Optoelectronic Properties Prediction of Lead-Free Methylammonium Alkaline-Earth Perovskite Based on DFT Calculations.

Dynamical stability plays an essential role in phase transition and structure, and it could be a fundamental method of discovering new lead-free perovskite materials. The perovskite materials are well-known for their excellent optoelectronic properties, but the lead element inside could be a hindrance to future development. This research is trying to predict the promising cation candidates in the high-temperature application for lead-free perovskite materials from the replacement of lead in MAPbCl3 (MA = methylammonium) with alkaline-earth cations. The alkaline-earth cations are of a stable positive divalent sort, which is the same as Pb, and most of them are abundant in nature. Therefore, by improving the dynamical stability, the Mg2+, Ca2+, and Sr2+ cations replacement of lead ions could stabilize the perovskite structure by decreasing the imaginary part of phonon density of states. Finally, the density functional theory results show that the MACaCl3 could be a dynamic stable lead-free methylammonium perovskite material with an ultrawide band gap (5.96 eV).

Introduction

Environmentally friendly ultrawide band-gap materials need to be developed for the next-generation ultraviolet C luminescence applications in disinfection, biosensing, and environmental monitoring.[1−5] The organic–inorganic perovskite materials could be potential candidates for ultrawide band-gap optoelectronics due to their excellent carrier mobility and lifetime, high flexibility, and low formation temperature.[6−9] However, there is a lack of high external quantum efficiency (EQE) material for ultraviolet C devices (4.42–12.4 eV), and a new type of organic–inorganic perovskite could offer a solution. The density functional theory (DFT) calculation can determine the electronic structure and phonon dispersion diagram for the electrical and dynamic stability property of new organic–inorganic perovskite structures and determine the possibility for device application.[10−12] Previously, the DFT was typical for explaining experimental results by calculating the band structure.[13−21] However, the DFT is already used to predict new materials,[22−25] and the guidance of a DFT calculation can shorten the development timing and cost. Thus, this research conducts the DFT calculation with the GGA-PBE[26] and sx-LDA[27,28] functionals for new types of lead-free methylammonium (MA, CH3NH3) alkaline-earth perovskite searching. Furthermore, the geometry optimization calculation by the GGA-PBE functional could be a suitable method for moving the atoms and molecules to get the most stable structure with the lowest possible ground-state energy.

The perovskite structure ABX3 has a wide range of tolerance factors (0.8–1) for keeping the same cubic structure with different elements inside.[29−32] Previously, the DFT calculation was conducted for discussing the structure and electronic structure issue of the lead cation replacement with the alkaline-earth cations within MAPbI3.[33] However, the dynamic stability and possible electrical conductivity of the alkaline-earth perovskites are yet to be mentioned. Thus, this research is focused on the dynamic stability, electrical conductivity, and carrier mobility of the methylammonium alkaline-earth perovskite. MAPbCl3 has experimental wide band-gap values such as 2.88 eV (single crystal)[34] with a relatively stable perovskite structure with space group Pm3m. However, the DFT calculation of MAPbCl3 by the sx-LDA functional can offer a 2.74 eV value, which is closer to the experimental value of 2.88 eV. Therefore, this research uses the sx-LDA functional for the lead-free perovskite estimation. On the basis of the wide band-gap property of MAPbCl3, the lead ion will be replaced by alkaline-earth ions and form new perovskite structures. The calculation results demonstrate that the alkaline-earth cations, such as Mg2+, Ca2+, and Sr2+, might be potential candidates for methylammonium lead-free perovskites due to the better dynamic stability and wider band gap of methylammonium lead perovskite.

