Optical properties of GaAs1−xBix/GaAs quantum well structures grown by molecular beam epitaxy on (100) and (311)B GaAs substrates

In this work, the electronic bandstructure of GaAs1−xBix/GaAs single quantum well (QW) samples grown by molecular beam epitaxy is investigated by photomodulated reflectance (PR) measurements as a function of Bi content (0.0065 ≤ x ≤ 0.0215) and substrate orientation. The Bi composition is determined via simulation of high-resolution x-ray diffraction measurement and is found to be maximized in the 2.15%Bi and 2.1%Bi samples grown on (100) and (311)B GaAs substrates. However, the simulations indicate that the Bi composition is not only limited in the GaAsBi QW layer but extends out of the GaAsBi QW towards the GaAs barrier and forms a GaAsBi epilayer. PR spectra are fitted with the third derivative function form (TDFF) to identify the optical transition energies. We analyze the TDFF results by considering strain-induced modification on the conduction band (CB) and splitting of the valence band (VB) due to its interaction with the localized Bi level and VB interaction. The PR measurements confirm the existence of a GaAsBi epilayer via observed optical transitions that belong to GaAsBi layers with various Bi compositions. It is found that both Bi composition and substrate orientation have strong effects on the PR signal. Comparison between TDFF and calculated optical transition energies provides a bandgap reduction of 92 meV/%Bi and 36 meV/%Bi and an interaction strength of the isolated Bi atoms with host GaAs valence band (CBiM ) of 1.7 eV and 0.9 eV for (100) and (311)B GaAs substrates, respectively.


Introduction
GaAs 1−x Bi x has been intensively studied in the last years due to its remarkable properties [1][2][3] and its potential applications in near and mid-infrared optoelectronic as well as spintronic devices [4,5]. Replacing a small fraction of As with Bi in the host GaAs produces a large reduction in the bandgap energy of 60-90 meV/%Bi, accompanied with a rapid increase in the spin-orbit-splitting energy (Δ so ) [6,7]. The bandstructure of GaAsBi alloy can be determined using the valance band anticrossing (VBAC) model [8,9]. This model originally predicted that the localized Bi level affects solely valance band, while more recent studies have revealed that the conduction band (CB) is also affected from the localized Bi level by a 28 meV/Bi%, in line with virtual crystal approximation (VCA) [6]. Moreover, since there is a composition-dependent lattice mismatch between GaAs and GaAsBi, strain-induced effects on the CB and valence band (VB) should also be taken into account when determining the bandstructure of GaAsBi. While GaAsBi has been widely recognized as a promising material for novel optoelectronic and spintronic applications; epitaxy of GaAsBi is not mature yet. Due to the significant difference in atomic size between As and Bi, Bi cannot be incorporated in GaAs at high growth temperatures and the quality of Bi-containing alloys is critically controlled by the As/Ga ratio, Bi/As ratio and the growth temperature [10]. As it has been experienced in all variations of highly mismatched alloys, GaAsBi alloys have the tendency to incorporate defects, atomic clusters as well as inhomogeneities due to the unconventional growth conditions required for Bi incorporation [11][12][13]. These defects create localized levels above the VB and deep levels in the bandgap of GaAsBi. There have been some attempts to improve the crystal quality of grown alloys [14,15]. It has been recently reported that the incorporation of a small amount of nitrogen compensates for strain, resulting in enhanced crystal quality with the benefit of further bandgap reduction. Furthermore, it has been reported that growing GaAsBi on GaAs with different orientations rather than [100] enhances the photoluminescence (PL) intensity, but also modifies the bandgap energy due to the crystal direction-dependent physical parameters such as strain, effective mass etc [16,17]. However, there have been limited reports on GaAsBi epilayers grown on differently oriented GaAs substrates. Henini et al and Kudrawiec et al demonstrated that for the same Bi flux during molecular beam epitaxy (MBE) growth, incorporation of Bi into GaAs is larger in (311)B than in (100)-oriented GaAs substrates [18,19]. Patil et al investigated multiple GaAsBi quantum wells (QWs) grown on (411)A and (411)B GaAs and observed that both PL intensity and Bi incorporation were enhanced in (411)A orientation at high As 4 beam equivalent pressures [20].
