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Cluster-Assembled Semiconductor CdO Polymorph with Good Ductility, High Carrier Mobility and Promising Optical Properties Ruotong Zhang, Tielei Song, Zhifeng Liu, and Xin Cui J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07448 • Publication Date (Web): 25 Sep 2018 Downloaded from http://pubs.acs.org on September 27, 2018

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The Journal of Physical Chemistry

Cluster-Asembled Semiconductor CdO Polymorph with Good Ductility, High Carrier Mobility and Promising Optical Properties Ruotong Zhang, Tielei Song,* Zhifeng Liu and Xin Cui School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China *Address correspondence to [email protected]

Abstract Recently, the magic cluster Cd12O12 with cage-like structure has been experimentally synthesized, which is expected to serve as building block of desirable new material. Based on cluster-assembled bottom-up approach, herein we construct four kinds of stable low-density CdO polymorphs (i.e., SOD, LTA, FAU and EMT), which are energetically more stable than the high-pressure B2-CdO phase. In framework, the cage structure of the building block Cd12O12 is well preserved for all of these new phases. Our calculations show that the SOD phase with the lowest energy is mechanically, dynamically and thermally stable (at least to 500 K). Remarkably, the SOD is a very ductile (77 GPa bulk modulus) semiconductor with direct band gap of 1.57 eV. This optimal gap makes the SOD a promising photovoltaic material, which would have large absorption in the visible light region. Furthermore, the calculations of transport properties from deform potential approximation reveal that the SOD phase has not only lower effective mass, but also higher electron-dominated mobility (up to 9.6×103 cm2V-1s-1) with respect to that of the conventional CdO phases. These results highlight a bottom-up way to obtain the desired optoelectronic materials with cluster serving as building block.

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1 Introduction Different crystal structures (so-called polymorphs or phases) of the same composition usually exhibit distinct properties.1-3 Taking solid carbon as an example, the hexagonal layered phase (graphite) is very soft and can be employed as a lubricant, while the cubic structure (diamond) is extremely hard and is often used as an industrial cutting tool. The isoelectronic silicon can also exist in more than one crystalline allotropic form performing much different electronic properties.4-6 For instance, the diamond silicon (α-Si) is an indirect band gap semiconductor, and the recently synthesized open-framework Si24 (oC24) is reported to have a direct band gap of 1.3 eV.4 From these facts, one can realize that synthesizing or predicting a new stable polymorph is very significant for a conventional compound, which may greatly extend the range of properties and applications, and has potential to open a new research field for the development of advanced functional devices. Keeping this in mind, more and more efforts have been devoted to finding new structural modifications for various compounds.7-9 In experiments, some useful methods such as high pressure-induced phase transition,10 low temperature synthesis,11 and mechanical annealing12 have been extensively employed to find new phases. As for theory, the crystalline phase predictions from first principles calculations combined with various algorithms have also been wildly reported, which includes global optimization algorithm,13 particle swarm optimization algorithm,14,15 genetic algorithm,16 and so on. Compared with these theoretical methods, the bottom-up cluster-assembled approach is more interesting, due to the following two points. (i) The properties of building block clusters can be effectively tailored through the selection of geometry, size, charge state and composition.17-20 Therefore some magic clusters can mimic the chemical behavior of the traditional element in the periodic table, which is referred to as superatoms

21,22

. Nowaday, more and more efforts have been devoted to discovery

new superatoms, hoping to extend the scope of the third-dimension (3D) periodic table.20,23,24 Taking the element (i.e., superatom cluster) in such 3D table as building block, our ultimate goal is to design new materials with desired properties. (ii) The ACS Paragon Plus Environment

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manner of assembly often greatly influence the framework and electronic properties of the corresponding assembled materials. For example, our previous work show that the cage semiconductor clusters (i.e., Zn12O12 and Zn16O16) can construct the rare low-density frameworks of inorganic solid ZnO.25 Using As7- as building blocks, Chaki et al.

