B-Doped ZnO Nanoparticles: Defect Chemistry, Tensile Strain, and Tunable Optical Response

Abstract

ZnO and ZnO:5%B nanoparticles produced by sol–gel synthesis exhibit a single-phase wurtzite structure. X-ray diffraction (XRD) investigation reveals crystallite sizes in the range of $32.37–39.63$ nm and microstrain values on the order of $(1.98–8.03)\times {10}^{-4}$, despite the Uniform Stress Deformation Model (USDM) indicating the presence of considerable tensile stress. Significant band-tail states are introduced via boron doping, resulting in Urbach energies ranging from $110$ to $193$ meV and a narrowed optical band gap of $3.216$ eV. With a refractive index range of $2.05–2.71$, the material exhibits tunable optical characteristics. Violet and blue emissions originating predominantly from zinc interstitials (Znᵢ) and zinc vacancies (V_Zn) dominate the photoluminescence spectra, while oxygen interstitial-related contributions remain relatively weak. A high spin density is confirmed by electron spin resonance measurements, which reveal a strong defect-related signal at $g\approx 2.294$. The formation of Znᵢ/V_Zn defect centers due to charge compensation and ionic size mismatch induced by B³⁺ substitution for Zn²⁺ significantly modifies the band-edge states and optical constants. These defect-engineered properties render the material promising for applications in ultraviolet (UV) photodetectors, transparent conducting oxides, and electron transport layers in organic photovoltaic devices.

1. Introduction

Zinc oxide (ZnO) is widely regarded as a model n-type semiconductor whose prominence in nanotechnology stems from its characteristic optoelectronic parameters, including a direct wide band gap of approximately $3.37$ eV, a high exciton binding energy on the order of $60$ meV, and a strong visible emission band centered near $495$ nm with substantial spectral broadening [1,2,3,4,5].

ZnO nanoparticles have emerged as a highly adaptable material system for advanced electronic, photonic, and antibacterial technologies. Their high electron mobility exceeding $200$ cm²/V·s, together with superior thermal conductivity, supports efficient charge transport even under demanding operating conditions. In addition, the intrinsic nonlinear resistance behavior and adjustable surface electronic states of ZnO enable its application in high-sensitivity photodetectors, low-threshold light-emitting diodes, and radiation-tolerant sensing devices [6,7,8]. Importantly, ZnO’s inherent radiation resistance supports uses in the nuclear and aerospace industries, and its compatibility with wet chemical etching enables atomic-scale precision in device production. ZnO is at the forefront of functional nanomaterials research due to its unique properties [2,9,10].

Due to its many benefits, including low processing temperatures, great stoichiometric control, high chemical homogeneity, and inherent scalability, the sol–gel approach is widely used to fabricate ZnO-based nanostructures. In particular, the ability to introduce dopant elements into the precursor solution chemistry in a controlled manner [9,11] facilitates the engineering of defect populations ($V_O,V_{Zn},O_i,Z{n}_i$, etc.) and their associated optical–electronic properties [12]. However, while many studies focus on thin-film geometries, comprehensive investigations systematically correlating crystallite size, microstrain, specific surface area, and defect statistics with optical and magnetic responses within a unified data framework remain relatively limited for nanoparticles.

Boron (B) doping, due to its small ionic radius and +3 valence state, induces charge compensation and local strain fields in the ZnO lattice through substitutional/interstitial mechanisms [13,14,15,16,17]. This alters the relative abundances and energy levels of defects (zinc vacancies, oxygen vacancies, interstitial oxygen, and interstitial zinc ($Z{n}_i$)), thereby modifying band-edge transitions, the Urbach tail, the refractive index spectrum, and the photoluminescence (PL) emission map. In the literature, B-doped ZnO has mostly been reported for its enhanced conductivity and band gap modulation [18]. For instance, Atılgan and Özel [16] examined how the boron doping level influences the properties of ZnO thin films. They prepared B-doped ZnO films on glass substrates via spin coating, with boron concentrations ranging from 1% to 5%. Their analysis of electrical, optical, morphological, and structural properties revealed a strong dependence on B concentration.

In nanoparticles, quantifying the crystallographic stress/strain pair, correlating optical constants through multi-model approaches, and jointly interpreting PL/ESR data to reveal defect–optical–mechanical coupling have often remained secondary objectives.

This study aims to quantitatively elucidate the role of B doping by correlating the structural, mechanical, and optical responses of sol–gel synthesized Zn_1−xB_xO (x = 0.0 and 0.05) nanoparticles within a unified framework. In this context, X-ray diffraction (XRD) data were analyzed using the Williamson–Hall approaches (UDM/USDM/UDEDM) in addition to the Debye–Scherrer equation to separate crystallite size, microstrain, and internal stress contributions, thereby distinguishing peak-broadening effects arising from grain-size reduction and strain. The obtained structural parameters were cross-validated with optical measurements derived from the band gap and absorption edge. Moreover, the refractive index and extinction coefficient were estimated spectrally using the Kubelka–Munk transformation and various dispersion models. For direct monitoring of the defect landscape, the PL spectra were resolved using Gaussian decomposition, and the possible transition schemes for band-edge emission and deep-level bands in the visible region were discussed, along with defect-center assignments. Electron Spin Resonance (ESR) signals offered evidence for the presence of paramagnetic centers, supporting the PL interpretations. Thus, it was shown that B-doping redistributes microstrain and internal stress and that mechanical reconfiguration is reflected, via defect statistics, in the optical edge and sub-band emissions.

2. Results and Discussion

2.1. Characterization of ZnO: 5%B Nanoparticle

The X-ray diffraction (XRD) patterns of ZnO and ZnO: 5%B and the Rietveld refinement plot of ZnO: 5%B are shown in Figure 1a and Figure 1b, respectively. As shown in Figure 1a, the diffraction pattern is dominated by the (101) reflection, which is characteristic of the hexagonal wurtzite ZnO crystal structure (JCPDS Card No. 36-1451). No additional diffraction peaks attributable to secondary phases such as B₂O₃, BO₃, or BO₄ were detected within the instrumental resolution. Moreover, a comprehensive investigation was carried out using Rietveld analysis, and the obtained results were compared with those derived from XRD. According to the Rietveld analysis results, no secondary phase formation was observed in ZnO: 5%B nanoparticles, as shown in Figure 1b; in other words, only the ZnO phase was detected.

This absence of impurity-related reflections suggests that the incorporated B³⁺ ions are accommodated within the ZnO lattice, most likely through substitution at Zn²⁺ lattice sites.

It should be emphasized, however, that the absence of secondary crystalline reflections alone does not constitute direct proof of lattice-site occupancy, since amorphous boron–oxygen species or grain-boundary/adsorbed borate environments may remain undetectable by XRD.

However, the ionic radius of the Zn²⁺ ion in octahedral coordination is $0.74$ Å, while the Shannon radius of the B³⁺ ion is approximately $0.23$ Å. This indicates a significant radius mismatch ($\Delta r\approx 0.51 \AA$), showing that the B³⁺ ion is considerably smaller than the Zn²⁺ ion. This strengthens the conclusion that B doping will inevitably introduce substantial lattice strain and defect-mediated charge compensation.

Using the XRD data for ZnO and ZnO: 5%B nanoparticles, fundamental structural parameters such as bond length ($L$), dislocation density (δ), microstrain ($\epsilon$), unit cell volume, lattice constants, and lattice distortion (σ) were calculated. The calculated values are presented in

Table 1. Lattice characteristics, average particle sizes, unit cell volume, $c/a$, dislocation density ($\delta$) (the amount of defect in the sample), atom localization and displacement ($u$), and bond length ($L$) of ZnO and ZnO: 5%B nanoparticles.

