Nonlinear optical properties of CVD-synthesized CuS crystals Open Access

Copper sulfide (CuS) is an interesting binary compound owing to its exceptional optical, electronic, and catalytic characteristics.^1–6 It is a multifaceted material that manifests in diverse crystal structures, such as hexagonal covellite and orthorhombic anilite, among others.^7–10 The distinctive attributes of CuS crystals have resulted in a diverse range of applications, including but not limited to energy storage sensors, photovoltaic devices, and thermoelectric devices.^11–15 The crystals of CuS exhibit remarkable optical characteristics, such as elevated quantum yields of photoluminescence and exceptional absorption of visible light. The material’s robust light absorption properties have been utilized in various photovoltaic devices, including but not limited to dye-sensitized solar cells and thin-film solar cells, to optimize their efficiency.^16,17 Wet-chemistry techniques have been employed to synthesize CuS nanoparticles, which exhibit considerable potential as lithium/magnesium-ion battery components owing to their superior energy storage capabilities.^18,19 Furthermore, the photocatalytic characteristics of CuS have been investigated, wherein its considerable specific surface area has been identified as a pivotal factor in augmenting photocatalytic efficacy.²⁰ The characteristic feature of CuS renders it a viable contender for deployment in the domains of environmental remediation and hydrogen generation via water electrolysis. As reported by Fan et al., the light-harvesting and charge dissociation functionalities of heterostructured ZnIn₂S₄/CuS nanosheets can be considerably enhanced without requiring a co-catalyst.²¹ The observed improvement can be attributed to the robust interplay between the assembled p–n heterostructures, which effectively promotes the transfer and separation of charges. Zhu et al. recently showed the outstanding efficiency of CuS in the oxygen evolution reaction, exhibiting minimal overpotential and exceptional electrolytic endurance.²² Although there are many reports on the energy storage and photocatalysis applications of CuS, its physicochemical properties have not been thoroughly investigated. Consequently, a plethora of unexplored possibilities exist for uncovering novel CuS characteristics and uses in diverse domains, including energy conversion and storage, sensing, and optoelectronics. Further exploration of the characteristics of CuS and its analogous compounds has the potential to facilitate significant progress in the field of materials science and the innovation of advanced technologies.

In this work, CuS crystals were synthesized using a straightforward single-step chemical vapor deposition (CVD) technique at 600 °C. Detailed structural, morphological, and compositional analyses, including XRD, electron backscatter diffraction (EBSD), Raman spectroscopy, and XPS, revealed key insights into their properties. XRD confirmed the hexagonal covellite structure, while EBSD showed consistent in-plane alignment with some domain misorientations. Raman spectroscopy highlighted vibrational modes and thermal dynamics, further supporting the structural findings. Unexpectedly, the CuS crystals exhibited second harmonic generation (SHG), attributed to intrinsic lattice defects such as stacking faults and dislocations. The spectroscopic characterizations and SHG mapping revealed that these defects disrupt the lattice’s centrosymmetry, enabling the SHG response. This defect-induced symmetry breaking underscores the significant role of imperfections in shaping nonlinear optical behavior. These findings position CuS crystals as promising candidates for nonlinear optical applications while reinforcing their potential in catalysis and energy storage. This study links structural characteristics with optical functionality, paving the way for further exploration of defect-engineered materials in photonics and sensing technologies.

Copper(I) chloride (CuCl) powder was opted as the Cu source for the growth of CuS crystals due to its relatively low melting point temperature. A small, asymmetric crucible was chosen to this end, filled with scant amount of CuCl powder, and put in middle of tubular CVD furnace as can be seen in the schematic setup in the supplementary material (Fig. S1). During the synthesis process, the optimum growth temperature was found to be about 600 °C, lower than the other CVD synthesis of copper-based chalcogenides.^23,24 Additional information regarding the CVD growth process is provided in the experimental section. Figure 1(a) shows a typical optical micrograph of CuS crystals grown on a mica. The lateral length of the grown ultrathin CuS crystals can be up to 60 μm [Fig. 1(b)]. Mica is used as a substrate because of its atomic-level smooth and inert surface, which has been widely reported as a favorable substrate for ultrathin material synthesis.^25,26 We used different substrates for comparison and substrate effect influence, including SiO₂ and bare Si, and found that mica worked best in terms of crystal homogeneity, thickness, and size. Figure S2 shows the results of the as-grown CuS crystals on several substrates. Atomic force microscopy (AFM) height trace map shown in Fig. 1(c) confirms that the surface of CuS is very smooth and the thickness of the studied crystal is found to be about 14 nm. The x-ray diffraction (XRD) θ–2θ scan of the transferred CuS crystals on the SiO₂/Si substrate, shown in Fig. 1(d), unambiguously corresponds to the hexagonal phase of CuS (PDF No. 06-0464).²⁷ The pronounced characteristic peaks corresponding to the (002), (006), and (008) planes indicate that CuS crystals predominantly grow along the basal plane (00l). To further investigate the crystallographic orientation of the CuS crystals, electron backscatter diffraction (EBSD) was used. This technique is highly effective in characterizing the microstructure of materials.^28,29 As shown in Fig. 1(e), the EBSD inverse pole figure (IPF) map exhibits a consistent color contrast within the hexagonal domains along the basal plane of CuS ([00 l] direction). This observation implies that the hexagonal CuS crystal possesses a single-crystalline nature and a well-ordered in-plane orientation, which is in agreement with the XRD findings. However, the pole figure (PF) corresponding to the (0001) projection plane [Fig. 1(f)] reveals an impaired [0001] out-of-plane orientation. This finding suggests the existence of defects or lattice distortions within the CuS crystal structure, which may influence its properties.^22,30

