Exploring the optoelectronic structure and thermoelectricity of recent photoconductive chalcogenides compounds, CsCdInQ₃ (Q = Se, Te)

Abstract

The photoconductive quaternaries, CsCdInQ₃ (Q = Se, Te), have been recently synthesized and have been shown to be potential materials for hard X-ray and γ-ray detection. These materials have relatively high densities and band gaps in the range of 1.5–3 eV, which make them fulfill the requirement of hard detection devices. In the present work, we investigate the metal chalcogenide, CsCdInQ₃ as deduced from a full potential linearized augmented plane wave method based on density functional formalism. The direct band gaps are estimated at the level of the EV-GGA functional, as 2.11 and 1.75 eV for CsCdInSe₃ and CsCdInTe₃, respectively. These values are in good agreement with the experimental measurements (2.40 and 1.78 eV) obtained from solid-state UV-vis optical spectroscopy. Optical parameters, including the dielectric constant, absorption coefficient, energy loss function reflectivity and refractive index, were also reported to investigate the potential role of these metal chalcogenide compounds for solar conversion application. Our calculated optical band gap was compared to the measured experimental values on a Lambda 1050 UV-vis-IR spectrophotometer in the range of 300–1500 nm. The thermoelectric properties discuss the variation of the electrical and thermal conductivity, Seebeck coefficient and power factor with the temperature variation using the Boltzmann transport theory.

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I. Introduction

The increased demand on new compounds for imaging and detection capable of detecting hard X-ray and γ-rays has led to the conduction of intensive research on semiconductors in materials science engineering and also chemistry disciplines. Semiconductors are good detectors because they have a good energy resolution and the facility to fabricate compact arrays compared to other inorganic scintillation detectors.^1,2

Photoconductive semiconductors have been shown to be promising alternatives to expensive silicon in both forms, polycrystalline and amorphous.^3–5 The latter have a low stopping power for high energy photons, which limits their application to hard X-ray and γ-rays. Furthermore, germanium has a small band gap that requires operating at cryogenic temperatures to exhibit detection activity.⁶ Consequently, room-temperature semiconductors with high atomic numbers and wide band gaps are highly recommended to overcome all the limitations of silicon and germanium. Most importantly, wide band gap semiconductors have been long under development to make materials useful for medical and industrial imaging systems, as well as designing new detectors for high energy particle and astrophysics.⁶

Chalcogenides are potential candidates for hard X-ray and γ-ray detection because of their wide band-gap, good electro-transport properties and high resistivity. Since the early seventies, chalcogenides, such as cadmium telluride (CdTe), have been considered as promising semiconductor materials for hard X-ray and γ-ray detection. However, when compared to Si and Ge, CdTe is hard to use for nuclear spectroscopy due to its poor spectroscopic performance and lack of stability. In order to overcome the limitations of CdTe, research on the discovery of new chalcogenides that possess a wide band gap is growing exponentially.⁷ In fact, these materials are known to become more electrically conductive due to the absorption of electromagnetic radiation such as visible light, ultraviolet light, infrared light, and even gamma radiation.⁸ Photoconductive materials include a large variety of materials and structures such as the conductive polymer polyvinylcarbazole⁹ used extensively in photocopying (xerography) and lead sulfide, used in infrared detection applications.¹⁰

In general, metal chalcogenides are compounds made from a metallic element and a member of the chalcogenide family, namely, the elements oxygen, sulfur, selenium and tellurium. These materials are used for various applications such as: solar energy conversion and solar cells, semiconducting metal chalcogenide aerogels, infrared detection for optoelectronics, non-linear optics, thermoelectrics, hard detection and energy conversion.^8–10 The three latest applications are the scope of the present work, in which we report the results of ab initio investigations into the optoelectronic and thermoelectric properties of quaternary CsCdInQ₃ (Q = Se, Te). In fact, CsCdInQ₃ (Q = Se, Te) has been subject of experimental and theoretical studies performed by Hao Li et al.,¹¹ in which they synthesized the metal chalcogenides using a polychalcogenide flux technique. In addition to materials synthesis, the authors determined that these materials have a layered structure within a monoclinic symmetry. The measured electronic band gaps reported were found direct and large enough to be potentially interesting for applications in hard radiation detection. The optical band gap was measured using ground crystals and the absorption spectra from solid-state UV-vis optical spectroscopy. The density functional theory (DFT) calculations performed on these compounds have shown the limitation of the employed functional and the generalized gradient approximation (GGA)¹² used to determine the exact band gap values and performed a detailed comparison between both the chalcogenides. These materials are layered systems where the dimensionality reduction plays an important role in tuning their band gap. This interesting behavior makes CsCdInQ₃ (Q = Se, Te) band gap tuning possible for hard detection devices and thermoelectric conversion applications. Furthermore, due to huge demand on alternative materials for energy conversion and PV applications, we extend our investigation to the thermoelectric properties by the calculation of the figure of merit using the Boltzmann transport theory¹³ combined with density functional theory (DFT) outputs. Calculation of the optoelectronic and thermoelectric properties using an improved computational tool led us to understand the effect of structure/dimension perturbations on the band gap and related optical and thermoelectric properties. These findings will help experimentalists to find desirable methods to tune the electronic structures of CsCdInQ₃ (Q = Se, Te).

