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Adsorption of Bi adatom on InAs (001) – β2 (2 × 4) and α2 (2 × 4) surface: A first principles study
Materials Science in Semiconductor Processing 107 (2020) 104856
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Adsorption of Bi adatom on InAs (001) – β2 (2 � 4) and α2 (2 � 4) surface: A first principles study Kouloud Kourchid a, Ramzi Alaya a, e, Ahmed Rebey b, d, Mourad Mbarki a, c, * a
Laboratory for Physics of Materials and Nanomaterials Applied to the Environment (LaPhyMNE), Faculty of Sciences, University of Gabes, 6072, Gabes, Tunisia Unit for Research in Hetero-Epitaxy and Applications (URHEA), Faculty of Sciences, University of Monastir, 5019, Monastir, Tunisia c Physics Department, Faculty of Science of Jeddah, University of Jeddah, Saudi Arabia d College of Science, Qassim University, PO Box, 6622, Buraydah, Al-Qassim, Saudi Arabia e Department of Science, Rustaq College of Education, Ministry of Higher Education, 329- Rustaq, Oman b
A R T I C L E I N F O
A B S T R A C T
Keywords: InAs (001) surface Adsorption energy Bismuth Growth conditions
In this work, we have interested on the initial growth processes of bismuth on the InAs (001) - β2 (2 � 4) and α2 (2 � 4) reconstructed surfaces. First, we have calculated the adsorption energy of single Bi atom at different sites located on InAs (001) the surface. Next, we have studied the structural and the electronic properties of the Bi/ InAs(001) system. Finally, we have calculated the chemical potential in the gas phase (μBi) for Bi adatom as a function of gas temperature for different beam equivalent pressures (BEP). We have determined the pressure temperature diagrams (p-T) for different considered sites. Our results show that the adsorption-desorption behavior of Bi adatom depends on the growth conditions. We have demonstrated that the Bi atom is adsorbed on both β2 (2 � 4) and α2 (2 � 4) at low temperature and at low BEP of Bi. Our obtained results seem to be in agreement with those obtained by molecular beam epitaxy (MBE).
1. Introduction In the last few years, there is an intensive progress of materials growth techniques. It is so possible to elaborated complicate metallur gical structure thanks to high technological performing apparatus. Isotropic and anisotropic types of epitaxy are performed in order to retort to the requirement imposed by the high quality devices industries. Within the epitaxial community there are two technologies that are used in high volume, molecular beam epitaxy (MBE) and metal-organic vapor phase epitaxy (MOVPE). Choosing the best growth technology is based on the precise details of the grown structure and end application. The parallel development of in situ diagnostic growth methods is also one of other parameters that make able to master growth technology. Now, RHEED is the most system used for monitoring the kinetic of epitaxy. Precisely, it is the yet powerful method to study the first step of epitaxy. Such stage is related to a complex thermodynamic phenomena such as adsorption, desorption of adatoms and the surface reconstruction. It is remarked that this phase have profound effects on the quality end de vices. So, several attempts are developed to model these stochastic phenomena particularly that related to the interaction process and reconstruction of substrate surface. For the arsenide III-V
semiconductors stream, GaAs and InAs are the two used substrates destined to growth of devices operating in VIS-IR and Far-IR spectra, respectively. The comparison between them is the subject of several scientific papers [1] but it is not the object of this study. More concluding studies are carried out on GaAs because of its immense usefulness. Briefly, GaAs has the richest spectrum of surface re constructions, but the number and nature of the phase changes of InAs are sufficient to make them equally good candidates when growing ternary or quaternary alloys. InAs is considered as the most technolog ically important within the family of III-V compounds [2–4] operating in the short energy range (of about 0.3eV). This fact is encouraged by the emergence of new bismide alloys such as InAsBi hopping to replace the classical II-VI alloys such as HgCdTe in spectra detection larger then 4 μm. Despite huge number of difficulties, related to chemical nature of bismuth, the synthesis of these materials is in success progress [5–15]. Indeed, bismuth is characterized by high Z electronic number and high dimension (atomic radius) compared to gallium and indium which is giving rise to tendency of segregation [16–18]. Also, like to Te and Sb, Bi is a surfactant precursor yields to non conventional growth conditions. In order to control the interface mass transfer between the gas source and substrate, it is required to study the adsorption-desorption behavior
* Corresponding author. Physics department, Faculty of Science of Jeddah, University of Jeddah, Saudi Arabia. E-mail addresses: [email protected], [email protected] (M. Mbarki). https://doi.org/10.1016/j.mssp.2019.104856 Received 9 July 2019; Received in revised form 2 November 2019; Accepted 16 November 2019 Available online 21 November 2019 1369-8001/© 2019 Elsevier Ltd. All rights reserved.
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cutoff is fixed at 40 Ry. In our calculations, the Bi/InAs (001) system was modeled by a supercell with periodically repeated slabs in [001] direction. In order to prevent adatom-adatom interaction, the supercell has been tested to be sufficiently large. The slab is constituted of eleven atomic layers with a 15 Å-thick vacuum region separating the slabs in the z-direction. We have relaxed only the four upper atomic layers of As-terminated surface, and the positions of the atoms in the other layers are kept fixed at bulk positions. Indeed, we have calculated the interlayer relaxation with respect of the slab thickness and we have found that the relaxed effects are mainly localized within the four atomic layers. The interlayer re laxations are all converged when the slab thickness is larger than five. The dangling bonds in the bottom Arsenic layer were passivated by pseudo-hydrogen atoms (two atoms per As atom) with fractional charge Z equal to 0.75 electron and the resulting As–H bond length was found to be 1.508 Å. For the surface calculations, we have used our calculated equilibrium lattice parameters for the InAs bulk, In (bulk), As (bulk) and Bi (bulk) phases. The lattice parameters of In, As and Bi were determined from self consistent calculations by using the tetragonal structure for In and rhombohedral structure for As and Bi. The equilibrium lattice parameter obtained for InAs bulk phase a0 ¼ 5.99 Å, which is slightly smaller than the experimental one (6.05 Å) [23]. In order to investigate the adsorption-desorption behavior of Bi adatom on InAs (001)- β2 (2 � 4) and α2 (2 � 4) surface reconstructions, we have used the theoretical approach proposed by Kangewa et al. in Ref. [24]. Then, the Bi adsorption-desorption process can be described by comparing the free energy of an ideal gas per one particle, which is called chemical potential, μgas, with the adsorption energy (Ead). A net adsorption of the atom is observed when Ead is less than μgas, whereas a net desorption occurs when μgas is less than Ead. The chemical potential μgas is given by: 2 3 � �32 �� 2πmkB T 7 6 gkB T μ ¼ kB T ln4 (1) 5 p h2 =
where, kB is Boltzmann’s constant, T the gas temperature, g the degree of degeneracy of the electron energy level, p is the BEP of Bi atom, m the mass of one particle, h is Planck’s constant. Here, g and m for atomic Bi have the values of 4 and 3.471.10–25 kg, respectively.