Results and Discussion

Figure shows the MAPbCl3 and the alkaline-earth cations (Be2+, Mg2+, Ca2+, Sr2+, and Ba2+) that replace lead cation structures, and the precise atom positions and structure parameters are listed in Table S1. The structures after the structure optimization are shown in Figure a–f. Those alkaline-earth cation lead-free structures, after structure optimization, are listed with their parameters in Table S1. Indeed, the MABeCl3 and MAMgCl3 structures are distorted toward two-dimensional perovskites, as shown in Figure b,c. The lattice distortion is huge within the MABeCl3, 12.0%, −33.5%, and 9.1%, in the a-, b-, and c-axis directions, respectively. Therefore, the lattice volume of MABeCl3 undergoes a −19.6% change from the original MAPbCl3 structure and makes MABeCl3 unable to sustain the original structure. MAMgCl3 has the same distortion issue with 13.3% of the crystal volume, caused by three nonequal crystal axes. The other alkaline ion replacements made the lattice volume in MAPbCl3 change by −10.8%, 0.6%, and 14.7% for Ca2+, Sr2+, and Ba2+, respectively. All the structure optimization results about the atom positions within the structures are listed in Table S2. In fact, the lattice distortions are not small, but the calculation results demonstrate that MACaCl3, MASrCl3, and MABaCl3 could still maintain perovskite as the P space group. As for the tolerance factors (Goldschmidt factors) shown in Table , they are better to be 0.8–1 to sustain the perovskite structure and have better stability between 0.94 and 0.98. In Table , MABeCl3 and MAMgCl3 have the Goldschmidt factors higher than 1, making it hard to keep the perovskite structure, and MABaCl3, MAPbCl3, and MASrCl3 can sustain the structure with normal stability. Finally, MACaCl3 gets the most stable Goldschmidt factor of 0.96, probably having better stability for future device applications.

Figure 1

Structures of MAPbCl3 and the alkaline-earth cations replace lead-free perovskite structures. (a) The original MAPbCl3 structure (Pm3m). (b) Be2+ replaced Pb2+, the MABeCl3 structure. (c) Mg2+ replaced Pb2+, the MAMgCl3 structure. (d) Ca2+ replaced Pb2+, the MACaCl3 structure. (e) Sr2+ replaced Pb2+, the MASrCl3 structure. (f) Ba2+ replaced Pb2+, the MABaCl3 structure.

Table 1

Metal Ion Radius, the Energy of the System (E0), the Imaginary Part of Phonon Density of State (DOS), Debye Temperature (θD), and Goldschmidt Factor of Different Structures

	metal ion radius (Å)	Goldschmidt factor	energy of the system, E0 (eV)	imaginary part of phonon DOS (%)	Debye temperature,θD (K)
MAPbCl3	1.33	0.90	–64.25	1.78	102
MABeCl3	0.59	1.20	–54.92	3.94	178
MAMgCl3	0.86	1.07	–53.95	1.30	131
MACaCl3	1.14	0.96	–56.33	0	233
MASrCl3	1.32	0.91	–56.24	0.54	115
MABaCl3	1.49	0.86	–56.47	5.40	108

The phonon dispersion in the crystal has often been studied to determine the dynamic stability of a structure, and a stable structure normally only has positive vibration states within phonon dispersion. Because the crystal bonding energy will lose to negative vibration states within the structure’s phonon vibration, not only will the atomic bonding be broken but also the structure will disappear, finally. Also, the phonon dispersion diagram shows that the positive and negative vibration states can be regarded as real and imaginary states. Thus, the crystals that have negative frequencies might be unstable. The phonon dispersion and phonon density of states (DOSs) diagrams are shown in Figure a–f for MAPbCl3, MABeCl3, MAMgCl3, MACaCl3, MASrCl3, and MABaCl3, respectively. In Figure a, the MAPbCl3 has negative frequencies phonon dispersion, and the imaginary part of the whole phonon DOS is 1.78%, as shown in Table . MAPbCl3 has poor long-term stability under room-temperate ambient conditions. MAMgCl3, MACaCl3, and MASrCl3 have smaller negative frequencies phonon dispersion parts, which means that replacing Mg2+, Ca2+, and Sr2+ can decrease the imaginary part of a phonon DOS from 1.78% to 1.30%, 0%, and 0.54%, as shown in Table . Therefore, Mg2+, Ca2+, and Sr2+ might make the perovskite structure more dynamically stable in future lead-free perovskite devices. The energy of the system in each crystal is listed in Table by calculating under 0 K, and the phonon dispersion of a crystal offers a reliable stability reference. For example, MACaCl3 has 0% of the imaginary part of a phonon DOS, which means it is more stable than others and suitable for a future dynamically stable ultrawide band-gap lead-free perovskite device.

Figure 2

Phonon dispersion diagrams and phonon DOSs of (a) MAPbCl3, (b) MABeCl3, (c) MAMgCl3, (d) MACaCl3, (e) MASrCl3, and (f) MABaCl3 (PBE-GGA).

