Abstract good agreement in the particle size obtained


An electrochemical route has been employed to prepare undoped- and In-doped SnS thin films. Six samples including undoped- and In-doped SnS thin films were deposited on the fluorine-doped tin oxide (FTO) substrate. An aqueous solution containing 2 mM SnCl2 and 16 mM Na2S2O3 are used as the main electrolyte. Different In-doped SnS samples were prepared by adding a different amount of 1 mM InCl3 solution into the main electrolyte. The applied potential (E), time of deposition (t), pH and bath temperature (T) were kept at -1 V, 30 minutes, 2.1 and 60 ?, respectively. For all samples, except the In-dopant concentration, all the deposition parameters are the same. After preparation, X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM) with an energy dispersive X-ray analyzer (EDX) attachment, atomic force microscopy (AFM), and transmission electron microscopy (TEM) were used to determine structural properties of as-deposited films. XRD pattern showed that the synthesized undoped- and In-doped SnS thin films were crystallized in the orthorhombic structure. The shape of SnS crystals was spherical in the TEM image. X-ray peak broadening studies was done by applying Scherrer’s method, Williamson-Hall (W-H) models (assuming uniform deformation model (UDM), uniform strain deformation model (UDSM), and uniform deformation energy density model (UDEDM)), and size-strain plot (SSP) method. The crystallite size and lattice strain have been estimated using these methods. There was a good agreement in the particle size obtained from W-H- and SSP methods with TEM image.

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Keywords: X-ray analysis, SnS nanostructures, In-doping, Williamson-Hall, size-strain plot.



1. Introduction

In recent times, much attention has been focused on tin sulfide (SnS), with an extensive range of applications such as in near-infrared detectors, electrochemical capacitors 1, holographic recording, photovoltaic cells, and lithium-ion batteries, 2-8. SnS is a semiconductor belongs to the IV-VI group with the layered orthorhombic crystal structure, which it has a long b-axis with lattice constants of a = 0.4321 nm, b = 1.11923 nm, and c = 0.39838 nm 9. According to Fig. 1, SnS consists of two weakly van der Waals force bonded layers, in which atoms are tightly bonded with covalence bond. SnS has a variety of energy band gap depending on the preparation method, which it has been reported as 1.3–2.3 eV for direct band gap and 1.0–1.2 eV for indirect band gap 10. Because of the unique features of SnS such as high absorption coefficient (>104 cm?1) 11, suitable carrier concentration 9, plentiful in nature, non-toxicity, and cost efficiency, it was a promising candidate for use in absorber layers in thin film solar cell applications.

Various methods have been used to prepare SnS such as spray pyrolytic-deposition 12-14, molecular beam epitaxy (MBE) 15, hydrothermal method 6, 7, 16, chemical bath deposition 17-20, electron beam evaporation 21, 22, SILAR method 23, 24,and electrodeposition technique 11. Among these methods, the electrochemical technique is a good method due to simplicity, cost-efficiency, and the facility of controlling its parameters with high accuracy.

To estimate the crystallite size of material the Scherrer’s method has been applied. Nevertheless, two important factors including inhomogeneous strain and instrumental effects have not taken into account for acquiring crystallite size. Therefore, the Williamson-Hall (W-H)- and the size-strain plot (SSP) methods are an average method to have a much realistic estimation of the crystallite size and lattice strain 25. As we know, the deviation from perfect crystallinity creates a broadening of the diffraction peaks. From peak width analysis, it can be obtained the crystallite size and lattice strain. The particle size is almost bigger than crystallite size due to the aggregation of crystallite structures 26. In order to a real crystal deviate from a perfect crystal, the lattice strain has been created. The sources of lattice strain are the distribution of lattice constants arising from crystal imperfections, such as lattice dislocation, and the grain boundary triple junction, contact, or sinter stresses, stacking faults, coherency stresses etc. Some structural parameters such as peak width, the intensity of the peak and the shift in peak position are affected by crystallite size and lattice strain. The peak width and the lattice strain varies as 1/cos? and tan?, respectively 27. In order to obtain the crystallite size and lattice strain as a function of 2?, two methods named Williamson-Hall (W-H)- and the size-strain plot (SSP) methods can be applied.