Raman spectroscopy with a 532 nm excitation laser was used to investigate the intrinsic properties and identify the fingerprint of the CuS crystal structure. As shown in Fig. 2(a), the Raman spectrum of the CuS crystal shows four distinct Raman peaks at 90.1, 130, 279, and 471 cm⁻¹, representing E_2g, A₁, $Eg1$⁠, and A₁ modes, respectively. Among these peaks, the strong characteristic peak at 471.0 cm⁻¹ can be attributed to the stretching mode of the S–S bond, corresponding to the S₂ groups of the recognized crystal structure of CuS lattice. The spatially resolved Raman mapping images [Fig. 2(b)] of the four characteristic peaks (60, 138, 267, and 471 cm⁻¹) exhibit uniformity throughout the crystalline sheet of CuS. Temperature-dependent Raman spectroscopy is employed to study the atomic bonding and thermal expansion of the crystals.^31, Figure 2(c) shows the typical temperature-dependent Raman spectra for the grown CuS crystal at temperatures ranging from 80 to 300 K. Temperature-dependent Raman spectroscopy of CuS crystal provides valuable information about its thermal behavior as vibrational modes in its lattice structure. The relationship between temperature and CuS Raman modes can be expressed through a linear equation: ω(T) = ω₀ + χT, where ω₀, T, and χ are the Raman peak position at 0 K, the Kelvin temperature, and the first-order temperature coefficient, respectively. Raman modes at 60, 138, 267, and 471 cm⁻¹ labeled P1, P2, P3, and P4 each exhibit temperature coefficients (χ-values) that fall within the following parameters: −0.006 62, −0.026 77, −0.025 673, and −0.025 35 cm⁻¹ K⁻¹ respectively. Negative χ-values indicate that Raman mode frequencies decrease with an increase in temperature, suggesting an anharmonic behavior of lattice vibrations. The P1 mode exhibits relatively lower anharmonic behavior than other modes, suggesting that temperature variations may affect it less significantly as P2, P3, and P4 modes showed larger negative χ values, suggesting stronger anharmonic behavior [Fig. 2(d)]. This evidence suggests that these modes are susceptible to temperature variations and that thermal expansion or changes in bonding strength in response to temperature changes may have an impact.^32,33 In addition, previous studies have shown that the dominant temperature coefficient of low-dimensional materials is linked to the van der Waals interaction between layers, and this is often used to explain why the Raman peak shifting changes with temperature.^34–36 The χ-values mentioned above offer valuable information regarding the thermal characteristics of CuS, which could facilitate comprehension of its properties and potential utilization in devices that are sensitive to temperature.

