2D Ruddlesden–Popper X-FPEA₂PbI₄ perovskites for highly stable PeLED with improved opto-electro-mechanical properties

Abstract

We investigate the opto-electro-mechanical characteristics and stability of Ruddlesden–Popper X-FPEA₂PbI₄ perovskites, where X represents para (p), meso (m), and ortho (o) configurations. The findings reveal that the transition from para to meso and ortho configurations results in a progressive increase in the bandgap, with values of 2.097 eV, 2.133 eV, and 2.177 eV, respectively. Notably, p-FPEA₂PbI₄ exhibits superior stability, characterized by an enhanced formation energy of − 4.825 eV, compared to m-FPEA₂PbI₄ (− 4.647 eV) and o-FPEA₂PbI₄ (− 4.581 eV). Thus, p-FPEA₂PbI₄ emerges as a leading candidate for the active layer in perovskite light-emitting diodes (PeLEDs). Internal quantum efficiencies of 6.289% for PEA₂PbI₄ and 2.285% for p-FPEA₂PbI₄ have been achieved, both of which are higher than those of MAPbI₃. In contrast, the dependence of efficiency on temperature fluctuations for p-FPEA₂PbI₄ is 0.01 1/K, compared to PEA₂PbI₄’s 0.0282 1/K, highlighting its enhanced stability under temperature changes. Furthermore, the stability of the emission spectrum against temperature fluctuations for p-FPEA₂PbI₄, with a value of 0.0156 nm/K, is greater than that of PEA₂PbI₄, which has a value of 0.0245 nm/K. Although the efficiency of PeLEDs utilizing p-FPEA₂PbI₄ is somewhat lower than that of PEA₂PbI₄, its superior stability makes it a compelling choice for future applications, paving the way for more reliable and durable light-emitting devices.

Introduction

Direct and tunable bandgap, easy fabrication, low cost, and color purity are the significant properties of metal halide perovskite. The metal halide perovskites have been widely used in different applications, including light-emitting diodes (LEDs), solar cells, lasers, and sensors^{1,2,3,4,5,6,7,8,9}. The quasi-two-dimensional perovskites with Ruddlesden–Popper (RP) phase have the chemical formula of L₂A_n−1B_nX_3n+1, where L is a spacer cation, A is a small cation, B is a divalent metal cation, and X is a halide anion. The value of n shows the number of perovskite layers sandwiched between L cations. The quasi-2D perovskites are similar to multiple quantum wells (MQWs), and the width of the quantum well can be adjusted by the amount of n. The chemical formula of 2D perovskite is L₂BX₄ (n = 1). In this structure, L₂ and BX₄ represent the quantum barrier and the quantum well, respectively¹⁰.

The perovskite light emitting diode (PeLED) consists of a perovskite active layer sandwiched between the electron transport layer (ETL), and the hole transport layer (HTL). By applying a forward bias to PeLED, electrons and holes are injected into the active layer from the cathode side through the ETL and the anode side through the HTL, respectively. Subsequently, the electrons and holes recombine in the active region, leading the photon generation by the phenomenon of spontaneous emission¹¹. The main challenge of PeLEDs is their low stability. The most critical factor of its short lifetime is the instability of the active material. 2D perovskites are more stable than 3D perovskites¹². Also, the 2D perovskites with aromatic cations, such as phenylethylammonium (PEA), are more stable than aliphatic cations, such as butylammonium (BA)¹³. The fluorophenethylamine (FPEA) (FC₆H₄(CH₂)₂NH₃) aromatic cation is formed by replacing one hydrogen atom in the aromatic ring of the PEA (C₆H₅(CH₂)₂NH₃) cation with a fluorine (F) atom. The 2D perovskite with FPEA aromatic cation is more stable than PEA because the ionic radius of F is larger than that of hydrogen and the length of the cation in FPEA is larger than that of PEA¹³. Therefore, regarding stability, FPEA₂PbI₄ is a suitable option for use in the active layer of PeLED. To the best of our knowledge, the simulation of PeLED with 2D perovskites has not been done so far.

Some studies investigated the properties of 2D perovskite materials. The optical and electronic properties of BA₂PbX₄ are investigated with density functional theory (DFT) calculations by Silver et al.¹⁴. C. Song, et al.¹⁵ studied the electronic and optical properties of p-FPEA₂PbI₄ with DFT calculations. In another work, the mechanical properties of BZA₂PbI₄ perovskite were computed by DFT calculations¹⁶. In our previous work, we demonstrated that among the RP 2D perovskites with L₂PbI₄ formula (L = PEA, FPEA, BA, and BZA), FPEA₂PbI₄ exhibits greater thermodynamic, mechanical, and moisture stabilities, attributed to the presence of a fluorine atom in its structure¹². Consequently, altering the position of the fluorine atom can influence various properties of this material. Therefore, there is a need to thoroughly investigate the properties of X-FPEA₂PbI₄ (X = p, m, and o) perovskites to understand more about this material for use in different applications.

