MXene-GaAs heterojunctions: interface modeling, electronic properties and optical absorption

MXene has gained favor in the field of material research and development due to its excellent two-dimensional structural properties, electronic structure properties, scalability, etc The heterostructures with MXene on one end not only make full use of the characteristics of MXene itself but also have the potential for transformative and application-rich materials when combined with other materials on the opposite end. Inspired by potentials in MXene-contained heterojunctions, this study focuses on the MXene-GaAs heterostructures to better understand their binding characters, structure features, and electron structures. First, the heterostructures (GaAs-Ti3C2O, GaAs-Ti3C2F, and GaAs-Ti3C2OH) are modeled aiming to provide comprehensive insights into their formation. The results reveal that the MXene layer in these heterostructures plays a crucial role in protecting the GaAs crystal, as evidenced by the substantial binding energy observed. Among the three heterostructures, GaAs-Ti3C2OH shows the closest proximity at the interface, attributed to the strong binding between MXene surfaces and Ga atoms. Various analyses, including binding energy calculations, charge polarization evaluations, interface electrostatic potential biases, and electron localization function studies, yield valuable insights into the formation process of these heterojunctions. Moreover, the incorporation of MXene layers enables electron conduction, effectively transforming the heterostructures into Schottky barriers. The density of states (DOS) analysis reveals pronounced peaks near the Fermi levels, indicating excellent electron mobility. Notably, all three heterostructures demonstrate weak magnetic features of the surface GaAs near the Fermi levels, imparted by the MXene layers. Lastly, optical simulations predict an absorption peak located around 4.3 eV for GaAs-Ti3C2OH.


Introduction
Two-dimensional (2D) materials show their unique properties which may be significantly different from their 3D bulk complements.MXene is an intriguing class of two-dimensional materials that have emerged as a promising research topic in recent years.These materials exhibit a layered structure, with transition metal atoms sandwiched between two layers of carbon or nitrogen [1].A typical MXene contains a wafer-liked structure of n +1 layers of early transition metal and n layers of Carbon (or Nitrogen) in an alternative pattern that is protected by two layers of termination units (e.g.hydroxyl, oxygen, or fluorine) [2].MXenes were first introduced by Naguib et al in 2011 [3].The tunability of MXenes allows researchers to modify their properties to suit specific application requirements [4,5].MXenes are highly customizable materials in composition, surface functionalization, intercalation, layer thickness adjustment, hybridization, etc [6].Since 2011, the MXene family increases significantly with many new members with versatile chemical and physical properties.Even MXene alloys are proposed in theoretical investigations [7].
Due to their metallic nature, MXenes possess high electrical conductivities, making them attractive for applications in electronics and energy storage [8].MXenes have shown great potential in developing nextgeneration supercapacitors and batteries with enhanced performance and faster charge/discharge rates [9].
Their ability to accommodate ions and charge carriers within their layered structure provides a unique advantage for energy storage applications [10].In addition to their electrical properties, MXenes also demonstrate impressive electrochemical activity [11].The large surface area and abundant active sites on their layered structures provide opportunities for catalytic applications [12].This opens up avenues for MXenes to be used in fuel cells, water electrolysis, and other energy conversion devices.
For further construction needs in material science, MXenes also show their potential in forming heterostructures.One form of such heterostructures is layer-by-layer precisely chosen sequences [13].The fabrication of heterostructures incorporating 2D materials is simplified compared to constructing heterojunctions with bulk materials, as the interaction between the layers within a heterostructure relies on van der Waals forces.An advantage of the surface layer, also referred to as the layer of termination units, is its propensity for clean adhesion to semiconductors without significant interference [14].Extensive research efforts have been devoted to synthesizing or theoretically investigating various MXene-based heterostructures.For instance, the electronic structure of graphene/MXene heterostructures has been extensively studied [15].Zhao et al reported the electronic structure of MoS 2 /MXene heterostructures with extensive details [16].Sun et al reported the properties and synthesis of g-C 3 N 4 /MXene heterostructure [17].
Heterostructures involving MXenes have demonstrated remarkable chemical and physical properties, making them highly promising in various fields.These heterostructures exhibit notable catalytic efficiency [18], particularly in widely studied catalytic areas such as the N 2 reduction reaction (NRR) [19], hydrogen evolution reaction (HER) [20], and oxygen reduction reaction (ORR) [21].Furthermore, MXenes possess intriguing optical properties across different domains and may extend applications of traditional semi-conductors such as GaAs.Notably, a recent study reported an MXene/GaAs heterostructure with excellent photovoltaic efficiency [22], thereby expanding the potential applications of MXene-based heterostructures into new realms.Besides, replacing the gold electrodes from GaAs photodetectors by Ti 3 C 2 brings superior performance enhancement [23].Similar approach is applied to MXene/GaAs Schottky junction, exhibiting wide waveband sensitivity, high responsivity [24].In addition, similar structure, Ti 3 C 2 T x /GaN is fabricated using an easy-processing spraydeposition route, exhibiting high responsivity as a UV photodiode [25].Other variances of MXene/ semiconductor heterostructures such as MXene/Si [26], and MXene/Ga 2 O 3 [27] with special optical properties are also reported recently.
In this work, inspired by recent experimental results [22] and fruitful investigations of MXene/ semiconductor heterostructures, heterostructures of Ti 3 C 2 T x (T x = O, F, and OH) MXene and GaAs is investigated.Theoretical examinations focus on the formation and binding of the interfaces, binding between atoms near the interfaces, band structures and optical properties.With the modeling and simulations of binding interfaces which has not been systematically reported before, electron structure-oriented analysis can be applied for better understanding of in-depth mechanism form quantum theory level to inspire further design of MXene contained heterostructures.

