First-principles calculations of electronic structure and optical properties of Boron-doped ZnO with intrinsic
defects
Yen-Chun Peng,Chieh-Cheng Chen,Hsuan-Chung Wu ⇑,Jong-Hong Lu
Department of Materials Engineering,Ming Chi University of Technology,New Taipei 24301,Taiwan
a r t i c l e i n f o Article history:
Received 11August 2014
Received in revid form 27October 2014Accepted 27October 2014
Available online 15November 2014Keywords:
First principles B-doped ZnO Intrinsic defect
Electronic structure Optical property
a b s t r a c t
This study adopted first-principles calculations to evaluate the effects of intrinsic defects on the elec-tronic structure and optical properties of Boron-doped ZnO (BZO).Four types of defect were considered:non-defective (B Zn ),Zn vacancies (V Zn ),O vacancies (V O ),and interstitial Zn (Zn i ).Calculations of forma-tion energy illustrate that O-rich conditions tend to induce V Zn ,while O-poor conditions tend to induce V O and Zn i .With respect to electric properties,V Zn defects in BZO decrea carrier concentration as well as mobility,which conquently decreas the conductivity of
BZO.The existence of V O or Zn i defects in BZO leads to n-type conductive characteristics and increas the optical band gap.The existence of Zn i defects in BZO also increas the effective mass,which decreas the mobility and conductivity of BZO.As for the optical properties,the introduction of V Zn to BZO leads to an increa in transmittance in the visible light region,but a decrea in the UV region.The introduction of intrinsic V O and Zn i defects to BZO leads to a significant decrea in transmittance in the visible as well as UV regions.The calculated results were also compared with experimental data from the literature.
Ó2014Elvier B.V.All rights rerved.
1.Introduction
ZnO is an abundant,non-toxic material with a wide band gap (3.37eV)and transparent properties under visible light.ZnO has recently attracted considerable attention as an alternative for Tin-doped In 2O 3(ITO),which is currently the most common choice of transparent conductive oxide for a variety of applications [1,2].The resistivity of pure ZnO is on the order of 10À2X -cm,which is far higher than that of ITO (10À4X -cm order).A great deal of rearch has gone into enhancing the conductivity of ZnO through the addition of various dopants,which can mainly be divided into metals [
3–5]and non-metals [6,7].B-doped ZnO (BZO)thin film shows considerable promi for its superior photoelectric proper-ties and stability [8,9].Many groups have investigated the effects of process parameters on the electric and optical properties of BZO thin film,with the aim of optimizing performance [7–13].Miyata et al.[7]indicated that the transmittance of BZO thin film could be improved through the introduction of O 2gas from 0sccm to 10sccm.David et al.[10]reported that annealing temperature and atmosphere strongly affect the conductivity of BZO.Yang et al.[11]concluded that the low oxygen partial pressure during deposition increas the carrier density of oxygen vacancies,which leads to a strong decline in resistivity.However,resistivity in sam-ples produced under the high oxygen partial pressure is far higher than in samples deposited under low oxygen partial pressure,which suggests the existence of p-type carriers of Zinc vacancies in films grown under high oxygen partial pressure.Patil et al.[12]synthesized B-doped ZnO powders using a mechanochemical method.The photoluminescence (PL)spectra at room temperature is an indication that a greater number of oxygen vacancies exist in nonmetal-doped ZnO,compared to pure ZnO.In the fabrication of BZO microrods,Yılmaz et al.[13]investigated the influence of B diffusion doping on optical emission and defect formation.PL spec-tra results revealed that the intensity of the deep level visible band emission increas with an increa in annealing time,which implies a significant increa in the concentration of intrinsic defects.
As outlined above,various process conditions influence the type and number of intrinsic defects with a subquent influence on the electric and optical properties of BZO.Gaining a comprehensive understanding of the electric and optical characteristics of BZO would require in-depth study into the effects of intrinsic defects on the properties of BZO.First-principles calculations can provide information concerning materials at the microscopic scale to eluci-date the connection between structure and properties.It is well known that the u of conventional density functional theory
dx.doi/10.1016/j.optmat.2014.10.058
0925-3467/Ó2014Elvier B.V.All rights rerved.
⇑Corresponding author at:Department of Materials Engineering,Ming Chi University of Technology,84Gungjuan Road,Taishan,New Taipei 24301,Taiwan.Tel.:+8862290898994675;fax:+886229084091.
E-mail address:ut.edu.tw (H.-C.Wu).
