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Defect Formation in Carbon-doped Cuprous Iodide

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Hui Chen, Mu Gu*, Xiaolin Liu, Xuejun Guo, Bo Liu, Shiming Huang, Chen Ni

Shanghai Key Laboratory of Special Artificial Microstructure Materials & Technology, School of

Physics Science and Engineering, Tongji University, Shanghai 200092, P.R. China

Guoying Zhang

College of Science, China University of Mining and Technology, Xuzhou 221116, PR China

First-principles calculations have been performed to investigate the carbon-doped cuprous iodide. From the calculated results, carbon substituted for iodine (CI) is found to be an acceptor and substituted for copper (CCu) is found to be a donor. The formation energy of CCu is higher than that of CI, indicating a preference of carbon to be an acceptor for substitutional in CuI. Interstitial carbon (Ci) located at the octahedral site has the lower formation energy as compared to that located at the tetrahedral site. Three possible nearest-neighbor carbon complexes are discussed in detail, respectively. The Ci-CCu complex is unlikely to form due to the highest formation energy and the Ci-CI complex is energetically favorable and easy to form in carbon doped CuI under p-type conditions. However, all of the considered defects are not contributed to increase the p-type conductivity of CuI due to their high formation energies or deep levels.

  1. Introduction

In recent years, cuprous iodide (CuI) has received intense attention due to its unique features such as large band gap (3.1 eV), negative spin orbit splitting, electrosensitivity and photosensitivity [1-4]. At ambient conditions, CuI exists in the zinc-blend phase (γ-CuI), and is known as a p-type semiconductor with fast ion conductivity (0.1 Sïƒ-cm-1), large exciton binding energy (62 meV) and ultrafast scintillation property which decay time is about 90 ps [5-9]. The γ-CuI has a potential application in light emitting diode, field emission display, organic catalyst, and solid-state dye-sensitized solar cell as a hole conductor and so on [10–12].

The conductivity of undoped γ-CuI depends on the presence of iodine in stoichiometric excess due to the prevalence acceptor defects, specifically copper vacancies VCu [13]. In order to modify the intrinsic defects, doping control technologies are widely used [14-15]. Doping with anions or cations can affect intrinsic defects or induce new defect states which may contribute to n-type or p-type conductivity or form deep levels [16].

Carbon-doping has been widely used in other wide bandgap semiconductors, such as AlN, GaN, GaAs and ZnO. For example, Boguslawski et al. reported that carbon substitution for nitrogen is an effective acceptor and preferred in both GaN and AlN [17-18]. Carbon substituted for arsenic is found to be a very well behaved acceptor dopant in GaAs both experimentally and theoretically [19-21]. Tan et al. studied the effect of CZn-Oi defect in ZnO, and p-type ZnO films were obtained [22].

However, to the best of our knowledge, until now no investigation of carbon-doped CuI has been reported. Therefore, it is necessary to perform precise calculation of the formation energy for the carbon-doped CuI. In this paper, we investigate the behavior of carbon-doped CuI. In Section 2, we describe the computational details. In Section 3, we discuss the calculated results. Finally, we give a brief conclusion in Section 4.

  1. Computational details

The research has been performed by the density functional theory (DFT) calculation within the generalized gradient approximation (GGA) in the VASP code [23-24]. The Perdew-Burke-Ernzerhof gradient-corrected functional type pseudopotentials for Cu 3d104s1, I 5s25p5 and C 2s22p2 are used [25]. The electronic wave-functions are expanded in plane waves up to with the energy cut-off of 355 eV, and it is confirmed that the total energy is converged within 1×10-6 eV/atom. The zinc-blende structure of CuI is illustrated in Fig.1 (a) for the geometry optimization. The optimized lattice constant of a = 6.07 Å is in excellent agreement with the experimental value a = 6.05 Å [26]. In order to perform the defect-related calculation, it is necessary to use a supercell with a size large enough to avoid the interaction among the defects. After performing a convergence test, a 54-atom supercell with 3×3×3 unit cell is used in the defect calculations. Carbon interstitial (Ci) at the octahedral and tetrahedral sites [shown in Fig.1 (b) and (c)] and substitution for copper (CCu) and iodine (CI) are considered in the supercell calculations. All the atoms in the supercell are allowed to relax until the maximum residual force is less than 0.01 eV/Å.

