Introduction

The non-stoichiometry of n-type ZnO semiconductors primarily arises from oxygen vacancies (Ov), which introduce donor states just below the conduction band (CB) 1,2. Similarly, p-type SnO can be oxidized into higher-order oxides such as Sn₂O₃ and SnO₂ due to the compensation of native defects, oxygen vacancies and Sn interstitials by free electrons 3,4. Despite its poorer electrical performance compared to ZnO, SnO remains essential for applications requiring low power consumption, high operation frequency, and circuit reliability 5,6. However, individual transition-metal oxides (TMsO) often exhibit limitations that restrict their use in advanced electronics. To overcome these deficiencies, hybrid nanocomposites (NCs) composed of two or more TMsO can be engineered. These NCs leverage interfacial charge transfer between different oxides to fine-tune their electrical and physical properties 7,8,9,10.

ZnO and SnO nanosheets display versatile functional properties, making them promising candidates for communications systems, high-frequency antennas, Li-ion batteries, supercapacitors, and solar energy conversion devices 11,12,13,14. Integrating SnO into ZnO to form ZnSnO NCs enhances ZnO’s carrier mobility, although excess Sn content can lead to interstitial occupation and the formation of neutral defects 15. Notably, existing literature is predominantly focused on SnO₂-doped ZnO, with limited studies on SnO itself 16,17,18.

Cobalt ions (Co2⁺), with an ionic radius of 0.065 nm, are suitable dopants for replacing either Zn (0.074 nm) or Sn (0.093 nm), owing to their smaller ionic size 19,20,21. The incorporation of Co can also enhance surface charge through the formation of Co₃O₄ when Co2⁺ is oxidized to Co3⁺, or through electron transfer from O2⁻ to Co2⁺ or Co3⁺ 22,23,24. Similarly, Cu ions (0.073 nm) closely match the ionic radius of Zn and offer multiple oxidation states, Cu⁺, Cu2⁺, and Cu3⁺, enabling both p-type and n-type doping 25,26. Transitions from Cu2⁺ to Cu⁺ facilitate electron localization at surface defects in ZnO and SnO matrices 27. Thus, tailoring the composition of ZnSnO NCs with Co or Cu doping up to substitution levels of 0.50 creates a promising class of (ZnSn)₁₋ₓMₓO NCs (M = Co or Cu).

Lattice vibrations in solid-state materials, detectable via Fourier-transform infrared (FTIR) spectroscopy, are critical for applications including optical Kerr shutters (OKS), switching devices, and infrared detectors 28,29. FTIR analysis reveals insights into carrier concentration and defect-related spin vacancies, with characteristic absorption bands linked to TMs through interatomic vibrations, and the stretching/deformation of adsorbed H₂O 30. Mechanical properties such as Debye temperature, Poisson’s ratio, elastic modulus, hardness, and acoustic wave velocity can also be extracted 31,32.

The presence of multiple valence states in TMsO lattices suggests a polar-ionic conduction mechanism facilitated by electron hopping and defect interactions 33,34. This mechanism is characterized by complex dielectric constants (ε′ and ε″) across frequencies up to 20 GHz 8. NCs exhibiting high ε′ are beneficial for communication technologies, while those with lower ε′ are suited for nonlinear optical and high-frequency antenna applications 7,35.

According to Koop’s theory, solid NCs comprise highly conducting grains separated by less conductive grain boundaries, leading to frequency-dependent conduction behavior 36,37. Additionally, Jonscher’s power law supports a hopping conduction model with non-Debye relaxation, an important factor for solar cell efficiency 38. NCs with a dielectric constant on the order of 10⁶ and dielectric loss near 10 are promising for energy storage applications and efficient dielectric response 39,40. Quality (Qfactor) and fill (Ffactor) factors serve as metrics of performance in supercapacitors and solar cells, with Q-factors reaching up to 10,000 at 1 MHz 41,42.

Doping ZnO with transition metals alters its dielectric properties and ac conductivity through hopping mechanisms 43,44,45. Similarly, TM-doped SnO NPs show improved dielectric constant (ε), dielectric loss (tanδ), and ac conductivity (σₐc) 46,47. Cole–Cole plots confirm grain-boundary dominated conduction, whereas ZnO-doped SnO₂ NCs exhibit reduced ε and tanδ with increasing frequency and temperature 48,49.

Our previous studies explored the effects of Cu and Co doping on the structural, optical, and magnetic properties of ZnSnO NCs 50,51. Cu doping yielded a mixture of nanosheets and nanorods, while Co doping resulted in uniform nanocube morphology. Both dopants reduced the band gap and enhanced room temperature ferromagnetism. In this work, we extend our investigation to the mechanical and dielectric properties of ZnSnO NCs as influenced by Co and Cu concentrations. For comparative purposes, the properties of pure ZnO and SnO NSs are also assessed. To our knowledge, no comprehensive sequence-based study on these NCs has been reported.