Fig. 1. Schematic of InAs (001)- β2 (a), α2 (2 � 4) (b) surface reconstruction; crosses indicate the considered adsorption sites Ai (i ¼ 1, …,5) and Bi (i ¼ 1, …,5) on the β2 and α2 surfaces, respectively, (for the gray ball is the indium and the yellow is the arsenic) with notation for the interlayer distance; equilibrium bond lengths between surface atoms are given in Angstrom.
The adsorption energy Ead is obtained by: Ead ¼ Etot
Esubstrate
Eatom
(2)
where Etot is the total energy of the surface with ad-atom, Esubstrate the total energy without adatom, and Eatom is the isolated atom energy estimated by calculating the atom in an empty cell. In this work, we have used the statics instead of the kinetics to construct the surface diagram-phases of the adsorbed atoms. In the following, we describe our calculations for Bi adsorbed on both β2 (2 � 4) and α2 (2 � 4) reconstructed surfaces.
of adatoms on the considered surface. As mentioned by Ratsch et al. [19] the α2 (2 � 4) and β2 (2 � 4) reconstructed InAs (100) surfaces are stable in both situations corresponding to As poor and rich conditions. The analysis of the introduction of Bi on these surfaces is of crucial interesting in understanding the growth of Bi related materials as a thin film or as a surfactant factor. In this work, we have performed ab-initio calculations to investigate the adsorption-desorption of Bi on the α2 (2 � 4) and β2 (2 � 4) InAs (001) surfaces. The adsorption-desorption behavior of single Bi ad-atom on InAs (001) is discussed by calculating adsorption energy and the pressure temperature phase diagram (p, T).
3. Result and discussion 3.1. Adsorption energy; structural and electronic properties of Bi/InAs (001) 3.1.1. InAs (001) clean surface First, we have performed the relaxation of the β2 (2 � 4) and α2 (2 � 4) InAs (001) clean surfaces (without adsorbate). Indeed, the atomic relaxation phenomenon on the surface leads to the displacement of the external atomic planes, which causes the increase or decrease of the interlayer distance. This induces a change on two-dimensional periodicity of the surface layers and new type of crystal symmetry will appear on the surface. Fig. 1 (a) shows the top and side view of the
2. Computational details We have performed ab initio calculations by using the pseudopo tential method as implemented in the Quantum Espresso package (PWSCF) [20] which is suitable for material modeling based on density functional theory (DFT) [21]. For the Brillouin-zone sampling, we have used the (2 4 1) Monkhorst–Pack [22] mesh, and the kinetic energy 2
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Fig. 2. Adsorption configurations for the Bi adatom at different sites: (a) at A1 site, b) at A2 site, c) at A3 site, d) at A4 site, e) at A5 site, (a’) at B1 site, (b’) at B2 site, (c’) at B3 site, (d’) at B4 site, (e’) at B5 site.
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arsenic-terminated β2 (2 � 4) InAs (001). As shown in Fig. 1 (a), the surface unit cell for the clean β2 surface contains three As dimers located on the top and third atomic layers. The calculated bond lengths of arsenic dimers on the top and third layers are the same and equal to 2.43 Å. These values are in good agreement with those reported in Refs. [25,26]. The top most dimers are nearly symmetric, while a small buckling of 0.05 Å occurs for the anion dimer in the third atomic layer. Fig. 1(b) shows the top and side view of arsenic terminated α2 (2 � 4) InAs (001). The α2 (2 � 4) InAs (001) clean surface contains two As dimers within the (2 � 4) surface unit cell. The two As dimers are located in the top and the third substrate layer, with bond lengths equal to 2.46 and 2.41 Å, respectively. Furthermore, the bond length of indium dimers in the second layer is equal to 2.82 Å. We note that the As dimers in the first and the third atomic layers are symmetric, which is in reasonably agreement with the result obtained by Miwa et al. [27].
