Improved epitaxial growth of TbAs film on III–V semiconductors

Lanthanide monopnictides (LN-V), also called rare-earth monopnictides (RE-V), are interesting for a wide range of potential applications.¹ Due to similarities in the crystal structure between the rocksalt LN-Vs and zincblende III−V semiconductors, including the common group V sublattice sites and close lattice constant, the epitaxial integration of LN-V with common III−V semiconductors can be achieved.^1–6 Therefore, a variety of applications based on LN-V/III–V materials have been studied and demonstrated. For example, LN-V nanostructures embedded in III–V matrices have been used for applications including thermoelectrics,^7–9 tunnel junctions,¹⁰ terahertz generation and detection,^11–14 and plasmonics.^15–17 In addition to LN-V nanostructures, LN-V films are also of interests. For example, due to the variety of lattice constants of LN-V materials, lattice matched ternary RE-V alloys have been epitaxially grown on different III–V semiconductors, such as ScErAs on GaAs¹⁸ and ScErSb on InAs.¹⁹ Similarly, due to the different optical properties possessed by LaAs²⁰ and LuAs²¹ individually, high-quality La_1 − xLu_xAs alloy films have been reported as a designer plasmonic material with tunable plasmonic wavelengths from 3.0 to 8.5 μm.²² 

TbAs is also a potentially useful material in the LN-V material class. For example, the incorporation of TbAs nanoparticles in III–Vs has been demonstrated to improve the figure of merit for thermoelectric materials.^8,9 Despite such technological relevance, the growth and properties of bulk TbAs have remained relatively unexplored. One instance of heteroepitaxial growth of TbAs films on GaAs via molecular beam epitaxy (MBE) has been reported previously;²³ measurements of those films indicate they are degenerately doped semiconductors, which contradicts the semimetal prediction from theoretical calculations. However, the relaxation and polycrystallinity in those films make the experimental observations rather difficult to interpret. Therefore, the exploration of the growth of epitaxial, high crystal quality TbAs on III–Vs is crucial not only for realizing its full potential for device applications but also for further understanding of its fundamental properties.

In this paper, we study the fundamental heteroepitaxial growth of high-quality TbAs films on both (001) InP:Fe and (001) GaAs substrates. The lattice constant of TbAs is 5.82 Å, which is 0.83% smaller than that of InP and 2.95% larger than GaAs. Due to this drastically different strain condition of TbAs on (001) GaAs and InP:Fe substrates, comparison of the growth on each substrate provides insight into the nucleation and growth of TbAs films. The resulting morphology and optical properties of these MBE-grown TbAs films are also investigated and compared.

Two TbAs films were grown, one on the intrinsic (001) GaAs substrate and the other on the intrinsic (001) InP:Fe substrate. A Veeco GENxplor solid source MBE equipped with effusion cells for In, Ga, Tb, and a two-zone, valved cracker source for As₂ is used. The growth temperature was monitored using band edge thermometry. Beam equivalent pressures (BEPs) of Ga, In, and As₂ were measured using an ion gauge beam flux monitor (BFM). The high desorption temperature of Tb causes it to condense on the BFM filament, thereby making subsequent readings inaccurate, so the Tb cell flux was calibrated using the cell temperature and not BEP. Before the growth, the GaAs and InP:Fe wafers were deoxidized under an As₂ overpressure of 1 × 10⁻⁵ Torr at 620 and 530 °C, respectively. After desorbing the native oxide, a 150 nm buffer layer of either GaAs or In_0.53Ga_0.47As was grown on the GaAs and InP:Fe substrates, respectively. After the buffer layer, the As₂ overpressure was halved and the two TbAs films were both deposited at a growth temperature of 490 °C. Although the same Tb cell temperature and the same deposition time were used, scanning electron microscopy (SEM) measurements suggested that the thicknesses of the two films were 820 nm on the GaAs substrate and 1150 nm on the InP:Fe substrate. This thickness difference is attributed to a difference in Tb flux at the same cell temperature caused by a change in the Tb surface area as the source material was being depleted. Finally, both TbAs films were capped with a 100 nm GaAs or In_0.53Ga_0.47As layer to prevent oxidation.