Experimental details

Hydrothermal synthesis of (ZnSn)1-xMxO NCs

The synthesis and characterization of ZnO and SnO nanosheets, along with (ZnSn)1−xMxO NCs, where M = Co or Cu, using a facile hydrothermal process, were reported in our previous work. In that study, the influence of Co and Cu concentrations on the structural, optical, and magnetic properties of (ZnSn)1−xMxO NCs was examined in detail 50,51. In this experiment, (ZnSn)1−xMxO nanocomposites (NCs), where M = Co or Cu and x = 0.1–0.5, were synthesized via a hydrothermal method using ZnCl₂·6H₂O, SnCl₂·2H₂O, CuCl₂·6H₂O, and CoCl₂·6H₂O as precursors. The procedure involved: (a) dissolving 1 M NaOH in 20 mL of double-distilled water with magnetic stirring at room temperature for 30 min; (b) preparing 1 M metal salt solutions in 20 mL of double-distilled water according to stoichiometric ratios; (c) gradually adding NaOH to the metal solution under constant stirring to form hydroxide precipitates within 1 h; (d) transferring the precipitate to a Teflon-lined autoclave and heating at 140 °C for 12 h, followed by natural cooling to room temperature; (e) washing the resulting powder with ethanol and distilled water, then drying at 400 °C for 3 h.

Lattice vibration and dielectric properties characterization

FTIR spectra of the nanopowders were recorded in the 400–4000 cm⁻1 range at a scan rate of 2 cm∙s⁻1 using a Nicolet iS10 spectrometer. The experimental density (ρexp) of the nanocomposites (NCs) was measured via the water displacement method. Water density (ρw) was calculated using ρw = mw/Vw, where mw and Vw are the mass and volume of water, respectively. A 0.5 g sample (ms) was placed in a 5 mL flask filled with water. The displaced water mass was determined by mw = mt − ms, and its volume as Vw = mw/ρw. The sample volume (Vs) was estimated as Vs = 5 − Vw, and its density computed using ρs = ms/Vs. Dielectric behavior was analyzed at room temperature using a high-resolution Alpha analyzer and a Novo Control broadband dielectric converter within 100 mHz–20 MHz. The composite powders were finely ground, thoroughly mixed, and compressed into disc-shaped pellets with a diameter of 1 cm and a thickness of approximately 0.3 cm using a hydraulic pressure of 5 tons and positioned between gold-plated stainless-steel electrodes for measurement.

Results and discussion

FTIR analysis

Figure 1a shows FTIR spectra of ZnO, SnO nanosheets, ZnSnO NCs, and (ZnSn)1-xMxO NCs (M = Co or Cu) at different composition ratios. The FTIR spectrum of ZnO nanosheets exhibited several active vibrations at 455, 695, 1410, 1624, 2367, 2926, and 3440 cm-1. The observed bands at 455 and 695 cm-1 are induced by the stretching vibrations of Zn–O bonds in hexagonal ZnO structure 52,53. On the other hand, the characteristic vibrations induced by OH bending and stretching of adsorbed water molecules were detected at 1410 and 3440 cm-1, respectively 54. Other detected vibrations at 1624, 2367, and 2926 cm-1 could be ascribed induced by the vibration of various carbonyl groups induced by the adsorbed CO2 from surrounding 55. The FTIR spectrum of SnO nanosheets exhibited several bands at 482, 527, and 590 cm-1 that distinguish various stretching vibrations of the Sn–O bond 7,56,57. The FTIR spectrum of ZnSnO NCs exhibited multiple vibrations at 420, 530, 1620, 2926, and 3440 cm-1 that matched with detected modes in either ZnO or SnO nanosheets. Figure 1b exhibits FTIR spectra of Co-series NCs at varying Co content. It was observed that the characteristic vibrations of absorbed OH and CO2 on the surface of Co-series NCs were slightly affected by replacing (Zn-Sn) ions with Co. However, there was an observable change in the characteristic TM–O bonds vibration with changing Co or Cu-content. The fundamental stretching TM–O vibrations of Co-series NCs were detected at 575, 595, 605, 585, and 570 cm-1 corresponding to Co ratio (x) of 0.1, 0.2, 0.3, 0.4, and 0.5, respectively. Figure 1c exhibits FTIR spectra of Cu-series NCs at different Cu content, where the average TM–O stretching vibration at Cu content of 0.1, 0.2, 0.3, 0.4, and 0.5 was detected at 533, 533, 517, 515, 507 cm-1, respectively.

Fig. 1
figure 1

FTIR spectra of ZnO, SnO nanosheets, and ZnSnO NCs (a), (ZnSn)₁₋ₓCoₓO (b), and (ZnSn)₁₋ₓCuₓO NCs (c).