II. Structural description and computational details

CsCdInQ₃ (Q = Se, Te) are considered as layered structures and crystallize in the monoclinic space group C2/c. The structure of CsCdInTe₃ as shown in Fig. 1, is iso-structurally analogous to CsCdInSe₃ but a slight difference occurs for the five Cd²⁺ and In³⁺ sites were they have a mixed occupancy.¹¹ The valence sum for Cd²⁺ is around 2.25, whereas for In³⁺ it is found to be 3.20. From crystallography considerations and following the experimental measurements,¹¹ a typical structure is obtained, as displayed in Fig. 1.

Fig. 1 Structure of the metal chalcogenide, CsCdInQ₃ (Q = Se, Te).

In order to study properties, such as the energy band structures, total and partial density of states and optical properties of CsCdInTe₃ and CsCdInSe₃, investigations were carried out using the full potential linearized augmented plane wave method (FP-LAPW) using the computation package (WIEN2k)¹⁴ in the field of DFT. In the FP-LAPW method, the unit cell is decomposed into the (1) muffin tin (MT) sphere (non-interacting) and (2) interstitial region. We have implemented the Monkhorst–Pack k-point mesh of 16 × 5 × 16 in the irreducible Brillouin zone (IBZ) for self-consistent calculations. For the optimization of the structure, the generalized gradient approximation (GGA)¹² was used while the Engel Vosko generalized gradient functional (EV-GGA)¹⁵ was used for the optical properties. For self-consistent computation, both the total energy and charge of the compounds are relaxed up to 0.00001 eV and 0.0001 eV, respectively. The entire basis sets i.e. Cs (6s, 5p, 4d), Cd (5s, 4p, 4d), In (5s, 5p, 4d), Se (4s, 4p, 3d) and Te (5s, 5p, 4d) were studied using down-folding methods.¹⁶

BoltzTraP code¹³ was also used to calculate the entire transport coefficient under constant scattering time of the crystalline materials on the basis of the Boltzmann transport theory¹³ and the rigid band approach, which effectively explained the electronic structure and transport coefficients of numerous compounds. In these calculations, we ignored the temperature dependence on the E–K curve (energy band structure). Using the above approaches, with the exception of the Seebeck coefficient (S), the remaining transport coefficients i.e. electrical conductivity (σ), thermal conductivity (κ_ele), and power factor (S²σ), can be calculated with constant relaxation time (τ).

III. Optoelectronic properties

The calculated band structures (BS) and density of states (DOS) are displayed in Fig. 2(a) and (b) for CsCdInSe₃ and CsCdInTe₃, respectively. Their band gaps are direct and are found to be 2.11 eV and 1.75 eV from the EV-GGA functional. These values are almost in good agreement with the experimental measurements found at 2.40 and 1.78 eV for CsCdInSe₃ and CsCdInTe₃, respectively. Our calculated band gap values are closest to the experimental values measured with diffuse reflectance as found equal to 1.81 eV for CsCdInTe₃ and somehow good compared to the measured band gap of 2.17 eV for CsCdInSe₃. Deep research into these compounds is showing that other measurements based on diffuse reflectance and absorption methods¹¹ are giving band gaps of 2.17 eV for CsCdInSe₃ and 1.81 eV for CsCdInTe₃. We can see that our calculations are in better agreement with these later measurements than the first method reported in the literature.¹¹ Furthermore, this finding proves that the discrepancy observed between our calculation and experimental band gap is not related to the method employed, EV-GGA (actually the most robust in band gap calculation). Furthermore, the first theoretical study dealing with these chalcogenides was performed on the level of semi-local approximation like GGA,¹¹ and revealed a direct band gap of 1.53 eV (I) and 1.39 eV (II) at the Γ-point, which are underestimated when compared to the experimental band gaps. To correct these calculations, the authors have suggested performing more exact methods such as screened exchange LDA,¹⁷ GW approximation,¹⁸ or hybrid functional.¹⁹ From our investigation, we show that EV-GGA¹² is sufficient to reproduce the right band gap extracted from the optical measurements.

