Temperature dependency of excitonic effective mass and charge carrier conduction mechanism in CH3NH3PbI3−xClx thin films

In this paper we explain the temperature dependence of excitonic effective mass and charge carrier conduction mechanism occurs in CH3NH3PbI3−xClx thin films prepared by chemical dip coating (CDC), spray pyrolysis (Spray) and repeated dipping-withdrawing (Dipping). Hall Effect study confirmed that prepared CH3NH3PbI3−xClx samples are p-type semiconductor having carrier concentration of the order of ~ 1016 cm−3. The charge carrier mobility, mean free path and mean free life time were found to decrease with increasing temperature due to polaronic effect. The excitonic effective mass is estimated to (0.090–0.196)me and excitonic binding energy (15–33) meV, well consistent with Wannier-Mott hydrogenic model and the nature of exciton is likely to be Mott-Wannier type. From electrical measurement, it was observed that charge carrier conduction in CH3NH3PbI3−xClx is governed by migration of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{I}}^{-}$$\end{document}I- and CH3N \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{H}}_{3}^{+}$$\end{document}H3+ vacancies and vacancy-assisted diffusion processes depending on temperature.


Scientific Reports
| (2021) 11:10772 | https://doi.org/10.1038/s41598-021-90247-x www.nature.com/scientificreports/ of charge-carriers, grain boundary barrier height, carrier mean free path-life time in CH 3 NH 3 PbI 3−x Cl x still perplexes the researchers. It is well known that the mixed halide perovskite undergoes a phase transition from orthorhombic-tetragonal-cubic at 160 K and in between (315-330) K, respectively 18,19 . However, the study of charge carrier dynamics is limited to tetragonal phase while it is also important to explore such properties for cubic phase above room temperature (RT).
Recently, it is reported that charge carries generate self-induced rotation of the organic part (CH 3 N H + 3 ), which polarizes lead halide perovskite lattice to form quasi-particle polarons [20][21][22][23][24][25] . The conception of polaron is used to explain intrinsic electrical properties because it describes the interaction between charge carriers and phonons. The interaction of charge carriers with the organic part has significant influence on the effective mass, temperature and magnetic field dependent carrier transport and electrical conductivity of the mixed halide perovskite material.
In our previous work we report the characterization of nano-crystalline CH 3 NH 3 PbI 3−x Cl x thin films prepared on glass substrate by chemical dipping-withdrawing (CDC) 2 , spray pyrolysis (Spray) 5 and repeated dipping-withdrawing (Dipping) 3 techniques in an ambient atmosphere. Our study confirmed the presence of tetragonal and mixed cubic-tetragonal phase in CH 3 NH 3 PbI 3−x Cl x thin film. The film morphology was composed with spherical, rod, cuboid and polyhedral like crystal grains of sizes 100 nm to 2 μm 2,3,5 . However, this article concentrates on the charge carrier transport of CH 3 NH 3 PbI 3−x Cl x thin films using Hall Effect and dc-electrical conductivity measurement as a function of temperature, ranging from RT to 378 K. The carrier concentration, mobility, excitonic effective mass, excitonic binding energy, Fermi level, grain boundary barrier height and mean free life time of charge carriers are calculated from Hall Effect study. Furthermore, activation energies in CH 3 NH 3 PbI 3−x Cl x thin films are exposed from electrical study. The effect of polarons on charge carrier dynamics and possible carrier conduction mechanism in CH 3 NH 3 PbI 3−x Cl x thin films has been discussed. Therefore, in-depth study of charge carrier transport and conduction mechanism above RT for CH 3 NH 3 PbI 3−x Cl x may provide a broader impact in the arena of perovskite research.

Results
Temperature dependent Hall effect study. Temperature dependent Hall voltage measurement is done at a constant magnetic field of 9.815 KG and the variation of Hall voltage is shown in Fig. 1. From the Hall Effect study Hall mobility (µ H ) and carrier concentration (n c ) have also been calculated.
From Fig. 1 it is seen that the Hall voltage is positive and increased up to a certain temperature after which it decreases all through the measured temperature range for all samples. The positive sign of Hall voltage indicates that CH 3 NH 3 PbI 3−x Cl x is a p-type material. It is reported that a lot of Pb, CH 3 NH 3 , I and Cl vacancies present in the films 17,26,27 as because precursor solution was prepared by dissolving CH 3 NH 3 I and PbCl 2 at a molar ratio 3:1. However, Pb and CH 3 NH 3 vacancies play the vital role for p-type conductivity of prepared CH 3 NH 3 PbI 3−x Cl x thin films because of the lower formation energy of Pb and CH 3 NH 3 compared to halogen vacancies.
