Energetics and Atomic Structures of Cu2Te Overlayers on CdTe(111

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Energetics and Atomic Structures of CuTe Overlayers on CdTe(111) Jin-Ho Choi, Wenguang Zhu, Kai-Ming Ho, Deliang Wang, and Zhenyu Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511776e • Publication Date (Web): 10 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Energetics and Atomic Structures of Cu2Te Overlayers on CdTe(111) Jin-Ho Choi,1,2 Wenguang Zhu,1,2 Kai-Ming Ho,3,1,2 Deliang Wang,4 and Zhenyu Zhang1,2,* 1

International Center for Quantum Design of Functional Materials (ICQD), Hefei National Laboratory

for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, 230026, China 2

Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 3

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Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, 230026, China

ABSTRACT Although Cu2Te is widely used as a back contact material in CdTe solar cells, the exact atomic structure of the Cu2Te/CdTe interface remains unclear. Using firstprinciples calculations within density functional theory, we search for possible structures of Cu2Te overlayers on CdTe(111) surfaces based on our recent theoretical determination of a stable layered structure of bulk Cu2Te. We discover that the unstrained bulk-like configuration is energetically more favorable than various epitaxial configurations due to their significant energy costs associated with the inplane strain, even though the first epitaxial overlayer is already more stable than bulk Cu2Te. Our thermodynamic analysis further confirms that the unstrained bulk-like interface structure is still stable at typical experimental growth temperatures (~700 K). It is also found that van der Waals forces play a considerable role in the stacking of the Cu2Te overlayers. These findings are discussed in connection with existing and new experimental results, and will likely stimulate future systematic experiments.

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INTRODUCTION Thin-film solar cells are one of the most promising classes of solar cells because of their relatively high efficiencies and low production costs.1-6 Among different kinds of thin-film solar cell materials, cadmium telluride (CdTe) has attracted particular attention due to its optimal band gap (~1.45 eV) and high light-absorption coefficient.7-11 Nevertheless, the highest efficiency of CdTe solar cells achieved so far is 19.6%,12 still much lower than the theoretical limit of ~29%.13 On the other hand, a critical issue of CdTe solar cells is the long-term instability characterized by gradual efficiency loss, which is likely to be closely related to the specific contact materials.9 For CdTe solar cell devices, Cu containing materials have been widely used to improve the back contact to CdTe and the photovoltaic conversion efficiency.9 It has been found that Cu atoms diffuse into and react with the CdTe film, precipitating to form a Cu2Te phase at the interface.9,14,15 The Cu2Te phase can dramatically modify the electronic property of the contact interface, and may also help to form an Ohmic contact to the CdTe film.14 However, the Cu2Te overlayer has also been known as a main source of excess Cu, which can diffuse deep into the CdTe film, potentially causing the long-term instability.9,16 These factors demonstrate the importance of Cu2Te phases in the overall performance of CdTe solar cells. It has recently been found that the interface structures of the constituent materials can significantly affect the device performance of thin film solar cells.10,17,18 For example, the structural properties of CdTe grain boundaries and their passivation contribute to the enhancement of carrier separation, which in turn improves the cell efficiency of CdTe solar cells.18 An earlier experiment also reported that the interface structure of Cu2Te back contacts can play an important role in the performance of


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CdTe solar cells: the structural changes of Cu2Te contacts by thermal treatment resulted in a large difference of the cell efficiency up to ~4%.19 However, in contrast to the grain boundary cases,10,18 the exact atomic structure of the Cu2Te/CdTe interface has been largely unexplored, hindering further studies for improving the quality and stability of the back contacts in CdTe solar cells. In this paper, we use first-principles calculations within density functional theory (DFT) to search for preferred interface structures of Cu2Te overlayers on CdTe(111) surfaces. The present work is enabled by the recent finding of a low-energy layered structure for bulk Cu2Te,20 in which six strongly covalently bonded atomic layers form one building block (hereafter referred as one sextuple layer, or 1-SL), and adjacent SLs are weakly held together by van der Waals (vdW) interactions. Our studies identify two candidate configurations for the first Cu2Te overlayer, one is epitaxially strained and another is bulk-like unstrained, both of which have lower formation energies than bulk Cu2Te. However, the unstrained bulk-like configuration is energetically more favorable than the epitaxial configuration. Moreover, the subsequent overlayers prefer the bulk-like configuration, on either the strained or unstrained first SL. Our thermodynamic analysis further confirms that the unstrained bulk-like interface structure is still stable at typical experimental growth temperatures of ~700 K. In addition, we find that vdW forces play a considerable role in the stacking of the Cu2Te overlayers. These results consistently point to the unstrained bulk-like interface configuration as the most probable structure of Cu2Te/CdTe(111) interface, stimulating further structural identifications in future systematic experiments.