Fig. 2 Calculated band structure, and the total and partial density of states of: (a) CsCdInSe₃ and (b) CsCdInTe₃.

The projected density of states (PDOS) calculations for CsCdInQ₃ (Q = Se, Te) are shown in Fig. 2(a) and (b), and demonstrate that the valence band maxima (VBM) are mainly composed of Se(Te) 4p(5p)-orbitals. Cd 4d-orbitals contribute to a much lesser extent to the VBM and the conduction band minima (CBM) consists of hybridization bands made up of Se(Te) 4p(5p)-orbitals and In 5s-orbitals.

Before turning our attention to the optical properties, it is important to notice that the decrease in the measured and even calculated band gap values from the initial chalcogenides compounds can be explained using the “concept of reduction” and “dimensional reduction” introduced in materials II–VI,²⁰ and more recently in designing new radiation detection materials such as the alkali metal chalcogenides.²¹ In fact, it was proven that compounds containing very high Z elements such as the binary Hg-based binary chalcogenides can lead to ternary compounds with a high band gap (>1.6 eV), high resistivity and specific density. For the present compounds, the insertion of [CdQ] layers into the CsInQ₂ structure form CsCdInQ₃ with a dimensional increase (i.e. a band gap decrease) compared to the initial compound, CsInQ₂ leading to suitable band gap for X-ray and γ-ray detection.

Given the stability and apparent broad range of the CsCdInQ₃ electronic structure type, we expect to be able to tune the optical band gap further by changing Q to Se or Te. We display in Fig. 3(a)–(c), the real and imaginary parts of the dielectric constants (ε₁(ω) and ε₂(ω)), the absorbance coefficient I(ω) and energy loss function L(ω), respectively. We have calculated the imaginary part ε₂(ω) using EV-GGA potential (Fig. 3(a) and (b)). From the ε₂(ω) plots, we analyzed that the threshold energy (critical point) occurred at 2.11 and 1.75 eV for the corresponding band gaps of CsCdInSe₃ and CsCdInTe₃, respectively. At this critical point, the optical transitions between the valence band maximum and conduction band minimum are direct as deduced from the band structures. The existence of an abrupt increase in the curve beyond this energy is due to the occurrence of more inter-band transitions.

Fig. 3 Calculated optical properties using EV-GGA: (a) imaginary part of the dielectric function (b) real part of the dielectric function (c) absorption coefficient (d) energy loss function (e) reflectivity and (f) refractive index.

