Quantitative nanometer-scale characterization of densification in fused silica via s-SNOM

Abstract

Fused silica is extensively used across various industries due to its superior properties, but densification can significantly alter its performance. Detecting these changes requires high spatial resolution, which challenges the limits of current testing methods. This study explores the use of scattering-type scanning near-field optical microscopy (s-SNOM) to analyze densification in fused silica through a combination of experimental techniques—atomic force microscopy-based infrared spectroscopy (AFM-IR) and s-SNOM—and computational methods, including first-principles calculations and the finite dipole model (FDM). The findings reveal that near-field phase signals are more accurate than amplitude signals in reflecting changes in densification. Building on these results, a quantitative model for characterizing densification in fused silica is proposed. These findings are compared with the results from the literature and comparison results show good concordance. This study introduces a nanoscale range precise, nondestructive method for assessing densification, offering a novel and reliable approach for characterizing point defects in fused silica.

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Introduction

Fused silica is widely used in optical applications such as high-energy laser systems, laser communications, and photolithography due to its durability, thermal stability, and excellent ultraviolet transmittance.^1–6 However, the performance of optical components, including laser output and optical transmittance, can be compromised by internal damage.^7,8 Research shows that such damage is often linked to changes in the chemical structure, with densification frequently identified as a key factor leading to further chemical deterioration.^9,10 Among these, densification is often considered as the precursor that causes various types of chemical damage.¹¹ The loosely packed atomic structure of fused silica makes it particularly susceptible to densification under external pressure. While processing methods like grinding and polishing can reduce surface densification, subsurface damage remains a challenge, impacting the overall performance of optical components.¹² Thus, accurately characterizing densification is crucial for maintaining the integrity and effectiveness of these components.

Characterization of densification is a long-standing issue. Taylor first conducted a study on the plastic deformation of optical glass.¹³ Theoretical models, such as strain-field analytical models and elliptical constitutive models, have been used to analyze and predict the densification of fused silica from the perspective of densification evolution and formation mechanisms.^14–16 Finite element methods have also been used to evaluate densification.¹⁷ However, current models and finite element studies are mostly based on analysis and prediction results under certain assumptions. Additionally, molecular dynamics has also been employed to characterize densification as a micro-scale analytical method.¹⁸ However, the accuracy of the obtained results was also limited. Many studies have also focused on the experimental characterization of densification. Spectroscopic methods, such as Raman spectroscopy, have been used to assess the local densification behavior of fused silica under nanoindentation.¹⁹ However, the accuracy of Raman-based densification assessment was significantly limited if the experimental configurations do not match the indentation parameters.²⁰ This limitation is because the resolution of Raman spectroscopy is restricted by factors such as the incident laser wavelength, laser spot diameter, and numerical aperture (NA) of the objective lens. Consequently, there is a significant need for a high-precision method for characterizing the densification of fused silica.

In recent years, s-SNOM has been demonstrated to be effective for characterizing the surface and subsurface microstructures of materials such as fused silica and single-crystal silicon.^21–25 It offers high chemical sensitivity and spatial resolution at the nanoscale level. Huber et al.²⁶ used near-field infrared light to detect the local strain field of silicon carbide crystals for the first time based on the nanoindentation method, which demonstrated the sub-surface detection capability of SNOM. Additionally, He et al.²⁷ demonstrated the feasibility of combining s-SNOM with reactive molecular dynamics to explain the chemical structural changes in silica glass under nanoindentation and nanoscratch. However, previous research mainly analyzed the SNOM signal by directly comparing the results obtained by other measurement methods or analysis methods and did not directly start from the analysis of the near-field signal to quantify the relationship between the referenced SNOM signal and the subsurface structure change. In particular, there is a lack of quantitative analysis of subsurface structures.

In this work, the densification of fused silica under nanoindentation was characterized through near-field optical experiments. First-principles calculations were used to analyze the causes of the near-field optical response linked to densification, revealing the connection between the optical response and the degree of densification in fused silica. A quantitative model was developed to characterize densification based on the near-field phase. The findings help differentiate between various nanoscale defects, improve our understanding of how densification impacts the optical component performance, and provide guidance for refining processing techniques.

