Structural and electronic properties of CuI doped with Zn, Ga and Al

Journal of Physics and Chemistry of Solids 74 (2013) 1122–1126

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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs

Structural and electronic properties of CuI doped with Zn, Ga and Al Jiajie Zhu a, Mu Gu a,n, Ravindra Pandey b a b

Department of Physics, Tongji University, Shanghai 200092, PR China Department of Physics, Michigan Technological University, Houghton, MI 49931, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 9 May 2012 Received in revised form 28 January 2013 Accepted 15 March 2013 Available online 26 March 2013

The structural and electronic properties of CuI doped with Zn, Ga and Al are investigated using density functional theory. The calculated results find that the solubility of the cation dopants considered is primarily determined by the difference in the electronic configurations between host and dopants. The order of the formation energy of the dopants is predicted to be E(ZnCu)4E(AlCu) 4E(GaCu) in CuI. Furthermore, dopants at the octahedral interstitial sites have lower formation energies as compared to dopants located at the tetrahedral interstitial sites in the lattice. The defect complex consisting of ZnCu and the copper vacancy (ZnCu þ VCu) is predicted to be preferred in the lattice, suggesting that incorporation of Zn is expected to enhance the concentration of copper vacancies in CuI. & 2013 Elsevier Ltd. All rights reserved.

Keywords: A. Optical materials A. Semiconductors C. Ab initio calculations D. Defects D. Electronic structure

1. Introduction Scintillators are light functional materials, converting highenergy rays such as X-ray and γ-rays to visible light. They are extensively used in high energy physics and nuclear medicine to detect X-rays or γ-rays. Recently, the cubic cuprous iodide (CuI) has drawn much attention due to its fast decay time of 130 ps of the ≈420 nm luminescence, and is proposed as a candidate material for the ultrafast scintillating devices [1–4]. Although the decay time of the ≈420 nm luminescence is very fast, its light yield of 570 photon/MeV is quite low compared to that of the wellknown LSO:Ce material with the light yield of 30,000 photon/MeV, thus influencing its energy resolution [5]. Experimental and theoretical efforts are now focused on the ways to enhance the ≈420 nm luminescence of CuI which is attributed to the recombination of the donor–acceptor pair (DAP) in the lattice [6]. Perera et al. observed that the luminescence increases immediately after exposure to iodine vapor, thus attributing it to transition from the conduction band to a trap level introduced by the surface iodine [7]. Gao et al. reported that not only iodine annealing but also air annealing can enhance the luminescence at 430 nm [4]. However, Zheng et al. found that the 420 nm luminescence depends on the growth direction of CuI film [8]. They argued that it arises from the iodine vacancy on more tightly packed (111) plane instead of surface iodine in the lattice. Thus, the viewpoints of Perera et al. and Zheng et al. contradict each other because the surface iodine vacancy is expected to be filled during iodine annealing. On the other hand,

n

Corresponding author. E-mail address: [email protected] (M. Gu).

0022-3697/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2013.03.010

Wang et al. reported that the p-type nature of CuI is due to copper vacancies in the lattice [9–11]. This is supported by Chen et al. who suggested the luminescence at 428 nm to be associated with copper vacancies in CuI [12]. Furthermore, the luminescence at 431 nm was found to decrease with decreasing conductivity of CuI film [13]. Perera et al. also found the similar relationship between luminescence and conductivity in CuI after exposure to the iodine vapor [7]. Considering that the light yield of CuI is closely related to the concentration of the copper vacancies in the lattice, we propose to investigate the role of cation dopants in stabilizing the copper vacancies in CuI. Since a copper vacancy has a negative effective charge in the CuI lattice, one can stabilize the copper vacancy by doping the lattice with divalent and trivalent cations as per the charge compensation requirement. In this study, we consider cations such as Zn2 þ , Ga3 þ and Al3 þ as dopants in CuI calculating their stability and electronic properties in the lattice. Note that CuI crystallizes in the zinc-blende structure at the room temperature. The ionic radii of Cu þ , Zn2 þ , Ga3 þ and Al3 þ are 77, 74, 62 and 53.5 pm, respectively. On the other hand, the electronic configurations of Cu þ , Zn2 þ , Ga3 þ and Al3 þ are 3d104s1, 3d104s2, 3d104s24p1, 3s23p1 respectively. The electronegativity of Cu, Zn, Ga and Al are 1.9, 1.65, 1.81 and 1.61, respectively. We briefly describe the computational method in Section 2. Results are discussed in Section 3, and summary is given in Section 4.