There are also prominent peaks in the ε₂(ω) for CsCdInTe₃, as well as for the CsCdInSe₃ compound that have a maximum magnitude among the other components occurring at around 4 and 5.8 eV for CsCdInTe₃ and at 5 and 6.3 eV for CsCdInSe₃. These maximum peaks are caused by the electric dipole transitions between the valence and conduction band. The magnitude of ε₂(ω) constantly decreases at higher energies for both the compounds. At intermediate energies, the maximum anisotropy exists among the three components of the dielectric constant. At this stage of the calculation, we used the Kramers–Kronig relation²² to extract the real part ε₁(ω) for the dielectric function from the imaginary part using (where p is the principal value of integral). The calculated real part ε₁(ω) of the dielectric function for CsCdInQ₃ is displayed in Fig. 3. The maximum peak of magnitude at 8.6 (a.u) is located at around 2.25 eV for CsCdInTe₃ and 6.6 (a.u) at 3.1 eV for CsCdInSe₃. It is important to point out here that we have only calculated the electronic contribution because both the electrons and ions contribute to the dielectric constant of the compounds. Furthermore, the static dielectric constant values were found equivalent to 6 and 4.8 for CsCdInTe₃ and CsCdInSe₃, respectively. In Fig. 3(c), we display the absorption coefficient I(ω) as calculated using EV-GGA, the absorption spectrum starts at 2.0 eV for both chalcogenides and attained a maximum value at about 7.0 and 7.8 eV for CsCdInTe₃ and CsCdInSe₃, respectively. Beyond this energy region, the absorption curves decrease, and then start to increase. From the dielectric constants, we can determine the energy loss function L(ω) as . The functions, as displayed in Fig. 3(d), are useful for providing information on the electronic system interacting with the incident electron beam. For both chalcogenides, our ELF shows a broad spectrum in the energy range 2.0–14.0 eV. The significant feature of L(ω) is that the main peaks represent the characteristics plasma resonance occurring at a plasma frequency corresponding to energy (12.0 eV for CsCdInTe₃ and 12.2 for CsCdInSe₃). At this point of energy, the reflectivity spectrum shows a sudden reduction in the curve as is shown in Fig. 3(e). For both chalcogenides, these curves show that the reflectivity increases with energy and reaches a maximum value of 70% at around 13.5 eV. Reflectivity is found to be 15%, (17%) for CsCdInTe₃ (CsCdInSe₃) at zero vibration, the valleys in the reflectivity spectrum correspond to the peaks in the energy loss function of Fig. 3(d). For both compounds, we have also calculated refractive index n(ω) shown in Fig. 3(f). The refractive indices increase with energy in the lower energy region and reached maximum values at 2.8 and 3.5 eV for CsCdInTe₃ and CsCdInSe₃, respectively.

IV. Thermoelectric properties

The temperature dependent electrical conductivity, thermal conductivity, Seebeck coefficient, power factor and ZT for both CsCdInTe₃ and CsCdInSe₃ compounds are displayed in Fig. 4. These properties are responsive to the energy band gap values. As for the experimental values, our found band gaps are direct and show a variation with temperature induced by the thermal excitation of electrons. On the basis of the calculated energy band structure and density of states, one can easily calculate the electrical conductivity, σ^ave, under constant relaxation time as a function of temperature. Fig. 4(a) shows a linear increase in the electrical conductivity (σ^ave) of both the compounds CsCdInSe₃ and CsCdInTe₃ when the temperature was increased from 100 to 800 K. σ^ave is increases due to the excitation of the carrier from the valence band to the conduction band when the temperature increases and induces an increase in the number of carrier concentrations devoted to conduction. The CsCdInSe₃ depicts low electrical conductivity at small carrier concentration up to 350 K but beyond this temperature σ^ave increases when compared to CsCdInTe₃. The behavior of σ^ave might be inter-related to the valence shell electronic configuration of the Se and Te atoms. The lattice and electronic parts contribute to the total thermal conductivity and each change differently with temperature. In the theoretical model, we ignore the lattice thermal conductivity κ_lat and pay attention to the electronic part of the thermal conductivity κ_ele. Thermal conductivity directly varies with the following parameters: (i) carrier concentration (ii) electrical conductivity and (iii) mobility of the carrier i.e. κ_e = σμn. The electronic thermal conductivity κ_ele of CsCdInSe₃ and CsCdInTe₃ is 3.15 × 10¹⁴ W m⁻¹ K⁻¹ s⁻¹ at low temperature (100 K) and 2.18 × 10¹⁴ W m⁻¹ K⁻¹ s⁻¹ for CsCdInSe₃ and 2.22 × 10¹⁴ W m⁻¹ K⁻¹ s⁻¹ for CsCdInTe₃ at high temperature (800 K). Fig. 4(b) shows a linear increase in the thermal conductivity κ_ele of both the compounds when the temperature increases from 100 to 800 K. Thermal conductivity κ_ele of CsCdInSe₃ is greater than CsCdInTe₃ and mainly originates from the electronic part.

Fig. 4 Calculated thermoelectric properties as a function of temperature: (a) electrical conductivity, (b) thermal conductivity, (c) Seebeck coefficient, (d) power factor and (e) figure of merit.