The formation temperature of an unknown lead-free methylammonium perovskite could guide material synthesis and device fabrication. Further, a thermodynamic calculation can offer the Debye temperature value and the higher Debye temperature (θD) of a crystal that accompanies a higher melting temperature and higher formation temperature. Therefore, the temperature-dependent heat capacity, entropy, and Helmholtz free energy are shown in Figure S1a–c (0–500 K) and Figure S1d–f (0–3000 K). According to the Debye model, the Debye temperature (listed in Table ) could be obtained by the linear relationship of the heat capacity. Hence, the MAMgCl3 (θD = 131 K), MACaCl3 (θD = 233 K), and MASrCl3 (θD = 115 K) structures might need higher formation temperatures than MAPbCl3 (θD = 102 K) for a future experiment due to the higher Debye temperatures.

The electrical band structures of the MAPbCl3 and the alkaline-earth cations (Be2+, Mg2+, Ca2+, Sr2+, and Ba2+) replace lead structures in Figure a–f, with the Fermi levels all set as zero. The critical points of the Brillouin zone within the Pm3m space group of MAPbCl3 and alkaline-earth cation-replaced structures are E (111), A (110), Y (010), Z (001), B (100), Γ (000), and C (011), and Γ is the center point of the Brillouin zone. In Figure , the results are different DFT calculation results using sx-LDA, and the PBE-GGA results are shown in Figure S2. In Figure a, the valence band maximum (VBmax) and conduction band minimum (CBmin) of MAPbCl3 are −0.2 and 2.54 eV on the E (111) critical points. The direct band gap with proper bandwidth makes it a suitable material for a green light optoelectronic device. As for the replaced ones, in Figure b–f, their bandwidths are 5.71, 4.29, 5.96, 5.8, and 5.58 eV. And, MABeCl3 is the only direct band-gap lead-free methylammonium alkaline-earth perovskite.

Figure 3

Electronic band structures and DOSs of (a) MAPbCl3, (b) MABeCl3, (c) MAMgCl3, (d) MACaCl3, (e) MASrCl3, and (f) MABaCl3 (sx-LDA).

In Table , except for MAPbCl3 (453 nm), all methylammonium alkaline-earth perovskites have the ultraviolet C range (100–280 nm) properties. In Table , the band gap of MAPbCl3 is 2.74 eV with 5.1% deviation from the experimental results by 2.88 eV (single crystal).[34] Therefore, the DFT band gap calculation using the sx-LDA functional has a low deviation (5.1%) with the thin-film experimental result and could be used to predict the band gaps of methylammonium perovskites in which lead was replaced with alkaline-earth cations. Furthermore, MAMgCl3 has the lowest band gap (4.29 eV), while the other materials have band gaps that are each more than 5 eV. This might be caused by the different ion radii and the electron orbits. Indeed, the Goldschmidt factor of MAMgCl3 is slightly larger than 1, at 1.07, and this might be the reason for the influence of the orbital and band gap. According to different Goldschmidt factor values, structure variations might change the band gaps.

Table 2

Semiconductor Band Information of MAPbCl3, MABeCl3, MAMgCl3, MACaCl3, MASrCl3, and MABaCl3

sx-LDA	VBmax (eV)	CBmin (eV)	carrier transfer (VBmaxto CBmin)	band gap (eV/nm)
MAPbCl3	–0.20	2.54	(111) to (111)	2.74/453
MABeCl3	–0.21	5.48	(000) to (000)	5.71/217
MAMgCl3	–0.22	4.06	(111) to (000)	4.29/289
MACaCl3	–0.22	5.73	(110) to (000)	5.96/208
MASrCl3	–0.21	5.58	(111) to (000)	5.80/214
MABaCl3	–0.21	5.37	(111) to (000)	5.58/222