26

synthesized a series of cluster-assembled ionic solids with different

architectures, which have band gap energy ranging from 1.69 to 1.98 eV. As a matter of fact, cluster-assembly has become one of promising approaches to predict or discovery new phases. Recently, the small semiconductor CdO clusters have been synthesized,27 and their structural and electronic properties have been characterized by conventional and time-resolved spectroscopy combined with density functional calculations. The results show that these small clusters can serve as the potential candidates for building new cluster-assembled materials with needed properties. Inspired by this experiment, in this work we chose the interesting sodalite cage cluster Cd12O12 as the building block to construct the possible metastable CdO polymorphs with promising application in photoelectronics. Moreover, the motivation of our work is also based on the fact that there are scarce studies about CdO polymorphs, especially about the low-density phases.28-30 Although the CdO has applications similar to that of other II-VI semiconductor (e.g., ZnO), it is unique in that its ground state structure is neither wurtzite (B4) nor zinc blende (B3), but it crystallizes in a cubic rocksalt (B1) lattice like sodium chloride, with octahedral cation and anion centers.31-33 In order to clarify the high pressure structures of CdO, the first-principles total energy calculations of various CdO polymorphs, such as B1, cinnabar, orthorhombic cmcm, cesium chloride (B2), nickel arsenide, B3 and B4) have been carried by Guerrero-Moreno et al.31 Different from the CdSe and CdTe, the stable orthorhombic cmcm and cinnabar structures34 are not exist for CdO. Under the high pressure of 89 GPa, the ground state B1 would transform to B2 phase. With respect to the B1 phase, the conventional B3 and B4 phase of CdO possesses lower mass density. From this point, one may naturally ask that whether there exist unconventional low-density phases which hold good stability ACS Paragon Plus Environment


and better physical properties so as to enrich the application of CdO compound. Inspired by this question, we construct four cluster-assembled polymorphs taking the synthesized Cd12O12 as building block. Interestingly, all of them are energetically more stable than the high-pressure and high density B2-CdO phase. More importantly, among these new phase the most stable SOD phase is characterized as a ductile semiconductor with direct band gap of 1.57 eV. Such optimal band gap makes the SOD phase a promising photovoltaic material. The stabilities, mechanical properties and transport properties for this exciting phase are presented in following discussion. 2 Computational details In this paper, our first-principles calculations on cluster-assembled materials are performed using the plane-wave pseudopotential density functional theory as implemented in Vienna ab initio Simulation Package (VASP code).35 Electronic exchange and correlation effects are treated with the generalized-gradient approximation (GGA) functional introduced by Perdew, Burke, and Ernzerhof (PBE).36 The electron–ion interaction is described by projector-augmented-wave (PAW) method.37 The energy cutoff, convergence criteria for energy and force are set to 500 eV, 10-4 eV and 0.02 eV/Å, respectively. The Brillouin zone is represented by the Monkhorst-Pack special k-point scheme with a gird density of 2π × 0.02 Å-1. Ionic relaxation is performed with the standard conjugated gradient algorithm. The phonon spectrum are performed using the finite displacement method implemented in the Phonopy code.38 3 Results and discussions 3.1 Crystal structure and stability Taking the synthesized Cd12O12 cluster

27

as the building block, we construct four

kinds of assembled phases through four types intercluster interactions (i.e., H1, H2, C and S) like the case of ZnO.25 The optimized primitive cells together with the coordination of building block are illustrated in Figure 1. One can clearly see that the


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sodalite cage structure of isolated Cd12O12 is stable enough to survive in all of the proposed phases without structural collapse. In them, each Cd(O) atom has four O (Cd) neighbors forming sp3-like hybridization, which is different from B1-CdO having a 6-fold-coordinated environment for every atom. Therefore, these assembled phases have nanoporous and lower-density features (see the density ρ in Table 1) with respect to the traditional phases. Once these new low-density phases are synthesized in experiment, the special porous structure will make them have a great prospect of application in endohedral doping, atom transport, and heterogeneous catalysis.

