Influence of strain on the InAs_1 – xSb_x composition

InAs_1 – xSb_x has the smallest direct bandgap among the common III–V alloys. This is one of many desirable properties of InAs_1 – xSb_x, setting it apart as the most viable III–V challenger to HgCdTe for long-wavelength infrared (LWIR) detector applications.¹ InAs_1 – xSb_x also has strong spin–orbit coupling and the largest g-factor among semiconductors that can interface well with superconductors. These properties drive recent interest in InAs_1 – xSb_x for studies of modern physics phenomena such as topologically protected states.² 

The growth of mixed group III alloys, such as In_zGa_1 – zAs, is generally very straightforward. When grown using stable fluxes and typical substrate temperatures (for which re-evaporation is negligible), the resulting films have mole fractions that are predictable and based directly on group III flux ratios.

In contrast, we cannot predict the constituent mole fractions in mixed group V alloys based only on the group V flux ratios, as they are also dependent on the interaction between the group V's and the group III's. For instance, the composition of InAs_1 – xSb_x results from a complex interaction of As and Sb with each other and with indium. Other factors affect the composition to varying degrees, such as the substrate temperature,^3,4 the presence of surfactants,^3,4 the growth rate,⁵ and, as we discuss in this article, the strain state. The composition of InAs_1 – xSb_x, whether grown as a bulk alloy or into a strained layer superlattice (SLS), is dependent on these factors, and the codependence of each of these parameters on each other is far from completely established. Despite these challenges, the quality of unstrained, unrelaxed InAs_1 – xSb_x bulk alloys, or InAs_1 – xSb_x /InAs_{(1 – y)}Sb_y SLS structures grown on GaSb (001) substrates has greatly improved in recent years through highly tuned molecular beam epitaxy (MBE) growth techniques. We have repeatedly demonstrated thick, lattice-matched InAs_1 – xSb_x films of various compositions with dislocation densities below the transmission electron microscopy (TEM) detection limit and strong optical properties.⁶ 

In this paper, we focus on strain, which influences compositions in both mixed group III and group V alloys, as reported in studies of In_1 – xGa_xN,⁷ and GaAs_1 – xBi_x.⁸ We observe that the sign and degree of strain also influences incorporation in InAs_1 – xSb_x. Strained InAs_1 – xSb_x films tend to resist changes in the group V mole fractions despite growth conditions that should promote compositional change. For instance, a past study showed InAs_1 – xSb_x /InAs_1 – ySb_y SLS structures have an overall maximum amount of Sb that will incorporate depending on its mismatch with the substrate. Changing the period or individual layer thickness, or the substrate temperature, did not substantially increase the incorporation.⁹ In this study, we find that InAs_1 – xSb_x grown close to lattice-matching conditions resists changing its group V mole fractions in a manner that would further increase its mismatch with the GaSb substrate. This effect of self-latching to the substrate lattice constant is beneficial since it means that the fluxes may not have to be adjusted as precisely as otherwise needed.

We grew the samples in a solid source Gen II MBE system equipped with valved, cracked Sb and As cells. The GaSb substrates were quartered 2 in. wafers, epi-ready, and exactly oriented along [001]. We examined all samples with high-resolution x-ray diffraction (XRD) and selected samples with TEM and energy dispersive spectroscopy (EDS). We collected four XRD scans, including two symmetric (004) scans measured before and after a 180° rotation in phi, and two asymmetric (115) scans. The first (115) scan had a high angle of instance, and the second had a low angle of incidence and a phi rotation of 180°. This standard method measures the in and out of plane lattice parameters, as described by Krost et al.,¹⁰ and allows us to extract the strain and composition.

In Series A and B, we alter the composition and strain by changing the substrate temperature. In series C, we alter the strain and composition by changing the Sb/As flux ratio, which causes differing degrees of compressive and tensile lattice mismatch in stacked triple-layers. Section III details the growth parameters with the data in chart form for each series.

Table I summarizes all data and growth conditions for series A and B. The InAs_1 – xSb_x samples have two different Sb/As flux ratios for a large range of substrate temperatures as measured by pyrometer. Series A (samples A1–A11) was grown with an Sb/As flux ratio of 1.05 and temperatures ranging from 320 to 490 °C. For our typical growth temperature of 415 °C, we would expect that an InAs_1 – xSb_x film grown with Sb/As of 1.05 would have an Sb mole fraction of ∼0.48. Series B (samples B1–B11) had a flux ratio of 0.07 and a 340–490 °C temperatures range. Under this flux condition, we would expect InAs_1 – xSb_x to have an Sb mole fraction near lattice match (0.089) at our typical growth temperature of 415 °C.

Figure 1 plots the Sb mole fraction as determined by x-ray as a function of growth temperature. The horizontal dashed line denotes the lattice-matched Sb mole fraction of 0.089.

