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Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation
Journal Pre-proof Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation Yu Diao, Lei Liu, Sihao Xia PII:
S1386-9477(19)31384-0
DOI:
https://doi.org/10.1016/j.physe.2019.113843
Reference:
PHYSE 113843
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Physica E: Low-dimensional Systems and Nanostructures
Received Date: 12 September 2019 Revised Date:
7 November 2019
Accepted Date: 19 November 2019
Please cite this article as: Y. Diao, L. Liu, S. Xia, Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation, Physica E: Lowdimensional Systems and Nanostructures (2019), doi: https://doi.org/10.1016/j.physe.2019.113843. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation Yu Diao, Lei Liu*, Sihao Xia Department of optoelectronic technology, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China Corresponding author: Lei Liu; E-mail: [email protected]
Abstract The electronic and optical properties of composition-tunable Ga1-xAlxAs and InyGa1-yAs nanowires are investigated and compared utilizing first-principle calculations based on density functional theory. In the established nanowire models, nine different compositions (x/y=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1) are considered. The results show that increasing Al constituent can enhance the stability of Ga1-xAlxAs nanowires, while increasing In content in InyGa1-yAs nanowires results in an opposite trend. Among all nanowires, In0.75Ga0.25As nanowire exhibits the lowest work function. Interestingly, Ga1-xAlxAs nanowires with Al composition less than 0.5 are direct band gap materials, while increasing Al content to 0.5 or above will induce indirect band gap. All InyGa1-yAs nanowires are all direct band gaps. Moreover, with increasing Al and In component, the absorption peak, reflection peak and refractive index for Ga1-xAlxAs are all blue shifted while inversely those of InyGa1-yAs nanowires are all red shifted. All calculations lay important foundation for the design and preparation of Ga1-xAlxAs and InyGa1-yAs nanowires based optoelectronic devices. Key words: Composition-tunable; GaAlAs nanowires; InGaAs nanowires; Electronic properties; Optical properties
1. Introduction In the past decades, semiconductor nanowires have attracted great interest for their wide
application fields [1-4]. As the common III–V semiconductor nanowires, GaAs and InAs nanowires show enormous promise as building blocks of various nanoscale optoelectronic devices, such as light-emitting diodes, detectors and photovoltaic devices [5-9]. However, the band gap for these binary III–V nanowires is invariable, thus they are just suitable for the nanodevices with specific wavelength. To satisfy the demand for higher sensitivity and wider spectral response range, ternary GaAlAs and InGaAs nanowires are respectively proposed to offer a wider application prospects in the blue extension and near-infrared optoelectronics field, which thanks to their tunable bandgap. The physics properties of GaAlAs and InGaAs nanowires will be changed with the variation of Al and In constituent. Zou et al. developed a graded band-gap AlGaAs/GaAs wire photocathode [10]. Compared with GaAs wire photocathode, the photoemission for photocathodes with linearly graded Al composition ranges of 0 to 0.1, 0.2, 0.3, and 0.4 are enhanced by 29.5%~43.8%. Liu et al. proposed a GaAs nanowire cathode with graded Al composition structure as photon-enhanced thermionic emission device for higher conversion efficiency [11]. Beleckaite et al. utilized terahertz time-domain spectroscopy to observe the terahertz emission properties of composition-tunable InGaAs nanowire arrays. Results show there appears a substantially enhanced THz emission efficiency with In composition decreasing from 1 to 0.5 [12]. Zota et al reported an improved InGaAs nanowire MOSFETs by increasing the Indium content from 0.53 to 0.63 [13]. Although some progress has been made in the growth and applications of GaAlAs and InGaAs nanowires, the research on their fundamental properties is still at the early stage. So far, extensive theoretical and experimental efforts have been devoted to study the electronic and optical properties of bulk GaAlAs, bulk InGaAs, GaAs nanowires and InAs nanowires [14-19]. However, a detailed comparative research on the effect of different compositions on electronic and optical properties of GaAlAs and InGaAs nanowires is relatively lack. In fact, the comparison of these two nanowire materials can allow us to recognize which component of nanowires are suitable for different applications. In addition, it will also allow us to compare the properties of nanowire structure with those of bulk ones, which is beneficial to predict the future challenges. In this work, the first-principles method is employed to systematically investigate on the optoelectronic properties of composition-tunable Ga1-xAlxAs and InyGa1-yAs nanowires. Nine different Al and In constituents are considered to establish III-As nanowire models, including
x/y=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1. Cohesive energy, work function, atomic structure, band structure, density of state, absorption coefficient, reflectivity and refractive index of different nanowires are calculated and analyzed. This research lays an important theoretical basis for the fabrication and application of Ga1-xAlxAs and InyGa1-yAs nano-based optoelectronic devices.
2. Computational details All first-principle calculations in this work were accomplished with employing the quantum mechanics software CASTEP based on the density functional theory [20]. Perdew, Burke, Ernzerhof (PBE) method with generalized gradient approximation (GGA) function were used for the exchange-correlation potential [21, 22]. The electron wave function was expanded in plane waves with a cutoff energy of 480 eV. The first Brillouin zone was sampled by a 1×1×5 Monkhorst k-point grid. A larger vacuum region of 15 Å was adopted to avoid the interference between periodic structures. The geometries were fully relaxed using the conjugated gradient method until the total energy converged to 10-3 eV and the forces of all atoms were smaller than 10-4 eV/Å. The valence-electron configurations for Ga, As, Al, In were respectively treated as 3d104s24p1, 4s24p3, 3s23p1, 4d105s25p1. Most of experiment results have reported that wurtzite GaAs nanowires have stronger stability than the zinc-blende ones when the diameter is smaller than 15 nm [23]. Therefore, wurtzite structure is selected as the crystal structure of nanowires. Besides, the wurtzite GaAs nanowires have hexagonal across sections with six facets orthogonal to the growth direction, where these side facets are oriented (10-10) and (11-20). According to these experimental observations, the wurtzite GaAs nanowire model along [0001] orientation are established, and the top view and side view of corresponding model are shown in Fig. 1(a). The modelling details of GaAs nanowires can be found in our previous work [24]. The surface of nanostructures is usually unstable due to the existence of surface dangling bonds, and its surface charge are often neutralized by surface passivation [25]. Hence, surface atoms of GaAlAs and InGaAs nanowires in this work are all passivated by hydrogen atoms to remove localized energy state close to or at the Fermi level and avoid the effect of additional charge transfer on the photoelectric properties [24, 26, 27]. Namely, the surface effects on nanowires are not discussed in this paper. In Fig. 1(a),
there are 48 Ga, 48 As and 48 H atoms in GaAs nanowire model. Although the used nanowire size is far smaller than the synthesized GaAs nanowires, it is believed that the calculations can still predict the trends of electronic and optical properties [28, 29]. The Ga1-xAlxAs and InyGa1-yAs nanowires are respectively built by substituting the Ga atoms of GaAs nanowires with Al and In atoms. Here, nine different Al and In compositions are considered, including 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1. Taken Ga0.75Al0.25As nanowires as an example, we have performed a comparative research on the effect of different Al substitution configurations on the structural stability of Ga0.75Al0.25As nanowires. The detailed atomic structures and calculations are given in Supplementary material S1. Results imply that all substitution atoms tend to distribute uniformly at each atomic layer of nanowires due to its lower energy. According to the results of Yang et al and Xia et al [30, 31], it is found that the selection of substitution atoms obeys the spatially para-position symmetric distribution, which can make the model obtain the minimum energy. Thus, based on the minimum energy principle of symmetric distribution model, we try to make Al and In substitution atoms distribute uniformly and symmetrically at each atomic layer in the modelling process of Ga1-xAlxAs and InyGa1-yAs nanowires. The Ga1-xAlxAs and InyGa1-yAs nanowires with different Al and In constituents are displayed in Fig. 1(b)~1(i), which are respectively obtained by replacing 0, 6, 12, 18, 24, 30, 36, 42 and 48 Ga atoms with Al and In atoms..