C:\Users\Think\Desktop\CuI_C\CuI_C.jpg

Fig.1. Crystal structures of zinc-blende CuI: (a) perfect crystal, (b) tetrahedral interstitials and (c) octahedral interstitials. [Cu: red, I: blue, C: black].

The formation energy of carbon with the charge state q in CuI can be given as [17]

(1)

where Etot is the total energy of the defect supercell, nCu, nI and nC are the numbers of Cu, I and C atoms in the supercell, μ is the corresponding chemical potential, EVBM is the energy of the valence-band maximum in bulk CuI and V is the electrostatic alignment between the doped host and the pure host according to the electrostatic potential of I atom in the core region (for the doped system, the I atom is chosen with the furthest one away from the defect in the supercell). The Fermi level is defined to be zero at the valence-band maximum (VBM) and have a maximum value of 3.1 eV at the conduction-band minimum (CBM) [27]. μC is chosen as the calculated energy per atom of graphite. μCu is obtained from a calculation for face-centered cubic Cu metal, and μI from the requirement that μCu+μI equals the energy per Cu–I pair in bulk zinc-blend CuI. These choices for μCu and μI define Cu-rich conditions, reflecting the growth of CuI in the presence of Cu metal. The alternative condition considered herein is I rich where CuI is assumed to be in equilibrium with I2 gas during growth. These two conditions represent limits for CuI growth conditions.

  1. Results and discussion

We start by considering a single C impurity substituting for iodine (denoted by CI), or substituting for copper (denoted by CCu), or at the interstitial site (the octahedral and tetrahedral interstitial sites are denoted by Ci-oct and Ci-tet, respectively). A substitutional impurity in the CuI crystal with zinc-blend symmetry has four nearest neighbors. The bond lengths for C to the nearest-neighbor and formation energies in different charge states in both Cu-rich and I-rich conditions for CI and CCu are listed in Table 1, and a plot of formation energy versus Fermi level in different charge states is shown in Fig.2. Only the charge state with the lowest formation energy at particular Fermi level is shown, the charge state of dopant is represented by the slope of the segment and the kink gives the value of the transition level between different charge states of dopants. In Fig.2, CI is energetically favorable while CCu is difficult to form under the Cu-rich conditions. It is observed that the C impurity can exist in several charge states at each site. These states correspond to different occupations of the carbon 2p shell physically. We note that the C impurity at the iodine site leads to large displacements of the neighboring atoms. In the neutral charge state (), the four neighbors copper atoms are closer to the carbon and the Cu-C bond is 28.5% shorter than the corresponding bulk Cu-I bond 2.63 Å. For , and , the Cu-C bonds reduce by 28.9%, 29.3% and 29.7%, respectively, suggesting that the additional electron localizes on the C atom and attracts the positively charged Cu atoms over a wide range of EF values. Under the Cu-rich conditions, the formation energies of CI and CCu are 4.05eV and 6.35 eV when the Fermi level is 0 eV, respectively. Under the I-rich conditions, the formation energy of CI increases by 0.34 eV and the formation energy of CCu decreases by the same amount. CI is seemed to be favored over CCu for all Fermi levels in both Cu-rich and I-rich conditions. Thus, carbon is preferentially incorporated at the iodine site in CuI and acts as an acceptor. The +/0 transition energy for CCu is 0.77 eV, whereas the transition energies of 0/- , -/-2 and -2/-3 for CI are 0.45, 1.22 and 2.03 eV, respectively. The high ionization energy of CI indicates that C is not a desirable acceptor to increase the p-type conductivity of CuI.

Table 1

Bond lengths for C to the nearest-neighbor and formation energies (eV) Ef for CI and CCu as a function of EF in various charge states, where EF is defined to be zero at the VBM.

