Nonlinear optical response, theoretical efficiencies, and high photosensitivity of CH₃NH₃PbI_3−xCl_x thin films for photonic applications

Nonlinear optics (NLO) is a specialized branch of optics, which has developed remarkably in the past few decades. These developments open a new window for photonic and optoelectronic research. In this journey, NLO materials play a forefront role in creating a gigantic impact on the applied features of NLO. The NLO materials interact with photons, create nonlinear responses, and gained remarkable attention for their potential applications in electro-optical switching, frequency mixing, sensing, optical oscillations, optical information, communication processing, and so forth.^1,2 On the other hand, the fabrication of noble photoresponsive, high detection efficiency with low background noise, and cost effective photodetector becomes attractive to the researcher. The next generation photodetector would be fabricated by hybrid nanostructure based materials with their new intriguing features. Recently, organic photodetectors are gained considerable attention due to their easy and low cost fabrication process, advantage of large area fabrication, and wide range of materials to fabricate ultraviolet,³ near-infrared,⁴ and color selective⁵ photodetectors. Under low light conditions, the detection of weak photocurrents with a low external quantum efficiency (EQE) is crucial for a photodetector. However, a shortcoming of an organic photodetector is its relatively low EQE values. Therefore, obtaining ultra-high EQE under low light conditions is the major challenge for organic photodetectors.

Among different NLO materials, organic–inorganic MAPbX₃-based perovskites (MA = CH₃NH₃, X = I, Cl, Br) became a new research frontier in recent years. They exhibit a myriad of properties ideal for photovoltaics (PV) applications. These materials are also favorable candidates for light harvesting,⁶ solid state lighting,⁷ visible light communications,⁸ waveguides,⁹ sensors,⁵ thin-film electronic devices,¹⁰ and highly sensitive x-ray detectors.¹¹ Importantly, the high tunable chemical components, multiple structures, molecular polarization, high absorption coefficients due to the s–p anti-bonding coupling, and capability to generate free carriers lead to outstanding nonlinear optical properties of the material, which permit a wide-ranging scope of NLO and photonic applications.

Recent studies also suggest that the organic–inorganic perovskites show high optical nonlinearity due to the change in the orientation of organic cation compared with all-inorganic perovskites.^12,13 However, a few research groups studied linear and nonlinear optical properties of tri-iodide CH₃NH₃PbI₃ and mixed halide CH₃NH₃PbI_3−xCl_x thin films.^12–22 

From those studies, the dielectric constant (ε) ∼ 6.5,¹⁹ high absorption coefficient,¹⁸ and the refractive index n_r = 2.3–3.4^{13–15,18,20} for the CH₃NH₃PbI₃ thin film in the visible range were observed. The values of n_r = 2.4–2.6 and extinction coefficient k = 0.26–1.29 are reported for the CH₃NH₃PbI_3−xCl_x thin film.²² Some other optical constants, such as dispersion parameters, energy loss function, and the interband transition strength, are also imperative in NLO materials. These parameters play a crucial role in designing spectral dispersion devices. The performance of different integrated optical devices can be enhanced by controlling the dispersion parameters. Therefore, the knowledge of the interaction of photons with matter can be studied by means of the transmittance and absorbance as well as nonlinear optical constants that are decisive to understand the optical behavior of the thin-film devices. It is noteworthy that there are no such reports available regarding the determination of dispersion parameters, energy loss functions, and the interband transition strengths for mixed halide organic–inorganic perovskite CH₃NH₃PbI_3−xCl_x thin films.