The temperature dependent carrier concentration (left scale) and mobility (right scale) for (a) CDC, (b) spray and (c) dipping deposite CH 3 NH 3 PbI 3−x Cl x thin films are shown in Fig. 2. The carrier concentration and mobility of dipping deposited sample is found almost half of the CDC and spray deposited samples. However, RT mobilities are found higher for all our samples than previously reported works 6,14,16,19,[28][29][30][31][32] . Table 1 shows a comparison of RT mobilities for perovskite CH 3 NH 3 PbI 3−x Cl x obtained in different studies. It is reported that the breaking of inversion symmetry generates Rashba effect 33 which enhance longitudinal optical phonon scattering by displacing the organic part or Pb-halogen bending or stretching and limits the increase of charge-carrier mobility at room temperature.
The carrier concentration and mobility can be affected by both magnetic field and temperature but the effect of temperature is dominant. In this study, the carrier concentration of all CH 3 NH 3 PbI 3−x Cl x samples is found to increase exponentially ( Fig. 2) with increasing temperature but mobility shows completely an opposite trend. Such behavior can be explained as: the presence of Pb, CH 3 NH 3 and halogen vacancies in mixed halide perovskite creates free dipolar polarons by inducing a rotational re-organization of organic CH 3 NH 3 dipoles 20 ; such polarons   where E a is the acceptor ionization energy, N a is the acceptor density, m * h is the effective mass of hole, T is the absolute temperature, K B is the Boltzmann constant and ħ is the reduced Planck constant. The value of E a can be obtained from the slope of ln n c T − 3 4 vs. 1/T graph (Fig. 3). From figure it is clear that the variation of carrier concentration with temperature can be defined by two discrete temperature regions (TR): TR-I (298-343) K and TR-II (344-378) K. In TR-II, the values of ln n c T − 3 4 decrease linearly with inverse temperature, whereas, in TR-I, it decreases monotonically with lower slope compared to TR-II. The effective mass of hole m * h can be found out using E a as, where ε is the dielectric constant of the material and ε 0 is the permittivity of free space. Several research groups used dielectric constant ε = 5.6 to 25.7 (for high to low frequency) and excitonic effective mass μ* = 0.1m e for calculating excitonic binding energy of perovskite. However, in this study ε = 9 has been used for calculating m * h according to hydrogenic model 35 . The values of m * h are estimated to 0.16m e , 0.42m e , 0.38m e (m e is the rest mass of electron) in the TR-I and 2.16m e , 2.23m e , 3.04m e in the TR-II for CDC, spray and dipping deposited samples, respectively. The estimated m * h is found in good agreement with recently reported values 36,37 . Taking the effective mass of electron m * e = 0.21m e from theoretical calculations 38 , the excitonic effective mass μ* is estimated to (0.090-0.196)m e using equation, 1/μ* = 1/m * e + 1/m * h and tabulated in Table 2. The estimated μ* in TR-I is close to ~ 0.104m e 35 , found for tetragonal phase (≥ 145 K). However, μ* in TR-II is found high because of non-parabolic nature of valance bands in CH 3 NH 3 PbI 3−x Cl x . Theoretical study 39 suggested that lead vacancies diminish antibonding atomic orbital overlap resulting in flatten of valance bands. Moreover, polaronic effect 40 and strong hydrogen bonding due to van-der-Waals interactions 39 may also increase μ * .
The excitonic binding energy, E b of all perovskite samples has been calculated using the equation, The excitonic binding energy is found (15-24) meV for TR-I and (32-33) meV for TR-II, which is well consistent according to Wannier-Mott hydrogenic model. This variation of E b in TR-I and TR-II is due to temperature dependent polaronic effect of CH 3 NH 3 PbI 3−x Cl x . The extending radius of the lowest bound state r * is calculated to ascertain the nature of excitons in CH 3 NH 3 PbI 3−x Cl x using the equation, r * = ε (m e /μ * ) r b , where, r b is the Bohr radius. The r * is estimated to 5.29 nm, 3.40 nm, 3.52 nm in TR-I and 2.49 nm, 2.48 nm, 2.43 nm in TR-II for CDC, spray and dipping deposited samples. The value of r * is larger than the lattice constants (either cubic or tetragonal) of CH 3 NH 3 PbI 3−x Cl x indicating that the exciton is weak and likely to be Mott-Wannier type.