Methods

Sample preparation

Corning 7980 fused silica with dimensions of 20 mm × 20 mm × 1 mm was used as the sample. The nanoindentation experiments were conducted using a standard diamond berkovich indenter. Nanointendation experiments were conducted using a nano-indenter tester at room temperature with a relative humidity of 40%. Both loading and unloading rates were set to 50 μm s⁻¹, and the hold time was 15 seconds. Different indentation loads were applied to investigate the relationship between the degree of densification under indentation and the near-field optical signal. The loads of 500 mN, 300 mN, and 250 mN were selected for the comparative indentation experiments in this paper respectively. Nine indentation tests were conducted on the same sample under the same conditions to ensure repeatability. The samples were subsequently annealed at 1000 °C. The temperature was maintained for 2 hours, followed by slow cooling in the furnace at a rate of 5 °C min⁻¹ to room temperature.

AFM-IR and s-SNOM setups

Nanoscale infrared spectroscopy and near-field optical experiments were performed using a NanoIR2S system (Bruker). The schematic diagram of the experimental setup is shown in Fig. 1a. This system facilitates both AFM-IR and s-SNOM measurements, allowing simultaneous acquisition of morphological information during the measurement process. For the AFM-IR measurements, the probe (PR-EX-TnIR-A-10, ANASYS) was operated in contact mode with a cantilever tip radius of 30 nm and a force constant of 5 N m⁻¹. The natural frequency of the probe is ω₁ (75 kHz). The IR laser is focused on a metal-coated AFM tip. As shown in Fig. 1b, the sample absorbs the incident laser to generate a local thermal expansion, employing mid-IR tunable quantum cascade lasers (Daylight Solutions, Inc.). This expansion exerts a mechanical force on the cantilever which was converted into an optoelectronic signal by a four-quadrant photodetector. The measurement range spans from ∼950 cm⁻¹ to ∼1220 cm⁻¹, with a spectral data resolution of 2 cm⁻¹. Measurements were taken at seven positions on each indentation, with 50 measurements averaged at each position to ensure accuracy. A consistent distance between each measurement point was maintained to mitigate the effects of unavoidable thermal drift during the detection process of AFM-IR.

Fig. 1 (a) Schematic diagram of equipment; (b) schematic diagram of AFM-IR; (c) schematic diagram of s-SNOM.

Fig. 1c presents the schematic diagram of the s-SNOM setup, which operates by probing the evanescent field at the sample surface. For s-SNOM measurements, the probe (PR-EX-SNM-A-10, ANASYS) was operated in tapping mode with a cantilever tip radius of 30 nm and a force constant of 42 N m⁻¹. The probe vibrates at a frequency of ω₂ (250 kHz). The probe acts as a scattering medium of the near-field optical signals. Background noise suppression is performed using pseudo-external difference interferometry. A lock-in amplifier demodulates the signal at the nΩ frequency of the cantilever oscillation at the nth harmonic to obtain the near-field amplitude (S) and phase signals (φ). Throughout this work n = 3. The resolution of the s-SNOM image was 256 × 256, and the size of the measurement area was determined according to the size of the indentation.

Details of first principles calculations

First-principles calculations were performed based on density functional theory (DFT) and the Cambridge Serial Total Energy Package (CASTEP) code. The model contains twelve O atoms and six Si atoms. The initial lattice model parameters are α = β = γ = 90°, a = 8.50436 Å, b = 4.910 Å, c = 5.402 Å. Models with different degrees of densification were obtained through geometrical optimization. The plane-wave basis set with an energy cut-off of 500 eV was applied. The generalized gradient approximation (GGA) and Perdew–Burke–Ernzerhof (PBE) were used to calculate the interaction between silicon and oxygen. Ultrasoft pseudopotentials were used to represent the interactions between the valence electrons and ionic core. The BFGS algorithm was used for the geometry optimization calculations. The k-point meshes in the Brillouin zone were constructed using the Monkhorst–Pack method.²⁸ The energy threshold was set to 1.0 × 10⁻⁵ eV per atom, the maximum force threshold was 0.03 eV Å⁻¹, the maximum stress threshold was 0.05 GPa, the maximum displacement threshold was set to 0.001 Å, and the self-consistent field tolerance (SCF tolerance) was set to 1.0 × 10⁻⁶ eV per atom.

Results and discussion

Fig. 2a shows the morphology of the 250 mN indentation. AFM-IR measurements were conducted at multiple positions of the indentation, as shown in Fig. 2a. The measurement points of AFM-IR were uniformly distributed, ranging from the fused silica substrate to the center of the indentation. In total, seven positions were measured, with four of these inside the indentation. These four positions were selected to represent varying degrees of glass densification under pressure.

Fig. 2 AFM-IR spectra at different positions of the indentation; (a) indentation morphology and measurement location diagram; (b) AFM-IR spectra.