In this work, six samples (containing undoped SnS and In-doped SnS) have been synthesized by electrochemical deposition from an aqueous solution. With the use of XRD data, the crystallite size, lattice strain, and other related parameters have been achieved by applying following methods. Three models of the W-H method containing: (i) uniform deformation model (UDM), (ii) uniform strain deformation model (UDSM), (iii) uniform deformation energy density model (UDEDM), and the size-strain plot (SSP) method. The crystallite size values acquired from Scherrer’s-, W–H, and SSP methods confirmed by TEM image. There is no report on W–H method, and SSP analysis of nanostructured In-doped SnS thin films.


2. Experimental

2.1. Materials and processing

A three-electrode electrochemical cell was applied to deposit Nanostructured In-doped SnS thin films on fluorine-doped tin oxide (FTO) coated glass substrate. The effective dimension of FTO substrates (used as working electrode) was considered as 1 cm × 1 cm. The anode and the reference electrode were a platinum sheet and a saturated calomel electrode (SCE), respectively. The electrolyte was 2 mM SnCl2 and 16 mM Na2S2O3, and the In-dopant was supplied by a 1mM InCl3 aqueous solution. The pH of the electrolyte was 3.8, which is reduced to 2.1 by adding diluted H2SO4. The FTO and platinum sheet was cleaned in an ultrasonic bath and then rinsed with ethanol/acetone and distilled water. All deposition parameters except the In-dopant concentration were kept constant during electrochemical process. The bath temperature and deposition time considered as 60 ? and 30 minutes, respectively. The deposition potential was tuned at -1 V for all samples by a computer-controlled electrochemical analyzer (potentiostat, Autolab, A3ut71167, Netherlands). At the end of the electrodeposition process, the substrates were taken out from the bath. Then they washed with distilled water and lastly dried with an air jet. The formation of SnS on FTO substrates is occurred according to the following reaction,

According to the above reactions, the Na2S2O3 is unstable in acidic media. Therefore, it is easy to separate the sulfur, and consequently, the Sn2+ and S reduced at the cathode (substrate). In this research, we performed our analyses on six samples with different In-dopant concentrations. The undoped SnS named as In 0, and the In-doped SnS thin films named as In 1-In 5. Using EDX analysis, the atomic percentage of In-dopant in In 1, In 2, In 3, In 4, and In 5 samples obtained 1.30, 2.13, 2.59, 2.90, and 3.58 %, respectively.

2.2. Characterization of the films                                   

To examine the phases of the deposited thin films, a Philips X’Pert-MPD X-ray diffraction diffractometer (XRD) system with Cu-K? radiation has been employed. Elemental analysis was performed by a TE-SCAN field emission scanning electron microscope (FESEM) with an energy dispersive X-ray analyzer (EDX) attachment was used. The surface topography of the deposited samples checked by atomic force microscopy (AFM- ARA AFM). A PHILIPS CM120 TEM was used to study the shape and size of SnS particles. Varian-Cary Eclipse room temperature photoluminescence (PL) was used to analyze the optical properties of nanostructured SnS thin films.



3. Results and discussion

3.1. XRD analysis

X-ray diffraction (XRD) test is a robust nondestructive method that used for characterizing the structural phases of various materials. It offers information on crystal structure, phase analysis, preferred crystal orientation (texture), and other structural parameters, such as average grain size, crystallinity, lattice strain, and crystal defects. X-ray diffraction pattern is the fingerprint of the periodic atomic arrangements in a given material. Therefore, XRD is a unique method in determination of crystallinity of a compound. Fig. 2a depicted the XRD patterns of undoped- and In-doped SnS thin films. All the films showed polycrystalline nature with the orthorhombic crystal structure of preferred orientation. The observed peak position values compared with the standard JCPDS files and the Miller indices of SnS compound referring to JCPDS 039-0354. As it was evident in this figure, the preferred orientations of In 0, In 1, In 2, and In 3 samples were (021) and (111). Whereas, those were (101) and (040) for In 4 and In 5 samples. Therefore, it is interesting that the increase in In-dopant concentration leads to change in preferential orientation of as-deposited In-doped SnS thin films. Also, no trace of In, In2O3, and In2S3 or other impurities cannot be detected in all samples. As it is observed in XRD patterns, with an increase in In-dopant concentration, the peaks will become less intense and broader, which indicating a decrease in crystallinity of samples. Hence, it shows a significant increase in crystalline defects and mismatching due to In-doping.