Fig. 1. Models of Ga1-xAlxAs and InyGa1-yAs nanowires with different Al compositions (x) and different In compositions (y). (a) x/y=0.125; (b) x/y=0.25; (c) x/y=0.375; (d) x/y=0.5; (e) x/y=0.625; (f) x/y=0.75; (g) x/y=0.875; (h) x/y=0.875; (i) x/y=1.
2. Results and discussions 2.1 Structural and stability properties Through geometry optimization, all Ga1-xAlxAs and InyGa1-yAs nanowire structures are stable. The relative stability of Ga1-xAlxAs and InyGa1-yAs nanowires are estimated by calculating the cohesive energy Ecoh based on the following formula:
Ecoh = (∑ nα µα − Etot ) / ∑ nα α
α
(1) where Etot is the total energy of Ga1-xAlxAs and InyGa1-yAs nanowires undergoing structural optimization. nα denotes the number of α atoms (Ga, As, Al, In, H). µα is the chemical potential of α atoms. The chemical potentials for Ga and As atoms that rely on material growth conditions are regarded as the most stable energy of substance. The chemical potential of H is the
half of total energy of H2 molecule. The calculated cohesive energy for Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al and In compositions are shown in Fig. 2(a). Obviously, the increase of Al and In constituent have different effects on the cohesive energy of Ga1-xAlxAs and InyGa1-yAs nanowires. For Ga1-xAlxAs nanowires, the cohesive energy exhibits a monotonically increasing trend with the range of Al component from 0 to 1, indicating that the stability of Ga1-xAlxAs nanowires are enhanced. While in InyGa1-yAs nanowire cases, the cohesive energy continuously decreases, and the lowest value is obtained in InAs nanowire model. This phenomenon can be explained by the atomic radius difference of Ga, Al and In (radius: Al
Fig. 2. (a) Cohesive energy, (b) work function and (c) band gap of Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al constituents (x) and different In constituents (y).
The work function is an essential parameter to evaluate the optoelectronic properties of semiconductors, which is defined as the difference between vacuum level and the Fermi level. Fig. 2(b) gives the calculated work function for Ga1-xAlxAs and InyGa1-yAs nanowires. GaAs (x/y=0) nanowire has a work function of 5.134 eV. It is clear to see that the work function of Ga1-xAlxAs nanowires increases linearly with the rise of Al component, which means that the difficulty of photoelectrons escaping from the nanowires is increased. While for InyGa1-yAs nanowires, with increasing In constituent, the work function increases after an initial decrease, and the work function reaches the minimum when In composition is 0.75. These results suggest that the work function of GaAs-based nanowires can be adjusted with different Al and In components. Furthermore, due to lower work function compared with other nanowires, In0.75Ga0.25As nanowires can be employed as the vacuum photoemission nano-devices. After optimization, the atomic structures of Ga1-xAlxAs and InyGa1-yAs nanowires experience series of changes. The average bond lengths of Ga-As, Al-As and In-As bonds along and perpendicular to the [0001] orientation are respectively counted. Table 1 lists the calculations for bond length of Al and In composition at 0, 0.25, 0.5, 0.75, 1. It can be found that the bond length obeys the order of In-As > Ga-As > Al-As. Long bond length means there has less electrons overlapping together and the corresponding bond population is reduced, which also verifies that the stability of these three bonds follows Al-As > Ga-As > In-As. For Ga1-xAlxAs nanowires, the bond lengths of Ga-As parallel to [0001] orientation are larger than those perpendicular to [0001] orientation, while the bonds length results for Al-As bonds are just the opposite. Besides, with increasing Al component, the bond length of Ga-As bonds parallel to [0001] orientation slightly increase, while no obvious change occurs vertical to [0001] orientation. Differing from Ga-As bonds, the bond length of Al-As bonds present an increasing trend as Al composition increases. In InyGa1-yAs nanowire models, Ga-As bonds and In-As bonds perpendicular to [0001] orientation possess longer bond lengths than those parallel to [0001] orientation. This is because the stress between atoms along the axial direction of InyGa1-yAs nanowire is greater than that in the horizontal direction, so atoms on (0001) surface can obtain more relaxation. Similar to the bond length variation of Al-As bonds in Ga1-xAlxAs nanowires, the bond length of In-As bonds increases with the increase of In constituent. These results imply that different Al and In components have a great impact on the atomic structures of Ga1-xAlxAs and InyGa1-yAs nanowires.
Table 1 Bond length of Ga1-xAlxAs and InyGa1-yAs nanowires at Al and In constituent of 0, 0.25, 0.5, 0.75 and 1. X denotes Al or In. Nanowires GaAs Ga0.75Al0.25As Ga0.5Al0.5As Ga0.25Al0.75As AlAs In0.25Ga0.75As In0.5Ga0.5As In0.75Ga0.25As InAs
Average bond length (Å) (Ga-As)//[0001]
(Ga-As)⊥[0001]
(X-As)//[0001]
(X-As)⊥[0001]
2.475 2.474 2.476 2.478 / 2.473 2.476 2.479 /
2.474 2.473 2.474 2.474 / 2.480 2.502 2.493 /
/ 2.446 2.453 2.462 2.467 2.616 2.619 2.629 2.621
/ 2.454 2.459 2.467 2.468 2.630 2.650 2.670 2.662
Table 2 Bond population and charge transfer index of Ga1-xAlxAs and InyGa1-yAs nanowires at Al and In constituent of 0, 0.25, 0.5, 0.75 and 1. Nanowires GaAs Ga0.75Al0.25As Ga0.5Al0.5As Ga0.25Al0.75As AlAs In0.25Ga0.75As In0.5Ga0.5As In0.75Ga0.25As InAs
Bond populations Ga-As
Al-As
In-As
0.600 0.564 0.558 0.552 / 0.561 0.554 0.548 /
/ 0.634 0.632 0.631 0.633 / / / /
/ / / / / 0.511 0.504 0.493 0.693
Charge transfer index 0.471 0.482 0.497 0.512 0.545 0.468 0.455 0.440 0.392
The electronegativity value of elements used in this work are Ga (1.81), As (2.18), Al (1.61), In (1.78), respectively [32]. The larger the electronegativity difference between two elements, the formed bonds will show more electrovalent properties than the covalent properties. The calculated average bond populations for Ga1-xAlxAs and InyGa1-yAs nanowires are listed in Table 2. The formed Ga-As, Al-As and In-As are all polar covalent bonds. From Table 2, the average bond population of Al-As is greater than that of Ga-As and In-As bonds. This is because the longer the bond length, the weaker the stability of bond, the less the bond population. For Ga1-xAlxAs nanowires, the average bond population of Ga-As bonds presents a decreasing trend with the increase of Al atoms, while the change in those of Al-As bonds is tiny. In InyGa1-yAs nanowires, as In constituent increases, the bond population of Ga-As bonds increases and that of In-As bonds decreases. The global charge transfer index, which is defined as the ratio of topologic charge and
the nominal oxidization state, of Ga1-xAlxAs and InyGa1-yAs nanowires are used to measure the separation from the ideal ionic model [33]. The calculations are shown in Table 2. The charge transfer index of all nanowires are between 0.3~0.6, which is good agreement with reported values [33]. With increasing Al composition, the charge transfer index increases monotonously, indicating that the polarity of Ga1-xAlxAs nanowires are enhanced. However, the charge transfer index of InyGa1-yAs nanowires decreases with the rise of In constituent, meaning that the polarity of InyGa1-yAs nanowires are reduced.
