Ti Impurity Effect on the Optical Coefficients in 2D Cu2Si:A DFT Study∗

Bromand Nourozi,Arash Boochani,Ahmad Abdolmaleki,Elmira Sartpi,Pezhman Darabi, and Sirvan Naderi

1Department of Physics,Islamic Azad University,Kermanshah Branch,Kermanshah,Iran

2Department of Physics,Lorestan University,Khoramabad,Iran

3Young Researchers and Elite Club,Kermanshah Branch,Islamic Azad University,Kermanshah,Iran

1 Introduction

The amazing electronic behavior of graphene leads to a high mobility concluding from the hexagonal sheet structure.[1]Considering the Dirac cone graphene materials,several electronic and spintronic behaviors[2−5]such as ballistic charge transport,[6]high mobility,[7]and quantum Hall effects[8]are appeared.According to some restriction in carbon graphenes,many 2D materials are synthesized and predicted such as Silicene,Germanene,[9]and Ti2B.[10]It is reported that 2D materials with the honeycomb structure have different physical behaviors than those in bulk phase.[11]Hence,it is necessary to find a new class of 2D materials with new electronic,magnetic and optical properties to use in some industrial applications such as optoelectronic,spintronic,and solar cell devices.

After discovery of graphene,[12]new 2D materials have been considered such as BN,[13−14]tertialy B-C-N,[15]etc.These 2D materials have more unique physical properties than carbon graphene and are very attractive in the electronic and optoelectronic industries.Most of the 2D chemical and physical structures have tri-coordinated motifs,as their graphene structures are illustrated,[16−22]so only a few samples of these materials have been reported by quasiplanar tetra coordinated structure.Hoffmanet al.,were the first group reportingbased on tetra coordinated carbon motifs.In addition,new planar hexacoordinated structures,such as the 2D boron were predicted by computational studies.[23]

In recent years,making planar hyper coordinate 2D materials has been a big challenge as their compound elements do not mach. The planar hyper coordinate molecules were firstly predicted by Schlegeret al.,[24]a class of materials,which are very interesting in scienti fic and industrial points of view,and also B2C monolayer in the quasi planar hexa-coordinate carbon shape has been recently investigated.[25]

Due to the transition metals applications in the electronic industry,they are even more attractive.The 2D materials based the Cu atom have the interesting electronic and optical treatment.Recently,2D Cu2Si has been synthesized by laying down the Cu cluster on Si(111),[25]also,as well as ab-initio calculations indicated the good stability of this 2D material.The electronic calculations by Yanget al.[26]have shown the metallic behavior for the 2D Cu2Si.Furthermore,this 2D material has strong chemical bonding between atoms and high implant sti ffness.The optical properties of the 2D Cu2Si have been less considered so far,and also according to the metallic behavior of the 2D Cu2Si,it is expected that by absorbing Ti to its structure,the electronic and the optical properties of the 2D Cu2Si:Ti have been improved for optoelectronic and solar cell applications.

Since Ti belongs to the transition metals,there is a good compatibility between its electronic structure and Cu atom,thus Ti is placed instead of Cu in the 2D Cu2Si.By doping Ti into the 2D Cu2Si,the electronic and the optical properties are changed signi ficantly.Additionally,it is noticeable that by adding Ti,magnetic behaviors emerge in the 2D Cu2Si:Ti especially at the Fermi level.In Sec.2 the computational details are explained and the thermodynamic stability,the electronic and the magnetic properties are calculated in Sec.3.Finally,the optical properties are reported in Sec.4.

2 Computational Methods

Calculations are based on the density functional theory(DFT)framework and the FP-LAPW method with the GGA approximations.[27−29]After optimization of the input parameter,the RKmax,Gmax,and KPoint are selected as 8.0,13.0,5000,and 8.0,13.5,500 for the pure and the impurity cases respectively. The lattice parameters of the 2D Cu2Si hexagonal super lattice are set toa=b=23.374(Bohr)andc=18.897(Bohr).The structures are relaxed by miniposition command with 1.0 a.u./dyne accuracy,and the optical calculations are performed by the RPA approximation.[30]For better comparison,the 2D Cu2Si and the 2D Cu2Si:Ti shapes are shown in Fig.1.

