Atomic and electronic structures of charge-doping VO₂: first-principles calculations

Abstract

The atomic and electronic structures of charge-doping VO₂ are investigated by using first-principles calculations. Hole doping is more conducive to stabilizing the structure of VO₂ than electron doping. The controllable phase transition temperature is coupled with changes in atomic and electronic structures. With the increase in hole density, the V–V chains and twisting angle experience a dramatic change, and the band gap (0.69–0 eV) is rapidly reduced due to orbital switching between the d_x²−y² and d_z²/d_yz orbitals. However, as the electron density increases, the band gap (0.69–0.502 eV) narrows slightly, while the V–O bond lengths significantly increase. The current results provide up a variable way to tune the VO₂ phase transition temperature through charge-doping.

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1. Introduction

Vanadium dioxide (VO₂) is an attractive thermochromic material due to its reversible metal–insulator transition (MIT) from a high-temperature rutile phase (R) to a low-temperature monoclinic phase (M) at a phase transition temperature (T_c) of about 68 °C. Across the MIT, VO₂ exhibits a dramatic change in its electrical and optical properties.¹ Therefore, VO₂ is not only attracting wide scientific interest but also has great technological applications in optoelectronic devices,^2,3 sensors,⁴ and smart windows.^5–7

Given the diverse potential applications for VO₂, modulation of the phase transition behavior and decreasing the T_c close to room temperature are the main hottest topics in VO₂ researches. The control of phase transition in VO₂ was successfully implemented with multiple ways including doping,^8,9 point defects,^10,11 external strain,¹² electric fields,¹³ and surface and interface engineering.¹⁴ In most of these modulations, doping was proposed to play a strong role in mediating the phase transition temperature of VO₂. Recently, it is reported that charge-doping could effectively decrease the T_c of VO₂. What's the effect of the two types of charge injection, i.e. the hole or electron injection, on the tuning the MIT of VO₂? For example, Zhang et al.¹⁵ found that the reduction of the T_c is essentially ascribed to the charge injection as the dopants by the first-principles calculations. The surface adsorption of F₄TCNQ molecules assists the phase transition of VO₂ film due to the surface charge transfer.¹⁶ Substitution N-doping or interstitial N-doping in VO₂ allows for a significant reduction in the phase transition temperature from 80.0 to 62.9 °C.¹⁷ Zhang et al. also found that the T_c of the metal–insulator transition process decreases with a value of ∼18 °C for N-incorporated VO₂ thin films, and the narrowing of the charge doping results in the attenuation of the interaction within the V–V dimer in the M1 phase.¹⁸ Dai et al. reported that 2.93% F-doped VO₂ foil exhibits an increased solar-heat shielding ability (35.1%), excellent solar modulation ability (10.7%) and appropriate visible transmittance (48.7%).¹⁹ On the other hand, the incorporation of electrons in the VO₂ lattice could also induce its metal–insulator transition.^20–22 For example, NH₃ can act as a reductant to inhibit the over-oxidization of VO₂, resulting in inferior thermochromic properties.²⁰ Boron at the interstitial site provides three electrons, and thus, boron doping of VO₂ could drastically reduce the T_c at a rate as large as 31.5 °C per at% B.²¹ According to recent theoretical predictions, T_c can be reduced by 27 K per at% W at the GGA+U level or by 18.6 K per at% W at the HSE06 level, which is attributed to W-doping providing three electrons and inducing a large structural distortion in the lattice.²² Actually, the electron or hole-injection in VO₂ is implemented through these concrete methods such as the doping of N, B, F and other metals. For instance, from the point view of the semiconductor doping process, the W atom has one more valence electron than the V atom, so one W atom substituting for a V atom in VO₂ injects only one additional electron into the compound, whereas a B atom which possess two valence electrons in the 2s orbital at an interstitial site can inject its two 2s electrons into the VO₂. In addition, the N is widely considered to be the most promising p-type dopant due to its similar size to oxygen, resistance to forming AX centers.¹⁸ The F atom leads to the loss of the V⁴⁺–V⁴⁺ pairs, as electrons from the donors are injected into the V-3d valence band, resulting in the formation of V⁴⁺–V³⁺ pairs via charge transfer.¹⁹ Experimentally, Andreev et al. observed that hydrogen atoms penetrated into the VO₂ film during thermal decomposition could lead to a lowered phase transition temperature.²³