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Various mechanical parameters of the micro-crystalline lattice could be estimated from the Debye temperature (θD) of the main stretching lattice vibration mode according to the relation 58,59:

$${\uptheta }_{{\text{D}}} \left( {\text{K}} \right) = \frac{{{\text{hc}}\overline{{\Delta {\upnu }}} }}{{{\text{K}}_{{\text{B}}} }} = 1.44\overline{{\Delta {\upnu }}}$$
(1)

where \(\Delta {\overline{\nu }}\) refers to the average wavenumber (cm-1) of the TM–O stretching vibration band, h is Planck’s constant (6.625 × 10–27 erg∙s), c light speed (3 × 1010 cm∙s–1), and KB is Boltzmann constant (1.38 × 10–16 erg∙K–1). Several mechanical parameters were also determined, such as force constant (Kt), NCs porosity (PS), Poisson’s ratio (γ), and stiffness constants (S11, S12), according to the relations 2:

$${\text{K}}_{{\text{t}}} = 0.0076{\text{W}}^{2} \overline{{\Delta {\upupsilon }}}$$
(2)
$${P}_{s}= \left(1-\frac{{\rho }_{exp}}{{\rho }_{th}}\right)$$
(3)
$$\gamma =0.324 (1-1.043{P}_{s})$$
(4)

where W is the molecular weight, ρexp and ρth refer to the average densities based on experimental technique and XRD theoretical value. It is known that γ value could demonstrate the mechanical deformation behavior of materials, where materials with γ values < 0.26 exhibit ductile elastic deformation like metals. Whereas materials with γ > 0.26 are brittle and exhibit plastic deformation such as ceramic-based materials. According to Table 1, ZnO and SnO nanosheets, ZnSnO NCs, and NCs of Co and Cu-series exhibited brittle mechanical deformation behavior since all estimated γ > 0.26. Other mechanical parameters were estimated using the Kt and γ values including Young modulus (Y), shear modulus (G), bulk modulus (β), and hardness (H) are determined by the following relations 60:

Table 1 Mechanical and elastic wave propagation properties of ZnO, SnO nanosheets, ZnSnO NCs, and (ZnS)1-xMxO NCs (M = Co or Cu) at varying composition ratios.
Full size table
$${S}_{11}=\frac{{K}_{t}}{a}; {S}_{12}= \frac{{S}_{11}\gamma }{1-\gamma }$$
(5)
$$\text{Y}= \frac{\left({\text{S}}_{11}-{\text{S}}_{22})({\text{S}}_{11}+{2\text{S}}_{12}\right)}{\left({\text{S}}_{11}+{\text{S}}_{12}\right)};\text{G}= \frac{\text{Y}}{2(\upgamma +1)};\upbeta = \frac{{\text{S}}_{11}+{2\text{S}}_{12}}{3}$$
(6)
$$H= \frac{Y\left(1-2\gamma \right)}{6(1+\gamma )}$$
(7)

According to the estimated values in Table 1, SnO nanosheets are stiffer than ZnO nanosheets because ZnO have a lower Y value. This behavior demonstrates the Y-value increase of ZnSnO NCs relative to ZnO nanosheets. It can be observed that the incorporation of other TMs ions (i.e., Co or Cu) in the internal lattice of ZnSnO NCs induced a slight variation of Y-values and the associated elastic mechanical parameters with changing composition ratios up to 0.30. A further increase in external TMs was associated with an observable reduction in Y-value. This behavior indicated that the incorporation of either Co or Cu ions enhanced the flexibility of ZnSnO NCs lattice. Moreover, the variation of NCs of Co and Cu series mechanical properties is more sensitive to the concentration than the TMs type. By knowing the material’s mechanical properties, some of the lattice vibration dynamics parameters such as propagation velocity of longitudinal wave, shear wave, and the corresponding mean velocities according to the following relations 61:

$${\nu }_{L}= \sqrt{\left(\frac{{S}_{11}}{{\rho }_{th}}\right)};{\nu }_{s}= \sqrt{\left(\frac{G}{{\rho }_{th}}\right);}\frac{1}{{\nu }_{m}^{3}}=\frac{1}{{\nu }_{L}^{3}}+\frac{1}{2{\nu }_{s}^{3}}$$
(8)

Due to the variation in material stiffness, SnO nanosheets exhibited a higher proportion velocity than ZnO nanosheets and ZnSnO NCs. Besides, incorporating either Co or Cu ions in ZnSnO NCs induced inhabitation in elastic wave propagation velocity, where the reduction in elastic wave propagation was affected by the concentration of transition metal type.

Dielectric analysis

The real and imaginary dielectric constants (ε′, ε″) of materials are used to reveal the ability of the dielectric medium to store electrical energy, which can be expressed mathematically by the quality factor (Qfactor). On the other hand, the dielectric loss tangent (tan δ) refers to the thermal dissipation of stored electrical energy within dielectric medium. The tan δ and Qfactor could be estimated from the frequency-dependent behavior of ε′ and ε″ according to the following relations 62,63.

$$tan\delta =\frac{{\varepsilon }^{^{\prime\prime} }}{{\varepsilon }{\prime}}; {Q}_{factor}= \frac{1}{tan\delta }$$
(9)