Table 1 Adsorption energies (Ed) and bond lengths Bi–As and Bi–In in the studied adsorption sites. Bi sites
Ed (eV)
(A1) (A2) (A3) (A4) (A5)
-3.32 3.30 3.28 2.55 2.56
Bi Bi Bi Bi Bi
|Bi–As|min (Å)
|Bi–In| min (Å)
2.65 2.68 2.68 2.66 2.66
– 3.14 3.14 – –
3.1.2. Bi/InAs (001) - (2 � 4) β2 In order to understand the growth process it is necessary to explore where the atom species adsorb and how strongly they are bound to the surface. In this part, we have calculated the adsorption energies of a single Bi adatom at different adsorption sites on the InAs (001) - (2 � 4) β2. In our work we have adopted the calculations performed by Rosini et al. [28]. Indeed, Rosini et al. have performed the potential energy cal culations (PES) and they have identified eleven adsorption sites on InAs (001) surface. We have chosen only the five most favor sites. Fig. 1(a) shows schematically the five positions for the Bi adatom labeled as A1, A2, A3, A4 and A5. The optimized structures of the Bi adsorbed on different sites of the InAs (001) - (2 � 4) β2 surface are given in Fig. 2. Table 1 gives the data for adsorption at high-symmetry sites indicated above, as well as for other adsorption geometries. As can be seen from this table, the adsorption energy corresponding to the Bi adatom at the A1 site is the lowest one and is equal to 3.32 eV. It should be noted also that the Bi adsorption energies at A2 and A3 sites are almost the same. This is not surprising, because the nearest neighbor atoms of the adsorbed Bi atom at A2 and A3 sites are also the same. The adsorption energies at A4 and A5 positions are almost the same and equal to 2.55 and 2.56 eV, respectively. These energies are higher than at A1 by 0.77 eV. These results show that the Bi adatom prefers the A1 site. Since the Bi adatom at the A1 site is only twofold coordinated at the As dimer located in the third atomic layer (see Fig. 2(a)), its bonding orbital deviate to some extent from the bulk sp3 character. In this case, Bi adsorbed at A1 position stretches the bond length of As dimers towards 2.48 Å. Compared our model with the clean InAs (001)-2x4 surface, there are five additional electrons coming from the Bi adatom in each 2 � 4 unit cell. In this case the two dangling bond in the As dimer will be filled, keeping two other non saturate dangling bonds at the Bi adatom. The Bi adatoms at the A2 and A3 sites are fourfold coordinated: originally there are two As dimers in the top layer and one As dimer in the third layer, and after Bi adsorption, four bonds are formed connecting Bi with two As atoms situated in the first layer and with two In atom located in the second layer. In this case, we note that the As dimer at the first layer is broken after Bi adsorption, and the distance between the As atoms increases towards 3.71 Å (see Fig. 2 (b) and 2(c)). In the A4 and A5 sites the Bi adatoms are bonded to two As dimers located in the top layer (see Fig. 2(d) and (e)). In Table 1 we present optimal Bi–As and Bi–In bond lengths for Bi/ InAs(001) surfaces. It should be noted that the interatomic distance between As and the nearest Bi neighbors at A1 site is 2.65 Å above the substrate, while the positions at the A2 and A3 sites are 2.68 Å higher than the substrate and the A4 and A5 positions are located at 2.66 Å above the substrate. Fig. 3 (b) shows the electronic band structure of the clean InAs (001) - (2 � 4) β2 surface along the high symmetry directions on the surface Brillouin zone (Γ-J0 - K- J- Γ) (see Fig. 3(a)). The dashed areas represent the bulk band structure. We have identified four non dispersive occupied electronic states labeled as V1–V4, which lie below the bulk valence band
Fig. 3. (a) Brillouin zone of InAs (001) surface. Electronic band structure of (b) InAs (001) β2 - (2 � 4) clean surface (c) Electronic band structure of Bi adsorbed at A1 site of the InAs (001) β2 - (2 � 4) surface.
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Fig. 4. (a) Total electronic charge density plots for the Bi/InAs(001)-β2 (2 � 4) surface for the planes defined in Fig. 2(a). Partial electronic charge density plots at the K point for the clean InP(001)-β2 (2 � 4) surface at K point for: (b) occupied state V1, (c) unoccupied state C1.
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is, the formation of the most stable Bi–As bond reduces the surface-state density in the band gap region, resulting in reduction in the surface recombination velocity. On the other hand, Fig. 4 (a) shows the total valence charge density of the bonding between Bi adatom at A1 site. It is seen that the Bi adatom is linked to the two As atoms through covalent bonds. The highest occupied surface state V1 originates from the antibonding π* hybridizations of py orbitals of the third Bi–As layer and the lowest unoccupied state C1 originates from the hybridizations of py orbitals of the Bi adsorbed atoms with contribution of σ bonding between the As–As dimer (see Fig. 4 (b) and (c)). In order to understand the distribution the electronic charge, we have represented in Fig. 4 the total and partial charge density. As seen in Fig. 4(a–c), the high density of isolines is located between As dimer and Bi atom. This indicates the covalent interaction of the adsorbed Bi atom and the As dimer atoms. On the other hand, this increase of the electron density confirms the for mation of chemical Bi–As bonds and consequently chemisorption of Bi atom on the InAs (001) surface.
Table 2 Adsorption energies (Ed) and bond lengths Bi–As and Bi–In in the studied adsorption sites. Bi sites Bi Bi Bi Bi Bi
(B1) (B2) (B3) (B4) (B5)
Ed (eV) 3.05 3.16 3.06 3.61 3.44
|Bi–As|min (Å)
|Bi–In| min (Å)
2.88 2.85 – 2.63 2.72
2.91 3.27 2.94 3.30 3.12
maximum (VBM) which is in agreement with other theoretical result [27]. Note that the surface states V2 and V3 are degenerate at K point and the surface energy band gap is equal to 0.57 eV. For the surface with Bi atom adsorbed at A1 site, the calculated band structure show the exis tence of only three occupied surface states (V1–V3) (see Fig. 3 (c)). That