Table 1. The structural parameters, i.e., space group S, lattice constants ( a and c in Å), mass density (ρ in g/cm3) and volume per CdO unit ( Å3) and cohesive energy per CdO unit (eV/CdO) for the clustered-assembled phases SOD, LTA, FAU and EMT. For comparison the corresponding data for the conventional phases including B1, B2, B3 and B4 are also provided. Previous calculated values are presented in the parenthesis brackets. Phases

S

a

SOD

Pm3n (223)

LTA

c

ρ

V0

E0

6.31

5.12

42.0

-7.788

Fm3c (226)

10.70

5.91

51.1

-7.693

FAU

Fd3 (203)

11.17

5.19

58.1

-7.620

EMT

P31c (163)

11.96

4.52

58.1

-7.620

B1

Fm3m (225)

4.78

8.28

27.40

-7.909

19.3

(4.777)39 B2

Pm3m (221)

(27.150)31 8.92

2.94 (2.936)39

B3

F43m (216) P63mc (186)

6.22

5.157 3.638

-7.118

(25.410)31

(5.150)31 B4

25.49

5.82

6.39

(3.660)31


34.30

-7.875

(34.10)40

(-7.80)40

34.28

-7.896

(33.99)40

(-7.82)40


Fig. 1 The atomic structures for the four considered Cd12O12-assembled phases (the acronyms of SOD, LTA, FAU, and EMT are named according to the nomenclature of the International Zeolite Association) constructed from the possible intercluster interactions (i.e., H1, H2, C and S). The corresponding structural parameters are provided in Table 1.

To examine the energy stability of these Cd12O12-assembled structures, we have calculated the total energy versus volume by introducing isotropic deformations. As is illustrated in Figure 2a, one can find that the B1 phase occupies the lowest equilibrium energy, indicating that it is the most stable phase among all the considered phases. This is consistent with the theoretical result that B1 is the ground state structure of CdO at room temperature.31 Additionally, one can see that all the cluster-assembled phases are metastable with respect to the ground state B1. Among these assembled low-density phases, SOD is the most stable one holding the lowest energy [E0 (SOD) < E0 (LTA) < E0 (FAU) ≈ E0 (EMT)]. It should be noted that all of them are more stable than the high-pressure phase B2, implying that there are no energetic limitations in experimental synthesis relative to high-pressure phase. Therefore, we believe that these cluster-assembled phases would be the attractive synthesis targets in experiment like the case of high-pressure phase for the II-VI semiconductor compound.10


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Fig. 2 (a) Total energy versus volume for the considered phases of CdO, in which the curves are obtained using the third-order Birch−Murnaghan EOS.41 (b) The phonon dispersion curves and (c) the fluctuations of potential energy as a function of the molecular dynamic simulation steps at 500 K for the SOD phase which has the lowest energy among the clusters-assembled phases. (d) The relative enthalpies ΔH of SOD with respect to B1 as a function of pressure. For comparison, the corresponding ΔH of conventional B3 and B4 phases are also presented.

Since these assembled phases have similar structural characteristics (holding the same building block and sp3-like Cd-O hybridization), our following discussion will just focus on the SOD phase which has the lowest total energy (see Figure 2a). Generally, the energy stability of a structure can not ensure that it is also dynamically and thermally stable. In order to scrutinize whether the SOD phase is dynamically stable, we calculate its phonon spectrum by the finite displacement method linear response method.38 As is shown in Figure 2b, the absence of imaginary frequency