(DFT)leads to a considerable underestimation of the calculated band gap in ZnO [14–16].In our previous study [17],we ud the DFT plus Hubbard U (DFT +U)method to avoid underestimat-ing the
band gap.This approach reduced the differences in calcu-lated band gap and lattice constant to within 1%of the experimental values.The current study extended the utilization of the DFT +U method to calculate and analyze the effects of intrin-sic defects (V Zn ,V O ,and Zn i )on the formation energy,crystal struc-ture,electronic structure,and optical properties of BZO.The results clarify the connections among the fabrication process,structure,and properties of BZO,for u in determining the criteria for future material designs.2.Calculation methods
This study considered a 2Â2Â2supercell of a Wurtzite ZnO,including 16Zn atoms and 16O atoms,as shown in Fig.1.A B-monodoping model was constructed by substituting one Zn atom (number 1site)with one B atom (B Zn model),which correspond to the B concentrations of 6.25at.%.We also considered three intrinsic defects in the B Zn structure,in which Zn vacancies
(B Zn V Zn ),O vacancies (B Zn V O ),and interstitial Zn (B Zn Zn i )are repre-nted as 2,3,and 4,respectively.The V Zn ,V O ,and Zn i concentra-tions corresponds to doping levels of 6.25, 6.25,and 5.88at.%,respectively.The defect concentration could be reduced using a larger supercell for the real systems;however,this study was lim-ited with regard to computer resources.Therefore,the properties of the defects calculated from a 2Â2Â2ZnO supercell such as this could be ud as qualitative analysis.
1
4
3
2
Zn
O B
Table 1
Formation energy and optimized structure of BZO with varying intrinsic defects.
Formation energy (eV)Optimized structure O-rich
O-poor Zn–O (Å)B–O (Å)4V (%)ZnO –– 1.981–
–B Zn
3.750.39 1.996 1.526À3.1B Zn V Zn 5.68 5.81 1.993 1.530À3.3B Zn V O 7.550.70 1.995 1.521À5.3B Zn Zn i
10.51
3.66
2.003
1.517
锚杆施工工艺流程
4.7
4.5 eV
2.15 eV
3.25 eV
4.68 eV
办理护照多少钱
4.41 eV
(a)
(b)
(c)
(d)
Band structures of B-doped ZnO for (a)B Zn ,(b)B Zn V Zn ,(c)B Zn V O models.
Y.-C.Peng et al./Optical Materials 39(2015)34–3935稻香尤克里里
All models prented in this study were developed using CASTEP software [18].Structural optimization was performed on each model before calculating properties.The Monkhorst–Pack scheme [19]K-points grid sampling in the supercells was t at 4Â4Â2.Electron–ion interactions were modeled using the ultrasoft pudo-potential method [20].The valence configurations of the atoms were 4s 23d 10for Zn,2s 22p 4for O,and 2s 22p 1for B.The elec-tron wave functions were expanded in plane wave with an energy cutoff of 380eV.In the structural optimization process,the change in energy,maximum force,maximum stress,and maximum displacement tolerances were t at 10À5eV/atom,0.03eV/Å,0.05GPa,and 0.001Å,respectively.The energy convergence crite-rion for t
he lf-consistent field was t at 10À6eV.To describe the electronic structures more accurately,we adopted the DFT +U d +U p method [21],in which the U d value for Zn-3d and the U p value for O-2p orbitals were t at 10and 7eV,respectively.The band structures,band gaps,and Zn-3d orbital locations of pure ZnO,which were ud for the lection of U d and U p values,can be referenced in our previous rearch [17,22].
3.Results and discussion 3.1.Optimized structure
The average bond lengths and volume difference ratio,as obtained from geometric optimization,are summarized in Table 1.In pure ZnO,each Zn atom is bonded to its three horizontal and one vertical oxygen neighbors.The average bond length of Zn-O is 1.981Åand optimized lattice constants are a =b =3.249Åand
c =5.232Å,which are in agreement with the experimental values of a =b =3.249,c =5.206Å[23].Following the substitution of one B atom for one Zn atom (B Zn model),the Zn–O bon
d length is longer than that of B–O (1.526Å).This is becaus
醉晚亭e the B 3+radius (0.27Å)is smaller than that o
f Zn 2+(0.74Å)[24].Therefore,the cell volume of B Zn model shrinks,which is consistent with the experi-mental results [25].Clearly,the prence of Zn or O vacancies in BZO also leads to a shrinkage in volume.Converly,the prence of interstitial Zn leads to a longer Zn–O length and expansion in volume.