In this study, the electronic bandstructure of GaAs 1−x Bi x /GaAs QW samples grown on (100) and (311)B substrates with various Bi compositions are determined by room temperature photomodulated reflectance (PR). Highresolution x-ray diffraction (HR-XRD) results are used to interpret the obtained optical transitions from PR spectra. The strain-included VBAC model together with VCA is utilized for calculating optical transition energies. The transition types and energies are obtained for various Bi contents and substrate orientations.

Sample structure and growth procedure
We have studied six GaAsBi samples with various Bi compositions. All samples were grown by MBE with the same growth conditions to understand the effects of the substrate orientation and Bi incorporation on the optical properties of the samples. Three samples were grown on semi-insulating (100) GaAs, and the others were grown on semi-insulating (311)B GaAs substrates. The growth of GaAsBi QW samples started with a 370 nm thick GaAs buffer layer. The first 300 nm was grown at 580°C with a high As overpressure; after which the growth temperature was decreased to 320°C during growth of an additional 70 nm of GaAs to enhance the incorporation of Bi in the QW. This was followed by a 10 nm thick GaAsBi QW layer and a 50 nm GaAs cap layer grown at the same temperature (see figure 1). The growth rate was 0.4 μm h −1 for all layers. For efficient Bi incorporation, the atomic As/Ga flux ratio for the QW and cap layer was kept close to the stoichiometric value.

Experiments
To determine the Bi composition of the samples, HR-XRD measurements were carried out using a Bruker D8 Discover x-ray diffractometer. An asymmetric 2-bounce Ge 220 channel-cut monochromator was used to select the Cu Kα 1 line at λ=1.540 56 Å and to collimate the incident X-ray beam. From the experimental data, the change of the Bi concentration profile through the sample was determined by simulations based on dynamical scattering theory. Unfortunately, for only two samples, the XRD diffraction patterns revealed well-defined fringes; therefore Bi compositions could be determined for only two samples, and PR measurements were utilized to determine Bi compositions for the other four samples.
PR in the bright configuration mode was carried out by using a 650 nm diode laser as a pump source and a 100 W halogen lamp as a probe source at room temperature. The laser light intensity was kept at 0.3 W cm −2 . The reflected light was dispersed by a 0.5 m monochromator, and an edge filter (Newport FSQ-RG715) was placed in front of the entrance slit of the monochromator to avoid second-order of the spectrum. The signals were detected by conventional lock-in detection techniques.
2.3. Analysis method of PR results for determination of optical transition energies PR signal was analyzed by using low electric field TDFF given as [21,22] where C, AE, E, E J and Γ are the amplitude, phase, photon energy, optical transition energy, and line-broadening, respectively. The type of critical point depending on the dimension of the structures is represented as n j , and its values are 3 and 2.5 for the QW and bulk layers, respectively. The modulus of the individual resonance (MIR) or magnitude of the complex quantity can be obtained from equation (1) with the parameters taken from the fitting as MIR shows the optical transition starting and finishing point. The peak position of MIR corresponds to the optical transition energy. In this study, the observed PR spectra consisted of overlap of band-to-band and localized or inhomogeneityrelated transitions. In the analyzing of the localized or inhomogeneity related transition procedure, for the sake of the simplicity, n j is chosen to be 3 or 2.5 depending on transitions in epilayer or QW. This choice slightly affects the analysis of the PR spectra and determined parameters. The details of the fitting procedure can be found elsewhere [22][23][24].