Figure 2a, b reveals the frequency-dependent variation of ε′ and ε″ of ZnO and SnO nanosheets, and their hybrid ZnSnO NCs. In general, it can be observed that both ε′ and ε″ have high values in the low-frequency region, followed by a gradual decrease with increasing applied signal frequency. This behavior could be attributed to the enhancement of surface polarization in the low-frequency region due to charge trapping at the interfacial grain boundaries. With increasing the applied signal frequency, the provided energy induces higher oscillation of trapped charges and facilitates interfacial charge transfers. This behavior is associated with the inhibition of charge polarization at high-frequency regions 64,65. Ternary ZnSnO NCs exhibited higher ε′ and ε″ than nanosheets ZnO and SnO nanosheets, indicating the improvement of surface polarization in the heterostructure NCs compared with the corresponding pure binary phases. The material dielectric properties are mainly determined by the space charge polarization, which is directly related to the migration of mobile charge through hopping between nearby localized state defects 66. ZnO and SnO nanosheets have different crystal structures; hence, the formation of heterostructure ZnSnO NCs is expected to contain abundant surface defect states at grain boundary interfaces. These defect states alter the distribution of trapping centers, promoting charge displacement and enhancing surface polarizability and dielectric constant under applied field 67,68.

Fig. 2
figure 2

ε′ and ε″ vs frequency of ZnO, SnO nanosheets, and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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Figure 2c, d exhibits the frequency-dependent variation of ε′ and ε″ of (ZnSn)1-xCoxO NCs at varying Co content (x), where a slight reduction in ε′ and ε″ of ZnSnO NCs was observed in the low-frequency region with changing x up to 0.40, whereas a strong decrease was observed at a higher x of 0.5. This revealed that incorporating Co-ions in ZnSnO NCs occurred by replacing Zn or Sn ions in bulk lattice sites, which did not strongly affect the dynamics of interfacial defect states. At x = 0.50, Co ions introduced localized defect states as pinning centers, which hindered surface charge migration, reduced surface polarizability, and lowered the dielectric constant compared to ZnSnO NCs.

On the other hand, the variation of ε′ and ε″ with the applied frequency is more sensitive to the composition in the case of ZnSnO NCs doping with Cu shown in Fig. 2e, f. Incorporating Cu into ZnSnO NCs at low concentrations (≤ 0.20) significantly reduced ε′ and ε″. A further increase in Cu content had a milder effect. This indicates that Cu ions are more strongly altered interfacial defect states and surface polarizability than Co ions, with low Cu levels having a greater impact than higher levels.

Figure 3a, b presents the frequency-dependent tan δ and Q-factor plots for ZnO nanosheets, SnO nanosheets, and ZnSnO NCs. ZnSnO NCs exhibit significantly higher energy loss across the entire frequency range, indicating enhanced conductivity and interfacial charge transport due to reduced intermolecular forces. This reduction facilitates changes in dipole orientations and induces polarizability variations under varying electric fields. 69. Additionally, SnO nanosheets show a pronounced increase in Q-factors throughout the radio frequency range (20 kHz–20 MHz), suggesting strong electromagnetic absorption compared to ZnO nanosheets and ZnSnO NCs, which exhibit minimal absorption across the same range. Figure 3c, d shows the frequency-dependent tan δ and Q-factor plots for (ZnSn)₁₋ₓCoₓO NCs. Peaks in the tan δ plots, observed with increasing Co content up to x = 0.30, indicate resonance between the applied electric field and the orientational polarization response at specific frequencies. The tan δ value of (ZnSn)₁₋ₓCoₓO NCs decreased below 10 Hz as x increased from 0.1 to 0.4, followed by a recovery at x = 0.5. Overall, Co-doped NCs exhibited lower tan δ than ZnSnO NCs, suggesting suppressed conductivity. This behavior implies that Co ion incorporation strengthens internal molecular forces and reduces thermal energy dissipation from the applied electric field. Meanwhile, the Q-factor appears less sensitive to Co-ion doping concentrations, indicating a more stable energy storage response across the composition range, as shown in Fig. 3d. Figure 3e, f shows tan δ and Q-factor plots for Cu-doped ZnSnO NCs. Cu incorporation significantly reduced tan δ, suggesting stronger intermolecular forces, lower conductivity, and decreased thermal dissipation. At low Cu content (x = 0.10), the Q-factor rose sharply in the radio frequency range but declined with higher concentrations.

Fig. 3
figure 3

tan δ and Q-factor vs frequency plots of ZnO, SnO and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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Figure 4a, b reveals plots of real impedance (Z′) and imaginary impedance (Z′′) of ZnO and SnO nanosheets, as well as ZnSnO NCs. ZnO and SnO nanosheets exhibited similar impedance characteristics, where very high Z′ and Z′′ values were observed below 100 Hz followed by a gradual decrease at higher frequencies. ZnSnO NCs showed a significant reduction in Z′ and Z′′ values compared to ZnO and SnO nanosheets. Additionally, the Z′ value of ZnSnO NCs was saturated over a long frequency range extended up to 1 MHz, followed by a gradual decrease at higher frequencies. Conversely, Z′′ was slowly increased with an increase in signal frequency up to 1 MHz, followed by a gradual decrease at higher frequencies. The peak frequency of Z′′ is commonly used to identify the relaxation dynamics within dielectric materials, where the relaxation time (τ) can be estimated according to the following relation 70:

Fig. 4
figure 4

Plots of Z′ and Z″ vs frequency of ZnO, SnO and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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$$\tau =\frac{1}{2\pi {f}_{max}}$$
(10)

The estimated τ of ZnO and SnO nanosheets, ZnSnO NCs, and (ZnSn)1-xMxO NCs (M = Co or Cu) was recorded in Table 2.