3.2.Formation energy
To examine the relative stability of BZO with intrinsic defects in neutral charge state,the defect formation energy can be expresd as follows:[26,27]
E f ðD Þ¼E tot ðD ÞÀE tot ðZnO Þþ
X
n i l i
ð1Þ
where E tot (ZnO)and E tot (D )are the total energy in pure ZnO and in the defective systems,respectively.n i is the number of i atoms removed from or added to the supercell.If an atom i
s removed from the supercell,n i is positive,otherwi is negative.l i is the chemical potential of atom i .Formation energy depends on the growth envi-ronment during the preparation process,which can be O-rich or O-poor (Zn-rich).In thermo-dynamic equilibrium,D l Zn +D l O =D H f (ZnO),where D H f (ZnO)reprents the formation enthalpy of ZnO.For the chemical potential of B,this study adopted the relation of 2D l B +3D l O 6D H f (B 2O 3)under O-rich conditions and l B =l B(bulk)under O-poor conditions,where D H f (B 2O 3)reprents the
(a)
(b)
(c)(d)
V Zn
V O
Zn i
B
Zn
O
O density difference for (a)B Zn ,(b)B Zn V Zn ,(c)B Zn V O ,and (d)B Zn Zn i models.The red,orange,yellow,green,and interpretation of the references to color in this figure legend,the reader is referred to the web version 36Y.-C.Peng et al./Optical Materials 39(2015)34–39
formation enthalpy of B2O3.D l i reprents the chemical potential of atom i referred to as the elemental solid/gas of l i(bulk/molecule).
It is well known that a defective structure with lower formation energy forms more readily and denotes an incread occurrence of defects.Table1prents a summary of the calculated formation energy of BZO with various intrinsic defects,bad on the neutral charge state.With the existence of B Zn,E f(B Zn V Zn)<E f(B Zn V O)<E f (B Zn Zn i)under O-rich conditions,implying that O-rich conditions are more likely to induce the formation of V Zn,followed by V O and Zn i.Under O-poor conditions,E f(B Zn V O)<E f(B Zn Zn i)<E f (B Zn V Zn),which implies that O-poor conditions are more likely to induce the formation of V O.As a result,process conditions,such as O2gasflow rate and substrate temperature,largely determine the type of intrinsic defects that form in BZO during pre
paration. The occurrence of V O is far more likely under a low-O atmosphere, and V Zn is more likely to occur under a high-O atmosphere.
For the sake of comparison,we also calculated the formation energy of a single intrinsic defect(V Zn and V O)in pure ZnO.The calculated values of E f(V Zn)and E f(V O)are3.09and4.33eV under O-rich conditions and6.58and0.84eV under O-poor conditions. Thus,we can e that the formation energy of a Zn vacancy from pure ZnO(E f(V Zn))is greater than that obtained from BZO
(E f(B Zn V Zn)ÀE f(B Zn)=1.93eV under O-rich conditions and
5.42eV under O-poor conditions).This demonstrates that Zn vacancies form more easily in BZO than in ZnO.The results are similar to tho calculated for O vacancies,which implies that B-doping facilitates the formation of V Zn and V O.Previous studies [12]obtained similar results,indicating that a greater number of oxygen vacancies or defects exist in BZO than in pure ZnO.
3.3.Electronic structure
To clarify the influence of intrinsic defects on the electronic structure of BZO,we calculated the band structure,difference in charge density,and density of states(DOS),as shown in Figs.2–4,respectively.I
n our previous study[17,22],the calculated band structure revealed a band gap of3.37eV in pure ZnO,which is in excellent agreement with values obtained in experiments.In the prent study,we focus on the properties of BZO with intrinsic defects.
Fig.2prents the band structures for BZO with various intrin-sic defect models.The Fermi level indicated by the dotted line was t to zero.Fig.2(a)shows the situation in which a Zn atom in pure ZnO is replaced by a B atom,in which the Fermi level shifts from the valence band(VB)maximum to the bottom of the conduction band(CB),resulting in a shallow donor level at the bottom of the CB.The shallow donor level at B doping caus an increa in the optical band gap to4.5eV at B concentration of6.25at.%,which is well known as the Burstein-Moss effect[28].The definition
of Fig.4.Density of states for(a)B Zn,(b)B Zn V Zn,(c)B Zn V O,and(d)B Zn Zn i models.
optical band gap is from the top of
for n-type miconducting materials and the bottom of conduction band for materials.Similar tendencies were experiment-bad studies[29,30].As东风好作阳和使
in the vicinity of B impurities appears atoms.The calculated Mulliken bond and B–O bonds are0.371and0.658, that a B–O bond is more covalent than Mulliken bond population reprents characteristics).As shown in Fig.4(a),
to the bottom of CB are the Zn-4s and
a few O-2s and O-2p orbitals.The main extra electron tofill up the CBM.