The calculated X-ray diffraction pattern of stability-improved alkaline-earth cation perovskites MAMgCl3, MACaCl3, and MASrCl3 are shown in Figure a–c, and the three prominent peaks are 29.9°, 26.0°, and 27.5° (in 2θ) for MAMgCl3, 32.5°, 16.1°, and 31.5° (in 2θ) for MACaCl3, and 15.4°, 31.1°, and 30.2° (in 2θ) for MASrCl3. These data are the reference for future syntheses and device applications. Figure d shows the temperature-dependent electrical conductivity of MAPbCl3 and the alkaline-earth cations (Be2+, Mg2+, Ca2+, Sr2+, and Ba2+) that replace lead structures. The exact values are listed in Table . Indeed, MAPbCl3 has a theoretical electrical conductivity of 2.8 × 10–6 Ω –1m–1 (at 300 K), which is close to the room temperature experimental electrical conductivity of MAPbCl3, which is 2.7 × 10–6 Ω –1 m–1.[34] Those results convince us that the DFT calculations can offer theoretical electrical conductivity values for unknown alkaline-earth cations in the replacement of lead in perovskite structure estimations. The alkaline-earth cation replacements can increase the band gap, as can be seen in Figure , but decrease the electrical conductivity, and MAMgCl3 has the highest electrical conductivity compared to the other alkaline-earth cation perovskites in Table . And, the lead-free methylammonium alkaline-earth perovskites might be suitable for high-temperature devices and applications. At 1000 K, the calculated electrical conductivities of MAPbCl3, MABeCl3, MAMgCl3, MACaCl3, MASrCl3, and MABaCl3 are 9.57, 5.93 × 10–7, 6.38 × 10–3, 2.70 × 10–8, 3.84 × 10–7, and 3.00 × 10–7 Ω –1 m–1, respectively.

Figure 4

X-ray diffraction patterns and temperature-dependent electrical conductivity, carrier mobility, and carrier density of the alkaline-earth cation replacement structures. (a) MAMgCl3 diffraction pattern. (b) MACaCl3 diffraction pattern. (b) MASrCl3 diffraction pattern. (d–f) Temperature-dependent electrical conductivity, carrier mobility, and carrier density of MAPbCl3 and the alkaline-earth lead-free perovskite structures.

Table 3

Temperature-Dependent Electrical Conductivity of MAPbCl3, MABeCl3, MAMgCl3, MACaCl3, MASrCl3, and MABaCl3

T (K)	MAPbCl3 (Ω–1 m–1)	MABeCl3 (Ω–1 m–1)	MAMgCl3 (Ω–1 m–1)	MACaCl3 (Ω–1 m–1)	MASrCl3 (Ω–1 m–1)	MABaCl3 (Ω–1 m–1)
300	2.80 × 10–6	0	0	0	0	0
400	4.86 × 10–4	0	3.18 × 10–32	0	0	0
500	1.15 × 10–2	0	2.37 × 10–9	0	0	0
600	9.97 × l0–2	6.40 × 10–34	3.13 × 10–7	0	0	5.27 × 10–36
700	0.48	4.54 × 10–31	1.05 × 10–5	1.94 × 10–33	1.95 × 10–31	1.68 × 10–31
800	1.64	1.55 × 10–9	1.49 × 10–4	5.48 × 10–31	7.92 × 10–10	6.52 × 10–10
900	4.32	4.20 × 10–8	1.19 × 10–3	1.24 × 10–9	2.45 × 10–8	1.95 × 10–8
1000	9.57	5.93 × 10–7	6.38 × 10–3	2.70 × 10–8	3.84 × 10–7	3.00 × l0–7

Figure e shows the temperature-dependent carrier mobility, and the values are listed in Table . The alkaline-earth cations that replace lead will increase the carrier mobilities within the structures. For discussing the carrier mobility deviations between experiment and calculation, the experimental carrier mobility of MAPbCl3 at 300 K is 4.14 (cm2 V–1 s–1),[35] which is close to the calculated result (5.2 cm2 V–1 s–1). MAMgCl3 has the highest carrier mobility within the alkaline-earth cation perovskites, namely, 0.04 cm2 V–1 s–1 at 500 K. The most stable MACaCl3 has the carrier mobility of 0.24 cm2 V–1 s–1 at 900 K. These indicate that MAMgCl3 could be applied in an ultraviolet C luminescence device with a 289 nm emission peak, and the carrier mobility might be 0.04 cm2 V–1 s–1 under 500 K. Still, the MACaCl3 device needs to operate under a higher temperature such as 900 K. Finally, this research predicts the alkaline-earth cation perovskite might be helpful according to the calculated carrier mobility. The carrier density values of MAPbCl3 and alkaline-earth cation-replaced structures are shown in Figure f. MAPbCl3 has the largest and constant carrier density (7.2 × 1019 electron/cm3) below 1500 K, and the same trend occurs with MAMgCl3 with lower carrier density (5 × 1019 electron/cm3). MACaCl3 and MABeCl3 have much lower amounts (3.5 × 1019 and 2.75 × 1019 electron/cm3) with opposite signs. On the contrary, MASrCl3 and MABaCl3 have nearly zero. And, the results show that MAPbCl3, MAMgCl3, and MASrCl3 are n-type semiconductors with the electron as the dominant carrier. MABeCl3, MACaCl3, and MABaCl3 are p-type semiconductors with the hole as the dominant carrier with negative carrier (electron) density.