Overall, the Sb mole fraction decreases with increasing growth temperature for the substrate temperatures examined in this study. We discussed growth temperature effects on Sb incorporation in our previous study.^3,4 Haugan et al. more recently observed a similar decrease in Sb in InAs_1 – xSb_x for increasing growth temperatures over the range of 400–440 °C.¹¹ In Fig. 1, we notice a striking plateau in this trend over a ∼50 °C temperature range for compositions near lattice match in series B.

Figure 2 illustrates this trend clearly by plotting the percentage change in Sb mole fraction versus the percentage change in substrate temperature. The baseline is the Sb mole fraction for the two samples grown at 415 °C. Negative changes in mole fraction percentages refer to a decrease in the Sb mole fraction relative to the sample grown at 415 °C, and negative changes in temperature percentages refer to temperatures lower than 415 °C. For visual clarity, we only labeled the endpoints of each series. Samples A1–A11 are completely relaxed, and the compositions are not affected by strain; therefore, we can easily fit a linear relationship for this temperature range. The behavior of the B series as shown in Fig. 2 indicates a resistance to growth temperature-induced composition changes for films grown near lattice-matched conditions.

All samples except B1–B8 have thicknesses that are orders of magnitude above the Matthews–Blakeslee¹² critical thickness for InAsSb. Although some films retain strain well above critical thickness,¹³ it is reasonable to expect samples that are magnitudes of order thicker to be completely relaxed. This assumption proves reasonable in the XRD measurements. Figure 3 plots the XRD measured relaxations as a function of (a) mole fraction and (b) growth temperature. The A series films are highly mismatched to the substrate, and are almost completely relaxed, as shown in Figs. 1 and 3. Therefore, we do not expect strain influences in the group V mole fractions for A1–A11. The linear composition/substrate temperature relationship shown in Figs. 1 and 2 for series A affirms this expectation.

For the B series, the Sb mole fraction plateaus for a temperature range of around 50°. These mole fractions are at or extremely close (within 0.0025) of the lattice match mole fraction. It implies a “latching effect” where the film has a limited but noticeable ability to incorporate selectively the group V species needed to minimize strain. Again, we chose this Sb/As ratio because it reliably produces lattice-matched films for grown at 415 °C and measured by XRD at room temperature. We notice in Fig. 3 that the “latching effect” seems more pronounced on the “colder” side of this temperature.

Figure 4 plots relaxation as a function of lattice mismatch for series B. Relaxation for compressive and tensile films is not symmetric about the lattice-matched position. This is not surprising since there are numerous reports showing a larger critical thickness for tensile strained versus compressively strained films.^14,15

Since the “latching effect” occurs for substrate temperatures ranging from 385 to 415 °C, it might be worth changing our standard growth temperature for InAs_1 – xSb_x from 415 °C to the middle of this range (∼400 °C). We have not yet optimized the growth temperature for InAs_1 – xSb_x. In a future work, we will determine if the optical and crystalline properties of InAs_1 – xSb_x grown at temperatures closer to the middle of the “latching window” improve relative to films grown at 415 °C. The findings in this study indicate that InAs_1 – xSb_x may be tolerant to small deviations in flux or substrate temperature. It may be beneficial to grow materials in the middle of the temperature range that enhances this tolerance.

Series C was initially grown to expand our dataset for establishing the nonlinear relationship of the Sb/As flux ratio to the InAsSb composition. Multilayer stacks allow multiple data points from a single growth, saving substrates and growth time. We also wanted to examine the compressive versus tensile defect morphology in InAsSb.

We grew two samples with three InAs_1 – xSb_x layers at a substrate temperature of 415 °C. The targeted Sb/As flux ratios were 0.09, 0.18, and 0.27. Figure 5 shows a schematic of the triple layer structures C1 and C2. For Sample C1, we began by depositing the layer that we expected to be closest to (although slightly in excess of) the lattice match mole fraction and then increased the Sb/As ratio in two steps, resulting in three 0.75 μm thick layers. We reversed the layer order for Sample C2, etc., i.e., we deposited the most highly mismatched, higher Sb content first and then reduced the Sb concentration for the next two layers.

The group III cell temperatures and the group V valve position for C1 and C2, along with the shutter sequence (which is the same for both samples), are shown in Fig. 6.

Figure 7 shows the recorded chamber and beam flux monitor pressure throughout the growth. The pressure gauges logged the same overall system pressures versus time (which are mostly driven by As) corresponding to the same Sb/As ratios for samples C1 and C2. From this and the plot of the growth logs in Fig. 6, we can see that the source cell temperatures and the flux conditions were the same in layer 1, sample C1 and in layer 3, sample C2, just as layer 3 in C1 had the same growth conditions as layer 1 in C2. The second layer in both samples had the same growth conditions. Therefore, the only difference between the layers in C1 and C2 that had the same growth conditions was its lattice mismatch with the underlying layer.

