Review of virtual substrate technologies for 6.3 Ångström lattice constants

Many III–V alloys of interest for device designs have lattice constants between those of commercially available substrates. Thus, it has long been a desire to overcome the limitation of fixed lattice constants when growing epitaxial materials. One approach for solving the problem is to use a pseudomorphic layer—a lattice mismatched layer with a thickness below that where dislocations are formed—the critical thickness. The method has been applied successfully, for example, in the case of modulation-doped AlGaAs/InGaAs/GaAs field effect transistors, where very good electron transport can be sustained within a strained, dislocation-free, InGaAs layer, despite its limited thickness.¹ 

A related approach is to use strain-balanced combinations of materials with larger and smaller lattice constants than the substrate, each layer again with a thickness below the critical thickness. Although not able to produce a structure with a nonstandard lattice constant, the method allows growth of strained superlattices (SLSs) with unlimited thickness, representing a material with new properties that are different from those of constituents.² Of special interest are SLSs with type II bandgap line-up that can produce effective bandgaps that are smaller than the constituents and even smaller than their bulk alloy.³ This approach has been used with some success to reach the small bandgaps needed for infrared (IR) detection, using so called, type II strained-layer superlattice materials (TIISLS). These are typically designed in the GaSb/InGaSb- or InAs/InAsSb-systems grown on GaSb.

Just being able to respond to light of the desired wavelength is, however, not sufficient for a high-performance detector. Properties like optical absorption-strength and unimpeded isotropic transport of photo-excited electrons and holes strongly influence the device performance—properties that are superior in bulk materials. The so-called “Ga-free” TIISLS, i.e., InAs/InAsSb on GaSb, illustrate these concerns. The SL can be thought of as InAsSb with a periodic modulation of Sb (between 0 and a finite value and an average concentration of 9%) in the growth direction, which allows dislocation-free growth and an extension of the absorption wavelength from ∼4.5 μm (lattice matched bulk InAs_0.91Sb_0.09) to wavelengths even beyond the long-wavelength (LWIR) band (>12 μm). Unfortunately, the large difference in lattice mismatch between InAs and GaSb on one hand and InSb and GaSb on the other dictates the use of very thick InAs- and very thin InAsSb-layers, a ratio that increases the smaller the desired SLS bandgap is. An SLS designed that way suffers from optical absorption⁴ and electron and hole transport⁵ properties that are significantly reduced compared to bulk InAsSb materials (the effect on the hole transport is particularly strong). Methods for producing high-quality bulk InAsSb are, therefore, of considerable interest.

The minimum bandgap of InAsSb occurs for a lattice constant close to 6.3 Å, which is why we use this number as a rubric for this technology. Ga and Al can be further added to the material while maintaining the same lattice constant, albeit requiring a change in the Sb/As composition. The addition of these elements enables heterostructure designs with some of the largest bandgap differences among III–V-materials as well as intriguing band-line-ups.⁶ In order to take advantage of these properties, the large lattice mismatch between 6.3 and 6.1 Å (GaSb) or 6.5 Å (InSb) must be managed.

The importance of the efficacy of the lattice mismatch management is well illustrated by InAsSb. Although it was known for a long time to have the smallest bandgap⁷ among III–V alloys,⁸ it was set aside in the early 1990s since measurements seemed to indicate that it was not small enough to reach the long-wavelength infrared band.⁸ Unfortunately, the decision was based on investigations of mainly defect-dominated materials. By using a virtual substrate (VS) approach based on the theoretical work by Tersoff,⁹ we have been able to produce InAsSb of sufficient quality so that its intrinsic properties could be investigated. The results show a material that contrary to earlier impressions, not only can cover the entire LWIR band^10,11 (Fig. 1), but also closely resembles HgCdTe, the current LWIR performance standard, in other aspects.¹² This is an example of a functioning VS being an enabling technology.

Even though our VS approach allows determination of basic materials and device properties, it remains to be established if it, or indeed any VS, is good enough for large device array development. IR detector arrays can be seen as a critical test case since they are some of the largest devices made from semiconductors and are usually sensitive to crystalline defects. The first question that needs to be addressed then is what the density of threading dislocations needs to be? Even for the well-studied case of HgCdTe, there is no publicly available information on what density allows what technical application to be addressed, although a general consensus seems to be that a density of at most 10⁵ cm⁻² is a cut-off with more demanding applications requiring numbers in the mid to high 10⁴ cm⁻² range.¹³ One must then also ask the question if the detrimental effects of the density and type of dislocations are the same in II–VI and III–V materials—specifically in antimonides. To our knowledge, a detailed understanding of the device impact of dislocations and the underlying physics does not exist even for HgCdTe, so the actual requirements for antimonide-based device arrays must await experimental determination.

A significant related problem is to find a suitable tool for determining crystalline defect densities at this order of magnitude. Cross-sectional transmission electron microscopy (TEM) can be a useful method during the development of a VS growth process, but it is not sufficient due to its very narrow field of view. Simply put, if any threading dislocations are observed in a cross-sectional TEM image, the material is not of device quality by the standards we are discussing here. Recent progress in x-ray topography (XRT), however, is now enabling such investigations.¹⁴ We have been able to apply XRT on thick InAsSb-layers and determine promising defect densities that are close to the target values.