Fig. 2b shows the AFM-IR measurement results at different measurement points. All spectral data were normalized and sorted by measurement positions. From the substrate to the deepest part of the indentation, the primary Si–O stretching bands in the AFM-IR spectra exhibited negligible redshifts or blueshifts. This suggests that the structural changes caused by nanoindentation did not significantly alter the chemical composition or infrared absorption properties. These structural changes cannot be characterized by infrared spectroscopy. The amplitude spectra of AFM-IR revealed three main peaks at ∼1070 cm⁻¹, ∼1170 cm⁻¹, and ∼1200 cm⁻¹. The ∼1070 cm⁻¹ band is attributed to the asymmetric stretching of Si–O–Si (bridging oxygen, BO), and the ∼1170 cm⁻¹ and ∼1200 cm⁻¹ bands are typically LO mode, which is mainly influenced by the incident angle of the laser rather than the internal vibration modes of fused silica.^29,30 Notably, the amplitude spectrum intensity of the ∼1070 cm⁻¹ band is significantly stronger than that of the other bands. As a typical amorphous material, fused silica has a low atomic packing density. Under external stress, the densification process is frequently accompanied by asymmetric stretching, such as a decrease in the Si–O–Si bond angles and elongation of Si–O bonds. Due to its inorganic and non-metallic properties, fused silica exhibits a relatively weak dipole excitation effect with a metal-coated probe, resulting in a very weak near-field response. Therefore, the strongest infrared response at the ∼1070 cm⁻¹ band was chosen to describe the densification process of fused silica.

The s-SNOM signal is derived by analysing the interaction among three factors: the probe, the sample, and the incident light. The fluctuation of the morphology will influence the coupling between the incident light and the other two factors, which will have a significant impact on the obtained near-field signal. Consequently, many studies employing s-SNOM to investigate subsurface information focused on planar samples, which are conducive to obtaining more stable near-field signals.^31,32 To study the densification effects induced by indentation, the applied indentation load should be carefully controlled and kept within an optimal range. Excessive load will result in a significant residual depth of indentation and micro cracks. The large residual depth can lead to a light shielding. Cracks may cause the probe to lose contact with the sample during scanning, thereby extending the near-field interaction of the probe into the surrounding air. This will have a great impact on the accuracy of the obtained s-SNOM signal. At the same time, the indentation load should not be too small. Since fused silica is an inorganic amorphous oxide, the near-field signal generated by the incident light is inherently weak. A load that is too small will result in a densified region that is insufficiently large, preventing a clear contrast ratio between the indentation and the surrounding substrate. In addition, the demodulation of the third-order harmonic signal during the experiment further reduces the signal strength, making it even more challenging to obtain reliable results.

In short, an appropriate indentation load should be selected to ensure a smooth morphological transition and to avoid drastic changes, and the depth of the indentation should be controlled at the nanometer scale to avoid the shading effect and morphology re-reflection caused by excessive depth. At the same time, it is also necessary to ensure that the contrast ratio of the densification and the substrate region can be clearly reflected. Consequently, this study primarily focuses on the s-SNOM signals of indentation with a load no more than 500 mN. Within this load range, the fluctuation of the topography will not affect the near-field optical signal and the correlation analysis is discussed in Fig. 3.

Fig. 3 Near-field amplitude and phase diagrams before and after annealing of 250 mN indentation at 1070 cm⁻¹. (a) and (b) show the morphology; (d) and (e) show the amplitude; (g) and (h) show the phase; (c), (f), and (i) show the comparison of the morphology, amplitude, and phase before and after annealing along the dotted line, respectively.