COMPUTATIONAL METHODS


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The first-principles DFT calculations21 were carried out using the Vienna Ab-initio Simulation Package (VASP).22 We used the projector-augmented wave (PAW)23,24 method with the Perdew-Burke-Ernzerhof (PBE)25 exchange correlation functional. The cutoff energy used for the plane-wave basis set is 280 eV, and the obtained formation energy of Cu2Te is essentially the same if a higher cutoff of 380 eV is used. The calculated equilibrium lattice constant for bulk CdTe is 6.577 Å, which agrees well with the experimental value of 6.477 Å. To compare Cu2Te/CdTe(111) interface structures consistently, the CdTe(111) surface was simulated by a twelve-layer p(2×6) super cell containing 72 Cd and 72 Te atoms, with a vacuum region of ~15 Å. The six bottom layers were fixed during structural relaxation and all other atoms were allowed to fully relax until the forces on each atom were less than 0.02 eV/Å. The surface Brillouin zone was sampled using a 3×1×1 k-point mesh. The formation energy or heat (∆H) of a Cu2Te/CdTe interface per Cu2Te formula unit (f.u.) is defined as ∆H = [Etot(Cu2Te/CdTe) - (Esub + nCuEtot(Cu) + nTeEtot(Te))]/nCu2Te, where Etot(Cu2Te/CdTe) is the total energy of the interface; Esub is the total energy of a reference CdTe substrate; nCd, nTe, and nCu2Te represents the number of Cd, Te, and Cu2Te units in the deposited Cu2Te overlayer, respectively; Etot(Cu) and Etot(Te) is the total energy of Cu and Te atom in its bulk form, which is face-centered cubic Cu and P3121 Te, respectively.

RESULTS AND DISCUSSION We now search for the preferred structures of the Cu2Te/CdTe contact interface in CdTe thin-film solar cells by first focusing on the behavior of the first SL of Cu2Te. Figure 1a displays the bulk structure of Cu2Te recently found by our global structure


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search20 using an adaptive genetic algorithm; a similar layered structure of Cu2Se bulk has also been predicted20 and confirmed26 experimentally. The layered nature of Cu2Te bulk offers a natural starting configuration in the structural search of Cu2Te/CdTe interfaces. On the experimental side, a few previous studies have speculated on epitaxial growth of Cu2Te overlayer on CdTe(111) films.14,19 Because most of the polycrystalline CdTe thin films are (111) faceted,15 growth of Cu2Te overlayers on CdTe(111) can be widespread in CdTe solar cells. There are two types of CdTe(111) surfaces, Cd-terminated (A) and Te-terminated (B). Both surfaces can undergo a structural reconstruction accompanied by the creation of atomic vacancies. However, the reconstructed surfaces are incompatible for the epitaxial growth of Cu2Te due to the atomic vacancies, which will be discussed later. We therefore first consider the unreconstructed CdTe(111) surfaces to investigate the epitaxial Cu2Te overlayer. The optimized structure of unreconstructed CdTe(111)-Te is displayed in Figure 1b, while unreconstructed CdTe(111)-Cd is found to be unstable and tends to reconstruct upon atomic relaxation. Since the Cu2Te SL possesses an atomic geometry of Te or Cu layer similar to the triangular geometry of the unreconstructed CdTe(111)Te surface (aside from the considerable lattice distortion along the b axis), the unreconstructed CdTe(111)-Te surface is compatible for epitaxial growth of Cu2Te (see insets in Figures 1a,b). The misfit values of the two crystals are 0.16 Å and 0.69 Å for the a and b axes, respectively, and the corresponding strains are ~2% and ~17%, indicating that Cu2Te overlayer is subjected to substantial stretch along the b axis during epitaxial growth. Such epitaxial growth is accompanied by the formation of Cu-Te bonds (Figure 1c) and strong interfacial coupling, which helps to compensate the strain energy cost for the stretched Cu2Te overlayer. The Cu atoms in the interfacial plane are coherently bonded to the topmost Te layer of CdTe(111) surface.