Fig.1 (Color online)(a)The 2D Cu2Si structure,(b)The 2D Cu2Si:Ti lattice by XCrysden code.

3 Results and Discussion

3.1 Electronic and Magnetic Properties

According to the other studies,the 2D Cu2Si has not good metallic treatment due to a few electron states at the Fermi level and lack of the magnetic property.[25−26]In the electronic discussions,the DOS diagram shows important information about metallic or non-metallic and magnetic or non-magnetic properties of matter.Figure 2(a)illustrates the 2D Cu2Si DOS at up and down spins indicating a completely isotropic behavior at the all energies below and above the Fermi level con firming the non-magnetic property of this compound,which is in good agreement with the other works.[25−26]

Considering Ar3d24s2and Ar3d104s1electronic structures of Ti and Cu atoms respectively,they are different in 4sand 3dorbitals so that Cu-3dis occupied while two electrons are located in Ti-3dorbital.It is clear that the Ti atoms produce the magnetic moment in the 2D Cu2Si:Ti compound,so the electronic calculations are based on spin polarization.The DOS diagram of the 2D Cu2Si:Ti is shown in Fig.2(b)in the up and down spins;it is clear that they have different behaviors especially at the Fermi level.It is shown that the DOS in both mentioned spins at the range of−10 eV to−2.5 eV have a completely isotropic behavior,but at the Fermi area[–1 eV,1 eV],it shows an anisotropic behavior(see Fig.2(c))claimed to the magnetic properties of 2D Cu2Si:Ti.So,the total and interstitial magnetic moments of the 2D Cu2Si:Ti are listed in Table 1.Moreover,the cohesive energy(EC)represents that the 2D Cu2Si:Ti has a good thermodynamic stability(Table 1)con firmed by Ti-Si bond length,which is less than the Cu-Si one.

Fig.2 (Color online)(a)Total 2D Cu2Si DOS versus energy,(b)Total 2D Cu2Si:Ti DOS versus energy,(c)Total DOS of 2D Cu2Si:Ti at Fermi area.

Table 1 The bond length of 2D Cu2Si in pure and impurity cases(˚A)with Cohesive energy(Ec),Atomic bond length(˚A)and Total magnetic moment(µB).

3.2 Optical Properties

The optical properties are described by the response of matter to incident light leading to the electronic structure such as the energy band gap,the conductivity,the semiconductor behavior and the glassiness.The 2D Cu2Si and Cu2Si:Ti have two symmetric directionsxandz,wherexis on the plane of the structure andzis perpendicular to it.The real part of the dielectric function Re(ε(ω))of the 2D Cu2Si is shown in Fig.3 for the two mentioned directions of the incident photon.After 10 eV of the photon energy,the Re(ε(ω))inxand thezdirections are completely similar and tend to a constant value about 1,therefore,at this energy range,the 2D Cu2Si response to incident light has not been changed.However,in the infrared and visible regions,their behaviors are completely different so the static value of Re(ε(ω))in thexandzdirections are 2 and screaming value,respectively indicating the metallic behavior in thexdirection.At(0–2)eV and(4–10.5)eV,the Re(ε(ω))xsign is negative while the Re(ε(ω))zin the vicinity of 9 eV is negative.Hence,no optical transitions occurred at these energy intervals.In addition,several roots are appeared at 3 eV and 9 eV for the Re(ε(ω))xand 8.5 eV and 9.5 eV for the Re(ε(ω))z,which by comparing the Im(ε(ω))and the Eloss curve,the Plasmon frequencies have been con firmed at the mentioned energies.

Fig.3(Color online)Real part of dielectric function for x and z directions for 2D Cu2Si and 2D Cu2Si with Ti impurity versus photon energy.