Sample	D (nm)	a (Å)	c (Å)	c/a	Volume, V (Å3)	$\mathit{\delta }\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$ (nm2)	u	L (Å)
ZnO	39.63	3.23	5.26	1.629	47.524	0.00064	0.376	1.9761
ZnO:5%B	32.37	3.239	5.189	1.602	47.144	0.00095	0.379	1.9712

. The detailed equations used to calculate these parameters have been thoroughly explained in earlier studies [12,19,20,21,22].

Based on the data presented in Table 1, it is evident that 5% B doping induces a pronounced structural reorganization in the ZnO wurtzite crystal lattice. With 5% B incorporation, the average crystallite/particle size decreases from $39.63$ nm to $32.37$ nm, indicating that the dopant atoms suppress grain growth and promote enhanced nucleation. Examination of the lattice parameters reveals a slight increase in the a parameter ($3.23\to 3.239$ Å), while the c parameter exhibits a noticeable reduction ($5.26\to 5.189$ Å). As a result, the c/a ratio shifts to a lower value of $1.6020$, deviating from the ideal wurtzite value (≈1.633). This behavior signifies an anisotropic lattice contraction predominantly along the c-axis, accompanied by the development of appreciable microstrain. Consistently, the unit cell volume decreases from $47.524$ ų to $47.144$ ų, indicating an overall lattice densification. The increase in dislocation density from $0.00064\times {10}^{-4}$ nm⁻² to $0.00095\times {10}^{-4}$ nm⁻² further confirms that B doping enhances the defect density within the crystal structure. Moreover, the rise of the internal parameter u from $0.376$ to $0.379$ reflects a deviation from the ideal tetrahedral geometry of wurtzite ZnO, implying increased local bond asymmetry and charge separation. In contrast, the shortening of the Zn–O bond length from $1.9761$ Å to $1.9712$ Å is consistent with bond tightening and lattice distortion arising from the substitution of smaller B³⁺ ions at Zn²⁺ lattice sites.

Importantly, the observed anisotropic lattice evolution (c-axis contraction and reduced unit-cell volume), together with the correlated defect-related optical signatures discussed below, is consistent with boron incorporation that perturbs the ZnO host lattice. This interpretation is also consistent with prior studies in which XRD peak shifts and lattice contraction, supported by XPS identification of B³⁺, were used to argue that boron dopants tend to occupy Zn lattice sites [20].

Overall, these results indicate that boron addition leads to a distinct structural modification in ZnO, characterized by grain refinement, anisotropic strain, increased defect density, and enhanced local polarization.

In ZnO: 5%B nanoparticles synthesized by the sol–gel method, it is necessary to carefully examine the stresses and strains to understand the defects formed due to B doping and the heat-treatment temperature. In the following, we assess stresses and strains in ZnO: 5% B nanoparticles using the Williamson–Hall (W–H) method [23] and compare the particle size with values obtained from Debye–Scherrer and W–H estimations.

2.2. Williamson-Hall (W-H) Analysis

The Debye–Scherrer equation was employed to compute the average crystallite size (Equation (1)) [24]:

$$D={\displaystyle \frac{K\lambda }{{\mathrm{\beta }}_{\mathrm{h}\mathrm{k}\mathrm{l}}\mathrm{c}\mathrm{o}\mathrm{s}\left(\theta \right)}}$$

(1)

where the full width at half maximum (FWHM) values of the three main diffraction peaks, (100), (002), and (101), were considered. $D$ is the volume-weighted crystallite size, $K=0.9$ for dimensionless form factor ($0.9$), λ for X-ray wavelength ($0.1540$ nm), β for line broadening in radians, and θ for Bragg angle in this expression.

Although the Debye–Scherrer formula can be employed to estimate the crystallite size, the lattice strain’s contribution to peak broadening is not taken into consideration. Moreover, the observed line broadening is known to be caused by a combination of microstrain (ε) and finite crystallite size:

$$\epsilon ={\beta }_{hkl}\left(4tan\left(\theta \right)\right)$$

(2)

According to Equations (1) and (2), these two parameters show distinct dependencies on the Bragg angle (θ), as seen by Stokes and Wilson [24].

To distinguish between these effects, the W-H analytical approach is employed. The fundamental idea is that tan(θ) is proportional to the strain-induced component of the integral breadth (βₕₖₗ). In this work, different versions of the W-H technique were used to evaluate the lattice strain ($\epsilon$), stress (σ), energy density (u), and crystallite size (D). These were the Uniform Deformation Energy Density Model (UDEDM) to determine $\epsilon ,\sigma ,u,$ and $D$; the Uniform Stress Deformation Model (USDM) to determine $\epsilon ,\sigma ,$ and $D;$ and the Uniform Deformation Model (UDM) to determine $\epsilon$ and $D$.

2.2.1. The Model of Uniform Deformation

It is challenging to distinguish the distinct contributions of lattice strain and crystallite size to XRD peak broadening. To resolve this, the W-H technique proposes a mathematical model that incorporates both effects. Mote et al. [25] later refined this expression, leading to Equation (3):

$${\beta }_{hkl} cos\left({\theta }_{hkl}\right)=K\lambda /D+4 \epsilon sin\left({\theta }_{hkl}\right)$$

(3)

The UDM framework’s W-H plots for ZnO and ZnO: 5%B are shown in Figure 2a and Figure 2b, respectively, where the x-axis is represented by $4\epsilon sin\left({\theta }_{hkl}\right)$ and the $y$-axis by ${\beta }_{hkl} cos\left({\theta }_{hkl}\right)$.

The data was fitted using a linear least-squares method with the formula $y\left(t\right)=A\times t+B$, where A is the slope of the graph of $\beta cos\left(\theta \right)$. The standard error sum of squares was minimized to identify parameters $A$ and $B$:

$$E\left(A,B\right)=\sum _{i=1}^N{\left[\left(B+A{t}_i\right)-Y_i\right]}^2$$

(4)

The slope of the linear fit represents the lattice strain ($\epsilon$) in this analysis, and the crystallite size ($D$) is calculated using the relation $D=K\lambda /y_{interception}$ from the $y$-intercept of the $\beta cos\left(\theta \right)$ axis.

Table 2. The crystallite size (D), lattice strain ($\epsilon$), and strain (σ) values for all different methods, namely, the Debye–Scherrer, the UDM, USDM, and UDEDM, for ZnO and ZnO: 5%B structure.

	UDM		USDM				UDEDM
Sample	D (nm)	ε (10−4)	D (nm)	σ (N/m2) (106)	εmax (10−4)	εavg (10−4)	D (nm)	u (103)	σmax (N/m2) (106)	σavg (N/m2) (106)	εmax (10−4)	εavg (10−4)
ZnO	42.09	2.57	41.52	0.029	1.98	2.29	41.82	0.0017	0.033	0.028	2.27	2.44
ZnO:5%B	38.57	8.03	38.24	0.097	6.72	7.77	38.51	0.0024	0.107	0.092	7.4	7.96

provides a summary of the crystallite sizes, lattice strains, and stresses that were obtained for ZnO: 5%B nanoparticles using the UDM.

Table 3. (a) Coefficient of determination ($R^2$), adjusted coefficient of determination ($R_{adj}^2$), the root of the mean squared error (RMSE), and the total sum of squares (SST) for ZnO nanoparticle. (b) The linear fit: $y\left(t\right)=A\times t+B$ for ZnO nanoparticle.

