Mixed tin (Sn) and lead (Pb) based perovskite thin films have been prepared by solution processing combining methylammonium lead iodide (MAPbI_{3}) and formamidinium tin iodide (FASnI_{3}) precursors. Optical response in the form of complex dielectric function (*ε* = *ε*_{1} + i*ε*_{2}) spectra and absorption coefficient (*α*) spectra of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} based perovskite films have been extracted over a spectral range 0.74 to 5.89 eV using spectroscopic ellipsometry. Absorption band edge energy changes as a function of composition for films including FASnI_{3}, MAPbI_{3}, and mixed x = 0.20, 0.35, 0.40, and 0.6 (FASnI_{3})_{1-x}(MAPbI_{3})_{x} perovskites. (FASnI_{3})_{0.60}(MAPbI_{3})_{0.4} is found to have the minimum absorption band edge energy near ∼1.2 eV.

Methylammonium lead iodide (MAPbI_{3}) based perovskites are promising light absorbing materials in solar cell applications with devices already demonstrating 22.1 % power conversion efficiency.^{1} Since MAPbI_{3} based photovoltaics are reaching the Shockley-Queisser limit for a single junction solar cell, lower band gap longer wavelength light absorbing perovskites are being investigated for integration in tandem solar cells. Literature reports several ways of making low band gap perovskite materials: substituting Pb by Sn in MAPbI_{3},^{2} substituting methylamine (MA) by formylamine (FA) and Pb by Sn in MAPbI_{3}^{3} and combining a formamidinium tin iodide (FASnI_{3}) precursor with a MAPbI_{3} precursor.^{4} Among those, combining a FASnI_{3} precursor with a MAPbI_{3} precursor makes a high-quality (FASnI_{3})_{1-x}(MAPbI_{3})_{x} film and has produced a 15% efficient solar cell, which is the highest efficiency for a low band gap long wavelength light absorbing Sn-Pb based perovskite solar cells to date.^{1,4}

For the MASn_{1-x}Pb_{x}I_{3} system Mosconi *et al.*^{5} (2014) has theoretically calculated the absorption coefficient (α) and Anaya *et al.*^{2} has reported experimental complex optical properties of MASn_{1-x}Pb_{x}I_{3} films. The optical properties of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} are reported by Liao *et al.*^{4} where the spectral range is limited to the absorption band edge energy region with numerical interpolation and extrapolation-based B-spline parameterizations applied. Here we report optical response in the form of the complex dielectric function (*ε* = *ε*_{1} + i*ε*_{2}) spectra of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} thin films over the spectral range from 0.74 to 5.89 eV. Spectra in *ε* determined in this work are obtained using a physics-based parametric model to deduce thin film thicknesses prior to numerical inversion to yield physically realistic values for optical response over a wider spectral range. From these spectra in *ε*, *α* is calculated to discern the absorption band edge energy, here denoted as *α* = 4000 cm^{-1}. The energies of above absorption edge critical points (CPs) for (FASnI_{3})_{1-x}(MAPbI_{3})_{x} thin films have been measured for different FASnI_{3} and MAPbI_{3} contents.

The FASnI_{3} precursor solution have been prepared as described in Liao *et al.*,^{4,6} which consists of 372 mg of SnI_{2} (Sigma-Aldrich) and 172 mg of formamidinium iodide (FAI) (Dyesol) with 15.6 mg of SnF_{2} dissolved in 800 μL N,N-dimethylmethanamide (DMF) (anhydrous, Sigma-Aldrich) and 200 μL dimethyl sulfoxide (DMSO) (anhydrous, Sigma-Aldrich). The MAPbI_{3} precursor solution consists of 461 mg PbI_{2} (Sigma-Aldrich) and 159 mg CH_{3}NH_{3}I (MAI) (Dyesol) with 11.3 mg Pb(SCN)_{2} (Sigma-Aldrich) dissolved in 630 μL DMF and 70 μL DMSO. (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, 0.60, and 1.00) precursor solutions are achieved by mixing stoichiometric ratios of MAPbI_{3} to FASnI_{3} precursors and kept for 30 min prior to spin coating. The precursors are spin-coated onto native oxide coated crystalline silicon (c-Si) wafers at 5,000 rpm for 60 s with diethyl ether dropped onto the spinning substrate. All perovskite films have been annealed at 100 °C for 5 min in a glove box. The polycrystalline nature and structure of samples prepared with these processing conditions have been previously reported.^{4}

