Optical and electronic properties of pyrite

doi:10.21203/rs.3.rs-3579047/v1

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Optical and electronic properties of pyrite

https://doi.org/10.21203/rs.3.rs-3579047/v1

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The optical and electronic properties of pyrite (FeS₂) mineral have been investigated by ex-situ spectroscopic ellipsometry measurements made on pristine (bulk) FeS₂. This method offers an alternative to petrographic microscopes used in many laboratories, as well as, in education and research institutions to study optical properties of rocks and minerals. The ability of spectroscopic ellipsometry to determine the dielectric function {ε (E) = ε₁ (E) + iε₂ (E)} of the material from its structural morphology, band gap, and electrical conductivity within the infrared spectral range (0.73–5.9 eV) is an added advantage over the optical microscopy that require ample time for thin section sample preparation to enable an optical light beam to be transmitted or reflected. As shown in this work, petrographic analyses of rocks and minerals using spectroscopic ellipsometry is a useful technique for optical studies of rocks and minerals with an added advantage over petrographic microscopy (optical microscopy).

Photonics/optics

Spectroscopy

ellipsometry

bandgap

optical

pyrite

In most geological investigations, analysing the optical properties of rocks and minerals is often based on optical microscopy of transmitted and reflected light that also serves for the identification of minerals, as well as texture studies. It also aids to establish the relationship between minerals and the stratification of rocks using polarized light that penetrate the interior of the sample and transmitted through the mineral by interacting with its internal structure [1, 2]. Optical mineralogy often uses a petrographic microscope (polarizing microscope) for the identification of the mineralogical composition of geological materials that can be attributed to their origin and evolution by measuring the refractive index, birefringence, pleochroism (mineral composition), microstructure, and other properties [3, 4]. This approach to optical studies is time-consuming, as the observer’s misjudgement cannot be overlooked.

Ellipsometry is a non-contact, fast, and non-destructive optical technique using polarized light that undergoes a change in polarization state as it reflects, or transmits, from a sample structure to characterize thin film and bulk materials [5]. It can be used to characterize material composition, roughness, thickness (depth), crystalline nature, doping concentration, electrical conductivity, optical properties, and more [6, 7]. Ellipsometry stands out as an important tool for the optical characterization of rocks and minerals since rocks mostly consist of agglomeration of fine-grained minerals and as well determine the electrical properties. Spectroscopic ellipsometry has been used to investigate the optical and electrical properties of gold bearing pyrite mineral from an alluvial gold deposit in Dunkwa on Offin in the central region of the republic of Ghana.

Precious gold occurs naturally in hydrothermal systems in association with sulfide the group of minerals, like pyrite and arsenopyrite, bonded chemically as metal, tiny pieces, or colloidal species of native gold [8–10]. Pyrite (FeS₂) consists of rare metal free elements of iron (Fe) and sulfur (S) that are nontoxic. Also known as fool’s gold, FeS₂ is one of the most common, nontoxic, and abundant Au-hosting minerals in most ore deposits [11]. With a suitable bandgap (E_g ≈ 1.36 eV), long minority diffusion length, and high absorption coefficient (σ), high quantum efficiency among other properties, pyrite is seen as a good semiconducting candidate for photovoltaic materials [12, 13]. The crystal structure of FeS₂ consists of a face centered cubic crystal lattice; where the Fe atom is octahedrally coordinated by six sulfur atoms [14]. Each sulfur atom is tetrahedrally bonded to one sulfur atom and three neighbouring Fe atoms [15, 16, 17]. The energy gap is a contribution of the 3d states of Fe that splits into a filled t_2g and an empty e_g states within the octahedral symmetry of sulfur ligands (S 3p orbitals) contributing to the conductivity of pyrite.