In this study, we investigate the optical, mechanical, and electronic properties, as well as the thermodynamic, thermal, and moisture stability of 2D Ruddlesden popper (RP) perovskites with the chemical formula of X-FPEA₂PbI₄ (X = p, m, and o). We utilize density functional theory calculations to assess their potential use in PeLED. To our knowledge, this is the first comprehensive investigation into the effect of the displacement of the fluorine (F) atom in the aromatic cation on the properties and stability of 2D perovskites X-FPEA₂PbI₄ (X = p, m, and o). Our results indicate that the p-FPEA₂PbI₄ perovskite exhibits high stability and is proposed as the active layer in PeLEDs. Furthermore, we simulate PeLEDs based on p-FPEA₂PbI₄, PEA₂PbI₄, and MAPbI₃ using the finite element method (FEM) and compare their internal quantum efficiency, external quantum efficiency, current–light intensity (L–I) curve, emission spectrum, and stability.

Simulation methods

Kohn–Sham equation

The foundation of DFT calculations is the Kohn–Sham (KS) equation, as expressed in Eq. (1), which is derived from the multi-particle Schrödinger equation. The Hamiltonian in this equation encompasses both kinetic energy (T) and potential energy (V). The potential energy consists of the nuclear potential (V_n), Hartree potential (V_H), and exchange–correlation potential (V_xc) (see section S1)¹⁷.

$$\begin{gathered} (T + V)\phi_{i} (r) = \varepsilon_{i} (r)\phi_{i} (r) \hfill \\ V = V_{n} + V_{H} + V_{xc} \hfill \\ \end{gathered}$$

(1)

The KS equation is solved using the iterative self-consistent field (SCF) method, as illustrated in Fig. 1.

Fig. 1

Algorithm of SCF for solving the KS equation.

The process begins with an initial guess for the electron density (n(r)). The Hartree and exchange potentials are calculated based on this electron density. Subsequently, the KS equation is solved and the electron density is recalculated. This new value is then compared to the initial guess, and the process continues until the two densities converge closely. By solving the KS equation, we can obtain the eigenvalues, eigenfunctions, total energy, and electron density¹⁷.

Electronic properties

Bloch’s theorem is employed for crystal structures characterized by periodic potential. The Bloch wave function, expressed in Eq. (2), consists of a periodic component (u_ik(r)) and a plane wave component (exp(ikr)). By substituting the Bloch wave function into the Kohn–Sham equation, we derive the crystalline version of the equation, as illustrated in Eq. (3). This refined equation is instrumental in obtaining the band structure of the material. In this equation, i represents the eigenstate index and k denotes the wave vector^17,18.

$$\psi_{nk} (r) = u_{nk} (r)\exp (jkr)$$

(2)

$$\begin{gathered} [ - \frac{1}{2}(\nabla + ik)^{2} + V_{tot} ]u_{ik} = \varepsilon_{ik} u_{ik} (r) \hfill \\ V_{tot} (r) = V_{n} (r) + V_{H} (r) + V_{xc} (r) \hfill \\ \end{gathered}$$

(3)

The effective mass of charge carriers (i.e., electrons and holes) is derived from the band structure as¹⁹:

$$m^{*} = \frac{{\hbar^{2} }}{{\frac{{\partial^{2} E}}{{\partial k^{2} }}}}$$

(4)

Optical properties

To calculate the optical properties with DFT calculations, the imaginary part of the dielectric function (ε₂(ω)) is first determined from Fermi’s golden rule as²⁰:

$$\varepsilon_{2} (\hbar \omega ) = \frac{{2q^{2} \pi }}{{V\varepsilon_{0} }}\sum\limits_{k,v,c} {| < \Psi_{k}^{c} |u.r|\Psi_{k}^{v} > |}^{2} \delta (E_{k}^{c} - E_{k}^{v} + \hbar \omega )$$

(5)

In this equation, the parameters q, V, ħω, u, and ε₀ are the electronic charge, the volume of a primitive cell, the photon energy, the polarization of the incident electric field, and the dielectric constant in the vacuum, respectively. In addition, ψ_kv and ψ_kc denote the wave functions of electrons in the valence and conduction bands, respectively. The term includes the delta function for energy conservation. Next, the real part of the dielectric function (ε₁(ω)) is calculated from ε₂(ω) using the Kramer-Kronig relation as:

$$\varepsilon_{1} (\hbar \omega ) = 1 + \frac{2}{\pi }\int\limits_{0}^{\infty } {\frac{{\omega ^{\prime}\varepsilon_{2} (\omega ^{\prime})}}{{\omega ^{{\prime}{2}} - \omega^{2} }}}$$