Table 2 τ, Z′ (g), Z′ (gb), Rb, Ceff, s, Wm, and αe parameters of ZnO and SnO nanosheets, ZnSnO NCs, and (ZnSn)1-xMxO NCs (M = Co or Cu).
Full size table

It can be observed that ZnSnO NCs have a lower relaxation time than ZnO or SnO nanosheets, demonstrating that ZnSnO NCs have faster relaxation dynamics due to the improvement of interfacial polarization conductivity 71,72. Figure 4c, d exhibits Z′ and Z′′ plots of (ZnSn)1-xCoxO NCs at varying Co content, where incorporating Co ions increased Z′ and Z′′ values compared to ZnSnO NCs and shifted the saturation frequency to the lower frequency side. The increase of Co content induced a further increase in Z′ and Z′′ and shifted the saturation frequency to a higher frequency side compared with low Co content. Co-series NCs exhibited higher τ compared with ZnSnO NCs as illustrated in Table 2 Incorporation of Co ions was found to slow the dielectric relaxation of ZnSnO NCs, with higher Co content leading to more pronounced relaxation delays. In contrast, (ZnSn)₁₋ₓCuₓO NCs exhibited a marked increase in Z′ and Z′′ at Cu concentrations of 0.10 and 0.20, followed by a decline at higher levels, as shown in Fig. 4e, f. Additionally, Cu-series NCs displayed a saturation frequency shift toward lower frequencies at Cu content below 0.20, then gradually shifted to higher frequencies with further Cu incorporation, opposite to the trend observed in (ZnSn)₁₋ₓCoₓO NCs. Similarly, the incorporation of Cu ions also contributed to slower dielectric relaxation, akin to Co ions. However, in contrast to the Co-series, ZnSnO NCs with lower Cu content exhibited slower relaxation dynamics compared to those with higher Cu levels. This contrasting behavior highlights a strong dependence of the relaxation characteristics on both the type and concentration of transition metal dopant ions in ZnSnO NCs.

Figure 5 shows the Cole–Cole plots of ZnO and SnO nanosheets, ZnSnO NCs, and (ZnSn)₁₋ₓMₓO (M = Co or Cu) NCs at varying M content. ZnO and SnO nanosheets revealed that a single semicircle represented the bulk impedance of individual grains, as illustrated in Fig. 5a. On the other hand, ZnSnO NCs exhibited smaller bulk impedance compared with ZnO and SnO nanosheets, as well as another impedance component representing the interfacial grain boundary, as illustrated in Fig. 5b. High Co concentration in doped ZnSnO NCs led to a significant increase in impedance, whereas low Cu content induced higher impedance than high Cu content, as shown in Fig. 5c, d. The real impedance components of bulk grains (Z′(g)) and grain boundaries (Z′(gb)) were extracted from the Cole–Cole plots and summarized in Table 2. Additional parameters, including bulk resistance (RB) and effective capacitance (Ceff) were derived from the frequency-dependent behavior of real impedance (Z′(ω)) according to the following relation 73

Fig. 5
figure 5

| Z″| vs Z′ plots of ZnO, SnO and ZnSnO NCs (a), (ZnSn)₁₋ₓCoₓO NCs (b), and (ZnSn)₁₋ₓCuₓO NCs NCs (c).

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$${Z}{\prime}(\omega )=\frac{{R}_{B}}{1+(\omega {C}_{eff}{R}_{B}{)}^{2}}\to \frac{1}{{Z}{\prime}}=\frac{1}{{R}_{B}}+{\omega }^{2}{C}_{eff}^{2}{R}_{B}$$
(11)

ZnSnO NCs exhibited a pronounced reduction in RB compared to ZnO and SnO nanosheets (Table 2). Co-doping at low concentrations (< 0.20) increased RB relative to pure ZnSnO NCs, but higher Co content led to a decrease. In contrast, Cu-doped ZnSnO NCs showed RB values higher than undoped ZnSnO but lower than Co-doped variants. These trends suggest that Co and Cu ions introduce localized structural defects that hinder charge transport and elevate bulk impedance. Notably, ZnSnO NCs displayed a substantial increase in Ceff to 0.491 µF and a low RB of 1300 kΩ, attributed to enhanced surface polarization and hopping conductivity. Both Co and Cu doping restricted interfacial charge movement, resulting in lower Ceff than in undoped ZnSnO, as shown in Table 2. For energy storage applications, Li-ion batteries require a small RB and low Ceff, while supercapacitors favor low RB and high Ceff 74. Accordingly, pure ZnSnO and NCs doped with 0.40 Co or Cu are suited for supercapacitors, whereas NCs with 0.10 Cu are better candidates for Li-ion batteries.

