School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China
† Corresponding author. E-mail:
yqguo@ncepu.edu.cn
1. IntroductionI–III–VI2 semiconductors with chalcopyrite structures have received a great deal of attention due to their excellent optical properties such as visible and infrared light-emitting diodes, infrared detector, etc.[1–8] Since the band gap 
of chalcopyrite semiconductors covers most of the energy spectra for the visible light (1 eV–3 eV), the maximum absorption of the solar spectrum can be utilized for the energy conversion and cause these chalcopyrites to develop into the possible substrates for the fabrication of optoelectronic devices.[2,9–17] The solar cells based on CuInSe2 and CuInS2 have already reached efficiencies of 18.8% and 12%, respectively.
Since CuInTe2 is a direct band gap semiconductor, in order to minimize the requirements for minority carrier diffusion lengths, it can be made as either n- or p-type semiconductor with a variety of potentially low-cost homojunction and heterojunction applications as an alternative to monocrystalline and polycrystalline silicon technology.[11,12,16,18–21] Some relevant studies have been reported. Gonzalez and Rincón reported the optical absorption and phase transitions of CuInTe2.[3] Mi analyzed systematically the optical properties of CuInTe2 by the first principle based on the electronic band structures.[22] Li et al. have calculated the band structure of CuInTe2 by the first principle for explaining the mechanism of the thermoelectric property based on electronic structure.[23] However, the first principle approach needs to introduce many approximations according to the atomic structure of the material, and its calculus calculation process is more complicated.
Rare earth ions doping into the semiconductor could enhance the luminescent and fluorescent properties due to its specific 4f electronic structure and unique optical properties such as high quantum efficiencies of absorption light at short wavelength and subsequent emission light at long wavelength.[24–28] The carrier concentration of Cd-doped CuInTe2 has been reported by Cheng et al.[18] The goal of our study on rare earth doping in CuInTe2 material is to study the essential photoelectric mechanism of an Eu-doped CuInTe2 semiconductor with chalcopyrite structure and investigate the correlation between their electronic structures and hybridization energy levels. In this study, empirical electron theory (EET) has been used to study the valance electric structures and band gap of Eu-doped CuInTe2 since it has the advantage of being a simple calculation model without any integral and differential modes and much more parameters.
2. Theoretical modelsThe EET includes four basic hypotheses for the atomic hybridization states and one calculation method, so-called the bond length difference (BLD), where the atomic valence and dimensional characteristics are the two key factors to characterize the valence states in a solid molecule.[27–29] The four basic hypotheses and the bond length difference (BLD) have been systematically illustrated in Refs. [30]–[32], and a conclusion has been obtained that the covalence electron number originating from all bonding atoms is equal to the total number of valence electronic pairs formed by all covalent bonds in the system. The absolute difference 
between the theoretical and the experimental bond length is defined as a criterion for checking the reasonability for determining the final hybridization state with BLD. If the 
is less than 0.05 Å, the calculations are acceptable.[28,33]
The number of equivalent bonds for one bond in EET is defined as[28]
where
is the number of equivalent bonds of the
α bond,
IM is the number of atoms in the molecular formula, and
IS is the coordination number of atoms for the
α bond. For
IK, if the bond forms in the same type of atom such as Cu–Cu, In–In, Te–Te or (Eu,In)–(Eu,In),
IK is equal to 1; if not,
IK is equal to 2.
[28] In the Appendix
A, the numbers of
s,
p, and
d electrons are listed in the hybridization tables of Cu, In, Te, and Eu. Besides, the model of cohesive energy is also supplied.
2.1. Results and discussionIn this paper, the Eu content-dependent valence electronic structures and cohesive energies for CuIn1−xEuxTe2 have been analyzed.
2.2. Structural parametersAccording to our previous study of the structures and electric transports of Eu-doped CuIn1−xEuxTe2 (CIET),[25] Eu-doping into CuInTe2 still stabilizes the tetragonal chalcopyrite structure, and its lattice parameters and atomic occupations are listed in Table 1.[25]
Table 1.
Table 1.
 Table 1.
Lattice parameters and atom occupation of CuIn1−xEuxTe2.
