Polarization dependent photoluminescence and optical anisotropy in CuPt B -ordered dilute GaAs 1-x Bi x alloys

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I. INTRODUCTION
The dilute GaAs1−xBix alloy is thus far the most extensively investigated material among Bicontaining III-V semiconductors. 1,2Incorporation of large Bi atoms into the lattice produces perturbations mainly to the valence band states, which leads to the bandgap bowing, as well as large spin-orbit band splitting.The interest in this alloy arises from its potential and already implemented applications in near-to mid-infrared range optoelectronics,− lasers, photodetectors, solar cells. 1 Despite wide-scale physical properties investigations of bismides, only rather recently, in the early 2010s, were the first reports made on the observation of spontaneous CuPt-type atomic ordering in GaAsBi. 3,4e CuPt-type atomic ordering in conventional III-V alloys, most notably in GaxIn1−xP and GaAs1−xSbx, is well known from its discovery in the late 1980s. 5[12] A perfectly CuPtB-type ordered zinc-blende AB0.5C0.5 alloy is a superlattice of alternating AB and AC monolayers on (1 ̅ 11) or (11 ̅ 1) planes, conventionally termed as B+ and B− subvariants.
The ordered conventional III-V alloys have been predominantly investigated at the commensurate compositions x  0.5 where the ordering parameter can approach unity.On the other hand, dilute bismides are typically synthesized at Bi concentrations close to x  0.05.An expected value of the ordering parameter is thus one order of magnitude lower,  ~ 0.1, than in the conventional semiconductors.Another distinctive feature of bismides is that epitaxial GaAsBi layers are grown compressively strained due to a lattice mismatch with GaAs substrate, while the conventional ordered III-V alloys are usually deposited on lattice-matched substrates, namely GaInP on GaAs and GaAsSb on InP.
These features make the ordering analysis in dilute strained alloys a difficult task, which may be a reason for the lack of publications investigating relationships between the ordering and physical properties in bismides.4][15][16][17] The present article examines the influence of the ordering on GaAsBi optoelectronic properties.This is the first study that reports the optical anisotropy in GaAsBi alloys.This article is organized as follows.Firstly, the experimental methods are described.Then, a comprehensive structural analysis of the investigated bismide samples is presented.Polarized photoluminescence (PL) and spectroscopic ellipsometry results are then reported and discussed in regards to theoretical predictions for an ordered alloy.The article ends with summary and outlook.

