Effect of Sm doping into CuInTe2 on cohesive energy before and after light absorption

Tai Wang(王泰), Yong-Quan Guo(郭永权), and Cong Wang(王聪)

School of Energy Power and Mechanical Engineering,North China Electric Power University,Beijing 102206,China

Keywords: CuIn1−xSmxTe2,empirical electron theory(EET),light absorption bandgap,hybridization energy

1. Introduction

The I–III–VI2chalcopyrite is investigated for its potential applications in nonlinear optical device, semiconductor laser device, and solar cells[1–6]due to its excellent photoelectric properties such as large absorption coefficient,direct bandgap,large nonlinear susceptibility in the infrared region.[7–11]The conversion efficiency η of Cu(In,Ga)(Se,S)2in solar cell with thin-film absorber layer has reached up to 22.6%.[10]However,single phase Cu(In,Ga)(Se,S)2is not easily prepared due to its composition deviation in the synthesizing process, and causes the impurities to form. Owing to the existence of toxical p-type CdS in Cu(In,Ga)Se2thin-film solar cells,its potential application is limited. The CuInTe2has a direct bandgap of 1.06 eV at room temperature,[12]which matches the light absorption bandgap of solar energy conversion. Therefore,CuInTe2is predicted to have stronger quantum confinement effect and larger Bohr radius of exciton than the CuIn(S/Se)2due to the covalent property of Te.[7]

The double layers Cu(In, R)Te2/Cu(In, R)Te2(R=rare earth) are designed for controlling the charge transport by modulating the valent state of the rare earth, e.g.Ce4+for ptype and Eu2+for n-type,[12–15]which can simplify the synthesis technology from three-layer ZnO/CdS/CIGS to two-layer Cu(In, R)Te2/Cu(In, R)Te2. Since the rare earth element has an excellent light transmission, it can be used to replace the transparent ZnO front electrode layer. After the rare earth element, which has specific 4f electronic structure and unique optical properties such as subsequent emission light at long wavelength and high quantum efficiencies of absorption, is doped into a semiconductor, its luminescent and fluorescent properties can be enhanced.[16–18]Sm is usually in two kinds of valence states,i.e.Sm2+and Sm3+. Sm ion substituted for In in CuInTe2might adjust the charge transport type of semiconductor (Sm2+for n type). Thus, CuIn1−xSmxTe2chalcogenide might be developed into a promising absorber material for new-generation solar cells due to its low toxicity and good optical property.

In this study,the empirical electron theory(EET)is used to investigate the effect of Sm doped into CuInTe2on the cohesive energy before and after light absorption. The calculation of EET is very simple without any integral and differential calculations, and the number of its various parameters are much less than those of the other approaches such as the first principle and molecular field theory. The essential mechanism of light absorption can be revealed by the correlation between the properties and valence electron structure.

2. Calculation methods

The EET, which is based on Pauling’s valence electron theory and quantum theory,consists of three hypotheses and a bond length difference method(BLD).[15,19–27]

Hypothesis 2 According to the state superposition principle of quantum mechanics, the σ-th hybridization state is superposition of h state and t state,the hybridization states are discontinuous. A parameter of K is introduced for calculating the proportion Chfor h state and Ctfor t state.[30,31]

The σ-th hybridization state is given by

The numbers of various electrons Nσcan be calculated from Nσ=ChNh+CtNtwhere Nhand Ntare the number of electrons in h state and t state,respectively.

Hypothesis 3 Pauling’s equation is modified for calculating accurately the covalent bond length Duv(nα)between u and v atoms,which is expressed as

where Ru(l)and Rv(l)are single bond radii of u and v atoms,respectively,the third term on the right-hand side denotes the effect of electron cloud overlap between u and v atoms,which induces the u–v bond length to elongate or shrink along the bonding direction;the coefficient β denotes the ability of electronic clouds to overlap each other, and the value of β is determined to be 0.6 for metal and alloy and 0.71 for the nonmetal in Pauling’s valence and bond theory. The nαdenotes the number of covalent electron pairs in the α-th u–v bond. In the EET, modification is done according to the maximum of nαas shown below:[28]

BLD: According to hypothesis III, the shortest bond length Duv(nA)should be written as

Then we have

for the other bond lengths Dst(nα),α =B,C,...,N.