(6)

Finally, the complex refractive index (N = n_r + ik) can be calculated from the complex dielectric function (ε(ω)) as follows:

$$\varepsilon = \varepsilon_{1} + i\varepsilon_{2} = N^{2}$$

(7)

$$\varepsilon_{1} = n_{r}^{2} - k^{2} ,\varepsilon_{2} = 2n_{r} k$$

(8)

The exciton binding energy (E_bx) is computed using the reduced effective mass (m_r) and the static dielectric constant (ε_s) as¹⁹:

$$\begin{gathered} E_{bex} = 13.6\frac{{m_{r} }}{{\varepsilon_{s}^{2} }},\frac{1}{{m_{r} }} = \frac{1}{{m_{e} }} + \frac{1}{{m_{h} }} \hfill \\ \hfill \\ \end{gathered}$$

(9)

Mechanical properties

To investigate the mechanical properties of perovskite materials, we first calculate the elastic constants (C_ij). The elastic constants, according to Hooke’s law in Voigt notation, are expressed as²¹:

$$\sigma_{i} = C_{ij} \varepsilon_{j}$$

(10)

where σ_i is stress and ε_j is strain.

Using DFT calculations, the elastic constants can be determined as:

$$\Delta U = \frac{\Omega }{2}\sum\nolimits_{i = 1}^{6} {\sum\nolimits_{j = 1}^{6} {c_{ij} e_{i} e_{j} } }$$

(11)

ΔU is the total energy change under external force, Ω is primitive cell volume, and e_ij is strain-related deformation vectors. The conditions for the mechanical stability of the monoclinic crystal structure are as follows²²:

$$\begin{gathered} C_{11} > \, 0, \, C_{22} > 0, \, C_{33} > 0, \, C_{44} > \, 0, \, C_{55} > 0, \, C_{66} > 0 \hfill \\ C_{11} + C_{22} + C_{33} + 2C_{12} + 2C_{13} + 2C_{23} > 0 \hfill \\ C_{33} C_{55} - 2C^{2}_{35} > \, 0, \, C_{44} C_{66} - 2C^{2}_{46} > \, 0, \, C_{22} + C_{33} - 2C_{23} > \, 0 \hfill \\ \end{gathered}$$

(12)

The mechanical properties, including bulk modulus (B), Young’s modulus (E), Shear’s modulus (G), and Poisson’s ratio (υ), are expressed from the C_ij and approximations of Voigt (upper limit of values), Reuss (lower limit of values) and Hill (average values) with the following equations²³:

$$B_{V} = \frac{1}{9}[(C_{11} + C_{22} + C_{33} ) + 2(C_{12} + C_{13} + C_{23} )]$$

(13)

$$G_{V} = \frac{1}{15}[(C_{11} + C_{22} + C_{33} ) - (C_{12} + C_{13} + C_{23} ) + 3(C_{44} + C_{55} + C_{66} )]$$

(14)

$$E_{V} = \frac{{9B_{V} G_{V} }}{{3B_{V} + G_{V} }}$$

(15)

$$\upsilon_{V} = \frac{{3B_{V} - 2G_{V} }}{{2(3B_{V} + G_{V} )}}$$

(16)

$$B_{R} = \frac{1}{{[(S_{11} + S_{22} + S_{33} ) + 2(S_{12} + S_{13} + S_{23} )]}}$$

(17)

$$G_{R} = \frac{15}{{[4(S_{11} + S_{22} + S_{33} ) + 3(S_{44} + S_{55} + S_{66} ) - 4(S_{12} + S_{13} + S_{23} )]}}$$

(18)

$$E_{R} = \frac{{9B_{R} G_{R} }}{{3B_{R} + G_{R} }}$$

(19)

$$\upsilon_{R} = \frac{{3B_{R} - 2G_{R} }}{{2(3B_{R} + G_{R} )}}$$

(20)

$$B_{H} = \frac{{B_{V} + B_{R} }}{2}$$

(21)

$$G_{H} = \frac{{G_{V} + G_{R} }}{2}$$

(22)

$$E_{H} = \frac{{E_{V} + E_{R} }}{2}$$

(23)

$$\upsilon_{H} = \frac{{\upsilon_{V} + \upsilon_{R} }}{2}$$

(24)

The subscripts V, R, and H in these equations represent the Voigt, Reuss, and Hill approximations, respectively. A Poisson’s ratio value of 0.26 serves as a threshold between ductility and brittleness; thus, for values greater than 0.26, perovskite exhibits ductile behavior. Additionally, lower values of mechanical moduli—such as the bulk modulus, Young’s modulus, and shear modulus—indicate greater flexibility of the material.