Simulation methods
In the pursuit of examining the electron structure properties, Density Functional Theory (DFT) serves as a valuable tool for conducting simulations.VASP is employed with the PBE functional as the exchangecorrelation potential for simulations in this work.In light of the lattice constant, particular attention is given to the 〈111〉 direction of GaAs, which serves as the designated surface of exposure to contact the MXene (see modeling part in the next section).To obtain stable structures of the heterojunctions, geometry relaxations are applied to the MXene only with the GaAs geometry fixed.In addition, as heterostructures, the K point space is set to 3 ´3 ´1 to allow the periodic boundaries to extend along a and b directions.A more than 10 Å vacuum layer is added to the c (perpendicular) direction of the junction.The relaxed geometry with interatomic forces below 0.01 eV/ Å is accepted to make further exploration of the properties of the interface.In the simulation of density of states (DOS), the K point mesh is increased to 6 ´6 ´1 which reaches the maximum capacity of the computer.
With the results of DFT simulations, the binding energy can be simulated as: --E b is the binding energy which is calculated as the difference between the combined energy E hetero and the summation of isolated parts, E MXene and E GaAs .A represent the area of the interface.Similarly, we can simulate the charge difference as The charge difference, denoted as n diff is determined by subtracting the net charge density distribution n hetero from the sum of two separate charge components.The analysis of binding energy and charge difference provides valuable insights into the interaction mechanism underlying the formation of the heterostructure.This approach enables a comprehensive examination of charge redistribution as a manifestation of the interaction between distinct materials.Furthermore, to gain deeper insights into the chemical bonding at the interface, the Electron Localization Function (ELF) is employed as a tool to extract the bond features.

Lattice match at the interface
Before any further simulations can be made, it is critical to find the geometrical structures of the heterojunction.
As one can see from the experimental results (figure 1(A), adopted from reference), there is a clear interface between the GaAs crystal and the MXene lattice.Therefore, the lattice match between the two materials should be considered.However, the lattice constant of GaAs and MXene are 5.75 and 3.08 (figures 1(B)-(C)), which cannot be matched directly.The 〈100〉 plane of GaAs is not the expected plane next to the interface.In the 〈111〉 plane of GaAs, the distance between two neighboring Ga atoms is 4.06 Å (figure 1(B)).Thus, a 3 × 3 supercell of pure GaAs (the lattice constant is 12.198) along 〈111〉 direction matches a 4 × 4 supercell of pure MXexe (the lattice constant is 12.3152).One can evaluate the mismatch as follows: Mismatch a a a a 0.5 0.96% 3 The mismatch between the two pure materials is below 1% which is sufficiently small.As a result, one can expect the formation of the heterojunction as shown in figure 1(D).