The above experimental and theoretical results indicate that the T_c and phase transition behavior of VO₂ can be effectively controlled by charge doping. However, the role of type of charge on the reduced phase transition temperature is still a debate and remains to be settled. Therefore, it is of vital importance to reveal the underlying mechanism on the effects of charge-doping on the phase transition behavior for realizing the rational tuning of the phase transition temperature.

2. Computational details

The calculations were conducted with the Vienna ab initio simulation package (VASP).^24,25 The potentials were of the projector augmented wave type (PAW) type, and the exchange-correlation part of the density functional was treated within the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE).^26,27 Given the strong on-site Coulomb repulsion among the V-3d electrons, the Hubbard parameter U was added to the PBE functional.²⁸ As discussed in ref. 9 and 10 the value was chosen as 3.4 eV in the PBE+U formalism. The valence electron configurations for V (3d³4s²) and O (2s²2p⁴) atoms were used in the calculations. 530 eV was used as the plane-wave cut-off energy. The Brillouin zone sampling mesh parameters for the k-point set were chosen as 5 × 5 × 5 for the electronic structures. These parameters were used to ensure a total energy converges of 1 × 10⁻⁵ eV per unit cell and a maximum force of 0.01 eV Å⁻¹. The charge density was tuned by changing the total number of electrons in the unit cell, with a compensating jellium background of opposite charge added or subtracted.²⁹

The formation enthalpy of pristine or charge-doped VO₂ was calculated as

where ΔH_f is the formation enthalpy of pristine or charge-doped VO₂. E_V (bulk) is the chemical potential of V in the bulk phase. is the total energy of the oxygen molecules.

The phase transition temperature (T_c) can be quantitatively calculated via³⁰

where T_c,0 is the transition temperature of pure VO₂ and a value of 340 K is adopted from ref. 2. ΔH and ΔH₀ are the enthalpy changes associated with the phase transition for doped and pure VO₂, respectively. The enthalpy is approximated as the Helmholtz free energy, which can be obtained from our DFT calculations by neglecting the pV term for condensed matter and omitting the entropy contribution at 0 K.

As shown in Fig. 1(a and b), the basic calculations were performed in the supercells with 2 × 2 × 2 and 2 × 2 × 4 primitive unit cells for VO₂(M) and VO₂(R) phases, respectively. Table 1 lists the calculated structural parameters. The theoretical lattice parameters obtained in this work are in good agreement with the previously reported experimental data.³¹

Fig. 1 Crystalline structures of monoclinic (a) and rutile (b) phases of VO₂. V and O atoms are represented by gray and red spheres, respectively.

Table 1 Lattice parameters of pristine VO₂(M) and VO₂(R)

Systems	a (Å)	b (Å)	c (Å)	α (°)	β (°)	γ (°)	V (Å^3)	Ref.
VO2(M)	5.743	4.517	5.375	90	122.6	90	117.466	Exp.^31
VO2(M)	5.626	4.637	5.454	90	121.704	90	121.021	This calc.
VO2(R)	4.552	4.552	2.852	90	90	90	59.095	Exp.^31
VO2(R)	4.652	4.652	2.789	90	90	90	60.336	This calc.