Spectroscopic ellipsometry measurements are performed on (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, 0.60, 1.00) perovskite films using a multichannel single rotating compensator instrument^{7,8} (M-2000, J. A. Woollam Co.) with a spectral range from 0.74 to 5.89 eV. Ellipsometric spectra in *N* = Cos 2Ψ, *C* = Sin 2Ψ Cos Δ, and *S* = Sin 2Ψ Sin Δ are collected at 60° and 70° angles of incidence. The experimental ellipsometric spectra at these two angles of incidence are fitted simultaneously to an optical and structural model. The structural model consists of a finite thickness surface layer and perovskite film on top of a semi-infinite c-Si with a 20 Å thick native oxide. The structural model for the FASnI_{3} film requires two surface layers with different relative void volume fractions in the fitting procedure. Ellipsometric spectra collected are analyzed using a least square regression analysis and an unweighted error function *σ*^{9} defined by:

where, *N* = number of measured values and *M* = number of fit parameters. Experimental data is denoted as “exp” and that generated by the model is labeled “mod”.

A divided spectral range analysis procedure^{10–12} is used to determine the structural parameters including film thicknesses, surface roughness layer thicknesses, and void fractions in surface layers as presented in Table I. In the divided spectral range analysis procedure, the full measured spectral range from 0.74 to 5.89 eV is divided into two portions: (i) low photon energies where the film is non-absorbing and (ii) high photon energies above the absorption band edge where film is highly absorbing. This approach allows the use of physically realistic parametric models to describe *ε* in the appropriate spectral range to obtain the structural parameters of each sample in the least squares regression fit. This portion of the analysis is only to deduce structural parameters, in this case layer thickness, surface roughness, and relative void fraction within the surface roughness layer. Due to the change in absorption band edge with composition for (FASnI_{3})_{1-x}(MAPbI_{3})_{x} samples, different sets of low and high energy ranges are used, as listed in Table II.

(FASnI_{3})_{1-x}
. | . | . | . | . | . | . |
---|---|---|---|---|---|---|

(MAPbI_{3})_{x}
. | x = 0 . | x = 0.2 . | x = 0.35 . | x = 0.4 . | x = 0.60 . | x = 1 . |

Interface | 205 ± 29 Å | |||||

(Surface / Film) | $$0.26 ± 0.02 | 0 Å | 0 Å | 0 Å | 0 Å | 0 Å |

void$$ | ||||||

470 ± 16 Å | 336 ± 3 Å | 340 ± 1 Å | 144 ± 8 Å | 192 ± 10 Å | 411 ± 9 Å | |

$$0.090 ± 0.007 | $$0.185 ± 0.002 | $$0.158 ± 0.001 | $$0.25 ± 0.01 | $$0.24 ± 0.01 | $$0.057 ± 0.001 | |

void$$ | void$$ | void$$ | void$$ | void$$ | void$$ | |

Film Thickness (Å) | 1945 ± 17 | 2494 ± 4 | 2505 ± 2 | 3338 ± 11 | 3497 ± 12 | 4178 ± 10 |

Mean Square Error (σ) | 3.9 x 10^{-3} | 5.5 x 10^{-3} | 2.7 x 10^{-3} | 7.4. x 10^{-3} | 8.1 x 10^{-3} | 8.3 x 10^{-3} |

