Al doping on electronic structure and optical properties of ZnO

Results in Physics 15 (2019) 102649

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Effect of Cu/Al doping on electronic structure and optical properties of ZnO Jianfeng Dai a b

a,b

b,⁎

b

b

, Zhongqiang Suo , Zengpeng Li , Shanshan Gao

T

State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou 730050, China School of Science, Lanzhou University of Technology, Lanzhou 730050, China

ARTICLE INFO

ABSTRACT

Keywords: Cu/Al co-doped ZnO Electronic structure Conductivity Optical properties

The stability, electronic structure, conductivity and optical properties of Cu/Al doped ZnO in the condition of different concentrations and different positions were studied by using the first-principles generalized gradient approximation plane-wave pseudopotential method combined with Hubbard U correction based on density functional theory. Geometric optimization and energy calculations for the original structure of pure ZnO, Zn0.96875R0.03125O (R replaces Cu or Al) and Zn1−x−yCuxAlyO (x, y = 0.03125, 0.03125; 0.0625, 0.03125 and 0.03125, 0.0625). The results show that the co-doped systems are more stable than single-doped, and each of the systems is easier to form under O-rich conditions. When doping at the same concentration, the volume of the system with different impurity atoms on the same horizontal plane is small. In this paper, the co-doping can greatly reduce the band-gap of ZnO, so that the absorption edge of each system is red-shifted, the absorption of Zn0.90625Cu0.0625Al0.03125O in visible light is the strongest. The carrier mobility and conductivity of each system were calculated by the relative quantity of carriers and the effective mass. It is found that co-doping is more beneficial to the conduction than single-doping, and the influence of the concentration of Al on the conductivity of the system is larger than that of Cu.

Introduction ZnO is a direct wide band-gap compound semiconductor. The exciton binding energy is 60 mV [1], the band-gap is 3.37 eV at room temperature [2], ZnO is non-toxic, inexpensive and resource-rich [3]. In recent years, ZnO has been found quite a few uses in optics, magnetism and mechanics [4], such as Light Emitting Diode [5], Laser Direct structuring [6,7], energy storage, catalysis, dyes, solar cells [8], electronic devices, gas sensing, etc [9]. However, ZnO is insensitive to visible light due to the wide band-gap, it can just absorb ultraviolet light [10], and the conductivity and carrier concentration of the original materials are relatively low, which limits its application in conductive materials or optoelectronic applications [11]. To improve the electronic properties of ZnO in applications, doping is the most commonly used method [11–13]. Doping can cause sharp changes in electrons, optics and magnetism by changing the electronic structure of ZnO [14–17]. Among the transition metal doping, Cu is studied more because the electronic structure and atomic size of two atoms of Cu and Al are similar. Fang [18] investigated that as the Cu doping concentration increases, the photoluminescence intensity decreases at an excitation wavelength of 325 nm. Kayani [19] observed that the film crystallite size increases as the Cu doping ratio increases

⁎

from 2 wt% to 10 wt%. The optical band gap is significantly decreased. Das [20] discovered that the ZnO band-gap decreases with Cu doping. Slimi [21] found that the absorption spectrum of Cu doped ZnO is redshifted when the crystallite size of the nanoparticles is 32–38 nm. In summary, the introduction of Cu particles can reduce the band-gap of ZnO, and the visible light absorption is red-shifted and enhanced. However, Al doping hardly changes the light transmittance of ZnO, Lassar [22] claimed that Al and Ga are the best dopants for transparent conductive ZnO thin film. Li [23] prepared an Al-doped ZnO thin film by RF magnetron sputtering, with the increase of sputtering power and the resistivity decreased, the light absorption edge shifted to the shortwave direction. D. Sengupta [24] obtained high light conversion rate particles by controlling the concentration of Al-doped ZnO. M.Maache [25] prepared a film of Al-doped ZnO by the spin coating method and found that the transmittance in the visible range is greater than 75%. Sreedhar [26] prepared Al-doped ZnO by magnetron sputtering, when the magnetic field was applied, the light transmittance in the ultraviolet and visible regions was 90%. Abbassi [27] studied the light absorption, transmission and optical constants of doping on ZnO, found that Ga and Al increase the band-gap. Yang [28] used a magnetron sputtering method to prepare Cu/Al co-doped ZnO thin films with different doping ratios. Doping copper and aluminum into the film can reduce the