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3. Results and discussion

3.1 Charge induced phase transition for VO₂

Fig. 2(a and b) shows the total energies (E_tot) of charge doping in M and R phase as a function of charge density. It can be found that the total energies of charge-doping M phase VO₂ are gradually lower than those of R phase as the charge doping increases, indicating that it is more difficult to obtain R phase VO₂ than the M phase under current conditions. The similar results have been also appeared in electron-injection in two-dimensional transition metal dichalcogenides.³² Fig. 2(c and d) shows the formation enthalpy of charge-doped VO₂. The trend of the formation enthalpy of electron doping and that of hole doping are contrary. The formation enthalpy of VO₂ linearly increased with the increase in electron density, while the formation enthalpy of VO₂ decreased with the increase in hole density. In addition, hole doping system is more negative than the pristine one, and the electron doping system is less negative than the pristine one, suggesting that hole doping system is more stable than the electron doping. Thus, we conclude that hole doping is more conducive to stabilize the structure of VO₂ than electron doping. This phenomenon has been found in IIA element doping of VO₂(M).⁹ Zhang et al. reported that the introduction of some electrons in VO₂ via W doping results in the instability of the structure.²²

Fig. 2 Total energies (E_tot) of charge doping in M and R phase as a function of charge density, and formation energy of charge doped VO₂. (a) Hole doping, (b) electron doping, (c) charge doped VO₂(M), and (d) charge doped VO₂(R).

The dependence of T_c on the charge doping concentration is presented in Fig. 3(a and b). As shown in Fig. 3(a), the T_c of VO₂ is found to be almost linearly proportional to the hole-doping density. It is clearly shown that when the hole density is set at 4.28 × 10²¹ cm⁻³, the phase transition of VO₂ could take place at 162.44 K, which is lower than the room temperature of 298 K. This observation is consistent with the experimental observation that hole doping could trigger the MIT below 340 K.¹⁷ Wan et al. reported that the reduced phase transition temperature for hole doped VO₂ is due to the fact that hole doping modifies the V-3d orbital occupancy and thus weakens the electron–electron correlation, lowering the crystalline stability energy.¹⁷ Dai et al. found that F-doping can effectively decrease the T_c to 35 °C at 2.93% F in VO₂ and that F-doping VO₂ smart glass foils exhibit excellent thermochromism in the near-infrared region.¹⁹ However, the situation for electron-doping is not the same as that of hole-doping. As shown in Fig. 3(b), when the electron density increases from 0 to 2.1 × 10²¹ cm⁻³, T_c gradually increases. However, once the electron density is greater than 2.1 × 10²¹ cm⁻³, T_c rapidly decreases. For example, an electron density of 2.1 × 10²¹ cm⁻³ corresponds to a ΔT_c of 11.72 K for electron-doped VO₂, i.e., the phase transition from the rutile phase to the monoclinic phase occurs at 351.72 K. However, an electron density of 1.12 × 10²² cm⁻³ will result in a ΔT_c as large as −25.32 K, implying the reduction in T_c to 314.68 K. Actually, the T_c is related with the charge concentration. In the range of charge concentration, the T_c is almost linearly proportional to the charge density. Experimentally, when cooled down to 120 K, H_xVO₂ (x > 4%) films exhibit metallic properties, and the ΔT_c was around −55 K per at% H.²³

Fig. 3 Dependence of the phase transition temperature (T_c) in VO₂ on the charge density. (a) Hole-doping, and (b) electron doping.