The position of Fermi level E F can be determined by knowing the value of E a , N a and m * h of the following equation The values of E a , N a and E F for both higher and lower temperature regions are tabulated in Table 2. The parameters n c and N a are not equal but vary with temperature and film processing methods as well, indicates CH 3 NH 3 PbI 3−x Cl x is very sensitive to environment, chemical composition, growth parameters etc. The Fermi energy is found negative means E F lies below the acceptor level.
Grain boundary parameters and grain size calculations. The transport properties of a polycrystalline semiconductor are generally influenced by grain boundary effect. According to grain boundary trapping model 41 , the trapping states create a depletion region in the grain and a potential barrier at the interface. In a semiconductor sample the relation between charge carrier mobility and grain boundary barrier height can be expressed as where, ϕ b is the grain boundary barrier height and ζ is the grain size. The slop of ln(μ h T 1/2 ) vs 1/T graph (Fig. 4) gives the barrier height ϕ b and intercept will provide grain size ζ.
The barrier height and grain size of all samples have been estimated for two different temperature regions (TR-I, TR-II) and tabulated in Table 3. From table it is clearly seen that the formation of bigger grain size is favorable at low temperature (TR-I) for mixed halide perovskites.
Mean free path and mean free time calculations. According to conventional Drude-Sommerfeld model, the carrier mean free path (L m ) and mean free time (τ m ) in CH 3 NH 3 PbI 3−x Cl x thin films can be calculated from the following equations The variation of L m and τ m with temperature for CDC, spray and dipping deposited CH 3 NH 3 PbI 3−x Cl x thin films are given in Fig. 5.  I TR-II TR-I TR-II TR-I  TR-II  TR-I TR-II TR-I TR- www.nature.com/scientificreports/ From figures it is seen that both L m and τ m are lower at TR-I compared to TR-II. The magnitudes of L m and τ m decrease with the increase of temperature except a sudden jump at around 340 K. The polaronic effect originated from rotational re-organization of CH 3 NH 3 dipoles enhances trap assisted recombination with increasing temperature which reduces the carrier mean free path and mean free life time.
In the mixed halide perovskite, the transition from tetragonal to cubic phase occurs at temperature ~ 330 K 19,42 due to the tilted inorganic PbI 6 octahedral and disparity of organic CH 3 N H + 3 rotation. Such phase transition can modify the physical properties of mixed halide perovskites, though it does not cause remarkable change in optical and photovoltaic properties 43 . Recently, tetragonal to cubic phase transition is associated with the relative strength of the metal-halogen and hydrogen bonds as reported 44 . In our study, during the temperature dependent Hall measurement we have applied a magnetic field of ~ 1 T. This magnetic energy shifted the tetragonal to cubic phase transition at slightly higher temperature at (340-344) K.

Conduction mechanisms and activation energies.