Corresponding author. E-mail address: [email protected] (Z. Suo).

https://doi.org/10.1016/j.rinp.2019.102649 Received 21 June 2019; Received in revised form 5 September 2019; Accepted 5 September 2019 Available online 11 September 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

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resistivity of the ZnO film (the magnitude decreases from 108 to 10−2). When the same length of copper wire and aluminum wire are co-doped, it has little effect on the transmittance of ZnO in the visible range. In conclusion, there are many studies on Cu or Al single-doped ZnO, but there are few co-doped. Even if co-doping experiments have emerged, the theoretical calculation is rarely discussed, and the nature of co-doping needs further investigation. Based on the above-mentioned issues, we have performed systematic studies on the Cu/Al co-doped ZnO with different ratios and different positions using first-principles calculations based on density functional theory (DFT), and we have explained macroscopic phenomena from the micro-level, then further guides the experiment. For comparison, corresponding undoped ZnO systems have also been considered.

Table 1 The supercell parameters and formation energy after lattice optimization. Structure

A B C D1 D2 E1 E2 F1 F2

Computational details

a/Å

b/Å

3.286 3.283 3.282 3.278 3.276 3.278 3.275 3.284 3.274

3.286 3.283 3.282 3.278 3.283 3.269 3.282 3.268 3.280

c/Å

5.283 5.287 5.292 5.290 5.282 5.297 5.279 5.296 5.283

V/Å3

49.401 49.359 49.365 49.239 49.204 49.156 49.144 49.229 49.164

Ef /eV O-rich

Zn-rich

−3.582 −4.962 −10.159 −16.021 −16.231 −21.786 −21.611 −25.466 −26.216

−1.380 −6.578 −8.857 −9.068 −11.040 −10.165 −14.719 −15.469

create electron holes in the single doping, which becomes the acceptor energy level, then the selected cell cannot shield the Coulomb coupling effect under the periodic boundary condition. In the case of co-doping, due to the incorporation of Al3+ ions, the excess positive charge in the system may charge the adjacent Cu+ and oxidize it to Cu2+. Besides, the Cu ion was Cu2+ in the literature [21].

Theoretical models Under the natural condition, the wurtzite structure of ZnO is the most stable. It belongs to the P63 mc space point group [29], and its unit cell is formed by the hexagonal close row of Zn and the hexagonal close row of O in the c-axis direction. The lattice constant of ZnO in the experiment are a = b = 3.249 Å, c = 5.206 Å, c/a = 1.602, α = β = 90°, γ = 120°. Based on the wurtzite ZnO cells, nine supercells (2 × 2 × 4) were established using the CASTEP module in Materials Studio 2017, these supercells are represented by A, B… F1 and F2, respectively. Structure A is pure ZnO, just like Fig. 1a. Structures B and C are Cu single-doped and Al-doped ZnO, respectively. Single-doped atoms are at R in Fig. 1a. The co-doped structure is shown as b-g in Fig. 1.

Results and discussions Analysis on lattice parameters and stability The most stable structure was obtained after optimizing the initial structure, as shown in Table 1. Results showed that the lattice parameters of pure ZnO (structure A), Cu single doping ZnO (structure B) and Al single doping ZnO (structure C) are consistent with the experimental value [4,40,41], the experimental value of c/a in pure ZnO is 1.602, this paper is 1.607, the error is only 0.31%. The a, c, and c/a in the literature [42] is 0.3254 nm, 0.522 nm and 1.6037, the error with this paper is only 0.9%, 1.2% and 0.2%, so the calculation results are reliable. Doping makes the ZnO volume slightly smaller, the radius of the doped particles is very close (Zn2+0.74 Å > Cu2+0.73 Å > Al3+0.54 Å [22]), so the lattice constant changes little and the material does not have significant lattice distortion. This reduces the internal stress of the film, indirectly improving the quality of the film [4,20]. The volume of the structure C is slightly larger than B since the repulsion between the positive charge in the system is larger after Al3+ doping. The energy of the system is increased and the volume is increased. Since the concentration of Al3+ in structure F (F1 and F2) is greater than E (E1 and E2), the volume of F is slightly larger than E. When doping at the same concentration, the volume of the system with different impurity atoms on the same horizontal plane is small, just like structure D2, E2, and F2. The formation energy of each system can be calculated as follows. [22,4]