The Real part of dielectric function Re(ε(ω))of the 2D Cu2Si:Ti alongxandzdirections are shown in Fig.3,representing the metallic and semiconductor behaviors in both directions,and the static values of the real part of the dielectric function Re(ε(0))are in finitive and 2.2 forzandxdirections,respectively.By increasing photon energy,the Re(ε(ω))xis considerably increased and dramatically decrease at+1 eV(infrared region),respectively,so it has two roots in this region indicating the metallic treatment in the infrared region,and getting incident photons at low energies,the surface electrons are vibrated causing the Plasmon frequencies.The Re(ε(ω))xreaches to a constant and small value in the UV area indicating no response to the incident photon energy.

A quick look at the Re(ε(ω))xgraph indicates lack of sensible fluctuations in the visible area,but a moderate loop in the Re(ε(ω))zis observed in Fig.3.The Re(ε(ω))xreaches a plateau after the two roots(4.4 eV and 5.5 eV)in the UV edge showing low response of the 2D Cu2Si:Ti to incident light at the mentioned energy range.In contrast,the Re(ε(ω))zhas a different behavior in UV area so that by increasing photon energy,a signi ficant escalation is observed while there are two roots at the energy range of 9 eV to 10 eV.

It is noticeable that Re(ε(ω))xfrom 1 eV to 2.2 eV and Re(ε(ω))zfrom 9 eV to 10 eV have negative sign con firming the occurrence of no optical transition at the mentioned energy ranges for the 2D Cu2Si:Ti compound.The imaginary part of the dielectric function Im(ε(ω))illustrates the electronic structure of matter.Each peak of the Im(ε(ω))represents the electron transition from an occupied to an unoccupied level.Comparing the diagrams of Fig.3,it is clear that adding Ti to the 2D Cu2Si causes no signi ficant change in thezdirection,while inxdirection,owing to its high fluctuations in lower energy((0–2)eV),the metallic behavior is observed con firming the intraband transition.

The Im(ε(ω))for the coplanar and the perpendicular components(xandz)of the 2D Cu2Si are illustrated in Fig.4.From zero to 10 eV,they are extremely anisotropic so that the static amount of Im(ε(ω))xtends to in finity.By increasing the photon energy in the visible area,the Im(ε(ω))xis considerably dropped con firming the Re(ε(ω))xroot and the first Plasmon frequency in this area.Moreover,the high amount of the Im(ε(ω))xin the infrared region indicates the high metallic behavior and the intraband transitions.

Afterward,the second main peak of Im(ε(ω))xis appeared on the UV edge(4 eV),but no peak exists for the Im(ε(ω))zbefore 2 eV con firming the semiconductor behavior in the optical view.It has three peaks in the UV region,each peak indicates the electron transition from occupied to unoccupied levels(from Cu-p,Cu-dand Ti-dto Cu-dand Ti-dorbitals)causing the intraband or interband transitions.

The Im(ε(ω))of the 2D Cu2Si:Ti graphene is shown in Fig.4 for thexand thezdirections. The optical anisotropy of this parameters for the mentioned directions is observed so that the Im(−ε(ω))xreaches its highest peak at 0 eV to 4 eV,and it is decreased by increasing the photon energy.Another small peak is seen at 4.2 eV(UV edge).However,the Im(ε(ω))zhas a completely different behavior so that it is started at 4.2 eV and reached its highest peak at 5.7 eV,then two smaller peaks occurred in the area of 8 eV to 10 eV.

Fig.4 (Color online)The Imaginary part of dielectric function of 2D Cu2Si&2D Cu2Si:Ti versus photon energy in the x&z directions.

It is noticeable that the all Im(ε(ω))curves in both directions are leveled out to zero after fluctuations at 12 eV,and after this energy the incident light completely transmits in both directions.On the visible edge(2 eV),the Im(ε(ω))xtends to in finity indicating the high metallic behavior and intraband transition in this direction.The different response of the 2D Cu2Si:Ti to the incident photons in thexandzdirections indicates a promising optical sensor for electronic and optoelectronic devices.It should be mentioned that by adding Ti to the 2D Cu2Si,the second peak of the Im(ε(ω))xis decreased and in contrast,the first peak is increased showing a greater tendency to the metallic properties in the 2D Cu2Si:Ti.