II. EXPERIMENTAL
Samples S1-S5 were grown using a solid source Veeco GENxplor MBE system, equipped with Veeco As valved cracker and a conventional Dual Filament bismuth source.Semi-insulating GaAs substrates (AXT, Inc.) were employed.The substrate temperature was controlled by a thermocouple (TC) and also monitored with a kSA BandIT broadband pyrometry module (BandIT).The kSA 400 reflection high-energy electron diffraction (RHEED) system was used for in-situ surface characterization.Each substrate was outgassed at 200℃ in the load-lock and afterwards at 300℃ in the buffer chamber.The removal of native oxide was performed at 600-620℃ (BandIT reading) under As2 flux ~5×10 -6 Torr beam equivalent pressure (BEP).Samples S1-S5 included a nominally 100 nm thick standard-grown GaAs buffer layer.Growth of a GaAsBi layer in samples S1-S5 was performed at 400°C (TC reading), which corresponded to ~310°C BandIT reading.The initial conditions for GaAsBi layer growth in all samples (S1-S6) were first set by observing in RHEED surface reconstruction transitions on a calibration GaAs wafer at around 600°C.At such conditions, it was assumed that III/V atomic flux ratio was close to unity.To maintain the stoichiometry conditions for the growth of bismides, the flux of As2 was reduced by closing the As cracker valve aperture by 1-2 mils.The bismide layer growth rate in all samples was kept at ~500 nm/hr.The bismide sample S1 was deposited using Bi BEP 6.0×10 -8 Torr.GaAsBi layer in S3 was grown at the Bi BEP of 7.6×10 -8 Torr, while samples S2, S4, and S5 were grown by keeping identically Bi BEP at 6.7×10 -8 Torr.
Incorporation of Bi in the lattice could be influenced by the distinct substrate offcut angles.Sample S6 was synthesized using an SVT-A MBE chamber equipped with the same sources and As-cracker as in the Veeco chamber.A p-type exact (001) Ge substrate (AXT, Inc.) was employed, and native oxides from the substrate were removed at 640°C (TC).The first part of the GaAs buffer layer, approximately 5 nm thick, was grown at 400°C using migrationenhanced epitaxy.The substrate temperature was then increased to 500°C and a further 50 nm of GaAs buffer was deposited.The GaAsBi layer was grown at 350°C (TC) with the Bi/Ga ratio 0.35-0.37.X-ray diffraction (XRD) data was acquired by a Rigaku Smartlab diffractometer equipped with 9 kW rotating Cu anode X-ray generator (Kα1 line), scintillation detector SC-70, and a linear Dtex/Ultra detector.Reciprocal-space mapping (RSM) of ( 004) and (115) reflections was used to evaluate layer relaxations, lattice parameters, and Bi concentrations, using lattice constants GaAs=5.653Å, GaBi = 6.324Å. Superlattice ½{111}-type reflections were acquired in skewsymmetric configuration.
An aberration-corrected JEOL-JEM ARM200CF scanning transmission electron microscope (STEM) operated at 200 kV was used for imaging.Probe convergence semi-angle was set to 22 mrad, high-angle annular dark-field (HAADF) detector inner and outer semi-angles were set to 90 and 370 mrad, respectively.For low-angle annular dark-field (LAADF), the inner and outer detector semi-angles were 40 and 160 mrad, respectively.Additional imaging was performed in a Nion Ultrastem 200 operating at 100kV with a probe semi-angle of 32 mrad and HAADF detector semi-angles of 70 and 200 mrad.All data were processed with Gatan Digital Micrograph GMS3.Cross-sectional lamella samples, nominally 20-25 nm thick, were prepared using focused-ion beam (FEI Helios Nanolab 650).
Sample surface morphologies were characterized by atomic force microscopy (AFM), using a Dimension 3100 SPM system with a Nanoscope IVa controller (Veeco Instruments Inc., USA).
Multiple sample areas ~1.5x1.5 µm 2 in size were scanned.Surface morphology and elemental composition was also examined using scanning electron microscopy (SEM, FEI HELIOS Nanolab 650) equipped with an energy dispersive X-ray spectrometer (EDX) from Oxford Instruments.
Photoluminescence measurements were carried out using a DPSS laser (532 nm) as an excitation source, with the intensity kept at ~ 5 kW/cm 2 , a 0.4 m monochromator SPM-2, and a thermoelectrically-cooled InGaAs photodetector.To minimize polarization effects of the monochromator grating, the sample axes [110] and [1 ̅ 10] were rotated relative to the monochromator slit by 45.The Glan−Taylor prism with extinction ratio < 5×10 -6 was used as polarization analyser placed in front of the monochromator slit.Low temperature PL spectra were measured by mounting samples on the cold finger of a liquid nitrogen cryostat.
The polarized transmittance spectra and spectra of normalized Mueller matrix components were recorded with a dual rotating-compensator ellipsometer RC2 (J.A. Woollam, Co., Inc.) at the normal light incidence.After calibration, a straight-through measurement of a Mueller matrix in the air was performed.All recorded Mueller matrix components were found to be within 0.005 of the ideal value.The linear in-plane birefringence and linear dichroism spectra were determined from the experimental Mueller matrix spectra by the analytic inversion method. 18