(FASnI_{3})_{1-x}
. | . | . | . | . | . | . |
---|---|---|---|---|---|---|

(MAPbI_{3})_{x}
. | x = 0 . | x = 0.2 . | x = 0.35 . | x = 0.4 . | x = 0.60 . | x = 1 . |

Interface | 205 ± 29 Å | |||||

(Surface / Film) | $$0.26 ± 0.02 | 0 Å | 0 Å | 0 Å | 0 Å | 0 Å |

void$$ | ||||||

470 ± 16 Å | 336 ± 3 Å | 340 ± 1 Å | 144 ± 8 Å | 192 ± 10 Å | 411 ± 9 Å | |

$$0.090 ± 0.007 | $$0.185 ± 0.002 | $$0.158 ± 0.001 | $$0.25 ± 0.01 | $$0.24 ± 0.01 | $$0.057 ± 0.001 | |

void$$ | void$$ | void$$ | void$$ | void$$ | void$$ | |

Film Thickness (Å) | 1945 ± 17 | 2494 ± 4 | 2505 ± 2 | 3338 ± 11 | 3497 ± 12 | 4178 ± 10 |

Mean Square Error (σ) | 3.9 x 10^{-3} | 5.5 x 10^{-3} | 2.7 x 10^{-3} | 7.4. x 10^{-3} | 8.1 x 10^{-3} | 8.3 x 10^{-3} |

(FASnI_{3})_{1-x}(MAPbI_{3})_{x}
. | Low Energy (eV) . | High Energy (eV) . |
---|---|---|

x = 0.00 | 0.74 - 1.30 | 1.50 - 5.50 |

x = 0.20 | 0.74 - 1.20 | 1.45 - 5.50 |

x = 0.35 | 0.74 - 1.15 | 1.35 - 5.50 |

x = 0.40 | 0.74 - 1.15 | 1.35 - 5.50 |

x = 0.60 | 0.74 - 1.20 | 1.45 - 5.50 |

x = 1.00 | 0.74 - 1.40 | 1.66 - 5.50 |

(FASnI_{3})_{1-x}(MAPbI_{3})_{x}
. | Low Energy (eV) . | High Energy (eV) . |
---|---|---|

x = 0.00 | 0.74 - 1.30 | 1.50 - 5.50 |

x = 0.20 | 0.74 - 1.20 | 1.45 - 5.50 |

x = 0.35 | 0.74 - 1.15 | 1.35 - 5.50 |

x = 0.40 | 0.74 - 1.15 | 1.35 - 5.50 |

x = 0.60 | 0.74 - 1.20 | 1.45 - 5.50 |

x = 1.00 | 0.74 - 1.40 | 1.66 - 5.50 |

Spectra in *ε* over the non-absorbing low photon energy range where *ε*_{2} = 0 is parameterized by using the Sellmeier expression^{13} and a constant additive term to *ε*_{1}, *ε*_{∞,} represented by:

where *A* is the amplitude of the Sellmeier expression and *E*_{0} is the resonance energy which must be outside the measured spectral range. Spectra in *ε* for photon energies greater than the absorption band edge is parameterized by using critical point parabolic band (CPPB) models^{14} for *ε*_{2} and Kramers-Kronig consistent integration of *ε*_{2} along with a Sellmeier expression and a constant additive term, *ε*_{∞}, to determine *ε*_{1}. Leguy *et al.*^{15} reported that the critical points in MAPbX_{3} (X=Cl, Br, I) are due to zero dimensional transitions, often a characteristic of localized excitations. We have also used zero dimensional CPPB oscillators for all parameterization and CP analysis of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} The expression for parameterization of *ε* at high photon energies is:

where, *l* is the lower limit of the high photon energy spectral range in Table II and *A*_{n} is the amplitude, *Γ*_{n} is the broadening, *E*_{n} is the critical point energy, and *φ*_{n} is the phase projection factor of each CPPB oscillator. Spectra in *ε* for surface roughness layers are represented by Bruggeman effective medium approximations^{16} consisting of a variable void and material fractions. The advantage of this procedure is physically realistic models describing *ε* are applied over the appropriate spectral ranges to determine the structural parameters in a least squares regression fit without making assumptions about the behavior of *ε* in the low absorbing near band gap region where the incorrect parametric model may lead to erroneous structural parameters.^{10}