.
| Compound |
CuInTe2 |
CuIn0.9Eu0.1Te2 |
CuIn0.8Eu0.2Te2 |
CuIn0.7Eu0.3Te2 |
| Space group |
I-42d |
I-42d |
I-42d |
I-42d |
| a/Å |
6.1910 |
6.1912 |
6.1899 |
6.1898 |
| c/Å |
12.4077 |
12.4073 |
12.4056 |
12.4091 |
| Cu(4a) |
(0, 0, 0) |
(0, 0, 0) |
(0, 0, 0) |
(0, 0, 0) |
| In/Eu(4b) |
(0, 0, 1/2) |
(0, 0, 1/2) |
(0, 0, 1/2) |
(0, 0, 1/2) |
| Te(8d) |
(0.21991, 1/4, 1/8) |
(0.21819, 1/4, 1/8) |
(0.22156, 1/4,1/8) |
(0.21626, 1/4,1/8) |
| Table 1.
Lattice parameters and atom occupation of CuIn1−xEuxTe2.
. |
2.3. Crystal structure and strong bondsAccording to the structural parameters of CIET compounds in Table 1, the structural frame is drawn using the Diamond software as shown in Fig. 1. The experimental bond distances and atomic coordination numbers can be measured, and the number of equivalent bonds Iα can be calculated from Eq. (1). The related bonding parameters are supplied in Tables 2–5. The bonds are corresponding to the first most and the second most strongest bonds between Cu–Te and Te–In(Eu) as also shown in Fig. 1.
Table 2.
Table 2.
Table 2.
Bonding rule of CuInTe2.
.
| Bond order |
Bonding atom |
 |
Bond length/Å |
Bond order |
Bonding atom |
 |
Bond length/Å |
| 1 |
Cu–Te |
8 |
2.5797 |
6 |
Cu–In |
8 |
4.3822 |
| 2 |
In-Te |
8 |
2.7943 |
7 |
Cu–Cu |
4 |
4.3822 |
| 3 |
Te–Te |
4 |
4.1227 |
8 |
In–In |
4 |
4.3822 |
| 4 |
Te–Te |
8 |
4.2568 |
9 |
Te–Te |
8 |
4.5196 |
| 5 |
Cu–In |
8 |
4.3777 |
10 |
Te–Te |
4 |
4.6486 |
| Table 2.
Bonding rule of CuInTe2.
. |
Table 3.
Table 3.
Table 3.
Bonding rule of CuIn0.9Eu0.1Te2.
.
| Bond order |
Bonding atom |
 |
Bond length/Å |
Bond order |
Bonding atom |
 |
Bond length/Å |
| 1 |
Cu–Te |
8 |
2.5741 |
6 |
Cu–In, Eu |
8 |
4.3822 |
| 2 |
In, Eu–Te |
8 |
2.8009 |
7 |
Cu–Cu |
4 |
4.3822 |
| 3 |
Te–Te |
4 |
4.1008 |
8 |
In, Eu–In, Eu |
4 |
4.3822 |
| 4 |
Te–Te |
8 |
4.2500 |
9 |
Te–Te |
8 |
4.5278 |
| 5 |
Cu–In, Eu |
8 |
4.3788 |
10 |
Te–Te |
4 |
4.6674 |
| Table 3.
Bonding rule of CuIn0.9Eu0.1Te2.
. |
Table 4.
Table 4.
Table 4.
Bonding rule of CuIn0.8Eu0.2Te2.
.
| Bond order |
Bonding atom |
 |
Bond length/Å |
Bond order |
Bonding atom |
 |
Bond length/Å |
| 1 |
Cu–Te |
8 |
2.5846 |
6 |
Cu–In, Eu |
8 |
4.3815 |
| 2 |
In, Eu-Te |
8 |
2.7874 |
7 |
Cu–Cu |
4 |
4.3815 |
| 3 |
Te–Te |
4 |
4.1355 |
8 |
In, Eu–In, Eu |
4 |
4.3815 |
| 4 |
Te–Te |
8 |
4.2626 |
9 |
Te–Te |
8 |
4.5110 |
| 5 |
Cu–In, Eu |
8 |
4.3769 |
10 |
Te–Te |
4 |
4.6326 |
| Table 4.
Bonding rule of CuIn0.8Eu0.2Te2.
. |
Table 5.
Table 5.
Table 5.
