- Email: [email protected]
Defects in mercuric iodide: an APW investigation
ARTICLE IN PRESS
Physica B 340-342 (2003) 918–922
Defects in mercuric iodide: an APW investigation F. Ayresa,*, W.V.M. Machadoa, J.F. Justob, L.V.C. Assalia a b
Instituto de F!ısica, Universidade de Sao * Paulo, CP 66318, 05315-970 Sao * Paulo, Brazil Escola Polit!ecnica, Universidade de Sao * Paulo, CP 61548, 05424-970 Sao * Paulo, Brazil
Abstract We carried a theoretical investigation on the structural and electronic properties of mercuric iodide in the red tetragonal crystalline phase, and its respective intrinsic defects. The calculations were performed using the total energy spin-polarized augmented plane wave method and the generalized gradient approximation, considering full atomic relaxation. The results were compared to available experimental data. r 2003 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 61.72.Ji Keywords: Mercuric iodide; High-energy detectors; HgI2 ; APW+lo methods
1. Introduction Mercuric iodide (HgI2 ) is a semiconducting material with potential applications in high-energy (g- and X-ray) spectroscopy [1]. HgI2 carries a unique combination of properties lacking in silicon and germanium, which make it suitable for radiation detection at room temperature: a large band gap energy (2:13 eV at 300 K) and large photoelectric absorption cross-sections, which are determined by the large atomic numbers of both Hg (80) and I (53) atoms [2]. However, a number of problems, such as the mechanical stability and the control over defect concentrations during crystal growth, still precludes its widespread use [1,3]. Due to its layered bonding nature, the critical resolved shear stress is very small and the material is essentially brittle at room temperature [4]. *Corresponding author. E-mail address: [email protected] (F. Ayres).
Additionally, the material has low hole mobility, which would be essential for a proper detector operation. High concentrations of intrinsic and extrinsic defects, working as recombination centers, are believed to be responsible for such low mobility [3]. Therefore, there are at least two welldefined fronts to investigate mercuric iodide: fundamental issues, such as the electronic and optical properties, and the growth issues, such as defect and impurity effects. HgI2 in its red tetragonal phase is a layered material with two HgI2 molecules per unit cell. In this phase, it belongs to the D4h space group, ( and whose lattice parameters are a ¼ b ¼ 4:361 A ( c ¼ 12:450 A [1]. The HgI4 tetrahedra are stacked in layers, bounded by weak van der Waals interactions between adjacent iodine (I–I) planes, as shown in Fig. 1. In terms of the electronic properties, low-temperature photoluminescence (PL) studies have been used for characterization of intrinsic and extrinsic defects in HgI2 [5–7].
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.09.236
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
Fig. 1. Primitive cell of red HgI2 : The figure shows the lattice parameters a and c; and the internal parameters h and u: Dark and light gray balls represent the iodine and mercury atoms, respectively.
Several emission bands have been observed, which are likely correlated to excitons, vacancies, or residual impurities (such as copper, silver, indium, tin, palladium, and carbon). However, there is still considerable controversy about the nature of such PL lines. While some authors associated PL lines to iodine vacancies [5,6], others associated the same lines to mercury vacancies [7].