3.2 Atomic and electronic structures of charge-doped VO₂

The reduction in T_c for charge-doped VO₂ should be coupled with the changes in the atomic and electronic structure, as discussed in the next section. For charge-doped VO₂(M), as shown in Fig. 4(a and b), the lattice parameters b and c of are slightly increase, and the lattice parameter a remains nearly unchanged under the considered electron density. However, these parameters (a, b, c) slightly decrease with increasing of hole density. This outcome further confirms that the reduction in the T_c in hole doped VO₂ is due to the shorter a-axis length.^33,34 Moreover, the lattice parameter a expressing the V–V chains promotes the transition from the monoclinic phase to the rutile phase at a lower temperature than that of pristine VO₂. Applying the compression strain along the a-axis balances the V–V distance. In addition, applying the compression strain along the a-axis results in the overlapping of d orbitals, which increases the d bandwidth and then forces it to transition from the monoclinic phase to the rutile phase, thus causing the reduction in T_c. Experimentally, Fan et al. reported that stretching of a-axis will increase the T_c of VO₂ films.³³ Muraoka et al. found that the appearance strain along the a-axis from VO₂/TiO₂ thin films has a large influence on the MIT of VO₂.³⁴ Therefore, hole doping in the concentration range considered is able to promote the phase transition in VO₂. The opposite is true for electron doping. For charge-doped VO₂(R), as shown in Fig. 4(c and d), the c axis is slightly shorten, and then slightly elongated in the hole-doping VO₂(R), while the c axis is slightly elongated in electron-doping VO₂(R). This may attribute the fact that the charge-injection would induce variable orbital occupancy, which is similar to the experimental results.¹⁹

Fig. 4 Lattice parameters of (a) hole or (b) electron doped VO₂(M), and (c) hole or (d) electron doped VO₂(R). The inset figure is the variation of c, i.e., Δc (c − c₀). The c and c₀ are the supercell lengths along the c-axis at equilibrium and charge-doped VO₂.

It is reported that the V–V chains are one of the key characteristics of VO₂ in determining the atomic and electronic properties at different phases.^35,36 As shown in Fig. 1, in pristine VO₂(R), all the V atoms arrange uniformly along the c axis with nearest-neighbor V–V distances of 2.788 Å. However, pristine VO₂(M) exhibits Peierls distortion in the V–V chains along the a-axis, in which the short and long V–V bonds (2.520 Å vs. 3.143 Å) are arranged alternately. Compared with those of pristine VO₂(M), as shown in Fig. 5(a and b), the short and long V–V bond distances are nearly unchanged and still maintain the dimerization characteristics after electron doping. However, hole doping results in a gradual shortening of the long V–V bond distances and a gradual elongation of the short V–V bond distances below a critical hole density of 6.48 × 10²¹ cm⁻³. This phenomenon could also be observed experimentally in the intermediate phase of VO₂(M2), in which only half of the V atoms are dimerized, while the other half form chains of is equally spaced atoms.³⁷ Once above the critical hole density, the alternatively short and long V–V bond distances jump, and the equidistant V–V bond distances (2.7–2.8 Å) are similar to the V–V bond length in VO₂(R) (as shown in Fig. 5(a)). These results indicate that VO₂ transits from the monoclinic phase to the rutile phase within the range of a certain hole-doping density. Yuan et al. proved that the appearance of this phenomenon is attributed to a strong lattice-hole coupling.³⁸ Experimentally, it is found that a critical hole density induces a sudden rapidly variable V–V bond, which is related to the critical excitation influence.^39–42 As shown in Fig. 5(c), the V–V distances in the hole-doping VO₂(R) has a very fast change into alternatively short and long bond distances, for the V–V chains. In contrast, as shown in Fig. 5(d), the V–V distances in electron-doping VO₂(R) seem slightly to increase. Therefore, it can be concluded that the hole-injection has greater influence on the V–V bond lengths than the electron-injection in VO₂.

Fig. 5 Dependence of V–V distances in (a) hole or (b) electron doped VO₂(M) and (c) hole or (d) electron doped VO₂(R) on the charge-doping density. The long V–V bonds denote V–V⁽¹⁾, and the short V–V bonds denote V–V⁽²⁾. The inserted figure shows the V–V bonds in the VO₂(M). The V and O atoms are indicated by the gray and red spheres, respectively.