Bindings in heterojunctions
Based on the expectation of the lattice matching, one can expect the heterostructure formation depends on the electrostatic binding of the bulk GaAs and layers of MXene sheets.) [28].But the GaAs attract the MXene side with at least −0.634J m −2 binding energy.The GaAs-induced improvements in binding to MXene sides are consistent among different variations of MXene with a most significant binding of −2.118 J/m 2 .Such significant enhancement in binding energy indicates the stronger stability of the MXene adhesion.This partially answers the origination of the experimental stability of the heterostructure which is stable for 30 days [22].MXene is not only a functional part of the heterostructure but also a protection layer to prevent the formation of an oxidation layer on the GaAs surface.
In addition, the distances between MXene layers and the GaAs bulk vary in different heterojunctions.The GaAs-Ti 3 C 2 OH structure shows the shortest separation while the GaAs-Ti 3 C 2 F shows the largest separation.As the MXene layers are decorated with more complicated structures, the contained Ti and C atoms may get further away from the GaAs bulk.

Charge in heterojunctions
With the charge difference analysis which is simulated with equation (2), the redistribution of the electrons can be visualized by the isosurfaces of the charges.As the formation of the interface, electrons transfer from the surface of GaAs to MXene and leave holes behind in the absence of electric fields.This is due to the higher electronic affinity of the functional groups on MXene (O, F, and OH units on the surfaces) than bulk GaAs.As shown in figure 2(A), one can see the significant concentration of electron clouds around oxygen atoms near the interface.To compare such charge redistribution, one can split electron affinity of function groups into bonding affinity and excess affinity.The bonding affinity refers the interaction within MXene (Ti-O, Ti-F or Ti-OH) while the exess affinity influence the electron across the interface.The excess affinity of such a layer of oxygen atoms is the most significant among the 3 different interfaces.In contrast, the excess affinity of F is much weaker than that of O (figure 2(B)) due to its limitation by Ti-F bonding.The H atom in OH of the MXene also shows some excess affinity (similar to hydrogen bonds) but the electrons have been pushed to the middle of the interface (figure 2(C)).
Concretely, such electron redistribution can be quantified by plotting the planar average of the ab plane along the c-axis (figure 2(D)).In general, electrons and holes show polarization near the interface in all 3 heterostructures.GaAs-Ti 3 C 2 O shows the largest amplitude in the polarization while GaAs-Ti 3 C 2 F shows the smallest amplitude.In the GaAs-Ti 3 C 2 OH structure, the hydrogen atoms push the polarization close to the interface and leave a rapid but sharp change near the interface.

Properties at the interface of the heterostructure
Besides the charge redistribution near 3 interfaces, the intrinsic driving in electron redistribution is analyzed via electron static potentials (ESPs) which represent the total electric potential as the nuclei and electron cloud as static charges.By taking the planar average across the ab plane and plotting the averaged value along the c direction, the electric features can be seen.As shown in figure 3(A), all 3 heterostructures show a bias from the GaAs side to the MXene side which indicates the intrinsic driving.The peaks near the interfaces (black solid lines) are the results of the equilibria after charge redistribution.When further optical or electric fields are applied, charge flow towards the MXene side can be expected.A bulk layer The work function is also calculated to show the balance effect at the interface.As shown in table 2, WF defines the energy cost for an electron to escape from the Fermi level to escape.The GaAs-Ti 3 C 2 OH interface shows the smallest work function among the 3 heterostructures.Such an effect can be linked to the bonding details in the neighborhood of OH units.With the help of hydrogen atoms, it cost less energy for electrons to escape from the MXene side of the GaAs-Ti 3 C 2 OH structure.This also indicates a lower electron affinity which may potentially benefit the catalytic process of such heterostructure.
To visualize the chemical bonds, Electron Localization Functions (ELFs) are plotted in color plots.There are no covalent bonds near the interfaces (no ELF = 0.8 isosurfaces) which confirms the electrostatic interaction at the interface.The ionic character increases as GaAs-Ti 3 C 2 O (figure 3(C)), GaAs-Ti 3 C 2 F (figure 3(B)), and GaAs-Ti 3 C 2 OH (figure 3(D)) indicated by the more and more pronounced isosurfaces on the decoration units.The strong ionic features of hydrogen atoms on MXexe can be linked to its short distance from GaAs bulk.Besides, there are some free electron features near the interface in OH in the extension of hydrogen atoms toward Ga atoms.