Stability

The formation energy (FE) of the 2D perovskite with the general formula L₂BX₄ is calculated using Eq. (25), where E expresses the total energy of the material and its components. A higher absolute value of FE indicates greater thermodynamic stability of the material²⁴.

$$FE = E(L_{2} BX_{4} ) - (2E(LX) + E(BX_{2} ))$$

(25)

To assess moisture stability, the adsorption energy (E_ads) of water on the surface of perovskite is calculated as²⁵:

$$E_{ads} = E_{water/surface} - E_{water} - E_{surface}$$

(26)

A negative value of E_ads indicates that the water molecule (H₂O) is more strongly attracted to the perovskite surface. Conversely, a positive E_ads value suggests that the water molecule is repelled from the surface of the perovskite.

Efficiency of LEDs

To calculate the LED efficiency, the carrier transport model is first solved using Eq. (27). In this equation, ϕ represents the electrostatic potential, μ is the mobility of carriers, D is the diffusion coefficient, q is the electron charge, n is the electron density, p is the hole density, N_D is the donor concentration, and N_A is the acceptor concentration. In addition, G_n and G_p denote the generation rates, while R_n, and R_p are the recombination rates. By solving the equations of the carrier transport model, the values of n, p, and ϕ can be obtained²⁶.

$$\begin{aligned} \frac{\partial n(t)}{{\partial t}} & = G_{n} - R_{n} + \frac{1}{q}\nabla \left[ { - q\mu_{n} n\nabla \phi + qD_{n} \nabla_{n} } \right] \\ \frac{\partial p(t)}{{\partial t}} & = G_{p} - R_{p} + \frac{1}{q}\nabla \left[ { - q\mu_{p} p\nabla \phi - qD_{p} \nabla_{p} } \right] \\ \nabla .(\varepsilon \nabla \phi ) & = - q(p - n + N_{D} - N_{A} ) \\ \end{aligned}$$

(27)

Next, we calculate the carrier rate equation using Eq. (28), where R = R_n-G_n or R = R_p-G_p represents the net recombination rate. Moreover, A denotes the nonradiative Shockley–Read–Hall (SRH) recombination, B is the radiative recombination, and C is the Auger recombination.

$$\frac{dn}{{dt}} = - R = - (An + Bn^{2} + Cn^{3} )$$

(28)

The internal quantum efficiency (IQE) is calculated as the ratio of radiative recombination to nonradiative recombination using Eq. (29).

$$IQE = \frac{Bn}{{A + Bn + Cn^{2} }}$$

(29)

Considering excitonic recombination, the IQE for 2D perovskites is modified as²⁷:

$$IQE = \frac{{Bn + k_{exciton} }}{{A + k_{exciton} + Bn + Cn^{2} }}$$

(30)

The EQE is calculated from the IQE using Eq. (31), assuming that the light emission occurs from the edge. In this equation, n_r is the refractive index of the active layer²⁸.

$$EQE = \frac{IQE}{{2n_{r}^{2} }}$$

(31)

The optical output power (L) is related to total photon flux (ϕ_t) and external quantum efficiency (EQE) as:

$$L = \phi_{t} .h\nu = EQE(\frac{I}{q}h\nu )$$

(32)

Here, the total photon flux (ϕ_t) is defined as:

$$\phi_{t} = R_{spon} .V_{0}$$

(33)

where V₀ is the active layer volume. The total spontaneous emission rate (R_spon) per unit volume is expressed by²⁹:

$$R_{spon} = \int\limits_{{E_{g} }}^{\infty } {\frac{1}{{\tau_{r} }}} f_{c} (1 - f_{v} )g(E)dE$$

(34)

where f_c is the Fermi –Dirac distribution in the conduction band, fv is the Fermi –Dirac distribution in the valence band, g(E) is the joint density of states and τ_r is the radiative recombination lifetime.

Results and discussions

Structural properties

The crystal structure and lattice parameters of X-FPEA₂PbI₄ (X = p, m, and o) perovskites are shown in Fig. 2. At room temperature, these perovskites exhibit a monoclinic crystal phase³⁰.

Fig. 2

Crystal structure and lattice parameters of X-FPEA₂PbI₄.

The spacer cation FPEA (FC₆H₄(CH₂)₂NH₃) is characterized as an aromatic cation. In its structure, the ammonium group (NH₃) is linked to the aromatic ring via a carbon chain. The position of the fluorine (F) atom on the aromatic ring leads to three distinct configurations: para (p)-FPEA, meso (m)-FPEA, and ortho (o)-FPEA, as depicted in Fig. 3. Importantly, it has been observed that the experimental lattice parameters remain consistent regardless of the position of the F atom on the aromatic ring.

Fig. 3

The aromatic spacer cation of (a) p-FPEA, (b) m-FPEA, and (c) o-FPEA.

The optimized lattice parameters and primitive cell volumes of X-FPEA₂PbI₄ (X = p, m, and o) are obtained through DFT calculations and used to determine the stability and various properties of the perovskites. These parameters are presented in Table 1 (see section S1).