Fig. 3 illustrates the morphology, near-field amplitude and phase images of a fused silica indentation created under a pressure of 250 mN at ∼1070 cm⁻¹. To verify that the observed near-field response is due to structural changes from densification, annealing experiments were conducted on the indentation. Since densification in fused silica can be fully reversed at the right annealing temperature, the morphology before and after annealing are shown in Fig. 3a and b and compared in Fig. 3c. Post-annealing, the morphology shows significant changes, with the material flowing and accumulating at the indentation edges while maintaining a trigonal geometry, indicating the reversal of densification. The amplitude and phase signals obtained by s-SNOM need to be referenced to accurately reflect the relative changes of the signals. Since this study considers the near-field optical response of densification, which mainly reflects the changes in the properties of the material relative to the original state, the amplitude and phase of indentation were calibrated with reference to the signal from the fused silica substrate without defects after etching. The amplitude, as shown in Fig. 3d, decreases steadily from the edge to the center of the indentation, reaching its lowest point at the deepest part. This change is attributed to subsurface microstructural alterations caused by the indentation process. In contrast, Fig. 3g shows that the phase varies in the opposite direction, with a shift of up to 70° from the edge to the center. Fig. 3f presents the near-field amplitude results before and after annealing. The amplitude within the indentation after annealing shows abrupt changes over a small area, with no distinct pattern. However, Fig. 3i shows that the phase contrast between the indentation and the surrounding substrate nearly disappears after annealing. Meanwhile, the results of the morphology, amplitude, and phase after annealing show that even if the morphology fluctuates greatly, it will not be reflected in the s-SNOM signal, indicating that the choice of indentation load in this study is appropriate. The indentation data after etching in the ESI† also prove that the morphology has little effect on the SNOM signal. These findings suggest that the near-field amplitude and phase responses primarily reflect the densification phenomenon of fused silica. However, the phase variation provides a more accurate and clear indication of the degree of densification than amplitude variations.

Fig. 4 displays the morphology and near-field phase of the indentations subjected to varying pressures. As the load increased from 250 to 500 mN, the morphology changed significantly, as the indentation depth increased from 719 to 970 nm. However, the near-field phase signal inside the indentations did not show the same phenomenon as that observed in the morphology. The near-field phase of the indentations increases slowly, but remains consistently around 70°. This occurs because the hydrostatic pressure at the bottom of the indentation reaches the maximum limit with a berkovich indenter, capping the degree of densification at around 18%, regardless of the applied pressure at the deepest part of the indentations.¹⁷ This further suggests that near-field phase measurements can effectively reflect the degree of densification.

Fig. 4 Morphology and near-field optical phase results of indentation with different pressures.

In order to obtain models with different densification degrees for first-principles calculations, the degree of densification at different positions of the 250 mN indentation was preliminarily obtained by Raman spectroscopy. Fig. 5a illustrates that as the distance from the center decreases, the peak shift of the D2 band relative to the original position gradually increases, corresponding to an increase in the degree of densification.^33,34 The degree of densification at different positions is obtained as 5.86%, 10.88%, and 15.02%. In the subsequent first-principles calculations, models with different degrees of densification were established based on the values obtained by Raman spectroscopy.

Fig. 5 (a) Raman spectra at different positions; (b) the real and imaginary part of the dielectric constant of fused silica with different degrees of densification; (c) schematic diagram of the point dipole model; (d) schematic diagram of the finite dipole model; (e) comparison of the phase between experimental and calculated results; (f) comparison of the degrees of densification between the 250, 300, and 500 mN indentation calculated from the quantitative relationship model and the 300 mN indentation of the literature.

The change in the dielectric constant was determined through first-principles calculations. By applying varying pressures, the lattice parameters of the model gradually decreased, leading to optimized structures with different degrees of densification. The degrees of densification were obtained from the results of Raman experiments. Fig. 5b shows the relationship between the degree of densification and the real and imaginary parts of the optical dielectric constant calculated from the fused silica models. As densification increases, the real part of the dielectric constant changes almost linearly, with a maximum change rate of just 6%. In contrast, the imaginary part exhibits exponential growth: it increases slowly by 2% as densification rises from 0% to 5.8%, but experiences a rapid increase of 170% when densification goes from 5.8% to 18.48%. This suggests that the near-field optical response to densification is primarily driven by the absorption changes related to the imaginary part of the dielectric constant.

To investigate the relationship between the s-SNOM signal and changes in dielectric constant due to densification, it is necessary to employ a mathematical model that accurately describes the interaction between the incident light, the sample, and the probe.³⁵ Among the commonly used models are the finite dipole model, which approximates the probe as an elongated and conductive spheroid, and the point dipole model, which treats the probe as a conductive sphere with radius R. Simplified models of PDM and FDM are shown in Fig. 5c and d. Although the mathematical calculation of FDM is more complicated than that of PDM, it can provide a more accurate simulation of the interaction between the probe and the semin-infinite sample within the quasistatic approximation. Particularly in the field of infrared illumination, it is often used to establish the relationship between the dielectric constant of the sample and the s-SNOM signal.^21,35 While PDM simplifies the number of parameters in the model and the process of mathematical calculation, it also compromises accuracy. Therefore, in this study, FDM was employed as an inversion procedure to establish the relationship between the dielectric constant and the s-SNOM signal. The AFM tip is simplified as a conductive spheroid in the FDM. To enhance the accuracy of signals obtained using FDM and to suppress the influence of background noise, high-order harmonic demodulation is applied to the near-field signal. The method is to take n_th Fourier coefficients at time t to obtain n_th demodulation scattering coefficients.³⁵ The details are described in the ESI.† FDM shows that when light illuminates the tip and sample, the near-field optical response is mainly caused by the change of the dielectric constant of the material.³⁶ When densification occurs, changes in the atomic structure of the material affect the movement of electrons within the atoms, leading to variations in the dielectric constant under laser excitation at different wavelengths. Therefore, the near-field optical response can be characterized by calculating the dielectric constant for different densification models.

