The Electronic Structures and Optical Properties of Electron Tuned Fe-Doped SnO 2 Materials

By means of the full-potential linearized augmented plane-wave method (FP-LAPW), the electronic structures and optical properties of Sn 15 FeO 32 with electron-injection are studied.The results show that Fe-doped SnO 2 materials are all direct transition semiconductors. The Fermi level goes into conduction band gradually and the band gap decreases with the increase of electron injection. The peaks of optical properties, such as the imaginary part of dielectric function and absorption spectra, change greatly at low energy. The absorption spectra exhibit blue shift, and the optical absorption edge increases, which are consistent with the change of the band gaps.


Introduction
The diluted magnetic semiconductors (DMS) have attracted a lot of experimental and theoretical attention [1][2][3][4] because their spin and charges can be manipulated, which will hereby induce many interestingly magnetic and magnetooptic characteristics.Though the magnetic and electronic properties in some typical DMS systems, such as SnO 2 , ZnO, and GaN, have been investigated extensively, many challenges to realize DMS materials for practical applications [5][6][7] still exist.
As a wide band-gap semiconductor, doped SnO 2 play a promising role in short-wavelength LED, gas sensor, and laser diode due to its large band gap (3.6 eV) and high exciton binding energy (130 meV) at the room temperature [8][9][10].The electronic structures, magnetic, and optical properties of transition metal (Co, Cr, Mo, Eu, etc.) doped SnO 2 bulk semiconductors materials have been researched in theory and experiment [11][12][13].As the important one of the family, the structures and optical properties of Fe-doped SnO 2 have also caused much attention [14][15][16].Adhikari et al. [17] fabricated Fe-doped SnO 2 nanoparticles with a chemical coprecipitation method and studied their structures and magnetism.Kim et al. [18] studied the structure, magnetic and optical properties, and Hall effects of Co-and Fe-doped SnO 2 .When Fe doped SnO 2 , for charge balance, Fe ions must have the ionic valence of Fe 4+ without introducing any defects [19].But Fe ions do not have 4+ oxidation state; hence, the holes are created.So the electronic injection is necessary to obtain the better performance of SnO 2 .It is well known that the injection of electrons into semiconductors is indispensable to realize spin-related devices, such as spin transistors [20].The bleach in the absorption spectra by using size-dependent electron injection from excited CdSe quantum dots into TiO 2 nanoparticles is observed.It can be theoretically predicted using the first principles calculation, even if there are many difficulties such as the room temperature and external magnetic field in experiment [21,22].In this work, first-principles spin polarized calculations were used to explore the electron injection into Fe-doped SnO 2 , and its optical and magnetic properties were studied in order to understand the transition mechanism.

Computational Details
The first-principle calculations are performed using FP-LAPW as implemented in WIEN2k code [23,24].The exchange and correlation effects are treated with the generalized gradient approximations (GGA) [25,26].The parameter of  mt  max is chosen to be seven ( mt is the smallest muffintin radius in the unit cell and  max is the cut-off for the plane wave).The cut-off energy required in the calculations of the solid state is 0.0001Ry.For k-space integration, a grid of 4 × 3 × 3k points in the first Brillouin zone is used.Atomic sphere radii of Sn, O, and Fe atoms are set to be 2.0, 1.8, and 2.0 a.u, respectively.The lattice parameters of SnO 2 crystals are consistent with the experimental values, which are  =  = 0.4737 nm,  = 0.3186 nm, and  =  =  = 90 ∘ [27].