(a)
Method	${\mathit{R}}^{\mathbf{2}}$	${\mathit{R}}_{\mathit{a}\mathit{d}\mathit{j}}^{\mathbf{2}}$	RMSE (×10−5)	SST (×10−7)	Correlation Coefficient
UDM	0.819	0.793	6.2	1.5	0.905
USDM	0.802	0.774	6.5	1.5	0.896
UDEDM	0.816	0.789	6.3	0.2	0.903
(b)
Method	$\mathit{A}$	$\mathit{B}$	Relative Error	$\mathit{p}$-Value for $\mathit{y}$-Intercept	$\mathit{p}$-Value for Slope
UDM	$2.56\times {10}^{-3}$	$3.29\times {10}^{-3}$	$2.70\times {10}^{-8}$	$1.67\times {10}^{-9}$	$7.9\times {10}^{-4}$
USDM	$2.85\times {10}^{-2}$	$3.33\times {10}^{-3}$	$2.95\times {10}^{-8}$	$1.12\times {10}^{-9}$	$1.09\times {10}^{-3}$
UDEDM	$1.92\times {10}^{-3}$	$3.31\times {10}^{-3}$	$2.75\times {10}^{-8}$	$1.26\times {10}^{-9}$	$8.45\times {10}^{-4}$

a,b shows the relative errors for B concentration (using $N=9$ reflection peaks) as well as the optimal parameters $A$ (slope) and $B$ (intercept) for the linear fits. Figure 2a and Figure 2b display the appropriate Williamson-Hall plots $\left(\beta cos\right(\theta )$ versus $4sin\left(\theta \right))$, where the red lines indicate the linear fits for ZnO and ZnO: 5%B nanoparticles, respectively.

According to the values in Figure 2a,b, the fits show a positive slope. Section 2.3 presents a statistical analysis of these findings.

2.2.2. The Uniform Stress Deformation Model

All crystallographic directions are assumed to have isotropic strain under the UDM. This assumption, however, frequently does not apply to nanoparticles, where a more realistic analysis requires accounting for the anisotropy of the crystal’s Young’s modulus. The USDM and the UDEDM were developed to overcome this constraint [25].

Mote et al. [25] produced a modified equation in the USDM by substituting the anisotropic term $\sigma /E_{hkl}$ for the isotropic lattice strain ${\epsilon }_{hkl}$ in the UDM, where $E_{hkl}$ is the Young’s modulus perpendicular to the set of crystal planes $\left(hkl\right)$. The expression that results from this refinement is:

$${\beta }_{hkl}cos\left({\theta }_{hkl}\right)=K\lambda /D+4 \sigma /E_{hkl} sin\left({\theta }_{hkl}\right)$$

(5)

The Young’s modulus $E_{hkl}$ for a hexagonal crystal structure is given by [26,27]:

$$E_{hkl}={\displaystyle \frac{{\left[h^2+\frac{{\left(h+2k\right)}^2}{3}+\left(\frac{a}{c}\right)\right]}^2}{S_{11}{\left[h^2+\frac{{\left(h+2k\right)}^2}{3}\right]}^2+S_{11}{\left[h^2+\frac{{\left(h+2k\right)}^2}{3}\right]}^2{+S}_{33}{\left(\frac{al}{c}\right)}^4+\left(2S_{13}+S_{44}\right){[h^2+\frac{{\left(h+2k\right)}^2}{3}]\left(\frac{al}{c}\right)}^2}}$$

(6)

and is a function of the elastic compliances $S_{ij}\left[m^2{N}^{-1}\right]$ where $S_{11}=7.858\times {10}^{-12},S_{13}=-2.206\times {10}^{-12},S_{33}=6.94\times {10}^{-12},S_{44}=23.57\times {10}^{-12}{m}^2{N}^{-1}.$

The USDM is represented by Equation (6), in which anisotropic strain results from the assumption that the stress is constant across all crystallographic orientations. The uniform stress $\sigma$ is obtained from the slope of the linear fit in the appropriate W-H plot of $\beta cos\left(\theta \right)$ and $4sin\left(\theta \right)(1⁄E\text{\_}hkl)$, and the crystallite size $D$ is obtained from the intercept on the $\beta cos\left(\theta \right)$ axis using the formula $D=K\lambda /y_{interception}$.

Figure 3a and Figure 3b display the curves of $\beta cos\left(\theta \right)$ versus $4sin\left(\theta \right)(1⁄E\text{\_}hkl)$ (the USDM) for ZnO and ZnO:5%B, respectively; The USDM-estimated stress, lattice strain, and crystallite size are shown in Table 2. It was fitted using a linear least-squares method, $y\left(t\right)=A\times t+B$. In Section 2.2.1, the error function was provided using Equation (4). Table 3b and

Table 4. (a) Coefficient of determination ($R^2$), adjusted coefficient of determination ($R_{adj}^2$), the root of the mean squared error (RMSE), and the total sum of squares (SST) for ZnO:5%B. (b) The linear fit: $y\left(t\right)=A\times t+B$ for ZnO:5%B.

(a)
Method	${\mathit{R}}^{\mathbf{2}}$	${\mathit{R}}_{\mathit{a}\mathit{d}\mathit{j}}^{\mathbf{2}}$	RMSE (×10−4)	SST (×10−6)	Correlation Coefficient
UDM	0.627	0.574	3.2	1.9	0.792
USDM	0.724	0.684	2.7	1.9	0.851
UDEDM	0.682	0.637	2.9	1.9	0.826
(b)
Method	$\mathit{A}$	$\mathit{B}$	Relative Error	p-Value for y-Intercept	p-Value for Slope
UDM	$8.02\times {10}^{-4}$	$3.59\times {10}^{-3}$	$7.10\times {10}^{-7}$	$6.39\times {10}^{-5}$	$1.1\times {10}^{-2}$
USDM	$9.68\times {10}^{-2}$	$3.62\times {10}^{-3}$	$5.25\times {10}^{-7}$	$1.27\times {10}^{-5}$	$3.63\times {10}^{-3}$
UDEDM	$6.28\times {10}^{-3}$	$3.59\times {10}^{-3}$	$6.05\times {10}^{-7}$	$2.85\times {10}^{-5}$	$6.08\times {10}^{-3}$

b show the relative errors with the optimized $A$ and $B$ values, where $N=9$ (the number of the reflection peaks) for ZnO and ZnO: 5%B nanoparticles, respectively.

2.2.3. The Energy Density Model of Uniform Deformation (UDEDM)

Mote et al. [25] developed the UDEDM, another W-H model, to determine the energy density $u$ of a crystal. According to this method, anisotropic lattice strain originates from an isotropic deformation energy density. Equation (7) illustrates the relationship between strain ϵ and u for a homogeneous energy density:

$$u_{ed}={\displaystyle \frac{{\epsilon }^2{E}_{hkl}}{2}}$$

(7)

based on Hook’s law. Therefore, Mote et al. [25] improved Equation (5) to obtain Equation (1):

$${\beta }_{hkl}cos\left({\theta }_{hkl}\right)={\displaystyle \frac{K\lambda }{D}}+4{\left(2{\displaystyle \frac{u_{ed}}{E_{hkl}}}\right)}^{{\displaystyle \frac{1}{2}}}sin({\theta }_{hkl})$$

(8)

The UDEDM is represented by Equation (8). Applying a linear least-squares fit enables the slope of the line to estimate the energy density $u$ when ${\beta }_{hkl}cos\left({\theta }_{hkl}\right)$ and $4{\left({\displaystyle \frac{2}{E_{hkl}}}\right)}^{{\displaystyle \frac{1}{2}}}sin({\theta }_{hkl})$ are given to the $y$-axis and $x$-axis, respectively. The intercept on the $\beta cos\left(\theta \right)$-axis provides the crystallite size $D$, or $D=K\lambda /y_{interception}$. The plots of $\beta cos\left(\theta \right)$ versus $4sin\left(\theta \right)\surd (2⁄E_{hkl})$ (the UDEDM) for ZnO and ZnO: 5%B are displayed in Figure 4a and Figure 4b, respectively.

