Optical properties of doping electrochromic M 0.125 W 0.875 O 3 ( M =Mo, Nb, Ta, Ti, V): A first-principles study

: Tungsten trioxide (WO 3 ) is a representative electrochromic material that can change their optical properties under the action of a voltage pulse and has attracted great interest in the applications of energy efficient windows. Models of various W 0.125 M 0.875 O 3 and Li x M 0.125 W 0.875 O 3 ( M =Mo, Nb, Ta, Ti, V) were built to simulate the bleached and colored state of WO 3 materials by first-principles calculations, respectively. The calculations show that doping systems of Li x M 0.125 W 0.875 O 3 ( M = Nb, Ta, V) lead to an enhancement of the modulation efficiency in invisible light and a decrease in the modulation efficiency in near infrared region (NIR). Ti doping boosts an excellent high efficiency of NIR modulation, while no modulation was observed in the visible light region. Mo doping remarkably promotes the coloration efficiency in both NIR and visible regions. The specific characteristics of doped WO 3 systems deserve more exploration of their application in green house or thermal modulation smart window.


Introduction
Firstly reported by S. K. Deb in 1969, WO3 has attracted a huge amount of interests due to its electrochromic property [1]. This phenomenon characterizes the WO3 material as a kind of smart electrochromic material to be utilized on smart windows where the color and optical properties may change according to individual needs. With the change of temperature, WO3 presents different polymorphisms, such as ε-WO3, δ-WO3, γ-WO3, β-WO3, with the crystalline structures of monoclinic, triclinic, monoclinic and orthorhombic, respectively [2]. All polymorphisms involve the tilting of W-O octahedrons. The more W-O octahedrons tilt, the less symmetry WO3 possesses.
Moreover, there exist other different structures in WO3. For instance, h-WO3 is another well-known polymorphism of WO3 with hexagon tunnels, which is synthesized by the solvothermal method with a water-controlled release process [3] and a-WO3 is a structure of glass state with disordered WO6 octahedral in it. In general, WO3 exhibits a monoclinic crystalline structure in the room temperature. The structure of pure γ-WO3 can be described as distorting perovskite structure (ABO3) without atom in A site [4,5].
The electrochromic property of WO3 can be interpreted by different models. Faughnan's model, which is also called the intercalation/deintercalation model, is a widely accepted one [7,8]. The alkali metal ions enter the WO3 layer (light yellow) and locate at WO6 octahedral sites ( Fig. 1 (a, b)), which may result in the formation of tungsten bronze LixWO3 (blue) [2,4]. This process is called intercalation and deintercalation process of Li + , which can be realized through a combined device with electrolyte, conducting glass, WO3 layer and a counter electrode. Once the WO3 is placed into the sandwich appliance ( Fig. 1 (c)) [9], the coloration happens in the WO3 material when there exists a positive voltage on both sides of the WO3 layer while it fades if the voltage is negative [10]. The coloration happens within only a few seconds after the voltage is applied. Besides, the color of WO3 layer will also vary according to different voltages [6]. The WO3 layer is nearly transparent before the injection of ions 3 and yet it becomes dark blue and opaque after the injection of ions (with a range of concentration), which indicates that the optical properties of the WO3 layer in the visible light can be adjusted [11]. According to the work by L. Berggren [12], changes of optical properties in infrared light also take place along with the coloration and the fading. The absorption coefficient increased from 0 to nearly 5×10 5 cm -1 during the coloration period hence results in a thermal regulation [13].
In experiments, alkali ions, such as H + , Li + , Na + are always employed as the intercalated ions [1]. However, H + ions in WO3 system are unstable and can be easily captured by W 6+ to form C-H2O and WO3·xH2O, which may affect the reversibility of devices [14] and the diffusion is more efficient for ions with smaller ion radii [15], hence in this paper, Li + is selected. It is inspected that the color of WO3 material is related to the number of alkali ions. WO3 will appear to be dark blue if the concentration of injected ions is lower than 0.5. In fact, concentration of injected ions is often lower than 0.3 in experiments [16]. There are many problems remaining to be solved in WO3 material, such as long response time, low cycle index, modulation efficiency and optical properties, etc. [9] Several methods have been taken to deal with these problems such as elemental doping [17], construction of microstructure [18], the designation of interfaces [19], etc. For instance, through construction of microstructure, Jiao et al. [20]synthesized the 4 nanostructured WO3 film with an excellent reversibility to more than 1000 circles.