According to the results calculated regarded as an intrinsic defect under the B Zn V Zn model(Fig.2(b)),when donor levels coexist,the empty states produced trons from the B Zn donor level,resulting level as well as the formation of p-type band gap of B Zn V Zn can be narrowed to eration of conduction electrons requires energy from the Fermi level to the CB, be required in the B Zn model.Thus,in may lead to a decrea in the carrier known that mobility is related to the time.The relaxation time could not be software and was assumed as a defects in BZO.The following
effects of the effective mass on the
near the Fermi level appear nearly
of carriers with a smaller curvature The larger effective mass is related to
Therefore,V Zn defects in BZO reduce both carrier concentration as well as mobility,which conquently increas the resistivity of BZO.Fig.3(b)shows that the O atoms surrounding a Zn vacancy gain fewer electrons(green color),implying the occurrence of a number of empty states of O atoms.The empty states are O-2p orbitals near the Fermi level,as shown in Fig.4(b).
V O and Zn i can be regarded as intrinsic defects in an O-poor environment.Fig.2(c)and(d)show the band structures in B Zn V O and B Zn Zn i models,in which n-type conductive characteristics appear and the optical band gap increas to4.68eV and4.41eV, respectively.One shallow donor state and one deep donor state occur in the two models.In the B Zn V O model,the deep donor level is probably the charge remaining in the oxygen vacancy (Fig.3(c));in the B Zn Zn i model,it is probably the covalence charge in the vicinity of the interstitial Zn atom(Zn i)(Fig.3(d)).Fig.4(c) and(d)show that the shallow donor level in both models origi-nated from B doping,whereas the deep donor level in the B Zn V O and B Zn Zn i models originated from the addition of V O and Zn i, respectively.The deep donor level in the B Zn V O model compris mainly Zn and O atoms;however,in the B Zn Zn i
model,it also includes B atom(B-2s and B-2p states).The shallow donor states provide conduction electrons;however,the deep donor states may contribute less to the increa in carrier concentration.Qual-itatively,the curvature of the energy band near the Fermi level in the B Zn Zn i model is smaller than that in the B Zn V O model.There-fore,Zn i defects prent in BZO increa the effective mass,which may conquently decrea the mobility and conductivity of BZO.会计档案管理制度
3.4.Optical properties
The optical properties can be described via the dielectric func-tion e(x)=e1(x)+i e2(x)[31].The imaginary part of the dielectric function e2(x)is calculated as follows:e2¼2e2
p
企业调研
X e0
X
k;v;c
u c
k
uÁr
j j u v k
2
d E c
k
ÀE v
k
四个月的宝宝
Àx
ÀÁ
ð2Þ
where e is the electronic charge;X is the unit cell volume;u is the vector defining the polarization of the incident electricfield;x is the frequency of light;and u c k and u v k are the wave functions of the conduction and valence bands,respectively.
Fig.5(a)shows the e2(x)of BZO with various intrinsic defects. In the B Zn model,a blue-shift in the intrinsic absorption edge occurred due to an enlarged optical band gap as compared with ZnO.The shallow donor levels mentioned in Section3.3resulted in an absorption peak at1.2eV.The absorption peaks in the intrin-sic defect models were as follows:B Zn V Zn(0.3eV),B Zn V O(1.5eV), and B Zn Zn i(0.9eV).The peaks resulted in enhanced absorption in the visible range.The peak of B Zn V Zn is the lowest,which can probably be attributed to the transition between occupied states and unoccupied states near the Fermi level.In the B Zn V O,and B Zn Zn i models,the absorption in the visible range may be the result of a shift from the shallow and deep donor occupied states to the unoccupied states of the conduction band.
Fig.5(b)prents the transmittance of BZO under various defec-tive models.Table2prents the calculated values for average transmittance associated with each model under UV and visible light.It is should be noted that the calculated results were bad on the doping levels of B(6.25at.%),V Zn(6.25at.%)V O(6.25at.%), and Zn i(5.88at.%).The average transmittance of pure ZnO is89.2 %in t
he visible region and65.6%in the UV region.Fig.5(b)shows that the incorporation of B into ZnO decread transmittance in the range of800–1200nm(infrared region)and400–800nm(visible light region),but incread transmittance in the range of200–400nm(UV region),compared with pure ZnO.When V Zn was introduced to BZO,transmittance in the visible light region was Optical properties of BZO with varying intrinsic defects.(a)Imaginary dielectric function,(b)Transmittance.
38