2. Theoretical model While there has been considerable experimental work on mercuric iodide over the last few decades, theoretical investigations have not been so prolific. They have been limited to ab initio [8–10], and semi-empirical [11] investigations on the electronic and optical properties of bulk HgI2 using the experimental structural parameters. Here, on the other hand, we carried the first ab initio investigation on HgI2 taking into account full atomic relaxation and geometry optimization. The calculations were carried using the all electron augmented plane waves plus local orbitals (APW+lo) method [12], implemented into the WIEN2k package [13]. Previous ab initio investigations [8– 10] treated the exchange–correlation potential using the density functional theory [14,15] in the local density approximation (LDA) [16,17]. Considering the bonding nature of HgI2 ; here we treated the exchange–correlation potential with the generalized gradient approximation (GGA)
919
potential [18]. It is well established in the literature that the LDA calculations fail in treating the van der Waals interactions [19], underestimating the intraplanar lattice parameter and overestimating the interplanar lattice parameter. Although LDA fails in describing weak interactions, the previous ab initio investigations [8–10] presented a good description of the electronic band structure of HgI2 ; since those properties are mostly determined by the predominantly covalent Hg–I bonds, which are reasonably well described by LDA. However, for other properties of HgI2 which involve atomic relaxation, the GGA approximation becomes important. In order to perform the calculations, the maximum length of the plane waves was chosen 6:5=R; where R is the smallest radius of atomic spheres (RHg ¼ RI ¼ 2:5 a:u:). The Brillouin zone (BZ) was sampled by 64 k-points, which were reduced to a set of 6 k-points in the irreducible BZ (IBZ) [20]. Self-consistent interactions were performed with the following convergence criteria: on total energy (105 Ry per unit cell), total charge in each atomic sphere (105 electronic charges per atom), and forces (101 mRy=a:u:). The properties of defects in HgI2 were computed by a 54-atom reference supercell, which was built by taking 3a 3a c: In that case, the IBZ integration was performed at the ð1=4; 1=4; 1=4Þ in a 2 2 2 mesh [20]. The formation energies of Hg and I vacancy defects were obtained by [21] Ef ðVHg Þ ¼ Etot ðHgI2 : VHg Þ E54 ðHgI2 Þ þ mHg ; ð1Þ Ef ðVI Þ ¼ Etot ðHgI2 : VI Þ E54 ðHgI2 Þ þ mI ;
ð2Þ
mHg þ ð1 gÞDf H HgI2 ; mI ¼ mI þ mHgI2 ¼ mHg þ 2mI : The first term in Eqs. (1) and (2) is the total energy of the supercell calculations with the Hg and I vacancies, respectively, and the second term is the total energy of 54-atom reference supercell. For g ¼ 0; the environment is I-rich and Ef ðVHg Þ is minimum, and for g ¼ 1 it is Hg-rich and Ef ðVI Þ is minimum.
where mHg ¼ 1 HgI2 ; and 2gDf H
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
3. Bulk properties and van der Waals interactions In order to get all the lattice and internal parameters of the red HgI2 crystal, we performed total energy minimization with full geometry optimization on all degrees of freedom. These ( and calculations led to the values of: a ¼ 4:62 A ( c ¼ 12:66 A; the I–I plane distance being h ¼ 0:231c; the I–Hg planes distance u ¼ 0:125c; and the bulk modulus B ¼ 0:22 Mbar: A comparison of our results with available experimental data is presented in Table 1. These parameters were obtained by fitting the Murnaghan equation of state over the data. The cohesive energy of HgI2 was calculated by the difference between the total energy of crystalline system and the sum of energies of all free atoms. We found Ecoh ¼ 3:17 eV per HgI2 molecule, which is consistent with the energies of typical semiconducting materials. In terms of the electronic band structure, we find a direct band gap of 1:11 eV or 0:84 eV when the spin–orbit coupling is included, which are smaller than the experimental value of 2:13 eV at 300 K [1]. Our results should be compared to values coming from other theoretical investigations: 0:52 eV [8], 1:1 eV [9], and 0:95 eV [10]. One of the major problems with HgI2 is its mechanical stability at room temperature, which is a result of the weak bonding between adjacent iodine planes. Plastic deformation flow is controlled by the formation and propagation of dislocations [23]. In mercuric iodide, deformation by easy glide occurs mostly by the formation and motion of dislocations lying between adjacent iodine layers [24]. Therefore, understanding the interactions between these iodine planes is important in terms of the mechanical stability of the material. In order to describe the interaction between these iodine planes, we varied the distance
between iodine without relaxing the iodine atoms with relation to their mercury neighbors. The total energy variation as a function of the distance between adjacent iodine layers is shown in Fig. 2. The results were fitted to a Buckingham equation [25], since a fitting based on a pure Lennard-Jones function was not possible. ( A e 6 r exp a 1 fI2I ðrÞ ¼ B þ r 1 6a a Req 6 ) Req r
ð3Þ
( For the HgI2 crystal, we obtained Req ¼ 3:46 A and a binding energy Eb ¼ 0:12 eV per surface atom (2:65 kcal=mol). This binding energy is comparable to the typical London dispersion energy of 2 kcal=mol [25].