From Eqs.(5)and(6),we have

In this study, the 4b crystal position is disorderedly occupied by In and Sm in unit cell of CuIn1−xSmxTe2, In and Sm are taken as a kind of atom M at 4b site, i.e., M =(1 −x)·In+x·Sm. The average model is used to calculate the numbers of various electrons and averaged single bond radius as listed below:

The cohesive energy of intermetallic compound follows an equation as given below[31–35]

3. Results and discussion

Figure 1 shows the structural frame of CuIn1−xSmxTe2,which is built based on the refined structural parameters.[37]The experimental bond lengths are measured based on the atomic ordinates and the numbers of equivalent bonds Iαare calculated based on the atomic coordination numbers. Table 1 lists the experimental bond lengths and numbers of equivalent bonds in CuIn1−xSmxTe2. The valence electron structures of CuIn1−xSmxTe2are calculated by the BLD method. The CuInTe2is chosen as an example,and its equivalent bonds Iα,i.e.,experimental and calculated bond lengths are listed in Table 2. The maximum of covalent electron pair nAis 1.4628,thus, β is 0.71 according to Eq. (4). The calculated bond lengths fit to the experimental ones well (∆D=−0.0070 ˚A),showing that the calculated results are acceptable.

Fig.1. Crystal structure of CuIn1−xSmxTe2.

Table 1. Various bonds,bond lengths,and bond numbers of CuIn1−xSmxTe2.

Table 2. Valence electronic structure of CuInTe2.

Table 3. Key parameters of cohesive energy for CuIn1−xSmxTe2.

Table 4. Hybrid states and hybrid energy of CuIn1−xSmxTe2.

According to the above-mentioned valence electronic structural parameters, all hybridization energy levels of CuIn1−xSmxTe2are calculated from Eq. (11), and their results are listed in Table 4. The valence electronic structure of CuIn1−xSmxTe2shows that the hybrid states of Te and Sm are close to the h state, however, Cu and In prefer to occupy the high hybrid state, which are closes to the t state. The hybridization energy decreases with Sm content increasing.

The light absorption causes the energy level to transit from the static state to the high energy state in CuIn1−xSmxTe2as shown in Fig.2. The transitions are from the 3rd energy level to the 4th energy level for CuInTe2and from the 1st to 5th energy level for the other ones. The energy difference between the two energy levels matches the experimental absorption bandgap of CuIn1−xSmxTe2[37]with the relative differences ranging from 1.290% to 6.108% as listed in Table 5. Based on the valence electron structure, the light absorption mainly affects the hybrid states of Cu and In atoms as shown in Fig.3, where the solid blue line and dashed red line denote the energy before (static state) and after (excited state) light absorption, respectively. The difference in energy between the two states is corresponding to the light absorption bandgap. It is very clear that the hybridization energy of CuIn1−xSmxTe2decreases significantly with the increase of Sm doped into CuInTe2before and after light absorption. However,the decreasing slope slowly falls down after light absorption,which causes the light absorption bandgap to broaden from 0.9952 eV to 1.6862 eV with Sm content increasing:this phenomenon might be due to the special valence electron structure of Sm,which is favorable for enhancing the light absorption in a wider range for the potential solar cell applications.Fig.4.Various electron numbers versus Sm content for CuIn1−xSmxTe2in static state and excited state.

Fig.2. Optical transition energy from static energy level to excited energy level in CuIn1−xSmxTe2.

Fig.3. Hybridization energy versus Sm content for CuIn1−xSmxTe2 in static state(solid line)and excited state(dashed line).

Table 5. Hybrid states,energy,and light absorption bandgaps of CuIn1−xSmxTe2.

