Impact of Residual Strains on the Carrier Mobility and Sability of Perovskite Films

1. Introduction

Perovskite is a promising material with unique optical and electrical properties [1]. However can be very sensitive to environmental factors including humidity, oxygen and heat [2,3]. They can make the perovskites unstable and limit their integration into commercial devices. Recently, reports have suggested that stability enhancement could be achieved by the release of residual strains [4]. Although residual strains are well known, , the first studies on strains in perovskites were reported less than a decade ago [5]. The problems associated with residual strains and their impact on material and device stability remains an active research field [6]. In time, this deeper understanding could translate into significant improvement of perovskite devices. In this work, we use thermally-induced strain release to explore the origin of residual strains in perovskite films and their impact on the electrical and optical properties, as well as their stability.

1.1. Stress Origin in Perovskite Films

Generally, stresses in perovskite films mainly have three origins: intrinsic, mechanical, and thermal [7]. Because of the polycrystalline and heterogeneous nature of perovskite films, residual strains can stem from macroscopic, mesoscopic or microscopic deformations [8,9]. Residual strains in thin films are usually the consequence of thermal stresses or other external conditions occurring during grain coalescence or growth [4,10]. Indeed, it is largely due to the coefficient of thermal expansion (CTE) and lattice offset between the film and substrate [5,11]. These stresses can modify the structure of the crystal lattice and consequently impact the mobility of charge carriers, band gap and the stability of the film [12,13].

1.2. Impact on Electrical, Optical Properties and Stability

Perovskite-based solar cells (PSCs) have achieved efficiencies up-to 24.2 % in just a few years [14], However, their instability remains the main factor limiting their large-scale commercialization [15]. Efforts were made to reduce the moisture sensitivity of perovskite materials and improve the chemical stability of the electron and hole transport layers [16,17]. Strains can cause distortion of the crystal structure of perovskite [4,18]. Band structure calculations suggest that the band gap increases as the strain changes from compressive to tensile [19]. Small lattice strains in perovskite thin films can have major consequences on carrier recombination, electronic band structure, crystallinity, and crystal phase stability [20,21,22]. The bandgap variations due to strains can result in a change of the absorption spectrum of the perovskite film [5]. The presence of surface defects and grain boundaries in perovskite films can also create trap states impacting their stability [23]. It is also well known that strains can weaken the bonds and increase the defect density and degradation in perovskite films [12,24,25].

1.3. Regulation of Strain in Perovskite Films

Residual strains in perovskite films can affect their physical, optical, and electrical properties and impact their stability [26]. In turn, releasing residual strains in perovskite films could potentially be used to controllably improve their properties or stability. Several techniques can be used to release strains, including (1) regulation of local strains through the synthesis, (2) stress release by thermal expansion, or (3) adjusting the lattice offset between film and substrate [5]. It has been established that the intrinsic instability of perovskite films can result from annealing-induced residual strain accelerating their degradation [12,27]. This work will focus exclusively on the temperature-induced strain relaxation of methylammonium lead-halide provskite films in order to improve their optical and electrical properties and increase their stability. We measure the residual strains in perovskite films after annealing using the Williamson-Hall technique and GIXRD. We correlate these results with Hall effect measurements to improve the optoelectronic properties of our perovskite films. We also use Raman micro-spectroscopy measurements to probe the impact of thermally-induced strain release on the stability of perovskite films. Our findings indicate that achieving temperature-induced relaxation requires annealing within the temperature range 75 to 85 ${}^{\circ }\mathrm{C}$ to achieve high carrier mobility, low activation energy, high average speed, and improved stability. We also find that this optimized annealing process reduces defect density.

2. Experimental Section

Perovskite layers are prepared on glass substrates by cleaning them sequentially with acetone, isopropanol, and DI solution for 15 minutes each. A layer of commercial $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ ink from Ossila (used as received) is deposited on the substrates by spin-coating at 2000 rpm for 30 $\mathrm{s}$. The resulting films are annealed on a hot plate for 2 hours at different temperatures, ranging from 50 ${}^{\circ }\mathrm{C}$ to 110 ${}^{\circ }\mathrm{C}$. The residual strains are characterized by using XRD. Hall effect measurements are used for carrier mobility. Finally, UV-Vis absorption and Raman micro-spectroscopy are used to assess perovskite film degradation.