2. Computational method Electronic structure calculations are carried out using the projector augmented plane-wave (PAW) method as implemented in Vienna ab

J. Zhu et al. / Journal of Physics and Chemistry of Solids 74 (2013) 1122–1126

1123

Fig. 1. Crystal structures of zinc-blende CuI: (a) perfect crystal, (b) tetrahedral interstitials and (c) octahedral interstitials. [Cu: blue, I: red, dopant: green]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

initio simulation package (VASP) [14–15]. The generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) is adopted for the exchange-correlation potential [16]. The zinc-blende structure of CuI is illustrated in Fig. 1(a) for which the calculated lattice parameter is 6.07 Å. The calculated lattice parameter is in excellent agreement with the experimental value of 6.05 Å [17]. The calculated cohesive energy of the bulk CuI is −5.56 eV as compared to the experimental value of −5.32 eV [18–20]. For calculations of the formation energy, we consider the (3  3  3) supercell containing 54 atoms. The presence of a uniform background charge is assumed to compensate the presence of the charged dopants in the lattice. The Brillouin-zone integrations are performed with the 4  4  4 k-point mesh. The shape of the supercell and positions of all atoms are relaxed until the residual force on each atom is less than 0.01 eV/Å. Note that a choice of a larger unit cell (i.e. 4  4  4) consisting of 128 atoms does not modify the predicted order of stability of dopants in CuI; though it leads to lowering of the formation energy of the neutral ZnCu by about 0.07 eV and that of the charged AlCu2 þ by 0.18 eV. Negligible changes in the lattice distortion for the larger unit cell are seen. Furthermore a larger unit cell does not modify density of states relative to that obtained using the (3  3  3) unit cell. We therefore believe that the (3  3  3) unit cell considered is satisfactory in predicting the stability and electronic properties of dopants in CuI. The formation energy ΔHf(D,q) of a defect in the charge state q depends on both the Fermi level and chemical potentials of species related to the defect and can be given as [21]: ΔH f ðD, qÞ ¼ ΔEðD, qÞ þ ∑ni μi þ qðEF þ EVBM Þ

ð1Þ

ΔE(D,q) is the difference between the total energy of the supercell containing a point-defect D in the charge state q and that of the supercell representing the perfect lattice. ni and μi are the number of atoms removed from the supercell and chemical potentials of the constituent, i. EVBM and EF are the valenceband maximum (VBM) and Fermi level referenced to VBM. EF then ranges from VBM to the conduction-band minimum of the band structure. The so-called p-type (n-type) condition is then represented by the values of EF that are close to the top of the valence band (the bottom of the conduction band). It is well known that the GGA-DFT level of theory underestimates the band gap of any given materials. We therefore use the so-called the scissor approximation to shift the minimum of the conduction band to match the experimental value of the band gap of 3.1 eV [22].