Previously, X-ray photoelectron spectroscopy (XPS) has been applied by Pettenkofer et al. (1991) and Bronold et al. (1994) to study surface reactions of FeS₂ crystals and to immobilize the Fermi level near the edge of the valence band at the surface [18, 19] in order to determine the reason for the low volatile organic compounds (VOCs), sometimes referred to as chemical pollutants in pyrite in photovoltaic devices, based on ligand field theory on the Fe-S coordination. The electronic transport properties have also been studied on the single crystals of cubic and thin films of FeS₂ at low temperature on n-type carriers to account for their low efficiency in the conduction band activity [20]. Hall effect measurements were deployed by Walter et al. [21] to explain the transport mechanism that occurs about 3 nm from the surface of the conduction band of cubic FeS₂ single crystals having a p-type surface.

To date, there have been very few studies on the optical response of FeS₂ using techniques such as spectroscopic ellipsometry [22] and optical reflectance [23, 24].

The electronic structure of FeS₂ can be characterised by obtaining comprehensive information on the optical response of pyrite using the complex dielectric function ε = ε₁ + iε₂ and complex refractive index N = n + ik, where $N=\sqrt{\epsilon }$. In the present study, the optical and electronic properties of FeS₂ have been investigated using spectroscopic ellipsometry in order to assess the usefulness of the technique in exploring geological samples as an alternative to petrographic microscopes in optical mineralogy studies.

The crystal structure of a pristine FeS₂ sample was first verified by X-ray diffraction to be the cubic $P\stackrel{-}{a}3$ space group (lattice constant a = 5.41 Å); clearly distinguished from the marcasite crystal structure since both pyrite and marcasite share the same FeS₂ stoichiometry. The bulk sample surface was polished and cleaned with alcohol prior to the measurement. Standard ellipsometry measurements were performed on the pristine pyrite sample with a dual rotating compensator ellipsometer, the RC2® from J.A. Woollam Co., Inc. at 45°, 55° and 65° incidence angle, in the spectral range of 0.73–5.9 eV. Analysis of the ellipsometic data was done using the software CompleteEASE®, also from J.A. Woollam Co., Inc [14]. The optical modelling of the ellipsometric angles Ψ and Δ in the Jones formalism consisted of 6 Lorentzian oscillators [14] and one Tauc-Lorentz oscillator [15], representing the dielectric function of the material. How well the model represents the sample was quantified by the Root mean squared error, the MSE, between the generated and the experimental data, as

$$MS{E}_{NCS}=1000\sqrt{\frac{1}{3n-m }{\sum }_{i=1}^{n}\left[{\left({N}_{{E}_{i}}-{N}_{{G}_{i}}\right)}^{2}+{\left({C}_{{E}_{i}}-{C}_{{G}_{i}}\right)}^{2}+{\left({S}_{{E}_{i}}-{S}_{{G}_{i}}\right)}^{2}\right]}$$

where n is the wavelengths, m is the number of fit parameters,

and $N=\text{cos}\left(2{\Psi }\right), C=\text{sin}\left(2{\Psi }\right)\text{cos}({\Delta }), S=\text{sin}\left(2{\Psi }\right)\text{sin}\left({\Delta }\right)$. The factor 1000 is introduced because a state of-the-art instrument will produce N, C, S parameters with an accuracy of $\approx 0.001$. This implies that the MSE value will be $\approx 1$for an ideal model.

Figures 1 and 2 show the experimentally determined (solid lines) Psi (ψ) and Delta (Δ), and the generated (dotted lines) data from the model with strong interference observed in ψ and Δ in the transparent region below 300 nm. The root mean squared error (MSE) for this model is 1.919 signifying a good fit between experimental and model data. However, measurements were performed on a relatively rough, hand-polished sample and no roughness was included in the modelling. It is therefore reasonable to anticipate that some of the structural properties have affected the optical properties of the model, and that the model should be looked upon as an effective optical model. Taking these considerations into account, the model represents the optical properties of the sample quite accurately.

p>Figures 3 and 4 show the complex refractive index, n and k, and the dielectric function extracted from the model as determined by fitting a bulk parametric model to the ellipsometry measurements. From the imaginary part of the dielectric function, the absorption coefficient, $\alpha$, was calculated as shown in Fig. 5.