2.2 Electronic properties The band structures of Ga1-xAlxAs and InyGa1-yAs nanowires ranging from -2 eV to 3 eV are plotted in Fig. 3, where Al and In composition at 0, 0.25, 0.5, 0.75 and 1 are taken an example. In Fig. 3(a), we can see that GaAs and Ga0.75Al0.25As nanowires are direct band gap materials, while Ga0.5Al0.5As, Ga0.25Al0.75As and AlAs nanowires have indirect band gaps. Obviously, all InyGa1-yAs nanowire models shown in Fig. 3(b) are direct band gaps, which is beneficial for electrons jumping from the valence band to the conduction band. These results are in good agreement with previous reports on energy bands of bulk Ga1-xAlxAs and InyGa1-yAs materials [14, 15]. The calculated band gap for Ga1-xAlxAs and InyGa1-yAs nanowires as a function of Al and In composition are displayed in Fig. 2(c). For wurtzite GaAs nanowires without H passivation, the band gap is experimentally estimated to be less than 1.52 eV [34-36]. In this work, the calculated band gap of GaAs nanowires with H passivation is 1.63 eV, which is slightly larger than the experiment value for GaAs nanowires without H passivation. This is mainly because the H-passivated treatment removes the electron states induced by surface dangling bonds and increases the band gap. However, the diameter of actual synthesized GaAs nanowires is far larger than that used in this work (~12 Å). Based on the results of Copple et al., the band gap of GaAs nanowire increases as the wire size decreases due to the quantum confinement [37]. Therefore, it is predicted that the calculated band gap in this work is less than the experiment value of hydrogenated GaAs nanowires with the same size. This is because the band gap of materials are usually underestimated by DFT calculations [38]. Due to lack of experimental band gap for wurtzite GaAs nanowires with the diameter of 12 Å, we can’t apply an appropriate scissor operate to compensate the correction during the process of analyzing band structure and the following
optical properties. On the other hand, the experimental research on the electronic structures and optical properties for Ga1-xAlxAs and InyGa1-yAs nanowires are still at the early stage, so no relative experiment results can be applied to correct the error in the optical properties caused by undervalued band gap. Even so, in the case of no correction, it is enough to predict the physical properties of Ga1-xAlxAs and InyGa1-yAs nanowires roughly by observing the change trend of electronic and optical properties, which has been verified in our previous work [39]. The theoretical band gap value of bulk Ga1-xAlxAs and InyGa1-yAs material are also presented in Fig. 2(c) for the sake of comparison [40]. Interestingly, the variation trends of band gap for nanowires are similar to those for the bulk structures. With increasing Al and In constituent, the band gap of Ga1-xAlxAs nanowires increase, while those of InyGa1-yAs are reduced. The change of band gap mainly attributes to the movement of energy bands. From Fig. 3(a), it can be found that as Al component increases, the conduction band minimum (CBM) gradually shifts toward higher energy region and the valence band maximum (VBM) keeps basically unchanged, as a result the band gap increases. For InyGa1-yAs nanowires in Fig. 3(b), with the increase of In composition, the CBM moves to lower energy side and the VBM has no obvious change, which leads to the decline of band gap. The total density of states (TDOS) for Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al and In constituents are calculated, as shown in Fig. 4. In Fig. 4(a) and 4(b), the valence bands of GaAs (x/y=0) nanowires consists of the lower valence band with the energy from -15.63 eV to -8.96 eV and the upper valence band from -6.98 eV to 0.26 eV. The conduction bands are located the energy ranging during 1.46 eV and 3.5 eV. There appears a sharp peak at -14.45 eV, and this peak is gradually weaken with the rise of Al composition, but little change with the variation of In constituent. When Al content is up to 1, this peak completely disappears in AlAs nanowires. For Ga1-xAlxAs nanowires, the larger the Al composition, the smaller the width of upper valence band, illustrating that the effective mass of holes on the top of valence band increases. Besides, the peak near 2.13 eV of Ga1-xAlxAs nanowire at Al component of x=0 constantly shifts to higher energy side as Al component increases, which is consistent to the movement results of the conduction bands. For InyGa1-yAs nanowires, the TDOS curves for different In compositions are nearly the same. To have a deeper insight into the change of electron states induced by different Al and In
compositions, the partial density of states (PDOS) for Ga, Al and In atoms in Ga1-xAlxAs and InyGa1-yAs nanowires are provided, as depicted in Fig. 4(c) and 4(d). Because the number of As atoms in these two-type nanowires are fixed, the PDOS of As atoms will not have obvious change in the nanowires with different compositions, which has been verified in our previous work [24, 31]. Accordingly, the PDOS of As in GaAs nanowires can be found in Ref. [24]. For Ga1-xAlxAs nanowires, the lower valence band comes from Ga-s, Ga-d and As-s orbits, and there occurs a sharp peak near -14.45 eV for Ga-d electronic states. The upper valence bands are contributed by the orbitals hybridization of Ga-s, Ga-p, Al-s, Al-p and As-p state. As the Al composition increases from 0 to 1, the peaks of Ga-s, Ga-p state electrons decrease and those of Al-s and Al-p orbitals increase. The electronic states on the bottom of conduction bands are mainly formed by Ga-p, Al-p and As-s, As-p orbital hybridization. For InyGa1-yAs nanowires, the lower valence bands are induced by the interaction of Ga-d, In-d and As-s state electrons. The peaks appeared at -14.45 eV are composed of Ga-d and In-d electronic states. With the increase of In composition, the peak value of Ga-d state electrons decreases while those of In-d state increases, as a result the total state electrons remain unchanged. The upper valence bands are mainly caused by the joint effect of electronic states of Ga-s, Ga-p, In-s, In-p and As-s, and the top of valence bands are determined by Ga-p, In-p and As-p state electrons. Moreover, the state electrons on the CBM come from the orbitals hybridization of Ga-p, In-p and As-s, As-p.