3. Results and Discussion

In Figure 1, characterization of the films by X-ray diffraction (XRD) confirms the crystallization of the sample in a perovskite structure, with the presence of the standard peaks associated with the (110), (220), and (330) reflection planes, respectively. The peak intensity at 14° suggests that the main orientation of the perovskite film is (110) [28]. XRD can also characterize the residual strains through the lattice parameters. Indeed, the tensile or compressive strains can be respectively associated with the shift of the peaks to lower or higher diffraction angles. Residual strains are often non-uniform and complex to analyze from the peak position alone. Another indicator of strains is the broadening of the XRD peaks compared to the fully-relaxed state [19,29].

3.1. Williamson Hall Characterization

The Williamson Hall (W-H) equation 1 can be used to quantify the strain-induced broadening resulting from crystal imperfections [30,31,32], and structural imperfections such as dislocations, vacancies, stacking defects [33,34]:

$${\beta }_{hkl}.cos{\Theta }_{hkl}=k\frac{\lambda }{D}+4\epsilon .sin\Theta$$

(1)

where ${\beta }_{hkl}$ is the fullwidth halfmaximum (FWHM) of the peak, k is the Scherrer constant equal to 0.94, $\lambda$ is the X-ray source wavelength and D is the crystallite size, ${\theta }_{hkl}$ is the peak position (${}^{\circ }$) and $ϵ$ is the strain. The fundamental difference between WH’s method and Scherrer’s method is that WH considers both the crystallite size and microstrains which are often interrelated.

Williamson-Hall curves in Figure 2 show the $cos{\theta }_{hkl}$ vs 4.$sin{\theta }_{hkl}$ evolution measured from $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ films annealed at 25, 50, 70, 90 and 110 ${}^{\circ }\mathrm{C}$. The residual strain can be calculated directly from the slope for each curve fitting. In Figure 2, the strain values calculated reveal an interesting trend. It starts with relatively high compressive strain at low annealing temperatures (below 40 ${}^{\circ }\mathrm{C}$). The residual strains decrease as the annealing temperature increases to 70 ${}^{\circ }\mathrm{C}$. Over 90 ${}^{\circ }\mathrm{C}$, the residual strains become increasingly tensile. We can conclude from this first test that the annealing temperature can generates three areas of strains: compressive, tensile, and a relaxed zone at a temperature around 80 ${}^{\circ }\mathrm{C}$. Based on our observations, we can expect an improved performance of the perovskite films.

3.2. GIXRD Characterization

Grazing incidence XRD is a very useful technique to characterize the structure of thin films. It can also directly probe the strain distribution in perovskite films [5]. As such, we can use GIXRD to analyze the variations in the in-plane residual strains for the perovskite films annealed at different temperatures. The measurements shown in Figure 3a are performed in the $\omega$-mode [5,35], by fixing the angle ${\theta }_{hkl}$ and varying the instrument tilt angle$\psi$.

In Figure 3b,c, we analyze the strains in perovskite films annealed at 50, 70, 90, and 110 ${}^{\circ }\mathrm{C}$ using GIXRD. Figure 3b illustrates the plot of 2$\theta$ vs $si{n}^2(\varphi$), where the slope of the fitted curves yields the strain coefficients. A negative slope suggests tensile strains, while a positive slope suggest compressive strains. Figure 3d–h clearly indicate the distribution of compressive and tensile strain gradients for annealing temperatures from 50 to 110° C, respectively. While thermal energy can cause significant strain levels in the crystal lattice, it should be noted that the perovskite crystal structure still remains thermally stable between 50 ${}^{\circ }\mathrm{C}$ and 110 ${}^{\circ }\mathrm{C}$ [36]. These GIXRD strain measurements are consistent and strongly support the W-H measurements from Figure 2. In Figure 3, residual strains appear compressive at temperatures below 70 ${}^{\circ }\mathrm{C}$ and tensile at temperatures above 90 ${}^{\circ }\mathrm{C}$. We can infer that strain relaxation can be achieved between 75-85 ${}^{\circ }\mathrm{C}$. Based on the XRD (W-H) and GIXRD analysis, we concur that $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ has a relaxed cubic structure at 80 ± 5 ${}^{\circ }\mathrm{C}$ (from 80 ${}^{\circ }\mathrm{C}$ the mixed crystals of perovskite transform from tetragonal to cubic phase) this relaxed symmetrical structure is favorable to improved electrical properties [36,37].