Table 2 displays the estimated stress, crystallite size, and lattice strain as determined by the UDEDM.

It was fitted using a linear least-squares method, $y\left(t\right)=A\times t+B$. In Section 2.2.1, the error function was provided using Equation (4). Table 3b and Table 4b show the relative errors with the optimized $A$ and B values, where $N=9$ (the number of the reflection peaks) for ZnO and ZnO: 5%B nanoparticles, respectively.

Among the Williamson–Hall approaches considered in this work, the uniform stress deformation model (USDM) yields results closest to those reported in previous studies [28]. Notably, the crystallite dimensions estimated using the USDM are in strong agreement with those obtained independently from TEM analysis, as shown in Table 1. The maximum stress and microstrain calculated via UDEDM for the nine peak planes (Figure 1) are presented in Table 2. Our observations indicate that the USDM is more suitable for nanoparticles than the UDEDM, which contradicts the conclusions of Mote et al. [25]. Table 2 presents a comparative overview of crystallite sizes derived using the Debye–Scherrer formula and UDM, USDM, and UDEDM.

The USDM shows that the average microstrain values for the nanoparticles are highly consistent, suggesting that the average microstrain affects both the energy density and the stress. These results are consistent with the findings of Mahendiran et al. [28]. Using the ICDD data file (Card No. 36-1451) for ZnO, which corresponds to the X-ray diffraction data for the nine planes, including their lattice characteristics and diffraction peaks, the phase identification was verified.

For ZnO and ZnO:5%B, the linear fits show a positive slope, as indicated in Figure 2b, which indicates positive uniform stress ($\sigma$) and, thus, tensile strain. Due to point defects in the lattice, anisotropic microstrain is also indicated by the existence of this tensile strain. The crystallite size (D) for the ZnO: 5%B nanoparticle is compared across four distinct approaches: Debye–Scherrer, UDM, USDM, and UDEDM.

Section 2.3 provides a detailed discussion of the corresponding statistical data for the UDM, USDM, and UDEDMs.

Since the stress values are positive, it can be concluded that the structures undergo tensile stress. This also indicates the presence of anisotropic microstrain, likely due to point defects. Using the UDEDM method, average and maximum stress and microstrain values were obtained from the nine peak planes, as reported in Table 2. Notably, the crystallite size decreases with increasing dopant concentration.

2.3. Statistical Analysis

MATLAB’s (R2020b) built-in function was used to evaluate the accuracy of the linear regression models; the relevant statistical metrics for the UDM, USDM, and UDEDMs are presented in Table 3a and Table 4a. Even if the Total Sum of Squares (SST) and Root Mean Square Error (RMSE) values are roughly ${10}^{-8}$ and ${10}^{-4}$, respectively, these metrics are not enough to verify the validity of the fits. From Table 3a and Table 4a, it can be concluded that the linear model provides a good fit for the ZnO and ZnO:5%B samples, as their coefficients of determination ($R^2$) are bigger than $0.8$. For pure ZnO, correlation coefficients above $0.8$ indicate strong agreement compared to 0.65 in ZnO:5%B. However, relying solely on R² values and correlation coefficients can be misleading, as the F-statistic—which compares the linear regression model against a constant model—must also be considered. The p-value indicates the significance of the F-statistic.

The best results were obtained for pure ZnO, where the $p$-values for slopes were approximately ${10}^{-4},{10}^{-3},$ and ${10}^{-4}$ for the UDM, USDM, and UDEDM methods, respectively, compared to ${10}^{-2},{10}^{-3},$ and ${10}^{-3}$ for ZnO:5%B; and the $y$-intercept $p$-values were around ${10}^{-9}$ and 10⁻⁵, as seen in Table 3b and Table 4b. In other cases, the model either provides a good fit to the data or exhibits varying degrees of significance.

2.4. The Morphology of Nanoparticles

ZnO: 5%B nanoparticles were characterized using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Figure 5a presents the particle size distribution of ZnO:5% B nanoparticles at a magnification of $1$ μm. The SEM micrograph clearly reveals compact, quasi-spherical, and agglomerated particle morphologies.

Figure 5c shows the particle size analysis of ZnO:5% B nanoparticles obtained using ImageJ software (version 1.54p) with Gaussian fitting. The average particle size was determined to be $30.61$ nm. A slight discrepancy was observed between the average particle size obtained from ImageJ analysis (version 1.54p) and the values estimated directly from the XRD results, as summarized in Table 1.

Figure 5b illustrates the elemental composition of ZnO:5% B nanoparticles as determined by energy-dispersive X-ray spectroscopy (EDS). The observed EDS peaks and their relative intensity variations are consistent with the nominal precursor concentrations used during synthesis. The presence of only Zn, O, and B peaks, with no detectable signals from extraneous elements, confirms the intended doping composition of the synthesized samples.

Figure 6 displays TEM images of ZnO: 5% B nanoparticles at magnifications corresponding to $2$ nm and $20$ nm, respectively. The TEM image in Figure 6 shows that the nanoparticles tend to form agglomerates. TEM analysis further reveals that the sol–gel–synthesized ZnO:5% B nanoparticles exhibit well-defined ZnO crystalline features, in good agreement with the sharp XRD patterns shown in Figure 1. As observed in the inset of Figure 6, the crystalline nature of the ZnO: 5%B nanoparticles is evident from the clear alignment of atomic planes across the micrograph, with an interplanar spacing of approximately $291$ pm, which falls within the experimental range of $0.28\pm 0.01$ nm. The d-spacing was estimated from the lattice-fringe pattern using FFT/line-profile analysis.

When the lattice parameters $a=3.239$ Å and $c=5.189$ Å given in Table 1 for ZnO:5%B are used, the interplanar spacing of the (100) plane for the wurtzite hexagonal structure is calculated as:

$$d_{\left(100\right)}={\displaystyle \frac{\sqrt{3}}{2}}a\approx 0.866a$$

(9)

In other words, $d_{\left(100\right)}\approx 0.866\times 3.239,\mathrm{\AA }=2.806 \mathrm{n}\mathrm{m}.$

By comparison with the experimentally obtained values, we confirmed that the interplanar spacing is ($0.28\pm 0.01$ nm); therefore, this value is consistent with the (100) crystallographic plane.

2.5. Optical Properties

2.5.1. UV-Vis Absorption Spectroscopy

The UV-Vis absorption spectrum of a sol–gel prepared sample of ZnO and ZnO: 5%B nanoparticles is shown in Figure 7.

2.5.2. Band Gap Calculation

The diffuse reflectance $R_{\infty }\left(\lambda \right)$, obtained in relation to the $~100$% reference (BaSO₄/PTFE), was translated into the Kubelka–Munk function because the absorption coefficient α could not be directly determined in ZnO and ZnO:5%B nanoparticles. A Tauc plot was created to find $E_g$, assuming $S\left(\lambda \right)$ approximately constant close to the edge and taking $F\left(R_{\infty }\right)\propto \alpha$.

$$F\left(R_{\infty }\right)={\left(1-R_{\infty }\right)}^2/\left(2R_{\infty }\right)=K/S$$

(10)

In this case, $K$ stands for effective absorption, $S$ for effective scattering, and $R_{\infty }$ for reflectance in the $0–1$ range. It is possible to write $F\left(R_{\infty }\right)\propto \alpha$ if it is assumed that $S$ is weakly wavelength-dependent close to the absorption edge.

