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The bound states of a particle confined in a one-dimensional finite square well cannot be solved analytically, since the eigen-energies are determined by transcendental equations. Here, we numerically calculate the bound states and show their non-classical properties, using Wigner's quasi-probability distribution (also called the Wigner functions) in the phase space (x, p). In contrast to the infinite-well case, we find that the Wigner functions spread over the space dimension x, get squeezed along the momentum dimension p, and show negativity outside the well. Negativity in a Wigner function indicates non-classical properties of the bound states. [ABSTRACT FROM AUTHOR]

We investigated the effects of Fe doping and point defects (oxygen and tin vacancies, VO and VSn, respectively) on the ferromagnetism of SnO2 through first-principles calculations by using generalized gradient approximation + U under density functional theory. Calculation results show that Fe-doped SnO2 with VO or VSn exhibit long-range ordered ferromagnetism and Curie temperature above room temperature. The system has different magnetic properties with different doping modes, which are beneficial to the magnetic adjustment of dilute magnetic semiconductor (DMS). The double-exchange effects among the electrons of O–2p and Fe–3d states are the origin of ferromagnetism in Sn15FeO31. Similarly, ferromagnetism in Sn14FeO32 is derived from the double-exchange effects among the electrons of O–2p and Fe–3d states. These effects are produced by hole carriers after complexes form by Fe doping and VO or VSn. Simultaneously, Sn14FeO32 shows a half-metallic behavior, thus resulting in 100% conduction hole polarizability, which is highly beneficial to DMSs as a hole-injection source. Moreover, results also show that the decreased distance between Fe and vacancies (VO or VSn) lowers formation energy and thus increases the system stability. [ABSTRACT FROM AUTHOR]

We investigated the effects of Fe doping and point defects (oxygen and tin vacancies, VO and VSn, respectively) on the ferromagnetism of SnO2 through first-principles calculations by using generalized gradient approximation + U under density functional theory. Calculation results show that Fe-doped SnO2 with VO or VSn exhibit long-range ordered ferromagnetism and Curie temperature above room temperature. The system has different magnetic properties with different doping modes, which are beneficial to the magnetic adjustment of dilute magnetic semiconductor (DMS). The double-exchange effects among the electrons of O–2p and Fe–3d states are the origin of ferromagnetism in Sn15FeO31. Similarly, ferromagnetism in Sn14FeO32 is derived from the double-exchange effects among the electrons of O–2p and Fe–3d states. These effects are produced by hole carriers after complexes form by Fe doping and VO or VSn. Simultaneously, Sn14FeO32 shows a half-metallic behavior, thus resulting in 100% conduction hole polarizability, which is highly beneficial to DMSs as a hole-injection source. Moreover, results also show that the decreased distance between Fe and vacancies (VO or VSn) lowers formation energy and thus increases the system stability. [ABSTRACT FROM AUTHOR]

The effects of different doping proportions of Co doping and oxygen vacancies (VO) on the ferromagnetism of zinc oxide (ZnO) are controversial. To solve this problem, we investigated the effects of Co doping and point defects (VO, VZn, Hi, and Zni) on the ferromagnetism of ZnO through first-principle calculations by using generalized gradient approximation + U (GGA + U) under density functional theory. Results show that the closer the distance between Co and vacancies (VO or VZn), the lower the formation energy and the more stable the system will be. Co-doped ZnO with VO or VZn exhibits long-range ordered ferromagnetism and Curie temperature above the room temperature. Especially, Co-doped ZnO with VZn shows a half-metallic behavior, resulting in 100% conduction hole polarizability, which is highly beneficial for dilute magnetic semiconductors (DMSs) as a hole injection source. The ferromagnetism of Zn14CoO16 is caused by the double exchange effects among the electrons of the O–2p, Co–3d, and Zn–3d orbits mediated by the hole carriers after complexes were formed by the Co doping and Zn vacancy. Similarly, the origin of ferromagnetism in Zn15CoO15 is derived from the double exchange effects among the electrons of O–2p, Co–3d, and Zn–4s states mediated by the electron carriers after complexes were formed by the Co doping and O vacancy. In addition, the result shows that Co-doped ZnO with interstitial H (Hi) or Zn (Zni) is unfavorable for ferromagnetism and should be avoided experimentally. [ABSTRACT FROM AUTHOR]

The absorption edge shifted to long wavelength direction and short wavelength direction of two opposite experimental conclusions have been reported, when the band-gap and absorption spectra of -doped anatase 2 were studied. In order to solve this contradiction, the electronic structure and the optical property of heavy doped anatase 2 have been studied by the first-principles plane-wave ultrasoft pseudopotential method based on the density functional theory with +U method modification. The calculated results indicate that the higher the -doping is, the higher the total energy is, the worse the stability is, the higher the formation energy is, the more difficult the doping is, the wider the optical band-gap is, the more obvious the absorption edge shifting to short wavelength direction is, the lower the absorptivity and the reflectivity is, which is in agreement with the experimental results. The reasonable interpretation of the contradiction has been reported in this paper, too. [ABSTRACT FROM AUTHOR]

The absorption edge shifted to long wavelength direction and short wavelength direction of two opposite experimental conclusions have been reported, when the band-gap and absorption spectra of -doped anatase 2 were studied. In order to solve this contradiction, the electronic structure and the optical property of heavy doped anatase 2 have been studied by the first-principles plane-wave ultrasoft pseudopotential method based on the density functional theory with +U method modification. The calculated results indicate that the higher the -doping is, the higher the total energy is, the worse the stability is, the higher the formation energy is, the more difficult the doping is, the wider the optical band-gap is, the more obvious the absorption edge shifting to short wavelength direction is, the lower the absorptivity and the reflectivity is, which is in agreement with the experimental results. The reasonable interpretation of the contradiction has been reported in this paper, too. [ABSTRACT FROM AUTHOR]