The structural transition in VO₂ is accompanied by changes in the electronic band structure near the Fermi level that can be qualitatively understood within a crystal field model.³¹ As shown in Fig. 6(a), the twisting of the V–V chains causes splitting of the d_‖ orbital into filled bonding and empty antibonding orbitals, while making the π^* orbital move to a higher energy level, thus opening the band gap. Actually, the VO₂ phase transition is relative to the octahedral environment and the associated hybridization of the O-2p orbitals with the V-3d orbital.³¹ As shown in Fig. 6(b), for VO₂(M), each VO₆ octahedron shares edges with its neighboring octahedra, forming chains along the a-axis. In addition, the V-3d orbitals split into a combination of low-energy states and high-energy states, where the high-energy states involve the symmetry of the V–O bonds. In charge-doping VO₂(M), as shown in Fig. 6(c and d), the V–O distance is slightly lengthened with the increase in electron density, and could further decrease the p–d overlap.⁴³ The increase in the V–O bond results in the expansion of the lattice volume due to the decrease in c_R/a_R and further induces the reduction in T_c.⁴³ Therefore, we can conclude that electron doing makes the V–O bond length longer and thus reduces the T_c in VO₂. However, as the hole density increases, the V–O bond lengths are gradually reduced. When the hole density reaches 5 × 10²¹ cm⁻³, d₂ experiences a dramatic increase, and d₅ decreases sharply, which will increase the p–d overlap, and thus both the d_‖ and π^* orbitals are partially occupied at Fermi level.⁴³ This phenomenon confirms that VO₂ may experience a metal–insulator transition.

Fig. 6 (a) Bandwidth scheme of pristine VO₂, (b) an octahedron at the center of VO₂, (c and d) the V–O bond lengths in charge doped VO₂(M), and (e and f) the V–O bond lengths in hole-doped VO₂(R). The bond distances in VO₂(M) are d₁, d₂, d₃, d₄, d₅ and d₆. The bond lengths in VO₂(R) are the equatorial and apical V–O.

As shown in Fig. 6(e), in the VO₂(R), the apical and equatorial V–O bond lengths increase with the increase of electron density, which is due to the decrease in the ration of c/a. However, as shown in Fig. 6(f), the apical and equatorial V–O bond lengths decrease with the increase hole density.

Except for the variable V–O bond, the band gap evolution of charge-doped VO₂ is related to the atomic structure change described by the V–V chains and twisting angle δ and the electronic structure change described by orbital switching. As shown in Fig. 7(a and b), δ in the V–V chains of electron-doped VO₂ tends to gradually decrease, indicating that the V–V bond characterizes a dimerizing feature. However, when the hole density is from 0 to 4.28 × 10²¹ cm⁻³, δ in the V–V chains decreases monotonically, as the hole density increase further, the value of δ sharply decreases, finally reaching zero, which demonstrates that the alternatively short and long V–V bond distances in VO₂(M) quickly change into equal V–V bonds. In addition, the average twisting angle δ in the V–V chains exhibits excellent consistency with the band gap change of VO₂ from R to M1. As in Gao's previous discussion,³⁵ the significant dimerization in V–V, slight twisting of δ or the variable V–O bond can be regarded as the characteristic parameters of the structure-driven transition. As shown in Fig. 7(c), when the hole density is increased by 5.4 × 10²¹ cm⁻³, the band gaps of VO₂(M) linearly decrease and eventually decrease to 0 eV with the increase in hole density. The band gap undergoes a fast change, and exhibits a similar change tendency as the twisting angle δ. This phenomenon is consistent with the other result calculated from Lee et al.,¹⁴ who reported that VO₂ exhibits a significant band-gap narrowing for a charge concentration from 0.025 to 0.5 hole/electron per VO₂. Experimentally, Zhang et al. found that N atoms-substituted O atoms induce narrowing of the energy band gap due to weakening of the interaction within the V–V dimer with the hole injected into the d_‖ sub-bands.¹⁸ In contrast, as shown in Fig. 7(d), as the electron density increases from 0 to 1.2 × 10²² cm⁻³, the band gaps of VO₂(M) experience a slight reduction ranging from 0.69 eV to 0.502 eV. Apparently, electron doping induces a slow MIT, and its density has some effect on the phase transition. Theoretically, a fascinating rebound behavior of the transition temperature is observed. By increasing the doping concentration of W into VO₂, the MIT is tuned to a lower temperature at the beginning and then anomalously shifted to a higher temperature.⁴⁴

Fig. 7 (a and b) Average twisting angle (δ) of the V–V chains and (c and d) the band gaps in charge-doped VO₂(M). (a and c) Electron doping, and (b and d) hole doping. The inserted figure in (b) is the δ angle in the V–V chains in VO₂(M).