Theoretical model for determination of optical transition energies
To assign the optical transition energies observed in the PR spectra, we calculate the optical transition energies in GaAsBi QW structures. Since there is a lattice mismatch between GaAs and GaAsBi, in order to calculate the effect of Bi on the bandstructure of strained GaAsBi, we first determined the effect of strain on the band edge energies. To include strainrelated modifications, the Pikus-Bir Hamiltonian was used [25]. According to VCA, for the strained bulk GaAsBi grown on (100) GaAs, modified band-edge energies at k=0 are given as

GaAs Bi LH
GaAs 100 x x 1 where x is Bi composition, a and k are the VCA contributions to the Bi-induced changes to the CB, and heavy hole (HH)/light hole (LH) bands, respectively. E , CB GaAs E HH GaAs and E LH GaAs are CB, HH and LH band edges of bulk GaAs, respectively. E HH GaAs and E LH GaAs are taken as 0 eV. While the localized Bi level is far from CB edge; it has been shown that Bi also affects the CB edge and a contains the effect of localised Bi level [25,26]. The value of k is taken as 1.01 eV and a is taken as 2.82 eV [25]. a CB is the hydrostatic deformation potential coefficient for CB. e xx and e yy are in-plane, and e zz is out-of plane strain parameters, which are defined as where d v is the deformation potential, and C 44 is the elastic constant for VB of GaAs. The effect of localized Bi levels on the VB edge of GaAs was determined using the VBAC model. As a result of the VBAC model, VB splits into two levels, E + and E − , where E + represents the VB edge of GaAsBi [8,9,11]. By using the VBAC model and equations (4) and (5), the HH and LH energies were determined as where x is the Bi concentration, E Bi is the isolated Bi impurity energy level below VB maximum (−0.183 eV) [25]. C BiM is the interaction term of the VB of the host material with isolated Bi impurity level. In equations (10) In the second step, the quantized energy levels in GaAsBi QW are calculated by using finite QW approximation where CB and VB discontinuities are obtained using equations (3)- (11). In the calculations, the parameters were taken from [27] for GaAs and [28] for GaAsBi, except for the effective mass of samples grown on (311) [29]. The parameters used in the calculations are given in table 1. Some parameters used in the calculations are unknown for GaAsBi alloys in the literature; therefore for unknown GaAsBi parameters, we considered parameters of GaAs [7]. Figure 3 shows HR-XRD diffraction curves (2θ-ω scans) of two samples, whose HR-XRD results exhibit well-defined fringes around the sharp (100) and (311) diffraction peaks. This is an indication of a smooth interface between the epitaxial layer and substrate. The experimental diffraction curves were simulated by using dynamical scattering theory [31]. The best fits are shown as solid lines in figure 3. We find the Bi contents as 2.15% and 2.10% for the GaAsBi QW layer of the samples grown on (100) and (311)B substrates, respectively. As seen in the inset of figure 3, Bi composition is not limited in the QW layer, but spreads out from the GaAsBi QW, resulting in the formation of a GaAsBi epilayer. The thickness of the Bi-containing layers for both samples is much larger than the nominal GaAsBi QW thickness. Therefore, the Bi-containing layers behave like an epilayer, not exactly like a QW. Since the GaAs cap was grown at the same temperature as the GaAsBi QW, it can be thought that Bi atoms continue to move through the GaAs cap layer. The thickness of the Bicontaining layers is almost the same for both samples; however, the amount of Bi in the GaAs cap in the sample grown on (311)B GaAs is higher. Referring to the obtained Bi composition distribution shown in the inset of figure 3(a) and (b), the calculated bandgap and subband energy levels of the samples grown on (100) and (311) GaAs is illustrated in figure 4. The band alignment of the GaAsBi QW is type I as seen in figure 4, according to our calculations. It is wellknown that both low-temperature growth GaAs and GaAsBi contain localized levels [11,32]; therefore we also included   figure 4. It is worth noting that the localization energy levels are schematically