1 calculated data fitting curve
0.8 0.6
Energy (eV)
920
0.4 0.2 0 -0.2 0
2
4
6
8
distance (Å)
Fig. 2. Total energy versus I–I bond distance in HgI2 crystal describing the van der Waals interactions. Energy and distances are given in eV and Angstroms, respectively.
Table 1 Theoretical and experimental values of lattice parameters a and c; internal parameters u and h; bulk modulus, and band gap ðEgap Þ
This work Expt. [1]
( a ðAÞ
( c ðAÞ
u
h
B (Mbar)
Egap (eV)
4.619 4.361
12.660 12.450
0:135c 0:139c
0:231c 0:222c
0.22 0.44 [22]
1.11 2.13 ð300 KÞ
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
921
mobility in the material. On the other hand, our results show that mercury vacancy is a good candidate to increase the hole mobility.
5. Summary
Fig. 3. Contour plot of the total electronic density in the ½1 1 0 plane for (a) mercury vacancy; (b) perfect crystal; and (c) iodine ( 3: vacancy. The line separation is 0:05 e=A
4. Intrinsic defects Photoluminescence experiments have been used to investigate the properties of defects in HgI2 : However, there is considerable controversy about the nature of those PL lines [5–7]. Here, we computed the electronic and structural properties of mercury and iodine vacancies. In terms of relaxation, both vacancies cause negligible disturbance in the nearby neighboring atoms. This can be observed in Fig. 3, which shows the electronic charge density in an ½1 1 0 plane of the mercury and iodine vacancies. Iodine vacancy introduces a partially occupied energy level in the gap, near the conduction band bottom, with spin S ¼ 12: On the other hand, the mercury vacancy introduces a double-degenerated shallow energy level in the gap, near the top of the valence band, with spin S ¼ 1: We also computed the defect formation energies. For I-rich environment, we find Ef ðVI Þ ¼ 1:70 eV and Ef ðVHg Þ ¼ 1:96 eV: For Hg-rich environment, we find Ef ðVI Þ ¼ 1:16 eV and Ef ðVHg Þ ¼ 3:05 eV: Therefore, concentration of iodine vacancies in HgI2 should be considerably higher than the one of mercury vacancies in both I- or Hg-rich environments. These results indicate that the iodine vacancy is the primer candidate to explain the low hole
In summary, we carried the first ab initio investigation, which takes into account full atomic relaxation, on the properties of mercuric iodide. We quantified the binding energy between adjacent iodine planes, showing that such binding is a typical van der Waals interaction. Additionally, we found that both mercury and iodine vacancies cause negligible distortions in their respective neighbors, and both introduce partially occupied energy gap levels, which could be observed by electron paramagnetic resonance experiments. Based on the position of the defect levels, we find that iodine vacancy should be the one responsible by the low hole mobility in the material, which is consistent with Refs. [5,6].
Acknowledgements The authors acknowledge support from FAPESP and CNPq. The calculations were performed at the LCCA-CCE of the Universidade de S*ao Paulo.
References [1] M. Piechotka, Mater. Sci. Eng. R18 (1997) 1. [2] G.F. Knoll, Radiation Detection and Measurement, Wiley, New York, 2000. [3] X.J. Bao, T.E. Schlesinger, R.B. James, R.H. Stulen, C. Ortale, A.Y. Cheng, J. Appl. Phys. 68 (1990) 86. [4] J. Marschall, F. Milstein, Appl. Phys. Lett. 62 (1993) 2784. [5] X.J. Bao, T.E. Schlesinger, R.B. James, S.J. Harvey, A.Y. Cheng, V. Gerrish, C. Ortale, Nucl. Instrum. Methods Phys. Res. A 317 (1992) 194. [6] R.B. James, X.J. Bao, T.E. Schlesinger, A.Y. Cheng, C. Ortale, L. van den Berg, Nucl. Instrum. Methods Phys. Res. A 322 (1992) 435. [7] I.Kh. Akopyan, B.V. Bondarenko, O.N. Volkova, B.V. Novikov, T.A. Pavlova, Phys. Solid State 39 (1997) 58. [8] D.E. Turner, B.N. Harmon, Phys. Rev. B 40 (1989) 10516.