Table 1 Optimized lattice parameters and volumes of X-FPEA₂PbI₄ (X = p, m, and o).

Material stability

To investigate thermodynamic stability, the formation energy (FE) values for X-FPEA₂PbI₄ (X = p, m, and o) perovskites are calculated using DFT calculation and presented in Table 2. The p-FPEA₂PbI₄ perovskite is more stable than m-FPEA₂PbI₄ and o-FPEA₂PbI₄ due to its larger absolute value of FE. By examining the hydrogen bonding in these perovskites (see section S3), it can be concluded that pFPEA has a stronger hydrogen bond due to the shorter N…X distance. So, it is more stable.

Table 2 Formation energy of X-FPEA₂PbI₄ (X = p, m, and o).

Ab initio molecular dynamics (AIMD) combines molecular dynamics with quantum mechanical calculations, using first principles to derive atomic forces. This method provides accurate insights into the thermal stability and dynamics of materials. The NVT ensemble maintains a constant particle number, volume, and temperature, allowing the system to exchange energy with a heat bath. This is essential for simulating realistic thermal conditions in AIMD studies. The thermal stability of X-FPEA₂PbI₄ (X = p, m, and o) perovskites is explored using AIMD analysis with the NVT ensemble, with results shown in Fig. 4. In all three materials, the energy changes due to temperature variations around room temperature are minimal, indicating their thermal stability. Among these perovskites, p-FPEA₂PbI₄ exhibits the lowest energy changes, suggesting it has better stability compared to the other materials.

Fig. 4

Thermal stability of X-FPEA₂PbI₄ (X = p, m, and o) using AIMD simulation.

The values of adsorption energy for X-FPEA₂PbI₄ (X = p, m, and o) perovskites are presented in Table 3. The results show that p-FPEA₂PbI₄ exhibits greater stability against water exposure (indicated by a lower absolute value of E_ads), suggesting it has superior moisture stability compared to the other two perovskites. These findings are consistent with experimental results obtained using the contact angle method³¹. To calculate E_ads, the average from several cases involving the placement of water molecules on the perovskite surface is computed using DFT, as illustrated in Figs. S2–S4.

Table 3 Adsorption energy of X-FPEA₂PbI₄ (X = p, m, and o).

The results presented in Section S2 show that the formation energy of X-FPEA₂PbI₄ (X = p, m, o) is nearly 25 times larger than that of MAPbI₃. Thus, the thermodynamic stability of the proposed 2D perovskites is significantly higher than that of 3D perovskites. Comparing the adsorption energy values between MAPbI₃ and the proposed materials reveals that the moisture stability of X-FPEA₂PbI₄ (X = p, m, o) is approximately four times greater than that of MAPbI₃. Moreover, p-FPEA₂PbI₄ is more stable than PEA₂PbI₄, which has an FE value of − 4.689 eV¹³.

Electrical and optical properties

The values of the complex refractive index and dielectric function for X-FPEA₂PbI₄ (X = p, m, and o) perovskites are shown in Fig. 5. The refractive index at zero frequency (n_s) for p-FPEA₂PbI₄, m-FPEA₂PbI₄, and o-FPEA₂PbI₄ perovskite is 2.102, 2.067, and 2.059, respectively. In addition, the dielectric constant values at zero frequency (ε_s) for these perovskites are 4.420, 4.272, and 4.239, respectively. Variations in the refractive index and dielectric constant are proportional to changes in the position of the F atom on the aromatic ring. Reducing the distance between the negative charge (fluorine atom) and the positive charge (NH₃ part) in the organic cation decreases the dipole moment, which in turn reduces the polarization and dielectric constant³¹.

Fig. 5

Complex refractive index for X-FPEA₂PbI₄ (a) X = p, (b) X = m, and (c) X = o and dielectric function for X-FPEA₂PbI₄ (d) X = p, (e) X = m, and (f) X = o.

Figure 6a–c show the band structure and bandgap energy (E_g) for X-FPEA₂PbI₄ (X = p, m, and o) perovskites, respectively. The value of E_g varies with the position of the F atom. Specifically, the E_g values for p-FPEA₂PbI₄, m-FPEA₂PbI₄, and o-FPEA₂PbI₄ are 2.097, 2.133, and 2.177 eV, respectively. The bandgap inversely correlates with refractive index values.

Fig. 6

Band structure and bandgap energy of X-FPEA₂PbI₄ (a) X = p, (b) X = m, and (c) X = o without spin–orbit coupling effect.

The band structure and E_g for X-FPEA₂PbI₄ (X = p, m, and o) perovskites, considering the spin–orbit coupling (SOC) effect, are indicated in Fig. 7. The obtained values of E_g for p-FPEA₂PbI₄, m-FPEA₂PbI₄, and o-FPEA₂PbI₄ are 1.323, 1.329, and 1.357 eV, respectively.