3.1.3. Bi/InAs (001) - (2 � 4) α2 Fig. 1 (b) shows the InAs (001) - (2 � 4) α2 surface with the different adsorption sites labeled as B1, B2, B3,B4 and B5. We have calculated the adsorption energy of Bi adatom at different sites. Our calculated values are regrouped in Table 2. It should be noted that the adsorption energy at B4 site is equal to 3.61 eV, and it is the lowest one. On the other hand, the adsorption energies at B5 and B2 sites exceed the value calculated for B4 position by 0.17 eV and 0.45 eV, respectively. The adsorption energy at B1 and B3 are the highest ones, and are almost the same. Consequently, the B4 adsorption site is the most favorable one for the Bi adsorbed atom, and the B1 and B3 sites are the least favorable. As shown in Fig. 2(d’), the Bi adatom adsorbed at B4 site is fourfold coordinated, which leads to the bond breaking of the As–As dimer binding bond and to the formation of two Bi–As and Bi–In polar bonds. Thus, the broken of the As–As dimer bond provides a stable adsorption site of Bi. The Bi adatom at B2 and B3 sites is fourfold coordinated. For the B2 site, the Bi adatom is linked to three As atoms and one In atom (see Fig. 2 (b’)), this geometry can reproduce the bonding configuration of bulk Arsenic. However at the B3 site, the Bi adatom is bonded to four In atoms. In this case, the four Bi–In bonding lengths are equal to 2.94 Å (see Fig. 2(c’)). Fig. 5(b) shows the electronic band structure of the clean InAs (001)(2 � 4) α2 surface along the high symmetry directions on the surface Brillouin zone (Γ-J0 - K- J- Γ) (see Fig. 5(a)). We have identified four occupied surface states (V1–V4) and five unoccupied states Ci. The sur face energy band gap is equal to 0.57 eV. Fig. 5(c) shows the electronic band structure for the Bi adsorbed at B4 site. We identify only three occupied surface states (V1–V3). Thus the formation of new Bi–As and Bi–In bonding at the surface reduces the density of surface states in the band gap region. As can be seen from Fig. 6 (a), the calculated total valence charge density shows that Bi–As and Bi–In are linked through a covalent bonds. On the other hand, the highest occupied state V1 arises from the π bonding contribution of pz orbitals at As–As dimer in the first layer plus some contribution of σ orbital at Bi dandling bonds. The lowest unoccupied state C1 originates from π* antibonding contribution of pz orbitals due to the As dimer in the top layer (see Fig. 6(b–d)). As can be seen from Fig. 6(a–d), the distribution of the electronic charge density has a high density of isolines between the Bi and As and In atoms (see Fig. 6(c)), which indicates the strong covalent bonding between them, and then confirms the formation of Bi–As and Bi–In chemical bonds. 3.2. Surface phase diagram 3.2.1. Bi/InAs (001) - (2 � 4) β2 The Bi adatom at different considered sites (A1-A5) would be adsorbed when μBi > Ed. In Fig. 7, we have plotted the variation of the chemical potential μB for Bi adatom as a function of the gas temperature
Fig. 5. (a) Brillouin zone of InAs (001) surface. Electronic band structure of (b) The InAs (001) α2 - (2 � 4) clean surface (c) Electronic band structure of Bi adsorbed at B4 site of the InAs (001) α2 - (2 � 4) surface. 6
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Fig. 6. (a) Total electronic charge density plots for the Bi/InAs(001)-α2 (2 � 4) surface for the planes defined in Fig. 2(d’). Partial electronic charge density plots at the K point for: (b) and (c) occupied state V1, (d)) unoccupied state C1.
for the A1 site at different Bi-BEP. As an example, the μBi line, which is under the condition of Bi-BEP (pBi) at 1.0 � 10 7 Torr crosses the line of μBi ¼ Ead ¼ 3.32 eV at approximately 740 K. This suggests that the critical temperature for Bi adsorption at A1 site is in the order of 740 K at pressure pBi ¼ 1.0 � 10 7 Torr. On the other hand, we note that the critical temperature is equal to 707 K at pBi ¼ 1.0 � 10 8 Torr. The critical temperatures at different BEP conditions for different adsorption sites are plotted on the (p-T) surface diagram in Fig. 8(a–e). As shown in Fig. 8(a–c), the Bi adsorbed on A1, A2 and A3 sites will appear in the low Bi-BEP region (10 9 Torr) with low temperature 673 K. However, Fig. 8 (d) and (e) show that the Bi adsorbed on A4 and A5 sites will appear at low temperature 530 K at 10 9 Torr. The appearance of the Bi ad-atom significantly decreases above a temperature of 935 K. That means that the critical temperature of the Bi adsorption varies in the range of 530–935 K, which is consistent with the adsorption-desorption behavior by the comparison of the calculated temperature and pressure pBi range. It should be noted that these ranges of pressure and temperature are comparable to that used in MBE growth conditions [29–31]. Such coincidence leads to imagine the important role of microscopic surface rearrangement on the success and the quality of deposited layer as remarked in many cases [32,33]. Evidently, the qualitative comparison needs a specific experimental work taking into account the used pa rameters in this calculation. Eventually, this work will constitute a preliminary step to understand the first march of Bi as a catalyzing material for the formation of nanostructures.
Fig. 7. Bi chemical potential as a function of gas temperature of Bi/InAs (001)β2 - (2 � 4) surface.
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Fig. 8. Pressure-temperature phase diagram for the InAs (001)-(2 � 4) β2 surface. Experimental (Expt) results are also shown in this figure.
3.2.2. Bi/InAs (001) - (2 � 4) α2 We have calculated the variation of the chemical potential of the gas with respect to the gas temperature at different Bi-BEP for the different considered sites (B1–B5). The calculated surface phase diagrams (p,T) for the adsorption–desorption transition were displayed in Fig. 9(a–e). Fig. 9(a–b) shows that the phase boundary ranges from 648 K to 892 K. Therefore, the critical growth temperature of Bi at B1 and B2 positions is equal to 700 K for typical BEP of 10 7 Torr. Fig. 9-c reveals the p-T diagram for adsorption desorption transition for Bi adatom adsorbed at B3 site. We Remark that the phase boundary ranges from 628 K to 863 K.
As shown in Fig. 9-e, our result agrees well with the experiment, i. e, Bi droplets are obtained for MBE growth conditions at 700 K. For B4 and B5 sites, the boundary conditions vary from 737 K to 1000 K and 700 K–965 K, respectively. Our result is consistent with the experimental results during MBE growth conditions [29]. Our obtained result suggests that our theoretical calculation is practical for predicting the adsorption-desorption behavior on temperature and BEP.
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Fig. 9. Pressure-temperature phase diagram for the InAs (001)-(2 � 4) α2 surface. Experimental (Expt) results are also shown in this figure.
4. Conclusion
between 700 K and 1000 K for the α2 surface. Such results are encour aging to more understand the role of Bi in growth process and open the way to employ it in new eventual applications.
In this work, we have presented a first principle calculations to study the adsorption-desorption process of Bi adatom at different sites located on the α2 (2 � 4) and β2 (2 � 4) InAs (001) reconstruction surfaces. We have demonstrated that A1 and B4 sites located at β2 and α2 surfaces, respectively, are the most favorable. The analysis of the electronic properties allowed us to identify the Bi bonding character on the InAs (001) surface. We have determined the growth conditions by calculating the (p,T) diagrams. We have found that the critical temperature of the Bi adsorption varies between 530 K and 935 K for the β2 surface and
Remark. Ahmed Rebey is the academic noun of the author but the official name and surname is Hamad Alhadi Rebei. Declaration of competing interest We have no conflict of interest.