Fig. 3. Band structures of (a) Ga1-xAlxAs and (b) InyGa1-yAs nanowires.
Fig. 4. Total density of state (TDOS) and partial density of state (PDOS) of Ga1-xAlxAs and InyGa1-yAs nanowires 2.3 Optical properties In order to explore a desirable material employed in optoelectronic fields, it is necessary to perform a detailed research on optical properties of nanowire materials. In this section, through calculating the absorption coefficient, reflectivity and refractive index, the effect of different Al and In components (x=y=0, 0.25, 0.5, 0.75, 1) on the optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires can be further understood. The absorption coefficient of Ga1-xAlxAs and InyGa1-yAs nanowires as a function of Al and In components are presented in Fig. 5(a) and 5(b), respectively. Obviously, the absorption coefficient for all nanowire models are all in the level of 104 cm-1, implying that Ga1-xAlxAs and InyGa1-yAs
nanowires show excellent absorption characteristics. For Ga1-xAlxAs nanowires, the highest absorption peak is achieved at 4.73 eV with the absorption coefficient of 3.79×104 cm-1 when Al component is 0. With Al constituent increasing, this absorption peak shifts to the higher energy side and the corresponding peak value is slightly reduced. However, at the energy from 5.06 eV to 8.38 eV, the absorption coefficient of Ga1-xAlxAs nanowires increases with the rise of Al composition. For InyGa1-yAs nanowires, the absorption peak is red shifted and the value of related peak is increased as In component increases. This finding demonstrates that the increase of In content can significantly improve the absorption properties of InyGa1-yAs nanowires at the lower energy (0~4.66 eV). The calculated curves of reflectivity of Ga1-xAlxAs and InyGa1-yAs nanowires varying with photon energy are displayed in Fig. 5(c) and 5(d). As can be seen, the reflectivity coefficient of all nanowires are less than 0.12, meaning that Ga1-xAlxAs and InyGa1-yAs nanowires own excellent light-trapping property. When Al and In component is equal to 0, there exists two reflection peaks respectively located at 3.62 eV and 5.08 eV. The peak intensity decreases with Al component increasing, and conversely increases as In composition increases. Moreover, the width of reflection peaks are gradually narrowed by increasing Al component. When Al constituent is up to 1, the peak at lower energy disappears. This is because the peak at 3.62 eV is formed by the transition of Ga-p electronic state. However, in the case of InyGa1-yAs nanowires, these two peaks exhibit a redshift with the increase of In composition, and the peaks width is apparently extended. These results demonstrate that the rise of Al constituent is beneficial to reduce the photon energy loss induced by reflection, while increasing In composition will be not conducive to improve the efficiency of optical absorption. Fig. 5(e) and 5(d) depict the refractive index of Ga1-xAlxAs and InyGa1-yAs nanowires. In Fig. 5(e), it can be seen that the static refractive index values for Ga1-xAlxAs nanowires decrease with Al component increasing. For InyGa1-yAs nanowires, the static refractive index values increase as In constituent increases. As the photon energy increases from 0.02 eV to 2.78 eV, the refractive index of GaAs nanowire increases and reaches the maximum value of about 1.38. During the energy of 2.78 eV and 5.49 eV, the refractive index of GaAs nanowires decreases as photon energy increases, at this moment the nanowires show the properties of abnormal dispersion [41], and a minimum value of approximately 0.67 is obtained at 5.49 eV. Moreover, the energy needed to
reach the maximum and the minimum refractive index increase with the increase of Al composition, and decrease with increasing In constituent.
Fig. 5. Optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires. (a) Adsorption coefficient, (c) reflectivity and (e) refractive index of Ga1-xAlxAs nanowires. (b) Adsorption coefficient, (d) reflectivity and (f) refractive index of InyGa1-yAs nanowires.
4. Conclusions In this work, the electronic and optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires are investigated utilizing first-principle calculations. Results show that the stability of Ga1-xAlxAs nanowires are enhanced with Al constituent increasing, while that of InyGa1-yAs nanowires are weaken as In content increases. Among nanowires, In0.75Ga0.25As nanowire owns the lowest work function. Besides, the average bond length obeys the order of In-As > Ga-As > Al-As, and the
bond population follows the rule of Al-As > Ga-As > In-As, indicating that the stability of these three bonds is Al-As > Ga-As > In-As. According to the results of charge transfer index, increasing Al component can increase the polarity of Ga1-xAlxAs nanowires, while the polarity of InyGa1-yAs nanowires are reduced with the rise of In constituent. In addition, when Al composition varies between 0 and 0.5, Ga1-xAlxAs nanowires are direct band gap materials, while as Al composition is 0.5 or over, Ga1-xAlxAs nanowires will exhibit the properties of indirect band gap. For InyGa1-yAs nanowires, the band structures are all direct band gaps. Additionally, the variation trends of band gap for nanowires are similar to those for the bulk structures. With increasing Al composition, the conduction band shifts toward higher energy and the valence band keeps unchanged, which results in the increase of band gap. The downward movement of conduction band for InyGa1-yAs nanowires induced by the increase of In composition leads to the decline of band gap. Moreover, with increasing Al and In component, the absorption peak, reflection peak and refractive index for Ga1-xAlxAs are all blue shifted, but for InyGa1-yAs nanowires those are all red shifted. Ga1-xAlxAs and InyGa1-yAs nanowires present excellent absorption characteristics with absorption coefficient in the level of 104 cm-1. It is noted that some other important physics can also affect the photoelectric properties of Ga1-xAlxAs and InyGa1-yAs nanowires, such as the size effect, hydrogenated effect and dopant effect in nanowires, which are worthy to be explored in the following study [42-44]. All calculations provide valuable guidance for the design and preparation of Ga1-xAlxAs and InyGa1-yAs nanowires based optoelectronic devices.
Acknowledgements This work is supported by Qing
Lan Project of Jiangsu Province-China (Grant
No.2017-AD41779), the Fundamental Research Funds for the Central Universities-China (Grant No.30916011206) and the Six Talent Peaks Project in Jiangsu Province-China (Grant No.2015-XCL-008). Meishan Wang of Ludong University is greatly appreciated for the help of first principle calculations.
Conflict of interest The authors declare that they have no conflict of interests in either personal or financial aspects.
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Highlights 1. The optoelectronic properties of Ga1-xAlxAs and InyGa1-yAs nanowires are compared. 2. The Ga1-xAlxAs nanowires show more stability than InyGa1-yAs nanowires. 3. In0.75Ga0.25As nanowire owns the lowest work function. 4. Ga1-xAlxAs nanowires with Al composition of 0.5 or above induce indirect band gap. 5. Ga1-xAlxAs and InyGa1-yAs nanowires present excellent absorption characteristics.
Declaration of Interest Statement Title: Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation Author(s): Yu Diao, Lei Liu*, Sihao Xia ∗ To whom correspondence should be addressed. E-mail: [email protected]
Address: Department of optoelectronic technology, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
The authors declare that they have no conflict of interests in either personal or financial aspects.