Table 6. Valence electron structures of CuIn1−xSmxTe2 in static and excited states.

Table 6 lists the valence electron structures of CuIn1−xSmxTe2at static states and excited states, covering the numbers of various electrons. Sm doped into CuInTe2mainly affects the hybrid states of Cu and In,and causes various electrons to change as shown in Fig.4. In the static state,the electron numbers significantly fall down for dumb-pair electron nY, covalent electron ncand total electron nTwith Sm doping content increasing, however, for the number of lattice electrons nlincreases. The same phenomenon is also observed in the excited state; however, the decreasing tendency of total electron number tends to be slow. With the decrease of hybridization energy, the total electron number(nT)decreases from 15.2714 to 13.9503 and from 15.5773 to 15.3916 before and after light absorption, respectively, and the same tendency is also observed in covalent electron number(nc)from 13.9113 to 12.6503 for the static state and from 14.5774 to 14.0916 for the light absorption, the dumb-pair electron number(nY)decreases from 20.7285 to 19.0497 and from 20.4226 to 17.6083 before and after light absorption,respectively. However, the lattice electron number shows the reversal tendency, i.e., it increases from 1.3601 to 1.4881 and from 1.0000 to 1.3000 before and after light absorption, respectively. The abnormal decrease of nlis observed in CuIn0.7Sm0.3Te2since the Sm content is out of the solid solution region of CuIn1−xSmxTe2. These changes of valence electronic structure weaken the bonding ability due to the decrease of covalent electron number and induce the hybrid energy of CuIn1−xSmxTe2to decrease with Sm doping content increasing.

Figure 5 exhibits the changes of valence electron structure in CuIn1−xSmxTe2before and after light absorption. The differences in electron number ∆nelereflect the changes of valence electron number in s,p,and d orbits,the covalent electrons, lattice electrons, total electrons, and dumb-pair electrons before and after light absorption. The value of ∆neles increases for the total electron number and the covalent electron number, however, decreases for the dumb-pair electron number and the lattice electron number, which is due to the electron transformation driven by light energy. For revealing the mechanism of light absorption, the optical transition energy between two hybrid energy levels is discussed as shown in the inset plots in Fig.5, where the photoenergy directly drives the electron transformation from lattice electron in static energy state to s valent electron in excited energy. Meanwhile, the dumb-pair electrons are separated from a dumbpair of electrons in static state to two valence electrons in p and d orbitals in excited state. In a range of x>0.2,the electron transition only occurs for the dumb-pair electrons because CuIn1−xSmxTe2(x=0.3)is out of the solid solution.

Fig.5. Differences in electron number versus Sm content for CuIn1−xSmxTe2 after light absorption.

4. Conclusions

Based on EET studies,the cohesive energy of Sm doped into CuInTe2is strongly correlative to their valence electronic structure. The cohesive energy of CuIn1−xSmxTe2decreases significantly with the increase of Sm doped into CuInTe2before and after light absorption. The light absorption causes the energy level to transit from the static state to the high energy in CuIn1−xSmxTe2. The calculated optical absorption transition energy from the static state to the higher energy in CuIn1−xSmxTe2accords well with the experimental absorption bandgap of CuIn1−xSmxTe2. The Sm doped into CuInTe2mainly affects the electric structure of Cu and the electric structure of In, and the electron number of CuIn1−xSmxTe2significantly falls down for dumb-pair electron nY, covalent electron nc, and electron nTwith the increase of Sm doping content,however,the reversal increase happens to the number of lattice electrons nl,which weakens the bonding ability due to the decrease of covalent electron number and induce the the hybrid energy of CuIn1−xSmxTe2to decrease.

The mechanism of light absorption for CuIn1−xSmxTe2can be explained by photoenergy driving directly the electron transformation from lattice electron in static energy level to s valent electron in excited energy level. Meanwhile,the dumbpair electrons are separated from a pair of electrons to two electrons and excited into p,d orbitals of excited state,respectively. The energy bandgap of CuIn1−xSmxTe2is significantly widened with increasing Sm content due to its special valence electron structure, which is favorable for enhancing the light absorption in a wider range for the potential applications in solar cells.