Calculation methods The calculations were performed using density functional theory (DFT) [30], as implemented in CASTEP software in the Materials Studio 2017 package [31]. The exchange-correlation effect was treated using the Perdew Burke Ernzerh of [32] version of the generalized gradient approximation [33]. Electronic configurations used for calculation were Cu-3d104s1, Al-3s23p1, Zn-3d104s2, O-2s22p4, plane cutoff energy Ecut = 400 eV in reciprocal space, the K-points in the Brillouin zone was set to 3 × 3 × 2, the total energy convergence accuracy was 10−5 eV/ atom. The maximum tolerance of displacement was 0.001 Å, the convergence accuracy of stress was 0.05 GPa, the force of each atom was 0.03 eV/Å. Energy calculations were performed on each of the optimized systems to obtain electronic structures and optical properties. However, the GGA algorithm has self-interaction [34], so the calculated band-gap is inaccurate [35]. Therefore, this paper is correcting the band gap [36,37] with Hubbard U [38,39]. The calculated value of the bandgap is close to the experimental value when Cu-3d, Al-3p, Zn-3d and O2p take U = 4.5 eV, 3.5 eV, 10.5 eV and 7 eV, respectively. The formal charge of Cu atom in this paper was +2. If Cu+ replacing Zn2+ will

Efp = Epure

µZn

µO

Fig. 1. Supercell (2 × 2 × 4) model after lattice optimization. 2

(1)

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J. Dai, et al.

Ef = Etot

Epure + mµZn

nµCu

lµAl

(2)

conduction band minimum (CBM) is moved downward. Al doping causes the conduction band (CB) and the valence band (VB) to move significantly downward and the Ef shifts up. In the co-doped system, compared with the structure D, increasing the concentration of Cu can cause the valence band maximum (VBM) to move upward, and the impurity level in the band-gap becomes more complicated. Increasing the concentration of Al causes the Ef to move up and the VBM to move down. In structure B, the Ef is at VBM, the system exhibits P-type semiconductor characteristics. In other doping systems, the Ef enters the CB, and the semiconductor is N-type. Analysis of semiconductor types is consistent with related literature [4,22]. The TDOS and PDOS can further explore the mechanism of change in the band structure of each system. Fig. 3 shows that the CB in pure ZnO is composed of Zn-4s electrons, and the VB is mainly formed by hybridization of O-2p and Zn-3d, this is completely consistent with the analysis in the document [49]. Compared with A, the main peak after Cu doping has almost no movement, but an impurity peak of Cu-3d electrons was generated at 1.62 eV, it is indicated that Cu-3d acts on the band-gap to generate impurity levels. Although Al does not generate an impurity level in the band-gap, Al-3p electrons are present in a large amount in the CB, which causes an increase in the carrier concentration of CB and a band structure to move downward. The reason is that there is a more positive charge after Al3+ replaces Zn2+. These charges and a lot of Al-3p electrons obey the Fermi distribution function, so the Ef is pushed to a higher energy level, so the Ef of structure C moves up. The main peaks of the co-doped system move to the left because of the presence of Al-3p electrons and the higher the Al concentration, the greater the left shift, and the impurity levels appear in the band-gap of each system due to the Cu-3d electron. Comparing the structure D and C, the VB of D moves toward high energy, which can be understood as Cu dope into ZnO:Al, since Cu acts on the VBM, there is a p-d orbital repulsive effect between Cu-3d and O-2p of VBM, then the VB is pushed to the high energy region, and Cu-3d and O-2p under orbital hybridization in the band-gap to form impurity levels. It can be seen from E and F that when the doping concentration of Cu is increased, the VB is higher and the impurity level in the band-gap becomes wider and more complicated, some electrons of Cu-3d enter the CBM, and the electrons of Cu-3d in the structure E2 are filled from the VBM to the CBM, which is consistent with the above band structure; When the Al doping concentration is increased, electrons of Al-3p cause increased carriers, and the Ef is higher, the result is called Burstein-Moss [45], system becomes degenerate semiconductor. The impurity level in the band-gap can act as a jumper to reduce the energy required to move the carrier at the