All materials have been grown with solid source molecular beam epitaxy (MBE) using valved group V sources in two different systems (a Gen II and a Gen 930) in two different locations, demonstrating the portability of the process. The virtual substrates have been designed using two different alloys: an analog linear grade from GaSb to AlInSb or GaInSb. The Al-version produces a virtual substrate that is semi-insulating enough to allow Hall effect measurements of films grown on top,¹⁵ while the Ga-version can be made conducting with the help of Te-doping to enable back-contacting of the device material.¹⁶ 

Dislocation properties on entire 50 mm diameter wafers as well as smaller samples were determined with x-ray topography, which was performed using a Rigaku XRTMicron system equipped with a 1.2 kW, dual wavelength Cu/Mo rotating anode with a 70 μm microfocus x-ray source. To obtain Kα x-ray beams with low vertical divergence from either a Cu or a Mo anode, dual collimating mirrors were used. The sample was mounted on a specialized reflection/transmission goniometer with X, Y, and ϕ axes having a travel up to 200 mm diameter and 360° rotation. The diffraction images were collected using an x-ray camera having a pixel size of 5.4 μm with a 18 × 13.5 mm² field of view. XRT images with several diffraction conditions were used in both transmission and reflection geometry as listed in Table I along with their estimated penetration depth. Automated curvature correction procedure was performed to obtain the XRT image from the entire sample region. Image processing was performed to identify and quantify dislocations in the samples

Growth of InAsSb on VSs allowed us to determine the fundamental bandgap of the alloy as a function of composition, using photoluminescence and optical absorption.¹¹ This enables us to grow a VS with the appropriate lattice constant corresponding to the bandgap for any LWIR wavelength that is less than the maximum wavelength for InAsSb.

One might assume that it would be easier to grow a VS with a smaller shift of lattice constant from the underlying substrate than one with a larger shift. And this would lead to the notion that it would be easier to grow a Ga-free SLS on a VS with a modest increase in lattice constant compared to one with the larger increase needed to grow the bulk material with the same wavelength. But we have found that it is just as easy to grow a VS with a large shift as it is to grow one with smaller shift. Therefore, since the bulk material has inherent advantages in mobility and absorption strength, it makes more sense to grow the larger-shift VS with bulk material on top. Growth of a LWIR SLS on the VS would result in a material with most of the limitations of the SLS and all the difficulties associated with the growth of the VS.

The SLS on a VS is still an extremely promising technology as it can be used to further reduce the bandgap to below that of bulk InAsSb, i.e., <0.1 eV. Reduction to zero and indeed even inversion is possible.⁶ Due to the significant change in band edge positions as the alloy composition is changed from InAs to InSb, it is possible to design a “Ga-free” TIISLS from InAs_1-xSb_x/InAs_1-ySb_y, where x > y > 0 in the general case. (What is commonly known as the “Ga-free SLS” is a special case of x > 0, y = 0). Furthermore, since the lattice constant is a design parameter, it is now possible to choose the layer thicknesses in the SLS period to be similar, thus avoiding the lopsidedness in the special Ga-free SLS design on GaSb [Fig. 2(a)]. Since the period can also be made very thin, it allows maximum flexibility in the design of dispersion and, therefore, transport properties, while maintaining strong optical absorption.^4,6

The VS technology for 6.3 Å lattice constant has so far been applied to MWIR lasers,¹⁷ LWIR detectors,¹⁶ LWIR optical modulators,¹⁸ and studies of superconducting proximity effects in InAsSb surface quantum wells with in situ Al contacts.¹⁹ SLS on VS structures have also been used in detectors⁵ and modulators²⁰ as well as new structures for investigation of novel physics phenomena such as Dirac energy spectra and inverted bandgaps in SLS.²¹ 

The mismatch grading rate is an important design parameter. One can intuitively see that an extremely fast rate would probably not be effective, while a very slow one would lead to impractical growth times. We have not had time to optimize this parameter and have just chosen it to produce grade thicknesses of the order of 2–3 μm, as can be seen in the next example.

Using the XRT method, we characterized a sample consisting of a linear grade of Ga_xIn_yAl_1-x-ySb from x = 1–0, y = 0–0.326, over 2.2 μm, using a typical growth rate of 1 μm/h. The virtual substrate used x = 0 and y = 0.275 with a thickness of 0.5 μm. The InAs_0.59Sb_0.41 on top was 4 μm thick.

The XRT images, shown in Fig. 3, using g = 220 in transmission and g = 206 in reflection geometry, were used to investigate dislocations in the GaSb wafer and near-interface graded layers. The presence of slip bands and scratches was observed in the substrate. In the near-interface layers, a network of misfit dislocations was observed having mostly a regularly spaced pattern indicating uniform relaxation occurring in those layers. These dislocations were predominantly along the ⟨110⟩ direction with Burgers vector ½ (−110). There was some dislocation bunching observed, and the bunching mechanism is not clear. The average density of misfit dislocations was 5–10 × 10⁴ cm⁻².

