Electronic Properties of a New All-Inorganic Perovskite TlPbI_{3} Simulated by the First Principles
- Zhao Liu^{1},
- Ting Zhang^{1},
- Yafei Wang^{1},
- Chenyun Wang^{1},
- Peng Zhang^{1},
- Hojjatollah Sarvari^{2},
- Zhi Chen^{2}Email author and
- Shibin Li^{1}Email author
Received: 28 February 2017
Accepted: 20 March 2017
Published: 29 March 2017
Abstract
All-inorganic perovskites have been recognized as promising photovoltaic materials. We simulated the perovskite material of TlPbI_{3} using ab initio electronic structure calculations. The band gap of 1.33 eV is extremely close to the theoretical optimum value. Compared TlPbI_{3} with CsPbI_{3}, the total energy (−3980 eV) of the former is much lower than the latter. The partial density of states (PDOS) of TlPbI_{3} shows that a strong bond exists between Tl and I, resulting in the lower total energy and more stable existence than CsPbI_{3}.
Keywords
All-inorganic perovskite TlPbI_{3} CsPbI_{3} First principlesBackground
Hybrid organic–inorganic halide perovskites ABX_{3} (A is an organic cation, B is Pb or Sn, and X is a halide) have been widely used as solar cells and attracted enormous interest due to the low-cost and simple solution process for extensive production in the field of photovoltaic (PV) applications. The rapid rise of hybrid organic–inorganic perovskite solar cells has seen photoelectric conversion efficiencies rise from 3.8% [1] to 21.1% [2] in less than 6 years, although the fact that the perovskite absorber layers are subject to degradation because of heat and humidity. To overcome these issues, numerous investigations on enhancing the efficiency [3, 4] and long-term stability [5, 6] have been performed for years [7–12], and now, the perovskite with all-inorganic structure is a primary focus [13]. For solar cells, an appropriate band gap will give a satisfactory efficiency. And the band gap should be narrow enough to absorb a broad solar spectrum from near infrared to visible light. The open-circuit voltage Voc is always lower than the band gap energy because thermodynamic detailed balance requires the cell to be in equilibrium with its environment, which indicates that there is spontaneous light emission from the cell. Considering the two factors, the cubic cesium lead iodide (CsPbI_{3}) is a promising candidate for PV devices. Reference [14] reported the maximum efficiency occurs for a semiconductor with a band gap of 1.34 eV and is 33.7%.
Methods
In theory, the KS equation derived from DFT should be accurate [21]. But in the specific case, as E _{xc} is a function associated with the single electron density \( \rho \left(\overrightarrow{r}\right) \), it is necessary to find a function that can replace the single electron density. We can solve a set of φ _{ i } by taking v _{xc} into the KS equation. Then a new v _{xc} can be calculated with this φ _{ i }. Finally, we submit it into KS equation and solve. Repeat the iteration until a certain accuracy. The key problem is to find the appropriate exchange correlation energy E _{xc}. In the case of different calculation methods of exchange correlation energy E _{xc}, a series of DFT models have been reported [22]. The GGA method is more accurate because it has been combined with inhomogeneous electron gas to obtain \( {E}_x^{B88} \), \( {E}_x^{\mathrm{LYP}} \) and other parameters [23].
of which, X _{0} is the two derivatives of conduction-band bottom. a is the lattice constant. Instead of conduction-band bottom by valance-band maximum, the formula (6) is often applied to solve the effective mass of hole \( \frac{m_p^{*}}{m_0} \) [24].
The Brillouin zone was sampled with a 2 × 2 × 2 k-point set and built by 2 × 2 × 2 supercell. The simulated models using 6s^{2}4f^{14}5d^{10} and 5s^{2}4d^{10}5p^{6} as valence electrons for Tl and Cs, respectively, are carried out. Firstly, we use the ultrasoft pseudopotentials to optimize the Pm3m structures of both TlPbI_{3} and CsPbI_{3.} Then, we calculate the equilibrium volume and proper values of the lattice constants. After optimizing the crystalline structure, we calculate the total energy, band structure, density of states, and carrier concentration for two kinds of materials in the last.
Results and Discussion
The bond distances and bond angels of TlPbI_{3} and CsPbI_{3}
X = Tl | X = Cs | |
---|---|---|
X-Pb | 5.423 Å | 5.475 Å |
X-I | 4.428 Å | 4.471 Å |
Pb-I | 3.131 Å | 3.161 Å |
X-Pb-I | 54.736I | 54.736I |
The total energies of TlPbI_{3} and CsPbI_{3} are −3979.94 − 3154.36 eV independently. The lower total energy means the better stability. Thus, a conclusion that TlPbI_{3} has better stability than CsPbI_{3} is summarized theoretically.
Here, we select the valence-band maximum and conduction-band minimum for further analysis. As shown in Fig. 3b, the curvature of energy band in TlPbI_{3} is less than that in CsPbI_{3}. The conduction band of TlPbI_{3} is relatively smooth and conducive to receive electron from valence band, enhancing the existence of carries.
As illustrated in Fig. 4a–c, the conduction-band minimum of CsPbI_{3} is mainly composed by 6p state of Pb, and the valence-band maximum is contributed by 5p states of I. In Fig. 4d–f, the bottom of the conduction band of TlPbI_{3} is mainly composed by both 6p states of Tl and 6p states of Pb, and the top of the valence band is contributed by 5p states of I. As presented in Fig. 4d–f, Tl and I have a strong resonance peaks between −12 and −10 eV, resulting in a deep level state. It also explains why TlPbI_{3} is more stable than CsPbI_{3}.
Conclusions
We simulated the perovskite material of TlPbI_{3} with a band gap of 1.33 eV using ab initio electronic structure calculations and the band gap is extremely close to the theoretical optimum value. Compared TlPbI_{3} with CsPbI_{3}, the total energy (−3980 eV) of the former is much lower than the latter. The partial density of states (PDOS) of TlPbI_{3} shows that a strong bond exists between Tl and I, resulting in the lower total energy and more stable than CsPbI_{3}. Besides, we calculated the carrier concentration and found both the two materials have similar carrier concentration ranged from −20 to 50 °C.
Declarations
Acknowledgements
This work was supported by the National Natural Science Foundation of China under grant nos. 61421002, 61574029, and 61371046. This work was also partially supported by the University of Kentucky.
Authors’ Contributions
ZL designed and carried out the simulations. ZL and TZ participated in the work to analyze the data and prepared the manuscript initially. YW, CW, PZ, HS, ZC, and SL gave equipment support. All authors read and approved the final manuscript.
Competing Interests
The authors declare that they have no competing interests.
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