confirms that SOD phase is dynamically stable, indicating that the SOD structure corresponds to a minimum on the potential energy surface (PES). Furthermore, one may wander whether the PES minimum is deep enough to avoid the undesired phase transition when the surrounding temperature elevates. This can be examined by the first-principles molecular dynamics simulations (FPMDs). By constructing a 2×2×3 supercell containing 144 atoms, we perform the FPMDs at 500 K with a Nosé-Hoover thermostat. During the whole simulation times (5000 fs) with a time step of 1fs, no geometry reconstruction can be found except for some thermal fluctuations. This can be confirmed by the variation trend of potential energy and the snapshot of the structure at the end of the simulation (see Figure 2c). As a result, we can conclude that the SOD phase holds good thermal stability and can survive at least to 500 K. In addition to energetic, dynamic and thermal stability, the mechanical stability is also very significant for the practical application of a proposed new phase. Keeping this in mind, we compute the independent elastic constants of SOD phase from the strain-stress relationship.42 The value of C11, C12 and C44 is 112, 60 and 12 GPa, respectively. Interestingly, these values can well satisfy the mechanical stability criteria43 of a cubic phase, i.e., C11 > 0, C44 > 0, C11 > C12 and (C11+2C12) > 0, indicating that the SOD is mechanical stable. Moreover, the relative enthalpies versus pressure for the SOD phase with respect to the ground state B1 phase are also calculated to scrutinize the relative stability under different mechanical pressure. Since the Gibb’s free energy G is expressed as G = E + PV − TS, it should be equal to the enthalpy (H = E + PV) when T = 0 K. Therefore, the more stable phase at a given pressure should have the lower enthalpy value. As is illustrated in Figure 2d, the SOD phase is more stable than B1 in the negative pressure range (P < −1.87 GPa). This means that one can stabilize the SOD phase from the ground state B1 phase by triaxial tensile stress (making negative pressure environment). When the pressure is lower than −3.23 GPa, the SOD phase is even more stable than all the considered conventional phases. 3.2 Mechanical properties


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Derived from the computed elastic constants, then the mechanical parameters including bulk modulus B, shear modulus G, Yang's modulus E and Poisson’s ratio v are calculated for SOD phase. The bulk modulus B and shear modulus G are averaged according to Hill schemes.44 The Young’s modulus E is acquired through Hill approximation from the bulk modulus B and the shear modulus G, so as the Poisson’s ratio.45 The calculated results are listed in Table 2. Interestingly, the bulk modulus of SOD is 77 GPa, which is smaller than all of the conventional CdO phases and is only approximately 60% of that of the ground state B1 phase. This implies that the assembled low-density SOD phase possesses ultralow stiffness and better ductility with respect to the conventional phases. Usually, the ratio B/G is employed to distinguish between ductile and brittle materials. As Pugh proposed,46 a high (low) ratio B/G value is associated with good ductility (brittleness), and the critical value is about 1.75. The ratio B/G of SOD is about 4.28, which is much higher than that of B1 phase, implying that SOD has high ductile nature. Moreover, the Poisson’s ratio of a material can also be used to judge the brittleness/ductility. According to the Frantsevich rule, a large (small) Poisson’s ratio corresponds to ductility (brittleness), and the critical value is about 1/3. The calculated Poisson’s ratio of the SOD is 0.39, which also indicates that the SOD phase is more ductile than B1 phase. This agrees well with the estimation based on the B/G ratio. Table 2. The elastic constants Cij (GPa), bulk modulus B (GPa), shear modulus G (GPa) calculated by Hill approximation, and Poisson’s ratio ν for the cubic SOD phase. For comparison, the corresponding results of the ground state B1 phase with available theoretical values (listed in the parenthesis brackets) are also presented. Polymorphs

C11

C12

C44

B

G

E

B/G

v

SOD

112

60

12

77

18

50

4.28

0.39

B1

189

99

48

129

47

125

2.74

0.33

(190.91)30

(101.94)30

(48.06)30



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For practical engineering application, the anisotropy of mechanical properties is significant to a proposed material. In order to clarify the anisotropic properties of SOD phase, we calculate the surface contours of direction-dependent Young’s modulus based on the following equation: 1 s  s11  2( s11  s12  44 )( l12l22  l22l32  l32l32 ) E 2

where sij is the inverse of elastic constant matrix Cij; l   sin   sin 

(1) l   sin   cos  ,

and l   cos  refer to the directional parameters to three principal

axes. As illustrated in Figure 3a, the obvious anisotropy can be seen clearly. Using the Zener anisotropic index47 defined as Z = 2C44/(C11– C12), we can further describe the elastic anisotropy of SOD phase in quantitative. For an isotropic material, the Zener factor is equal to 1. When Z is larger than 1, the maximum Young’s modulus should be along [111] direction for a cubic crystals. If it is smaller than 1, the maximum value should be along [100] direction. The computed Zener ratio of SOD phase is 0.46, consisting with the anisotropy of Young’s modulus displayed in Figure 3a. Specifically, the maximum Young’s modulus (71 GPa) is along [100] direction, while the minimum Young’s modulus (35 GPa) is along the direction of [111].