Electron structure of the heterostructure
Besides previous simulations of the heterostructures, band structures are also simulated using DFT.As shown by the previous work, the band gaps of MXene are 0-0.1 eV [29] which is much smaller than the 1.42 eV bandgap of GaAs.Thus, the GaAs-MXene heterostructure should be classified as the type of Schottky heterostructure [24] and is closer to the type I (symmetric) heterostructure according to the band structure based classification strategy [30].
In addition, the elemental projections (colored band in figures 4(A), (D) and (G)) on the band structure indicate the composition of the band which helps to understand the formation of Schottky barrier in the band structure.By focusing on the projection of Ga atoms, one can identify the contribution of the GaAs from the band structure (represented by blue lines in figures 4(A), (D) and (G)).E.g., the 'band structure' of Ga in figure 4(A) opens a gap from 0.3 eV to 1.3 eV.On the other hand, red lines represent the contribution from MXene layers which fill the bandgap of GaAs.In the Schottky heterostructures, electrons from MXene which move freely encounter barriers at the interfaces which prevent further movement to the GaAs side.Such barriers (indicated by white arrows in figures) are 1.3 eV, 0.9 eV and 1.0 eV in GaAs-Ti 3 C 2 O, GaAs-Ti 3 C 2 F and GaAs-Ti 3 C 2 OH, respectively.Though MXene layers work as the conductance channel of the heterostructure, for   3.6.Optical properties and excited states of GaAs-Ti 3 C 2 OH Formal results suggest better binding near the interface of GaAs-Ti 3 C 2 OH.Therefore, the optical properties of such an interface.To reduce the computational cost, the local field is switched off with independent particle approximation applied.Thus, the complex dielectric (tensor) function can be obtained.The xx and zz components of the complex dielectric (tensor) function are shown in figures 5(A)-(B).The xx component describes the response of the material when the incident light is perpendicular to the interface (and the electric field is parallel to the interface).In contrast, when the electric field of the incident light is perpendicular to the interface (from a grazing incidence), the response of the interface is much smaller.Based on the dielectric function, the distinction coefficient ( ) k w and the refraction index n( ) w can be calculated (figures 5(C)-(D)).In general, the refraction index drop usually matches the peak of the distinction coefficient.The distinction peak which is perpendicular to the absorption peak is located at 4.3 eV or 288 nm.Such ultraviolet absorption peak lies beyond the well-known first absorption peak of GaAs (near 3.7 eV or 335 nm) which may be due to the constraint of electrons brought by the H atoms on MXene of the heterostructure.Similar to the dielectric function, the distinction peak and the shifts of refraction coefficient do not change much for the interface is less responsive to a beam of grazing incidence light.

