| The magnetic and optical properties of Ce-doped ZnO systems have been widely studied.However,the effects of Ce-doping and interstitial H coexisting,and Ce-doping and O or Zn vacancies coexisting on the electronic structure,optical and magnetic properties of ZnO has yet to be explored,and the effects of different biaxial strains on undoped ZnO systems,Ce-doped ZnO systems,H-interstitial ZnO systems,Ce-doped ZnO systems with interstitial H,and Ce-doped ZnO systems with O or Zn vacancies remain unclear.To solve these problems,the crystal structure,formation energy,band structure,density of states,magnetism and absorption spectrum of undoped ZnO systems,Ce-doped ZnO systems,Hinterstitial ZnO systems,Ce-doped ZnO systems with interstitial H,and Ce-doped ZnO systems with O or Zn vacancies under different strains were calculated by the generalized gradient approximation + U method on the basis of density functional theory of the firstprinciples calculation.The effects of biaxial strain on the electronic structure,optical and magnetic properties of undoped ZnO systems,Ce-doped ZnO systems,H-interstitial ZnO systems,Ce-doped ZnO systems with interstitial H,and Ce-doped ZnO systems with O or Zn vacancies were identified.Firstly,the ZnO system with one Ce atom substituting one Zn atom was built and applied different biaxial strains to investigate the effects of different strain conditions on the optical properties and magnetic properties of Ce-doped ZnO system.The band gap of Cedoped ZnO system without strain narrowed compared with the undoped ZnO,the static dielectric constant decreased,and the imaginary part of the complex dielectric function and absorption spectrum moved to a low energy level.The formation energy of Ce-doped ZnO system decreased with increasing compressive strain,the system became stable,and the Cedoping became easy;the formation energy of Ce-doped ZnO system increased with increasing tensile strain,the system became unstable,and the Ce-doping became difficult.Doping didn’t change the direct band gap properties of ZnO.The band gap of the system widened,the imaginary part of the complex dielectric function moved to a high energy level,the static dielectric constant increased,and the absorption spectrum blue-shifted under the compressive strain conditions;the band gap of the system narrowed,the imaginary part of the complex dielectric function moved to a lower energy level,the static dielectric constant decreased,and the absorption spectrum red-shifted under the tensile strain conditions.The undoped ZnO system was non-magnetic under different strain conditions.Ce-doped ZnO system exhibit room temperature ferromagnetism in the absence of strain.The magnetic moments and Curie temperature of Ce-doped ZnO system decreased with increasing compressive and tensile strains.The doped system was ferromagnetic under-1% and 0% strains,and its Curie temperature was above the room temperature;the Curie temperature dropped below room temperature as the compressive strains were-3% and-2% and the tensile strains were 1% and 2%;the doped system transformed from ferromagnetic to antiferromagnetic as the compressive strains were-5% and-4% and the tensile strains were 3%,4% and 5%.Secondly,H-interstitial ZnO systems for different interstitial locations and Ce-doped ZnO systems with interstitial H for different Ce-H distances were built.The geometric structure of all systems was optimized to find the most stable supercells of H-interstitial ZnO systems and Ce-doped ZnO systems with interstitial H.The most stable supercells were applied different biaxial strains to investigate the effects of different strain conditions on the optical properties and magnetic properties of H-interstitial ZnO systems and Ce-doped ZnO systems with interstitial H.The band gap of H-interstitial ZnO systems and Ce-doped ZnO systems with interstitial H without strain increased compared with the undoped ZnO,the static dielectric constant increased,and the imaginary part of the complex dielectric function and absorption spectrum moved to a high energy level.The formation energy of H-interstitial ZnO systems and Ce-doped ZnO systems with interstitial H decreased with increasing compressive strain,the systems became stable,and the doping became easy;the formation energy of H-interstitial ZnO systems and Ce-doped ZnO systems with interstitial H increased with increasing tensile strain,the systems became unstable,and the doping became difficult.Doping didn’t change the direct band gap properties of ZnO.The band gap of the doped systems widened,the imaginary part of the complex dielectric function moved to a high energy level,the static dielectric constant decreased,and the absorption spectrum blueshifted under the compressive strain conditions;the band gap of the doped systems narrowed,the imaginary part of the complex dielectric function moved to a lower energy level,the static dielectric constant increased,and the absorption spectrum red-shifted under the tensile strain conditions.The H-interstitial ZnO system was non-magnetic under different strain conditions.Ce-doped ZnO system with interstitial H exhibit room temperature ferromagnetism in the absence of strain.The magnetic moments and Curie temperature of Ce-doped ZnO system with interstitial H decreased with increasing compressive and tensile strains.The system was ferromagnetic under-1%,0% and 1% strains,and its Curie temperature was above the room temperature;the Curie temperature dropped below room temperature as the compressive strains were-3% and-2% and