ARTICLE IN PRESS 922
F. Ayres et al. / Physica B 340-342 (2003) 918–922
[9] R. Ahuja, O. Eriksson, B. Johansson, S. Auluck, J.M. Wills, Phys. Rev. B 54 (1996) 10419. [10] A.K. Solanki, A. Kashyap, T. Nautiyal, S. Auluck, M.A. Khan, Phys. Rev. B 55 (1997) 9215. [11] Y.C. Chang, R.B. James, Phys. Rev. B 46 (1992) 15040. . . [12] E. Sjostedt, L. Nordstrom, D.J. Singh, Solid State Commun. 114 (2000) 15. [13] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn. Universit.at Wien, Austria, 2001. [14] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [15] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. [16] L. Hedin, B.I. Lundqvist, J. Phys. C 4 (1971) 2064.
[17] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [18] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [19] S. Tsuzuki, H.P. Luthi, . J. Chem. Phys. 114 (9) (2001) 3949. [20] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [21] K.O. Barbosa, W.V.M. Machado, L.V.C. Assali, Physica B 308–310 (2001) 726. [22] N. Kuroda, T. Iwabuchi, Y. Nishina, J. Phys. Soc. Japan 52 (1983) 2419. [23] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982. [24] G. Georgeson, F. Milstein, Nucl. Instrum. Methods Phys. Res. A 285 (1989) 488. [25] P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 1994.
Physica B 340-342 (2003) 918–922
Defects in mercuric iodide: an APW investigation F. Ayresa,*, W.V.M. Machadoa, J.F. Justob, L.V.C. Assalia a b
Instituto de F!ısica, Universidade de Sao * Paulo, CP 66318, 05315-970 Sao * Paulo, Brazil Escola Polit!ecnica, Universidade de Sao * Paulo, CP 61548, 05424-970 Sao * Paulo, Brazil
Abstract We carried a theoretical investigation on the structural and electronic properties of mercuric iodide in the red tetragonal crystalline phase, and its respective intrinsic defects. The calculations were performed using the total energy spin-polarized augmented plane wave method and the generalized gradient approximation, considering full atomic relaxation. The results were compared to available experimental data. r 2003 Elsevier B.V. All rights reserved. PACS: 61.50.Ah; 61.72.Ji Keywords: Mercuric iodide; High-energy detectors; HgI2 ; APW+lo methods
1. Introduction Mercuric iodide (HgI2 ) is a semiconducting material with potential applications in high-energy (g- and X-ray) spectroscopy [1]. HgI2 carries a unique combination of properties lacking in silicon and germanium, which make it suitable for radiation detection at room temperature: a large band gap energy (2:13 eV at 300 K) and large photoelectric absorption cross-sections, which are determined by the large atomic numbers of both Hg (80) and I (53) atoms [2]. However, a number of problems, such as the mechanical stability and the control over defect concentrations during crystal growth, still precludes its widespread use [1,3]. Due to its layered bonding nature, the critical resolved shear stress is very small and the material is essentially brittle at room temperature [4]. *Corresponding author. E-mail address: [email protected] (F. Ayres).