Species

Charge state

dC-neighbor(Å)

Ef (Cu-rich)

Ef (I-rich)

CI

0

1.88

4.05

4.39

-1

1.87

4.50-EF

4.84-EF

-2

1.86

5.72-2EF

6.06-2EF

-3

1.85

7.75-3EF

8.09-3EF

         

CCu

+3

2.47

6.26+3EF

5.93+3EF

+2

2.49

5.78+2EF

5.44+2EF

+1

2.52

5.57+EF

5.24+EF

0

2.64

6.35

6.01

Fig.2. Formation energies for CCu and CI as a function of the Fermi level under Cu-rich and I-rich limits. For each defect species, only the lowest-energy charge states with respect to EF are shown. The zero energy 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.

Table 2

Bond lengths for C to the nearest-neighbor and formation energies (eV) Ef for Ci as a function of EF in various charge states, where EF is defined to be zero at the VBM.

Species

Charge state

dC-neighbor (Å)

Ef (Cu-rich)

Ef (I-rich)

Ci-oct

+4

1.99

6.18+4EF

6.18+4EF

+3

1.98

5.48+3EF

5.48+3EF

+2

1.96

5.01+2EF

5.01+2EF

+1

1.94

4.72+EF

4.72+EF

0

1.92

5.01

5.01

         

Ci-tet

+4

3.16

7.99+4EF

7.99+4EF

+3

3.18

7.12+3EF

7.12+3EF

+2

3.21

6.39+2EF

6.39+2EF

+1

3.24

5.97+EF

5.97+EF

0

3.27

5.77

5.77

Fig.3. Formation energies for interstitials of C as a function of the Fermi level under Cu-rich and I-rich limits. For each defect species, only the lowest-energy charge states with respect to EF are shown. The zero energy 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.

For the case of the interstitial carbon, the formation energies of the octahedral and tetrahedral interstitial sites are shown in Fig.3. Four I atoms are nearest neighbors to a tetrahedral interstitial carbon, whereas four nearest neighbors of an octahedral interstitial carbon are Cu atoms. Table 2 gives the bond lengths for C to the nearest-neighbor and formation energies in different charge states of Ci in both Cu-rich and I-rich growth conditions. For the nearest neighbors, the four Cu atoms move to the octahedral interstitial carbon while the four I atoms are pulled away from the tetrahedral interstitial carbon. Interstitial carbon (Ci) located at the octahedral site has the lower formation energy as compared to that located at the tetrahedral site as shown in Fig.3. There no crossing of the formation energies for,,, and , suggesting the higher charge state of carbon interstitial at the tetrahedral site is not preferred in CuI. The carbon interstitial at the octahedral site is preferred in the +1 and 0 charge states, yields a +1/0 transition at 0.29 eV. Thus, interstitial carbon at the octahedral site is generally preferred and it should be the dominant compensating donor.

Fig.4. Relaxed structures for (a) CI-CCu, (b) Ci-oct-CCu and (c) Ci-oct-CI. [Cu: red, I: blue, C: black].

Generally speaking, pairs of impurities at neighboring sites are sometimes more stable than two distant single impurities [28]. In this case, three possible nearest-neighbor carbon complexes (CI-CCu, Ci-oct-CCu and Ci-oct-CI) are discussed. The relaxed structures for these complexes are shown in Fig.4, the bond lengths for the C-C and C to the nearest-neighbor and formation energies in different charge states are listed in Table 3, and a plot of formation energy versus Fermi level in different charge states is shown in Fig.5. The calculated C-C bond lengths in these three complexes are about 1.3 Å, which is in good agreement with the value of 1.4 Å in graphite [29]. Based on the calculated formation energies, the formation energy of the complexes is predicted to be Ef(Ci-oct-CCu) > Ef(CI-CCu) > Ef(Ci-oct-CI) under p-type conditions. The Ci-CCu complex has the highest formation energy among the considered defects, indicating that this complex is energetically unfavorable. The transition energies of 0/- , -/-2 and -2/-3 for CI-CCu are 0.14, 0.38 and 2.32 eV, respectively. The CI-CCu complex is suggested as a candidate based on its transition energies. However, it is noted that this complex is unlikely to form in p-type conditions due to the high formation energy. Under p-type conditions, the formation energy of Ci-CI complex is lowed by 0.65 eV as compared to CI under the Cu-rich conditions. It indicates that the Ci-CI complex is energetically favorable in carbon doped CuI under p-type conditions. The Ci-CI complex is preferred in the -1,-2 and -3 charge states. The transition energiesof -/-2 and -2/-3 are 2.01 and 2.52 eV, respectively. The transition energies of the Ci-CI complex in the band gap are rather deep so that they cannot play a role of acceptor.