Figure 8 shows the (004) x-ray rocking curves for samples C1 and C2. At first glance, it seems that although exposed to the same flux and cell temperature conditions, layer 1 in C1 and layer 3 in C2 have different mole fractions, as listed in the schematic of Fig. 9. Layer 3 in sample C2 is on the right hand side of the substrate peak, whereas layer 1 in sample C1 is just to the left of the substrate peak and near lattice match. The p’analytical epitaxy software finds that layer 3, sample C2 has a mole fraction of 0.02 Sb vs 0.09 for layer 1, sample C1. All of the other layers in the two samples give nominally the same mole fraction for layers grown with the same Sb/As ratio. The relaxations listed are relative to the GaSb substrate (Fig. 10).

The 0.02 Sb mole fraction in layer 3, sample C2 does not seem plausible. We examined sample C2 with EDS. Figure 10 shows the mole fraction profile, and the XRD and EDS data are plotted together in Fig. 11.

We notice in Fig. 11 that nearly fully relaxed layers exhibit the same mole fraction in C1 and C2 for the same Sb/As ratio. The EDS and XRD data for sample C2 also agree for layers 2 and 3.

There is a large disparity between the EDS data and the XRD data for sample C2, layer 3. TEM results, which we will discuss later, show cracks, and non-normal relaxation in layer 3, which is likely affecting the XRD results. Since the XRD and EDS are in reasonable agreement for the two other layers in the sample, and the EDS value of 0.13 for layer 3 is more in line with expectations and would be unaffected by unusual diffraction due to tensile strain relaxation, we believe that the EDS value is much more reliable.

Layer 1 in sample C1 is the only layer that we expected to show strain effects. For an Sb/As ratio of 0.09, we expect a mole fraction of ∼0.125. This is close enough to lattice match that it is unlikely to relax fully. The XRD indicates that it is 13% relaxed, with a mole fraction of 0.09, as shown in Fig. 11. The film has incorporated Sb nearer to lattice match conditions than the Sb/As flux ratio would suggest. Compare this to the mostly relaxed layer 3 in sample C2, which has a 0.13 Sb mole fraction (which is closer to that expected for Sb/As = 0.09) despite being grown with the same Sb/As ratio as sample C1, layer 1.

As with the samples in the first two series (A and B), we see that strain affects incorporation near lattice-matched conditions (layer 1, sample C1), whereas the other layers (relaxed) in samples C1 and C2 are unaffected by strain and have nearly the same mole fraction for the same Sb/As ratio. For nearly fully relaxed films, the sign of the mismatch (compressive versus tensile) seems to have no effect on mole fraction.

Figure 12 shows (a) (002) and (b) (220) dark field (DF) TEM images of sample C1. The defect morphology is consistent with that expected for compressive strain relaxation.¹⁶ The curved lines move with the beam and are thickness fringes. Figure 12(c) is an HRTEM image of layer 3, showing no unusual strain contrast, with flat, undistorted lattice fringes measuring as expected for a relaxed layer InAs_0.74Sb_0.26. Since tetragonal distortion and dislocation relaxation accommodate the strain relaxation, simple XRD analysis of the four collected scans gives accurate values for the strain and composition.

Figure 13 shows (002) DF images of sample C2. Layers 2 and 3 are tensile, and the sample relieves some of the strain by cracking, particularly in layer 3, and with surface undulations (as seen, for example, at the top of the crack on the left hand side). Simple XRD analysis measuring tetragonal distortions is, therefore, not appropriate for calculating the strain and the relaxation in these films.

InAs_1 – xSb_x is of interest because of its potential as an LWIR detector and for studies of modern physics phenomena such as topologically protected states. Through well controlled MBE growth and structural/chemical analysis, we have improved the quality of unstrained, unrelaxed InAs_1 – xSb_x across a wide mole fraction spectrum. This required a detailed study of mixed group V alloying, which is not straightforward due to the complex interaction of As and Sb with each other and with In.

In this study, we demonstrate that InAs_1 – xSb_x grown close to lattice matching resists changing its mole fraction in a manner that would further increase its mismatch with the GaSb substrate. We also determine that relaxation is not symmetric for tensile and compressive strains in InAs_1 – xSb_x. Layers that are nearly fully relaxed are largely unaffected by strain in terms of incorporation for a given Sb/As ratio, whether the film is compressive or tensile relative to the underlying layer.

It may be possible to optimize future growths by better defining the center of the growth condition window where the “latching effect” occurs, which would make the material more tolerant of normal deviations in flux and substrate temperature that occur over the time period required for MBE growth.

Stony Brook University acknowledges support of the Army Research Office (Award No. W911NF-16-2-0053).