Additionally, the material has low hole mobility, which would be essential for a proper detector operation. High concentrations of intrinsic and extrinsic defects, working as recombination centers, are believed to be responsible for such low mobility [3]. Therefore, there are at least two welldefined fronts to investigate mercuric iodide: fundamental issues, such as the electronic and optical properties, and the growth issues, such as defect and impurity effects. HgI2 in its red tetragonal phase is a layered material with two HgI2 molecules per unit cell. In this phase, it belongs to the D4h space group, ( and whose lattice parameters are a ¼ b ¼ 4:361 A ( c ¼ 12:450 A [1]. The HgI4 tetrahedra are stacked in layers, bounded by weak van der Waals interactions between adjacent iodine (I–I) planes, as shown in Fig. 1. In terms of the electronic properties, low-temperature photoluminescence (PL) studies have been used for characterization of intrinsic and extrinsic defects in HgI2 [5–7].
0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.09.236
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
Fig. 1. Primitive cell of red HgI2 : The figure shows the lattice parameters a and c; and the internal parameters h and u: Dark and light gray balls represent the iodine and mercury atoms, respectively.
Several emission bands have been observed, which are likely correlated to excitons, vacancies, or residual impurities (such as copper, silver, indium, tin, palladium, and carbon). However, there is still considerable controversy about the nature of such PL lines. While some authors associated PL lines to iodine vacancies [5,6], others associated the same lines to mercury vacancies [7].
2. Theoretical model While there has been considerable experimental work on mercuric iodide over the last few decades, theoretical investigations have not been so prolific. They have been limited to ab initio [8–10], and semi-empirical [11] investigations on the electronic and optical properties of bulk HgI2 using the experimental structural parameters. Here, on the other hand, we carried the first ab initio investigation on HgI2 taking into account full atomic relaxation and geometry optimization. The calculations were carried using the all electron augmented plane waves plus local orbitals (APW+lo) method [12], implemented into the WIEN2k package [13]. Previous ab initio investigations [8– 10] treated the exchange–correlation potential using the density functional theory [14,15] in the local density approximation (LDA) [16,17]. Considering the bonding nature of HgI2 ; here we treated the exchange–correlation potential with the generalized gradient approximation (GGA)
919
potential [18]. It is well established in the literature that the LDA calculations fail in treating the van der Waals interactions [19], underestimating the intraplanar lattice parameter and overestimating the interplanar lattice parameter. Although LDA fails in describing weak interactions, the previous ab initio investigations [8–10] presented a good description of the electronic band structure of HgI2 ; since those properties are mostly determined by the predominantly covalent Hg–I bonds, which are reasonably well described by LDA. However, for other properties of HgI2 which involve atomic relaxation, the GGA approximation becomes important. In order to perform the calculations, the maximum length of the plane waves was chosen 6:5=R; where R is the smallest radius of atomic spheres (RHg ¼ RI ¼ 2:5 a:u:). The Brillouin zone (BZ) was sampled by 64 k-points, which were reduced to a set of 6 k-points in the irreducible BZ (IBZ) [20]. Self-consistent interactions were performed with the following convergence criteria: on total energy (105 Ry per unit cell), total charge in each atomic sphere (105 electronic charges per atom), and forces (101 mRy=a:u:). The properties of defects in HgI2 were computed by a 54-atom reference supercell, which was built by taking 3a 3a c: In that case, the IBZ integration was performed at the ð1=4; 1=4; 1=4Þ in a 2 2 2 mesh [20]. The formation energies of Hg and I vacancy defects were obtained by [21] Ef ðVHg Þ ¼ Etot ðHgI2 : VHg Þ E54 ðHgI2 Þ þ mHg ; ð1Þ Ef ðVI Þ ¼ Etot ðHgI2 : VI Þ E54 ðHgI2 Þ þ mI ;
ð2Þ
mHg þ ð1 gÞDf H HgI2 ; mI ¼ mI þ mHgI2 ¼ mHg þ 2mI : The first term in Eqs. (1) and (2) is the total energy of the supercell calculations with the Hg and I vacancies, respectively, and the second term is the total energy of 54-atom reference supercell. For g ¼ 0; the environment is I-rich and Ef ðVHg Þ is minimum, and for g ¼ 1 it is Hg-rich and Ef ðVI Þ is minimum.