High-resolution transmission electron microscopy (HR-TEM), selected-area electron diffraction (SAED), and energy-dispersive x-ray spectroscopy (EDX) were utilized to investigate the structure and composition of the CuS crystals. Figure 3(a) shows the HR-TEM image, processed with fast Fourier transform (FFT) filtering, to provide a clear view of the atomic arrangement in the CuS lattice. The hexagonal lattice structure is evident, with an interplanar spacing of 0.35 nm measured between the intersecting (100) and (010) crystallographic planes at 120°. These observations confirm the material’s hexagonal structure, consistent with the covellite CuS phase. SAED analysis [Fig. 3(b)] further supports this finding, revealing a sixfold symmetric diffraction pattern along the [001] zone axis. In addition, secondary diffraction spots of lower intensity (highlighted in red) suggest the presence of stacking faults or domain misorientations within the lattice. Such phenomena have been widely reported to exist in various low-dimensional materials.^37–40 Complementary to the structural analyses, EDS measurements [Fig. 3(c)] confirmed the elemental composition of the crystals, revealing an atomic ratio of 52% Cu and 48% S. This slight deviation from the ideal CuS stoichiometry is attributed to the use of a copper-based TEM grid during analysis. Moreover, elemental mapping [Fig. 3(d)] showed a uniform distribution of Cu and S atoms across the crystal, confirming the overall stoichiometric integrity of the material. To further analyze surface composition, x-ray photoelectron spectroscopy (XPS) was performed. As shown in Fig. 3(e), the Cu 2p peaks were deconvoluted into two overlapping doublets using Gaussian fitting. The primary doublet, with binding energies at 931.9 eV (Cu 2p_3/2) and 951.6 eV (Cu 2p_1/2), corresponds to Cu²⁺ oxidation states, while a secondary doublet at 933.4 and 953.6 eV indicates Cu¹⁺ states, suggesting non-stoichiometric contributions or defect-related features.^41,42 The S 2p spectrum [Fig. 3(f)] shows peaks at 164.5 and 166.5 eV, corresponding to S 2p_3/2 and S 2p_1/2, consistent with covellite CuS crystals.

Building on our structural characterization, we will now focus on the second harmonic generation (SHG) response of CuS crystals. SHG serves as a reliable method for investigating crystal symmetry and exhibits heightened sensitivity to alterations in a material’s electronic and structural characteristics.^43–46 In centrosymmetric materials such as CuS, SHG is typically prohibited under the electric-dipole approximation due to the inherent symmetry of the lattice. However, our findings suggest that structural imperfections, such as stacking faults and dislocations, may disrupt the centrosymmetry of the CuS lattice. These defects can lead to the formation of multi-oriented domains within the crystal, enabling the generation of an SHG signal.^47,48 Our EBSD, SAED, and XPS analyses provide strong evidence of structural defects within the CuS lattice. SAED patterns, for instance, reveal streaks and secondary diffraction spots, indicative of stacking faults and minor domain misorientations. XPS analysis also suggests subtle variations in bonding environments, likely linked to non-stoichiometric contributions, reinforcing the conclusion that the CuS crystals contain intrinsic lattice defects; given this context, we explored the SHG response of CuS crystals. The SHG mechanism in CuS crystals is shown in Fig. 4(a), where an incident laser with a frequency of ω produces a nonlinear optical response at 2ω. The SHG response of the as-synthesized CuS crystal was measured under various incident laser wavelengths, spanning from visible to near-infrared light (760–1020 nm), as shown in Fig. 4(b). These results reveal a broad spectral response with distinct wavelength selectivity, indicative of the material’s nonlinear optical behavior. Interestingly, SHG intensity map [Fig. 4(b) inset] reveals step-like multi-domain features across the CuS lattice. These domains are likely associated with structural imperfections, such as stacking faults and localized strain, which naturally arise during the CVD growth process due to rapid crystal growth, substrate-induced strain, and local vapor supply variations []. These structural features are believed to break the intrinsic centrosymmetry of the CuS lattice, which would otherwise suppress SHG under the electric-dipole approximation. The presence of such defects creates localized regions with broken symmetry, thereby enabling the observed SHG response. Despite these domains, the SHG signal is remarkably consistent across the crystal lattice, underscoring the robustness of the nonlinear optical behavior. To further explore the SHG properties, the evolution of SHG intensity with incident laser power was systematically investigated. Under 800 nm laser excitation, the SHG signal at 400 nm showed a significant and consistent enhancement as the incident power increased from 0.7 to 1.6 mW [Fig. 4(c)]. The relationship between SHG intensity and laser power follows a quadratic dependence, as evidenced by the linear fit in the log–log plot [Fig. 4(d)]. The slope of 2.049 closely matches the theoretical value of 2 predicted by electric dipole theory, confirming that the nonlinear optical mechanism in CuS crystals is dominated by dipole contributions.⁴⁹ 

Before assessing polarization, we rotated the sample to a position where the highest SHG response could be generated by setting the initial azimuthal angle to 0°. In parallel (XX) and perpendicular (XY) directions, the typical sixfold symmetry pattern fitted proportionally with sin² 3θ and cos² 3θ can be detected, as shown in Figs. 4(e) and 4(f). A similar set of SHG studies was conducted on a different CuS crystal exhibiting different morphology, which demonstrated a commensurate SHG response, as shown in Fig. S3. It implied broken inversion symmetry that is characteristic of hexagonal-symmetric structures similar to other SHG sensitive materials. Due to this unique quality, CuS crystal possesses several intriguing features with considerable application potential in the field of nonlinear optics. Thus, CuS crystal’s promise in nonlinear optics increases the variety of materials available for these applications and presents new avenues for investigation into improving its performance and uncovering unanticipated capabilities.