Our previous work reports the structural, surface morphological, optical, charge carrier dynamics, electrical, and thermoelectric transport properties of CH₃NH₃PbI_3−xCl_x nano-crystalline thin films grown on the glass substrate under an ambient condition.^16,23–26 In this work, we extend our research by investigating the nonlinear optical response, e.g., critical optical dispersion relationship, complex dielectric features, energy loss phenomena, and interband transition strength of CH₃NH₃PbI_3−xCl_x thin films using the ultraviolet–visible (UV–vis) spectral study. The dispersion parameters are calculated by the Wemple–DiDomenico (WDD) and Sellmeier single effective oscillator model.^27,28 The ultimate or ideal efficiency and quantum efficiency of CH₃NH₃PbI_3−xCl_x are estimated theoretically. Furthermore, the photosensitivity and the detection efficiency of CH₃NH₃PbI_3−xCl_x as a photodetector have also been calculated. We hope that the findings of this study might be helpful to understand the physics of the nonlinear optical properties and photosensitivity occurring in CH₃NH₃PbI_3−xCl_x and useful for photonic and optoelectronic applications.

Organic–inorganic lead mixed halide perovskite (CH₃NH₃PbI_3−xCl_x) thin films are fabricated at ambient atmosphere by three distinct methods: (a) chemical dip-coating (CDC), (b) spray pyrolysis (spray), and (c) repeated dipping-withdrawing (dipping). Details of different steps for the preparation of CH₃NH₃PbI_3−xCl_x solution and the thin film fabrication processes are reported elsewhere.^16,23–26 The surface features are characterized by the atomic force microscope (AFM, Veeco, USA). The nonlinear optical responses of CH₃NH₃PbI_3−xCl_x are investigated using the transmittance T(%) and reflectance R(%) data obtained by a UV–vis double beam spectrophotometer (model: UV-1601 PC SHIJMADZU, Japan). The optical data were recorded in the wavelength range of 365–1100 nm with an interval of 1 nm. Different dispersion parameters are determined using the Wemple–DiDomenico (WDD) and Sellmeier single effective oscillator model. The ideal efficiency (η_I) and quantum efficiency (η_Q) of CH₃NH₃PbI_3−xCl_x are estimated theoretically using the following equations:^29,30

where I(λ) is the solar intensity of the standard air mass (AM) 1.5 direct circumsolar spectrum per wavelength interval,³¹ A(λ) is the absorbance, λ is the wavelength, λ_g is the bandgap wavelength, e is the electronic charge, and h is Planck’s constant. The absorption A(λ) of CH₃NH₃PbI_3−xCl_x thin films is calculated using the equation A(λ) = 1 − T(%) − R(%). Current due to illumination and dark is measured using a solar light 16S-Series 150–300 W UV solar simulator.

X-ray diffraction (XRD) study provides evidence that all the samples are polycrystalline. The details of XRD studies are reported elsewhere.^16,23–26 The 2D- and 3D-AFM micrographs of CH₃NH₃PbI_3−xCl_x samples, prepared by different deposition methods, are shown in Figs. 1(a)–1(f), respectively. The AFM micrographs showed that the grain sizes are different for deposited samples prepared under different techniques. The CDC deposited sample shows different sizes of nano-grain while the spray deposited sample exhibits needle like grains. In addition, the dipping deposited sample shows bulk grain with a deep void. Moreover, the AFM study also provides information about the surface roughness of the samples. The obtained average surface roughness (R_a) of CDC, spray, and dipping deposited samples is 4.797, 4.870, and 17.862 nm, respectively. Therefore, the AFM images revealed that surface morphology is strongly dependent on the fabrication methods. The smallest roughness and grain size were found for CDC and spray deposited samples while the largest roughness and grain size are attained for dipping deposited samples. Different parameters related to the surface morphology for CH₃NH₃PbI_3−xCl_x samples are tabulated in Table I, where L is the sampling length, rms is the root mean square roughness of a surface, R_a is the average roughness that measures the deviation of a surface from a mean height, R_max is the maximum height, R_Z is the average difference in the height between the highest peaks and lowest valleys relative to the mean plane, R_z is the number of points counted, Radius is the radius of the circle fitted to the data between the cursors, and Sigma is the mean square error of radius calculation.