In order to better investigate the effect of In-doping on the structural properties of SnS, the plot of I-2? for (111) plane diffraction peak (Fig. 2b) of all samples has been drawn. Due to the difference in the effective ionic radii between Sn2+ (0.93 A) and In3+ (0.80 A), a shift of (111) peak position to higher 2? has been observed.


The lattice parameters of undoped- and In-doped SnS thin films can be obtained from the following relation 28,

where (hkl) is the lattice plane index for the planes with higher intensity, i.e. (040), (021), (111) planes, and the dhkl is inter-planar distance. The calculated lattice parameters and other structural parameters of undoped- and In-doped SnS samples listed in Table 1. It is clear that the substitution of In3+ for Sn2+ in the SnS lattice leads to a decrease in the unit cell volume. The reason for this phenomenon is the smaller effective ionic radii of In3+ compared with Sn2+, which it caused a decrease in the dhkl and consequently unit cell volume. Fig. 3 shows the variation of lattice parameters of undoped SnS after In-doping. As it was apparent in this figure, due to the effective ionic radii of In3+ is smaller than Sn2+, an increase in In-dopant concentration in the SnS lattice leads to decrease in lattice parameters (a, b, and c). This occurrence clearly indicates that the In-dopant is substitutionally doped into SnS lattice.



Using atomic force microscopy (AFM) scanned over an area of 6µm × 6µm, the topographical examinations of In 0, In 1, and In 2 samples was done. Fig. 4 shows AFM images of deposited films. Therefore, the variation in the morphology of In-doped SnS nanostructures with an increase in In-dopant concentration showed that the In had been doped successfully in SnS lattice.


3.2. Crystallite size and strain

In this section, we use different methods to calculate crystallite size and lattice strain. These methods are Scherrer’s method, W-H method (including UDM, UDSM, and UDEDM), and SSP method.

3.2.1. Scherrer’s method

Using XRD patterns, the crystallite size (D) is estimated from Scherrer’s equation 29, 30,

 where D is the crystallite size, K is a shape-dependent constant equal 0.94, ? is the X-ray wavelength of Cu-K? radiation (0.154056 nm), ?hkl is the peak width at half maximum intensity (FWHM), and ?B is the Bragg’s angle. The width of the Bragg’s angle is formed by the combination of instrumental- and sample dependent effects. The instrumental effect is evaluated from the line broadening of a reference sample such as silicon. Therefore, considering the instrumental effect, ?hkl can be obtained as follows 29,

Scherrer’s equation can be rearranged by applying the corrected ?hkl as follows,

The crystallite size (D) was evaluated from the slope of cos? versus 1/?hkl plot using Eq. 5. Consequently, the value of k?/slope shows the crystallite size value. Fig. 5 depicts Scherrer’s plots of undoped- and nanostructured In-doped SnS thin films. It is clear that the crystallite size D of SnS is decreased after In-doping. The decrease in crystallite size of undoped SnS thin films after In-doping can be due to the difference in effective ionic radii of Sn2+ and In3+. Therefore, the crystalline quality of undoped SnS has been decreased after In-doping, which it could be attributed to the created lattice mismatch.


3.2.2. W-H methods

The Williamson-Hall (W-H) and size-strain plot (SSP) are two methods to estimate the crystallite size and lattice strain. In this paper, three models of a W-H method including UDM, UDSM, and UDEDM have been used to estimate the structural parameters. To examine the uniform strain in the crystalline lattices, a simplified method named UDM model is proposed. In this method, the W-H formula relies on the size broadening effect and strain broadening effect. Size broadening effect is described with   Debye-Scherer (?DS) formula as in Eq. 3, while the strain broadening term originated from imperfection and/or distortion in crystal lattices (Eq. 6).

In the above equation, ? is a maximum tensile strain, or maximum compressive strain and C is a constant that assumed as 4. The above relation originated from the differential of the Bragg equation (n?=2dsin?B) concerning the d-spacing and the diffraction angle. According to the lattice strain is considered as ?d/d=2?, the strain-inducing term is obtained as follows 31,

In order to ?hkl=??+?DS, the Eq. 8 obtained as follows 32,

By rearranging the above equation, the W-H relation (Eq. 9) is obtained 29.