During growth, the surface morphology was monitored with in situ reflection high energy electron diffraction (RHEED). High resolution x-ray diffraction (HR-XRD) was measured using a Rigaku Ultimate IV XRD with Cu Kα₁ source to study the crystal quality of the TbAs films. SEM was done on a JSM-7400F microscope. Optical characterization was performed with a Bruker Vertex 70 V Fourier transform infrared (FTIR) spectrometer. All the reflection data were normalized to the reflection of gold, which has nearly perfect reflection in this wavelength range.

The T-matrix method was applied to fit the experimental reflection data of each sample.^24,25 A four-layered structure was used in the calculations, including the air, the capping layer, the TbAs film, and the substrate. The air and the substrate are assumed to be infinitely thick, while the thickness of the capping layer and TbAs layer was taken from SEM and TEM measurements. The optical parameters of the capping layers are simply treated to be the same as the bulk GaAs/ In_0.53Ga_0.47As in modelling. The optical response of the TbAs layer was modeled with the Drude formalism,^25,26 which is

where $εs$ is the background permittivity of the material, which is fitted to be 17 for both TbAs films in this work; $ωp$ is the plasma frequency of the material; and Γ is the scattering rate for free carriers in the material, which is the sum of the collision rate of electrons with electrons, phonons, and defects such as surface roughness and grain boundaries.

During growth of the GaAs buffer layer on the (001) GaAs substrate, a $(2×4)$ reconstruction pattern was observed as expected. RHEED patterns along the $[11¯0]$ azimuth from the subsequent growth of TbAs on the GaAs buffer layer are shown in Figs. 1(a)–1(c). After the Tb shutter is opened, as shown in Fig. 1(a), the RHEED pattern quickly transitioned from a (2 × 4) to a (1 × 1) and from streaky to slightly spotty. This 1× reconstruction is consistent with the previous study of growing more than one monolayer of ErAs on GaAs.^2,6 The spotty pattern indicates the island growth mode in the initial growth of TbAs on (001) GaAs, consisting of either a Volmer–Weber (VW) or a Stranski–Krastanov (SK) growth mode. Shortly after the growth of ∼5 nm TbAs, a mix of {001} and {221} crystal orientations were observed, as shown in Fig. 1(b). Such misoriented {221} nuclei have been previously observed during the heteroepitaxial growth of rocksalt PbSe on zincblende III–V substrates²⁷ and were attributed to a short-range coincident site lattice, where the lattice tilts in a certain angle that a short-range lattice match is achieved.²⁸ This previous study found that these highly faceted {221} islands can later be overgrown by (001)-oriented nuclei due to geometric factors. However, such overgrowth was not observed with TbAs grown on the GaAs substrate in this study. In the initial stage of growth, the {001} diffraction pattern remained brighter and streakier than the {221} diffraction pattern, as shown in Fig. 1(b), where the diffraction dots were from {221} and streaks were from {001}. As growth proceeds, the {001} streaks gradually blurred and faded. After ∼230 nm of TbAs growth, as shown in Fig. 1(c), the {001} streaky pattern completely disappeared and only the {221} diffraction spots were observed. In addition, a weak polycrystalline ring pattern was formed. No further changes in the RHEED pattern were observed throughout the TbAs growth. This suggested the preferential growth of the {221} crystal orientations rather than the {001} orientation. One explanation for this observation is that the {221} planes have lower surface energies than {001} in rocksalt TbAs. Another hypothesis is that the compressive strain caused by the lattice mismatch prevents adatom exchange diffusion at the step edges.²⁹ This increases the Eherlich–Schowebel barriers³⁰ that make lateral coalescence of the {001} TbAs islands more difficult. This is consistent with our observations of the island growth mode at the initial stage of (001) TbAs deposited on GaAs, as shown in Fig. 1(a). The inhibited lateral coalescence of {001} islands and the preferential growth of mixed {221} crystal orientations eventually caused the epitaxial quality of the film to deteriorate and led to a polycrystalline TbAs film, which is indicated in the RHEED transition from Figs. 1(a) to 1(c).