The significance of surface smoothness of a thin film implies better crystallinity and hence lower scattering of electromagnetic (EM) waves, indisputably increasing the transmittance. The CDC and spray deposited samples show relatively improved crystallinity than that of the dipping deposited sample; hence, lower scattering can be expected from these samples.

In order to evaluate the optical properties of CH₃NH₃PbI_3−xCl_x thin films, the transmittance T(λ) and reflectance R(λ) data were taken in the wavelength range of 365–1100 nm [near-infrared (NIR)/-VIS regions], as shown in Figs. 2(a)–2(c).

The transmittance (left scale) of all samples varies from 56% to 72%. A downshift of the transmittance spectrum is observed in the wavelength range of 740–780 nm, which is consistent with previous reports,^17,18,21,32 indicating the band edge absorption for CDC and spray deposited samples. The transmittance of the dipping sample increases with increasing wavelength and becomes maximum at ∼740 nm and then it starts to decrease ≥740 nm. This indicates the absorption onset at the wavelength of ≥740 nm. It should be noted that the increase in free-carrier absorption may reduce the transmittance of all samples in the mid-visible to near ultra-violate region. The reflectance (right scale) of all samples is seen to vary from 3.4% to 6.3% and two reflection peaks are observed in each spectrum. The broad reflection peak at the wavelength of ∼820 nm is due to a superposition of higher excitonic and band-to-band transitions for the perovskite phase, whereas the reflection peak at the wavelength of 502 nm corresponds to the existence of the PbI₂ phase in CH₃NH₃PbI_3−xCl_x.

The investigation of the wavelength dependent refractive index (n_r) and the extinction coefficient (k) is very effective to understand the optical absorption processes in solids.³³ The wavelength dependent k and n_r of CH₃NH₃PbI_3−xCl_x thin films can be calculated using the following equations:

The nature of extinction coefficient (left scale) and refractive index (right scale) with wavelength is shown in Figs. 3(a)–3(c). For the CDC deposited sample, the value of k increases monotonically with the wavelength in the visible spectral range, becomes wavelength independent in the NIR range of 760–820 nm, and again increases linearly in the infrared region. In the case of the spray deposited sample, the value of k increases with wavelength till 690 nm, then decreases to 820 nm, and increases again in the infrared range. For the dipping deposited sample, k decreases slowly up to 560 nm and then increases sharply. It is clear that the extinction coefficient of each sample has the tendency to increase toward a higher wavelength corresponding to the total optical loss due to scattering and decrease in absorption.

The dispersion curve shows the complex behavior of the refractive index with the wavelength. It is seen that the value of n_r for the CDC deposited sample increases with the wavelength in the spectral range of ≤500 nm and 640–820 nm, which indicates anomalous dispersion. On the contrary, n_r decreases with the wavelength in the spectral range of 500–640 and ≥820 nm, which indicates normal dispersion. In the case of the spray deposited sample, normal dispersion occurs in the spectral range of 500–700 and ≥820 nm; otherwise, it displays anomalous dispersion. The dipping deposited sample displays normal dispersion at 550–640 and ≥830 nm, whereas anomalous dispersion is observed at the spectral range of ≤550 and 640–830 nm. It is found that the value of n_r varies from 1.43 to 1.48, 1.52 to 1.65, and 1.54 to 1.64 for CDC, spray, and dipping deposited samples, respectively. The lower value of n_r for the CDC deposited sample compared to that of the spray and dipping deposited samples is due to the effect of temperature during the film deposition process. Since the substrate and solution both were heated for a longer time in the CDC method compared to the spray and dipping methods, the CDC deposited sample becomes less dense, which allows light to travel faster than spray and dipping deposited samples, consequently decreasing the value of n_r. However, the calculated values of k and n_r are lower compared to the previously reported values.^{13–15,18,20,22} The low values of k and n_r are due to the miniature reflectance and enhanced transmittance of the CH₃NH₃PbI_3−xCl_x thin films.