Appendix A: The hybrid tables of Cu, Sm, In,and Te

The hybrid tables of Cu,Sm,In,and Te are shown in the following tables.

Table A1. A-type hybrid table of Cu.

Table A1. A-type hybrid table of Cu.

σ 1 2 3 4 5 6 7 8 9 Chσ 1 0.9999 0.9998 0.9983 0.9752 0.9502 0.9415 0.7997 07248 Ctσ 0.0001 0.0002 0.0017 0.0248 0.0498 0.0585 0.2003 0.2752 nTσ 5 5.0002 5.0004 5.0034 5.0496 5.0996 5.1170 5.4006 5.5504 nlσ 1 1 1 1 1 1 1 1 1 ncσ 4 4.0002 4.0004 4.0034 5.0496 4.0996 4.1170 4.4006 4.5504 Rσ(1) 1.1520 1.1520 1.1520 1.1520 1.1517 1.1513 1.1512 1.1492 1.1481 σ 10 11 12 13 14 15 16 17 18 Chσ 0.6896 0.6601 0.5194 0.2113 0.1297 0.0690 0.0075 0.0042 0 Ctσ 0.3104 0.3399 0.4806 0.7887 0.8703 0.9310 0.9925 0.9958 1 nTσ 5.6208 5.6798 5.9612 6.5774 6.7406 6.8620 6.9850 6.9916 7 nlσ 1 1 1 1 1 1 1 1 1 ncσ 4.6208 4.6798 4.9612 5.5774 5.7406 5.8620 5.9850 5.9916 6 Rσ(1) 1.1477 1.1472 1.1453 1.1410 1.1398 1.1390 1.1381 1.1381 1.1380

Table A2. Hybrid table of In.

Table A2. Hybrid table of In.

σ 1 2 3 4 5 6 7 8 9 10 Chσ 1 0.9996 0.9975 0.9755 0.8755 0.8735 0.7612 0.5495 0.3601 0 Ctσ 0.0004 0.0025 0.0245 0.1245 0.1265 0.2388 0.4505 0.6399 1 nTσ 3 3.0008 3.0050 3.0490 3.2490 3.2530 3.4776 3.9010 4.2798 5 nlσ 1 0.9996 0.9975 0.9755 0.8755 0.8735 0.7612 0.5495 0.3601 0 ncσ 2 2.0012 2.0075 2.0735 2.3735 2.3795 2.7164 3.3515 3.9197 5 Rσ(1)) 1.4420 1.4420 4.4418 1.4404 1.4339 1.4338 1.4265 1.4127 1.4004 1.3770

Table A3. Hybrid table of Te.

Table A3. Hybrid table of Te.

σ 1 2 3 4 Chσ 1 0.5544 0.0820 1 Ctσ 0 0.4456 0.9180 1 nTσ 2 2 2 2 nlσ 0 0 0 0 ncσ 2 2 2 2 Rσ(1) 1.313 1.4194 1.531 1.550

Table A4. Hybrid table of Sm.

Table A4. Hybrid table of Sm.

σ 1 2 3 4 5 6 7 8 9 10 Chσ 1 0.9635 0.9042 0.8235 0.7078 0.6249 0.2996 0.2085 0.0444 0 Ctσ 0.0365 0.0958 0.1765 0.2922 0.3751 0.7004 0.7915 0.9556 1 nTσ 3 3 3 3 3 3 3 3 3 3 nlσ 1 0.9635 0.9042 0.8235 0.7078 0.6249 0.2996 0.20857 0.0444 0 ncσ 2 2.0365 2.0958 2.1765 2.2922 2.3751 2.7004 2.7915 2.9556 3 Rσ(1) 1.4771 1.4901 1.5112 1.5398 1.5809 1.6104 1.7260 1.7584 1.8166 1.8325