Determination of the complete set of optical parameters of micron-sized polycrystalline CH3NH3PbI3−xClx films from the oscillating transmittance and reflectance spectra

The complete set of optical parameters of micron-sized polycrystalline CH3NH3PbI3−xClx films deposited by the vacuum co-evaporation of lead iodide and methylammonium chloride is determined by analysis of oscillating optical transmittance and reflectance spectra in the wavelength range 400–1000 nm. It is shown that for a medium and weak absorption region the envelope method is valid for the extraction of refractive index, extinction and absorption coefficient when is using only transmittance spectra. As well thickness of the film is determined from transmittance and reflectance spectra with interference-effect. The absorption coefficient for the strong absorption region and optical band gap (direct transition at Eopt = 1.62 eV) are calculated based on transmittance and reflectance spectra by using conventional approximated formulas.


Introduction
Application of films of various materials in electronics assumes knowledge of such parameters as thickness (d f ), refractive index (n f ), extinction (k f ) and absorption coefficient (α) and optical band gap (E opt ) in the case of semiconductors and dielectrics. For films of the same material deposited in different ways, these parameters can be very different. Therefore, the express determination of these parameters for technology development is quite important.
Desire to determine the complete set of optical parameters by a minimum number of measurements has led to a unified (all-in-one) solution for this problem based on the oscillating optical spectra. These oscillations are caused by the interference phenomenon occurring due to the relative difference between substrate and film refractive indices and thicknesses. Note that these developed express methods for determining the complete set of optical parameters of films are based only on spectrophotometric measurements, which are the simplest compared to other methods and doesn't require special external conditions. Besides, in the case of air/film/ substrate/air configuration and normal incident of light, the formulas based on the solution of the inverse problem of thin-film optics are very simple.
The basis for determining the optical parameters of films only from transmittance spectra with interferenceeffect is an envelope method developed by Swanepoel [1]. In terms of Swanepoel's method, which is based on the idea of Manifacier et al [2], n f , k f and α of films deposited on transparent finite thickness substrate can be calculated in the medium and weak absorption region by creating upper and lower envelopes of transmittance spectra. Then, the envelopes around the maxima and minima are considered as a continuous spectrum versus wavelength. Also, E opt and α in the strong absorption region (none oscillation region) are calculated by conventional approximated formulas. This method is applicable to any transmission spectrum showing an appreciable interference pattern. The major limitation is applicability to relatively thick films since at lower film thickness the interference extremes are spaced further apart and interpolation between these extremes becomes more difficult. Swanepoel's method is very practical for quick determination of a complete set of optical parameters of films, although the accuracy is limited by an absence of the right way to construct envelopes between interference extremes. It is appropriate to note that observation of oscillates on optical spectra strongly depends on film geometrical properties and suggests a homogeneous smooth surface with uniform thickness and homogeneity of the refractive index regardless of crystalline structure. If the thickness of the film, for example, is not uniform or is slightly wedge-shaped all interference effects are destroyed, and so the existence of oscillations on optical spectra for the relatively thick film is the primary indicator for the quality of filmformation technology.
The validity of Swanepoel's method was demonstrated on various films, such as a-Si:H, As-S, Ge-Sb-Se and similar chalcogenides, CdTe, ZnO, Cu 3 N [1, [3][4][5][6][7][8][9]. In this article, a complete set of optical parameters of micronsized polycrystalline CH 3 NH 3 PbI 3−x Cl x (MAPbI 3−x Cl x ) perovskite films are determined for the first time from independently measured oscillating transmittance (T) and reflectance (R) spectra via calculations based mainly on Swanepoel's method. The main interest in such organic-inorganic halide materials is caused by the possible use of them in solar cells. Efficiencies of photovoltaic devices based on these materials have reached over 20% (22.1% efficiency on CH 3 NH 3 PbI 3 absorber [10]). The serious obstacle for perovskite solar cells is their not sufficiently high stability to the humidity and ultraviolet radiation. But, it should be noted that mixing of CH 3 NH 3 PbI 3 compound with other halogens (chlorine and bromine) leads to an increase of stability to degradation [11,12] and also affects significantly on the physical properties. For example, MAPbI 3−x Cl x films show suited bandgap (1.6 eV), long electron and hole diffusion lengths (>1 μm [13,14]), and therefore are in demand for solar cell applications.
Almost all kinds of thin-film technologies are applicable to the fabrication of organic-inorganic halide films. But, we adhere to the opinion that vacuum technologies are more controllable for the synthesis of such complex films. Besides, vacuum deposition leads to the formation of void-free and good crystalline films, which are important factors for functional electronic devices. This is already shown in the article [15], where authors determined that the main x-ray diffraction (XRD) peaks are in identical positions for both solution-processed and vapor-deposited films which indicate that both techniques have produced the same MAPbI 3−x Cl x perovskite film, but vacuum-deposited films were relatively uniform, dense and void-free. As a precursor, they used methylammonium iodide (CH 3 NH 3 I; MAI) and lead chloride (PbCl 2 ). In this article, MAPbI 3−x Cl x films were synthesized by dual-source thermal evaporation technique in co-evaporation mode from precursors lead iodide (PbI 2 ) and methylammonium chloride (CH 3 NH 3 Cl; MACl) in contrast to [15]. During the coevaporation of MACl and PbI 2 , the process of chemical reaction and formation of MAPbI 3−x Cl x film on a glass substrate occurs. Optical quality polycrystalline films were produced without additional annealing, which confirms by the oscillation nature of optical spectra and XRD investigations.