represented, not calculated. Since we could not observe well-defined fringes in HR-XRD spectra of the other samples, the band alignment of the other samples was calculated by exploiting Bi composition obtained from TDFF analyzes of PR spectra given in the next subsection. The PR spectra are divided into two sections shown in figure 5. The right part of the PR spectrum at higher energies separated with a hatched area is related to PR signal from GaAs layers. We first discuss the GaAs-related section of the PR results. The PR amplitude of GaAs is much higher than that of GaAsBi grown on (100) GaAs; therefore, GaAsBirelated PR part at the left side of the hatched area was multiplied with a factor higher than one for clarity. On the contrary, the PR amplitude of GaAs grown on (311) GaAs is comparable with that of GaAsBi. GaAs-related PR signal has two distinct transition peaks for all samples except for the one with 1.4% Bi composition. The peak energies are slight deviates to lower or higher energies than the ideal bandgap energy of GaAs. Because of low-temperature growth conditions, two peaks at slightly lower and higher energies than the ideal bandgap energy of GaAs have been reported for lowtemperature growth GaAs [33]. Therefore, we believe that the peaks located at lower or higher energies originate from lowtemperature growth of the top GaAs layer. We do not further discuss the GaAs-related PR spectrum since it is out of the scope of this paper.  To analyze GaAsBi-related peaks, we consider both GaAsBi epilayers due to the extended Bi composition out of QW toward the top GaAs layer and GaAsBi QW layer as shown in figure 3. The TDFF-fitted PR and the calculated transition energies for (100) and (311)B GaAsBi/GaAs QW samples are given in tables 2 and 3, respectively. By using the determined Bi composition values from the HR-XRD results, the C BiM parameter is found from TDFF-fitted PR spectrum for the samples with 2.15 and 2.10% Bi grown on (100) and (311)B GaAs, respectively. It is known that C BiM does not depend on alloy composition; therefore we use the same C BiM parameter in the calculations to calculate optical transitions energies and find Bi composition for the other four samples. The C BiM parameter is found to be 1.7 eV for the GaAsBi with 2.15% Bi composition grown on (100) GaAs substrate which agrees with the recent values obtained for GaAsBi on (100) GaAs. [6,7,25,34]. C BiM parameters are determined as 0.9 eV for (311)B oriented samples, which are lower than the C BiM value for the sample grown on (100) GaAs. The electronic bandstructure and surface atomic bonding environment of the (311)B sample are different from conventional (100) GaAs materials, which change some properties of the materials such as the atomic potential, effective mass and atomic interaction. It is worth pointing out that the (311)B plane consists of both (100) and (111) surfaces [29,30]. The (311)B surface terminates with As atoms having three dangling bonds substrates. Black solid lines represent experimental results, and red and blue crossed-circle represent TDFF -fitted PR results of GaAsBi and GaAs layers, respectively. The MIR peaks are given below PR spectra. The hatched area is used to separate GaAs and GaAsBi layers PR signal. The results for the samples grown on (100) substrate are multiplied by a factor for clarity. Since the C BiM is a measure of the strength of the interaction between Bi level and GaAs CB, the reduced composition dependence of the bandgap of GaAsBi for (311) GaAsBi is attributed to the smaller C BiM value.

PR results
As seen from table 2 for the sample with 2.15% Bi composition grown on (100) GaAs substrates, the calculated E1-HH1 transition energy agrees with the TDFF-fitted PR results, whereas the calculated E1-LH1 transition energy of 1.27 eV does not match with experimentally found 1.31 eV transition energy. However, when we consider figure 4(a), it matches with the bandgap energy of 0.7%Bi containing GaAsBi epilayer; therefore this transition is ascribed to the bandgap of GaAsBi epilayer with 0.7% Bi composition in table 2. The bandgap of this epilayer is determined from bulk band edge energy of GaAs as formulated in equations (3)- (7).
