Introduction

The current demand for cost-efficient and renewable materials for energy applications has recently acted as a great driving force towards the development of low cost photovoltaic cells. The majority of commercial solar cells currently use crystalline silicon as the base semiconductor; in all probability, the most promising material for future solar generation will be one based on perovskite, this possessing efficiencies as high as 23.7%1. In spite of the surprising efficiency obtained, perovskite-based solar cell production faces problems related to stability, quite apart from the use of lead, a toxic element. With a view to overcoming this issue, some lead-free materials suitable for photovoltaic applications have gained the attention of researchers in recent years. In their studies, bismuth triiodide (BiI3)2,3,4,5 has revealed itself to be a promising candidate for photovoltaic applications, being a semiconductor with an adequate band gap for these purposes: 1.67 eV6. This material is versatile, and useful as the active absorbent layer in solar cells; it may also be suitable for conversion into a perovskite-like material such as MA3Bi2I9, which is additionally suitable for photovoltaic applications7,8,9. The efficiencies of devices using MA3Bi2I9 as absorber material are still very low (1.64%)9 and therefore optimization studies need to be performed to increase these values. In spite of this, the use of BiI3 in combination with PbI2 as precursors for a more stable perovskite CsPbxBiyI3 provided an efficiency of 11.47% in flexible substrates10.

In addition to the issue of the chemical stability of the semiconductors used in solar cell devices, other solar cell problems are associated with interface issues between the various materials used in the device structure. A typical perovskite solar cell is composed of 5–6 layers of various materials with differing thermomechanical properties. The difference in the inter-layer’s thermal expansion causes stress, and thus cracking, to appear within its structure.

We recently reported some preliminary results on stress and nanoindentation measurements of thermally evaporated BiI311. In this work, we employed the thermally-induced bending (TIB) technique12 and nanoindentation measurements13 to determine five thermomechanical properties: stress (σ), the coefficient of thermal expansion (CTE or α), nanohardness (H) and two elastic moduli related to Young’s modulus (E) and Poisson’s ratio (ν), namely, the biaxial Young’s modulus [E/(1 − ν)] and reduced Young’s modulus [E/(1 − ν2)]. There is little work addressing these subjects in photovoltaic-applied materials. Some of these properties have been reported for amorphous semiconductors14,15,16 and perovskite films deposited by solution processes17,18.

Results and Discussion

Optical and structural properties

Figure 1 shows the structural, morphological and optical properties of BiI3 films. The X-ray diffraction pattern (Fig. 1a) indicates that the films deposited on all substrates (Z-cut quartz, 〈111〉 silicon, 211 Precision glass, 7059 Corning glass and fused silica) have an R-3 rhombohedral crystal structure (JCPDS PDF # 48-1795)19 with a preferential orientation in the (003) direction. Figure 1b shows Tauc’s plot: (αhν)1/r versus hν, where α and hν are, respectively, the optical absorption coefficient and incident photon energy. Considering r = 2 for indirect allowed transitions20, the extrapolation of the Tauc’s plot linear region for (αhν)1/2 = 0 shows an estimated band gap of 1.71 eV, while the center of the photoluminescence emission at room temperature results in a value of 1.74 eV. Our results agree with those of R. E. Brandt et al.2, who through the use of DFT incorporating spin-orbit coupling encountered an indirect band gap of 1.73 eV; and with those of Nikolas J. Podraza et al.6, who determined that a single BiI3 crystal has an indirect band gap of 1.67 eV. The latter reached this value after several measurements aimed at solving discrepancies found in the literature, which varied from a direct band gap of 2.2 eV21 to an indirect one of 1.55 eV6. UV-Vis measurements performed in monocrystalline and solution-processed BiI3 films supplied respective values of 1.68 eV22 and 1.8 eV2. The index of refraction and the extinction coefficient as a function of photon energy appear in Fig. 1c.