Sample preparation and investigation details
Dual-source vacuum thermal evaporation technique was used to grow of MAPbI 3−x Cl x films from MACl and PbI 2 precursors on glass substrates at room temperature. For the evaporation of precursor materials, quartz crucibles were used. As much as both materials well sublimated, evaporating temperatures were adjusted bellow of PbI 2 melting point (412°C) and MACl flashpoint (208°C), which allows a suitable control of the deposition process. During the co-evaporation of precursors (source-substrate distance 5-10 cm and residual vacuum in chamber ∼10 −5 torr), the process of chemical compound synthesis on a glass substrate occurs (growth rate 100-200 nm min −1 ). Finally, as-deposited (PbI 2 +MACl) films were annealed in air at 100°C for up to 1 h.
The basic investigations of as-deposited and annealed films were carried out by (i) thickness and roughness measurements (Mitutoyo Surftest SJ-410 surface profilometer); (ii) investigation of morphology and structure (Magellan 400 scanning electron microscope (SEM) and x-ray Mini Diffractometer MD-10 with CuKα radiation source (radiation wavelength λ=1.54 Å), respectively); (iii) independent measurements of T and R at the near-normal incidence of light (spectrophotometer Filmetrics F20 (spectral range 400-1000 nm)). Films with a thickness of 1 to 4 μm were investigated.
The main result of the technological route is that as-deposited and annealed film practically similar by structural and optical quality, are void-free and mainly composed of nanorod-like crystals ( figure 1(d)). The surface roughness of annealed micron-sized film (measured on arbitrary areas across a length 500 μm) corresponds to ∼7-8 nm and differs a little from the glass substrate roughness (∼3-4 nm). XRD patterns of asdeposited and annealed film (figures 1(a), (b)) exhibit the same additive-free polycrystalline CH 3 NH 3 PbI 3 -like tetragonal structure [16]. Also, the optical measurements related to T spectra did not reveal any noticeable changes ( figure 1(c)).

Optical characteristics of MAPbI 3−x Cl x films
Only optical properties of annealed films deposited onto transparent glass substrate were studied in the case of air/film/substrate/air configuration and near-normal incident of non-polarized light (figure 2) since asdeposited and annealed films are practically similar by structural and optical quality (see figures 1(a)-(c)). Figure 3(a) shows T spectra of films with different thicknesses. It is seen that films exhibit high absorption and a sharp edge below 750 nm. The existence of oscillations is explained by the interference effect occurring due to d f = d s and n f ≠ n s under the conditions that d f and n f respectively are uniform and isotropic. Such conditions are met in our measurements. Note also that relatively thick films were investigated since at lower film thickness interpolation between extremes becomes more difficult. Beforehand we say that an explicit dependence of optical properties on film thickness is not observed. Therefore, the possibility of determining a complete set of optical parameters is shown for one of the films ( figure 3(b)).

The region of strong absorption
This region is characterized by interference-free transmittance and reflectance spectra. Taking into account absorption and single reflection for air/film/substrate/air configuration (see figure 2) α can be calculated from  independently measured T and R data by using of αd p =ln[(1−R)/T] approximated relation, where d p is the thickness of film measured, for example, by a profilometer. Note that this relation almost completely eliminates residual disturbance from the optical interference-effect and is applicable to any films, as long as the film is a homogeneous single layer [17]. Figure 4(a) shows the dependence of α (semi-logarithmic scale) from photon energy (E) for MAPbI 3−x Cl x film (thickness d p ≈2.7 μm) calculated from T and R data. In order to establish the nature of optical transitions, α was approximated by power-law αE=B(E−E opt ) m . This approximation shows that there is a direct (m=1/2) transition at 1.62 eV ( figure 4(b)).
There is no way to calculate n f and α independently in this region from the transmission spectrum alone. , where R is measured reflectance and k f =αλ/4π. But, if the relation (1−R)/T completely eliminate residual oscillations from the optical interference-effect when α calculated, yet residual oscillations on R leads to errors for n f data. Therefore, only an estimation is done for n f at 630 nm by using experimental determined values R=0.0864 and k f =0,085 (n f =1.7).