The electrical conduction process in CH 3 NH 3 PbI 3−x Cl x is rather complex. It is strongly dependent on temperature, vacancies or interstitial defects and activation energies of the materials. In general, CH 3 NH 3 PbI 3−x Cl x includes Pb, CH 3 NH 3 and halogen vacancies as suggested from theoretical and experimental studies 45,46 . The low energy vacancies create a rotational reorganization of organic CH 3 NH 3 dipoles resulting in free dipolar polarons in mixed halide perovskite 20 . Eames et al. 45 proposed that these vacancies migrate from one site to the neighboring site due to low activation energy. They found activation energies involved 0.58 eV and 0.84 eV for migrating I − and CH 3 N H + 3 vacancies, respectively. Futscher et al. 47 also reported that the predicted activation energies for migration of I − and CH 3 N H + 3 are (0.08-0.58) eV and (0.46-1.12) eV, respectively. Besides, grain boundary effect has an influence on carrier transport and the activation energies (0.18-0.27) eV were predicted for different grain size above 260 K 48 . In Fig. 6, it is clearly seen that there are three temperature regions where carriers are conducted through different conduction mechanisms. For further clarification, the activation energy was also calculated by Arrhenius equation which contains three separate activation energy terms,  I  TR-II  TR-I TR-II TR-I TR-II TR-I TR-II ΔE I  ΔE II ΔE  www.nature.com/scientificreports/ where, K B is the Boltzmann constant, T is the absolute temperature, σ I , σ II and σ III are pre-exponential factors and ΔE I , ΔE II and ΔE III are activation energies for region I, II and III, respectively. From the slope of lnσ vs 1000/T plot (inset of Fig. 6), the activation energies were calculated and tabulated in Table 3. From Fig. 6, it is seen that dc-electrical conductivity (σ dc ) decreases with increasing temperature in region I (294-317) K. The initial decrease is caused by the strong interactions in between organic-inorganic part and rotational disorder of methylammonium cation within perovskite structure. In addition, longitudinal optical phonon scattering may also decrease the conductivity with temperature in region I. The activation energy ΔE I (Table 3) is found negative in region I, suggesting the Fermi level is pinned to the valance band of all samples. In region II (318-357) K, the dc-electrical conductivity increase slowly with increasing temperature and ΔE II = 0.44, 0.51, 0.47 eV for CDC, spray and dipping deposited samples respectively, which indicates the migration of I − vacancies to PbI 6 octahedron edge [45][46][47] . In region III (358-378) K, σ dc increases rapidly and ΔE III ˃ ΔE II . The activation energies ΔE III are found close to 0.84 eV for CDC and spray deposited and ΔE III = 0.57 eV for dipping deposited samples. The rapid increase of σ dc in region III occurs because of diffusion or migration of CH 3 N H + 3 in addition to I − vacancies to PbI 6 octahedra or neighbor central vacant site [45][46][47] . Therefore, the conduction processes are attributed to the migration of I − and CH 3 N H + 3 suggesting the existence of ionic transport in CH 3 NH 3 PbI 3−x Cl x . Moreover, the concentrations of charge carriers (majority holes) which are activated with acceptor ionization energy (E a ) favorable for the transport across grain boundaries of CH 3 NH 3 PbI 3−x Cl x samples.

Synthesis.
Lead halide perovskite solution for fabricating CH 3 NH 3 PbI 3−x Cl x thin films was prepared using the following procedure. Methylamine (CH 3 NH 2 ) solution was mixed with hydroiodic acid and ethanol at room temperature. The solution was perturbed continuously by stirring with a magnetic stirrer at a constant speed in an ice bath for 2 h. The color of CH 3 NH 3 I solution transforms from red to transparent and heated at 100 °C for 4 h in a furnace to achieve white-colored CH 3 NH 3 I powder. Finally, CH 3 NH 3 I and lead(II) chloride powders were dissolved in anhydrous N,Ndimethylformamide at a molar ratio 3:1 to achieve a mixed halide perovskite precursor solution. CH 3 NH 3 PbI 3−x Cl x thin films have been fabricated at ambient atmosphere by three different methods. These methods are (a) Chemical dip-coating (CDC) (b) Spray pyrolysis (spray) and (c) Repeated dipping-withdrawing (dipping). The details of preparing CH 3 NH 3 PbI 3−x Cl x solution and different steps which have been made in these methods to deposit CH 3 NH 3 PbI 3−x Cl x thin films have been reported elsewhere 2,3,5 .
Characterization. Temperature dependent Hall voltage was measured at constant magnetic field of 9.815 KG using the conventional van-der-Pauw method. The magnetic field used for the study of Hall Effect was provided by electromagnets designed and produced by Newport instruments Ltd. England. The circuit arrangement for temperature dependent Hall Effect measurement is shown in Fig. 1S. A dc voltage from the power supply unit was applied in order to flow the sample current through the specimen. Current and voltages were measured by a digital electrometer and a digital multi-meter. A voltage stabilizer was used so that a steady supply of current without fluctuation was maintained through the magnet. A special designed heater was used to vary temperature. The variation of temperature is controlled by a variac and measured by a chromel-alumel thermocouple connected with a digital multi-meter.
The resistivity of all samples was measured by van-der-Pauw method. Experimental setup of the van-dar-Pauw's specimen to measure the resistivity with varying temperature is shown in Fig. 2S. The voltage and current of all samples were measured for different temperatures. The sample is fixed to a sample holder which is placed on a specially designed heater to vary temperature. The conductivity and activation energies of prepared samples have been calculated using resistivity data. The experimental details of temperature dependent Hall Effect measurement and resistivity measurement are shown in supplementary section.