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Appendix A. Supplementary data
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Adsorption of Bi adatom on InAs (001) – β2 (2 � 4) and α2 (2 � 4) surface: A first principles study Kouloud Kourchid a, Ramzi Alaya a, e, Ahmed Rebey b, d, Mourad Mbarki a, c, * a
Laboratory for Physics of Materials and Nanomaterials Applied to the Environment (LaPhyMNE), Faculty of Sciences, University of Gabes, 6072, Gabes, Tunisia Unit for Research in Hetero-Epitaxy and Applications (URHEA), Faculty of Sciences, University of Monastir, 5019, Monastir, Tunisia c Physics Department, Faculty of Science of Jeddah, University of Jeddah, Saudi Arabia d College of Science, Qassim University, PO Box, 6622, Buraydah, Al-Qassim, Saudi Arabia e Department of Science, Rustaq College of Education, Ministry of Higher Education, 329- Rustaq, Oman b
A R T I C L E I N F O
A B S T R A C T
Keywords: InAs (001) surface Adsorption energy Bismuth Growth conditions
In this work, we have interested on the initial growth processes of bismuth on the InAs (001) - β2 (2 � 4) and α2 (2 � 4) reconstructed surfaces. First, we have calculated the adsorption energy of single Bi atom at different sites located on InAs (001) the surface. Next, we have studied the structural and the electronic properties of the Bi/ InAs(001) system. Finally, we have calculated the chemical potential in the gas phase (μBi) for Bi adatom as a function of gas temperature for different beam equivalent pressures (BEP). We have determined the pressure temperature diagrams (p-T) for different considered sites. Our results show that the adsorption-desorption behavior of Bi adatom depends on the growth conditions. We have demonstrated that the Bi atom is adsorbed on both β2 (2 � 4) and α2 (2 � 4) at low temperature and at low BEP of Bi. Our obtained results seem to be in agreement with those obtained by molecular beam epitaxy (MBE).
1. Introduction In the last few years, there is an intensive progress of materials growth techniques. It is so possible to elaborated complicate metallur gical structure thanks to high technological performing apparatus. Isotropic and anisotropic types of epitaxy are performed in order to retort to the requirement imposed by the high quality devices industries. Within the epitaxial community there are two technologies that are used in high volume, molecular beam epitaxy (MBE) and metal-organic vapor phase epitaxy (MOVPE). Choosing the best growth technology is based on the precise details of the grown structure and end application. The parallel development of in situ diagnostic growth methods is also one of other parameters that make able to master growth technology. Now, RHEED is the most system used for monitoring the kinetic of epitaxy. Precisely, it is the yet powerful method to study the first step of epitaxy. Such stage is related to a complex thermodynamic phenomena such as adsorption, desorption of adatoms and the surface reconstruction. It is remarked that this phase have profound effects on the quality end de vices. So, several attempts are developed to model these stochastic phenomena particularly that related to the interaction process and reconstruction of substrate surface. For the arsenide III-V
semiconductors stream, GaAs and InAs are the two used substrates destined to growth of devices operating in VIS-IR and Far-IR spectra, respectively. The comparison between them is the subject of several scientific papers [1] but it is not the object of this study. More concluding studies are carried out on GaAs because of its immense usefulness. Briefly, GaAs has the richest spectrum of surface re constructions, but the number and nature of the phase changes of InAs are sufficient to make them equally good candidates when growing ternary or quaternary alloys. InAs is considered as the most technolog ically important within the family of III-V compounds [2–4] operating in the short energy range (of about 0.3eV). This fact is encouraged by the emergence of new bismide alloys such as InAsBi hopping to replace the classical II-VI alloys such as HgCdTe in spectra detection larger then 4 μm. Despite huge number of difficulties, related to chemical nature of bismuth, the synthesis of these materials is in success progress [5–15]. Indeed, bismuth is characterized by high Z electronic number and high dimension (atomic radius) compared to gallium and indium which is giving rise to tendency of segregation [16–18]. Also, like to Te and Sb, Bi is a surfactant precursor yields to non conventional growth conditions. In order to control the interface mass transfer between the gas source and substrate, it is required to study the adsorption-desorption behavior
* Corresponding author. Physics department, Faculty of Science of Jeddah, University of Jeddah, Saudi Arabia. E-mail addresses: [email protected], [email protected] (M. Mbarki). https://doi.org/10.1016/j.mssp.2019.104856 Received 9 July 2019; Received in revised form 2 November 2019; Accepted 16 November 2019 Available online 21 November 2019 1369-8001/© 2019 Elsevier Ltd. All rights reserved.
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cutoff is fixed at 40 Ry. In our calculations, the Bi/InAs (001) system was modeled by a supercell with periodically repeated slabs in [001] direction. In order to prevent adatom-adatom interaction, the supercell has been tested to be sufficiently large. The slab is constituted of eleven atomic layers with a 15 Å-thick vacuum region separating the slabs in the z-direction. We have relaxed only the four upper atomic layers of As-terminated surface, and the positions of the atoms in the other layers are kept fixed at bulk positions. Indeed, we have calculated the interlayer relaxation with respect of the slab thickness and we have found that the relaxed effects are mainly localized within the four atomic layers. The interlayer re laxations are all converged when the slab thickness is larger than five. The dangling bonds in the bottom Arsenic layer were passivated by pseudo-hydrogen atoms (two atoms per As atom) with fractional charge Z equal to 0.75 electron and the resulting As–H bond length was found to be 1.508 Å. For the surface calculations, we have used our calculated equilibrium lattice parameters for the InAs bulk, In (bulk), As (bulk) and Bi (bulk) phases. The lattice parameters of In, As and Bi were determined from self consistent calculations by using the tetragonal structure for In and rhombohedral structure for As and Bi. The equilibrium lattice parameter obtained for InAs bulk phase a0 ¼ 5.99 Å, which is slightly smaller than the experimental one (6.05 Å) [23]. In order to investigate the adsorption-desorption behavior of Bi adatom on InAs (001)- β2 (2 � 4) and α2 (2 � 4) surface reconstructions, we have used the theoretical approach proposed by Kangewa et al. in Ref. [24]. Then, the Bi adsorption-desorption process can be described by comparing the free energy of an ideal gas per one particle, which is called chemical potential, μgas, with the adsorption energy (Ead). A net adsorption of the atom is observed when Ead is less than μgas, whereas a net desorption occurs when μgas is less than Ead. The chemical potential μgas is given by: 2 3 � �32 �� 2πmkB T 7 6 gkB T μ ¼ kB T ln4 (1) 5 p h2 =
where, kB is Boltzmann’s constant, T the gas temperature, g the degree of degeneracy of the electron energy level, p is the BEP of Bi atom, m the mass of one particle, h is Planck’s constant. Here, g and m for atomic Bi have the values of 4 and 3.471.10–25 kg, respectively.