The impact of Co and Cu ions incorporation on the polarization conduction mechanism of ZnSnO NCs at room temperature (RT) was investigated across the applied frequency range. The total conductivity (σ) of the material arises from the frequency-independent DC conductivity (σDC) and the AC conductivity (σAC), which varies with the frequency of the applied electric field according to the relations 74,75:

$$\sigma_{t} (\omega ) = \sigma_{dc} + \sigma_{ac} = \sigma_{dc} + B\omega^{s}$$
(12)

where B, ω, and s represent proportionality constant, angular frequency, and exponent factor, respectively. The contribution of σAC in the total conductivity sharply increases with increasing frequency due to the strong improvement of charge carrier mobility 76. The hopping mechanism of charge transfer between interfacial defect states could be identified through the s-value, where the hopping mechanism is mainly caused by holes when 0 < s < 0.50, whereas electron conduction is dominant when 0.50 < s ≤ 1.00 77. Figure 6a, b illustrate the variation in σAC as a function of frequency, and lnσAC vs lnω plots for ZnO and SnO nanosheets as well as ZnSnO NCs. It was observed that the σAC gradually increases progressively with rising applied frequency, a characteristic behavior common to all the studied nanomaterials, indicating enhanced charge hopping mobility in the high-frequency region 78. Besides, ZnSnO NCs exhibited better σ than ZnO or SnO nanosheets because of the development of various interfacial structural defects like vacancies and interstitials in heterostructure NCs. These defect states act as localized trapping centers that facilitate charge transportation by hopping through reducing interfacial depletion width. ZnSnO NCs showed higher σ than ZnO and SnO nanosheets, due to interfacial structural defects, such as vacancies and interstitials within the heterostructured NCs. These defects act as trapping centers, enhancing charge hopping by reducing the interfacial depletion width 79. As listed in Table 2, ZnO and SnO nanosheets exhibited s-values greater than 0.5, indicating that polaron hopping occurred through bound electrons interacting with interfacial localized defect states 80. In contrast, polaron hopping in heterostructured ZnSnO nanocrystals (NCs) was hole-dominated, reflected by s-values below 0.5.

Fig. 6
figure 6

σAC and lnσAC vs frequency plots of ZnO and SnO nanosheets and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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Figure 6c, d illustrates the plots of σAC vs frequency and ln(σAC) vs ln(ω) for Co-doped ZnSnO NCs, where Co incorporation led to a reduction in σAC across the entire frequency range. This behavior was associated with the evolution of s-values, which remained below 0.5, confirming that Co doping did not alter the hole-based polaron hopping mechanism in ZnSnO NCs. Figure 6e, f presents similar plots for Cu-doped ZnSnO NCs, which demonstrate a charge transport mechanism highly sensitive to Cu concentration. As shown in Table 2, s-values increased significantly with Cu content up to x = 0.20, suggesting a shift toward electron-dominated hopping, but decreased again at higher doping levels. Accordingly, the hopping mechanism in (ZnSn)₁₋ₓCuₓO NCs at x = 0.20 and 0.30 was primarily electron-driven, unlike samples at other Cu ratios. Additional parameters describing the hopping conduction mechanism were evaluated using the correlated barrier hopping (CBH) model. These parameters include the polaron binding energy (Wₘ), average hopping distance (Rₕ), figure of merit (Fₘ), and the density of interfacial localized defect states (ND). Their estimation was carried out based on the following mathematical relations 70,81:

$${W}_{m}= \frac{6{K}_{B}T}{1-s};{{R}_{h}= \frac{{e}^{2}}{\pi {\varepsilon }_{o}{\varepsilon }{\prime}W}}_{m}$$
(13)
$${N}_{D}=\frac{24\sigma }{{\pi }^{3}{\varepsilon }_{\circ }{\varepsilon }{\prime}\omega {R}_{h}^{6}};{F}_{m}=\frac{\sigma }{{\varepsilon }{\prime}}$$
(14)

The estimated Wₘ values for ZnO and SnO nanosheets, ZnSnO NCs, and (ZnSn)1-xMxO NCs, as listed in Table 2, were lower than their respective optical band gaps, as reported in our previous studies 50,51. This observation confirms that charge transport in Co- and Cu-doped ZnSnO NCs occurs predominantly via a single polaron hopping mechanism 82. Moreover, the Wₘ values for Co- and Cu-doped series were higher than those of undoped ZnSnO NCs, indicating that Co and Cu ion incorporation enhances the interaction between interfacial defect states and excited charge carriers.