Wang et al. [13] discovered that the structure distortion may enhance the absorption from 10 1 to 10 4 cm -1 in light energy period of 0 to7 eV. Considering the doping, Gesheva et al. [21] evaluated the optical band gap energies of Mo doped WO3 and the optical band gap ranged from 2.9 eV to 3.1 eV, which changed the optical properties of WO3.
Park [22] observed that the Au doped WO3 had a reversed optical modulation to the pure WO3. Aliev and Shin [23] successfully modified the T90 (time taken for the transmittance change by 90% of the total difference between the fully bleached and fully colored states) of the WO3 layer 96 s to 68 s by TiO2 solid solution. Yoon-Chae Nah et al. [24] synthesized TiO2 and WO3 nanotubes interfaces to make the system exhibit a good cycling index.
As it is summarized by Niklasson G. A. and C.G. Granqvist [6], the modulation of visible light and infrared light always happens simultaneously. Accordingly, the modulation of light and heat of sunlight in WO3 occur together. As a result, the exchange of light and heat is coupled, which limits the usage of WO3 glass for situations that call for single modulation of light or heat, which remains an aspect to be improved.
WO3 is a kind of cathode electrochromic material [6] hence in the present study, we attempt to modulate the infrared light and visible light of the WO3 separately, via doping, such as Mo, Nb, Ta, Ti and V whose oxides have cathode electrochromic property, with the purpose of the modulating the visible light and infrared light separately and exploring more utilization of WO3. For example, to make WO3 material be transparent in visible light and infrared light in bleached state while has a high reflectivity in visible state and high transmissivity in infrared state. Therefore, dopant of a series of transition metals may result in the change in the band structure and the alteration of the spectrum, which can be implemented to modulate the electrochromic property of WO3.
The content of this paper is arranged as following: Computation details are profiled in Section 2. The basic structure of WO3 material is described in Section 3.1.
Section 3.2 includes the concentration of Li + ions and Section 3.3 contains the 5 calculation of electronic structures of doped WO3. Section 3.4 contains the summary of optical properties of MxWO3. At the end of this paper, the results are concluded in Section 4.
Optical properties of materials can be described by the reflectivity and the absorption, which are related to the dielectric function [28,29,30]: In this equation 2 ( ) describes the unoccupied (conduction band) and occupied (valence band) states, respectively. What's more, in this paper the direction of ε( ) is opted on the x axis since the crystallized WO3 film possesses a (2 0 0) orientation on the surface [31].With 2 ( ) and 1 ( ), reflection R(ω) and absorption α( ) can be acquired through equations: The coloration efficiency is also employed to evaluate the coloration of WO3, 6 which can be summarized as： In Equation 4, TC is the transmissivity in colored state and TB is the one in the bleached state. Here Q is a constant of electric charge. Equation 4 indicates that if TC<TB, the higher TC is, the lower η will be, vice versa.

Basic atomic structure of the bulk WO3
All WO3 models are established with the lattice structure of γ-WO3, which is also called room temperature phase (RT). and it tend to compare the optical properties among several systems, therefore, the GGA method is employed in the following calculations. Methods Ref.

Concentration of alkali ions in colored state of WO3
In colored state of WO3, the concentration of alkali ions may greatly affect the optical properties and electron structure of WO3 so that several models are built with different number of Li + to determine the concentration of Li + with a better coloration efficiency. dash lines highlight two infrared atmospheric windows.