Figure 1
figure 1

(a) X-ray diffraction pattern of bismuth triiodide thin films deposited on Z-cut quartz, 211 Precision glass, 7059 Corning glass, 〈111〉 silicon and fused silica (normalized at (003) peak). (b) Tauc’s plot (black) and photoluminescence spectra (red) of BiI3 thin films (the extrapolation of the curve to (αhν)1/2 = 0 and the center of the photoluminescence emission gives an estimated band gap of 1.71 eV and 1.74 eV, respectively). (c) Refractive index and extinction coefficient as a function of photon energy (the inset is a photo of a sample −25 mm × 5 mm in size). (d,e) Scanning electron microscope images of top view and cross section of BiI3 films, respectively and (f) AFM image.

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SEM images of thermally evaporated BiI3 films in Fig. 1(d,e) show a film 2.2 μm thick, homogeneously distributed along the substrate, and grain sizes of approximately 270 nm. Through AFM we were able to obtain a root mean square (RMS) roughness of 6 nm (Fig. 1f). Thicker and homogeneously distributed films are important parameters for both the stress and coefficient of thermal expansion measurements – see the description of said technique in Methods section. These characteristics are easy to obtain by using thermal evaporation, although the same cannot be said for spin coating23.

Stress, coefficient of thermal expansion and biaxial Young’s Modulus

We measured the film stress (σ) as a function of temperature in several substrates – see Fig. 2a. The thermally evaporated BiI3 films are tensile (positive stress) with an average stress of 28 ± 3 MPa at 300 K. This low value might be associated with thermal stress due to a non-intentional increase in the substrate temperature during film growth, which is caused by irradiation from the tungsten boat. Low stress values of films used in electronic devices, such as solar cells, are desirable because it prevents degradation due to stresses in the structure of the devices. Typical amorphous semiconductors used in these devices, such as amorphous silicon and germanium, usually demonstrate compressive stress of at least one order of magnitude higher14,15,24. On the other hand, perovskite films like CsxFA1−xPb(BryI1−y)3 has stress within the same range as the one here obtained for BiI317.

Figure 2
figure 2

(a) Typical stress versus temperature curves of BiI3 deposited on fused silica, 7059 Corning glass, 211 Precision glass and Z-cut quartz substrates; (b) derivatives of stress, extracted from (a), with respect to temperature (dσ/dT) of BiI3 versus CTE (or α) of the substrates. The data are average of measurements performed in five films deposited in each substrate at different runs. The CTE and biaxial Young’s modulus of BiI3 were extracted from the indicated fitting.

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Using only two substrates, it is possible to solve the linear system of two Eq. (2) (one for each substrate), calculate the biaxial Young’s modulus Ef/(1−νf) and CTE of BiI3. A graphical procedure to calculate these parameters, when more than two substrates are used, is displayed in Fig. 2b, which consists of plotting dσ/dT obtained from the derivative of curves shown in Fig. 2a as a function of substrate CTE12. The data slope is the biaxial Young’s modulus, with the intersection with the CTE axis (dσ/dT = 0) being film CTE. All data in Fig. 2b is an average of five samples with films approximately 2.2 μm thick for each substrate (Fig. 1e). Through these results we obtained a biaxial Young’s modulus of 19.6 ± 0.8 GPa and a CTE of 31 ± 1 (10−6 °C−1) for BiI3 thin films.

The CTE of glass substrates are typically in the 3–6 × 10−6 °C−1 range, being much smaller than that determined here for BiI3. Thus, solar cells or other electronic devices based on BiI3 deposited on glass may suffer degradation with time due to the marked mismatch between their thermal expansions. Conversely, a high value of BiI3 CTE makes it suitable for deposition onto polymeric substrates, since they possess high CTE25. Intrinsic stress or stress due to lattice mismatches may be reduced by the use of a buffer layer26,27. It is likely that with this procedure one is able to reduce the effect of stress due to a difference in thermal expansion. The inclusion, however, of an additional layer in electronic devices requires careful control of its effect in the device’s performance. Typical values for the coefficient of thermal expansion of conventional amorphous semiconductors (amorphous silicon and germanium) are in the 1–10 × 10−6 °C−1 range12,15, which is much smaller than the one obtained here for BiI3. As far as we are aware, no data for perovskite thin films have been reported yet.