Figure 7a illustrates the frequency-dependent Rₕ plots for ZnO and SnO nanosheets, and ZnSnO nanocrystals (NCs). SnO nanosheets exhibited a steady increase in Rₕ in the low-frequency region (< 1 kHz). Afterwards, Rₕ became almost saturated and less influenced by the applied signal frequency. In contrast, ZnO nanosheets showed a gradual increase in Rₕ across all frequencies, with values consistently lower than those of SnO nanosheets. An interesting observation was that ZnSnO NCs displayed frequency-independent Rₕ behavior below 1 kHz, followed by a sharp increase at higher frequencies. In the high-frequency range, Rₕ was lower than that of both ZnO and SnO nanosheets. Figure 7b presents the frequency-dependent Rₕ plots for (ZnSn)₁₋ₓCoₓO NCs. Co incorporation between x = 0.20 and 0.40 led to a substantial increase in Rₕ compared to ZnSnO NCs, while minimal variation was observed at other Co concentrations. Figure 7c shows that introducing Cu at x = 0.10 in (ZnSn)₁₋ₓCuₓO NCs caused a significant increase in Rₕ relative to both ZnSnO and (ZnSn)₁₋ₓCoₓO NCs. Additionally, the Rₕ response shifted toward lower frequencies compared to ZnSnO NCs. At higher Cu concentrations, Rₕ decreased, suggesting that x = 0.10 represents a critical composition for optimizing Rₕ response to applied polarization frequency.

Fig. 7
figure 7

Plots of Rh vs frequency of ZnO and SnO nanosheets, and ZnSnO NCs (a), (ZnSn)₁₋ₓCoₓO NCs (b), and (ZnSn)₁₋ₓCuₓO NCs (c).

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Figure 8a, b illustrates the frequency-dependent behavior of Nᴅ and the corresponding F-factor for ZnO and SnO nanosheets, as well as ZnSnO NCs. The formation of heterostructure interfaces between ZnO and SnO grains in ZnSnO NCs significantly increased Nᴅ and the F-factor compared to either pure ZnO or SnO nanosheets. The variation of Nᴅ with frequency revealed a metastable distribution of interfacial defect states, evidenced by a gradual decline in Nᴅ with increasing sinusoidal frequency. Meanwhile, enhanced polarization conductivity due to charge hopping was reflected in the progressive rise of the F-factor as frequency increased. Figure 8c, d presents the Nᴅ and F-factor plots of Co-series NCs, showing no significant change with Co content up to 0.40. A slight decrease in both values is observed at 0.50 Co content. Figure 8e displays Nᴅ plots of Cu-series NCs, where a sharp drop in Nᴅ occurs at 0.10 Cu concentration compared to ZnSnO NCs, followed by gradual recovery at higher Cu levels. This indicates that low Cu content more strongly influences the distribution of localized defect states than higher concentrations, opposite to the trend seen with Co doping. The F-factor of Cu-series NCs in Fig. 8f also shows a slight decline at 0.10 Cu content, with negligible variation at higher levels.

Fig. 8
figure 8

ND and Ffactor vs frequency plots of ZnO, SnO and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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The electronic polarizability (αe) could be estimated from the saturated value of the real dielectric constant (ε′∞) at the high-frequency region based on the Clausius–Mossotti formula given below 83,84:

$${\alpha }_{e}=\frac{3{W}_{m}}{4\pi {N}_{A}\rho }\left(\frac{{\varepsilon }_{\infty }{\prime}-1}{{\varepsilon }_{\infty }{\prime}+2}\right)$$
(15)

where NA is Avogadro’s number.

ZnSnO NCs exhibited lower αe than pure ZnO and SnO nanosheets, as illustrated in Table 2. Besides, incorporating Co ions strongly enhanced αe of ZnSnO NCs in contrast to Cu ions that diminished αe. It was observed that the lowest doping content of Co or Cu (i.e., x = 0.10) produced the highest effect compared with other compositions.

The electrical relaxation mechanism in dielectric materials could be investigated through the frequency-dependent features of real (M′) and imaginary (M″) electrical modulus complexes, which offer detailed insights into the charge transport dynamics, as described by the following equations 85:

$${M}{\prime}=\frac{{\varepsilon }{\prime}}{\left({\left({\varepsilon }{\prime}\right)}^{2}+{\left({\varepsilon }^{{\prime}{\prime}}\right)}^{2}\right)}$$
(16)
$${M}^{{\prime}{\prime}}=\frac{{\varepsilon }^{{\prime}{\prime}}}{\left({\left({\varepsilon }{\prime}\right)}^{2}+{\left({\varepsilon }^{{\prime}{\prime}}\right)}^{2}\right)}$$
(17)

Figure 9a, b shows the frequency-dependent M′ and M″ plots of ZnO and SnO nanosheets, and ZnSnO NCs, where a strong reduction in M′ and M″ of ZnSnO NCs compared to pure nanosheets is observed. The M′ of ZnO and SnO nanosheets started to saturate from 100 Hz, whereas saturation started from 1 MHz in the case of ZnSnO NCs.

Fig. 9
figure 9

M′ and M″ vs frequency plots of ZnO and SnO nanosheets, and ZnSnO NCs (a, b), (ZnSn)₁₋ₓCoₓO NCs (c, d), and (ZnSn)₁₋ₓCuₓO NCs (e, f).