The dispersion of the spectral dependent refractive index can be analyzed by the model of the single effective oscillator proposed by Wemple–DiDomenico,²⁷ 

where hν is the photon energy, E_d is the dispersion energy, and E₀ is the oscillator energy that is related to the optical bandgap E_g. The slope (E_oE_d)⁻¹ and the intercept E₀/E_d on the vertical axis of the straight line portion of (⁠$nr2$ − 1)⁻¹ vs $hυ2$ plot [Fig. 4(a)] provide the values of E_o and E_d. It is found that the oscillator energy E_o is associated with optical bandgap E_g by an empirical relationship E_o ≈ 2.41 E_g, E_o ≈ 2.42 E_g, and E_o ≈ 1.63 E_g for CDC, spray, and dipping deposited samples, respectively.^16,23,24 The zero frequency or static refractive index n_r(0), as well as the lattice or static dielectric constant ɛ_∞1 = $nr2$(0), is determined using the values of E_d and E₀. A measurement of interband transition strengths can also be determined from the moments of the optical spectrum M₋₁ = $EdE0$ and M₋₃ = $EdE03$⁠. The values of E₀ and E_d and moments M₋₁ and M₋₃ are presented in Table II. From Table II, it can be concluded that the dispersion energy and moments are different and vary with growth parameters of the films.

The long wavelength refractive index n_∞, average oscillator wavelength λ₀, and oscillator length strength S₀ are calculated using an empirical relationship termed the Sellmeier oscillator equation,²⁸ 

The slope of the resulting straight line [Fig. 4(b)] gives $1S0$ and the infinite-wavelength intercept gives $1S0λ02$⁠. Using the values of λ₀ and S₀, n_∞ has been calculated using the equation $n∞2$ = 1+ $S0λ02$⁠. According to classical oscillator theory, the interaction between the external electric field and free electrons is restricted. The collection of electron vibration introduced by a fraction of force is known as the plasma oscillation frequency ω_P and can be estimated using the Penn model $n∞2$ − 1 = S₀$ℏωPE02$⁠.³⁴ The values of n_∞, S₀, and ω_P are tabulated in Table II.

The susceptibility of a material is defined as the constant of proportionality that relates an electric field to the induced polarization density. The third-order nonlinear optical susceptibility χ⁽³⁾ or the nonlinear polarizability parameter and the electrical susceptibility (χ_elec) are calculated using the following equations in terms of the values of E₀, E_d, $nr2$⁠, and k² as

where A is a constant and equal to 1.7 × 10⁻¹⁰ esu. The variation of χ⁽³⁾ and χ_elec with wavelength is shown in Figs. 5(a)–5(c). From the figures, it is seen that χ⁽³⁾ (left scale) behaves in a similar fashion for all samples. The values of χ⁽³⁾ are found to be in the order of ∼10^-12 esu and it decreases sharply in the wavelength range of ≤500 nm and then it becomes flat. The decrease of χ⁽³⁾ may be attributed to the organic–inorganic bond length reduction.

The electrical susceptibility gives information about the ability of a material to polarize in response to an applied electric field. For the CDC deposited sample, the value of χ_elec increases with the increasing wavelength in the spectral range of ≤520 and 680–830 nm. On the other hand, χ_elec decreases with the increasing wavelength in the spectral range of 520–680 and ≥830 nm. In the case of the spray deposited sample, χ_elec increases in the spectral range of ≤500 and 720–820 nm but decreases at 500–720 and ≥820 nm. The value of χ_elec for the dipping deposited sample increases with the wavelength in the spectral range of ≤560 and 680–820 nm and decreases elsewhere. However, the value of χ_elec for spray and dipping deposited samples is higher than that of CDC, which signifies the greater capability to reduce the applied electric field inside the films.