The energy loss function diagram(Eloss)involves important information about the optical properties such as absorption,refraction and Plasmon frequency.Figure 5 shows the 2D Cu2Si and the 2D Cu2Si:Ti energy loss function curves in thexandzdirections.As it is clear from the Im(ε(ω))diagram,the most electron transitions belong to thexdirection,so the Eloss-xis occurred at lower energies than the Eloss-z.Each Eloss peak indicates the energy loss of the incident light lead to the Plasmon frequency or the light refraction.For example,the Elossxof the imaginary case has a peak at 4 eV equivalent to Re(ε(ω))xroot and signi ficant reduction of the re flectivity at this energy.It is concluded that the Plasmon frequency occurs at 4 eV photon energy,and also several peaks have been observed in Re(ε(ω))xfrom 6 eV to 8 eV.However,no loss of the incident light is occurred at the energy range of 0 eV to 5 eV,which by comparing with the Im(ε(ω))z,the lack of any electron transition at the mentioned energy range have been seen and the Re(ε(ω))zhas a relatively constant behavior.At 6 eV photon energy,the first Eloss-zpeak is occurred and the absorption and the re flection of the Re(ε(ω))zare decreased while conductivity is increased.Hence,this Eloss peak can not be a sign for the Plasmon frequency.The major Eloss-xand-zpeaks are at 10 eV and 11 eV,respectively.By comparing the Re(ε(ω))and the Im(ε(ω))curves,it is concluded that the volume Plasmon frequency area is located at this energy range,which the optical conductivity diagram con firms the above points in Fig.5.Comparing the pure and the impurity cases of 2D Cu2Si in Fig.5 indicates that there is no peak until 2.5 eV unlike the 2D Cu2Si:Ti.The first Eloss-xpeak in pure case is occurred at 2.5 eV that is smaller than the impurity case,and the main Eloss-xpeak is located at 11 eV,which is greater than the impurity case.In thezdirection,the maximum energy loss function is nearly half of thexdirection in maximum case.

Fig.5 (Color online)Eloss function of 2D Cu2Si and(:Ti)cases versus photon energy in x and z directions.

The optical conductivity is resulted from the electron transitions to the conduction bands caused by the incident radiation to matter including the important electronic and the optical information about the material.The optical conductivity in thexandzdirections are in agreement with the above discussions.The optical conductivity of the 2D Cu2Si in thexandzdirections are shown in Fig.6 and show high conducting property at zero energy along thexdirection with a gradually reduction at 2.5 eV.While the Plasmon frequency is occurred at this photon energy,the next peak occurs at 5 eV.Moreover,no conduction is observed until 3 eV in thezdirection,and in the UV region(6 eV,8 eV,and 9 eV)three peaks are seen.By increasing the photon energy after the main Plasmon frequency,the conductivity for both mentioned axes are decreased and tend to zero.

Figure 6 indicates a sharp reduction in the optical conductivity at 1 eV area for thexdirection con firming the Plasmon frequency at this energy(compatible with Re(ε(ω))xdiagram).Furthermore,the optical conductivity reduces gradually on the visible edge and reaches a plateau in the UV area by increasing the photon energy.A brief like in optical conductivity onzdirection shows that there is no conductivity before 2 eV con firming the semiconductor behavior and it experiences a steady improvement on the visible edge to reach a maximum at 5.5 eV,which is in agreement with the Re(ε(ω))zcurve.By adding the Ti impurity to the 2D Cu2Si,the conductivity behavior in thezdirection remains nearly the same as the pure case,but the static conductivity is finite and its maximum occurs in the infrared region.An important note is that the conductivity increases to a constant amount at higher energies(Fig.6).

Fig.6 (Color online)2D Cu2Si,2D Cu2Si:Ti conductivity in x and z directions versus photon energy.