Fig. 1. Schematic of InAs (001)- β2 (a), α2 (2 � 4) (b) surface reconstruction; crosses indicate the considered adsorption sites Ai (i ¼ 1, …,5) and Bi (i ¼ 1, …,5) on the β2 and α2 surfaces, respectively, (for the gray ball is the indium and the yellow is the arsenic) with notation for the interlayer distance; equilibrium bond lengths between surface atoms are given in Angstrom.
The adsorption energy Ead is obtained by: Ead ¼ Etot
Esubstrate
Eatom
(2)
where Etot is the total energy of the surface with ad-atom, Esubstrate the total energy without adatom, and Eatom is the isolated atom energy estimated by calculating the atom in an empty cell. In this work, we have used the statics instead of the kinetics to construct the surface diagram-phases of the adsorbed atoms. In the following, we describe our calculations for Bi adsorbed on both β2 (2 � 4) and α2 (2 � 4) reconstructed surfaces.
of adatoms on the considered surface. As mentioned by Ratsch et al. [19] the α2 (2 � 4) and β2 (2 � 4) reconstructed InAs (100) surfaces are stable in both situations corresponding to As poor and rich conditions. The analysis of the introduction of Bi on these surfaces is of crucial interesting in understanding the growth of Bi related materials as a thin film or as a surfactant factor. In this work, we have performed ab-initio calculations to investigate the adsorption-desorption of Bi on the α2 (2 � 4) and β2 (2 � 4) InAs (001) surfaces. The adsorption-desorption behavior of single Bi ad-atom on InAs (001) is discussed by calculating adsorption energy and the pressure temperature phase diagram (p, T).
3. Result and discussion 3.1. Adsorption energy; structural and electronic properties of Bi/InAs (001) 3.1.1. InAs (001) clean surface First, we have performed the relaxation of the β2 (2 � 4) and α2 (2 � 4) InAs (001) clean surfaces (without adsorbate). Indeed, the atomic relaxation phenomenon on the surface leads to the displacement of the external atomic planes, which causes the increase or decrease of the interlayer distance. This induces a change on two-dimensional periodicity of the surface layers and new type of crystal symmetry will appear on the surface. Fig. 1 (a) shows the top and side view of the
2. Computational details We have performed ab initio calculations by using the pseudopo tential method as implemented in the Quantum Espresso package (PWSCF) [20] which is suitable for material modeling based on density functional theory (DFT) [21]. For the Brillouin-zone sampling, we have used the (2 4 1) Monkhorst–Pack [22] mesh, and the kinetic energy 2
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Fig. 2. Adsorption configurations for the Bi adatom at different sites: (a) at A1 site, b) at A2 site, c) at A3 site, d) at A4 site, e) at A5 site, (a’) at B1 site, (b’) at B2 site, (c’) at B3 site, (d’) at B4 site, (e’) at B5 site.
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arsenic-terminated β2 (2 � 4) InAs (001). As shown in Fig. 1 (a), the surface unit cell for the clean β2 surface contains three As dimers located on the top and third atomic layers. The calculated bond lengths of arsenic dimers on the top and third layers are the same and equal to 2.43 Å. These values are in good agreement with those reported in Refs. [25,26]. The top most dimers are nearly symmetric, while a small buckling of 0.05 Å occurs for the anion dimer in the third atomic layer. Fig. 1(b) shows the top and side view of arsenic terminated α2 (2 � 4) InAs (001). The α2 (2 � 4) InAs (001) clean surface contains two As dimers within the (2 � 4) surface unit cell. The two As dimers are located in the top and the third substrate layer, with bond lengths equal to 2.46 and 2.41 Å, respectively. Furthermore, the bond length of indium dimers in the second layer is equal to 2.82 Å. We note that the As dimers in the first and the third atomic layers are symmetric, which is in reasonably agreement with the result obtained by Miwa et al. [27].