Fig. 7

Band structure and bandgap energy of X-FPEA₂PbI₄ (a) X = p, (b) X = m, and (c) X = o with SOC effect.

The band structure (with and without the SOC effect) exhibits a flat band in the Z–Γ region. This flat band region (Γ–Z) in the band structure corresponds to the x-axis in the real space which represents the quantum barrier effect in the multiple quantum well structure of 2D perovskites. This means that large effective mass and the flat band dispersion have no considerable effect on charge transport and the device’s efficiency. Therefore, to analyze the charge transport inside the device, we calculate the effective mass in the Γ–X dispersive region corresponding to the z-axis of the real space (along with the charge transport direction in the device). The calculated effective masses, and the obtained values of E_bx using Eq. (9) for X-FPEA₂PbI₄ (X = p, m, and o) perovskites are presented in Table 4. The decrease in E_bx with the change in the F position in p-FPEA₂PbI₄ compared to o-FPEA₂PbI₄ is attributed to the increase in dipole moment and dielectric constant.

Table 4 Effective masses, dielectric constants, bandgap energies, dielectric, and exciton binding energies of X-FPEA₂PbI₄ (X = p, m, and o).

Mechanical properties

Mechanical stability refers to the ability of a material or structure to maintain its shape and resist deformation under applied forces or loads. It indicates how well a material can withstand mechanical stress without undergoing failure, such as fracture, yielding, or excessive deformation. Mechanical stability is crucial for ensuring that materials can perform effectively in their intended applications, especially in structural components where safety and reliability are paramount. To investigate the mechanical stability conditions for X-FPEA₂PbI₄ (X = p, m, and o) perovskites, the elastic constants (C_ij) are obtained using DFT calculations and are presented in Table 5. By examining the conditions in Eq. (12), it is evident that all three perovskites are mechanically stable.

Table 5 The elastic constants of X-FPEA₂PbI₄ (X = p, m, and o).

The mechanical properties of X-FPEA₂PbI₄ (X = p, m, and o) perovskites, computed using VRH approximations, are presented in Table 6. From the obtained values, it can be concluded that o-FPEA₂PbI₄ is more flexible than the other two materials (i.e., m-FPEA₂PbI₄ and p-FPEA₂PbI₄). The position of the fluorine atom affects the steric hindrance around the cation. In o-FPEA, the proximity of the fluorine to the ammonium group creates a more favorable configuration that allows for greater movement and flexibility in the crystal structure. The specific bonding angles and distances in o-FPEA₂PbI₄ facilitate easier deformation under stress compared to the more rigid structures of m-FPEA₂PbI₄ and p-FPEA₂PbI₄. It should be noted that all three materials are ductile due to Poisson’s ratio being higher than 0.26.

Table 6 Mechanical properties of X-FPEA₂PbI₄ (X = p, m, and o).

Results of PeLED simulation

Here, a 2D perovskite-based PeLED is presented, as shown in Fig. 8a. Since p-FPEA₂PbI₄ possesses the most stability among the proposed materials (explained in Section “Results and discussions”–“Simulation methods”), it is chosen as the active layer of the PeLED. In addition, another 2D perovskite (PEA₂PbI₄) and a 3D perovskite (MAPbI₃) are investigated as active layers for comparison.

Fig. 8

(a) Schematic of PeLED and (b) The different structures of PeLEDs and energy levels of ETL, HTL, and active layer.

The proposed PeLED is examined using the following layer structure, as shown in Fig. S5 (a-m):

• Structure 1: HTL (poly[N, N′-bis(4-butyl phenyl)-N, N′-bis(phenyl)-benzidine] (poly-TPD))/Active layer (MAPbI₃)/ETL (1,3,5-Tris(1-phenyl-1h benzimidazole-2-yl)benzene (TPBi))

• Structure 2: HTL (Poly-TPD)/Active layer (PEA₂PbI₄)/ETL (TPBi)

• Structure 3: HTL (Poly-TPD) /Active layer (pFPEA₂PbI₄)/ETL (TPBi)

• Structure 4: HTL (poly (9-vinyl carbazole) (PVK))/Active layer (MAPbI₃)/ETL (1,3,5-Tris(3-pyridyl-3-phenyl)benzene (TmPyPB))

• Structure 5: HTL (PVK)/Active layer (PEA₂PbI₄)—ETL (TmPyPB)

• Structure 6: HTL (PVK)/Active layer (pFPEA₂PbI₄)/ETL (TmPyPB)

• Structure 7: HTL (Poly-TPD)/Active layer (PEA₂PbI₄)/ETL (TmPyPB)

• Structure 8: HTL (Poly-TPD)/Active layer (pFPEA₂PbI₄)/ETL (TmPyPB)