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The observed increase in M′ with rising frequency may be attributed to the conduction of charge carriers with short-range mobility, as well as the diminished restoring force opposing their motion under a steady electric field 86. On the other hand, the frequency-dependent plot of M″ in Fig. 9b shows that ZnO and SnO nanosheets share a low-frequency relaxation peak followed by semi-saturation at high frequencies, unlike ZnSnO NCs, which show a peak only in the high-frequency range. This behavior suggests that ZnO and SnO nanosheets possess long-range charge mobility, driven by interfacial polarization consistent with the Maxwell–Wagner–Sillars effect 87. In contrast, ZnSnO NCs demonstrate only short-range carrier mobility, likely governed by dipolar polarization at the metal oxide grain boundaries 88. Figure 9c, d demonstrate M′ and M″ plots of (ZnSn)1-xCoxO NCs, where the addition of Co ions enhanced M′ and M″ of ZnSnO NCs with changing starting frequency of saturation. M′ and M″ plots of Cu-series NCs in Fig. 9e, f showed several composition-dependent features compared to Co-series NCs. A strong improvement in M′ and M″ plots at low Cu content of 0.10 and 0.20, followed by a gradual reduction at higher Cu concentrations, overall, the frequency range. The M′ plots of Co-series NCs at x = 0.10 and 0.20 exhibited saturation starting at a low frequency of 5 kHz compared with ZnSnO NCs (1 M Hz). Besides, the starting frequency of saturation was shifted to higher frequencies with increasing Cu content. Based on the frequency-dependent M″ plots in Fig. 9d, f, both (ZnSn)₁₋ₓCoₓO and (ZnSn)₁₋ₓCuₓO nanocomposites exhibit short-range carrier mobility in the high-frequency region, similar to ZnSnO NCs. However, the relaxation peak for (ZnSn)₁₋ₓCuₓO NCs appears at a lower frequency compared to both ZnSnO and (ZnSn)₁₋ₓCoₓO NCs. This shift suggests that Cu doping enhances the charge transport dynamics by extending the mobility range, likely due to improved dipolar polarization and reduced interfacial barriers.

Doping ZnSnO nanocrystals (NCs) with Co or Cu ions significantly alters their properties, primarily due to changes in their internal structure, including crystallite and particle sizes, and the formation of specific interfacial grain boundaries; both dopants induce only slight changes in mechanical and elastic wave propagation properties, reduce ϵ and σAC​, and decrease Ceff​, while generally increasing Rh​; however, Co enhances αe in contrast to Cu ions which enhance M, Co exhibits lower tan δ without affecting the Q factor whereas Cu strongly decreases tan δ with a strong Q factor, Co leads to hole conduction while Cu exhibits polaron or hole conduction relative to its content, and Co induces a strong Z in contrast to Cu whose low content induces higher Z; additionally, increasing Co to 0.50 increases ND​ and F-factor, while 0.10 Cu content causes a slight decrease. While the crystallite size of ZnSnO NCs is 12.6 nm (between 20.70 nm for SnO and 7.70 nm for ZnO nanosheets), increasing Co up to 0.50 results in slight variations in crystallite size (e.g., 13, 13.2, 9, and 11.56 nm), whereas the Cu series shows a decrease (e.g., 18.45, 14.60, 12.40, 12.10, and 10.50 nm), demonstrating that both Co and Cu inhibit grain growth and induce distinct interfacial grain boundaries, with Co causing a more significant decrease in particle size than Cu at the same molar ratio, and further increasing Co or Cu leads to phase separation, recognizing cubic Co3O4, cubic Cu2O and monoclinic CuO phases were recognized as reported in our previous work 50,51. These internal structures played a significant role in dictating the variation in the physical properties of (ZnSn)1-xMxO NCs, with the specific incorporated metal (Co or Cu) determining the outcome. Consequently, some of these (ZnSn)1-xMxO NCs exhibited better dielectric characteristics compared to ZnO or SnO nanosheets, making them highly suitable for energy-related applications.

Conclusions

The composition-dependent mechanical and dielectric properties of hydrothermally synthesized quaternary (ZnSn)₁₋ₓMₓO NCs, where M = Co or Cu, were investigated at room temperature across varying dopant concentrations. SnO nanosheets exhibited higher mechanical coefficients than ZnO nanosheets, indicating superior stiffness, which correlates with decreased elastic wave propagation velocities. Meanwhile, ZnSnO NCs demonstrated intermediate mechanical coefficients and elastic wave velocities relative to those of ZnO and SnO nanosheets, suggesting effective hybridization between Zn and Sn cations within the ternary structure. ZnSnO NCs exhibited higher AC conductivity and dielectric constants compared to ZnO and SnO nanosheets, although Co and Cu doping reduced these properties due to increased defect states. Co lowered tan δ without affecting the Qfactor, while Cu improved both tan δ and the Qfactor significantly. The conduction mechanism shifted from polaron-based in ZnO and SnO to hole-dominated in ZnSnO and Co-doped variants, with Cu-doped NCs showing mixed conduction behavior. ZnSnO NCs had reduced impedance and polarizability, though high Co content reversed this trend; Cu maintained low values. Effective capacitance was enhanced in ZnSnO NCs but declined with doping, while the electric modulus decreased further upon Co or Cu incorporation. These changes, driven by structural differences and doping effects, highlight the promise of ZnSn-based NCs for energy storage applications.