Bonding rule of CuIn0.7Eu0.3Te2.
.
| Bond order |
Bonding atom |
 |
Bond length/Å |
Bond order |
Bonding atom |
 |
Bond length/Å |
| 1 |
Cu–Te |
8 |
2.5676 |
6 |
Cu–In, Eu |
8 |
4.3821 |
| 2 |
In, Eu-Te |
8 |
2.8081 |
7 |
Cu–Cu |
4 |
4.3821 |
| 3 |
Te–Te |
4 |
4.0922 |
8 |
In, Eu–In, Eu |
4 |
4.3821 |
| 4 |
Te–Te |
8 |
4.2423 |
9 |
Te–Te |
8 |
4.5368 |
| 5 |
Cu–In, Eu |
8 |
4.3768 |
10 |
Te–Te |
4 |
4.6815 |
| Table 5.
Bonding rule of CuIn0.7Eu0.3Te2.
. |
2.4. Energy at various valence electron hybridization statesFor studying the relationships between valence electron hybridization state and energy for CuIn1−xEuxTe2 semiconductors, the hybridizing parameters, which cover the covalent electrons of s, p, d, lattice electron, dumb electrons, and magnetic electrons in h and t states for Cu, In, Eu, and Te, could be determined using the BLD method with the empirical criterion 
Å based on the hybrid states of Cu, In, Eu, and Tein Appendix A.
The theoretical model of hybridization energy is presented in the supplement section. The hybridization parameters determined with BLD are selected as the initial parameters for calculating hybridization energies; if the energy difference between two hybridization states could fit the light absorption band-gap, the solution is acceptable. CuInTe2 is taken as a typical calculation example, the hybridization states of the valence electron so-called valence structure are supplied in Table 6, where I denotes the equivalent bond number, 
and 
refer to the calculated bond distance and experimental bond distance, respectively, and ΔD is the difference between 
and 
, nα denotes the number of valence electronic pairs distributed in each bond, and 
is the relative error.
Table 6.
Table 6.
| Table 6.
Valence electronic structure of CuInTe2.
. |
Based on the determined results of valence electron structures, the related hybridization energies are calculated and the results are listed in Tables 7–10. Owing to the multi-solution in the calculation, the observed band-gap is taken as a criterion for selecting the reasonable solution, if the energy difference between two hybridization states could fit the band-gap well (the fitting error is within 10%), the solution is acceptable.
Table 7.
Table 7.
Table 7.
Calculated values of hybrid state and hybrid energy of CuInTe2.
.
| σ |
Cu |
In |
Te |
Hybrid energy/kcal  mol−1 |
| 1 |
9 |
10 |
1 |
314.6231 |
| 2 |
11 |
10 |
1 |
318.1892 |
| 3 |
13 |
10 |
1 |
342.8708 |
| 4 |
17 |
9 |
1 |
319.9201 |
| 5 |
17 |
10 |
1 |
354.2455 |
| Table 7.
Calculated values of hybrid state and hybrid energy of CuInTe2.
. |
Table 8.
Table 8.
Table 8.
Calculated values of hybrid state and hybrid energy of CuIn0.9Eu0.1Te2.
.
| σ |
Cu |
In |
Te |
Eu |
Hybrid energy/kcal  mol−1 |
| 1 |
13 |
9 |
1 |
1 |
304.6148 |
| 2 |
13 |
10 |
1 |
1 |
334.8437 |
| 3 |
15 |
9 |
1 |
1 |
312.1502 |
| 4 |
15 |
10 |
1 |
1 |
342.6048 |
| 5 |
17 |
9 |
1 |
1 |
315.5869 |
| Table 8.
Calculated values of hybrid state and hybrid energy of CuIn0.9Eu0.1Te2.
. |
Table 9.
Table 9.
Table 9.
Calculated values of hybrid state and hybrid energy of CuIn0.8Eu0.2Te2.
.
| σ |
Cu |
In |
Te |
Eu |
Hybrid energy/kcal  mol−1 |
| 1 |
13 |
10 |
1 |
1 |
329.5607 |
| 2 |
15 |
9 |
1 |
1 |
309.9747 |
| 3 |
15 |
10 |
1 |
1 |
337.321 |
| 4 |
17 |
9 |
1 |
1 |
313.4229 |
| 5 |
17 |
10 |
1 |
1 |
340.8581 |
| Table 9.