Summary
In summary, the heterostructure of the MXene-GaAs complex is investigated with a model that matches the experimental images.The modeled heterostructures (GaAs-Ti 3 C 2 O, GaAs-Ti 3 C 2 F, and GaAs-Ti 3 C 2 OH) can be used to approach the electron structure based on DFT simulation results.As suggested by the binding energy, attractions between 3 variances of MXene and GaAs 〈111〉 surface are rather tight which makes the layer of MXene serve as a protector to the GaAs crystal.Among the 3 variances of MXene, GaAs-Ti 3 C 2 OH has the shortest separation at the interface which can be linked to the binding of H and Ga atoms.A further investigation shows that hydrogen atoms push the polarization close to the interface and leave a rapid but sharp change near the interface in the GaAs-Ti 3 C 2 OH structure.By quantifying the bias in ESP near the interface, the GaAs-Ti 3 C 2 OH shows the smallest work function which may be linked to the free electron feature between H and Ga atoms in its ELF.In addition, band structure shows 0 bandgap in all 3 heterostructures since MXene layers allow electrons to conduct which can be confirmed by projected band structures.The Schottky barrier of metal and GaAs is also approached via elemental projection of the band structures.The peaks in DOS indicate good mobility of electrons near Fermi levels.Besides, MXene layers in heterostructures allow weak magnetic features of surface GaAs near Fermi levels which can be seen in all 3 heterostructures.Last, optical simulations suggest the absorption peak of GaAs-Ti 3 C 2 OH is located near 4.3 eV.In this work, a special class of heterostructure, MXene-GaAs complexes are investigated with electron structure details.Limited by the research topic, other capabilities of such type of heterostructure such as chemical applications are not investigated.Simulation regarding the chemisorption can be focused on future works.Besides, due to the high customizability, other members in the MXene family may make the heterostructure transform into a semiconductor or insulator for wider use.Further related discussion may still need to push applications of such heterostructure to a new level.

Figure 1 .
Figure 1.Explorations in the MXene-GaAs heterojunction based on (A) a brief sketch of the heterostructure.STM image of the MXene-GaAs heterostructure can be find in [22].There is a clear interface in the heterojunction between two materials.(B) the crystal structure of GaAs with a lattice constant of 5.75.(C) the crystal structure of MXene (Ti 3 C 2 T x ) with a lattice constant of 3.08.(D) To match GaAs and MXene, the 3 × 3 supercell of the GaAs crystal in its 〈111〉 direction aligns well with the 4 × 4 supercell of the MXene crystal.The common lattice constant between the two supercells is about 12.2 Å. E) Side view of the heterostructure for better demonstration.

Figure 2 .
Figure 2. Charge difference plot near (A) the GaAs-Ti 3 C 2 O, (B) the GaAs-Ti 3 C 2 F, and (C) the GaAs-Ti 3 C 2 OH interfaces.For better representation, the c direction is aligned horizontally.Color code: red = electron excess (iso-surface value = 0.002); blue = electron insufficient (iso-surface value = −0.002).(D) the planar averaged charge difference of the 3 interfaces.

Figure 3 .
Figure 3. (a) Planar averaged total local potential of the heterostructure.Electron static potentials are the summations of ionic and Hartree potentials.The vacuum energy is plotted by horizontal dotted lines while the positions of the interfaces are denoted by vertical lines.(b) The iso-surface of the total local potential.(c) The electron localization function of the heterostructure.

Figure 5 .
Figure 5. Complex dielectric function of GaAs-Ti 3 C 2 OH heterostructure with (A) the xx and (B) the zz tensor components.Based on the dielectric function, the refraction index (n( ) w ) and the distinction coefficient ( ( ) k w ) along (C) xx and D) zz directions are plotted.
To better see the variance of GaAs-MXene in such heterostructure, MXenes (Ti 3 C 2 O, Ti 3 C 2 F, and Ti 3 C 2 OH) are evaluated and summarized in table 1.After DFT relaxation (the GaAs crystal is fixed while the MXene is allowed to move), the separation between the GaAs and Ti 3 C 2 OH is 1.52 Å the smallest value among the 3 junctions.The distance between the two materials in the GaAs-Ti 3 C 2 F structure is 2.32 Å, about 150% of the distance in the GaAs-Ti 3 C 2 OH structure.The next important feature in heterostructures is the interactions between parts.First, GaAs interact with the MXene with a significantly larger magnitude.As shown in table 1, the stacking interaction between MXene layers is −0.166J m −2 which is evaluated by calculating the difference in energy between a single layer MXene sheet and a MXene layer in its bulk (i.e.,

Table 1 .
Structure details at the junction.Distances and binding energies of GaAs and MXene are summarized.