As clearly observed, the onset of absorption starts slightly below 1.0 eV and increases towards higher energies, except for a small local minimum around 3.10 eV. From Fig. 5, the optical absorption coefficient α > 1 × 10⁵ cm^− 1 for photon energy (hν) > 1.00 eV, increases to 1.2 x 10⁵ cm^− 1 for photon energy (hν) > 5.00 eV.

Table I Parameters from the Lorentz model for the bulk crystal FeS₂ sample.

Oscillator (n)	1Tauc-Lorentz	2 Lorentz	3 Lorentz	4 Lorentz	5 Lorentz	6 Lorentz	7 Lorentz
Energy (eV)	1.64	1.77	2.07	2.36	2.92	3.79	4.93
Amplitude	52.1	9.05	5.81	4.56	1.88	4.51	6.08
Broadening	1.05	0.50	0.73	0.90	1.41	1.06	2.88
E_g	1.36	-	-	-	-	-	-

From Fig. 4, two absorption peak features are observed around 1.45 eV and 3.50 eV. The estimated band gap from Fig. 6, via the Tauc plot analysis of the absorption spectra is 1.36 eV, which is in close agreement with the common value of 1.40 eV reported for FeS₂, by Uchiyama et al. [16], signifying that the estimated value is a direct band gap. The transition of electrons within these energy levels determines the electronic behaviour of FeS₂ [16]. As our sample is from an alluvial Au deposit, the presence of native oxides on the FeS₂ surface may contribute to surface oxidation and other impurities that may cause broadening due to lattice vibrations and can affect the absorption process and consequently the bandgap.

The six Lorentz oscillators and the Tauc-Lorentz oscillator extracted in the complex dielectric function ε for the bulk FeS₂ sample agree with the results from Uchiyama et al [16]. From the spectra in Fig. 4, there is a large characteristic region between 1.50 and 2.00 eV, which can be attributed to movements of electronic orbitals between the Fe atoms. The characteristic feature between 3.00 and 4.00 eV is attributed to the combination of Fe 3d and S 3p orbitals in the chemical bonding [22]. The amplitude of the spectra is well resolved in the magnitude between 1.80 and 2.00 eV and gradually decreases at higher energies. From Fig. 4, the sharp global maximum at around 1.50 eV with a local maximum around 3.50 eV is attributed to charge transfer to oxygen ligands from the octahedral Fe atoms, whereas the local minimum around 2.50 is attributed to transitions of t_2g(Fe³⁺) → t_2g(Fe²⁺) and e_g(Fe³⁺) → e_g(Fe²⁺) which are mainly responsible for an increase in magnetic field or conductivity that reflect the direction of light propagation through the material. The transition of electrons within these energy levels determines the electronic behaviour of FeS₂.

The lowest amplitude of α = 6.00 x 10⁵ cm⁻ is observed at an energy of 2.30 eV. The bandgap of the pristine pyrite that shows a distinct absorption in the α and ε₂ spectra in agreement with literature [25, 26] can be attributed to defects in the sample caused by mechanical stress as the sample was taken with the aid of a geological hammer, impurities, oxides, or crystallinity that may display exponential band edges via optical absorption [27]. The observed high value of the absorption coefficient (α) makes FeS₂ an interesting candidate for photovoltaic (PV) technology applications, i.e., materials and devices that convert sunlight into electrical energy with absorption bands between 0.50 and 2.20 eV, as shown in Fig. 5, consistent with the literature [25]. As observed in Fig. 5, the value of α is higher at the first absorption peak (2.0 eV) and becomes smaller, analogous to transitions from absorption peaks, and becomes almost flat as FeS₂ looks dense with increasing energy [28]. As the FeS₂ is a fresh sample from an artisanal mining site, it likely contains impurities of oxides, carbonates, and carbon, as well as some transition metals. These impurity phases can limit the size of ordered regions and reduce the intended scattering time of charge carriers. As the impurities increase, the interfacial area increases because of the creation of free surfaces and grain boundaries, which cause a broadening of characteristic absorption peak features that can affect the absorption below the band gap.