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However, the strong interfacial coupling also transforms the atomic geometry of the Cu2Te SL into a three-atomic-layer building block (hereafter referred as one epitaxial layer, or 1-EL). The calculated interaction energy27 between the Cu2Te EL and the unreconstructed CdTe(111)-Te substrate is -446 meV/f.u., and the Cu2Te overlayer has a formation energy (∆H) of -215 meV/f.u., much lower than that of bulk Cu2Te (-158 meV/f.u.). We next present a previously unappreciated non-epitaxial structure of the 1-SL Cu2Te/CdTe(111) interface, which possesses an unstrained bulk-like Cu2Te structure simply deposited on the unreconstructed CdTe(111) surface (Figure 1d), and the corresponding formation energy is -244 meV/f.u., lower by 29 meV/f.u. than that of the epitaxial structure. The interaction energy between the unstrained Cu2Te overlayer and the CdTe(111) substrate is -104 meV/f.u., indicating a relatively weaker interfacial coupling than the epitaxial case. Due to the lattice mismatch along the b axis between the Cu2Te SL and the CdTe(111) substrate, the unstrained Cu2Te structure is 7/6 times denser than the CdTe(111) substrate or the epitaxial Cu2Te, as shown in Figure 1d. As a crosscheck, we note that rotations of the unstrained Cu2Te structure would result in distortions in the Cu2Te layer due to the partially formed CuTe bonds, making the rotated structures less stable than the un-rotated structures. We have also considered other epitaxial Cu2Te/CdTe structures where the first Cu2Te SL and CdTe(111) share Te atoms at the interface, which is actually the case of Cu2Te deposition on Cd-terminated CdTe(111). However, this epitaxial structure is found to be unstable, similar to the case of clean Cd-terminated CdTe(111). Finally, we have checked a relaxed but epitaxial Cu2Te/CdTe structure, but such configuration is found not to be stabilized. The CdTe(111) surfaces can be reconstructed with the creation of atomic


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vacancies to satisfy the electron counting rule.28 The reconstructed CdTe(111) surfaces not only have no geometric matching with the Cu2Te SL due to the atomic vacancy, but also are relatively unreactive, as shown below, which is unsuitable for the epitaxial growth of the Cu2Te overlayer. However, unlike the epitaxial structure, an unstrained Cu2Te layer can also be formed on reconstructed CdTe(111) surfaces, with no specific chemical bond formed at the interfaces. We find that the ∆H of an unstrained 1-SL Cu2Te is -157 and -156 meV/f.u. on the Cd- and Te-terminated reconstructed CdTe(111) surface, respectively, and the reduction for the Te-terminated surface indicates that the reconstructed CdTe(111) surface is much less reactive than the corresponding unreconstructed surface. It is now natural to ask whether the unreconstructed CdTe(111)-Te surface is energetically favorable, compared to the reconstructed CdTe(111)-Te surface. Our DFT calculations show that the clean reconstructed surface is more stable than the clean unreconstructed one, by ~0.87 eV per each atomic vacancy. However, the reconstructed and unreconstructed surfaces are almost equally favorable (within 0.01 eV per atomic vacancy) with the unstrained Cu2Te SLs, showing that both types of interfacial structures can be formed in an actual growth system. It is also conceivable that, upon the deposition of the first EL or SL, an initially reconstructed CdTe(111)Te surface could undergo a de-reconstruction process to adopt an unreconstructed configuration at the Cu2Te/CdTe interface. Now we go beyond the first overlayer of Cu2Te on CdTe(111). When the second and third EL of Cu2Te is added onto the first EL, the corresponding formation energies for the added layers are only -38 and -8 meV/f.u., respectively. Such dramatic reductions are mainly because the inter-EL coupling is relatively weak, as reflected by the inter-EL interaction energies of ~130 meV/f.u., while there is still a