The defect transition energy level ε(q/q′) is defined as the Fermi level where the formation energy of defect D in charge state q is equal to charge state q′, i.e. εðq=q′Þ ¼ ½ΔH f ðD, q, EF ¼ 0Þ−ΔH f ðD, q′, EF ¼ 0Þ=ðq−q′Þ:

ð2Þ

The chemical potentials of Cu and I in CuI are restricted by following conditions μCu þ μI ¼ EðCuIÞ

ð3Þ

μCu ≤EðCuÞ

ð4Þ

μI ≤EðIÞ

ð5Þ

where E(Cu), E(I) and E(CuI) and are the total energy of bulk Cu, I and CuI. In the Cu-rich limit, μCu ¼ EðCuÞ

ð6Þ

μI ¼ EðCuIÞ−EðCuÞ

ð7Þ

In the I-rich limit μI ¼ EðIÞ

ð8Þ

μCu ¼ EðCuIÞ−EðIÞ

ð9Þ

The chemical potentials of Zn Ga and Al atoms are restricted by the analogous conditions as Eq. (3). μZn þ 2μI ¼ EðZnI2 Þ

ð10Þ

μGa þ 3μI ¼ EðGaI3 Þ

ð11Þ

μAl þ 3μI ¼ EðAlI3 Þ

ð12Þ

Note that the chemical potentials of dopants are determined from the bulk values of the respective iodides.

3. Results and discussion We begin with the calculated values of the formation energies of intrinsic point defects in the host lattice to benchmark our modeling elements used in the study. A comparison of our results with a recent study of Wang et al. [11] employing the GGA-DFT level of theory with the PBE0 exchange and correlation functional shows an excellent agreement in predicting the nature of dominant intrinsic defects in CuI. In the limits of Cu-rich and I-rich growth conditions, the neutral copper vacancy (VCu) has the

J. Zhu et al. / Journal of Physics and Chemistry of Solids 74 (2013) 1122–1126

Table 1 Cation dopants in CuI: local distortions for q¼ 0 and transition levels. (RCu−I is 2.63 Å and negative ΔR represents the inward relaxation of near-neighbors in the lattice.). Cation dopants

Change in near-neighbor distance, Transition levels ε( þ/0) % (ΔR) (eV)

Substitutional ZnCu GaCu AlCu

≈8 ≈14 ≈15

Interstitial Zntet Gatet Altet Znoct Gaoct Aloct

≈13 ≈14 ≈16 ≈−2 ≈−2 ≈1

1.22 0.47

1.52 1.43 0.58 1.53 1.51

4.5 4.0

Formation energy (eV)

formation energies of −0.44 and −0.83 eV, respectively predicting the dominance of VCu in the host. Our predictions are consistent with the fact that Cu þ ions are carriers in the fast-ion conducting CuI suggesting the easier formation of copper vacancies in the lattice [23]. Furthermore, VCu in other Cu-containing compounds such as CuO and Cu2O is predicted to have the lowest formation energy in the lattice [21,24,25]. The near-neighbor distance (RCu-I) is 2.63 Å in the perfect CuI. The local distortion to the lattice induced by VCu is small. The near-neighbor ions only tend to move towards the vacancy site with R≈2% of RCu−I, where R is the change in near-neighbor distance. We now consider the cation dopants in CuI which can occupy either a substitutional site replacing Cu or tetrahedral and octahedral interstitial sites in the host lattice. The interstitial sites in the host are showed in Fig. 1. Four I atoms are nearest-neighbors to a tetrahedral interstitial dopant, whereas four nearest-neighbors of an octahedral interstitial dopant are Cu atoms. Table 1 gives the values of the local distortions to the lattice together with the thermodynamic transition levels of the defects. The local distortions to the lattice induced by the dopants seem to follow the trend in their ionic radii and effective charges. For ZnCu, nearestneighbors I atoms move away with R of 7.7% of the bond length. On the other hand, the local distortions are large (R 4 10%) for trivalent Al and Ga since their effective charge is −2 in the lattice. The tetrahedral interstitial dopants induce significantly large outward distortions in the lattice since their nearneighbors are iodine atoms. This is not the case with octahedral interstitial dopants as their near-neighbors are Cu atoms that appear to relax towards the dopants. Fig. 2 shows the variation of dopant formation energies in different charge states in both Cu-rich and I-rich growth conditions. Here, the charge state of a dopant is represented by the slope of the segment and the kink gives the value of the transition level between different charge states of the dopant. Note that increase of formation energy with EF suggests dopants to be donors in the lattice. Under the I-rich conditions, the substitutional Zn has the lowest formation energy with a transition level of about 1.2 eV. Under the Cu-rich conditions, ZnCu is more preferred but GaCu dominates when the Fermi level is above 1 eV. On the other hand, there exists no crossing of the formation energies for [GaCu]0, [GaCu] þ 1 and [GaCu] þ 2, suggesting the higher charge state of Ga is not preferred in CuI. Also, the formation energy of AlCu is the highest in both Cu-rich and I-rich conditions, due to a large difference in the electronic configurations between Al3 þ and Cu þ . Furthermore, the electronegativity values of Ga and Al are 1.81 and 1.61, respectively as compared to that of Cu of 1.90. For the case of the interstitial dopants, the octahedral site is generally preferred over the tetrahedral site (Fig. 3). This is