Experimental ellipsometric spectra and the parametric model fit for the (FASnI_{3})_{0.40}(MAPbI_{3})_{0.60} sample is shown as an example in Fig. 1. As a representative example, good agreement between model fit and the experimental data for (FASnI_{3})_{0.40}(MAPbI_{3})_{0.60} perovskite film and the low values of mean square error in Table I for all samples support the validity of this approach. Both 60° and 70° angle of incidence experimental data are used in fitting procedure to extract the structural parameters. Numerical inversion^{17} is then used to extract spectra in *ε* from ellipsometric spectra over the full 0.74 to 5.89 eV range after the structural parameters listed in Table I have been determined. In this way a particular model defining *ε* near the absorption onset is not required and bias toward a specific model in this range is reduced. The numerically inverted spectra in *ε* are then further analyzed to identify particular features pertaining to electronic transitions.

Fig. 2 shows spectra in *ε* of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, 0.60, and 1.00) perovskite films obtained from this approach. Above absorption edge CP energies are reported in Table III. These values are obtained by fitting the first derivative of *ε*_{2}, d*ε*_{2}/d*E*, to zero-dimensional CPPB oscillator models. This kind of approach using the first or second derivative of the optical response is applied to more accurately identify CP energy positions and other characteristics For these samples, the second derivative of *ε*_{2}, d^{2} *ε*_{2}/d*E*^{2} exhibits significant noise, so only the first derivative has been analyzed. CPs obtained for MAPbI_{3} from this analysis are similar to those obtained by analysis of the second derivative reported in literature.^{15} Additional CPs at 1.72, 2.45, 3.09, and 5.67 eV also appear here for MAPbI_{3}. The sensitivity to additional CPs and differences in position may be attributed due to different fitting procedures and relative purity of the samples. CPs for (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, and 0.60) films are also reported here. The lowest energy features above the absorption edge and relatively broad highest energy CPs within our spectral range at 1.70 to 1.87 eV and 5.5 to 5.7 eV remain relative stable for all compositions. The CP at 4.31 eV for MAPbI_{3} decreases in magnitude with increasing FASnI_{3} content for x = 0.40 and 0.60 with sensitivity lost for higher FASnI_{3} content films. The CP at 3.19 eV for MAPbI_{3} is present for high MAPbI_{3} content films (x = 1.00 and 0.60), blue shifts with increasing FASnI_{3} (x = 0.40), is not observed with addition of more FASnI_{3} (x = 0.35 and 0.20) indicating that this particular transition is suppressed for the alloy films, then appears at 4.03 eV for the FASnI_{3} film. The CP at 3.09 eV for MAPbI_{3} red shifts with increasing FASnI_{3} content reaching a minima at 2.01 eV for x = 0.20 followed by a relative blue shift to 2.21 eV for FASnI_{3}. The feature at 2.60 eV in MAPbI_{3} is not observed in the other films; similarly a feature at 2.11 eV is only observed in the x = 0.60 film. The sensitivity to these transitions may be obscured by other nearby features or result from differences in the band structure. The CP at 2.45 eV in MAPbI_{3} is continuously red shifted with addition of FASnI_{3} reaching a minimum at 1.89 eV. Overall, the maximum amplitude CP at 3.09 eV corresponds to a more MAPbI_{3}-like material while maximum amplitude CP at 2.21 eV corresponds to material with more FASnI_{3} characteristics. (FASnI_{3})_{0.6}(MAPbI_{3})_{0.4} is observed to have non-zero values of *ε*_{2} persisting to the lowest energies and has the lowest amplitude for above higher energy features. This behavior implies that the higher energy transitions are suppressed in favor of lower energy transitions between the valence and conduction bands with this mixture. The variation in CP positions and amplitude of features in *ε*_{2} depends upon the impact of Pb, Sn, MA, and FA on the band structure of the alloy. Overall, red and blue shifting of particular CP energies indicate the energy difference between valence and conduction bands narrow and widen, respectively. Reduced amplitude of a particular feature occurs with a reduction in the frequency of that particular electronic transition occurring. The appearance or loss of sensitivity to particular CP features in some films and not in others may imply that the particular transition strength has increased or decreased overall or relative to nearby greater amplitude features which may obscure it. The many CP features present and non-monotonic shifts with composition imply that multiple interactions are likely between the different metal and organic components.