The complex dielectric constant ε(ω) is a fundamental and intrinsic property of a material, which helps to understand the response of a crystal to an EM field. It is linked with the crystal structure and is essentially important to investigate the optical properties of a material. The dielectric constant ɛ is defined as ε(ω) = ε₁(ω) + iε₂(ω), where ε₁ is the real part of the dielectric constant and is associated with the energy stored within the medium and ε₂ is the imaginary part of the dielectric constant, which is related to the dissipation of energy into the medium. These values were calculated using the relations ε₁(ω) = $nr2−$ k² and ε₂(ω) = 2n_rk. The variation of ε₁ (left scale) and ε₂ (right scale) of the dielectric constant with wavelength is shown in Figs. 6(a)–6(c). From the figures, it is clear that the value of ε₁ is higher than the value of ε₂ for all samples. For CDC and spray deposited samples, two distinguished peaks are observed at wavelengths ∼520 and ∼820 nm. On the other hand, the first peak position of the dipping deposited sample shifted to ∼560 nm but the second one remains unchanged at ∼820 nm. However, the variation of ε₁ is similar to the dispersion curve due to the small value of the extinction coefficient and ε₁ starts to decrease sharply after 820 nm for all samples. The observed peaks indicate superfluous interactions between the incident photons and charge carriers of the samples at that wavelength.

The imaginary part of the dielectric constant ε₂ is linked with the electronic structure and, hence, the bandgap of semiconductor materials and represents the absorption of a material coupled with emission by free energy. From Figs. 6(a)–6(c), it is evident that ε₂ is higher for the CDC deposited film than other deposited samples. Furthermore, for the CDC deposited sample, the behavior of ε₂ is anomalous in the visible spectral region and starts to increase sharply at the wavelength <840 nm. For the spray deposited sample, ε₂ increases sharply reaching to a maximum in the visible region and becomes anomalous in the IR region. However, ε₂ is steady up to 600 nm and then it starts to increase sharply for the dipping deposited sample, which implies maximum absorption of the IR spectrum.

The energy loss functions are calculated from the complex dielectric constants, which measure the energy loss of charge carriers in the bulk and surface of a solid. The volume energy loss function (ELF_Volume) and surface energy loss function (ELF_Surface) are proportional to the energy loss of charge carriers, which travel into the bulk and surface of the material, respectively. The following equations are used to calculate ELF_Volume and ELF_Surface in terms of ε₁ and ε₂:

The ELF_Volume and ELF_Surface with photon energy are shown in Figs. 7(a)–7(c) for CDC, spray, and dipping deposited samples. It can be seen from the figures that ELF_Volume > ELF_surface, which indicates the possibility of charge carriers experiencing bulk excitation that is greater than surface excitation. Both these parameters display a fairly similar nature during the transmission through the bulk material and surface. A weak peak is observed at 780, 700, and 770 nm for CDC, spray, and dipping deposited thin films, respectively. The signature of a weak peak reveals the existence of a weak asymmetric mode of perovskite and the extinction may occur in this wavelength range.³⁵ 

The complex interband transition strength (J_it) is linked with the complex dielectric constant and represents the possibility to create a transition of charge carrier from the valence band to conduction band. The optical response of thin film materials in terms of the interband transition strength is given by the following equation:

where m is the mass of the electron, h is Planck’s constant, e is the charge of electron, and (hν) is the photon energy.

The wavelength-dependent Re Jit (left scale) and Im Jit (right scale) of CH₃NH₃PbI_3−xCl_x thin films are shown in Figs. 8(a)–8(c). From the figures, it appears that the variation of the interband transition strength with wavelength is almost the same for all samples. Both Re Jit and Im Jit decrease exponentially with increasing wavelength, which indicates poor electronic transition with increasing wavelength. Since the values of Re Jit and Im Jit are higher at the low wavelength region (≤780 nm), most of the absorption takes place in that region for CH₃NH₃PbI_3−xCl_x thin films. Subsequently, this increases the excitation of the charge carriers at a low wavelength region, which results in a transition from the valence to the conduction band. A small peak is observed at ∼780 nm for all samples, which leads to a single charge carrier excitation process in the films.