2+/+/0

AlCu

2+/+/0

3.5

AlCu

3.0 0

GaCu

2.5 2.0

0

GaCu

1.5

+/0

ZnCu +/0

ZnCu

1.0 0.5 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.5

Fermi energy (eV)

1.0

1.5

2.0

2.5

3.0

Fermi energy (eV)

Fig. 2. Formation energies of ZnCu, GaCu and AlCu as a function of Fermi energy under (a) Cu-rich limit and (b) I-rich limit. The zero value of EF is taken to be the top of the valence band. The superscript and slope of the segment represent the charge states of defects.

7 +/0

+/0

6

Formation energy (eV)

1124

Ali(oct)

Ali(tet)

+/0

Ali(tet)

+/0

5

Gai(tet)

+/0

+/0 Gai(oct)

Ali(oct) +/0

Gai(tet)

4

+/0

Zni(tet)

+/0

Zni(tet) +2/+/0

3

Zni(oct) +2/+/0

+/0

2

Gai(oct) 0.0

0.5

1.0

Zni(oct)

1.5

2.0

2.5

Fermi energy (eV)

3.0

0.5

1.0

1.5

2.0

2.5

3.0

Fermi energy (eV)

Fig. 3. Formation energies of interstitials of Zn, Ga and Al as a function of Fermi level under (a) Cu-rich limit and (b) I-rich limit. The zero value of EF is taken to be the top of the valence band. The superscript and slope of the segment represent the charge states of defects.

consistent with the fact that the octahedral interstitial dopants induce a smaller degree of relaxation of the surrounding host atoms. We also note that most of the ε(þ/0) transition levels associated with the interstitial dopants is in the middle of the band gap of CuI. All of the considered dopants cannot act as hole killers due to their high formation energies or deep donor levels. Overall, the solubility of dopants shows a descending trend from Zn to Ga and Al, which accords with a trend of the difference in their electronic configurations from the host Cu instead of the trend of their ionic radii. Considering that dopants associated with low formation energies are easier to incorporate in the lattice, the substitutional Zn can be expected to increase copper vacancies in CuI. Fig. 4 shows the formation energies as a function of Fermi level for some defect-complexes including [ZnCu þ VCu]. It also includes the results of the isolated VCu. Based on the formation energies, the dominant defect-complex appears to be [ZnCu þ VCu]. The formation energies of complexes in the p-type condition under the Cu-rich limit are lowered by 0.6∼0.9 eV as compared to the corresponding isolated dopants. Note that the Cu-rich conditions are prevalent during the crystal growth of CuI due to the addition of copper sheets as

J. Zhu et al. / Journal of Physics and Chemistry of Solids 74 (2013) 1122–1126

0/-

Formation energy (eV)

2

Gai-VCu

+/0/Zni-VCu

0/-

Gai-VCu

1

+/0/-

Zni-VCu

0/ZnCu-VCu

0

0/-

ZnCu-VCu

-1 -2

0/-

VCu

0/-

VCu

-3 -4 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.5

Fermi energy (eV)