According to Eq. 9, the crystallite size and lattice strain can be achieved. The slope and the y-intercept (at ?hkl.cos? = 0) values of the ?hkl.cos? vs. 4sin? plot show strain (?) and k?/D, respectively. The W-H diagrams of un- and In-doped SnS thin films shown in Fig. 6. As shown in this figure, due to the difference in the effective ionic radii of Sn2+ and In3+, by increasing the In-dopant concentration in the SnS lattice, the crystallite size and lattice strain of In-doped SnS samples decreased and increased, respectively.


To intrinsic anisotropic nature of elastic constant of materials, the microstrain is not uniform in all crystallographic direction. By considering the anisotropic nature of Young’s modulus, the UDSM and UDEDM methods have been used to measure structural characterizations of crystalline lattices. In the UDSM model, it is assumed that the lattice stress (?) is uniform in all crystallographic directions. Therefore, the anisotropic nature of elastic modulus of materials is responsible for the anisotropic nature of micro strain (?hkl) and energy density (u) 33. As we know, the Hooke’s law is valid in the elastic deformation zone. According to the Hooke’s law, the stress and strain have linear variations to each other. Therefore, the stress is obtained by using ? = ? Ehkl formula, which ?, ?, and Ehkl are lattice stress, lattice strain, and elastic modulus in the vertical direction to the crystalline planes (hkl) crystalline lattices, respectively. Therefore, the Eq. 9 modified by putting the value of ?=?/Ehkl as follows,


According to the above equation, the UDSM plot has been drawn by considering ?cos? as the y-axis and 4sin?/Ehkl as the x-axis. Therefore, the crystallite size and lattice stress are estimated from the y-intercept and the slope of this plot, respectively. Young’s modulus in the orthorhombic structures obtained as follows, 34,

where li is the unit vector for a particular (hkl) plane and s11, s12, s13, s22, s23, s33, s44, s55, and s66 are the elastic compliance of SnS with values of 11.92, -2.93, -4.32, 10.07, -8.2, 19.08, 19.46, 35.8, and 35.27 (TPa)-1, respectively.

The obtained results showed that an increase in In-doping concentration in SnS lattice results in a decrease and an increase in crystallite size and lattice stress, respectively. Therefore, it can be said that the micro tensile stress in the In-doped SnS thin films may be due to the formation of grain boundaries 32.

The other form of W-H method is UDEDM. In this method, the energy density (u) is assumed uniform in all crystallographic directions, while the deformation stress (?) is presumed anisotropic 33. According to the Hooke’s law in the elastic deformation zone, the energy density (u) defines as u=?2Ehkl/2. Therefore, the UDEDM formula is obtained by rearranging the Eq. 9, 

In order to estimate the crystallite size and energy density, the UDEDM graphs have been plotted. The UDEDM curves are drawn with ?cos? against 4sin?/(Yhkl/2)1/2. It is obvious in the Eq. 12 that the crystallite size (D) and energy density (u) are estimated by the y-intercept and slope of the fit, respectively. Based on Eq. 12, the crystallite size and energy density are calculated using the below equation. 

 According to UDEDM model, the crystallite size and energy density of undoped SnS are decreased and increased, respectively, after In-doping. As previously described, introduction an ion (In3+) with different effective ionic radii compared with Sn2+ in SnS lattice leads to create mismatch and imperfection in SnS lattice. Therefore, it increased the energy density in In-doped SnS crystalline lattice. According to Hooke’s law, an increase in energy density leads to an increase in lattice stress and lattice strain.


The calculated crystallite size values from W-H methods including UDM, UDSM, and UDEDM are in good agreement with each other. These are because the presence of strain in various models of W-H analysis has a minimal effect on the average crystallite size of SnS thin films. Also, the value of average crystallite size of un- and In-doped SnS samples estimated from Scherrer’s method and W-H analysis shows a variation, which this is due to (i) strain broadening effect and (ii) the difference in averaging the particle size distribution 26. Similar results were observed in 29.