Calculated values of hybrid state and hybrid energy of CuIn0.8Eu0.2Te2.
. |
Table 10.
Table 10.
Table 10.
Calculated values of hybrid state and hybrid energy of CuIn0.7Eu0.3Te2.
.
| σ |
Cu |
In |
Te |
Eu |
Hybrid energy/kcal  mol−1 |
| 1 |
13 |
10 |
1 |
1 |
319.5803 |
| 2 |
15 |
9 |
1 |
1 |
303.9720 |
| 3 |
17 |
7 |
1 |
1 |
281.7519 |
| 4 |
17 |
9 |
1 |
1 |
307.3936 |
| 5 |
17 |
10 |
1 |
1 |
330.7531 |
| Table 10.
Calculated values of hybrid state and hybrid energy of CuIn0.7Eu0.3Te2.
. |
2.5. Analyses and discussion of CIETFor studying the physical mechanism for CIET photovoltaic characteristics, the changes of valence electron structure induced by the photoelectric conversion effect, which include the electron transitions between various orbits and electron transformation between the valence electron and lattice electron, should be taken into account. The light absorption causes the increase of energy of the CIET system, and thus changes the relative electron structure. The electron numbers, which are distributed in various orbitals and lattice space, change due to the electron hopping between various orbitals or electron transformation from valence electron to lattice electron. The open voltage increases with lattice electron increasing.
For CuIn1−xEuxTe2 (x = 0, 0.1, 0.2, 0.3) semiconductors, the observed light absorption band-gap 
is defined as a property criterion for selecting the two hybridization energy levels. The transition between the two energy levels should be determined after light absorption. Since the band-gap 
(24.4436 kcal/mol) for CuInTe2, the energy difference between the two selected hybridization energy levels should fit 
well, that is, the relative error is within 10%. For selecting the two levels as shown in Table 7, the two hybridization states σ = 3, 4 are selected since the corresponding band-gaps are 342.8078 kcal/mole for σ = 3, and 319.9201 kcal/mole for σ = 4, respectively. Their energy difference is 22.9507 kcal/mol, which accords with the observed band-gap well. The valence electronic structures are listed in Table 11. The same calculations are performed for the other three CuIn1−xEuxTe2 semiconductors. The calculated valence electron structures are presented in Tables 11–14. Based on the above calculations, the diagram of hybrid electronic state transition induced by absorbing photons is shown as Figs. 2–5, where the symbols of −, 
, 
, 
denote covalent electrons, lattice electrons, and dumb pair electrons, respectively; s, p, d represent the relative electron numbers distributed in s, p, d orbitals.
Table 11.
Table 11.
| Table 11.
Valence electrons in the hybrid state of CuInTe2.
. |
Table 12.
Table 12.
| Table 12.
Valence electrons in the hybrid state of CuIn0.9Eu0.1Te2.
. |
Table 13.
Table 13.
| Table 13.
Valence electrons in the hybrid state of CuIn0.8Eu0.2Te2.
. |
Table 14.
Table 14.
| Table 14.
Valence electrons in the hybrid state of CuIn0.7Eu0.3Te2.
. |
As shown in Figs. 2–5, the light absorption induced electron transformations from covalent electron to lattice electron and from valance electron to dumb pair electron occur in an In atom. The increase of lattice electrons in lattice space is conducive to increasing the conductive ability and reducing resistivity, and the increase of dumb paired electrons causes the declination of the bonding energy for the CIET semiconductor.
For Cu atom, the electron transformation from dumb pair electron to covalent electron is observed after light absorption, which causes the increase of bonding energy. However, there is no change for Eu or Te. It implies that Eu doping into CuInTe2 affects the valence electron structures of Cu and In atoms. The hybridization states of Cu seem to be more sensitive to Eu doping. In single phase regimes of 
–0.2, Eu doping into CuInTe2 causes electrons to transform from a dumb pair electron into a covalent electron, and reduce the bonding energy. However, the tendency of electron transformation is to cause the reverse result from the single phase solution region, i.e., the covalent electrons transformed into the dumb pair electron. The same transformation is also observed for the In atom. It reveals that Eu doping is helpful for improving the light performance of CuInTe2 by adjusting the valence electron structures of Cu and In.