(FASnI_{3})_{1-x}
. | . | . | . | . | . | . | . | . | . |
---|---|---|---|---|---|---|---|---|---|

(MAPbI_{3})_{x}
. | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . |

x = 1.00 | 1.630 ± | 1.72 ± | - | 2.46 ± | 2.60 ± | 3.09 ± | 3.19 ± | 4.3 ± | 5.7 ± |

0.001 | 0.02 | 0.01 | 0.02 | 0.06 | 0.03 | 0.1 | 0.1 | ||

x = 0.60 | 1.310 ± | 1.65 ± | 2.11 ± | 2.36 ± | - | 2.8 ± | 3.17 ± | 4.4 ± | 5.6 ± |

0.004 | 0.05 | 0.01 | 0.02 | 0.2 | 0.07 | 0.1 | 0.2 | ||

x = 0.40 | 1.13 ± | - | - | ||||||

0.03; | 1.70 ± | 2.24 ± | 2.5 ± | 3.4 ± | 4.3 ± | 5.5 ± | |||

1.270 ± | 0.01 | 0.01 | 0.3 | 0.2 | 0.2 | 0.3 | |||

0.005 | |||||||||

x = 0.35 | 1.260 ± | 1.86 ± | - | 2.11 ± | - | 2.33 ± | - | - | 5.6 ± |

0.004 | 0.01 | 0.01 | 0.06 | 0.1 | |||||

x = 0.20 | 1.300 ± | 1.87 ± | - | 1.96 ± | - | 2.01 ± | - | - | 5.5 ± |

0.002 | 0.01 | 0.01 | 0.05 | 0.1 | |||||

x = 0.00 | 1.400 ± | 1.77 ± | - | 1.89 ± | - | 2.21 ± | 4.03 ± | - | 5.5 ± |

0.002 | 0.02 | 0.01 | 0.01 | 0.04 | 0.1 |

(FASnI_{3})_{1-x}
. | . | . | . | . | . | . | . | . | . |
---|---|---|---|---|---|---|---|---|---|

(MAPbI_{3})_{x}
. | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . | (eV) . |

x = 1.00 | 1.630 ± | 1.72 ± | - | 2.46 ± | 2.60 ± | 3.09 ± | 3.19 ± | 4.3 ± | 5.7 ± |

0.001 | 0.02 | 0.01 | 0.02 | 0.06 | 0.03 | 0.1 | 0.1 | ||

x = 0.60 | 1.310 ± | 1.65 ± | 2.11 ± | 2.36 ± | - | 2.8 ± | 3.17 ± | 4.4 ± | 5.6 ± |