S1386-9477(19)31384-0
DOI:
https://doi.org/10.1016/j.physe.2019.113843
Reference:
PHYSE 113843
To appear in:
Physica E: Low-dimensional Systems and Nanostructures
Received Date: 12 September 2019 Revised Date:
7 November 2019
Accepted Date: 19 November 2019
Please cite this article as: Y. Diao, L. Liu, S. Xia, Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation, Physica E: Lowdimensional Systems and Nanostructures (2019), doi: https://doi.org/10.1016/j.physe.2019.113843. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation Yu Diao, Lei Liu*, Sihao Xia Department of optoelectronic technology, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China Corresponding author: Lei Liu; E-mail: [email protected]
Abstract The electronic and optical properties of composition-tunable Ga1-xAlxAs and InyGa1-yAs nanowires are investigated and compared utilizing first-principle calculations based on density functional theory. In the established nanowire models, nine different compositions (x/y=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1) are considered. The results show that increasing Al constituent can enhance the stability of Ga1-xAlxAs nanowires, while increasing In content in InyGa1-yAs nanowires results in an opposite trend. Among all nanowires, In0.75Ga0.25As nanowire exhibits the lowest work function. Interestingly, Ga1-xAlxAs nanowires with Al composition less than 0.5 are direct band gap materials, while increasing Al content to 0.5 or above will induce indirect band gap. All InyGa1-yAs nanowires are all direct band gaps. Moreover, with increasing Al and In component, the absorption peak, reflection peak and refractive index for Ga1-xAlxAs are all blue shifted while inversely those of InyGa1-yAs nanowires are all red shifted. All calculations lay important foundation for the design and preparation of Ga1-xAlxAs and InyGa1-yAs nanowires based optoelectronic devices. Key words: Composition-tunable; GaAlAs nanowires; InGaAs nanowires; Electronic properties; Optical properties
1. Introduction In the past decades, semiconductor nanowires have attracted great interest for their wide
application fields [1-4]. As the common III–V semiconductor nanowires, GaAs and InAs nanowires show enormous promise as building blocks of various nanoscale optoelectronic devices, such as light-emitting diodes, detectors and photovoltaic devices [5-9]. However, the band gap for these binary III–V nanowires is invariable, thus they are just suitable for the nanodevices with specific wavelength. To satisfy the demand for higher sensitivity and wider spectral response range, ternary GaAlAs and InGaAs nanowires are respectively proposed to offer a wider application prospects in the blue extension and near-infrared optoelectronics field, which thanks to their tunable bandgap. The physics properties of GaAlAs and InGaAs nanowires will be changed with the variation of Al and In constituent. Zou et al. developed a graded band-gap AlGaAs/GaAs wire photocathode [10]. Compared with GaAs wire photocathode, the photoemission for photocathodes with linearly graded Al composition ranges of 0 to 0.1, 0.2, 0.3, and 0.4 are enhanced by 29.5%~43.8%. Liu et al. proposed a GaAs nanowire cathode with graded Al composition structure as photon-enhanced thermionic emission device for higher conversion efficiency [11]. Beleckaite et al. utilized terahertz time-domain spectroscopy to observe the terahertz emission properties of composition-tunable InGaAs nanowire arrays. Results show there appears a substantially enhanced THz emission efficiency with In composition decreasing from 1 to 0.5 [12]. Zota et al reported an improved InGaAs nanowire MOSFETs by increasing the Indium content from 0.53 to 0.63 [13]. Although some progress has been made in the growth and applications of GaAlAs and InGaAs nanowires, the research on their fundamental properties is still at the early stage. So far, extensive theoretical and experimental efforts have been devoted to study the electronic and optical properties of bulk GaAlAs, bulk InGaAs, GaAs nanowires and InAs nanowires [14-19]. However, a detailed comparative research on the effect of different compositions on electronic and optical properties of GaAlAs and InGaAs nanowires is relatively lack. In fact, the comparison of these two nanowire materials can allow us to recognize which component of nanowires are suitable for different applications. In addition, it will also allow us to compare the properties of nanowire structure with those of bulk ones, which is beneficial to predict the future challenges. In this work, the first-principles method is employed to systematically investigate on the optoelectronic properties of composition-tunable Ga1-xAlxAs and InyGa1-yAs nanowires. Nine different Al and In constituents are considered to establish III-As nanowire models, including
x/y=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1. Cohesive energy, work function, atomic structure, band structure, density of state, absorption coefficient, reflectivity and refractive index of different nanowires are calculated and analyzed. This research lays an important theoretical basis for the fabrication and application of Ga1-xAlxAs and InyGa1-yAs nano-based optoelectronic devices.
2. Computational details All first-principle calculations in this work were accomplished with employing the quantum mechanics software CASTEP based on the density functional theory [20]. Perdew, Burke, Ernzerhof (PBE) method with generalized gradient approximation (GGA) function were used for the exchange-correlation potential [21, 22]. The electron wave function was expanded in plane waves with a cutoff energy of 480 eV. The first Brillouin zone was sampled by a 1×1×5 Monkhorst k-point grid. A larger vacuum region of 15 Å was adopted to avoid the interference between periodic structures. The geometries were fully relaxed using the conjugated gradient method until the total energy converged to 10-3 eV and the forces of all atoms were smaller than 10-4 eV/Å. The valence-electron configurations for Ga, As, Al, In were respectively treated as 3d104s24p1, 4s24p3, 3s23p1, 4d105s25p1. Most of experiment results have reported that wurtzite GaAs nanowires have stronger stability than the zinc-blende ones when the diameter is smaller than 15 nm [23]. Therefore, wurtzite structure is selected as the crystal structure of nanowires. Besides, the wurtzite GaAs nanowires have hexagonal across sections with six facets orthogonal to the growth direction, where these side facets are oriented (10-10) and (11-20). According to these experimental observations, the wurtzite GaAs nanowire model along [0001] orientation are established, and the top view and side view of corresponding model are shown in Fig. 1(a). The modelling details of GaAs nanowires can be found in our previous work [24]. The surface of nanostructures is usually unstable due to the existence of surface dangling bonds, and its surface charge are often neutralized by surface passivation [25]. Hence, surface atoms of GaAlAs and InGaAs nanowires in this work are all passivated by hydrogen atoms to remove localized energy state close to or at the Fermi level and avoid the effect of additional charge transfer on the photoelectric properties [24, 26, 27]. Namely, the surface effects on nanowires are not discussed in this paper. In Fig. 1(a),
there are 48 Ga, 48 As and 48 H atoms in GaAs nanowire model. Although the used nanowire size is far smaller than the synthesized GaAs nanowires, it is believed that the calculations can still predict the trends of electronic and optical properties [28, 29]. The Ga1-xAlxAs and InyGa1-yAs nanowires are respectively built by substituting the Ga atoms of GaAs nanowires with Al and In atoms. Here, nine different Al and In compositions are considered, including 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1. Taken Ga0.75Al0.25As nanowires as an example, we have performed a comparative research on the effect of different Al substitution configurations on the structural stability of Ga0.75Al0.25As nanowires. The detailed atomic structures and calculations are given in Supplementary material S1. Results imply that all substitution atoms tend to distribute uniformly at each atomic layer of nanowires due to its lower energy. According to the results of Yang et al and Xia et al [30, 31], it is found that the selection of substitution atoms obeys the spatially para-position symmetric distribution, which can make the model obtain the minimum energy. Thus, based on the minimum energy principle of symmetric distribution model, we try to make Al and In substitution atoms distribute uniformly and symmetrically at each atomic layer in the modelling process of Ga1-xAlxAs and InyGa1-yAs nanowires. The Ga1-xAlxAs and InyGa1-yAs nanowires with different Al and In constituents are displayed in Fig. 1(b)~1(i), which are respectively obtained by replacing 0, 6, 12, 18, 24, 30, 36, 42 and 48 Ga atoms with Al and In atoms..