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considerable strain energy cost associated with the stretched Cu2Te. We next investigate the case of unstrained Cu2Te. As an unstrained second and third SL is placed onto the unstrained first SL, the corresponding formation energies for each added layer are identically -164 meV/f.u., lower than that of the bulk Cu2Te. Therefore, the unstrained Cu2Te SLs can readily grow on the unstrained first SL. The optimized structure of the 3-SL unstrained Cu2Te/CdTe(111) interface is displayed in Figure 2a. We may consider a mixed Cu2Te configuration where the first EL of Cu2Te is followed by unstrained SLs, as shown in Figure 2b. The corresponding formation energy for the unstrained second and third SL added onto the first EL is -174 and -164 meV/f.u., respectively, also lower than that of the bulk Cu2Te, indicating that the unstrained configuration is also energetically preferred on the first Cu2Te EL. It is notable that fabrications of back contact in CdTe solar cells commonly include an annealing process at high temperatures (~600 K), in order to form contact interfaces by precipitating deposited Cu atoms or recrystallizing amorphous Cu2Te overlayers.9,14,19 Therefore, the thermal stability of the Cu2Te/CdTe interface is worthwhile to investigate. To examine the thermal stability of our proposed Cu2Te overlayer structures, we calculate the free energy of the 1-SL or 1-EL Cu2Te/CdTe(111) interface by using the harmonic approximation and calculated vibrational frequencies.29 The free energies of the Cu2Te/CdTe(111) interfaces with respect to temperature are shown in Figure 3. The zero energy reference is the free energy sum of the clean CdTe(111) surface and bulk Cu2Te. It is notable that the epitaxial Cu2Te overlayer is higher in energy than bulk Cu2Te above the temperature of ~450 K, indicating thermal instability above this temperature. In contrast, the unstrained bulk-like interface structure still remains stable at 700 K, which is the upper limit of the typical experimental growth temperatures; the relative free energy


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becomes positive above ~1300 K. Thus, we can say that the unstrained structure is more consistent with experiments. To investigate the effects of vdW forces on the stacking of the Cu2Te overlayers, we have performed DFT calculations within the van der Waals density functional (vdW-DF)30,31 scheme. The calculated lattice constant of bulk CdTe is 6.561 Å. Figure 4 shows the relative formation energy (∆Hrel) of each unstrained Cu2Te SL, up to the fourth SL (approximately, 3 nm thickness). The zero energy reference is the formation energy of bulk Cu2Te. The relative formation energies within the vdW-DF scheme are much larger than the corresponding PBE values, showing that the vdW forces make the stacking of Cu2Te overlayer energetically more favorable. In the vdW calculations, the ∆Hrel of the strained 1-EL Cu2Te is 80 meV higher than that of the unstrained 1-SL one, indicating again that the unstrained bulk-like configuration is energetically more favorable. We now make closer connections with the previous experimental observations. A recent experiment reported that Cu2Te phases could be converted to Cu-free phases during an extended annealing process while the Cu2Te formation required a brief annealing at high temperatures.14 The metastability of Cu2Te phases was attributed to irreversible Cu diffusions into CdTe,14 which is consistent with the prevailing view of the long-term instability problem.9 A theoretical study attributed the driving force of Cu diffusion to the phase transitions to other CuxTe phases due to the energetic instability of bulk Cu2Te.32 However, our previous work found that Cu2Te bulk is comparably stable,20 and the present DFT calculations have further shown that the Cu2Te/CdTe interface can also be energetically and thermodynamically stabilized. These results may indicate that the metastability is caused by the thermal activation of irreversible Cu diffusion at the interface, rather than the intrinsic instability of the


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bulk Cu2Te. Note that the conversion of Cu2Te phases to Cu-free phases, instead of other CuxTe compositions,14 also points to the former. Before closing, we note that in actual device applications the amount of CdTe(111) facets can be reduced during the fabrication processes such as hightemperature annealing and post-deposition CdCl2 treatment.33 However, even after such processes, CdTe(111) facet is still dominant or its amount is comparable to those of other orientations.33 Moreover, the unstrained configuration of Cu2Te overlayer is compatible with other kinds of CdTe surfaces, as discussed above. Therefore, we can expect that the unstrained Cu2Te overlayer is widespread in CdTe solar cells. It is also notable that the unstrained Cu2Te overlayer is closely bound to CdTe(111), although the interfacial interactions are relatively weak; the interlayer spacing (~2.8 Å) is slightly longer than that (~2.7 Å) of the epitaxial one. Therefore, the interfacial resistance associated with vacuum tunneling is likely to be trivial. However, accurate determination of related parameters such as Schottky barrier height is further needed to understand the nature of carrier transport.