0.004 | 0.05 | 0.01 | 0.02 | 0.2 | 0.07 | 0.1 | 0.2 | ||

x = 0.40 | 1.13 ± | - | - | ||||||

0.03; | 1.70 ± | 2.24 ± | 2.5 ± | 3.4 ± | 4.3 ± | 5.5 ± | |||

1.270 ± | 0.01 | 0.01 | 0.3 | 0.2 | 0.2 | 0.3 | |||

0.005 | |||||||||

x = 0.35 | 1.260 ± | 1.86 ± | - | 2.11 ± | - | 2.33 ± | - | - | 5.6 ± |

0.004 | 0.01 | 0.01 | 0.06 | 0.1 | |||||

x = 0.20 | 1.300 ± | 1.87 ± | - | 1.96 ± | - | 2.01 ± | - | - | 5.5 ± |

0.002 | 0.01 | 0.01 | 0.05 | 0.1 | |||||

x = 0.00 | 1.400 ± | 1.77 ± | - | 1.89 ± | - | 2.21 ± | 4.03 ± | - | 5.5 ± |

0.002 | 0.02 | 0.01 | 0.01 | 0.04 | 0.1 |

The change in band edge energy with different compositions in (FASnI_{3})_{1-x}(MAPbI_{3})_{x} samples is shown in terms of *ε*_{2} and *α* in Fig. 3 and generally tracks with the lowest energy CP in Table III. For the x = 0.40 film, CPs near 1.13 and 1.27 eV contribute to the line shape of the absorption edge. It is not clear if these are two distinct CP features or if the line shape in this region is affected by absorption due to defect states. Spectra in *α* are deduced from using the imaginary part of complex refractive index (*N* = *n* + i*k* = *ε*^{1/2}) via *α* = *4πk/λ* where *λ* is the wavelength of probing light. MAPbI_{3} exhibits an absorption band edge energy ∼1.6 eV. This band edge energy decreases with increasing FASnI_{3} content, reaching a minimum ∼1.2 eV for (FASnI_{3})_{0.60}(MAPbI_{3})_{0.40}. The absorption band edge energy increases as more FASnI_{3} is added up to ∼ 1.4 eV. An interesting feature is that the absorption band edge energies for x = 0.60 and 0.35 are similar, however the CP features are different, particularly at higher energies, as observed in Figs. 2 and 3, respectively. Additionally, the x = 0.20 and 0.60 films have similar lowest energy CPs, but the magnitude of *α* differs at those energies. The variation in the above gap features may be more reflective of film composition than the absorption band edge energy or band gap shifts alone.

We have reported spectra in *ε* from 0.74 to 5.89 eV for (FASnI_{3})_{1-x}(MAPbI_{3})_{x} perovskite thin films. From the analysis of these spectra in *ε*, variations in the absorption band edge and higher energy CP transitions have been identified as functions of relative MAPbI_{3} and FASnI_{3} contents. The absorption band edge decreases with increasing FASnI_{3} content, reaches a minimum for (FASnI_{3})_{0.60}(MAPbI_{3})_{0.40}, and again increases with additional FASnI_{3} content. Compositional control can yield absorption band edges ranging from ∼1.2 to 1.6 eV. Variations in higher energy CPs transitions for (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, 0.60, and 1.00) films are observed as functions of x with some features remaining relatively stable with composition, others blue- or red-shifted, and additional non-monotonic trends. Overall this behavior implies a complex relationship may exist amongst the Pb, Sn, MA, and FA components and their cumulative impact on both optical response and band structure.

See supplementary material for tabulated complex dielectric function spectra (*ε* = *ε*_{1} + i*ε*_{2}) of (FASnI_{3})_{1-x}(MAPbI_{3})_{x} (x = 0.00, 0.20, 0.35, 0.40, 0.60, and 1.00) perovskite films.

This work was supported by University of Toledo start-up funds, the Ohio Department of Development (ODOD) Ohio Research Scholar Program (Northwest Ohio Innovators in Thin Film Photovoltaics, Grant No. TECH 09-025), the U.S. Department of Energy (DOE) SunShot Initiative under the Next Generation Photovoltaics 3 program (DE-FOA-0000990), and the National Science Foundation (CHE-1230246 and DMR-1534586).