where Efp is the formation energy of pure ZnO, Ef is the formation energies of doping ZnO, Etot is the total energies of the doped, Epure is the total energies of pure ZnO, μZn is the chemical potential of Zn, μO is the chemical potential of O, μCu is the chemical potential of Cu, μAl is the chemical potential of Al atoms. m is the number of Zn (removed from pure ZnO), n is the number of Cu, l is the number of Al atoms. Chemical potentials depend on experimental condition for material preparation 1 [43], µZn = EZn , µO = Epure µZn under Zn-rich condition, µO = 2 EO2 , µZn = Epure µO , while under O-rich condition [22]. EZn is the total energy of block Zn, EO2 is the total energy of O molecules. Table 1 shows that the formation of pure ZnO can be almost the same as the calculated value in literature [22] and is in agreement with the experimental values [44]. Formation energies for all kinds of doped ZnO are negative, meaning that all structures are energetically stable [45]. The formation energy of co-doping is lower than that of singledoping, indicating that the co-doped system is more stable, and each system is easier to form under O-rich condition. Al-doped ZnO is more stable than pure ZnO in literature [46], which is consistent with the results of this paper. Analysis on band structure and density of electronic states The band structure was obtained by the energy calculation, as shown in Fig. 2, the points of high symmetry in each system are the same, and the dotted line at 0 eV in Fig. 2 is the Fermi level (Ef). Results show that the band-gap value of the structure A is 3.322 eV, which is very consistent with the experimental value of 3.37 eV, the error is only 1.4%. Among them, the band-gap value of structure B and C is close to the experimental values of 3.159 eV [47] and 3.18 eV [48]. So the calculated value in this paper is reliable. It can be seen in Fig. 2 that the band-gap of each doping system has a reduction of different degrees, it indicates that the doping in this paper can reduce the band-gap of ZnO, thus improving the electrical and optical properties, etc. The doping does not change the band-gap type of ZnO, all systems are direct bandgap, which means that doped ZnO can be directly coupled with light to improve the luminous efficiency, and this is more favorable for luminescence than indirect band-gap due to the high probability of electronic transitions in the direct band-gap. The impurity level is generated in the band-gap, which can also increase the electronic transition rate, which is beneficial for the optoelectronic performance. The introduction of Cu particles produces impurity levels in the ZnO band-gap, the

Fig. 2. Band structure of each system. 3

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Fig. 3. The TDOS and PDOS of each system.

VBM to the CB, improve conductivity and change optical properties. The carrier concentration in the CB is also closely related to the conductivity of the system.

that the doping concentration of all systems in this paper are between 1.2660 × 1021 cm−3 and 1.2722 × 1021 cm−3, so these systems are degenerate semiconductor, which is consistent with the analysis in Section “Analysis on Band Structure and Density of Electronic States”. The conductivity of the system will be significantly improved after semiconductor degeneracy.