A. SAMPLE CHARACTERIZATION
Six GaAsBi samples, labelled S1−S6, were grown for this study, all epitaxially deposited by MBE (see Experimental section for more details).Samples S1−S3 were deposited on exact (001) GaAs substrates, while GaAs substrates with 2° and 6° offcuts toward the [1 ̅ 10] were used for samples S4 and S5, respectively.An exact (001) Ge substrate was employed for sample S6, which also included a nominally 50 nm thick GaAs buffer layer deposited on Ge.
The sample information is summarized in Table I.X-ray diffraction rocking-curve (XRD-RC) measurements were used to examine the structural quality of the bismide layers and determine their thickness [see Fig. 1(a)].As can be seen from the sharp peaks and resolved thickness fringes, high-quality single-phase epitaxial layers were achieved in samples S1−S5.XRD reciprocal-space mapping (RSM) showed that samples S1−S4 were fully biaxially compressively strained to GaAs substrates, while sample S5 showed ~ 2% lattice relaxation.GaAsBi is known to be resilient to lattice relaxation and layers well in excess of the critical thickness for dislocation nucleation are often observed.The bismuth concentrations, accounting for lattice relaxations, are presented in Table I 2 .The droplets on S2 were found to be composed of Ga, as was determined using energy-dispersive X-ray spectroscopy (EDX).Sample S5, on the other hand, displayed circular pits with a density of ~ 2 µm -2 .Among samples S1−S5, only S3 displayed phase-separated GaAs-like domains within the bismide layer, as was revealed by crosssectional STEM.The phase separation could be associated with higher surface roughness in S3.High-resolution STEM and STEM-EDX of the bismide layers showed no Bi segregation in S1−S5.1][22] This leaves atomic-scale configurational effects to be responsible for the optical anisotropy.Atomic-scale sample characterization and XRD CuPt-ordering measurements are presented next.

B. ATOMIC ORDERING
So-called skew-symmetric XRD-RC measurements were performed to probe the presence of ½{111}-type superlattice reflections associated with CuPt-type ordering. 23 Sample S4 grown on a 2° offcut substrate manifested the largest intensity of superlattice reflections.We note that no MBE growth optimizations were undertaken for the investigated samples to maximize the CuPt-type ordering.Our previous atomically-resolved STEM-EDX ordering parameter evaluation yielded a η = 0.07 value for a sample with 5.5 % Bi. 13,14 Although the ordering parameters for the present S1-S6 samples were not examined by EDX, one can expect them to be of the order of η ~ 0.1.Next, sample S6 is examined, which together with S1-S5, was used in the optical anisotropy analysis.This sample provides an additional test for ordering-induced optical effects because it contains domains whose CuPt-type ordering axes are rotated in a well-defined manner.A low-magnification LAADF image of the sample is shown in Fig. 2(c) with indicated Ge substrate, GaAs buffer, GaAsBi layer, and a protective Pt cap.Sample S6 is comprised of antiphase domains (APDs), the boundaries of which are marked by dashed vertical yellow lines.

Atomic
The APDs arise in the GaAs buffer layer epitaxially grown on the (001) Ge substrate due to mixed nucleation of Ga and As atoms on the non-polar Ge surface. 13,24As the growth proceeds,  A region containing two GaAsBi APDs near the GaAs buffer layer is shown in Fig. 3 APDs.This also explains the XRD observation of four ½{111}-type superlattice reflections in S6.

A. SCHEME OF OPTICAL TRANSITIONS
The spontaneous CuPt-type ordering in the conventional zinc-blende alloys and its influence on the electronic structure and optical properties has been extensively studied by Zunger, Wei, Mascarenhas, Zhang, and others. 5,6,8,25The CuPt-type ordering changes the cubic zinc-blende point symmetry Td to the trigonal C3v one.The perturbative part of the Hamiltonian, describing an influence of the ordering, has the same form as that of the uniaxial strain along the ordering direction, 25 namely the [1 ̅ 11] axis for the CuPtB+ subvariant.For illustrative purposes, Fig. 4( ordering axis rotates further away from the sample surface normal.The PL polarization ratio becomes  = 3/[1 + √2 sin(2) + sin 2 ], which is 2.7 and 2.3 for typical 2 and 6 offcuts, respectively. 6e normal-PL polarization dependence can be suppressed by epitaxial strain, which also lifts the vb degeneracy of zinc-blende semiconductors due to strain-induced vb splitting, Δe.
However, the strained layer becomes optically uniaxial with the optical axis perpendicular to the layer.Hence, in the presence of epitaxial strain and in the absence of ordering no polarization dependence is expected for normal light propagation.Therefore, in a general case, when both the CuPt-ordering and epitaxial strain are present, the normal-PL polarization dependence is expected to occur when the ordering-induced splitting is of the same order or larger than that due to epitaxial strain, Δc≳Δe.