The two important parameters, such as optical and electrical conductivities, are measured to observe the optical and electrical response of a material to wavelength or photon energy. These parameters can be calculated by the following equations:

where c is the speed of light, λ is the wavelength of light, and α is the absorption coefficient. The plot of σ_opt (left scale) and σ_ele (right scale) with wavelength for CDC, spray, and dipping deposited samples is shown in Figs. 9(a)–9(c).

It is seen that σ_opt decreases with increasing wavelength for CDC and spray deposited samples. For the dipping deposited sample, the value of σ_opt decreases with wavelength up to 730 nm and then it increases linearly. The optical conductivity of all samples is found to be in the order of 10¹³ s⁻¹. The high value of σ_opt is due to the change in the density of the localized state and the excitation of more charge carriers by photon energy in the films.^36,37 The value of σ_opt indicates that the prepared thin films are highly photoresponsive, resulting in an increase of electrons passing through the materials and recommends better conversion efficiency of the material.³⁸ The electrical conductivity (σ_ele) increases linearly with increasing wavelength and it is found to vary from 26 to 82 (Ω m)⁻¹. The low value of σ_ele indicates the semiconducting nature of CH₃NH₃PbI_3−xCl_x thin films.³⁹ 

The ideal efficiency (η_I) of a thin film is defined as the ratio of the solar absorption up to the bandgap wavelength of the sample and the total standard solar intensity, while the quantum efficiency (η_Q) is defined as the light absorption over all wavelengths. In order to set CH₃NH₃PbI_3−xCl_x thin films for device applications, η_I and η_Q are estimated using Eqs. (1) and (2), respectively. It is important to note that the carrier recombination is not considered to estimate the theoretical efficiencies. The ideal efficiency and quantum efficiency of the CH₃NH₃PbI_3−xCl_x thin films are displayed in Fig. 10.

It is seen that the maximum η_I and η_Q are estimated to be 17.4% and 13.7%, respectively, for the spray deposited sample. Chen et al.⁴⁰ reported the optoelectronic effect of Cl in CH₃NH₃PbI₃(Cl)-based perovskite solar cells, and this protocol leads to solar cells, leading to the power conversion efficiencies (PCE) of 17.91%, which is an excellent agreement with our theoretical calculation. However, the lower value of η_I for the dipping deposited sample is due to the higher bandgap and large defects in the structure of the sample compared to other samples.

Figure 11(a) shows the variation of photocurrent I_L due to the photoillumination of different CH₃NH₃PbI_3−xCl_x samples. From Fig. 11(a), it is clearly observed that, in all the samples, I_L produced high photocurrent, and the rate of photocurrent production increases with increasing bias voltage. It should be remembered that the spray deposited sample demonstrates a large photocurrent, which could be due to better crystallinity of the film; however, a breakdown nature is observed at a higher bias voltage around 8 V. The other samples show saturations at 2.5 and 4 V, respectively. Among these samples, the dipping based sample shows less photocurrent and photodiode feature followed by CDC and spray deposited samples, which is interconnected to the surface morphology of the sample. It should be noted that the value of photocurrent is 100 times higher than that of the dark current. Therefore, this photodiode will be more effective to harvest visible light irradiation into electricity.