3.3. SEM Characterization

SEM analysis can be used to examine the change in granularity and microstructure caused by the residual strains. Distortions and internal strains can arise from the growth of superstructures and nanostructures, as well as from the substitutions with elements with different sizes [6]. Figure 4a–d show SEM micrographs for the perovskite films after annealing at 50, 70, 90, and 110 ${}^{\circ }\mathrm{C}$. The grain size evolution indicates that grains appear at 50 ${}^{\circ }\mathrm{C}$ (Figure 4a). The presence of solvents in the precursor leads to high pinhole densities due to minimal evaporation. Increasing the annealing temperature reduces pinhole density and increases the average grain size [38]. The maximum average size of 746 $\mathrm{n}\mathrm{m}$ is achieved with 90 ${}^{\circ }\mathrm{C}$ annealing (Figure 4g). At 110 ${}^{\circ }\mathrm{C}$ and above, microstructural changes (grain size and surface filing) start to appear (Figure 4d,h). These strain-induced alterations in the perovskite film’s granularity and microstructure potentially compromise its stability and accelerate its degradation.

3.4. Hall Effect Characterization

Carrier mobility can be directly measured using the Hall-effect technique represented in Figure 5. Here, a transverse magnetic field of 0.7 $\mathrm{T}$ is applied to all samples. In Figure 5, all samples display a p-type behavior indicated by the positive Hall voltage. This expected result can be explained by the large amounts of Pb, $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{I}$, Cl vacancies and I present in the film [39,40]. Due to lower formation energies, Pb and $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3$ vacancies are known to play a significant role in the p-type behavior of $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ thin films [41,42]. Due to lower formation energies, Pb and $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3$ vacancies are known to play a significant role in the p-type behavior of $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ thin films [42,43,44]. Figure 5 shows the Hall effect measurements used to identify the corresponding change in carrier mobilities and resistivities with increasing annealing temperatures. The carrier mobility reaches its highest value of 10 $\mathrm{c}$$\mathrm{m}$/$\mathrm{V}$/$\mathrm{s}$ at 80 ${}^{\circ }\mathrm{C}$, which is consistent with previous reports [45,46]. We already established that $C{H}_{3}N{H}_{3}Pb{I}_{3-x}C{l}_x$ films annealed at this temperature are strain-relaxed. Above 75 ${}^{\circ }\mathrm{C}$ (relaxation zone), the structure adopts cubic symmetry and can achieve high stability since the entropy reduction in the inorganic cage compensates for the high dynamic disorder of the organic cations methylammonium [37,47]. This cubic phase is also known to offer better electronic properties than the orthorhombic and tetragonal phases for symmetry reasons [48,49,50].

The thermal behavior for the Hall mobility can be described by the expression [51]:

$${\mu }_T\left(T\right)={\mu }_0\left(T\right).exp\left(\frac{E_a}{k_B.T}\right)$$

(2)

where, ${\mu }_0$ is the exponential prefactor, $k_B$ is the Boltzmann constant and Ea is the activation energy. Figure 6 shows ln(${\mu }_H$) as a function of 1000/T measured between 298 and 385 °$\mathrm{K}$. The activation energy Ea corresponds to the potential energy barrier height [51], and it can be directly extracted from the slope of the linear fit. From Figure 6, the activation energy for perovskite films with compressive strains is found to be 400 $\mathrm{m}$, while tensile strain reduces the activation energy to 50 $\mathrm{m}$. These results are also consistent with previous reports [52]. This change in activation energy originates from the slope at approximately 80${}^{\circ }\mathrm{C}$, suggesting significantly-reduced activation energy due to film relaxation. It has been previously reported that ${\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3}^{+}$ and ${\mathrm{I}}^{-}$ vacancies can easily migrate to a neighboring site due to their low activation energy [53]. This variation of the activation energy with temperature can be directly associated with the film’s residual strains [54].