B. POLARIZED PHOTOLUMINESCENCE
The polarized PL measurements along a sample-surface normal were performed at room (RT, 300 K) and liquid nitrogen (80 K) temperatures.Representative PL spectra of samples S1, S4, and S6 are shown in Fig. 5.7][28] The PL intensity of GaAsBi with increasing Bi concentration tends to be weaker and PL spectra become noisier.This is also evident in the non-uniform lattice of S6 composed of APDs.GaAsBi alloys manifest pronounced exciton localization effects, which are usually evident at low temperatures in the temperature dependence of PL.A typical feature is the so-called PL "s-shape" due to exciton hopping and trapping at the localized Bi-related density of states near the VB maximum. 29,30 seen in Fig. 5, the samples grown on GaAs substrates consistently show higher intensity for The RT polarized PL ratio  =  [110] / [1 ̅ 10] in samples S1−S5 is in the range 1.6−2.4.At liquid nitrogen temperature,  values remain in a similar range of about 1.5−1.9.We note that the PL spectra at 80 K show a complex inner structure most likely associated with the "s-shape".The red-blue-red shift typically occurs near this temperature in GaAsBi alloys, and so determination of the polarized PL ratios could be inaccurate at this temperature.There are several reasons why the observed R ~ 2 parameter may deviate from the theoretical.Firstly, the R = 3 value corresponds to unstrained epitaxial layers.As mentioned above, in the presence of epitaxial strain the polarization dependence expected to decrease.7,25 Also, at RT the E0,2 optical transitions may still occur and would tend to decrease the R value.Other factors, such as excitonic band-edge transitions and the size of ordered domains could likewise influence the polarization ratio.6 Considering that large epitaxial vb splitting, as compared to an ordering-induced one, would tend to suppress the R value, it is instructive to examine their possible magnitudes.The strains and epitaxial splitting Δe in the bismide layers can be easily calculated for given values of elastic constants C12/C11 = 0.46 and the deformation potential b = −2 eV, which for dilute GaAsBi can be taken to be equal to those of GaAs.31,32 The calculated epitaxial splitting is about Δe ~ 45 meV at the Bi concentration x = 0.05.Therefore, the ordering-induced splitting in the investigated dilute bismide samples should be of the order Δc ~ 40 meV or more.
4][35] Since the effective vb splitting due to ordering and epitaxial strain is expected to combine as a geometric mean rather than add linearly, the experimental Δ ~ 60 meV value supports the Δc ~ 40 meV estimate. 25The ordering-induced splitting Δc ~ 40 meV in bismides is rather large, as compared to its value in the conventional semiconductors.Indeed, Δc in ordered GaInP alloy is predicted to be only ~ 2 meV at the order parameter  = 0.1. 36At the  ∥ [1 ̅ 10] polarization, the optical density experiences a sharp increase at photon energies of about 1.17, 1.06, and 1.07 eV for samples S1, S3, and S4, respectively, which coincide with the spectral positions of the PL peaks (see Eg values in Table 1) with an accuracy of a few percent.A sharp increase of optical density begins at higher photon energies of about 1.23, 1.12, and 1.13 eV (for samples S1, S3, and S4, respectively), which correspond to the expected onsets of the E0,2 optical transitions from the lower vb branch to the conduction band.
This phenomenological determination of the E0,1 and E0,2 energies from spectral positions of peaks in optical density derivative spectra allows to estimate the vb splitting,  = E0,2 − E0,1, which is found in S1-S5 samples to be about  ~ 60 meV.
To check the influence of atomic ordering on the optoelectronic properties of bismides, we indicating polarization dependent refractive index. 37Any possible higher energy features in these spectra are obscured due to absorption in GaAs substrate.
The transmission-mode spectroscopic ellipsometry measurements of transmittance and birefringence-dichroism spectra are comparatively easy to perform and can be used as a test for the presence of CuPt-type ordering.We have carried out the test on more than 10 bismide samples MBE-grown under various growth conditions and Bi concentraions (not shown here), with the result that all of them manifested polarization anisotropy.This preliminary observation suggests that the spontaneous atomic ordering in bismides is widespread.