It is evident that for all samples grown on (100) GaAs, the E1-HH1 transitions are matched with the TDFF fitted results, but the higher energy transitions do not match with the calculated E1-LH1 transition. Using the Bi compositions obtained from HR-XRD results, the higher energy transitions than E1-HH1 transitions are attributed to the bandgap energy of GaAsBi epilayers with 0.2%Bi and 0.5%Bi for 0.65%Bi and 1.9%Bi containing GaAsBi samples, respectively. However, considering that the top GaAs layer is grown at lowtemperature, the transition energy attributed to GaAsBi with 0.2%Bi composition may also arise from a localized levelrelated transition in GaAs. Furthermore, this transition cannot be ascribed for E1-LH1 since the line width of 1.405 eV transition as 20 meV is too narrow to include the E1-LH1 transition. Due to the uncertainty, a question mark is added in table 2 for the 0.65%Bi containing sample.
PR linewidth tends to increase with increasing Bi composition and the linewidth is broader compared to reported values [11,35,36], which can be related to the non-uniform Bi distribution in the samples as well as Bi-related localized states such as Bi pair, cluster and relatively low band-edge fluctuations [11,12].
As seen from table 3 for the 2.1%Bi containing sample grown on the (311)B GaAs substrate, the TDFF fitted results match with the calculated E1-HH1, E1-LH1 and E1-HH2 transition energies. The HH and LH separation is quite small due to a lower strain effect on the band-edge compared to the samples results grown on (100) substrate. Although E1-HH2 transition is forbidden in principle, it is possible to observe this transition in QW structures due to the broken crystal symmetry [37]. The three calculated transition energies are very close to each other; therefore cannot be separated at the PR spectrum due to broad line-width as 90 meV. According to optical transition calculations, the peak energy of 1.393 eV may be ascribed for 0.9%Bi containing extended layer for 2.10%Bi containing samples. Moreover, considering lowtemperature growth GaAs, the transition energy may also be ascribed to localized level-related transition. Due to this uncertainty, the question mark was added in table 3 for the 2.10%Bi containing samples. Similar results are obtained for the other samples. As for the 0.8%Bi containing samples, 1.413 eV transition energy may also be related to E1-HH2 transition in GaAsBi epilayer or localized level-related transition in low-temperature growth GaAs top layer. A composition dependent characteristic of the quantized level sequence in QW is observed for the samples grown on (311)B GaAs substrate. Batty et al [30] showed that the GaAs effective HH mass in GaAs/AlGaAs heterostructures is twice as large as that of (100) GaAs. Nötzel et al reported for GaAs/AlAs that effective HH mass is larger at directions with higher Miller indices than at [100] [29]. This significant change in HH effective mass shifts the HH2 below LH1 quantized level in the QW for the 2.1%Bi containing (311)B oriented samples (see table 3). Since the strain effect on the band-edge of the (311)B samples is lower than the samples grown on (100) substrate, the separation of the HH1 and LH1 is smaller, which also contributes to facilitate the HH2 level to move above LH1. As a conclusion, increasing Bi composition causes a change in the sequence of the quantized levels in the QW, which is not observed for the samples grown on (100) GaAs.

Conclusion
The composition dependence of the bandgap energy of GaAsBi grown on (100) and (311)B GaAs has been calculated with the VBAC model, including strain-induced effects. The PR transitions have been well fitted by the TDFF. Due to the strain effect and smaller effective mass values at [100], HH and LH quantized energy levels are well-separated from each other, and the only quantized E1-HH1 transition has been observed for the samples grown on (100) substrate. We have observed higher energy transition, E1-HH1, E1-LH1, E1-HH2, due to the smaller strain and higher effective mass values at [311] for the samples grown on (311)B. We have found that the effective bandgap energy decreases with increasing Bi concentration for all samples. PR linewidth tends to increase with Bi concentration for all (100) grown samples. We have observed a composition dependence of the quantized hole level sequence for the samples grown (311)B, that HH2 moves above LH1 for the sample with %2.1 Bi.