Density of States (DOS).
The calculated total DOS of the Sn 15 FeO 32 supercell is shown in Figure 1.It can be seen that Fe substitutions into SnO 2 DMS induce exchange-split impurity states in the band gap, and the size of impurity states increases with the increase of injected electrons.When the concentration of injected electrons is less than 1.0, the material shows a half-metallic behavior with the majority spin being semiconducting and the minority spin being metallic with sufficient unfilled states above the Fermi level.The 100% spin polarization carriers suggest that electroninjected Fe-doped SnO 2 can be used for spin injection where highly polarized spin current is desired.With the increase of the injected electrons, the conduction band moves to valence band gradually.Besides that, the DOS near the Fermi level reverses when the injected electron is 1.0.When the concentration of injected electrons is large than 1.0, the material shows a metallic behavior with both the majority spin and minority spin across the Fermi level.
The total and partial DOS of Sn 15 FeO 32 supercell with electron-injection concentration  = 0 and 1.0 are presented in Figure 2 3d and O 2p when electron-injection concentration is 1.0, and Fe 3d turns to down from spin up, indicating that particles reverse has happened.When the bands are in the range from 0.3 to 2.6 eV, the states mainly derive from Fe 3d.When the bands locate in the range from 2.6 to 6.0 eV, the states mainly derive from Sn 5p.

Band
Structure.The band structure of Sn 15 FeO 32 supercell is shown in Figure 3, when  = 0.5.At the Fermi level, occupied and not occupied electrons exist when spin down and up, respectively.Figure 4 shows the band structures of spin-up Sn 15 FeO 32 with the concentration of inject electrons to be 1.0 and 1.5.Furthermore the band gaps become narrower and narrower until zero with the increase of the injected electrons, indicating the excellent conductivity.Each band structure displays a direct band gap at the highly symmetric G point as well as in pure SnO 2 , as shown in [28].

Optical Properties.
It is well known that the interaction of a photon with the electrons can be described according to time-dependent perturbations of the ground-state electronic states, and the optical transitions between occupied and unoccupied states are caused by the electric field of the photon.More importantly, solid dielectric function reflects the information between energy band structure and optical spectral lines and can characterize the physical properties of materials.The formula of dielectric function is defined by where  1 () is the real part of the function, while  2 () is the imaginary part.The real part  1 () of the dielectric function can be evaluated from the imaginary part  2 () by the Kramer-Kronig relationship, while the imaginary part  2 () has the following expression [29]: Among this, ℎ = ℎ/2,  is the mass of free electrons,  is the charge of free electrons,  is the frequency of incident photons,  represents the conduction band,  represents valence band, BZ represents the first Brillouin Zone, and  is the reciprocal vector.
Figure 5 shows the imaginary spectra of optical dielectric function  2 (), with the number of ions of 0, 0.3, 0.5, 1.0, 1.2, and 1.5.There are three main dielectric peaks ranging from 7.0 to 14.0 eV.The first peak at about 7.1 eV should mainly be caused by the transition between O 2p state in the highest valence band and Sn 5s in the lowest conduction band.The second peak located at about 9.8 eV mainly derives from the transition from O 2p to Sn 5p state, which is reflected by the DOS.The peak at 14.0 eV can be attributed to the combination of the transition between O 2s and Sn 5s and that between Fe 3d and Sn 5p.At the same time, there are some unapparent folded peaks, and they could be attributed to multilevels direct or indirect transition.From 0 to 5.0 eV, the peaks changed greatly, which are in consistency with the DOS in Figure 1.
Figure 6 shows the absorption spectra with the number of ions of 0, 0.3, 0.5, 1, 1.2, and 1.5.In the imaginary spectra of optical dielectric function, three main dielectric peaks exist ranging from 7.2 to 12.0 eV, which have no significant differences between various electron-injections, and are in consistency with the dielectric function in Figure 6.As the electron concentrations increase, the overall curves move to the high energy, that is the blue-shift.From 0 to 5.0 eV, the peaks changed greatly, the results are consistent with the Ref 30 of Fe-doped TiO 2 .The spectra become smooth gradually, and the float/drift of the intensities is not apparent, indicating that such optical and electronic devices can work relatively stable.

Conclusions
In summary, the band structure, the total and partial DOS, and the optical properties of Sn 15 FeO 32 with electron injection have been investigated by the FP-LAPW method.With the increase of the injected electrons, the conduction band moves to valence band gradually.The SnO 2 material shows half-metallic properties when the injected electron is less than 1.0.There exists strong coupling interaction between Fe atom and O atom.For the optical properties (the imaginary part of dielectric function, absorption, and reflection), we found that the peaks changed greatly at low energy, the blue shift occurred, and the optical absorption edge increased.