Hardness and reduced Young’s Modulus

Figure 3 shows a typical load-displacement curve obtained from nanoindentation measurements performed on a BiI3 film. For this single measurement, one obtains a reduced Young’s modulus of 27.8 GPa and a hardness of 0.79 GPa.

Figure 3
figure 3

Typical nanoindentation curve of a 2.2 μm-thick BiI3 film deposited on 211 Precision glass.

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It is a well-known fact in this field of study that the mechanical properties of substrates greatly affect hardness measurements. Thus, we carried out the nanoindentation measurements as a function of penetration depth, from 2% to approximately 50% of film thickness on BiI3 films (2.2 μm), so to evaluate this effect. Figure 4a demonstrates that the hardness of BiI3 films displays similar behavior in all substrates, indicating that the substrate does not greatly affect the measurements in a broad range of penetration depths, as expected for soft films deposited onto hard substrates28. Higher hardness values on the films’ surfaces were attributed to indentation size effect (which is to be expected in soft materials) and related to strain gradient plasticity28,29. An increase in the error bar for this region likely relates to defects in the surface. Since this region (~100 nm thick) is much thinner than the film thickness (2.2 μm), TIB measurements are not much affected by these defects. To use such films in devices, these defects can be reduced by the improvement in the deposition process, or by the use of passivation treatments, for instance. Hardness has a tendency to stabilize at the same value (0.76 ± 0.01 GPa) in penetration depths from 10% to 50% of film thickness, regardless of the substrate, indicating that this value is that which best represents the hardness of BiI3 thin films. P. M. Johns30 reported a value of 0.68 ± 0.014 GPa, obtained through dynamic indentation measurements, using atomic force microscopy in the (001) orientation of BiI3 crystal – which is comparable to the value we obtained for our microcrystalline films. 0.76 GPa may not be a high hardness value, but it is sufficient to permit the handling of a device without affecting its integrity; in fact, smaller values (inside the 0.2–0.45 GPa range) have been reported for few perovskite films18. The values for typical amorphous semiconductors (silicon and germanium) are, however, one order of magnitude higher31,32.

Figure 4
figure 4

Maximum penetration depth dependence of hardness (a) and reduced Young’s modulus (b), obtained by nanoindentation for 2.2 μm thick BiI3 films deposited on 211 Precision glass, 7059 Corning glass, Z-cut quartz, 〈111〉 silicon and fused silica.

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After a maximum penetration depth of 10% film thickness, one may observe a deviation of the reduced Young’s modulus (Er) (Fig. 4b). It is likely that this behavior is associated with the substrates’ mechanical properties28. The substrates’ hardness and Young’s modulus, determined using the same nanoindentation apparatus, are much higher than those of the films (see Methods section). These characteristics are positive for hardness determination, but the elastic constant of the thin films are more dramatically affected by the substrate than is the measurement of hardness, as reported by R. Saha et al.28. Considering this, one assumes that the average values obtained with indentation to the order of 10% penetration depth (27.1 ± 0.5 GPa) best represent the reduced Young’s modulus for BiI3 films. Sun et al.18 reported Young’s modulus for a number of lead halide perovskite single crystals in the 8–16 GPa range.

Table 1 summarizes the five thermomechanical properties of the BiI3 films that we obtained in this study. For the sake of comparison, the obtained biaxial [E/(1 − ν) = 19.6 ± 0.8 GPa] and reduced [E/(1 − ν2) = 27.1 ± 0.5 GPa] Young’s moduli are smaller than those theoretical (51.1 GPa and 40.9 GPa respectively) calculated by adopting Young’s modulus and Poisson’s ratio (38.3 GPa and 0.25 GPa respectively) obtained by DFT calculation for the R-3 monocrystalline phase of BiI333. P. M. Johns reported experimental data for the bulk modulus (16.6 ± 5.5 GPa) determined by dynamic indentation using atomic force microscopy for the (001) surface of BiI3 crystal30. Since our films are microcrystalline, we expected the elastic moduli to be smaller than those in single crystals, due to a discontinuity in the structure at the microcrystalline grain boundaries, which also reduces the coordination number and thus, Young’s modulus. The small values of biaxial and reduced Young’s moduli permit a good amount of flexibility, as these indicate that a greater deformation in the material structure is possible when a force is applied, making BiI3 suitable for deposition on flexible substrates.