where mHg ¼ 1 HgI2 ; and 2gDf H
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
3. Bulk properties and van der Waals interactions In order to get all the lattice and internal parameters of the red HgI2 crystal, we performed total energy minimization with full geometry optimization on all degrees of freedom. These ( and calculations led to the values of: a ¼ 4:62 A ( c ¼ 12:66 A; the I–I plane distance being h ¼ 0:231c; the I–Hg planes distance u ¼ 0:125c; and the bulk modulus B ¼ 0:22 Mbar: A comparison of our results with available experimental data is presented in Table 1. These parameters were obtained by fitting the Murnaghan equation of state over the data. The cohesive energy of HgI2 was calculated by the difference between the total energy of crystalline system and the sum of energies of all free atoms. We found Ecoh ¼ 3:17 eV per HgI2 molecule, which is consistent with the energies of typical semiconducting materials. In terms of the electronic band structure, we find a direct band gap of 1:11 eV or 0:84 eV when the spin–orbit coupling is included, which are smaller than the experimental value of 2:13 eV at 300 K [1]. Our results should be compared to values coming from other theoretical investigations: 0:52 eV [8], 1:1 eV [9], and 0:95 eV [10]. One of the major problems with HgI2 is its mechanical stability at room temperature, which is a result of the weak bonding between adjacent iodine planes. Plastic deformation flow is controlled by the formation and propagation of dislocations [23]. In mercuric iodide, deformation by easy glide occurs mostly by the formation and motion of dislocations lying between adjacent iodine layers [24]. Therefore, understanding the interactions between these iodine planes is important in terms of the mechanical stability of the material. In order to describe the interaction between these iodine planes, we varied the distance
between iodine without relaxing the iodine atoms with relation to their mercury neighbors. The total energy variation as a function of the distance between adjacent iodine layers is shown in Fig. 2. The results were fitted to a Buckingham equation [25], since a fitting based on a pure Lennard-Jones function was not possible. ( A e 6 r exp a 1 fI2I ðrÞ ¼ B þ r 1 6a a Req 6 ) Req r
ð3Þ
( For the HgI2 crystal, we obtained Req ¼ 3:46 A and a binding energy Eb ¼ 0:12 eV per surface atom (2:65 kcal=mol). This binding energy is comparable to the typical London dispersion energy of 2 kcal=mol [25].
1 calculated data fitting curve
0.8 0.6
Energy (eV)
920
0.4 0.2 0 -0.2 0
2
4
6
8
distance (Å)
Fig. 2. Total energy versus I–I bond distance in HgI2 crystal describing the van der Waals interactions. Energy and distances are given in eV and Angstroms, respectively.
Table 1 Theoretical and experimental values of lattice parameters a and c; internal parameters u and h; bulk modulus, and band gap ðEgap Þ
This work Expt. [1]
( a ðAÞ
( c ðAÞ
u
h
B (Mbar)
Egap (eV)
4.619 4.361
12.660 12.450
0:135c 0:139c
0:231c 0:222c
0.22 0.44 [22]
1.11 2.13 ð300 KÞ
ARTICLE IN PRESS F. Ayres et al. / Physica B 340-342 (2003) 918–922
921
mobility in the material. On the other hand, our results show that mercury vacancy is a good candidate to increase the hole mobility.