Analysis on semiconductor degeneracy It is known from the knowledge of semiconductor physics that the impurity concentration is greater than or equal to 1018 cm−3 at room temperature, the carrier concentration in the system is too high, electronic arrangement no longer obeys the Boltzmann distribution function due to the Pauli incompatibility principle, and it obeys the Fermi distribution. The Ef enters the CB, and the nature of the system is close to that of the metal. The electron mobility of the system varies drastically with the doping concentration and it is no longer a constant, and the doping concentration is smaller, the conductivity is higher. Such semiconductors are called degenerate semiconductors. Table 2 descripts

Analysis on conductivity The relevant parameters of the carriers are shown in Table 2, where m 0 is the mass of free electrons. Carriers of structure B are electron holes, but the other structures are electrons. The relative quantity of holes or electrons is obtained by integrating the density of state between VBM or CBM and Ef in TDOS, the relative number of electrons increases sharply due to the entry of Cu-3d electrons into CBM in codoping system. As can be seen from the literature [43], the relative

Table 2 The impurity concentrations and Carrier related parameters. Model

B

C

D1

D2

E1

E2

F1

F2

Impurity concentrations/×1021 cm−3 Carrier Relative quantity Concentration/×1021 cm−3 Effective quality/×m0kg

1.2662 0.288 0.3646 1.6126

1.2660 0.323 0.4089 2.7857

1.2693 9.560 12.134 2.5427

1.2702 8.533 10.838 2.6542

1.2714 8.821 11.215 2.5813

1.2717 9.858 12.537 2.5681

1.2695 11.033 14.007 3.1292

1.2722 11.054 14.063 2.6909

4

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electron number divided by the total volume of the structure after optimization is the electron concentration. The effective mass of the carriers of the along high symmetry point from G to F was calculated in each system by the method of the second derivative of the energy level at the VBM or CBM. The conductivity( i ) formula as follows [43] i

high in the same concentration doped system and the conductivity is strong. It can be seen from the literature [43] that the Bohr radius (a0 ) is larger, the conductivity of the system is stronger. The ionization energy (Ei ) of the electron is smaller, the metalloid is stronger. The Calculated is as follows [50].

(3)

= µi n i q

where µi is the carrier mobility, ni is a relative quantity of carrier, qis the basic charge. It can be seen from formula 3 that the carrier concentration is higher, the conductivity is stronger when the carrier mobility and the basic charge are constant. In this case, the conductivity of structures B and C in the doping system is relatively low, indicating that the conductivity of the co-doped system is better than that of single doping, and F2 has the best conductivity in this. The µi in formula 3 is determined by the formula 4. [43]

µi =

qi m

(4)

T is the where i represent the relaxation time. In addition, i temperature, Ni is the ionized impurity concentration. When the temperature, basic charge and effective quality (m ) are constant, the carrier mobility is only related to Ni , µi and Ni are inversely related. Therefore, the impurity doping concentration is smaller when the same system is doped with the same atom, the carrier mobility is higher, this is consistent with the results of the analysis in Section 3.3. In short, conductivity can be expressed as the formula 5. [43] i

=

r m0 am

(6)

Ei =

m E0 m 0 r2

(7)

where r is the relative dielectric constant, E0 is the ionization energy of the hydrogen atom on the ground state, is the fine structure constant. Only m in the formula (6) and (7) is a variable, so the m is smaller, the is bigger, the more beneficial to conduction, just like Bohr radius of D1, E2 and F2 are larger than D2, E1 and F1, the conductivity is stronger than the latter. The results are consistent with the conductivity analysis above.

T3/2 , Ni

i ni q

=

0

Analysis on optical properties The optical properties of the semiconductor are inseparable from the Kramers–Kronig dispersion relationship. The dielectric function diagram ( ( ) ) can be drawn through the real part ( 1 ( ) ) and the imaginary part ( 2 ( ) ) in the dispersion relation, as shown in Fig. 4. [51,52]