• Structure 9: HTL (Poly-TPD) /Active layer (PEA₂PbI₄)/ETL (TmPyPB)

• Structure 10: HTL (PVK)/Active layer (pFPEA₂PbI₄)/ETL (TPBi)

• Structure 11: HTL (PVK)/Active layer (PEA₂PbI₄)/ETL (TPBi)

• Structure 12: HTL (PVK)/Active layer (pFPEA₂PbI₄)/ETL (TPBi)

The ETL, HTL, and active layer thicknesses are set at 30, 60, and 80 nm, respectively, and the device area is 0.1 cm². The simulation parameters for the PeLED with different materials at room temperature include electron affinity (χ_e), bandgap energy (E_g), dielectric constant (ε_r), density of states in the conduction band (N_c), density of states in the valence band (N_v), mobility (μ), SRH recombination (A), radiative recombination (B), and Auger recombination (C), as listed in Tables S7 and S8. The energy levels of the materials used in the PeLED are illustrated in Fig. 8b.

IQE is calculated using Eqs. (27–30). The results for the proposed PeLED structures are shown in Fig. 9. From these results, it can be seen that the PeLED with MAPbI₃ exhibits the lowest efficiency, while PEA₂PbI₄ has the highest efficiency. The p-FPEA₂PbI₄-based PeLED achieves lower efficiency than PEA₂PbI₄; however, according to Table 3, it offers greater stability. The reduced efficiency of p-FPEA₂PbI₄ can be attributed to its lower exciton binding energy compared to PEA₂PbI₄. Conversely, the enhanced stability of FPEA₂PbI₄ arises from the substitution of an F atom for H in the aromatic ring, which has a larger atomic radius, thereby increasing the length of the cation. In addition, changes in the ETL and HTL layers impact efficiency more significantly in 3D perovskites than in 2D perovskites. Therefore, PeLEDs utilizing 2D perovskites exhibit better stability. Based on the efficiency values for all three active layer materials, the combination of TPBi for the ETL layer and the Poly-TPD for the HTL layer yields the highest efficiency values. Consequently, we choose these materials for the ETL and HTL layers of the PeLED structure.

Fig. 9

The IQE values of PeLED for different ETLs and HTLs for (a) MAPbI₃, (b) PEA₂PbI₄, and (c) p-FPEA₂PbI₄.

The IQE values under temperature fluctuations (from T = 290 K to T = 300 K) are presented in Fig. 10. The results indicate that the efficiency fluctuations for PeLEDs with 2D perovskite active layers are significantly lower than those for 3D perovskites. Consequently, PeLEDs utilizing 2D perovskites exhibit better stability. The changes in efficiency due to temperature fluctuations for p-FPEA₂PbI₄, PEA₂PbI₄, and MAPbI₃ are 0.01 (1/K), 0.0282 (1/K), and 0.038 (1/K), respectively. These findings align with the thermodynamic stability of the perovskite materials. Thus, the more stable the perovskite material used in the active layer, the more stable the efficiency of the PeLED component under temperature fluctuations.

Fig. 10

The IQE of PeLED for different temperatures for (a) MAPbI₃, (b) PEA₂PbI₄, and (c) p-FPEA₂PbI₄.

The EQE value is calculated according to Eq. (31). Figure 11 displays the EQE curves with respect to temperature fluctuations. The variations in EQE with temperature fluctuations for p-FPEA₂PbI₄, PEA₂PbI₄, and MAPbI₃ are 0.0112 1/K, 0.032 1/K, and 0.043 1/K, respectively. Consequently, the PeLEDs with an active layer of p-FPEA₂PbI₄ demonstrate better EQE stability in response to temperature fluctuations.

Fig. 11

The EQE of PeLED with different active layers (a) MAPbI₃, (b) PEA₂PbI₄, and (c) p-FPEA₂PbI₄.

Figure 12 presents the light output (L)- current (I) for PeLEDs with different active layers. From these curves, it can be concluded that p-FPEA₂PbI₄ exhibits better L–I stability against temperature fluctuations, while PEA₂PbI₄ has a higher light output value than the other materials. The variations of L with temperature fluctuations at 100 mA for p-FPEA₂PbI₄, PEA₂PbI₄, and MAPbI₃ are 0.00073 1/K, 0.0012 1/K, and 0.0043 1/K, respectively.

Fig. 12

The L–I curve of PeLED for different active layers (a) MAPbI₃, (b) PEA₂PbI₄, and (c) p-FPEA₂PbI₄.