Figure 11(b) shows the I_D–V_D characteristics as a function of bias voltage for CH₃NH₃PbI_3−xCl_x samples prepared by different deposition methods. From Fig. 11(b), it is clearly observed that the value of dark current, I_D, increases with increasing bias voltage for the spray deposited sample while the value of I_D increases up to a certain biasing voltage and then becomes almost constant level for the dipping and CDC samples. It is noted that, at a lower biasing voltage, the dark current of the dipping deposited sample shows that the zig-zag nature could be due to less adjustment of the metal contact to the film surface. The production of dark current in an organic photodiode is mainly attributed due to the charge carrier injection from the metal contacts into the organic semiconductors⁴¹ or bulk thermal emission within the photodiode.⁴² The lower value of I_D is apparent for the sample deposited by the dipping method followed by high I_D for CDC and spray deposited samples, respectively. The value of I_D reaches its saturation value at a biasing voltage of 3.5 V for the dipping based sample, while for the CDC based sample, it becomes 4.5 V. On the other hand, for the spray deposited sample, I_D increases monotonically with increasing bias voltage.

We have also calculated the photosensitivity, S_P, of different CH₃NH₃PbI_3−xCl_x samples to estimate the effect of the deposition method in photoexcitation. The photosensitivity, S_P, was obtained from the ratio of the detected photocurrent and the dark current. Figure 11(c) represents the bias voltage-dependent photosensitivity of CH₃NH₃PbI_3−xCl_x samples. From Fig. 11(c), it is depicted that a sharp absorption peak is observed at around 2 V for all the samples and then decreases except for CDC samples. From this figure, it can be clearly seen that the height of the photosensitivity peak depends on the bandgap of the CH₃NH₃PbI_3−xCl_x films, which are interconnected to the crystallinity of the samples. Therefore, CH₃NH₃PbI_3−xCl_x is highly photosensitive at a low bias voltage and absorbs maximum radiation and, hence, maximum photocurrent. These results showed that the dipping deposited sample is highly photosensitive at a low bias voltage while the rest of the samples show significant sensitivity in the whole range of a bias voltage.

From Fig. 11(d), it is seen that the carrier life time sharply decreases with increasing bias voltage for all the samples. It is also seen that the carrier life time is higher for the dipping based sample followed by lower life of CDC and spray deposited samples. It is well known that the higher the carrier life time, the lower the recombination rates; hence, the dipping based sample has a lower recombination rate and higher conductivity. The attenuating carrier life time occurs because the rotational re-organization of CH₃NH₃ dipoles produced the polaronic effect, which enhances the trap assisted rate of recombination with increasing bias voltage and hence diminishes the carrier life time.

The detection efficiency of a detector can be estimated by two essential parameters, namely, photoresponsivity, R_P and EQE. The photoresponsivity, R_P, can be assessed by the ratio of output current to the incident photon energy on the effective illuminated area of the detector.⁴³ In addition, EQE measures the probability of electron–hole pairs that contribute to the external photocurrent generated due to single photon illumination upon the detector. Hence, the quality of performance can be calculated from the number of electrons perceived per incident photon. These two parameters can be estimated by using the following equations:

where I_L is the photocurrent due to illumination, I_D is the dark current, I is the intensity of the incident radiation, S is the effective area of illumination, h is Planck’s constant, e is the charge of electron, and λ is the wavelength of the incident radiation.

It is depicted that the EQE value of CH₃NH₃PbI_3−xCl_x samples increases with increasing bias voltage up to a specific value for each sample and then becomes saturated in the middle biasing voltage; however, at higher voltage, the value of the EQE increases is attributed to the generation of more electron–hole pairs at a higher bias voltage. In an organic photodiode, EQE and R usually increase with increasing bias voltage due to the enrichment of charge extraction capability and eventually should attain to the saturation limit.^44,45 On the contrary, the value of I_D increases with increasing bias. In this work, we found that the spray deposited sample shows maximum EQE among the three samples though there is a breakdown-like characteristic at around 8 V bias voltage. However, CDC and dipping synthesized samples show saturating behavior at around 4.5 and 2.5 V, respectively. The increase in the EQE with increasing bias voltage is due to the degree of surface roughness of the different samples, which eventually affects the absorption spectra.