Table 1 Thermomechanical properties of BiI3 obtained by nanoindentation and thermally induced bending techniques: stress at 300 K (σ300K), hardness (H), coefficient of thermal expansion (CTE or α), and biaxial [E/(1 − ν)] and reduced [E/(1 − ν2)] Young’s moduli.
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By using the biaxial [Ef/(1 − νf)] and reduced [Ef/(1 − νf2)] Young’s moduli of the films it would be possible, in principle, to separately calculate Ef and νf34; however, it may only be possible to adopt this method for isotropic material. As observed here, Fig. 1a, BiI3 is an anisotropic material, with a preferential orientation in the (003) direction. The biaxial Young’s modulus extracted from TIB measurements relates to a direction parallel to the surface; and the reduced Young’s modulus obtained by nanoindentation is not limited to one specific orientation. Thus, applying a combination of these two methods for extracting Poisson’s ratio and Young’s modulus separately may provide incorrect data.

Conclusions

The thermomechanical properties of BiI3 were determined for films prepared by thermal evaporation. The stress of the films was slightly tensile. By adopting different substrates with different thermal expansion coefficients, we calculated the coefficient of thermal expansion for the BiI3 films: (31 ± 1) × (10−6 °C−1), which is much greater than that of currently adopted substrates for solar cell manufacturers. The films presented a hardness of ~0.8 GPa, thus rendering them appropriate for electronic devices lacking protective coatings. Two elastic moduli related to Young’s modulus and Poisson’s ratio – the biaxial and reduced Young’s moduli – were obtained (19.6 ± 0.8 GPa and 27.1 ± 0.5 GPa respectively). By applying these two techniques therefore, we were able to obtain five useful thermomechanical properties in BiI3 films: stress, hardness, coefficient of thermal expansion, and reduced and biaxial Young’s moduli.

Methods

Sample preparation

Bismuth triiodide (BiI3) thin films were grown by the thermal evaporation of BiI3 powder (Sigma Aldrich, 99.999% trace metal basis) using a tungsten crucible, on double-sided polished substrates. The chamber base pressure was 2 × 105 Torr, and 25 mm × 5 mm substrates were located above the crucible, at a distance of 9 cm. After deposition, film annealing occurred at 140 °C for 1 h, the final thickness being of about 2.2 μm. We used substrates with known mechanical properties: fused silica, 〈111〉 silicon, 211 Precision Glass, 7059 Corning Glass and Z-cut quartz, the properties of which are presented in Table 2.

Table 2 Properties of fused silica, 〈111〉 silicon, 7059 Corning glass, 211 Precision glass, and Z-cut quartz substrates: coefficient of thermal expansion (CTE), Young’s modulus (Es), Poisson’s ratio (νs), Es/(1 − νs2) calculated by using Es and νs, reduced Young’s modulus Er = Es/(1 − νs²) and hardness (H) experimentally determined by nanoindentation, and thickness.
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Optical and structural properties

We measured X-ray diffraction (XRD) with a Bruker D8 Advanced diffractometer, using a Cu Kα radiation source. Transmittance data were collected with a UV-Vis M51 spectrophotometer from Bel Photonics. The optical constants were recovered from the transmittance data using the PUMA (Pointwise Unconstrained Minimization Approach) package35. A FIB-SEM Nova 200 Nanolab spectrometer generated the michograph images. We collected the photoluminescence (PL) spectra by exciting the material with a 442 nm laser with an integration time of 60 s. The film thickness and curvature we obtained at room temperature using a Dektak 150 Surface Profiler.