( )=

2

(5)

m

It can be known from Eq. (5) that the smaller the effective mass of carriers, the more the relative number of carriers, the more favorable to conduct electricity. In order to facilitate the study of conductivity, this paper sets i as a constant, substitute the existing data into formula 5 to obtain an estimate of the conductivity of each system. The estimated values are as shown in Table 3. It can be seen from Table 3 that co-doping has better conductivity than single-doping, the results show that co-doping can greatly improve the conductivity of ZnO, which is consistent with the conclusion of the document [28]. Found by calculation that when Al(3 cm): Cu(2 cm) is doped in literature [28], the impurity ratio is similar to the structure F in this paper, when Al(3 cm): Cu(4 cm) is doped in document [28], the impurity ratio is similar to Structure D. In this paper, the electrical conductivity of structure F is slightly higher than structure D, but in this experiment, the electrical conductivity of structure D is slightly higher. This paper thinks that literature [28] is macro-doping, the impurity concentration is relatively high, but this article is a nanomaterial with nano-effects, which differs from the nature of macro materials, so the results are slightly different. The effective masses of D1, E2 and F2 are all smaller than D2, E1 and F1, respectively, but the conductivity is stronger than the latter. The average value of the conductivity of doping ZnO from different positions of the same atom can be obtained that when the concentration of Cu or Al is increased, the concentration of Al has a greater influence on the conductivity of the system, just as the conductivity of F is greater than E. Conductivity is also affected by the carrier concentration. When the carrier changes greatly and the effective mass changes little, the number of carriers is decisive for conductivity. The carrier changes largely, so the carrier concentration is

1(

1(

)=1=

2(

)=

( )= R( ) =

2 0

' 2( )

BZ

V ,C

2 1 (

2 [

'2

0

C 2

(8)

) + i 2( ) 2

d

(9)

2 |MCV (k )|2 · (ECk (2 )3

)+

2 2(

)

1(

) + j 2( )

1

1(

) + j 2( ) + 1

1(

EVk

) d3k

(10) (11)

)]1/2

2

(12)

where BZ is the first Brillouin district, C is CB, V is VB, is the Planck constant, K is the inverted lattice, is the angular frequency, 0 is the density of medium, is the displacement, j is the constant, |MCV (k )|2 is the momentum transition matrix elements, ECk and EVk are the energy of CBM and the energy of VBM, respectively. Fig. 4 shows that pure ZnO has four main peaks at 4.4 eV, 8.9 eV, 12.5 eV and 14.8 eV, respectively. From the analysis of the energy band structure and density of states of ZnO, it can be seen that the first peak is mainly caused by the optical transition between the O-2p state electron at the VBM and the Zn-4s state near the CBM, the second peak is mainly caused by the transition between the Zn-3d state and the O-2p state, and the third and fourth peaks are caused by the transition between the Zn-3d state and the O-2s state in the VB. The latter three main peaks in each doping system have almost no movement, and only the first main peak has changed, indicating that the doping has a relatively large influence on the low energy region of ZnO. When Cu is doped ZnO, the absorption edge moves from 2.48 eV to 1.16 eV, which causes the light absorption redshift. When Al is doped, the absorption edge moves from 2.48 eV to 3.24 eV, which causes a blue shift. The redshift occurred in all the co-

Table 3 The impurity concentrations and Carrier related parameters. Model Conductivity/×10−8 i Conductivity(Average of D, E and F)/×10−8