The detective efficiency of a photodiode, D_P, assesses the figure of merit of photodetector. It is defined as the inverse of equivalent noise power^46,47 and can be calculated by the following equation:

where R_P is the photoresponse, e is the charge of the electron, and J_D is the dark current density. The detector would be able to detect the incident weak signals if its detectivity is high. The photoresponsivity, EQE, and the detectivity of the fabricated diode of CH₃NH₃PbI_3−xCl_x as a function of bias voltage are presented in Figs. 12(a)–12(c) for the samples synthesized by different methods. From Fig. 12, it is clearly revealed that the detectivity increases with increasing bias voltage for all the samples. Among the three samples, the spray deposited sample shows maximum detectivity in the whole range of the bias voltage while the sample prepared by the dipping process shows saturating behavior after 3 V. The saturated detectivity of the dipping based sample is ∼6 × 10¹¹ cm Hz^1/2 W⁻¹, while that for the CDC based sample is ∼8 × 10¹¹ cm Hz^1/2 W⁻¹. In addition, the spray deposited sample shows an increasing trend even at a higher bias voltage while a sharp breakdown is observed at 8.5 V.

The nonlinear optical response and the estimated efficiency of the CH₃NH₃PbI_3−xCl_x thin films deposited under ambient atmospheric conditions by chemical dip coating (CDC), spray pyrolysis (spray), and repeated dipping-withdrawing (dipping) methods have been studied systematically. From the linear and nonlinear optical analyses, it is comprehended that the properties of CH₃NH₃PbI_3−xCl_x thin films depend on the growth conditions and deposition methods. The transmittance and reflection spectra of all samples demonstrated that they vary with the wavelength from 56% to 72% and 3.4%–6.3%, respectively. The dispersion of the refractive index is evaluated using the Wemple–DiDomenico single oscillator model. The oscillator energy (E₀) of CDC and spray deposited samples are related to optical bandgap (E_g) by an empirical equation E₀ ≈ 2.41 E_g, but for the dipping sample, it follows E₀ ≈ 1.63 E_g. The value of n_r, λ₀, and S₀ is determined using the Sellmeier oscillator equations. The third-order nonlinear optical susceptibility is found in the order of 10⁻¹² esu. The electrical susceptibility is higher for spray and dipping deposited samples compared to the CDC sample, which gives insights into the greater capability to reduce the electric field inside the samples. From the dielectric study, the interaction between the incident photons and charge carriers is obvious in CH₃NH₃PbI_3−xCl_x. It is found that ELF_volume (volume energy loss function) is higher than ELF_surface (surface energy loss function) for CH₃NH₃PbI_3−xCl_x. A weak peak observed in each sample indicates the existence of the weak asymmetric mode of the perovskite thin film. The interband transition parameters are higher at a low wavelength region (≤780 nm), indicating that most of the high absorption takes place in that region. The value of σ_opt obtained is high and the order is 10¹³ s⁻¹ for CH₃NH₃PbI_3−xCl_x, which confirms very high photoresponse of the film and recommends better conversion efficiency of CH₃NH₃PbI_3−xCl_x. In this study, the highest theoretical efficiency of CH₃NH₃PbI_3−xCl_x is estimated as 17.4%. From the photosensitivity study, it is seen that the current due to illumination is 100 times higher than that of the dark current. The external quantum efficiency (EQE) and photodetectivity of CH₃NH₃PbI_3−xCl_x increase with increasing bias voltage, which accredited the generation of more electron–hole pairs at a higher bias voltage. Overall, the experimental and theoretical results indicate that the CH₃NH₃PbI_3−xCl_x thin film is a potential candidate for optoelectronic and photonic applications.

All authors gratefully acknowledge Professor Dr. Abu Bakar Md. Ismail, Solar Energy Laboratory, Department of Electrical and Electronic Engineering, University of Rajshahi, Rajshahi 6205, Bangladesh, for providing the photoelectrical measurement.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding authors upon reasonable request.