Stress, coefficient of thermal expansion and biaxial Young’s Modulus

The thermally induced bending technique (TIB) was utilized to determine film stress as a function of temperature (Fig. 5). Fundamentally speaking, a laser beam passes through a beam splitter, creating two beams that reach the film, these being reflected onto two position detectors, from which one can calculate the curvature radius (R) of the film-substrate composite. When the sample undergoes heating its curvature changes due to a difference between the CTE of the substrate and the film. Thus one may calculate the temperature dependence of stress [σ(T)] in the film, using the modified Stoney equation36,37:

$${\rm{\sigma }}({\rm{T}})=[\frac{{{\rm{E}}}_{{\rm{s}}}}{1-{{\rm{\nu }}}_{{\rm{s}}}}]\frac{{{\rm{t}}}_{{\rm{s}}}^{2}}{6{{\rm{t}}}_{{\rm{f}}}}(\frac{1}{{\rm{R}}({\rm{T}})}-\frac{1}{{{\rm{R}}}_{0}}),$$
(1)

where t is the thickness, and subscripts s and f respectively refer to the substrate and film. 1/R and 1/R0 refer to the curvature of the film-substrate sample, and the substrate before deposition, respectively.

Figure 5
figure 5

Scheme for the apparatus used in the thermally induced bending technique, to determine the curvature dependence of the film-substrate composite as a function of temperature.

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The derivative of stress with respect to the temperature dσ/dT relates to the substrate (αs) and the film (αf) coefficients of thermal expansion by Eq. (2):

$$\frac{{\rm{d}}{\rm{\sigma }}}{{\rm{dT}}}=[\frac{{{\rm{E}}}_{{\rm{f}}}}{1-{{\rm{\nu }}}_{{\rm{f}}}}]({{\rm{\alpha }}}_{{\rm{s}}}-{{\rm{\alpha }}}_{{\rm{f}}}).$$
(2)

Using two substrates with different thermal expansion coefficients one can solve Eq. (2) in order to extract the CTE and Young’s biaxial modulus [Ef/(1 − νf)] of a given film12. Thick films (having a thickness of at least 1 micron) are required for these measurements due to a limitation in the technique, which demands that one bends a thick substrate (thickness of about 500 μm) inside a small temperature range (of less than 100 °C). In light of this, the thicker the film the more appropriate it is for this measurement. In addition, measurements are made by the use of two laser beams 10 mm apart, thus requiring a homogenous film distributed along the substrate.

For these measurements, we adopted a 30 mW helium-neon laser and heated the samples in an argon atmosphere from room temperature to 130 °C, at 6.3 °C/min, the samples remaining at this temperature for 20 minutes. Following this, they underwent cooling to room temperature, followed by heating and then further cooling. The stress temperature dependence was obtained during the two cooling cycles, from room temperature to 80 °C. Five BiI3 films were deposited on each type of substrate in different deposition runs, to reduce uncertainty regarding the thermomechanical properties encountered in the extracts.

Hardness and reduced Young’s Modulus

We carried out nanoindentation measurements of the BiI3 films using a Berkovich diamond tip (NanoTest-300) with a dwell time of 20 seconds, and the load-displacement curves we analyzed through the Oliver and Pharr method13. Detailed description of the system and procedures appear elsewhere38. Hardness (H) and reduced Young’s modulus (Es/(1 − νs2) of all substrates were also determined by nanoindentation (Table 2). The values for glassy (amorphous) substrates (fused silica, 211 Precision Glass and 7059 Corning Glass) are very close to the calculated ones using reported data for Young’s modulus (Es) and Poisson’s ratio (νs). This is unsurprising, since these substrates are isotropic. Conversely, for crystalline substrates (〈111〉 silicon and Z-cut quartz), which are anisotropic, the experimental reduced Young’s modulus determined by nanoindentation is different from the one calculated. This is because indentation with a Berkovich diamond tip involves several crystalline orientations with various mechanical properties.