i

B

C

D1

D2

E1

E2

F1

F2

0.50

0.33

10.56 9.795

9.03

9.60 10.19

10.78

9.99 10.76

11.54

5

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stronger than E1. When the wavelength is more than 500 nm, the light absorption of structures D1 and F1 are comparable, the F2 is slightly smaller than D2. Structure C has the weakest light absorption in this paper. The impurity level of D1 and E2 is connected to the CB and close to the VB, so the redshift of D1 and E2 are most obvious. The absorption of structure E in the visible light range is the strongest compared to other structures, which is mainly caused by two aspects. On the one hand, the impurity level of Cu-3d generated in the band-gap reduces the VBM electronic transition to the energy required for CBM, so the energy of visible light may excite electrons to the CB. On the other hand, the repulsion effect between Cu-3d and O-2p reduces the band-gap width, and the electronic transition of VBM is further facilitated. Also, the concentration of Cu in the structure E is the largest, so the absorption of visible light is the strongest. The light absorption of structure F is not as good as E because the concentration of Cu is small and the concentration of Al is too high, which causes the orbital of electrons below the Ef in CB to be in full or semi-full state. The transition requires more energy, so the absorption becomes weaker. F1 absorption is stronger than F2. It may be the impurity level of F2 is far away from CBM, so that when it acts as a springboard, the electrons from VBM need more energy to enter CB, so that the transition becomes slower and the absorption is weakened. There are many experiments on light absorption in the visible light range. However, there are few studies in the infrared region. This paper shows that when ZnO is co-doped with Cu/Al, the light absorption can be greatly red-shifted and it is possible to absorb in the infrared region, it can guide the experiment. It can be seen from Fig. 5b that the Cu single-doped ZnO has high reflectivity and light absorption, so the light transmittance of structure B is not good. The transmittance of Al single doped is the worst, even if Al single-doped ZnO causes the blue shift, it is impossible to completely transmit in the visible light range because it will reflect. The reflectance of structures F1 and F2 are comparable, indicating that doping at different locations has little effect on the reflectivity of structure F. The reflectance of structures D2 and E2 is also similar. In the visible light range, D1 has the lowest reflectance when wavelength is less than 678 nm, and E1 is the lowest when it is larger than 678 nm. In conjunction with Fig. 5a and b, D1 or D2 may be the most translucent. In summary, structure E is suitable for light-absorbing materials, while structure D is suitable for light transmissive film.

Fig. 4. The imaginary parts of the Dielectric Function.

doped systems, among them, the structure D has the highest absorption peak around 0.83 eV, E is the second, and F is the lowest. The above analysis shows that material properties can be changed by changing dopants. Substituting the data of the dielectric function into Eqs. (11) and (12) can calculate the absorption coefficient ( ( ) ) and reflectivity (R( ) ) of the system, as shown in Fig. 5. The results show that pure ZnO just absorbs a small amount of light with a wavelength of less than 480 nm because its band-gap is wide, and it is difficult for visible light to provide enough energy for the O-2p and Zn-4s electrons at VBM to the transition. When Cu is doped with ZnO, as shown by structure B, the light absorption is red-shifted, which is completely consistent with the conclusions obtained in the experiment [4]. Structure C is Al-doped ZnO, it can be seen from the blue line in the Fig. 5a that the light absorption has a significant blue shift, which is in full accordance with the experimental results in the literature [53]. The above data shows that the calculation results in this paper are reliable. The Cu doping can be red-shifted, because the impurity level acts as a springboard generating in the Cu-3d electrons of the band-gap, so that the energy required for the VBM electron transition to the CBM is reduced, so the low-energy light can excite the electron. The Al doping can be blue-shifted, because the Al-3p electrons accumulate in the CBM, which causes the Ef to move to the high-energy region, and the energy required for the VBM's electronic transition to CB to increase, so high-energy light can excite electrons, the absorption edge is close to the violet light. Fig. 5a illustrates that structure E absorbs most strongly in the visible region. When the wavelength is less than 64 nm, the structure E1 absorbs stronger than E2, and in the band greater than 464 nm, the absorption of E2 is

Conclusion In conclusion, the stability, electronic structure, conductivity and optical properties of Cu/Al doped ZnO in different concentrations and different positions are investigated by first-principles calculations. It is confirmed by optimization and formation energy calculation that the stability of all the Cu/Al co-doped ZnO is better than single-doping. The

Fig. 5. Absorption coefficient (a) and reflectivity (b) of pure and doped ZnO. 6

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co-doping doesn’t cause lattice distortion, and each system is easier to form under the O-rich environment. By exploring the band structures and state densities, we found that the band-gap decreases from 3.37 eV to 1.130 eV, and appeared at the impurity level in the band-gap. The conductivity of the co-doping is better than the single doping, when the band gap is smaller in the same doping system, the smaller the effective mass, the more beneficial to the conduction. The influence of the concentration of Al on the conductivity of the system is larger than that of Cu, from the imaginary part of complex dielectric function and absorption spectra, we found that a large red-shift occurs in the Cu/Al codoped ZnO. There are absorption peaks in the infrared region and the absorption of Zn0.90625Cu0.0625Al0.03125O is stronger in the visible light range.

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