In order to reveal the kinetic limit for charge-driven phase transition in VO₂, we performed CINEB calculations to obtain the phase transition barriers. As shown in Fig. 8(a), we redefined the lattice parameters for VO₂(R) from tetragonal and monoclinic view to better reveal the kinetic limit for charge-driven phase transition in VO₂ (As listed in Table 2). Fig. 8(b) shows the energy curves of M-to-R phase transition in pristine and charge-doping VO₂ with certain density. It can be found that the energy barriers are too higher for VO₂ transiting from M phase to R phase, indicating that it requires additional conditions to drives the M-to-R phase transition, such as the temperature, pressure and light radiation.³²

Fig. 8 (a) Structures of VO₂ (M/R) and (b) energy barriers from M to R phase under different charge doping.

Table 2 Calculated lattice parameters for VO₂ (M/R)

VO2	a (Å)	b (Å)	c (Å)	α (deg)	β (deg)	γ (deg)	Ref.
R	4.609	4.609	2.785	90	90	90	35
Monoclinic R	5.575	4.653	5.427	90	120.936	90	This calc.
M	5.610	4.571	5.393	90	121.9	90	35
M	5.648	4.634	5.450	90	121.64	90	This calc.

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To elucidate the possible driving forces behind the MIT, we further calculated the total and partial densities of states (DOSs) of charge-doped VO₂(M). As shown in Fig. 9(a), for pristine VO₂(M), the electrons around E_F occupy the t_2g-state d_x²−y² orbital (π), while the conduction is mainly occupied by the e_g-state d_z² orbital (σ). At hole densities of 2.1 × 10²¹ cm⁻³ and 4.28 × 10²¹ cm⁻³, the band gaps of VO₂(M) are reduced to 0.515 eV and 0.34 eV, respectively. Near the E_F, the electrons dominantly occupy the d_x²−y² orbital and d_yz orbital. In contrast, fewer electrons occupy the d_z² orbital (σ). More importantly, this electronic structure characteristic remains from 0 to 6.48 × 10²¹ cm⁻³ (the critical hole density). Interestingly, when the hole density reaches the critical hole density, VO₂ exhibits metallic properties, as shown in Fig. 9(d). There is a strong interaction near the Fermi level between the d_x²−y² and d_z² orbitals. This result is also consistent with the previous discussion on the significant dimerization in V–V and a slight twisting of δ, which could be regarded as the characteristic parameters of the structure-driven transition. However, from Fig. 9(e–h), the Fermi levels are shifted into the conduction band to varying degrees with the increase in electron doping. The states near the Fermi level are mainly occupied by the d_z² orbital, while the valence bands mainly consist of the d_x²−y² orbital. Furthermore, it can be observed that the electronic structure of VO₂ changes slightly for different electron concentrations. More importantly, although there are some changes in the band gap from 0.597 eV to 0.502 eV and the location of E_F, this electronic structure characteristic remains as electron doping increases. Therefore, it can be concluded that the band gap of VO₂ with charge doping should be attributed to an electron-correction-driven Mott transition in which orbital switching occurs between the d_x²−y² and d_z² states. Experimentally, by soft-X-ray absorption spectroscopy, orbital-assisted MIT is also observed in VO₂.⁴³

Fig. 9 Total and projected density of states (DOS) of (b–d) hole-doped and (e–h) electron-doped VO₂(M). The concentrations of charge are (a) pristine, (b) 2.1 × 10²¹ cm⁻³, (c) 4.28 × 10²¹ cm⁻³, (d) 8.8 × 10²¹ cm⁻³, (e) 1.04 × 10²¹ cm⁻³, (f) 4.28 × 10²¹ cm⁻³, (g) 7.63 × 10²¹ cm⁻³, and (h) 1.12 × 10²² cm⁻³. The Fermi level (E_F) is set to 0 eV.