Since crystalline, epitaxial TbAs films are desired for both device applications and fundamental study, we wanted to determine whether the TbAs epitaxial quality could be improved by suppressing the growth of the {221} misorientations. Generally, the energy of an epitaxial film growth comprises the interfacial energy, the surface energy of the epilayer, and the strain energy introduced from the lattice mismatch.³¹ Since calculating the surface energy of the {001} and {221} TbAs on GaAs is complicated at this point, we chose to change only one parameter: the strain energy. To manipulate the strain condition, TbAs was grown on the (001) InP:Fe substrate. A lattice matched In_0.53Ga_0.47As layer is deposited on top of the (001) InP:Fe substrate to create a smooth and strain/relaxation free buffer layer. Noted that growing a TbAs film on a virtual ternary InGaAs substrate with the same lattice constant as TbAs was initially considered but was not conducted in this work, as the difficulty in interpreting XRD or optical data caused by a relaxed buffer layer containing dislocations is considered. Figures 1(e)–1(g) show the reconstruction pattern observed during the growth of TbAs on the (001) InP:Fe substrate along the $[11¯0]$ azimuth. Figure 1(d) shows the RHEED pattern observed during the initial deposition of ∼60 nm TbAs after the growth of In_0.53Ga_0.47As buffer on the InP:Fe substrate. A $(1×1)$ {001} reconstruction pattern was observed. This implies that the early growth stage of TbAs on the In_0.53Ga_0.47As buffer lattice matched to the InP substrate is dominated by {001} nuclei and their lateral coalescence. This {001} reconstruction pattern remained clear and streaky through the growth, indicating relatively large and flat {001} nuclei. A very dim and spotty diffraction pattern from the {221} nuclei islands appeared as the growth continued. Figure 1(e) corresponds to the RHEED image taken after deposition of ∼400 nm TbAs, where {221} diffraction spots were observed. There were no noticeable changes in the RHEED pattern throughout the duration of TbAs deposition. The TbAs total deposition measured ∼1150 nm.

The similar mixed orientation of TbAs on both InP and GaAs substrates indicates that the origin of {221} nuclei is most likely due to energetic reasons rather than structural strain. However, the smaller lattice mismatch of the InP substrate can suppress the growth of such {221} misoriented nuclei and leads to overall high crystal quality. This effect is attributed to the enhanced growth of {001} islands caused by lowering the Eherlich–Schowebel barriers by controlling the strain condition.^29,30

In addition to the in situ RHEED study and TEM, HR-XRD measurements were performed to further understand the epitaxial quality of the TbAs films on different III–V substrates. Figure 2(a) shows a wide range symmetric 2θ-ω scan of the TbAs grown on InP and GaAs substrates from 20° to 120°. Figures 2(b) and 2(c) show the 2θ-ω scan with a better resolution around the (004) and (006) diffraction peaks, respectively. For the growth of ∼1150 nm TbAs on InP, only (002), (004), and (006) diffraction peaks are observed in Fig. 2(a). The split of each diffraction peak can be clearly noticed, which is expected because the InP lattice constant exceeds the TbAs lattice constant by 1.6%. For the growth of ∼820 nm TbAs on GaAs, a small peak between the (006) TbAs and (006) GaAs diffraction peaks appeared besides the prominent {00h} peaks. This is also observed in the fine scan around the (006) diffraction peaks as shown in Fig. 2(c). This small peak likely results from the misoriented {221} defects; however, the peak is too noisy to draw further conclusion. This peak is not observed for TbAs grown on InP. We were not successful at measuring the {221} peaks of these samples with both symmetric and asymmetric XRD measurements; therefore, the fraction of {221} islands versus {001} cannot be quantitively determined. The difficulty in measuring {221} peaks can be attributed to one or both of the following: (221) is forbidden while (442) is equivalent to (006) in terms d-spacing; the {221} islands are small and embedded with a very short range of periodic crystal spacing. As shown in Fig. 2(b), 2θ peaks at 63.338° and 63.93° are from InP (or In_0.53Ga_0.47As) and GaAs, respectively. Therefore, the 2θ peak at 66.054° is attributed to TbAs, which corresponds to an out-of-plane lattice constant $a⊥=5.82Å$⁠. Due to the thicker TbAs film grown on InP, a weaker signal from the InP substrate is collected than that from the GaAs substrate. Since the as-measured out-of-plane lattice constant is the same as the unstrained TbAs lattice, the TbAs films grown on both substrates have relaxed. TbAs peak positions of the two samples are generally the same after considering the broadening and slight asymmetry in the InP substrate peak measured, which would cause a small shift in the peak assignment. Thus, the degree of relaxation between the two TbAs films should be very close.