Fig. 4(c) represents the computed Seebeck coefficients S^ave under temperatures ranging from 100 to 800 K with different doping materials. The calculated Seebeck coefficients for both compounds are strongly dependent on the temperature and carrier concentration, in which we can see an inverse relation of the carrier concentration and Seebeck coefficients.²³ It is clear from Fig. 4(c) that both compounds (CsCdInSe₃ and CsCdInTe₃) are p-type compounds. The S^ave of CsCdInSe₃ shows an abrupt increase with temperature up to 250 K, while for CsCdInTe₃ the Seebeck coefficient increase steadily with temperature up to 450 K and indicate stability between 450 to 600 K. Beyond 250 K, it decreases due to an increase in the carrier concentration and temperature (for CsCdInSe₃). At higher temperatures (800 K), both compounds show dispersive nature i.e. the value of the Seebeck coefficient reaches 180 μV K⁻¹ for CsCdInSe₃ and 183 μV K⁻¹ for CsCdInTe₃. One can also observe a very small decrease in the value of S^ave in CsCdInTe₃ with an increase in temperature when compared to CsCdInSe₃. These findings confirm the dependence of S^ave on changes in temperature and carrier concentration. One can see from the energy band structure (displayed in Fig. 2(a)) that bands are less dispersive around the Fermi level and at lower energy, hence, the effective mass values will be smaller for the corresponding fundamental particles i.e. electrons and holes, leading to a smaller value of the Seebeck coefficient. Furthermore, both compounds have different dispersion in their bands, which are also responsible for the changes in the magnitude of the Seebeck coefficient.

The power factor S²σ shown in Fig. 4(d) can be calculated from the thermoelectric power and electrical conductivity. For an increase in temperature, from 100 to 800 K, S²σ increases from 0.30 to 2.12 × 10¹¹ W m⁻¹ K⁻² s⁻¹ for CsCdInSe₃ and reaches a value of 1.97 × 10¹¹ W m⁻¹ K⁻² s⁻¹ for CsCdInTe₃. In addition, one can have a maximum power factor by replacing Te with Se. This indicates that CsCdInSe₃ has the larger carrier concentration when compared to CsCdInTe₃. The calculated power factors of both p-type compounds rapidly increase due to an increase in carrier concentration with increasing temperature. The increase in electrical conductivity is responsible for the greater value of the power factor. These findings confirm that CsCdInSe₃ is more suitable for thermoelectric devices than CsCdInTe₃ because its thermoelectric properties can be effectively enhanced at high temperatures.

Combining the electrical conductivity and Seebeck coefficient time's temperature over thermal conductivity, we obtain the figure of merit i.e. ZT = S²σT/κ of both chalcogenides is shown in Fig. 4(e). It is clear from Fig. 4(e) that the figure of merit (ZT) for both compounds show different behavior at low temperature, in particular from 100 to 350 K, and then increases parallel with temperature beyond 350 K. Comparing the figures of merit (ZT), i.e. 0.75 for CsCdInSe₃ and 0.71 for CsCdInTe₃, one can easily conclude that the first compound is better than the second compound along the entire temperature interval. Fig. 4(e) indicates that ZT is affected by two parameters: (i) temperature and (ii) doping element. Greater ZT mainly originate from higher electrical conductivity and lower thermal conductivity. In addition, changes in the values of (ZT) from 0.60 to 0.75 suggest that CsCdInSe₃ is a very prominent material for both types of uses: cooling devices and thermoelectric applications, while CsCdInTe₃ can be used only in thermal devices. Most importantly, the figure of merit for both compounds show a strong dependence on temperature.

V. Conclusions

In the present work, we have investigated, using a full potential linearize augmented plane wave method based on density functional formalism, the metal chalcogenide, CsCdInQ₃ (Q = Se, Te) in view of their potential applications in detector devices for X-ray and γ-rays, and thermoelectric devices. The optoelectronic properties show a direct band gap, estimated at the level of EV-GGA, at 2.11 and 1.75 eV for CsCdInSe₃ and CsCdInTe₃, respectively. These findings agree well with the solid-state UV-vis optical spectroscopy measurements (2.40 and 1.78 eV, respectively). Our computed optical band gap was compared to the measured experimental values using a Lambda 1050 UV-vis-IR spectrophotometer in the range of 300–1500 nm. Both of the CsCdInQ₃ show interesting thermoelectric properties making them potential candidates for cooling and thermal devices.

Acknowledgements

The work of W. Khan was developed within the CENTEM project, Reg. no. CZ.1.05/2.1.00/03.0088, co-funded by the ERDF as part of the Ministry of Education, Youth and Sports OP RDI program. MetaCentrum and the CERIT-SC under the program Centre CERIT Scientific Cloud, Reg. no. CZ.1.05/3.2.00/08.0144. Jan Minar for the support in the discussion within the EU-COST action MP1306 (EUspec).

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