To summarize, we successfully synthesized CuS crystals using a single-step CVD technique, achieving thicknesses as low as 14 nm and lateral dimensions up to 60 μm, showcasing the scalability and precision of the growth process. The temperature-dependent Raman measurements provided detailed insights into the vibrational properties of CuS, reflecting its structural dynamics. A particularly intriguing outcome of this study was the observation of an unexpected SHG response, which we attribute to intrinsic lattice defects, such as stacking faults and multi-domains. These structural imperfections break the centrosymmetry of the CuS lattice, enabling nonlinear optical behavior. Polarization-dependent SHG measurements further validated this symmetry-breaking mechanism, which is consistent with the hexagonal crystal structure of CuS. These findings underline the dual role of structural imperfections in CuS crystals—not only as lattice disruptions but also as enablers of nonlinear optical phenomena. The demonstrated SHG response expands the scope of CuS beyond its established applications in catalysis and electronics, positioning it as a promising material for nonlinear optics and photonics. This work opens new avenues for exploring the optical properties of CuS and tailoring its performance for advanced technological applications.

CuS crystals were grown in a tubular furnace with a single temperature zone and atmospheric pressure CVD conditions. A quartz boat containing CuCl powder (97%, Sigma-Aldrich) was placed in the middle of the temperature zone. S powder (99.5%, Sigma-Aldrich) was inserted at the upstream end of the tube, and the temperature was maintained at 200. Substrates, e.g., cleaved fluorphlogopite mica, were positioned 8 cm apart from the furnace’s center in the downstream position. The tube was pumped and cleaned with 500 SCCM Ar flow to drain air prior to heating. Then, the furnace was heated to 600 °C at a rate of 30 °C/min using steady 50 SCCM Ar as the carrier gas, and it was held at that temperature for 30 min.. After the procedure was concluded, the furnace was allowed to cool naturally.

CuS crystal morphologies were examined using an OM (BX51, OLYMPUS) and an AFM (Bruker Dimension Icon). The crystalline structure, orientation, and composition were investigated using XRD (λ: 1.54 Å, D2 phaser, Bruker), XPS (AXIS-ULTRA DLD-600W, Kratos), EBSD (FEI Quanta650), and TEM (Tecnai G30 F30, FEI). Raman spectra were acquired using a confocal Raman system (Alpha 300R, WITec) equipped with a 532 nm laser.

SHG measurements were performed in a Raman system (alpha300RS+, WITec) with a reflection mode under normal incidence excitation using a femtosecond laser as the excitation source. A mode-locked Ti:sapphire laser with a pulse duration of 140 fs and repetition rate of 80 MHZ generated the output laser with a continually varying wavelength ranging from 340 to 1600 nm, which was then filtered into an optical parametric oscillator (Chameleon Compact OPO-Vis). A dichroic beam splitter was used to reflect the laser beam into the 100× objective lens with a spot size of roughly 1.8 µm and communicate the reflected SHG signal. The reflected SHG signal was then filtered with a short pass (SP) filter before being sent to the spectrometer and CCD. The collected polarized SHG signal was sent through a linear polarized analyzer for SHG polarization measurement by rotating the sample with a step of 10° relative to fixed light polarization. All the experiments were carried out in a natural setting.

Refer to the supplementary material for additional details. Figure S1 shows the schematic of the CVD setup, the growth profile of CuS crystals, and structural diagrams depicting the side and top views of the CuS crystal. Figure S2 shows optical and AFM images of CuS crystals grown on different substrates, along with their corresponding Raman spectra. Figure S3 shows SHG mapping under 800 nm laser excitation, SHG spectra at different incident powers, and polarization angle-dependent SHG intensity measurements.

The authors acknowledge funding from the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant No. 120N885.

The authors have no conflicts to disclose.

Abdulsalam Aji Suleiman: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Reza Rahighi: Data curation (supporting); Formal analysis (supporting); Writing – review & editing (supporting). Amir Parsi: Data curation (supporting); Formal analysis (supporting); Writing – review & editing (supporting). Talip Serkan Kasirga: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

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