Fig. 3 (a) Surface contours of Young’s modulus in different directions and (b) shear modulus on different planes [i.e., (111), (110) and (100)] for SOD polymorph.


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Furthermore, the anisotropic behavior of shear modulus G has important effect on the material toughening, thus it is worth to make a detail discussion about the anisotropy of G for the proposed SOD phase. The direction dependent G for a cubic system is defined as:

1 = 4 s11( l12 m12 + l22m22 + l32 m32 ) + 8s12 ( l1l2m1m2 + l1l3m1m3 + l2l3m2m3 ) + G s44[( l1m2 + l2 m1 ) 2 + ( l1m3 + l3m1 ) 2 + ( l2 m3 + l3m2 ) 2 ]

(2)

where m1, m2 and m3 represent the directional parameters for the three principal axes ( m   cos  cos  cos   sin  sin  , m   cos  sin  cos   cos  sin  , m  sin cos , in which χ is defined as the shear orientation on the particular plane determined by θ and φ). It is interesting that the (100) and (111) planes are isotropic (see Figure 3b), while the (110) plane shown high degree of anisotropy. To quantitatively elucidate the anisotropy of the considered planes, a shear anisotropic index (ZG) can also be defined like the case of Young’s modulus: ZG=Gmax/Gmin. For the isotropic (100) and (111) planes the ZG is equal to 1. As for the (110) plane, the maximum of shear is 26 GPa, and the minimum is 12 GPa. The deduced ZG is 2.15, indicating that the shear modulus of the corresponding plane has high isotropy. 3.3 Electronic structure and optical properties To explore the performance of optical absorption, we firstly calculate the electronic band structure of SOD phase because the conversion efficiency of a photovoltaic material is closely related to the band. The computed band structure of SOD from the GGA/PBE method is plotted in Figure 4a. One can see that SOD is a direct band gap semiconductor with the conduction band minimum (CBM) and valence band maximum (VBM) located at the Γ (0, 0, 0) point. The value of band gap is calculated to be 0.30 eV at GGA/PBE theory level which usually significantly underestimates the band gap. Since the HSE06 functional48 has been shown to predict much better electronic properties than GGA/PBE, here we recompute the calculation



of band structure (see Figure 4b). Interestingly, the band gap increases up to 1.57 eV, which is much larger than that of B1 phase (0.8 eV from HSE06). To provide more detail insight into the electronic structure of SOD phase, we also calculate the orbital-resolved band structures for different orbits of Cd and O atoms. From Figures 4c and 4c, one can find that the VBM is mainly contributed by the localized O2p and Cd4d states. This means that there has strong p-d hybridization in the SOD phase, resulting in that there exist heavy hole band. As for CBM, the unlocalized Os and Cds orbits are the main components, which is feasible for forming linear-like dispersion and light electron band.

Fig. 4 Electronic band structures of SOD from GGA/PBE (a) and HSE06 (b) methods. Orbital-resolved electronic band structures for different orbits of Cd (c) and O (d) atoms at the GGA/PBE theory level.


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It has been well confirmed that a semiconductor with a direct band gap about 1.40 eV is most suitable for use as solar absorption material.49,50 Remarkably, the direct band gap (1.57 eV) of our proposed SOD phase is almost identical with that of the proposed Si20-T phase50 (1.55 eV) and very close to the optimal value. On the basis of this fact, the imaginary part (see Figure 5a) of the dielectric function of SOD from the HSE06 is calculated for measuring the optical absorption performance. As we can see, the optical absorption in SOD just starts at the direct gap transition energy of 1.57 eV, which means that the direct gap transition in SOD is dipole allowed. More importantly, there is much higher absorption in the visible light region (see the shaded area with "Visible" mark in Figure 5a). This is highly desirable for the solar cell application with high photoelectric transformation efficiency. Although the exciton effect may change the shape of the absorption curve in the low energy region, the basic optical absorption ability of SOD should remain almost the same like the case found in the semiconductor silicon.51 This can be understood by the fact that the SOD phase has the isoelectronic properties and the sp3-like tetracoordinated bonds like the silicon phase. From the above discussions, it is reasonable to believe that the SOD phase would be a promising candidate for making high-efficiency solar cells.