Pristine pyrite crystallizes in the cubic $P\stackrel{-}{a}3$ space group (lattice constant a = 5.41 Å), has a face centered cubic (fcc) [14] sublattice of Fe²⁺ ions that bonds with sulfur atoms dominating the anion sites [29]. The cubic Pa̅3 space group of pyrite has the Fe⁴⁺ atoms bonded to six equivalent S²⁻ atoms to form corner-sharing FeS₆ octahedra, while the S²⁻ atoms are bonded in a 3-coordinate geometry to three equivalent Fe⁴⁺ atoms. Thus, in the pyrite, there exists a Fe²⁺ S₂²⁻ separation for which the sulfur ions have dimers of paired persulfide resulting in a distorted octahedra harmonization for Fe²⁺ that sits in its diamagnetic d⁶ configuration, whereas each sulfur atom bonds to three Fe ions in a tetrahedral structure with its dimer partner [29]. The sulfur vacancies in the pyrite act as dopants, enhancing the conductivity of the pyrite, which is solely defined by the Fe 3d and S 3p states. The topmost part of the valence band is formed by the overlap of basically nonbonding Fe 3d-t_2g states, while the bottom of the conduction band is composed primarily of Fe 3d-e_g states (Fe 3d-e_g* and S 3p-ppσ* states), with the sulfur S 3p states located nearby the valence and conduction bands [29]. Thus, the conductivity of pyrite consists primarily of orbitals from the Fe surface atoms with less contribution from the S 3p orbitals because, in the valence band, the Fe 3d states dominate close to the Fermi level (E_F). Below the E_F, the e_g states of Fe 3d orbitals interact with the S₂ (dimers) sp³ hybrid orbitals and chemically bond to the two iron centres to form σ-bonds. The hybridization between Fe 3d and S 3p states, creates a charge transfer excitation from the completely filled Fe 3d-t_2g orbitals to the empty Fe 3d-e_g antibonding states. Therefore, a shift in the binding energy (E_b) along the e_g states of empty orbitals will covalently bond to other ligands due to σ interactions [30–32]. Thus, by understanding the conductivity of surface and bulk conditions from the optical and electrical characterization of FeS₂, it should be possible to improve the electrical properties for PV applications.

Optical properties and electronic structure of pristine pyrite (FeS₂) have been determined over a spectral range between 0.73–5.9 eV using spectroscopic ellipsometry. The complex dielectric function ε for the pristine bulk crystal shows seven interband absorption peaks. The investigated pyrite sample originating from the alluvial environment contains oxides, carbonates, and other impurities that appear to improve the conductivity of FeS₂.

We conclude that the application of ellipsometry in optical characterization of rocks and minerals appears to be distinctive since the optical response of materials is engineered by its crystallinity. Thus, since minerals that constitute rocks mostly consist of fine-grained sediments, the application of spectroscopic ellipsometry (optical microscopy) in mineral identification and textural parameters is vital in mineralogical studies. The results aid to better understand the electronic structure and related optical properties of pyrite, which will, in turn facilitate in the development of applications such as high-performance pyrite solar cells.

Acknowledgements

We thank the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971). M.M. acknowledges financial support from the Swedish Energy Research (Grant No. 43606-1) and the Carl Tryggers Foundation (CTS20:272, CTS16:303, CTS14:310).

Author contributions:

Gabriel Kofi Nzulu: Conception and design, data collection, formal analysis, investigation, methodology, software, analysis and interpretation of results, validation, visualization, manuscript composition, and review & editing.

Roger Magnusson: Experimental (methodology), formal analysis, supervision, validation, software, analysis and interpretation of results, and review & editing.

Martin Magnuson: Conception and design, formal analysis, funding acquisition, project administration, supervision, validation, methodology, software, analysis and interpretation of results, and review & editing.

Conflicts of interest or competing interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data and code availability: Data will be made available upon request.

Supplementary information: Not Applicable.

Ethical approval: Not Applicable.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Optical and electronic properties of pyrite

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