Table 3

C-C and C to the nearest-neighbor bond lengths and formation energies (eV) Ef for complexes as a function of EF in various charge states, where EF is defined to be zero at the VBM.

Species

Charge state

dC-C(Å)

dC-neighbor (Å)

Ef (Cu-rich)

Ef (I-rich)

CI-CCu

+3

1.31

1.95

5.83+3EF

5.83+3EF

+2

1.31

1.96

5.26+2EF

5.26+2EF

+1

1.31

1.96

4.85+EF

4.85+EF

0

1.30

1.97

4.74

4.74

-1

1.30

1.97

4.88-EF

4.88-EF

-2

1.30

1.98

5.26-2EF

5.26-2EF

-3

1.31

1.98

7.58-3EF

7.58-3EF

           

Ci-CCu

+4

1.34

2.05

8.76+4EF

8.43+4EF

+3

1.32

2.04

7.90+3EF

7.57+3EF

+2

1.31

2.02

7.27+2EF

6.94+2EF

+1

1.30

2.00

6.87+EF

6.54+EF

0

1.29

1.99

6.73

6.40

           

Ci-CI

+4

1.29

1.90

5.75+4EF

6.08+4EF

+3

1.29

1.90

4.61+3EF

4.94+3EF

+2

1.29

1.91

4.13+2EF

4.46+2EF

+1

1.28

1.89

3.62+EF

3.95+EF

0

1.27

1.89

3.40

3.73

-1

1.27

1.90

3.40-EF

3.73-EF

-2

1.27

1.91

5.41-2EF

5.74-2EF

-3

1.27

1.93

7.93-3EF

8.26-3EF

Fig.5. Formation energies for complexes as a function of the Fermi level under Cu-rich and I-rich limit. For each defect species, only the lowest-energy charge states with respect to EF are shown. The zero energy 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.

  1. Summary

In summary, we have calculated the formation energies for carbon-doped CuI using first principles based on density functional theory. According to our calculations, carbon is found to be an acceptor when substituted for iodine (CI) and a donor when substituted for copper (CCu). The formation energy of CCu is higher than that of CI, indicatinga preference of carbon to be an acceptor for substitutional in CuI. Interstitial carbon (Ci) located at the octahedral sites is generally preferred as compared to at the tetrahedral site and it should be the dominant compensating donor. Three possible nearest-neighbor carbon complexes CI-CCu, Ci-oct-CCu and Ci-oct-CI are discussed in detail, respectively. Among the considered defects, the Ci-CCu complex is found to be unlikely to form due to the highest formation energy, the Ci-CI complex has the lowest formation energy under p-type conditions. It is suggested that the Ci-CI complex is energetically favorable in carbon doped CuI. However, the transition energies of the Ci-CI complex in the band gap are rather deep so that they cannot play a role of acceptor. Overall, all of the considered defects are not contributed to increase the p-type conductivity of CuI due to their high formation energies or deep levels.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant nos. 91022002, 11375129, 11305115 and 11179019), the Significant National Special Project of the Ministry of Science and Technology of China for Development of Scientific Instrument and Equipment (Grant No. 2011YQ13001902). We are grateful to the High Performance Computing Center of China University of Mining and Technology for the award of CPU hours to accomplish this work.

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