The optical band gap $E_g$ can be computed using the following formula between the absorption coefficient ($\alpha$) and the photon energy ($hv$):

$$\alpha h\upsilon =k{\left(h\upsilon -E_g\right)}^{{\displaystyle \frac{1}{n}}}$$

(11)

The optical band gap and energy-independent constants are denoted by $E_g$ and $k$, respectively, in Equation (11). Since ZnO has direct permitted transitions and $F\left(R_{\alpha }\right)$ is proportional to $\alpha$, $n$ is assumed to be $1/2$. Therefore, Equation (4) can be changed to:

Equation (11) uses the symbols $E_g$ for the optical band gap and $k$ for the energy-independent constants. Since $F\left(R_{\alpha }\right)$ is proportional to $\alpha$, and ZnO has direct allowed transitions; $n$ is taken to be $1/2$. Consequently, Equation (10) can be modified to:

$$F\left(R_{\alpha }\right)h\upsilon =k{\left(h\upsilon -E_g\right)}^{{\displaystyle \frac{1}{2}}}$$

(12)

Stated differently, ${\left(F\left(R_{\alpha }\right)h\upsilon \right)}^2=k^2(h\upsilon -E_g)$. The slope of the graph of ${\left(F\left(R_{\alpha }\right)h\upsilon \right)}^2$ vs. energy, shown in Figure 8, was estimated between 350 and 400 nm using a linear fit $y\left(h\upsilon \right)=A\times h\upsilon +B$ in the least-squares sense. Equation (13) provides the error formula for A and B, which was minimized to achieve this.

$$E\left(A,B\right)={\sum }_{i=1}^N{\left[A {\times \left(h\mathrm{\upsilon }\right)}_i+B-{\left({\left(F\left(R_{\alpha }\right)h\mathrm{\upsilon }\right)}^2\right)}_i\right]}^2$$

(13)

The parameters A and B, together with the corresponding relative error values, are summarized in

Table 5. Fitting curve function $\left(h\upsilon \right)=A\times h\upsilon +B$, band gap energy ($E_g$), and variance (${\sigma }^2$) for ZnO and ZnO: 5%B nanoparticles.

A	B	${\mathit{E}}_{\mathit{g}}$	${\mathit{\sigma }}^{\mathbf{2}}$
0.0554	−0.1819	3.28	$7.87\times {10}^{-9}$
0.2023	−0.6506	3.216	$2.16\times {10}^{-6}$

, where $N=9$ denotes the total number of data points.

2.5.3. Refractive Index Calculations

In 2019, Naccarato et al. [11] showed how chemistry influences the band gap, the high refractive index connection, and why certain of the 4000 semiconductor material classes would perform better. They examined several models that used band gap measurements to determine the refractive index. These models include those of Ravindra et al. [29], Moss [30], Hervé and Vandamme [31], Reddy and Anjayenulu [32], and Kumar and Singh [33].

The refractive index values obtained in this study range from $2.09$ to $2.71$, as summarized in

Table 6. Various techniques for calculating refractive indices ($n$) using band gap energy ($E_g$) for ZnO and ZnO: 5%B nanoparticles (effective refractive index values estimated from $E_g$-based empirical models; not wavelength-dependent dispersion $n\left(\lambda \right)$).

Sample	${\mathit{E}}_{\mathit{g}}$	Moss [30]	Hervé and Vandamme [31]	Kumar and Singh [33]	Reddy and Anjayenulu [32]	Ravindra et al. [29]
ZnO	3.28	2.3199	2.2493	2.2957	2.6960	2.0504
ZnO:5%B	3.216	2.3313	2.2666	2.3104	2.7110	2.0901

. These values represent effective refractive indices estimated from $E_g$-based empirical models, rather than wavelength-dependent dispersion data $n\left(\lambda \right)$. Accordingly, the refractive indices calculated using the models presented in Table 6 and

Table 7. Refractive index formula based on the models.

Model	Refractive Index (n) Formula
Moss [30]	${\left({\displaystyle \frac{95}{E_g}}\right)}^{{\displaystyle \frac{1}{4}}}$
Hervé and Vandamme [31]	$\sqrt{1+{\left({\displaystyle \frac{13.6}{E_g+3.47}}\right)}^2}$
Kumar and Singh [33]	${3.3668\left(E_g\right)}^{-0.32234}$
Reddy and Anjayenulu [32]	${\left({\displaystyle \frac{154}{E_g-0.365}}\right)}^{{\displaystyle \frac{1}{4}}}$
Ravindra et al. [29]	$4.084-0.62E_g$

are reliable. Based on the five models, Tripathy [34] reported the corresponding validity ranges for energy band-gap values in 2015, as listed in

Table 8. Model-based reliability ranges for the energy band gaps.

Model	Confidence Intervals of Band Gaps
Hervé and Vandamme [31]	2.00 eV < Eg < 4.00 eV
Kumar and Singh [33]	2.00 eV < Eg < 4.00 eV
Reddy and Anjayenulu [32]	1.10 eV < Eg < 6.20 eV
Ravindra et al. [29]	1.50 eV < Eg < 3.50 eV
Moss [30]	0.17 eV < Eg < 3.68 eV

.

2.5.4. The Urbach Energy Calculation

According to the following connection, the absorption coefficient ($\alpha$) at band boundaries has an exponential dependence on photon energy ($h\nu$), according to the Urbach law:

$$\alpha ={\alpha }_0{e}^{{\displaystyle \raisebox{1ex}{$h\nu $}\!\left/ \!\raisebox{-1ex}{$E_u$}\right.}}$$

(14)

where ${\alpha }_0$ is a constant and $E_u$ is the Urbach energy representing the impact of all potential faults [34]. The Urbach energy ($E_u$) is determined using the following relation:

$$E_u={\left[{\displaystyle \frac{d\left(\ln \left(\alpha \right)\right)}{d\left(h\nu \right)}}\right]}^{-1}$$

(15)

where $\alpha$ is the absorption coefficient and is the photon energy [35,36]. These values can be linked to the breadth of the localized states in the band gap. Figure 9 displays $\ln \left(\alpha \right)$ versus photon energy $h\nu$ (eV) of ZnO and ZnO: 5%B structure.

Owing to the discrete nature of the tabulated absorption coefficient data, the first derivative of $\ln \left(\alpha \right)$ with respect to photon energy ($h\nu$) was approximated numerically. For this purpose, three finite difference techniques (the 3-point backward, 3-point central, and 5-point formulas) were utilized. The associated approximation errors are of second and fourth order, respectively. The derived parameters for the ZnO:5%B structure are listed in

Table 9. The Urbach energy values $E_u$ in meV calculated at $E_g$ by three different finite difference methods, namely, 3-point backward, central, and 5-point finite difference methods (FDM) of ZnO and ZnO: 5%B structure.

	3-Point Backward F.D.M. (meV)	3-Point Central F.D.M. (meV)	5-Point F.D.M. (meV)
ZnO	110.60	110.60	110.60
ZnO:5%B	192.35	184.85	191.53

.

Bindu and Thomas [37] reported an Urbach energy ($E_u$) of $490$ meV for undoped ZnO nanoparticles. In contrast, the present results indicate that B incorporation at a concentration of 0.05 increases the Urbach energy. In this study, $E_u$ is employed as a quantitative descriptor of local potential fluctuations and short-range structural disorder.

As listed in Table 9, the extracted $E_u$ values lie in the range of approximately $184–193$ meV. These values are evaluated in conjunction with the optical band gap ($E_g$), photoluminescence-derived defect populations ($V_O$ and $V_{Zn}$), and key structural parameters, including micro-strain ($\epsilon$), internal stress ($\sigma$), dislocation density ($\delta$), internal positional parameter ($u$), and bond length ($L$). Overall, the increase in $E_u$ indicates that B-induced disorder in ZnO nanoparticles broadens the band-tail states and can influence optical transition processes.