the tensile strains was 2%;the doped system transformed from ferromagnetic to antiferromagnetic as the compressive strains were-5% and-4% and the tensile strains were 3%,4% and 5%.Finally,Ce-doped ZnO systems with O or Zn vacancies for different Ce-V(point vacancise)distances were built.The geometric structure of all systems was optimized to find the most stable supercells of Ce-doped ZnO systems with O or Zn vacancies.The most stable supercells were applied different biaxial strains to investigate the effects of different strain conditions on the optical properties and magnetic properties of Ce-doped ZnO systems with O or Zn vacancies.The band gap of Ce-doped ZnO systems with O vacancies without strain increased compared with the undoped ZnO,the static dielectric constant increased,and the imaginary part of the complex dielectric function and absorption spectrum moved to a high energy level.The band gap of Ce-doped ZnO systems with Zn vacancies without strain decreased compared with the undoped ZnO,the static dielectric constant increased,and the imaginary part of the complex dielectric function and absorption spectrum moved to a low energy level.The formation energy of Ce-doped ZnO systems with O or Zn vacancies first increased and then decreased with increasing compressive strain,whereas that of Ce-doped ZnO systems with O or Zn vacancies decreased with increasing tensile strain.Doping didn’t change the direct band gap properties of ZnO.The band gap of the doped systems widened,the imaginary part of the complex dielectric function moved to a high energy level,the static dielectric constant decreased,and the absorption spectrum blue-shifted under the compressive strain conditions;the band gap of the doped systems narrowed,the imaginary part of the complex dielectric function moved to a lower energy level,the static dielectric constant increased,and the absorption spectrum red-shifted under the tensile strain conditions.Ce-doped ZnO system with O or Zn vacancies exhibit room temperature ferromagnetism in the absence of strain.The magnetic moments and Curie temperature of Ce-doped ZnO system with O or Zn vacancies decreased with increasing compressive and tensile strains.For Ce-doped ZnO system with O vacancies,the system was ferromagnetic under-2%,-1%,0%,1%,2%,3% and 4% strains,and its Curie temperature was above the room temperature;the Curie temperature dropped below room temperature as the compressive strains were-4% and-3% and the tensile strains was 5%;the doped system transformed from ferromagnetic to antiferromagnetic as the compressive strains was-5%.For Ce-doped ZnO system with Zn vacancies,the system was ferromagnetic under-1%,0% and 1% strains,and its Curie temperature was above the room temperature;the Curie temperature dropped below room temperature as the compressive strains were-3% and-2% and the tensile strains were 2% and 3%;the doped system transformed from ferromagnetic to antiferromagnetic as the compressive strains were-5% and-4% and the tensile strains were 4% and 5%.The mechanism of the effect of strain on the band gap is that the compressive strain makes the atomic spacing in the system decrease,the electron clouds of each atom overlap more severely,so that the repulsion between the electrons occupying the same energy level is enhanced,resulting in the valence band maximum and conduction band minimum both move to the high energy level,but the conduction band minimum moves significantly more than the valence band maximum,resulting in a wider band gap;the tensile strain makes the atomic spacing in the system increase,the electron clouds of each atom overlap is reduced,so that the repulsion between the electrons occupying the same energy level is reduced,the valence band maximum and conduction band minimum both move to the low energy level,but the conduction band minimum moves significantly more than the valence band maximum,resulting in a narrow band gap.The mechanism of the effect of strain on magnetism is that the compressive strain reduces the distance between the magnetic atoms in the system,and the electron clouds overlap more severely,so that the repulsion between two unpaired spin electrons with the same spin direction increases and the energy of the system increases.When the compressive strain increases to a certain degree,in order to minimize the energy of the system,one of the two spin electrons undergoes a spin overturn,which cancels out the spin magnetic moment,resulting in the system changing from a ferromagnetic state to an antiferromagnetic state.In addition,the tensile strain increases the distance between the magnetic atoms in the system and the electron cloud overlap decreases,so that the magnetic exchange between the two magnetic atoms is reduced.When the tensile strain increases to a certain degree,the magnetic exchange in the system completely disappears,causing the system to change from a longrange ordered ferromagnetic state to a disordered antiferromagnetic state.The results indicated that the bandgap and absorption spectrum of all of the systems in this paper can be controlled by strain.Moreover,for the magnetic systems Ce-doped ZnO systems,Ce-doped ZnO systems with interstitial H,and Ce-doped ZnO systems with O or Zn vacancies,the magnetic moment,Curie temperature,and FM–AFM also can be controlled by strain.These results can serve as a reference for the design and preparation of Ce-doped ZnO optical materials,Diluted magnetic semiconductor materials,and magnetic switches. |
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