The full width half maximum (FWHM) of the TbAs peaks can be determined from these HR-XRD scans, as summarized in Table I, which provides an important qualitative comparison on epitaxial quality and defect density of the TbAs grown on different substrates. For the TbAs sample grown on the GaAs substrate, the FWHM of the TbAs (004) peak is 1260 ± 142 arcs, while it measures as 680 ± 35 arcs for the TbAs layer grown on InP. The FWHM of the (006) peak of TbAs grown on InP is also much narrower than the one grown on GaAs. The large differences in the FWHM of the TbAs peaks cannot be simply ascribed to the difference in film thicknesses. Instead, the significantly narrower FWHM implies higher crystalline quality of the TbAs film when grown on InP substrates than on GaAs substrates and is consistent with the in situ RHEED characterization.

In order to examine the quality of the cube-on-cube epitaxy of TbAs on different substrates, in-plane XRD and a 360° phi scan on the {224} peaks of TbAs grown on GaAs and InP were obtained. Figure 3(a) shows the asymmetric 2θ-ω scan of the two samples around their (224) diffraction peaks. Given that the InP and GaAs (224) peak positions are 80.0336° and 83.7752°, respectively, the peaks at ∼80.8° are, thus, from TbAs, which is consistent with a lattice constant $a∥=a⊥=aTbAs=5.82Å$⁠. The out-of-plane measurements are, therefore, consistent with in-plane measurements, indicating full relaxation of the TbAs films. Similar to the out-of-plane measurements, a much smaller (224) peak FWHM of TbAs grown on InP than on the GaAs substrate is measured as well. The FWHM of the TbAs (224) peak is 1306 ± 18 and 2055 ± 377 arcs for the growth on top of InP and GaAs substrates, respectively. This is expected because the misoriented and faceted {221} islands behave as 3D defects and thus deteriorate the crystal ordering in both in-plane and out-of-plane directions. Figure 3(b) shows the 360° pole figure of the TbAs (224) diffraction peak of the two samples. The 90° rotational symmetry of TbAs grown on the (001) InP:Fe substrate was observed, where four poles are 90° apart from each other. This demonstrates a good cube-on-cube epitaxial relationship with no evidence of twisted grains or tilted growth in the TbAs film. However, similar 90° rotational symmetry was not observed for the TbAs grown on (001) GaAs as we rotated the sample stage along the normal axis, indicating that the majority of the TbAs crystal planes are tilted away from the (001) planes.