Despite the relatively moderate sensitivity of the refractive index models [30,31] to B-concentration, the growth in $E_u$ may contribute to the slight variations in the $n\left(E_g\right)$ relationships that these models anticipate. The changes in $E_g$ at the millielectronvolt (meV) scale have a small but noticeable impact on the refractive index ($n)$. $E_u$, thus, may affect the refractive index (n) indirectly through disorder-induced band-edge modifications (via $E_g$), rather than serving as a direct controlling parameter.

$E_u$ tends to rise as a result of the agglomeration and grain-boundary enrichment seen in SEM. Since the Urbach tail is particularly sensitive to short-range bond distortions and localizations originating from grain boundaries and interfaces, the relationship between $E_u$ and XRD-derived Debye–Scherrer is not one-to-one. Instead, Debye–Scherrer provides information about long-range order within the crystal. Therefore, the observed increase in $E_u$ upon B incorporation is more consistently interpreted as a signature of enhanced local disorder and band-tail broadening, rather than a simple monotonic function of crystallite size.

2.6. FTIR Studies

Fourier-transform infrared (FTIR) spectroscopy was employed to evaluate the chemical bonding structure and the possible incorporation site of boron in ZnO:5%B nanoparticles. The FTIR spectra of ZnO and ZnO:5%B nanoparticles are shown in Figure 10. As seen from the figure, this direct comparison reveals whether the bands in the $1451–1382$ and $1028–1250$ cm⁻¹ regions are intrinsic to ZnO surface chemistry or are enhanced by boron incorporation.

The broad absorption band observed in the $3200–3700$ cm⁻¹ region is attributed to O–H stretching vibrations of surface-adsorbed water molecules and/or hydroxyl (–OH) groups, which arise from the high specific surface area of ZnO nanoparticles. The pronounced band around ≈3675 cm⁻¹ further supports this assignment. The weak bands observed at approximately ≈2988 and ≈2901 cm⁻¹ can be associated with C–H stretching vibrations of trace residual organic species that may originate from the synthesis process.

In the mid-frequency region, the multiple-band structure observed in the $1451–1382$ cm⁻¹ range is commonly associated with carbonate (CO₃²⁻) or C–O vibrational modes; however, it has also been reported in the literature that this region can partially overlap with boron–oxygen-based local environments (BO₃/BO₄ units) [38].

Notably, the corresponding spectral features in the $1451–1382$ cm⁻¹ region are also observed in undoped ZnO, supporting the view that this band group is predominantly related to carbonate/C–O surface species (e.g., atmospheric CO₂ adsorption), with possible partial overlap from borate-related local environments in the B-doped sample.

Nevertheless, the absence of a single broad and dominant absorption band characteristic of an amorphous boron oxide (B₂O₃) glassy structure indicates that significant boron oxide phase segregation is unlikely [39].

In particular, the bands observed in the $1028–1250$ cm⁻¹ range ($1028,1057,1066,1075,1230,1242,$ and $1250$ cm⁻¹) can be considered consistent with boron–oxygen (B–O) vibrational modes and/or B–O–Zn linkages formed via oxygen within the ZnO lattice.

Compared to undoped ZnO, the band group in the $1028–1250$ cm⁻¹ region becomes more pronounced in ZnO:5%B, which strengthens its association with boron-related local bonding environments rather than solely generic ZnO surface vibrations.

The presence of these bands suggests that boron chemically interacts with the ZnO matrix and can be incorporated into the oxide network without forming a separate crystalline boron oxide phase. The enhancement of this band group in the FTIR spectrum indicates that the surface and/or local bonding environments of ZnO nanoparticles are modified by boron incorporation.

Such local changes in bonding chemistry, particularly due to the different charge state and ionic radius of B³⁺ compared to Zn²⁺ ions, can induce charge imbalance and local lattice distortions within the host lattice. This, in turn, increases the likelihood of forming intrinsic defects such as oxygen vacancies ($V_O$) and zinc vacancies ($V_{Zn}$). Indeed, the defect-related emission bands observed in the visible region of the photoluminescence (PL) spectrum are consistent with these structural and chemical modifications identified by FTIR, including the differences relative to undoped ZnO, indicating the activation of defect states.

Finally, the broad and intense absorption observed in the low-wavenumber region (<600 cm⁻¹) is a characteristic signature of Zn–O lattice vibrations, confirming that the ZnO host phase is preserved.

While the appearance and strengthening of the $1028–1250$ cm⁻¹ band group in ZnO:5%B supports boron-related local bonding environments (B–O and/or B–O–Zn linkages) and confirms chemical interaction of boron with the oxide network, FTIR alone cannot unambiguously distinguish substitutional lattice incorporation from borate species located at surfaces or grain boundaries. Therefore, the FTIR results are interpreted here as complementary evidence consistent with boron-induced local bonding modification, in agreement with the XRD/Rietveld lattice perturbation trends and the defect-related optical response discussed in the following sections.

2.7. Photoluminescence (PL)

PL measurements were performed at an excitation wavelength of $300$ nm to probe defect-related states, defect concentrations, and crystalline quality in ZnO:5%B nanoparticles. As illustrated in Figure 11, the emission spectrum spans a broad wavelength range from approximately $3.54 \mathrm{to} 1.46 \mathrm{eV} (350$ to $850$ nm). The PL spectrum further reveals that the emission intensity of the ZnO:5%B nanoparticles reaches its overall maximum at around $3.18$ eV ($390$ nm), corresponding to the near-band-edge (UV/violet) emission.

Consistent with our previous findings [12] and earlier reports in the literature, n-type ZnO semiconductors typically exhibit two distinct photoluminescence features: a broad visible emission band and a sharp ultraviolet (UV) emission peak. In ZnO-based nanostructures, the visible emission is commonly associated with intrinsic and extrinsic defect states; however, the UV emission serves as an indicator of both defect concentration and crystalline quality [19,20,21]. The UV emission originates from near-band-edge (NBE) recombination processes, primarily involving excitonic transitions between electrons in the conduction band and holes in the valence band. This near-band-edge emission is a hallmark optical property of ZnO, arising from its wide direct bandgap. A pronounced and narrow UV emission peak is generally indicative of high crystallinity and a low density of structural defects in ZnO nanoparticles. As evident from the UV emission spectrum presented in Figure 11a, the ZnO:5% B nanoparticle sample exhibits a well-defined and sharp UV emission peak.

Deep-level (DL) emission, commonly referred to as visible emission, is generally categorized into two broad spectral bands. The first emission band spans violet, blue, green, yellow, and orange wavelengths, while the second band extends into the red and near-infrared (NIR) regions. These emission features originate from radiative recombination processes involving various intrinsic defects and impurity-related states within the ZnO crystal lattice. Typical defect centers associated with these emissions include zinc interstitials ($Z{n}_i$), oxygen vacancies ($V_o$), oxygen antisites $O_{Zn}$, zinc vacancies ($V_{Zn}$), and oxygen interstitials ${(O}_i$), each contributing to characteristic emission energies.

It should be noted, however, that deep-level emission bands in ZnO are not uniquely assignable to a single defect species without complementary evidence (e.g., temperature/excitation dependence, time-resolved PL, or controlled-atmosphere annealing). Therefore, the following attributions are presented as literature-guided and non-unique.

$$f\left(\lambda \right)=a{e}^{-{\displaystyle \frac{{\left(\lambda -b\right)}^2}{2c^2}}}$$

(16)

To elucidate the defect states responsible for the emission features observed in Figure 11, the photoluminescence spectra were analyzed using the Gaussian peak deconvolution based on the model defined in Equation (16), implemented through the Fityk software package (version 1.3.1).