XRT imaging using g = 206 and g = 224 in the reflection mode was used to investigate the dislocations in the top InAsSb layer by aligning to this layer’s peak. Figure 4 shows XRT from the entire wafer as well as comparison of various XRT images that were magnified from a smaller region. The image appears to have a woven cloth-like pattern that arises from formation of misfit dislocations that are severely bunched and highly nonuniformly spaced. It appears that strain builds up and forms several misfit dislocations in bunches instead of continuous relaxation. This is likely due to complex adatom diffusion of group V elements and how they stick to the growth surface. It can be seen that in contrast to the near-interface region, as seen in the magnified images, the array of misfit dislocations in the top InAsSb layer is also curved, which contributes to evolution of high lattice curvature in the film. The management of relaxation and formation of more uniform misfit dislocation in the higher lattice mismatched layers with higher Sb composition is critical to realize films with lower lattice curvature.

XRT imaging on a smaller sample was also performed. Figure 5 shows the XRT image with g = 224 showing contrast from the top InAsSb layer. In addition to the array of misfit dislocations, there are several threading dislocations (TD) that appear along the misfit dislocations as bright dots, as seen in the magnified inset in Fig. 5. The contrast of a single TD typically appears as a bright dot and a dark shadow, but these appear as larger dots that are likely due to a cluster of TDs. The width of a single TD can be approximated as $W≈| b →|g ξ / 2 π$⁠, where $b →$ is Burger’s vector and g and ξ are the diffraction vector and x-ray extinction depth, respectively. The estimated width of a single TD for XRT imaging conditions used in Fig. 5 is calculated to be ∼5 μm using this relation. The dot contrast in the magnified inset is ∼20 μm in diameter. This indicates the presence of a TD cluster of at least 3 and less than 10 dislocations at the bright dots. If there were higher number of segregated dislocations, the dot would appear significantly more elongated along one of the four symmetrical crystal orientations. The density of these dots was counted to be ∼1 × 10⁵ cm⁻², indicating an averaged TD density of less than 1 × 10⁶ cm⁻². The detailed impact of different types of dislocations in detectors is not entirely clear, although it is reasonable to assume that they at least provide undesirable recombination centers. The clustering of TDs may enhance these issues but of course also lowers the overall density and probability of finding a problem area in a particular imaging pixel. The cluster density is, therefore, more representative of performance limiting defects, and their density of the order of ∼1 × 10⁵ cm⁻² is promising, which justifies further exploration of this material for LWIR detector arrays.

Although the measured dislocation densities and distributions are promising, there is clearly room for substantial improvements. So far, we have spent very little effort on optimization of the growth conditions of the VS or the InAsSb itself. Looking in more detail at the Tersoff theory for grading designs, it is immediately apparent that it is not dependent on the actual materials system used. However, in our experience, the choice of materials does indeed affect the results. Lattice matching a mixed group-V compound, such as InAsSb, to a mixed group-III material, such as AlInSb, which has been the approach we followed up until now, presents a nontrivial control problem. Extremely careful source characterization and stabilization are required. However, since InAsSb can be grown lattice matched to GaSb, it is obvious that the entire VS grade structure can be executed in InAsSb by simply varying the Sb/As-ratio, while following the same lattice constant rate increase with time as was done in group III grades. A detailed investigation of this will be presented later. Another fruitful way forward would be to theoretically develop refined grading models, which would include specific materials properties and perhaps predict an optimum grading profile in terms of grade rates and thickness.

Virtual substrates using analog linear grades have allowed us to produce InAsSb and related alloys containing Al and Ga, with a quality that enabled us to measure the materials’ intrinsic properties, in contrast to earlier investigations where the results were confused by high defect densities. The VS approach has allowed the design of LWIR detector materials as well as other new electro-optic devices, such as optical modulators, and enabled new structures for investigation of novel physics phenomena. The density of threading dislocations measured by XRT show clusters of defects at the 10⁵ cm⁻² range, a level that is reasonable for detector array development. Further experimental and theoretical studies of the effect of the materials used for the grades and the exact rate of change of the compositions are expected to be fruitful.

The author N.A.M. would like to acknowledge ONR funding at NRL. The authors affiliated with Stony Brook University acknowledge the support by DEVCOM Army Research Laboratory through the Center for Semiconductor Modeling and by Army Research Office Award No. W911NF2010109.

The authors have no conflicts to disclose.

Stefan P. Svensson: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – original draft (lead). Nadeemullah A. Mahadik: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Gela Kipshidze: Data curation (equal). Dmitri Donetski: Conceptualization (equal); Data curation (equal); Writing – original draft (equal). Jingze Zhao: Data curation (equal). Gregory Belenky: Conceptualization (equal); Data curation (equal); Methodology (equal); Writing – original draft (equal).

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