Fig. 5 (a) Imaginary part of dielectric functions from the HSE06 calculation for SOD phase. (b) Carrier (electron) mobility of SOD phase compared with that of the considered conventional phases, i.e., B1, B3 and B4.



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3.4 Carrier mobility Generally, in a solar cell the recombination between electron and hole would largely decrease the solar conversion efficiency after producing photoelectrons. In this context, large carrier mobility is desired. To examine whether the SOD phase has large carrier mobility, we perform the necessary calculation for the transport properties of SOD by using the deformation potential approximation (DPA).52 Under DPA, the carrier mobility (μ3D) for a 3D crystal material can be obtained by the following equation:  3D 

23 / 2 1/ 2 C3D  4e 2 *5 / 2 3 El m ( k BT ) 3 / 2

(2)

where El represents the deformation potential constant of VBM for hole and CBM for electron along the transport direction, which can be obtained by investigating the energy change of the corresponding band under lattice compression and dilatation

Table 3. Effective mass mi* (m0), deformation potential Eli (eV), and carrier mobility μi (×103 cm2·V-1·s-1) along the basis vector x, y and z directions for electron and hole of SOD at 300 K. For comparison, the results of conventional phases are also presented. Phase

Carrier type

mx(y)*

SOD

electron

0.17

7.75

9.6000

hole

2.23

8.04

0.0140

electron

0.24

10.83

3.500

B1

mz*

Elx(y)

Elz

μx(y)

μz

0 B3 B4

hole

4.76

6.38

0.0057

electron

0.20

7.82

5.9100

hole

3.92

6.45

0.0050

electron

0.38

0.32

11.42

8.16

0.5580

2.3920

hole

10.26

9.68

7.86

6.97

0.0003

0.0006


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(using a step of 0.5 %). The term m* denotes the effective mass in the transport direction, defined by

1 2E  2 2 * m  k

. C3D is the elastic modulus along the corresponding

transport directions, which refers to the related elastic constants. The eﬀective mass, deformation potential, and carrier mobility of electron and hole along the three basis vector directions are listed in Table 3. Owing to the cubic symmetry, the effective mass of SOD phase displays isotropic characteristic in x, y and z directions, i.e., mx*=my*= mz*. As we can see in Table 3, the effective masses of SOD are smaller than the corresponding value of the conventional phases in any directions, especially for the electron. This derives from the more significant dispersions in band structure along the corresponding directions (see Figure 3a). Since the effective mass can strongly influence the carrier mobility (μ = eτ/m*53), it is natural to deduce that the small effective mass of SOD would induce higher carrier mobility. As is expected, for both electron and hole the carrier mobility of SOD is larger than the corresponding value of the traditional phases. More interestingly, the electron mobility of SOD is as large as 9.6×103 cm2·V-1·s-1 at room temperature, which is about three times larger than the case of ground state B1 phase (see Figure 5a). Additionally, this value is much larger than that of the hotly pursued phosphorene54 and MoS2.55 Therefore, the cluster-assembled SOD would be an ideal photovoltaic material for solar energy conversion. 4. Conclusion Taking the experimentally synthesized Cd12O12 cluster as building block, we predict a class of new low-density CdO phases. Among these phases, the SOD-CdO phase has the lowest energy. Our calculations show that this structure is not only mechanically and dynamically stable, but also thermally stable above room temperature (at least up to 500 K). Interestingly, the SOD-CdO is a soft semiconductor with an optimal direct gap of 1.57 eV for sunlight harvesting. Moreover, the calculation of carrier mobility indicates that the SOD phase has better transport performance (up to ~104 cm2V-1s-1) than the conventional CdO phases.



These results highlight a bottom-up way to obtain the desirable photovoltaic materials with inorganic clusters serving as building blocks.

Acknowledgments This work is currently supported by the National Natural Science Foundation of China (No. 11604165) and Natural Science Foundation of Inner Mongolia (No. 2016BS0104).

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