Table 1 Adsorption energies (Ed) and bond lengths Bi–As and Bi–In in the studied adsorption sites. Bi sites
Ed (eV)
(A1) (A2) (A3) (A4) (A5)
-3.32 3.30 3.28 2.55 2.56
Bi Bi Bi Bi Bi
|Bi–As|min (Å)
|Bi–In| min (Å)
2.65 2.68 2.68 2.66 2.66
– 3.14 3.14 – –
3.1.2. Bi/InAs (001) - (2 � 4) β2 In order to understand the growth process it is necessary to explore where the atom species adsorb and how strongly they are bound to the surface. In this part, we have calculated the adsorption energies of a single Bi adatom at different adsorption sites on the InAs (001) - (2 � 4) β2. In our work we have adopted the calculations performed by Rosini et al. [28]. Indeed, Rosini et al. have performed the potential energy cal culations (PES) and they have identified eleven adsorption sites on InAs (001) surface. We have chosen only the five most favor sites. Fig. 1(a) shows schematically the five positions for the Bi adatom labeled as A1, A2, A3, A4 and A5. The optimized structures of the Bi adsorbed on different sites of the InAs (001) - (2 � 4) β2 surface are given in Fig. 2. Table 1 gives the data for adsorption at high-symmetry sites indicated above, as well as for other adsorption geometries. As can be seen from this table, the adsorption energy corresponding to the Bi adatom at the A1 site is the lowest one and is equal to 3.32 eV. It should be noted also that the Bi adsorption energies at A2 and A3 sites are almost the same. This is not surprising, because the nearest neighbor atoms of the adsorbed Bi atom at A2 and A3 sites are also the same. The adsorption energies at A4 and A5 positions are almost the same and equal to 2.55 and 2.56 eV, respectively. These energies are higher than at A1 by 0.77 eV. These results show that the Bi adatom prefers the A1 site. Since the Bi adatom at the A1 site is only twofold coordinated at the As dimer located in the third atomic layer (see Fig. 2(a)), its bonding orbital deviate to some extent from the bulk sp3 character. In this case, Bi adsorbed at A1 position stretches the bond length of As dimers towards 2.48 Å. Compared our model with the clean InAs (001)-2x4 surface, there are five additional electrons coming from the Bi adatom in each 2 � 4 unit cell. In this case the two dangling bond in the As dimer will be filled, keeping two other non saturate dangling bonds at the Bi adatom. The Bi adatoms at the A2 and A3 sites are fourfold coordinated: originally there are two As dimers in the top layer and one As dimer in the third layer, and after Bi adsorption, four bonds are formed connecting Bi with two As atoms situated in the first layer and with two In atom located in the second layer. In this case, we note that the As dimer at the first layer is broken after Bi adsorption, and the distance between the As atoms increases towards 3.71 Å (see Fig. 2 (b) and 2(c)). In the A4 and A5 sites the Bi adatoms are bonded to two As dimers located in the top layer (see Fig. 2(d) and (e)). In Table 1 we present optimal Bi–As and Bi–In bond lengths for Bi/ InAs(001) surfaces. It should be noted that the interatomic distance between As and the nearest Bi neighbors at A1 site is 2.65 Å above the substrate, while the positions at the A2 and A3 sites are 2.68 Å higher than the substrate and the A4 and A5 positions are located at 2.66 Å above the substrate. Fig. 3 (b) shows the electronic band structure of the clean InAs (001) - (2 � 4) β2 surface along the high symmetry directions on the surface Brillouin zone (Γ-J0 - K- J- Γ) (see Fig. 3(a)). The dashed areas represent the bulk band structure. We have identified four non dispersive occupied electronic states labeled as V1–V4, which lie below the bulk valence band
Fig. 3. (a) Brillouin zone of InAs (001) surface. Electronic band structure of (b) InAs (001) β2 - (2 � 4) clean surface (c) Electronic band structure of Bi adsorbed at A1 site of the InAs (001) β2 - (2 � 4) surface.
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Fig. 4. (a) Total electronic charge density plots for the Bi/InAs(001)-β2 (2 � 4) surface for the planes defined in Fig. 2(a). Partial electronic charge density plots at the K point for the clean InP(001)-β2 (2 � 4) surface at K point for: (b) occupied state V1, (c) unoccupied state C1.
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is, the formation of the most stable Bi–As bond reduces the surface-state density in the band gap region, resulting in reduction in the surface recombination velocity. On the other hand, Fig. 4 (a) shows the total valence charge density of the bonding between Bi adatom at A1 site. It is seen that the Bi adatom is linked to the two As atoms through covalent bonds. The highest occupied surface state V1 originates from the antibonding π* hybridizations of py orbitals of the third Bi–As layer and the lowest unoccupied state C1 originates from the hybridizations of py orbitals of the Bi adsorbed atoms with contribution of σ bonding between the As–As dimer (see Fig. 4 (b) and (c)). In order to understand the distribution the electronic charge, we have represented in Fig. 4 the total and partial charge density. As seen in Fig. 4(a–c), the high density of isolines is located between As dimer and Bi atom. This indicates the covalent interaction of the adsorbed Bi atom and the As dimer atoms. On the other hand, this increase of the electron density confirms the for mation of chemical Bi–As bonds and consequently chemisorption of Bi atom on the InAs (001) surface.
Table 2 Adsorption energies (Ed) and bond lengths Bi–As and Bi–In in the studied adsorption sites. Bi sites Bi Bi Bi Bi Bi
(B1) (B2) (B3) (B4) (B5)
Ed (eV) 3.05 3.16 3.06 3.61 3.44
|Bi–As|min (Å)
|Bi–In| min (Å)
2.88 2.85 – 2.63 2.72
2.91 3.27 2.94 3.30 3.12
maximum (VBM) which is in agreement with other theoretical result [27]. Note that the surface states V2 and V3 are degenerate at K point and the surface energy band gap is equal to 0.57 eV. For the surface with Bi atom adsorbed at A1 site, the calculated band structure show the exis tence of only three occupied surface states (V1–V3) (see Fig. 3 (c)). That