CONCLUSION In conclusion, we have carried out detailed first-principles studies of the atomic structures and energetics of Cu2Te/CdTe contact interfaces in CdTe solar cells. Our results consistently point to the unstrained configuration of the Cu2Te overlayer as the most probable structure of the Cu2Te/CdTe interface, a central finding calling for future experimental tests.

AUTHOR INFORMATION Corresponding Author


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*E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was supported in part by the Chinese Academy of Sciences Fellowships for Young International Scientists (2011Y2JB10), National Natural Science Foundation of China (Nos. 11034006, 11374273, 11350110325, 51272247, and 60976054), and National Research Foundation of Korea (2012R1A6A3A03040199).


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Cd a

a

Figure 1. The optimized structures of (a) Cu2Te bulk, (b) unreconstructed CdTe(111)Te surface, and Cu2Te/CdTe(111) interfaces with (c) 1-EL of Cu2Te, (d) 1-SL of unstrained Cu2Te. The top views of the atomic layers indicated by the dashed rectangles are given in the insets of (a), (b) and (d), respectively. In (a), the unit cell of the bulk Cu2Te is indicated by the solid lines. In the top view of (d), the numbers of honeycomb rings along the b axis are labeled.


16

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(a)

(b)

-164

-164

-164

-174

-244

-215 b

b

a

a

Figure 2. The optimized structures of Cu2Te/CdTe(111) interfaces with (a) three unstrained SLs and (b) the first EL followed by two unstrained SLs on the unreconstructed CdTe(111)-Te surface. The numbers denote the formation energies for each Cu2Te EL or SL (in meV/f.u.).


17


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Page 18 of 25

Figure 3. The calculated free energies of the Cu2Te/CdTe(111) interfaces with respect to temperature. The zero energy reference is the free energy sum of the clean CdTe(111) surface and bulk Cu2Te.


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Figure 4. The relative formation energy of unstrained Cu2Te SLs on CdTe(111) within the PBE and the vdW-DF schemes. The zero energy reference is the formation energy of bulk Cu2Te.


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Page 20 of 25

Table of Contents


20

(a)

Page 21 of 25

1 2 3 4 5 6 7 8 9c 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 c25 26 27


(b)

4.65A b

7.90A 3.96A b

c

8.06A

a

a

(d)

(c)

7 6 6 5 5 4 4 3 3 Cu

b

c Plus Environment ACSTe Paragon Cd a

a

2 2 1 1

The Journal of Physical Chemistry (a) (b)Page 22 of 25 1 2 3-164 4 5 6 7 8-164 9 10 11 12 -244 13 b14 15 16 17 a

-164

-174

-215 ACS Paragon Plusb Environment

a

150

Free energy (meV)

Page 23 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23


Epitaxial

100

Unstrained 50 0 -50 -100 -150

0

100 200 Plus 300 400 500 600 700 ACS Paragon Environment

Temperature (K)

30 The Journal of Physical Chemistry Page 24 of 25 0

Hrel (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

-30 -60 -90

-120 vdW-DF

-150 -180

PBE

ACS Paragon Plus 1 2 Environment 3

SL number

4

Epitaxial Page 25 of 25 The Journal of Physical Chemistry 150

Free energy (meV)

Epitaxial 1 100 2 Non-Epitaxial 3 50 4 5 6 0 7 8Non-Epitaxial -50 9 10 -100 11 12 13 -150 ACS Paragon Plus Environment 14 0 200 400 15 Temperature 16

600

(K)

Energetics and Atomic Structures of Cu2Te Overlayers on CdTe(111

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