The absorption peaks of the 2D Cu2Si are presented in Fig.7.In the bothxandzdirections,absorption gaps are about 2.5 eV and then it is started the mentioned directions,respectively.The maximum absorption is at 10 eV photon energy,and the anisotropy behavior is clear from 2.5 eV to 11 eV.After 25 eV,the absorption drops to zero,i.e.the light is completely transmitted through the matter.

Fig.7 (Color online)Absorption function of 2D Cu2Si in pure and impurity cases versus photon energy in the in-plane and normal directions.

The 2D Cu2Si:Ti absorption diagram in thexandzdirections are shown in Fig.7.The absorption diagram in thexdirection is increased immediately by photon energy,thus the 2D Cu2Si:Ti has a good metallic behavior.The absorption diagram experiences a moderate escalation and reaches two higher peaks in the visible and UV area,and then it is decreased by increasing the photon energy to reach a smaller constant value.Conversely,there is no absorption in infrared region for thezdirection(an absorption gap).The absorption-zreaches a maximum at 5.5 eV,while the Re(ε(ω))zand the Im(ε(ω))zhave minimum and maximum,respectively.Two peaks are also located at the energy range of 9 eV to 9.7 eV indicating the main Plasmon frequencies.

Re flection parameter is an important optical parameter for matter representing the percentage of the light transmission and re flection in the material surfaces;metals have high re flection(about 90%),for example shining matters and non-metals are opaque.The 2D Cu2Si has complete re flection at zero energy in thexdirection,but it is nearly zero for thezdirection indicating the different behaviors for the two mentioned directions so that the light is fully transmitted in the direction perpendicular to 2D Cu2Si surface,and completely re flected in the coplanar state.By increasing the photon energy,the re flectivity in thezdirection is dropped signi ficantly at 3.5 eV(the visible area)to reach its second maximum at 4.7 eV.Figure 8 shows that for all energy ranges,the re flection in thezdirection is smaller than thexone con firming the high metallic behavior of the optical point of view.

It is clear that the static amount of the re flection for the 2D Cu2Si:Ti in thexdirection is 90%con firming its metallic behavior,whereas this compound shows the semiconductor behavior in thezdirection due to a low static re flectivity(Fig.8).By increasing the intensity of the incident light,where Re(ε(ω))zhas roots,a gradual reduction in the re flection on thezdirection is observed.The 2D Cu2Si:Ti re flection in thexdirection reaches a plateau(zero)after 10 eV and the optical incident light is transmitted completely.Moreover,this phenomenon is similarly occurred in thezdirection.

Fig.8 (Color online)Re flection index of 2D Cu2Si&2D Cu2Si:Ti versus photon energy in x&z directions.

4 Conclusion

In summary,calculations of the Ti impurity effect on the 2D Cu2Si are performed based on the DFT framework by the GGA approximation.In the pure case,the DOS diagrams cut the Fermi level and do not have magnetic moment,but the 2D Cu2Si:Ti has half-metallic behavior with the magnetic moment of 3.256µB.Furthermore,the Ti effect causes changing in the optical parameters,especially in the infrared and the visible area.

In the pure case,no optical transition occurred in thexdirection in the infrared and the visible areas,but in the impurity case,it has a Dirac peak in the infrared area.The major electron transitions are occurred from the Cudand the Ti-dto theS-pand the Cu-dorbitals.The absorption gap is reduced to zero in thexdirection and is sensitive to the incident light,but it is relatively the same in the pure and the impurity cases in thezdirection.According to the Ti atomic structure,the 2D Cu2Si:Ti has lower metallicity in zero energy,whereas its optical conductivity and re flectivity are smaller than the 2D Cu2Si case.

Owing to the semi-metallic behavior of Cu2Si:Ti at the Fermi level,it is expected that this compound will be used in the spintronics and giant magnetoresistance(GMR).In addition,by adding Ti to the 2D structure of Cu2Si,the light absorption gap alongxxhas been vanished,and an increase in the light absorption can be observed in the infrared and visible regions making this composition suitable for solar cells and optical devices.

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