Fig. 1. Models of Ga1-xAlxAs and InyGa1-yAs nanowires with different Al compositions (x) and different In compositions (y). (a) x/y=0.125; (b) x/y=0.25; (c) x/y=0.375; (d) x/y=0.5; (e) x/y=0.625; (f) x/y=0.75; (g) x/y=0.875; (h) x/y=0.875; (i) x/y=1.
2. Results and discussions 2.1 Structural and stability properties Through geometry optimization, all Ga1-xAlxAs and InyGa1-yAs nanowire structures are stable. The relative stability of Ga1-xAlxAs and InyGa1-yAs nanowires are estimated by calculating the cohesive energy Ecoh based on the following formula:
Ecoh = (∑ nα µα − Etot ) / ∑ nα α
α
(1) where Etot is the total energy of Ga1-xAlxAs and InyGa1-yAs nanowires undergoing structural optimization. nα denotes the number of α atoms (Ga, As, Al, In, H). µα is the chemical potential of α atoms. The chemical potentials for Ga and As atoms that rely on material growth conditions are regarded as the most stable energy of substance. The chemical potential of H is the
half of total energy of H2 molecule. The calculated cohesive energy for Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al and In compositions are shown in Fig. 2(a). Obviously, the increase of Al and In constituent have different effects on the cohesive energy of Ga1-xAlxAs and InyGa1-yAs nanowires. For Ga1-xAlxAs nanowires, the cohesive energy exhibits a monotonically increasing trend with the range of Al component from 0 to 1, indicating that the stability of Ga1-xAlxAs nanowires are enhanced. While in InyGa1-yAs nanowire cases, the cohesive energy continuously decreases, and the lowest value is obtained in InAs nanowire model. This phenomenon can be explained by the atomic radius difference of Ga, Al and In (radius: Al
Fig. 2. (a) Cohesive energy, (b) work function and (c) band gap of Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al constituents (x) and different In constituents (y).
The work function is an essential parameter to evaluate the optoelectronic properties of semiconductors, which is defined as the difference between vacuum level and the Fermi level. Fig. 2(b) gives the calculated work function for Ga1-xAlxAs and InyGa1-yAs nanowires. GaAs (x/y=0) nanowire has a work function of 5.134 eV. It is clear to see that the work function of Ga1-xAlxAs nanowires increases linearly with the rise of Al component, which means that the difficulty of photoelectrons escaping from the nanowires is increased. While for InyGa1-yAs nanowires, with increasing In constituent, the work function increases after an initial decrease, and the work function reaches the minimum when In composition is 0.75. These results suggest that the work function of GaAs-based nanowires can be adjusted with different Al and In components. Furthermore, due to lower work function compared with other nanowires, In0.75Ga0.25As nanowires can be employed as the vacuum photoemission nano-devices. After optimization, the atomic structures of Ga1-xAlxAs and InyGa1-yAs nanowires experience series of changes. The average bond lengths of Ga-As, Al-As and In-As bonds along and perpendicular to the [0001] orientation are respectively counted. Table 1 lists the calculations for bond length of Al and In composition at 0, 0.25, 0.5, 0.75, 1. It can be found that the bond length obeys the order of In-As > Ga-As > Al-As. Long bond length means there has less electrons overlapping together and the corresponding bond population is reduced, which also verifies that the stability of these three bonds follows Al-As > Ga-As > In-As. For Ga1-xAlxAs nanowires, the bond lengths of Ga-As parallel to [0001] orientation are larger than those perpendicular to [0001] orientation, while the bonds length results for Al-As bonds are just the opposite. Besides, with increasing Al component, the bond length of Ga-As bonds parallel to [0001] orientation slightly increase, while no obvious change occurs vertical to [0001] orientation. Differing from Ga-As bonds, the bond length of Al-As bonds present an increasing trend as Al composition increases. In InyGa1-yAs nanowire models, Ga-As bonds and In-As bonds perpendicular to [0001] orientation possess longer bond lengths than those parallel to [0001] orientation. This is because the stress between atoms along the axial direction of InyGa1-yAs nanowire is greater than that in the horizontal direction, so atoms on (0001) surface can obtain more relaxation. Similar to the bond length variation of Al-As bonds in Ga1-xAlxAs nanowires, the bond length of In-As bonds increases with the increase of In constituent. These results imply that different Al and In components have a great impact on the atomic structures of Ga1-xAlxAs and InyGa1-yAs nanowires.
Table 1 Bond length of Ga1-xAlxAs and InyGa1-yAs nanowires at Al and In constituent of 0, 0.25, 0.5, 0.75 and 1. X denotes Al or In. Nanowires GaAs Ga0.75Al0.25As Ga0.5Al0.5As Ga0.25Al0.75As AlAs In0.25Ga0.75As In0.5Ga0.5As In0.75Ga0.25As InAs
Average bond length (Å) (Ga-As)//[0001]
(Ga-As)⊥[0001]
(X-As)//[0001]
(X-As)⊥[0001]
2.475 2.474 2.476 2.478 / 2.473 2.476 2.479 /
2.474 2.473 2.474 2.474 / 2.480 2.502 2.493 /
/ 2.446 2.453 2.462 2.467 2.616 2.619 2.629 2.621
/ 2.454 2.459 2.467 2.468 2.630 2.650 2.670 2.662
Table 2 Bond population and charge transfer index of Ga1-xAlxAs and InyGa1-yAs nanowires at Al and In constituent of 0, 0.25, 0.5, 0.75 and 1. Nanowires GaAs Ga0.75Al0.25As Ga0.5Al0.5As Ga0.25Al0.75As AlAs In0.25Ga0.75As In0.5Ga0.5As In0.75Ga0.25As InAs
Bond populations Ga-As
Al-As
In-As
0.600 0.564 0.558 0.552 / 0.561 0.554 0.548 /
/ 0.634 0.632 0.631 0.633 / / / /
/ / / / / 0.511 0.504 0.493 0.693
Charge transfer index 0.471 0.482 0.497 0.512 0.545 0.468 0.455 0.440 0.392
The electronegativity value of elements used in this work are Ga (1.81), As (2.18), Al (1.61), In (1.78), respectively [32]. The larger the electronegativity difference between two elements, the formed bonds will show more electrovalent properties than the covalent properties. The calculated average bond populations for Ga1-xAlxAs and InyGa1-yAs nanowires are listed in Table 2. The formed Ga-As, Al-As and In-As are all polar covalent bonds. From Table 2, the average bond population of Al-As is greater than that of Ga-As and In-As bonds. This is because the longer the bond length, the weaker the stability of bond, the less the bond population. For Ga1-xAlxAs nanowires, the average bond population of Ga-As bonds presents a decreasing trend with the increase of Al atoms, while the change in those of Al-As bonds is tiny. In InyGa1-yAs nanowires, as In constituent increases, the bond population of Ga-As bonds increases and that of In-As bonds decreases. The global charge transfer index, which is defined as the ratio of topologic charge and
the nominal oxidization state, of Ga1-xAlxAs and InyGa1-yAs nanowires are used to measure the separation from the ideal ionic model [33]. The calculations are shown in Table 2. The charge transfer index of all nanowires are between 0.3~0.6, which is good agreement with reported values [33]. With increasing Al composition, the charge transfer index increases monotonously, indicating that the polarity of Ga1-xAlxAs nanowires are enhanced. However, the charge transfer index of InyGa1-yAs nanowires decreases with the rise of In constituent, meaning that the polarity of InyGa1-yAs nanowires are reduced.