Although the experimental spectra are commonly presented in wavelength space, the quantitative analysis of the emission components was performed in photon-energy space (E, eV), since luminescence bands correspond to electronic transitions between discrete energy levels [40]. Accordingly, the wavelength-dependent intensity data were converted to energy units using $E={\displaystyle \frac{hc}{\lambda }}$, and the appropriate Jacobian correction

$I\left(E\right)={\displaystyle \frac{I\left(\lambda \right){\lambda }^2}{hc}}$ was applied to account for the nonlinear $\lambda \leftrightarrow E$ transformation.

This conversion is necessary for physically meaningful Gaussian decomposition and for comparing peak positions/FWHM on an energy scale, as emphasized by Brik et al. [40] and commonly practiced in ZnO PL deconvolution studies reported in Uklein et al. [41] (e.g., ZnO band components expressed directly in eV).

The photoluminescence spectra of ZnBO nanoparticles that underwent Gaussian breakdown are shown in Figure 11b. There were twelve peaks in all, as the image illustrates. For compact reporting, these fitted sub-peaks were grouped into three conventional spectral regions (violet/blue/red) corresponding to the dominant visible-band contributions.

The following peaks represent emissions in the ultraviolet, violet, blue, red, and near-infrared (NIR) spectra: excitonic transitions occur between 3.27 and 3.26 eV ($379$ and $380$ nm). Zinc interstitials ($Z{n}_i$) are the source of violet emissions 3.25–2.87 eV ($382–432$ nm) [17]. Zinc vacancies ($V_{Zn}$) are responsible for the blue emissions 2.67–2.54 eV ($465–489$ nm). Interstitial oxygen ($O_i$) is shown by red emissions 1.71–1.65 eV ($727–750$ nm). The weak emission observed in the red–NIR region (>750 nm) is attributed to deep-level defect states (e.g., oxygen interstitials or complex defect configurations), rather than to oxygen vacancies [19]. The PL spectra of ZnO:5% B nanoparticles generated by the sol–gel technique and decomposed using a Gaussian distribution in the Fityk software (version 1.3.1) are shown in Figure 11b. It was observed that defects such as Zn vacancies ($V_{Zn}$), zinc interstitials ($Z{n}_i$), and interstitial oxygen ($O_i$) were present. By calculating the area under each observed peak, the dominant emission contributions were determined. The results are shown in

Table 10. The proportions of defects, emission ranges, emission sources, and peak locations using the Gaussian distribution were determined by analyzing the PL spectra of B-doped ZnO NPs using the Fityk software (version 1.3.1). (Reported “area under curve (%)” values represent relative spectral weights; qualitative indicator, not absolute defect concentration).

Area Under Curve (%)	Energy Range (eV)	Wavelength Range (nm)	Emission Range	Surface Defects
65.21	2.75–3.26	380–450	Violet	${(Zn}_i)\to {(V}_B)$	DL Emission
5.11	2.48–2.75	450–500	Blue	$\left({\mathrm{v}}_{Zn}\right)$
29.68	1.65–1.85	670–750	Red	${(O}_i)$

. Additionally, the relative spectral weights (area fractions) are summarized in Table 10. Here, “area under curve (%)” values are reported as relative spectral weights (area fractions) of the fitted emission components and should not be taken as rigorous defect concentrations. To address the $\lambda \leftrightarrow E$ nonlinearity, the spectrum was also evaluated in photon-energy space ($E={\displaystyle \frac{hc}{\lambda }}$) using the appropriate Jacobian correction, and the dominant emission contributions were found to remain qualitatively consistent.

Fit robustness was checked by varying initial peak positions/FWHM and the background model within reasonable bounds; the main peak-energy regions and their relative dominance remained unchanged (qualitatively). Therefore, the reported area fractions are used only as relative spectral weights within this specific fit model and should not be interpreted as quantitative defect concentrations.

This distribution suggests (qualitatively) a defect chemistry dominated by $Z{n}_i$ and $V_{Zn}$ resulting from the charge surplus and size mismatch caused by the substitution of B³⁺ for Zn²⁺. It is also consistent with the slight decrease in the band gap ($E_g=3.216$ eV) and the broadening of the Urbach energy.

The substitution of B³⁺ ions for Zn²⁺ triggers compensation mechanisms in the lattice due to both charge imbalance (B⁺³ and Zn⁺²) and size mismatch (B³⁺ being much smaller). As a result, point defects such as zinc vacancies (V_Zn, acceptors), zinc interstitials (Zn_i), and oxygen interstitials (O_i) are primarily formed. This defect enrichment is consistent with the experimentally observed increase in microstrain (ε) and stress (σ), as well as with the broadening of the Urbach energy to the range of 110 ȡ 193 meV and the slight narrowing of the band gap around E_g = 3.216 eV. In other words, the density of edge states has increased, the band edges have become blurred, and discrete/deep levels have significantly influenced the optical response. Therefore, this behavior is also consistent with the PL transition scheme (Figure 11c) and the paramagnetic centers observed in ESR signals.

2.8. Electron Spin Resonance

The ESR spectrum furnishes rich structural and electrical information, yielding critical insight into a material’s magnetic centers. It is particularly effective for probing defect structures and magnetic behavior in nanomaterials by identifying sites associated with ion vacancies or localized magnetic ions [22].

The spin Hamiltonian ($H$), which quantitatively characterizes the magnetic interactions experienced by a magnetic center, is used to analyze the properties of the ESR spectrum [19,22]. The spin Hamiltonian’s generic form is provided by:

$$H={\mu }_{B}S{g}_{e}H+H_{cf}+SDS+SAI+{\mu }_{N}I{g}_{n}H+SJS+J{S}_1{S}_2$$

(17)

The Zeeman effect, crystal-field splittings, and hyperfine couplings are some of the interactions that influence the spectral properties of electron spin resonance (ESR), such as line shape, position, and splitting. A detailed understanding of the local structure and magnetic environment of paramagnetic centers is made possible by analyzing these patterns. As a result, the ESR spectra of the B-doped ZnO nanoparticles were recorded in the first-derivative mode at ambient temperature. The experiments used $5$ mW microwave power, $100$ kHz field modulation, and a DC magnetic field applied perpendicular to the sample tubes and parallel to the microwave field. The ESR spectra are plotted as the derivative of absorption with respect to the external field (Figure 12).

The ESR spectra of ZnO: 5%B NPs in the $300–350$ mT magnetic field range are shown in Figure 12. To guarantee accurate spectral representation, background signals from the empty quartz sample tube and the microwave cavity were removed before plotting. Within the specified field range, a single, acute, and powerful resonance peak is consistently observed across all spectra.

As shown in Figure 12, ESR measurements were performed at room temperature (RT) to investigate the samples’ defect characteristics. A large, single resonance peak was observed in the spectrum. Both the peak-to-peak line width ($\Delta H_{pp}$) and the g factor were computed from the ESR data. For the ZnO: 5%B NPs annealed at RT, the ESR spectra and scaled experimental X-band ESR curves are shown in Figure 12.

The presence of structural flaws is responsible for the observed ESR peak intensity. The computed asymmetry factor ($P_{asy}$) values are shown in

Table 11. The ESR parameters for ZnO: 5%B NPs.