5. Summary
Fig. 3. Contour plot of the total electronic density in the ½1 1 0 plane for (a) mercury vacancy; (b) perfect crystal; and (c) iodine ( 3: vacancy. The line separation is 0:05 e=A
4. Intrinsic defects Photoluminescence experiments have been used to investigate the properties of defects in HgI2 : However, there is considerable controversy about the nature of those PL lines [5–7]. Here, we computed the electronic and structural properties of mercury and iodine vacancies. In terms of relaxation, both vacancies cause negligible disturbance in the nearby neighboring atoms. This can be observed in Fig. 3, which shows the electronic charge density in an ½1 1 0 plane of the mercury and iodine vacancies. Iodine vacancy introduces a partially occupied energy level in the gap, near the conduction band bottom, with spin S ¼ 12: On the other hand, the mercury vacancy introduces a double-degenerated shallow energy level in the gap, near the top of the valence band, with spin S ¼ 1: We also computed the defect formation energies. For I-rich environment, we find Ef ðVI Þ ¼ 1:70 eV and Ef ðVHg Þ ¼ 1:96 eV: For Hg-rich environment, we find Ef ðVI Þ ¼ 1:16 eV and Ef ðVHg Þ ¼ 3:05 eV: Therefore, concentration of iodine vacancies in HgI2 should be considerably higher than the one of mercury vacancies in both I- or Hg-rich environments. These results indicate that the iodine vacancy is the primer candidate to explain the low hole
In summary, we carried the first ab initio investigation, which takes into account full atomic relaxation, on the properties of mercuric iodide. We quantified the binding energy between adjacent iodine planes, showing that such binding is a typical van der Waals interaction. Additionally, we found that both mercury and iodine vacancies cause negligible distortions in their respective neighbors, and both introduce partially occupied energy gap levels, which could be observed by electron paramagnetic resonance experiments. Based on the position of the defect levels, we find that iodine vacancy should be the one responsible by the low hole mobility in the material, which is consistent with Refs. [5,6].
Acknowledgements The authors acknowledge support from FAPESP and CNPq. The calculations were performed at the LCCA-CCE of the Universidade de S*ao Paulo.
References [1] M. Piechotka, Mater. Sci. Eng. R18 (1997) 1. [2] G.F. Knoll, Radiation Detection and Measurement, Wiley, New York, 2000. [3] X.J. Bao, T.E. Schlesinger, R.B. James, R.H. Stulen, C. Ortale, A.Y. Cheng, J. Appl. Phys. 68 (1990) 86. [4] J. Marschall, F. Milstein, Appl. Phys. Lett. 62 (1993) 2784. [5] X.J. Bao, T.E. Schlesinger, R.B. James, S.J. Harvey, A.Y. Cheng, V. Gerrish, C. Ortale, Nucl. Instrum. Methods Phys. Res. A 317 (1992) 194. [6] R.B. James, X.J. Bao, T.E. Schlesinger, A.Y. Cheng, C. Ortale, L. van den Berg, Nucl. Instrum. Methods Phys. Res. A 322 (1992) 435. [7] I.Kh. Akopyan, B.V. Bondarenko, O.N. Volkova, B.V. Novikov, T.A. Pavlova, Phys. Solid State 39 (1997) 58. [8] D.E. Turner, B.N. Harmon, Phys. Rev. B 40 (1989) 10516.
ARTICLE IN PRESS 922
F. Ayres et al. / Physica B 340-342 (2003) 918–922
[9] R. Ahuja, O. Eriksson, B. Johansson, S. Auluck, J.M. Wills, Phys. Rev. B 54 (1996) 10419. [10] A.K. Solanki, A. Kashyap, T. Nautiyal, S. Auluck, M.A. Khan, Phys. Rev. B 55 (1997) 9215. [11] Y.C. Chang, R.B. James, Phys. Rev. B 46 (1992) 15040. . . [12] E. Sjostedt, L. Nordstrom, D.J. Singh, Solid State Commun. 114 (2000) 15. [13] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn. Universit.at Wien, Austria, 2001. [14] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. [15] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. [16] L. Hedin, B.I. Lundqvist, J. Phys. C 4 (1971) 2064.
[17] U. von Barth, L. Hedin, J. Phys. C 5 (1972) 1629. [18] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [19] S. Tsuzuki, H.P. Luthi, . J. Chem. Phys. 114 (9) (2001) 3949. [20] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [21] K.O. Barbosa, W.V.M. Machado, L.V.C. Assali, Physica B 308–310 (2001) 726. [22] N. Kuroda, T. Iwabuchi, Y. Nishina, J. Phys. Soc. Japan 52 (1983) 2419. [23] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982. [24] G. Georgeson, F. Milstein, Nucl. Instrum. Methods Phys. Res. A 285 (1989) 488. [25] P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 1994.