Band structures of LixWO3
Fig. 3 demonstrates band structures of various LixWO3 systems (x=0, 0.125, 0.25, 0.5, 1). When the concentration is 0 (pure WO3) (Fig. 3 (a)), as the Fermi level: EFermi is in the middle of band gap, the electron structure is in accord with Boltzmann distribution which indicates that WO3 is a conventional semiconductor material with a band gap of 1.154 eV.
Once alkali metal Li + ions are introduced into WO3, energy levels of Li + appear on the conduction band minimum CBM. In Li0.125WO3 system and Li0.25WO3 system ( Fig. 3 (b) and Fig. 3 (c)), band gaps are narrowed to 0.511 eV and 0.625 eV with EFermi raise up into CB. Three levels are noted by red arrows and electrons bounded on these levels give rise to the absorption of photon. These levels moving under EFermi because of the bonding between O 2p electrons and W 5d electrons. Besides the intrinsic absorption, impurity absorption in NIR region can be attributed to these levels if the lowest photon energy ℏ 0 is higher than EI (EI: ionization energy). Impurity absorption peak in NIR region of Li0.125WO3 system is smaller than the one of Li0.25WO3, which indicates that EI in Li0.25WO3 system is higher. In Li0.25WO3, as the system is a direct-gap semiconductor, the small peak at 2.75eV may be caused by exciton absorption. However, with the increase of the concentration x, the band structures tend to change. When the concentration is 0.5 and 1 (Fig. 3 (d) and (e)), Li0.5WO3 and LiWO3 have similar band structures. Especially in LiWO3, the system has a structure as CaTiO3 with high symmetry thus the band structure is also symmetrical. W atoms in Li0.5WO3 and LiWO3 are prone to be W 5+ . As a transition metal, bands of d electrons are not totally filled so that it can acquire more electrons.
As the energy levels of d electrons are lower than the ones of s electrons so that in the crystal energy levels shift down quite much under EFermi. Moreover, a series of W7M1O24 (M= Mo, Nb, Ta, Ti, V) crystals were built and 2 Li + ions are manually set in 2 A sites as it is mentioned in the introduction. According to the lowest energy principle, with each kind of M element, the position of 2 Li + is different in individual system.

Electronic structures of MxWO3
The band structures of γ-WO3 and M0.125W0.875O3 (M= Mo, Nb, Ta, Ti, V) in bleached states are demonstrated in Fig. 4. As Mo atom (4d 5 5s) has the similar electron structure to W atom (f 14 5d 4 6s 2 ) with six outside electrons, both Mo0.125W0.875O3 and pure WO3 accord with Boltzmann distribution with the EFermi in the middle of band gap 11 as it is demonstrated (Fig. 4 (a) and Fig. 4 (b)). Once Ta, Nb, V, Ti atoms are introduced into WO3, (Fig. 4 (c), (d), (e) and (f)) in bleached states, EFermi in all these four models are shifted down due to the different valences among W and Nb/Ta/V. W is hexavalent and Nb, Ta, V atoms are pentavalent and Ti atom is tetravalent. Once lower-valent atoms were introduced into WO3, the electron hole formed in lattices. As it is shown ( Fig. 4 (c), (d), (e) and (f)) that several acceptor energy levels (EA) appear on the valence energy levels (Ev) of WO3 and these systems perform as p-type semiconductors. EFermi in Nb, Ta, V doping systems appear near Ev while Ti doping system has a lower position of EFermi right in the valence band (Ev-EFermi=0.1965 eV), which indicates that with more impurity levels, Ti doping system is not only a p-type semiconductor but also a degenerate semiconductor. After Li + are inserted, in colored state, Li s-electrons occupy the conduction energy levels Ec position with bonds between O atoms (Fig. 5 (a)). Compared with bleached state (Fig. 4 (a)), the structure of the band does not change much while several bands move below EFermi. Both in the pure system and Mo/Nb/Ta/V doping system, EFermi is elevated into conduction band with a similar band structure. However, in Ti doping system, (Fig. 5 (f)

Optical properties of MxWO3 in bleached states and colored states
The