1.0

1.5

2.0

2.5

3.0

additional electronic states associated with dopants as shown in Fig. 5. For example, the Zn states appear in the band gap located at about 1.2 eV above the VBM in ZnCu-doped CuI. On the other hand, the states induced by Al appear at about 0.4 eV above the VBM in AlCu-doped CuI. No additional states are found in the band gap for GaCu-doped CuI as the Ga states are located inside the valence band (Fig. 5). Considering that the calculated band gap of CuI is 1.13 eV at the GGA-DFT level of theory, the donor levels introduced by ZnCu are located at about 0.13 below the bottom of the conduction band. On the other hand, the experimental value of the band gap of CuI is 3.1 eV [18–20], and the 420 nm ultrafast emission corresponds to 2.95 eV. Thus, the intrinsic donor level is estimated to be about 0.15 eV below the bottom of the conduction band. Our results therefore suggest that the dopant levels introduce by Zn may not be able to trap electrons during the emission process, thereby not affecting the scintillator performance.

Fermi energy (eV)

Fig. 4. Formation energies of [ZnCu þVCu], [Zni(oct) þ VCu] and [Gai(oct) þ VCu] as a function of Fermi level under (a) Cu-rich limit and (b) I-rich limit. The zero value of EF is taken to be the top of the valence band. The superscript and slope of the segment represent the charge states of defects.

60 Perfect

40 20 0

Density of state (arb. units)

1125

ZnCu

40 20 0

4. Summary First-principles calculations based on density functional theory are used to investigate structural and electronic properties of Zn, Ga and Al in CuI. The difference in electronic configurations between the host and dopants appears to be more important than the ionic radii in predicting the solubility of dopants in the lattice. A relatively low formation energy of the substitutional ZnCu followed by the octahedral interstitials Znoct and Gaoct in CuI is predicted. Altet has the highest formation energy among the considered defects. Altet and Gatet induce a relatively large distortion to the lattice. The [ZnCu þVCu] complex has the lowest formation energy among the defect complexes considered. The results suggest that an effective way to increase copper vacancy consists of the doping of CuI with Zn.

GaCu

40

Acknowledgments

20

This work is supported by the National Natural Science Foundation of China (Grant nos. 10875085, 91022002 and 2011YQ13001902) and the Innovation Program of Shanghai Municipal Education Commission (Grant no. 11ZZ29). Jiajie Zhu acknowledges the financial support from Department of Physics, Michigan Technological University during his visit.

0 AlCu

40 20 0 -6

-4

-2

0

2

4

Energy (eV) Fig. 5. Total density of states of the perfect CuI, ZnCu, GaCu and AlCu. Zero is taken to be top of the valence band of CuI.

a reducing agent [26]. The transition level of [ZnCu þVCu] is about 1.2 eV above VBM in CuI. Furthermore, the binding energy of [ZnCu þVCu] is about 0.30 eV and the local distortion in the lattice due to the defect complex is very small. Therefore, it can be predicted that doping of Zn may be an effective way to create copper vacancies in CuI. The total density of states (DOS) of the perfect CuI, ZnCu, GaCu and AlCu– doped CuI are illustrated in Fig. 5. For the perfect CuI, the valence band is mainly composed of three components: (i) the band at about −14 eV due to I-5s states (not shown here), (ii) the band from −3.5 eV to −5.5 eV due to Cu-4s, Cu-3d and I-5p states indicating a formation of Cu-I bond, and (iii) the sharp band near the VBM associated with Cu-3d states. The bottom of the conduction band is mainly composed of Cu-4s states. The details of DOS obtained from GGA(PBE)–DFT calculations are in agreement with those calculated using the FP-LAPW method [27]. The total density of states of CuI containing Zn, Ga and Al dopants are analogous to that of the perfect CuI, except some

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