${\mathit{I}}_{\mathit{p}\mathit{p}}$	$\mathit{\Delta }{\mathit{H}}_{\mathit{p}\mathit{p}}$	${\mathit{P}}_{\mathit{u}}$	${\mathit{P}}_{\mathit{l}}$	${\mathit{P}}_{\mathit{a}\mathit{s}\mathit{y}}$	${\mathit{N}}_{\mathit{s}}$	$\mathit{g}\mathbf{-}$Values
4564.1	120.68	23,553.64	−18,989.54	2.24	14,289.52	2.294

and were obtained using the following formula according to Arda et al. and the reference therein [19]:

$$P_{asy}=1-h_u/h_L$$

(18)

where $h_L$ and $h_u$ correspond to the lower- and upper-side absorption peak heights relative to the baseline. Additionally, the following formula was used to determine the number of unpaired electron spins ($N_s$):

$$N_s=0.285\times I_{pp}\times {\left(∆H_{pp}\right)}^2$$

(19)

where $I_{pp}$ is the signal intensity from peak to peak, and $∆H_{pp}$ is the entire width at half maximum of the resonance peak [19].

The g-factor and the peak-to-peak linewidth $∆H_{pp}$ were assessed to obtain a better understanding of the spin relaxation mechanisms seen in the ESR spectra. The resonance condition was used to calculate the g-factor:

$$h\nu =g{\mu }_{\beta }H$$

(20)

where ${\mu }_{\beta }$ is the Bohr magnet, $H$ is the resonance magnetic field, $\nu$ is the operating frequency of the X-band ESR spectrometer (9.45 GHz), and $h$ is Planck’s constant. When this equation is solved for $g$, the result is:

$$g=71.4477{\displaystyle \frac{\nu }{H}}$$

(21)

As seen in Figure 13, the $g$-factor was calculated and plotted using Equation (21).

Room-temperature X-band ESR spectra of ZnO: 5%B nanoparticles exhibit a single, intense resonance line within $300–350$ mT, characterized by $g=2.294$, a peak-to-peak linewidth $\Delta H_{pp}=120.7$ mT, and an asymmetry factor $P_{asy}=2.24$. The single dominant line indicates a dominant ESR-active paramagnetic response (i.e., a prevailing resonance feature within the measured field window), rather than a uniquely identifiable single defect species, while the relatively high $g$-value ($2.294$) together with the broad linewidth points to defect-localized spins (vacancy/interstitial related), substantial defect density, and enhanced spin–spin interactions within a strained/disordered lattice environment.

Because $g$-values and broad linewidths in ZnO-based systems can reflect overlapping contributions and relaxation effects, ESR is interpreted here as complementary evidence for defect-related paramagnetic centers, without assigning a unique microscopic origin solely based on $g$-values.

Consistently, the defect chemistry inferred from PL is dominated by zinc interstitials (Znᵢ) and zinc vacancies ($V_{Zn}$) with contributions from oxygen-related centers (Oᵢ) is qualitatively consistent with the presence of a strong ESR signal arising from a defect-rich paramagnetic environment. The fact that $P_{asy}>1$ and the large $\Delta H_{pp}$ further suggest magnetic microstructural heterogeneity between surface and core regions and multiple relaxation channels in the nanoparticles, in line with the relatively high population of unpaired spins ($N_s$). Here, $N_s$ is reported as a relative estimate based on the adopted analysis expression and experimental conditions, and it is used for qualitative/within-study comparison rather than as an absolute calibrated spin concentration

Overall, ESR confirms a defect-rich and locally strained/disordered magnetic environment associated with paramagnetic defect centers induced by B incorporation, which, together with the PL violet/blue bands, support a scenario wherein B³⁺→Zn²⁺ substitution drives charge-compensation and size-mismatch mechanisms as the primary sources of defects, as shown in Figure 11 and Table 11.

3. Materials and Methods

3.1. Experimental Procedure

ZnO: 5%B nanoparticles were synthesized via a sol–gel route using zinc acetate dihydrate (Zn(CH₃COO)₂·2H₂O) and boric acid (H₃BO₃) as the zinc and boron sources, respectively. Methanol (CH₃OH) was employed as the solvent to ensure homogeneous precursor dispersion, while monoethanolamine (MEA, C₂H₇NO) acted as a chelating and stabilizing agent.

Stoichiometric amounts of each precursor were accurately weighed using an analytical balance to prepare $0.25$ M solutions in $100$ mL beakers containing Teflon-coated magnetic stir bars. The precursor solutions were mixed with $80$ mL of methanol and $1500$ μL of MEA, sealed with Parafilm to prevent premature solvent loss, and magnetically stirred at $300$ rpm for $24$ h under ambient conditions. After stirring was completed, the Parafilm was removed to allow controlled solvent evaporation, resulting in the formation of a viscous gel. The magnetic stir bars were removed prior to heat treatment to prevent extraneous contamination.

Thermal processing of the dried gels was carried out in a furnace following a two-step calcination protocol. The samples were first heated to $400$ °C for $10$ min to decompose residual organic species, and subsequently annealed at $600$ °C for $30$ min to promote crystallization of the ZnO: 5%B nanoparticles. The resulting powders were ground to achieve a uniform particle-size distribution.

3.2. Structural Analysis

X-ray diffraction (XRD; Rigaku (Tokyo, Japan), Cu Kα) was used to characterize the sample’s structure. Scanning electron microscopy (SEM; JEOL JSM-5910LV (Tokyo, Japan)) was employed to characterize the surface morphology, and photoluminescence (PL) spectroscopy (Agilent Cary Eclipse (Santa Clara, CA, USA)) was used to evaluate its optical characteristics. With conventional conditions ($5$ mW power, $0.03$ s time constant), magnetic characterization was accomplished using electron spin resonance (ESR) spectroscopy on a Jeol JES-FA300 (Tokyo, Japan) spectrometer running at $9.45$ GHz with a TE₁₀₂ cavity. A static magnetic field range of $0–1000$ mT was used to record ESR spectra. The background signal of the resonant cavity and the empty quartz sample tubes was subtracted from the data to increase accuracy.

4. Conclusions

In this study, ZnO: 5% B nanoparticles synthesized via the sol–gel method exhibited a single-phase wurtzite structure, and their crystal integrity was confirmed by XRD. Analysis of line broadening revealed that the average crystallite size was in the range of $32.37–39.63$ nm, while the microstrain was on the order of $2\times {10}^{-4}$. Moreover, the positive slopes in the Williamson–Hall plots indicated that tensile stresses were dominant. Optical measurements using the Kubelka–Munk/Tauc approach yielded a band gap of $E_g=3.216$ eV, which represents a slight narrowing compared to pure ZnO. This result supports the conclusion that B³⁺→Zn²⁺ substitution increases the density of edge states and enhances the band-tailing effect. Indeed, the Urbach energy ($E_u=184–193$ meV) is consistent with short-range bond distortions and localization effects.

Refractive index values calculated from five different $n\left(E_g\right)$ models ranged between $2.05$ and $2.71$, confirming the material’s potential for optoelectronic applications within the wide band gap/high refractive index window.

Gaussian deconvolution of the PL spectrum revealed that the violet (Znᵢ) and blue (V_Zn) bands were dominant, while the red (Oᵢ) contribution was relatively limited. This defect chemistry indicates an enrichment of zinc vacancy/interstitial centers as an inevitable consequence of charge compensation and size mismatch. ESR measurements exhibited a single, broad, and intense resonance line ($g=2.294,\Delta H_{pp}\approx 120.7$ mT), suggesting the predominance of paramagnetic defect centers and a high defect density.

Because B doping in ZnO efficiently affects the crystal–chemical defect landscape while subtly changing band-edge states and optical constants, it has potential use in transparent conducting films, electron transport layers in organic photovoltaics (OPVs), and UV photo detection.