V. SUMMARY AND OUTLOOK
In this work, a structural and optical study of the dilute GaAs1-xBix alloys was carried out reporting spontaneous ordering-induced optical anisotropy effects.The epitaxial bismide layers MBE-grown on exact (001) substrates manifested both B+ and B-variants of CuPtB ordering, while the bismides grown on 2° and 6° offcut GaAs showed a single B+ variant.We also analyzed a bismide layer grown on an exact (001) Ge substrate, which included a GaAs buffer layer.The bismide was shown to be composed of CuPtB ordered columnar APDs, whose ordering axes are rotated by 90° with respect to each other around the growth axis.
The optical anisotropy was revealed in samples grown on exact and offcut (001) GaAs substrates via polarized photoluminescence and transmittance spectra, as well as by birefringence and linear dichroism measurements.The observed polarization dependence in all the optical measurements agreed with theoretical predictions for the CuPt ordering.No optical anisotropy was observed in the bismide sample composed of APDs, in which the anisotropy is not expected.Multiple sample surface and bulk characterization techniques, including SEM, AFM, XRD, and cross-sectional STEM, were employed to exclude other possible sources of structural anisotropies that may cause these optical effects.Atomic-scale HAADF analysis of Bi atom distribution and XRD suggests that the ubiquitous CuPtB ordering is responsible for the optical anisotropy.Further work will be needed to clarify the magnitude of the orderinginduced vb splitting in GaAsBi alloys, and to better understand the reasons for such pronounced effects at dilute Bi concentrations.Polarization anisotropy is an important factor to consider for future development of GaAsBi-based lasers and photodetectors.These findings elucidate spontaneous ordering effects in GaAsBi and encourage its further investigations.

Fig 2 .
Fig 2. STEM cross-sectional sample analysis.(a)-(b) Atomic-resolution HAADF images of GaAsBi sample S4 grown on offcut substrate and sample S1 grown on exact GaAs substrate.(c) Lowmagnification LAADF image of sample S6 showing numerous anti-phase boundaries indicated by yellow dashed lines.(d) Atomic-resolution HAADF image of S6 near a kinked {110}-type anti-phase boundary.Note the reversal of dumbbell polarity across the boundary.
GaAs grains coalesce forming anti-phase boundaries (APB), which then propagate into the epitaxial GaAsBi layer.Statistically equal amounts of either type of APDs nucleated from Ga or As atoms occur in this sample.Reasonably regular-sized 100−400 nm wide columnar APDs are seen with predominant {110}-type interface planes.A representative GaAsBi APB is shown in HAADF image [Fig.2(d)],where Bi atoms are seen to segregate along a kinked {110}-type boundary.A closer look shows that a polarity of group-III and group-V columns is reversed in the two crystallites.This can be seen by noting a polarity of the closely-spaced atomic-columns, so-called "dumbbells", oriented along the growth direction.Group-V columns with Bi in them are positioned on the top of each dumbbell in the right-hand side grain and are on the bottom in the left-hand one.

Fig 3 .
Fig 3. (a) Image derived from S6-sample HAADF micrograph near anti-phase boundary (APB) using pairs of ½{111} reflections, which are outlined in the Fourier transform inset.(b) Atomic model of the APB region.
figure was produced from a HAADF image of S6-sample by applying two pairs of circular photoluminescence will be determined by the E0,1 optical transitions to the upper, hh, vb branch.
the  ∥ [110] polarization as compared to the  ∥ [1 ̅ 10] one, while no polarization dependence is observed for sample S6.Since S6 is composed of crystallites whose ordering B-axes are rotated in-plane by a right angle, no polarization dependence is expected.Photoluminescence polarizations parallel to directions 45° and 135° from [110] were also tested, showing the same PL intensities for all samples S1−S6.The observed PL polarization dependence agrees with theoretical predictions for CuPtB-type ordered layers.

Table I .
Parameters of investigated samples: the type of substrate, GaAsBi layer thickness d, bismuth concentration, room-temperature bandgap Eg, and sample surface roughness Rq.GaAs substrate offcut angles are indicated for samples S4 and S5.
2,19XRD-RSM was not performed on S6 since the sample was of polycrystalline nature.