Since the hybridization states of Cu and In are affected by Eu doping, the three figures (Figs. 6–8) are supplied for understanding the physical mechanism for optical performance of CuInTe2 by Eu doping. The Eu doping into CuInTe2 induces the covalent electrons nc to decrease and the dumb pair electrons ny to increase for Cu and In atoms with increasing the Eu doping content in the single phase region. For the In atom, its s covalent electrons are converted into lattice electrons nl, and its p and d covalent electrons are converted into d dumb pair electrons with increasing Eu content; for the Cu atom, the electron transformation is influenced by Eu doping, and the covalent electrons transform into dumb pair electrons. The above-mentioned discussion reveals that the Eu doping has an effect on the band-gap width for each of CuIn1−xEuxTe2 semiconductors by adjusting 3d valence electrons of the Cu atom, and this adjusting action is helpful for improving the optical properties of CuIn1−xEuxTe2 semiconductors.
3. ConclusionsIn this paper, the valence electron structures and bang-gaps of Eu-doped CuIn1−xEuxTe2 semiconductors are calculated systemically by the EET method. The theoretical calculations accord with experimental results well. The theoretical results show that Eu doping into CuInTe2 mainly affects the valence electron structures of Cu and In atoms, and induces electron transformations from covalent electron to lattice electron and from valance electron to dumb pair electron after light absorption. The enlarged light absorption band gap is related to the increase of lattice electrons. It reveals the essential issue in the photoelectric affect is due to the change of valence electron structure induced by Eu doping.
Appendix A
The atomic state in a solid or a molecule is a hybridization of two atomic states, which can be called the h (head) and t (tail) states. At least one of them is the ground or near excited state. Both of them correspond to two stationary states, and a certain atomic state is the overlap of the two states. Both h and t states have their own numbers of covalent electrons nc, “lattice electron” nl, and the single bond radius R(1).[30] The numbers of s, p, and d electrons are listed in hybridization tables of Cu, In, Te, and Eu as follows: Tables A1–A4
Table A1.
Table A1.
| Table A1.
Hybrid levels for Cu.
. |
Table A2.
Table A2.
| Table A2.
Hybrid levels for In.
. |
Table A3.
Table A3.
| Table A3.
Hybrid Levels for Te.
. |
Table A4.
Table A4.
| Table A4.
Hybrid Levels for Eu.
. |
The theoretical model for calculating the crystalline cohesive energy was given first by Yu[27] in empirical electron theory (EET), and the crystalline cohesive energy 
is expressed as follows:
where
(kcal
Å/mol) with
, 2, 3, 4, 5, 7 or 13,
, 1, 0: for the elements in this study, their
b (kcal
Å/mol) values are 20.6044 for Cu, 32.894 for In, 37.500 for Te, 45.7317 for Eu;
,
, and
represent the bond number, the number of bonding electron pairs, and bond distance of
α bond;
f and
represent the abilities of covalent electron and crystalline electron to form bonds;
is the equivalent bond distance and expressed as
, with referring to covalent bonds around lattice electrons,
denotes the bonding capability of lattice electrons, and
, with
nT being the total number of valence electrons.
[2]a = 0.1542, C = 0.907P, for elements in V, VI, VII of B subfamily, Fe, Co, Ni in VIII, elements in BI, BII, their P values are in the order of 6, 5, 4, 3, 2, 1, and 0 (0 for BI, BII),
Empirical electron theory only supplies P values of B group elements, and therefore the binding energies of the A group elements containing dumb pair electrons need calculating with an appropriate guess and speculation. In this paper, we suppose that the P value of Cu is 0; the rare earth element Eu belongs to the III B group, so that the P value is 0; In and Te are the A group elements, whose P values are both 0. The calculation is carried out based on those conditions.
The formula for calculating the binding energy of a compound crystal is[33,34]
where
with an
α bond being formed between
u and
v atoms;
with
m and
n denoting the numbers of
u and
v atoms, respectively, in molecular formula;
with
fu and
fv denoting the bonding capabilities of
u and
v atoms when they form the
α bond; and
bu and
bv refer to the shielding coefficient (
b) values of
u and
v crystalline binding energy, respectively.