The spontaneous emission spectrum of the PeLED is examined at I = 100 mA, with temperature fluctuations from T = 290 K to T = 300 K. The results for the different active layer materials (i.e., MAPbI₃, PEA₂PbI₄, and p-FPEA₂PbI₄) are shown in Fig. 13. The full width at half maximum (FWHM) values in the emission spectrum, considering temperature fluctuations, are 0.0516 nm/K for MAPbI₃, 0.0245 nm/K for PEA₂PbI₄ and 0.0156 nm/K for p-FPEA₂PbI₄. Thus, the change in FWHM for p-FPEA₂PbI₄ is smaller under temperature fluctuations, indicating that it has better spectral stability.

Fig. 13

The spontaneous emission of PeLED with different active layers (a) MAPbI₃, (b) PEA₂PbI₄, and (c) FPEA₂PbI₄.

In Fig. 14, the changes in the FWHM of the emission spectrum with current variations for MAPbI₃, PEA₂PbI₄, and p-FPEA₂PbI₄ are measured as 0.00282 nm/mA, 0.00169 nm/mA, and 0.00138 nm/mA, respectively. This data indicates that p-FPEA₂PbI₄ exhibits the smallest change in FWHM with current variation, demonstrating superior spectral stability compared to MAPbI₃ and PEA₂PbI₄. This enhanced stability suggests that p-FPEA₂PbI₄ can be more reliable for applications requiring stable optical performance under varying operational conditions.

Fig. 14

The spontaneous emission of PeLED for different currents for (a) MAPbI₃, (b) PEA₂PbI₄, and (c) FPEA₂PbI₄.

The chromaticity coordinates of the LED emission are plotted on the Commission Internationale de L’Eclairage (CIE) 1931 color space diagram, as shown in Fig. 15. The position of the chromaticity point, labeled “B”, indicates that the LED emits light concentrated in this portion of the visible spectrum. The proximity of the chromaticity point to the outer boundary of the color space triangle suggests that the LED has an excellent degree of color purity at (0.7923, 0.2706), (0.400, 0.596), and (0.2015, 0.75512) for MAPbI₃, PEA₂PbI₄, FPEA₂PbI₄, respectively.

Fig. 15

The CIE 1931 chromatic coordinates for the PeLEDs with (a) MAPbI₃, (b) PEA₂PbI₄, and (c) FPEA₂PbI₄.

By examining these results, we observe that the stability of PeLEDs with an active layer of 2D perovskites (PEA₂PbI₄ and p-FPEA₂PbI₄) against temperature fluctuations is superior to that of the 3D perovskite (MAPbI₃). On the other hand, among the two 2D perovskites, PEA₂PbI₄ exhibits greater efficiency than p-FPEA₂PbI₄, although it is less stable. Therefore, we conclude that there is a trade-off between the stability and efficiency of PeLEDs. Table 7 indicates that p-FPEA₂PbI₄ is more stable than the other materials, while PEA₂PbI₄ exhibits higher efficiency compared to the others. Overcoming the trade-off between stability and efficiency in 2D perovskite-based PeLEDs is achievable through a combination of chemical modifications, structural optimization, and interface engineering. By carefully adjusting material properties, optimizing device structure, and improving interfaces, we can design PeLEDs that exhibit both high efficiency and long-term stability, making them suitable for practical applications.

Table 7 The tradeoff between properties of PeLED.

Conclusion

In this study, we conducted a comprehensive analysis of the stability and opto-electro-mechanical properties of RP 2D perovskites, focusing specifically on X-FPEA₂PbI₄, where X denotes different configurations: para (p), meso (m), and ortho (o). Our findings provide critical insights into how these variations influence both stability and efficiency, which are essential factors for their application in perovskite light-emitting diodes (PeLEDs). The comparative analysis of the three configurations indicated that p-FPEA₂PbI₄ stands out with a formation energy of − 4.825 eV, demonstrating superior thermodynamic stability compared to m-FPEA₂PbI₄ (− 4.647 eV) and o-FPEA₂PbI₄ (− 4.580 eV). This enhanced stability is particularly significant in practical applications, where environmental factors can lead to material degradation. Furthermore, p-FPEA₂PbI₄ exhibited lower efficiency variations under temperature fluctuations, quantified as 0.01 1/K, in contrast to 0.0282 1/K and 0.0415 1/K for PEA₂PbI₄ and MAPbI₃, respectively. This stability under varying real conditions positions p-FPEA₂PbI₄ as a highly reliable candidate for PeLED applications. With temperature fluctuations, the values of FWHM in the emission spectrum are 0.0516 nm/K for MAPbI₃, 0.0245 nm/K for PEA₂PbI_4, and 0.0156 nm/K for p-FPEA₂PbI₄. While PEA₂PbI₄ achieves the highest IQE of 6.289%, the trade-off between efficiency and stability becomes evident when considering the fluctuations associated with each material. The IQE for p-FPEA₂PbI₄ is 2.285%, which is lower than that of PEA₂PbI₄, however, it is compensated by its robust stability profile. This balance is crucial for the longevity and performance of PeLEDs, especially in commercial applications where consistent output is required.