3.2.3. SSP method

Size strain plot (SSP) technique is another suitable method to investigate the crystallite size and lattice strain. It is considered for the isotropic nature of the crystal structure which gives less weight to data from reflections at high angles, where the accuracy is usually lower 35. In this method, the Lorentzian function and the Gaussian function describe the crystallite size- and strain profile, respectively 25. According to the SSP method, the following relation is employed to describe the relation between lattice strain and crystallite size 36,

where A is a constant which equals ¾ for spherical particles. By plotting (?hkl.cos?.dhkl)2 versus d2hkl.?hkl.cos?  as shown in Fig. 9 (SSP plot), the crystallite size and lattice strain of undoped- and In-doped SnS thin films can be achieved. According to Fig. 9 and Eq. 13, the crystallite size and the lattice strain can be obtained from the slope and y-intercept (in which (?hkl.cos?.dhkl)2 = 0), respectively. The obtained results from Scherrer’s method, W-H method, and SSP method are summarized in Table 2. In addition, the obtained values of crystallite size and lattice strain for undoped- and In-doped SnS thin films using Scherrer’s-, W-H- and SSP methods are compared in Fig. 10. As can be seen in Fig. 10, with the increase of In-dopant concentration in the SnS lattice, the crystallite size decreased and subsequently, the lattice strain increased. It is due to the fact that with introducing the indium ions into SnS lattice, the lattice has been accompanied by mismatches related to different effective ionic radii of In3+ and Sn2+ ions. The results showed that the crystallite size obtained from Scherrer method is less than that of W-H and SSP method that it can occur due to the effect of strain value and shows that the role of strain is important 37. Consequently, it can be said that there is good accordance between structural parameters obtained from UDEDM, UDM, UDSM models, SSP method, and the results of the Scherrer’s formula and TEM image.

3.2.3. TEM method

In order to discover the reality of obtained data from XRD analysis, TEM analysis was applied. TEM is an excellent analysis to examine the size and the shape of deposited SnS. The TEM image for undoped SnS thin films is shown in Fig. 11. It is clear in TEM image that the average particle size is in good agreement with the average crystallite size estimated from W-H and SSP methods.

3.3. PL

Photoluminescence is light emission from any form of matter after the absorption of photons. PL is a non-destructive test for examination the crystalline quality of materials. The room temperature PL spectra of undoped- and In-doped SnS thin films are shown in Fig. 10. The photo-excitation wavelength was 350 nm. As it is evident in this figure, two emission peaks containing a blue emission peak at 482 nm and a green emission peak at 559 nm observed for all samples. Thus, the In-doped SnS thin films can be used as blue and/or green light emitters or other devices owing to these emission bands. Based on our investigations, these peaks are assigned to a high density of sulfur and tin vacancies and various kinds of defects such as interstitials, stacking faults, etc. 38, 39. Liu et al. observed two peaks at 365 nm and 464 nm for SnO2 nanoparticles that the peak at 464 nm is related to oxygen vacancies 40. The observed blue emission peak is similar to that reported in 38, 41, and the green emission peak is similar to that reported in 42. Due to PL detection limitations, the band-to-band emission (band gap energy) of undoped- and In-doped SnS samples is not seen. As it is obvious in Fig. 10, with an increase in In-dopant concentration in SnS lattice, a blue- or red shift has been seen compared to undoped SnS film. In addition, compared to the undoped SnS thin film, the PL intensity of In-doped SnS samples decreased that it showed the crystalline quality of In-doped SnS is decreased in comparison with undoped SnS film. This observance is in good accordance with XRD patterns.

4. Conclusion

Six deposited samples containing undoped SnS and In-doped SnS thin films have been prepared using an electrodeposition method on the FTO substrates. The results of XRD patterns clearly showed that all of the deposited thin films were orthorhombic polycrystalline. In this research, the line broadening investigations on un- and In-doped SnS thin films have been investigated. Therefore, the Scherrer’s method, modified forms of W-H (UDM) method, and the SSP method have been used to analyze the line broadening of undoped- and In-doped SnS (with different concentration of In-dopant) samples. The results obtained by these methods showed that an increase in In-dopant concentration in SnS lattice leads to a decrease in the crystallite size and an increase in the lattice strain. There were happened due to the variation in the effective ionic radii of In3+ and Sn2+ ions. Therefore, substitution of In3+ for Sn2+ in the SnS lattice leads to creates mismatches in the SnS crystal lattice. This lattice mismatch is responsible for the reduction of the crystalline quality and the increase in lattice strain. In addition, the result of TEM image confirms our obtained results.