Table 4

Temperature-Dependent Carrier Mobility of MAPbCl3, MABeCl3, MAMgCl3, MACaCl3, MASrCl3, and MABaCl3

T (K)	MAPbCl3 (cm2 V–1 s–1)	MABeCl3 (cm2 V–1 s–1)	MAMgCl3 (cm2 V–1 s–1)	MACaCl3 (cm2 V–1 s–1)	MASrCl3 (cm2 V–1 s–1)	MABaCl3 (cm2 V–1 s–1)
300	5.20	0	0	0	0	0
400	4.81	0	0	0	0	0
500	4.53	0	0.04	0	0	0
600	0.31	0	0.14	0	0	0
700	4.12	0	0.21	0	0	0
800	3.95	0.22	0.23	0	0.18	0.13
900	3.79	0.17	0.22	0.24	0.17	0.13
1000	3.64	0.12	0.18	0.23	0.16	0.12

Conclusions

This research tries to determine the possibility of the alkaline-earth cation perovskite as a potential lead-free ultrawide band-gap perovskite material according to the calculated dynamic structure stability, electrical conductivity, and carrier mobility. The Mg2+, Ca2+, and Sr2+ cation replacements of Pb2+ cation could improve the dynamic stability by reducing the imaginary part of the phonon DOSs. MACaCl3 is the most dynamically stable alkaline-earth cation perovskite; it not only has a Goldschmidt factor of 0.96 (lower deviation than 1) but also has the imaginary part phonon DOS of 0%. Our results point out that the imaginary part of phonon DOS could be a factor in evaluating the crystal stability of perovskite. The DFT calculation results of MAPbCl3 perovskite structures have calculated electrical conductivity and carrier mobility results close to the experiment results. Hence, the MACaCl3 structure could be predicted with a 5.96 eV band gap and with the electrical conductivity and carrier mobility as 1.24 × 10–9 Ω–1 m–1 and 0.24 cm2 V–1 S–1, respectively, at 900 K. Our calculation results shows that the MACaCl3 is a dynamic stable structure and could be a candidate for ultrawide band-gap high-temperature applications in the future.

Methods

The density functional theory calculations are processed by Vienna ab initio Simulation Package (VASP),[36−38] and different exchange-correlation functionals (GGA-PBE and sx-LDA) are chosen. The structural optimization is set up with a default plane-wave cutoff energy of 520 eV; the requested k-spacing is 0.2 per angstrom, which leads to a 6 × 6 × 6 mesh, and we are using first-order Methfessel-Paxton smearing with a width of 0.2 eV. Typically, the percentage of volume change from the original input cell toward the structural optimization cell is less than 20%. Then, the optimized structures were calculated by the functional of sx-LDA for a discussion of other electronic band structures. The calculation is set with 6 × 6 × 6 k-spacing mesh and Gaussian smearing width of 0.05 eV. The phonon and related calculations were processed by GGA-PBE, with the plane-wave cutoff of 500 eV and k-spacing of 5 × 5 × 5 mesh, and the Methfessel-Paxton smearing width was set as 0.2 eV. The semiconductor properties (electrical conductivity, carrier mobility, and carrier density) were calculated within Boltzmann’s transport theory, processed by GGAPBE, applying BoltzTraP based on the k-mesh and bands used for the Fermi surface above, with the chemical potential setting at 11 mu within 26 functions. The X-ray diffraction pattern calculation used the software Mercury.