Using the Hall mobility measurements from Figure 6, it becomes possible to access the mean carrier path length Lm and the mean free time (${\tau }_m$) (Figure 6) in the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ thin films using the conventional Drude-Sommerfeld model [42]:

$${\mu }_T\left(T\right)={\mu }_0\left(T\right).exp\left(\frac{E_a}{k_B.T}\right)$$

(3)

$$L_m={\mu }_H\left(\frac{{(3m_h^{*}.k_B.T)}^2}{e}\right)$$

(4)

Where ${m_h}^{*}$ is the effective mass of the hole given by the expression:

$$E_a=\frac{e^4.m_h^{*}}{2{(2{\epsilon }_0.{\epsilon }_r.h)}^2}$$

(5)

Where ${ϵ}_0$ is the permittivity of free space, and ${ϵ}_r$ is the relative dielectric constant used between 5.6 (high frequency) and 25.7 (low frequency) [42]. For the calculation of ${m_h}^{*}$ we assumed ${ϵ}_r$= 9 based on the hydrogen model [55]. The values of ${m_h}^{*}$ are estimated at 0.3 $\mathrm{m}$ and 2.4 $\mathrm{m}$ for the tensile and compressive films respectively [42,56,57], where $m_e$ represents the rest mass of the electron. Results from Figure 6 suggest that films subjected to compressive and tensile strains respectively have lower Lm and ${\tau }_m$, respectively. Both parameters peak at 80 ${}^{\circ }\mathrm{C}$, which corresponds to the relaxation region (strain-free) regime. At this temperature, mixed halide perovskites make the transition from the tetragonal to the cubic phase due to the tilt of the inorganic $\mathrm{P}\mathrm{b}{\mathrm{I}}_6$ octahedron and the rotational shift of the organic ${\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3}^{+}$, resulting in their increased average mobilities [50]. Consequently, these results confirm reports that phase shift can change the physical properties of mixed halide perovskites films and positively influence their electrical properties [42].

Figure 7a,b displays the absorption spectrum for samples annealed at 60${}^{\circ }\mathrm{C}$, 80${}^{\circ }\mathrm{C}$, and 110${}^{\circ }\mathrm{C}$ exhibiting compressive, relaxed, and tensile residual strains, respectively. The spectra in Figure 7a show stronger UV absorption for the tensile-strained and relaxed samples. When the residual strains transition from compressive to tensile, the bandgap of the film in Figure 7c show a slight increase from 1.56 to 1.57 . After four days of storage in an ambient environment, the absorption spectra from Figure 7b appearsis significantly reduced for both tensile- and compressively-strained samples, compared to the sample annealed at 80 ${}^{\circ }\mathrm{C}$. Moreover, this degradation as the strained samples become transparent also translates in a significant bandgap increase from 1.59 to 2.34 seen in Figure 7d–f. The low absorption of these samples can be attributed to incomplete crystallization during annealing at 60 ${}^{\circ }\mathrm{C}$. Poor-quality perovskite films often result from incomplete solvent DMF evaporation. Conversely, high-temperature annealing at 100 ${}^{\circ }\mathrm{C}$ promotes rapid solvent evaporation, preventing uniform surface filling and poor film quality as shown in Figure 4d.

3.5. Raman Characterization

Raman micro-spectroscopy measurements from Figure 8a,b are performed with a very low laser power of 0.5 $\mathrm{m}\mathrm{W}$ at 532 $\mathrm{n}\mathrm{m}$ wavelength to avoid any laser-induced damage. For the same reason, the laser beam as focused with a 10x objective. All measurements are done under ambient conditions. To perform the Raman measurements, we slowly increase the laser power until the main perovskite peaks are visible. Then the laser is shifted to a new position to record the Raman spectrum for a pristine perovskite. To avoid the laser intensity from impacting the perovskite film’s crystallization, we utilized Equation 6 to estimate the sample’s temperature based on the intensity ratio between Stokes/Anti-Stokes peaks [58,59] as shown in Figure 8b:

$$\frac{I_s}{I_{as}}={\left(\frac{{\vartheta }_0+{\vartheta }_v}{{\vartheta }_0-{\vartheta }_v}\right)}^{4}exp\left(\frac{E_p}{k_B.T}\right)$$

(6)

Where $k_B$ is the Boltzmann constant, ${\nu }_0$ is the frequency of the excitation source, and T is the sample’s temperature.