2.2 Electronic properties The band structures of Ga1-xAlxAs and InyGa1-yAs nanowires ranging from -2 eV to 3 eV are plotted in Fig. 3, where Al and In composition at 0, 0.25, 0.5, 0.75 and 1 are taken an example. In Fig. 3(a), we can see that GaAs and Ga0.75Al0.25As nanowires are direct band gap materials, while Ga0.5Al0.5As, Ga0.25Al0.75As and AlAs nanowires have indirect band gaps. Obviously, all InyGa1-yAs nanowire models shown in Fig. 3(b) are direct band gaps, which is beneficial for electrons jumping from the valence band to the conduction band. These results are in good agreement with previous reports on energy bands of bulk Ga1-xAlxAs and InyGa1-yAs materials [14, 15]. The calculated band gap for Ga1-xAlxAs and InyGa1-yAs nanowires as a function of Al and In composition are displayed in Fig. 2(c). For wurtzite GaAs nanowires without H passivation, the band gap is experimentally estimated to be less than 1.52 eV [34-36]. In this work, the calculated band gap of GaAs nanowires with H passivation is 1.63 eV, which is slightly larger than the experiment value for GaAs nanowires without H passivation. This is mainly because the H-passivated treatment removes the electron states induced by surface dangling bonds and increases the band gap. However, the diameter of actual synthesized GaAs nanowires is far larger than that used in this work (~12 Å). Based on the results of Copple et al., the band gap of GaAs nanowire increases as the wire size decreases due to the quantum confinement [37]. Therefore, it is predicted that the calculated band gap in this work is less than the experiment value of hydrogenated GaAs nanowires with the same size. This is because the band gap of materials are usually underestimated by DFT calculations [38]. Due to lack of experimental band gap for wurtzite GaAs nanowires with the diameter of 12 Å, we can’t apply an appropriate scissor operate to compensate the correction during the process of analyzing band structure and the following
optical properties. On the other hand, the experimental research on the electronic structures and optical properties for Ga1-xAlxAs and InyGa1-yAs nanowires are still at the early stage, so no relative experiment results can be applied to correct the error in the optical properties caused by undervalued band gap. Even so, in the case of no correction, it is enough to predict the physical properties of Ga1-xAlxAs and InyGa1-yAs nanowires roughly by observing the change trend of electronic and optical properties, which has been verified in our previous work [39]. The theoretical band gap value of bulk Ga1-xAlxAs and InyGa1-yAs material are also presented in Fig. 2(c) for the sake of comparison [40]. Interestingly, the variation trends of band gap for nanowires are similar to those for the bulk structures. With increasing Al and In constituent, the band gap of Ga1-xAlxAs nanowires increase, while those of InyGa1-yAs are reduced. The change of band gap mainly attributes to the movement of energy bands. From Fig. 3(a), it can be found that as Al component increases, the conduction band minimum (CBM) gradually shifts toward higher energy region and the valence band maximum (VBM) keeps basically unchanged, as a result the band gap increases. For InyGa1-yAs nanowires in Fig. 3(b), with the increase of In composition, the CBM moves to lower energy side and the VBM has no obvious change, which leads to the decline of band gap. The total density of states (TDOS) for Ga1-xAlxAs and InyGa1-yAs nanowires varying with different Al and In constituents are calculated, as shown in Fig. 4. In Fig. 4(a) and 4(b), the valence bands of GaAs (x/y=0) nanowires consists of the lower valence band with the energy from -15.63 eV to -8.96 eV and the upper valence band from -6.98 eV to 0.26 eV. The conduction bands are located the energy ranging during 1.46 eV and 3.5 eV. There appears a sharp peak at -14.45 eV, and this peak is gradually weaken with the rise of Al composition, but little change with the variation of In constituent. When Al content is up to 1, this peak completely disappears in AlAs nanowires. For Ga1-xAlxAs nanowires, the larger the Al composition, the smaller the width of upper valence band, illustrating that the effective mass of holes on the top of valence band increases. Besides, the peak near 2.13 eV of Ga1-xAlxAs nanowire at Al component of x=0 constantly shifts to higher energy side as Al component increases, which is consistent to the movement results of the conduction bands. For InyGa1-yAs nanowires, the TDOS curves for different In compositions are nearly the same. To have a deeper insight into the change of electron states induced by different Al and In
compositions, the partial density of states (PDOS) for Ga, Al and In atoms in Ga1-xAlxAs and InyGa1-yAs nanowires are provided, as depicted in Fig. 4(c) and 4(d). Because the number of As atoms in these two-type nanowires are fixed, the PDOS of As atoms will not have obvious change in the nanowires with different compositions, which has been verified in our previous work [24, 31]. Accordingly, the PDOS of As in GaAs nanowires can be found in Ref. [24]. For Ga1-xAlxAs nanowires, the lower valence band comes from Ga-s, Ga-d and As-s orbits, and there occurs a sharp peak near -14.45 eV for Ga-d electronic states. The upper valence bands are contributed by the orbitals hybridization of Ga-s, Ga-p, Al-s, Al-p and As-p state. As the Al composition increases from 0 to 1, the peaks of Ga-s, Ga-p state electrons decrease and those of Al-s and Al-p orbitals increase. The electronic states on the bottom of conduction bands are mainly formed by Ga-p, Al-p and As-s, As-p orbital hybridization. For InyGa1-yAs nanowires, the lower valence bands are induced by the interaction of Ga-d, In-d and As-s state electrons. The peaks appeared at -14.45 eV are composed of Ga-d and In-d electronic states. With the increase of In composition, the peak value of Ga-d state electrons decreases while those of In-d state increases, as a result the total state electrons remain unchanged. The upper valence bands are mainly caused by the joint effect of electronic states of Ga-s, Ga-p, In-s, In-p and As-s, and the top of valence bands are determined by Ga-p, In-p and As-p state electrons. Moreover, the state electrons on the CBM come from the orbitals hybridization of Ga-p, In-p and As-s, As-p.
Fig. 3. Band structures of (a) Ga1-xAlxAs and (b) InyGa1-yAs nanowires.