3.1.3. Bi/InAs (001) - (2 � 4) α2 Fig. 1 (b) shows the InAs (001) - (2 � 4) α2 surface with the different adsorption sites labeled as B1, B2, B3,B4 and B5. We have calculated the adsorption energy of Bi adatom at different sites. Our calculated values are regrouped in Table 2. It should be noted that the adsorption energy at B4 site is equal to 3.61 eV, and it is the lowest one. On the other hand, the adsorption energies at B5 and B2 sites exceed the value calculated for B4 position by 0.17 eV and 0.45 eV, respectively. The adsorption energy at B1 and B3 are the highest ones, and are almost the same. Consequently, the B4 adsorption site is the most favorable one for the Bi adsorbed atom, and the B1 and B3 sites are the least favorable. As shown in Fig. 2(d’), the Bi adatom adsorbed at B4 site is fourfold coordinated, which leads to the bond breaking of the As–As dimer binding bond and to the formation of two Bi–As and Bi–In polar bonds. Thus, the broken of the As–As dimer bond provides a stable adsorption site of Bi. The Bi adatom at B2 and B3 sites is fourfold coordinated. For the B2 site, the Bi adatom is linked to three As atoms and one In atom (see Fig. 2 (b’)), this geometry can reproduce the bonding configuration of bulk Arsenic. However at the B3 site, the Bi adatom is bonded to four In atoms. In this case, the four Bi–In bonding lengths are equal to 2.94 Å (see Fig. 2(c’)). Fig. 5(b) shows the electronic band structure of the clean InAs (001)(2 � 4) α2 surface along the high symmetry directions on the surface Brillouin zone (Γ-J0 - K- J- Γ) (see Fig. 5(a)). We have identified four occupied surface states (V1–V4) and five unoccupied states Ci. The sur face energy band gap is equal to 0.57 eV. Fig. 5(c) shows the electronic band structure for the Bi adsorbed at B4 site. We identify only three occupied surface states (V1–V3). Thus the formation of new Bi–As and Bi–In bonding at the surface reduces the density of surface states in the band gap region. As can be seen from Fig. 6 (a), the calculated total valence charge density shows that Bi–As and Bi–In are linked through a covalent bonds. On the other hand, the highest occupied state V1 arises from the π bonding contribution of pz orbitals at As–As dimer in the first layer plus some contribution of σ orbital at Bi dandling bonds. The lowest unoccupied state C1 originates from π* antibonding contribution of pz orbitals due to the As dimer in the top layer (see Fig. 6(b–d)). As can be seen from Fig. 6(a–d), the distribution of the electronic charge density has a high density of isolines between the Bi and As and In atoms (see Fig. 6(c)), which indicates the strong covalent bonding between them, and then confirms the formation of Bi–As and Bi–In chemical bonds. 3.2. Surface phase diagram 3.2.1. Bi/InAs (001) - (2 � 4) β2 The Bi adatom at different considered sites (A1-A5) would be adsorbed when μBi > Ed. In Fig. 7, we have plotted the variation of the chemical potential μB for Bi adatom as a function of the gas temperature
Fig. 5. (a) Brillouin zone of InAs (001) surface. Electronic band structure of (b) The InAs (001) α2 - (2 � 4) clean surface (c) Electronic band structure of Bi adsorbed at B4 site of the InAs (001) α2 - (2 � 4) surface. 6
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Fig. 6. (a) Total electronic charge density plots for the Bi/InAs(001)-α2 (2 � 4) surface for the planes defined in Fig. 2(d’). Partial electronic charge density plots at the K point for: (b) and (c) occupied state V1, (d)) unoccupied state C1.
for the A1 site at different Bi-BEP. As an example, the μBi line, which is under the condition of Bi-BEP (pBi) at 1.0 � 10 7 Torr crosses the line of μBi ¼ Ead ¼ 3.32 eV at approximately 740 K. This suggests that the critical temperature for Bi adsorption at A1 site is in the order of 740 K at pressure pBi ¼ 1.0 � 10 7 Torr. On the other hand, we note that the critical temperature is equal to 707 K at pBi ¼ 1.0 � 10 8 Torr. The critical temperatures at different BEP conditions for different adsorption sites are plotted on the (p-T) surface diagram in Fig. 8(a–e). As shown in Fig. 8(a–c), the Bi adsorbed on A1, A2 and A3 sites will appear in the low Bi-BEP region (10 9 Torr) with low temperature 673 K. However, Fig. 8 (d) and (e) show that the Bi adsorbed on A4 and A5 sites will appear at low temperature 530 K at 10 9 Torr. The appearance of the Bi ad-atom significantly decreases above a temperature of 935 K. That means that the critical temperature of the Bi adsorption varies in the range of 530–935 K, which is consistent with the adsorption-desorption behavior by the comparison of the calculated temperature and pressure pBi range. It should be noted that these ranges of pressure and temperature are comparable to that used in MBE growth conditions [29–31]. Such coincidence leads to imagine the important role of microscopic surface rearrangement on the success and the quality of deposited layer as remarked in many cases [32,33]. Evidently, the qualitative comparison needs a specific experimental work taking into account the used pa rameters in this calculation. Eventually, this work will constitute a preliminary step to understand the first march of Bi as a catalyzing material for the formation of nanostructures.
Fig. 7. Bi chemical potential as a function of gas temperature of Bi/InAs (001)β2 - (2 � 4) surface.
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Fig. 8. Pressure-temperature phase diagram for the InAs (001)-(2 � 4) β2 surface. Experimental (Expt) results are also shown in this figure.
3.2.2. Bi/InAs (001) - (2 � 4) α2 We have calculated the variation of the chemical potential of the gas with respect to the gas temperature at different Bi-BEP for the different considered sites (B1–B5). The calculated surface phase diagrams (p,T) for the adsorption–desorption transition were displayed in Fig. 9(a–e). Fig. 9(a–b) shows that the phase boundary ranges from 648 K to 892 K. Therefore, the critical growth temperature of Bi at B1 and B2 positions is equal to 700 K for typical BEP of 10 7 Torr. Fig. 9-c reveals the p-T diagram for adsorption desorption transition for Bi adatom adsorbed at B3 site. We Remark that the phase boundary ranges from 628 K to 863 K.
As shown in Fig. 9-e, our result agrees well with the experiment, i. e, Bi droplets are obtained for MBE growth conditions at 700 K. For B4 and B5 sites, the boundary conditions vary from 737 K to 1000 K and 700 K–965 K, respectively. Our result is consistent with the experimental results during MBE growth conditions [29]. Our obtained result suggests that our theoretical calculation is practical for predicting the adsorption-desorption behavior on temperature and BEP.
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Fig. 9. Pressure-temperature phase diagram for the InAs (001)-(2 � 4) α2 surface. Experimental (Expt) results are also shown in this figure.
4. Conclusion
between 700 K and 1000 K for the α2 surface. Such results are encour aging to more understand the role of Bi in growth process and open the way to employ it in new eventual applications.
In this work, we have presented a first principle calculations to study the adsorption-desorption process of Bi adatom at different sites located on the α2 (2 � 4) and β2 (2 � 4) InAs (001) reconstruction surfaces. We have demonstrated that A1 and B4 sites located at β2 and α2 surfaces, respectively, are the most favorable. The analysis of the electronic properties allowed us to identify the Bi bonding character on the InAs (001) surface. We have determined the growth conditions by calculating the (p,T) diagrams. We have found that the critical temperature of the Bi adsorption varies between 530 K and 935 K for the β2 surface and
Remark. Ahmed Rebey is the academic noun of the author but the official name and surname is Hamad Alhadi Rebei. Declaration of competing interest We have no conflict of interest.
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Materials Science in Semiconductor Processing 107 (2020) 104856
Appendix A. Supplementary data
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