers. As a result, once the MD networks reach a critical density, not much further plastic relaxation can be achieved, even with significantly increased layer thicknesses.

A double filter layer structure with two AlSb filter layers and a thick GaSb interlayer in between was realized to partly overcome the problem of strain hardening, limiting the plastic relaxation of the layers. An additional decrease of TD density by a factor of 3 down to low-$10^7 \text{ cm}^{-2}$ was measured for this structure. However, the reduction efficiency with plastic relaxation for the second set of AlSb layer and GaSb cap is slightly smaller than for the single filter layer case. The increasing local inhomogeneity in the distribution of TDs and their dislocation Burgers vectors, which can be observed with decreasing TD density, is considered to be responsible for the declining efficiency of dislocation reduction. Nevertheless, this study highlights the potential of multiple filter layer structures for TD reduction.

## ACKNOWLEDGMENTS

We thank M. Hanke for critical reading of the manuscript and valuable comments and C. Matzeck and S. Richter for TEM sample preparation. This work was partially supported by the France 2030 program (EquipEx EXTRA, ANR-11-EQPX-0016, and EquipEx+ HYBAT, ANR-21-ESRE-0026) and by the Deutsche Forschungsgemeinschaft and the French ANR within the DFG-ANR Project FILTER (ID No. 446180337/ANR-20CE92-0045). The authors acknowledge the financial support provided by the European COST Action OPERA (No. CA-20116) through the short-term scientific mission program and the use of the facilities of the Application Laboratory Electron Tomography (BALET) of the Paul-Drude-Institute (ERDF Project No. 2016011843).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

K.G. and A.G. contributed equally to this paper.
**K. Graser:** Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal). **A. Gilbert:** Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal). **J.-B. Rodriguez:** Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). **E. Tournié:** Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). **A. Trampert:** Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available
from the corresponding author upon reasonable request.

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