Finally, the optical properties of the TbAs films grown on different substrates were studied to understand the importance of suppressed crystal misorientations for potential applications. Since one of the potential applications of TbAs films is for plasmonics in short-wave to mid-wave IR, the reflection spectra for the two TbAs films grown on GaAs and InP substrates were measured, as shown in Fig. 4. The spectrum with higher reflection at long wavelengths is from the TbAs grown on InP substrate; the one with lower reflection at long wavelengths is from the TbAs film grown on GaAs substrate. The modeled data are also shown, which are obtained using a 4-layer T-matrix combined with the Drude model described previously. Good qualitative agreement between the experimental and modeled spectra has been achieved. From this model, the plasma wavelength of both TbAs films was determined to be 3.0 μm. On the experimental reflection spectra as shown in Fig. 4, the slope of the transition from low to high reflectivity of TbAs grown on InP is steeper than that on GaAs. This slope is indicative of the quality of a material, where a steeper slope usually implies a material with a lower scattering rate Γ. The scattering rate determined from the modeling was found to be 1.0 × 10¹⁴ rad/s for the TbAs film grown on the (001) InP:Fe substrate and 3.1 × 10¹⁴ rad/s for the TbAs film grown on the (001) GaAs substrate. We believe that the main scattering mechanism in these films is electron-grain boundary scattering^32–34 due to misoriented grains. By growing on a different substrate type, the size and density of misoriented grains are reduced, the mean free path of electrons is increased, and the scattering rate is therefore reduced. The approximately threefold reduction in the scattering rate highlights the importance of improved epitaxial quality of TbAs for potential plasmonic applications.

In this paper, we have detailed the heteroepitaxial growth and characterization of TbAs on two III–V substrates via MBE. It was found that the misoriented growth of TbAs on III–Vs can be well controlled by simply growing on a better lattice matched substrate. Moreover, by suppressing the growth of highly faceted TbAs, good cube-on-cube epitaxial arrangement of (001) TbAs has been maintained on the (001) InP:Fe substrate as opposed to the (001) GaAs substrate. Optical measurements suggest that a threefold reduction scattering rate of the as-grown TbAs film can be achieved. These results highlight the importance of suppressing crystal misorientations when growing dissimilar materials for potential device applications.

This material was based upon work supported by the National Science Foundation (NSF) under Award No. 1839056. The authors would like to thank Gerald Poirier from the Advanced Materials Characterization Laboratory at University of Delaware for help with the XRD equipment, and Yong Zhao, Jennifer Sloppy, and Chaoying Ni from W. M. Keck Center for Advanced Microscopy and Microanalysis at University of Delaware for help with the TEM measurements.

Stephanie Law is currently the Clare Boothe Luce Assistant Professor of Materials Science and Engineering at the University of Delaware (UD). She is an affiliate professor in the UD Department of Physics and Astronomy and the co-director of the UD Materials Growth Facility. She serves as an Associate Editor for the Journal of Vacuum Science and Technology. She received her B.S. degree in Physics in 2006 from Iowa State University and her Ph.D. in Physics in 2012 from the University of Illinois Urbana-Champaign. She worked as a postdoctoral researcher in the Department of Electrical and Computer Engineering at the University of Illinois Urbana-Champaign before joining the faculty at the University of Delaware in 2014. She has received the Presidential Early Career Award for Scientists and Engineers (PECASE) in 2019, the AVS Peter Mark Memorial Award in 2019, the Department of Energy Early Career award in 2017, and the North American Molecular Beam Epitaxy Young Investigator award in 2016. Her research interests include molecular beam epitaxy growth of semiconductors and van der Waals materials and heterostructures for optical applications in the infrared and terahertz spectral ranges.

Joshua M. O. Zide is a Professor and Graduate Program Director in the Materials Science and Engineering Department at the University of Delaware and the co-director of the UD Materials Growth Facility, an MBE growth user facility. He serves as an Associate Editor for the Journal of Vacuum Science and Technology. He received his B.S. with Distinction in Materials Science and Engineering from Stanford University and completed his Ph.D. in Materials at the University of California, Santa Barbara in 2007. Zide has received the International Thermoelectric Society Goldsmid Award (2007), the Young Investigator Award from the Office of Naval Research (2009), the North American Molecular Beam Epitaxy Young Investigator award (2011), the Department of Energy Early Career Award (2012), and the AVS Peter Mark Memorial Award (2014). His research interests include the molecular beam epitaxy growth of novel semiconductors and composite electronic materials for energy conversion and optoelectronic devices.