Fig. 10 shows the density of states of pure VO₂(R) and charge-doping VO₂(R). It is seen that pristine VO₂(R) and charge-doped VO₂(R) exhibit metallic properties as the Fermi level crosses the conduction band. Furthermore, electrons around Fermi level mainly occupy the d_x²−y² orbital and d_z² orbital. In addition, as the hole density increases, the former has a higher occupant than the latter. However, as the electron density increases, the occupant of d_z² orbital is higher than that of the d_x²−y² orbital. In general, there is a significant orbital switching between the d_x²−y² and d_z² orbitals accompanied by obvious V–V dimerization and a slight twisting of δ in the charge-doped VO₂.

Fig. 10 Total and projected density of states (DOS) of (b–d) hole-doped and (e–h) electron-doped VO₂(R). The concentrations of charge are (a) pristine, (b) 2.1 × 10²¹ cm⁻³, (c) 4.28 × 10²¹ cm⁻³, (d) 8.8 × 10²¹ cm⁻³, (e) 1.04 × 10²¹ cm⁻³, (f) 4.28 × 10²¹ cm⁻³, (g) 7.63 × 10²¹ cm⁻³, and (h) 1.12 × 10²² cm⁻³. The Fermi level (E_F) is set to 0 eV.

3.3 Discussion

Charge-doping greatly impacts on the atomic and electronic structures of VO₂. From the Fig. 3, it is found that the charge-doping including hole and electron-doping could trigger the phase transition of VO₂. More interestingly, the effect of hole doping on the T_c is greater than that of electron-doping. This is consistent with other calculation result. As is predicted by Zhang et al., the hole doping was superior to electron doping for modulating the phase transition of VO₂.³⁸ From a geometric viewpoint, the octahedra in VO₂ are orthorhombically distorted, making it possible to differentiate the V–O bonds. After electron-doping, the V–O bond length change significantly in VO₂(R). However, for hole-doping, the alternatively short and long V–V bond distances has very fast change into the equidistant V–V bond in VO₂(M). Furthermore, the twisting angle δ experiences a great change. These phenomena are ascribed to structure-driven transition due to the large δ and V–V bond length change.³⁵ From the electronic structure viewpoint, the characteristic of VO₂ transition from the semiconducting state to the metallic state appears due to the strong interaction between the d_x²−y² and d_z² orbitals near the Fermi level, which can be attributed to the electron-driven the transition. Therefore, it can be concluded that charge-doping may provide an efficient way to modulate the MIT in VO₂.

4. Conclusions

In summary, we performed first-principles calculations to investigate the behavior of charge doping and its influence on the phase transition temperature of VO₂. Charge doping could effectively modulate the T_c, assisting the VO₂ phase transition at room temperature. Hole doping induces a significant band-gap narrowing with increasing of hole concentration. The characteristic VO₂ transition from the semiconducting state to the metallic state appears once above the critical hole density (6.48 × 10²¹ cm⁻³), which is due to the strong interaction between the d_x²−y² and d_z² orbitals near the Fermi level. However, electron doping shows a slight band-gap narrowing with increasing electron concentration. The V–O bond lengths significantly increase. The results will provide insights into phase transitions of VO₂ thermochromic materials across the MIT suitable for applications such as smart windows.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully acknowledge support from the National Natural Science Foundation of China (51873102, 51972206), the Open Project Fund of Key Laboratory for Optoelectronics and Communication of Jiangxi Province (20181OEC001), the School-level Scientific Research Project of Hubei Polytechnic University (18xjz11R), and the Innovation Training Program of Hubei Province (S201910920031). The computation was conducted using the high performance computing platform of Shanghai University.

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