The inorganic-organic sublattices of the perovskite have different vibrational frequencies covering the range from 50 to 150 /$\mathrm{c}$$\mathrm{m}$ with phonon energies of 6-11 $\mathrm{m}$ (50- 90 /$\mathrm{c}$$\mathrm{m}$) and 11-20 $\mathrm{m}$ (90- 150 /$\mathrm{c}$$\mathrm{m}$) [60]. Figure 8c–e display the statistical temperature graphics calculated using Equation 6, for samples with residual tensile strains, no strains, and compressive strains for a phonon energy of 12 $\mathrm{m}$ at peak 100 /$\mathrm{c}$$\mathrm{m}$ [60]. The maximum temperature reached by the samples due to laser-induced heating is 324 °K. This value remains lower than the lowest annealing temperatures, ensuring that the 532 $\mathrm{n}\mathrm{m}$ laser-induced heating does not impact the crystalline structure of the different perovskite samples.

Finally, we can also evaluate the impact of different strain levels on the film degradation using Raman micro-spectroscopy. To do so, measurements are performed every 30 minutes for 4 days at a sufficiently low excitation power to prevent laser-induced heating. The Raman spectrum in Figure 8a clearly indicates the presence of vibrational peaks at 53, 65, 92, and 100 /$\mathrm{c}$$\mathrm{m}$ with a broader Raman band at 170 /$\mathrm{c}$$\mathrm{m}$, which can be attributed to the Pb-I and Pb-Cl perovskite layers [61]. The sharp peaks between 53 /$\mathrm{c}$$\mathrm{m}$ and 92 /$\mathrm{c}$$\mathrm{m}$ are attributed to the bending and stretching of Pb-I bonds, which are modes of inorganic cages [62]. Meanwhile, the bands at 100 /$\mathrm{c}$$\mathrm{m}$ can be attributed to the vibrations of the organic $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3^{+}$ cations [63]. After 24 hours, the peak intensity decreases, and no new vibrational bands are observed, implying the structure remained unaltered. It is known that incorporation of ${\mathrm{H}}_2\mathrm{O}$ into the crystal lattice is measured by solvating of $\mathrm{M}{\mathrm{A}}^{+}$ and the dissolving of the cations [64,65]. The absence of $\mathrm{M}{\mathrm{A}}^{+}$ can increase defect density and cause a slight displacement of atoms in the crystalline structure, leading to fluctuations in vibrational bands [65,66]. Figure 8a shows a redshift for all bands, suggesting an increased length of the chemical bond. Previous research confirms that the redshift in these bands results from stress exerted by the ${\mathrm{H}}_2\mathrm{O}$ molecule on the atomic bond related to this vibrational mode and the shift induced by the $\mathrm{M}{\mathrm{A}}^{+}$ vacancies [65]. However, the observed shift is not consistent, as the penetration of moisture in the film is not uniform due to the heterogeneity of the microstructural morphology, defects, and internal stresses.

In Figure 9a–c we compare the degradation of the strained films. As expected, results from Figure 9d–f clearly suggest that thermally-relaxed films show lower degradation compared with tensile- or compressively-strained films. Indeed, the average peak intensity decrease for the thermally-relaxed film never exceeds 10 %. In constrast, films with residual tensile and compressive strains respectively show a decrease in peak intensity of more than 20 % and 45 %. This is consistent with previous observations that strained films degrade more rapidly due to their crystal structure enabling easier incorporation of ${\mathrm{H}}_2\mathrm{O}$ molecules. Surface defects and strain-induced distortions in the crystal lattice weaken the structure, rendering it less resilient to external factors and thus accelerating its degradation [67,68].

4. Conclusions

This study shows a clear interrelationship between temperature-induced strains, charge carrier mobility, and the stability in solution-based perovskite films. Our findings show that these factors are interrelated and must be carefully considered in order to optimize the performance of perovskite materials. Our findings indicate that achieving temperature-induced relaxation requires annealing within the temperature range of 75 to 85 ${}^{\circ }\mathrm{C}$ for this specific precursor formulation. As a result, the $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{P}\mathrm{b}{\mathrm{I}}_{3-\mathrm{x}}\mathrm{C}{\mathrm{l}}_{\mathrm{x}}$ films annealed at 80 ${}^{\circ }\mathrm{C}$ demonstrate optimal performance due to their higher carrier mobilities, lower activation energies, high average speed, and improved stability. We find that these annealing temperatures reduce defect density and promote strain relaxation. These results could potentially minimize the impact of residual strain on optoelectronic properties and offer an alternative approach to optimize the performance of perovskite solar cells and other perovskite-based optoelectronic devices.