The region of medium and week absorption
The optical characterization of films in this region is given mainly based on Swanepoel's method [1] from independently measured oscillation existed T and R spectra (see figure 3(b)). For this region α ≠ 0 and exp(-αd p )<1. In terms of Swanepoel's method, the optical parameters of films can be calculated in the medium and weak absorption region by creating upper and lower envelopes of T spectra. Then, the envelopes around the maxima and minima are considered as a continuous spectrum versus wavelength (T M and T m ) via fitting by the mathematical program. In our case, fitting of T M and T m is carried out by a polynomial function of the thirdorder ( figure 5(a)).  Figure 5(c) shows the dependence of α from the light wavelength. Note that T 1 represents a curve passing through the fitted T M and T m smooth curves ( figure 5(a)). Then, k f is calculated from k f =αλ/4π relation (average value is 0.006 in 800-1000 nm wavelength region).

Thickness determination
Determination of d f is the number one problem for any film-formation technology. Advanced methods, such as scanning, transmission electron and atomic force microscopy, are applicable for this task, but there are not so practical, such as optical methods, which are very easy in technical performance. For example, in vacuum technologies, which are more flexible in comparison to others, the determination of d f on test-samples is fine carried out in situ at a certain wavelength by a spaced apart light-emitting diode containing optocoupler. However, this method needs a calibration, which is mainly performed by ex situ profilometer measurement. Also were used, but relatively infrequently, spectrophotometric measurements of oscillation existed T and/or R spectra. Let's see how it is done in the case of oscillation spectra shown in figure 6 (our case).
If n 1 and n 2 are the refractive indexes for two neighboring extrema at λ 1 and λ 2 , the film thickness may be calculated by the relation d=(λ 1 λ 2 )/4(λ 1 n 1 − λ 2 n 2 ), which is withdrawn from the basic equation for interference 2nd=mλ, where m is an integer for maxima and half-integer for minima. Although this relationship is correct, it is very sensitive to n f data. In our case, there is no way to calculate d f since we have big errors in comparison with profilometer measured data. However, since n f has a weak dispersion in an 800-1000 nm wavelength region, we can use the approximate expression d=(λ 1 λ 2 )/4n 0 (λ 1 − λ 2 ), where n 0 =2.15 is average refractive index. The calculated results for each pair of neighboring extrema λ 1 and λ 2 are presented in

About the accuracy of determined optical parameters and thickness
Although the application of the envelope method to determine the optical parameters of films from transmittance spectra with interference-effect leads to some inaccuracies associated with an absence of the right way to construct envelopes between interference extremes, it can be understood that the practicality of this method lies in the quickly determining of the complete set of optical parameters using only the spectrophotometric measurements of T and R.
Most often the obtained calculated results are compared with more accurate measurements of these parameters by ellipsometry. However, we give some estimates based on the accuracy of our measuring instruments.
For the extracting of n f , k f and α in the region of weak and medium absorption when is using only T spectra with interference-effect the values of T M and T m must be obtained. The maximum absolute accuracy of T M and T m measured on spectrophotometer Filmetrics F20 is not more than 1%. A similar situation is well described by Swanepoel in [1], where it is shown that 1% accuracy of T M and T m yields a relative error not more than 3% for the accuracy of the calculated values of n f and α. The results of our calculations with such accuracy were compared with the results of other authors performed by using ellipsometry and spectrophotometry [19][20][21] and there is a good agreement.
Although non-contact profilometers (for example, SJ-410 series) have certain difficulties in thickness measuring since always require a substrate-film border, they are highly precise (1 nm resolution) for the ex situ thickness and roughness measurement. Therefore, the thickness of the film extracted from the oscillating transmittance and reflectance curves (see section 3.3) was compared with profilometer data. Although the accuracy of determined wavelengths of neighboring extrema is precise (less than 1.5 nm), there are big errors for calculated d f data which are explained via absolute accuracy (not better than 1%) of measured T M and T m . The relatively better result compared to profilometer data gives when we use an average refractive index for this wavelength region.

Summary
In this article, the optical parameters of optical quality micron-sized polycrystalline MAPbI 3−x Cl x perovskite films are determined by using the spectrophotometric measurements of T and R. For these films it is shown at the first time, that in the medium and weak absorption region envelope method is valid for the extraction of n f , k f and α with an accuracy not worse than 3% when is using only T spectra with interference-effect. Also, α and E opt are calculated for the strong absorption region by using conventional approximated formulas.