Fig. 4. Total density of state (TDOS) and partial density of state (PDOS) of Ga1-xAlxAs and InyGa1-yAs nanowires 2.3 Optical properties In order to explore a desirable material employed in optoelectronic fields, it is necessary to perform a detailed research on optical properties of nanowire materials. In this section, through calculating the absorption coefficient, reflectivity and refractive index, the effect of different Al and In components (x=y=0, 0.25, 0.5, 0.75, 1) on the optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires can be further understood. The absorption coefficient of Ga1-xAlxAs and InyGa1-yAs nanowires as a function of Al and In components are presented in Fig. 5(a) and 5(b), respectively. Obviously, the absorption coefficient for all nanowire models are all in the level of 104 cm-1, implying that Ga1-xAlxAs and InyGa1-yAs
nanowires show excellent absorption characteristics. For Ga1-xAlxAs nanowires, the highest absorption peak is achieved at 4.73 eV with the absorption coefficient of 3.79×104 cm-1 when Al component is 0. With Al constituent increasing, this absorption peak shifts to the higher energy side and the corresponding peak value is slightly reduced. However, at the energy from 5.06 eV to 8.38 eV, the absorption coefficient of Ga1-xAlxAs nanowires increases with the rise of Al composition. For InyGa1-yAs nanowires, the absorption peak is red shifted and the value of related peak is increased as In component increases. This finding demonstrates that the increase of In content can significantly improve the absorption properties of InyGa1-yAs nanowires at the lower energy (0~4.66 eV). The calculated curves of reflectivity of Ga1-xAlxAs and InyGa1-yAs nanowires varying with photon energy are displayed in Fig. 5(c) and 5(d). As can be seen, the reflectivity coefficient of all nanowires are less than 0.12, meaning that Ga1-xAlxAs and InyGa1-yAs nanowires own excellent light-trapping property. When Al and In component is equal to 0, there exists two reflection peaks respectively located at 3.62 eV and 5.08 eV. The peak intensity decreases with Al component increasing, and conversely increases as In composition increases. Moreover, the width of reflection peaks are gradually narrowed by increasing Al component. When Al constituent is up to 1, the peak at lower energy disappears. This is because the peak at 3.62 eV is formed by the transition of Ga-p electronic state. However, in the case of InyGa1-yAs nanowires, these two peaks exhibit a redshift with the increase of In composition, and the peaks width is apparently extended. These results demonstrate that the rise of Al constituent is beneficial to reduce the photon energy loss induced by reflection, while increasing In composition will be not conducive to improve the efficiency of optical absorption. Fig. 5(e) and 5(d) depict the refractive index of Ga1-xAlxAs and InyGa1-yAs nanowires. In Fig. 5(e), it can be seen that the static refractive index values for Ga1-xAlxAs nanowires decrease with Al component increasing. For InyGa1-yAs nanowires, the static refractive index values increase as In constituent increases. As the photon energy increases from 0.02 eV to 2.78 eV, the refractive index of GaAs nanowire increases and reaches the maximum value of about 1.38. During the energy of 2.78 eV and 5.49 eV, the refractive index of GaAs nanowires decreases as photon energy increases, at this moment the nanowires show the properties of abnormal dispersion [41], and a minimum value of approximately 0.67 is obtained at 5.49 eV. Moreover, the energy needed to
reach the maximum and the minimum refractive index increase with the increase of Al composition, and decrease with increasing In constituent.
Fig. 5. Optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires. (a) Adsorption coefficient, (c) reflectivity and (e) refractive index of Ga1-xAlxAs nanowires. (b) Adsorption coefficient, (d) reflectivity and (f) refractive index of InyGa1-yAs nanowires.
4. Conclusions In this work, the electronic and optical properties of Ga1-xAlxAs and InyGa1-yAs nanowires are investigated utilizing first-principle calculations. Results show that the stability of Ga1-xAlxAs nanowires are enhanced with Al constituent increasing, while that of InyGa1-yAs nanowires are weaken as In content increases. Among nanowires, In0.75Ga0.25As nanowire owns the lowest work function. Besides, the average bond length obeys the order of In-As > Ga-As > Al-As, and the
bond population follows the rule of Al-As > Ga-As > In-As, indicating that the stability of these three bonds is Al-As > Ga-As > In-As. According to the results of charge transfer index, increasing Al component can increase the polarity of Ga1-xAlxAs nanowires, while the polarity of InyGa1-yAs nanowires are reduced with the rise of In constituent. In addition, when Al composition varies between 0 and 0.5, Ga1-xAlxAs nanowires are direct band gap materials, while as Al composition is 0.5 or over, Ga1-xAlxAs nanowires will exhibit the properties of indirect band gap. For InyGa1-yAs nanowires, the band structures are all direct band gaps. Additionally, the variation trends of band gap for nanowires are similar to those for the bulk structures. With increasing Al composition, the conduction band shifts toward higher energy and the valence band keeps unchanged, which results in the increase of band gap. The downward movement of conduction band for InyGa1-yAs nanowires induced by the increase of In composition leads to the decline of band gap. Moreover, with increasing Al and In component, the absorption peak, reflection peak and refractive index for Ga1-xAlxAs are all blue shifted, but for InyGa1-yAs nanowires those are all red shifted. Ga1-xAlxAs and InyGa1-yAs nanowires present excellent absorption characteristics with absorption coefficient in the level of 104 cm-1. It is noted that some other important physics can also affect the photoelectric properties of Ga1-xAlxAs and InyGa1-yAs nanowires, such as the size effect, hydrogenated effect and dopant effect in nanowires, which are worthy to be explored in the following study [42-44]. All calculations provide valuable guidance for the design and preparation of Ga1-xAlxAs and InyGa1-yAs nanowires based optoelectronic devices.
Acknowledgements This work is supported by Qing
Lan Project of Jiangsu Province-China (Grant
No.2017-AD41779), the Fundamental Research Funds for the Central Universities-China (Grant No.30916011206) and the Six Talent Peaks Project in Jiangsu Province-China (Grant No.2015-XCL-008). Meishan Wang of Ludong University is greatly appreciated for the help of first principle calculations.
Conflict of interest The authors declare that they have no conflict of interests in either personal or financial aspects.
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Highlights 1. The optoelectronic properties of Ga1-xAlxAs and InyGa1-yAs nanowires are compared. 2. The Ga1-xAlxAs nanowires show more stability than InyGa1-yAs nanowires. 3. In0.75Ga0.25As nanowire owns the lowest work function. 4. Ga1-xAlxAs nanowires with Al composition of 0.5 or above induce indirect band gap. 5. Ga1-xAlxAs and InyGa1-yAs nanowires present excellent absorption characteristics.
Declaration of Interest Statement Title: Comparative study on electronic and optical properties for composition-tunable GaAlAs and InGaAs nanowires from first-principles calculation Author(s): Yu Diao, Lei Liu*, Sihao Xia ∗ To whom correspondence should be addressed. E-mail: [email protected]
Address: Department of optoelectronic technology, School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
The authors declare that they have no conflict of interests in either personal or financial aspects.