Fig. 5e shows the phase results calculated by incorporating the dielectric constants into the FDM, alongside the experimentally obtained phase results inside the 250 mN indentation. As the distance from the indentation center increases, the phase gradually decreases and the trend of the calculated phase is very consistent with the experimental trend. However, the trends of the experimental and calculated results of amplitude differ significantly. The calculation results of amplitude are described in detail in the ESI.† These results also confirm the conclusion in Fig. 3 that the phase can better reflect the degree of densification than the amplitude.

The consistency of near field phase results indicates that there is a correlation between the experimental and calculated near-field phases during the densification process of fused silica, and the relationship is established through the change in the dielectric constant. Densification alters the dielectric constant, which in turn affects the near-field optical signal. Both computational and experimental results suggest that the near-field phase is a more accurate indicator of densification than amplitude. Thus, it is reasonable to establish a correlation between the near-field phase and the degree of densification in fused silica. Based on the theoretical calculations and experimental results, this relationship can be expressed as:

D = 5.8 exp(0.16φ) − 5.2 exp(−0.12φ),

where D is the degree of densification and φ is the near-field phase obtained experimentally.

Fig. 5f illustrates the degree of densification calculated by the empirical formula at various distances from the center for indentations with loads of 250, 300, and 500 mN. Additionally, recent results from Raman characterization of densification, as reported in the literature,²⁰ are included. The cited study focused on a 300 mN berkovich indentation, where the maximum densification reached 18.1%. This maximum is constrained by the inherent hydrostatic pressure limit of the berkovich indenter,¹⁹ capping the densification at approximately 18%. For the indentations with 500, 300, and 250 mN loads, the observed maximum degrees of densification were 18.6%, 17.2%, and 16.8%, respectively. It is worth noting that only the maximum densification degree of 500 mN indentation is close to 18%, while the other two are below the 18% limit. This discrepancy is due not only to significant errors in the edge data during the parameter fitting process. A more influential factor is the average effect over a large measurement area, since the maximum degree of densification occurs only on a very small scale. Despite this, the method remains effective for assessing densification in regions as small as a few tens of nanometers. As the distance from the center of the indentation increases, the degree of densification decreases progressively across different pressure levels. The trend of densification with distance from the indentation center is nonlinear.³⁷ The downward trends all show a slow, then fast, and finally slow phenomenon. At an equivalent distance from the center, the 300 mN indentation shows lower densification than the 500 mN indentation but higher than the 250 mN indentation. This is consistent with the observed densification behavior. For the 300 mN indentation, the results of the literature align well with the calculated results. Although there are some gaps in the densification assessment data at each point, the gaps are within the margin of error. Therefore, it is reasonable to characterize the degree of densification of indentation through the above relationship.

The empirical formula was fitted using exponential function with two number of terms due to the fact that the near-field phase and the near-field scattering intensity σ are exponentially related. Densification has a direct impact on the near-field scattering intensity σ. Since the degree of densification is a relative value that reflects the change in the structure of the material relative to the initial state, the difference between the two exponential terms was chosen to describe the densification. This method is well-suited for fitting complex curved shapes with few variables and the SSE and RMSE of the fitting function obtained in this way are the smallest compared to other fitting. The parameters of the empirical formula will change in different applications. The reason is that the fitting process is established by considering the densification phenomenon under different conditions and combining the calculation results of the dipole model, which takes into account the influencing factors such as the tip radius, tip material, and vibration frequency. However, the method for determining the parameters is universal. According to the method in this article, the fitting parameters under different conditions can be obtained to achieve quantitative characterization of densification.

Conclusions

In summary, the densification characteristic of fused silica was quantitatively described for the first time based on the near-field phase signal of s-SNOM. By combining near-field optical experiments, first-principles calculations and a theoretical model, the relationship between near-field optical responses and densification was analyzed. The findings show that the near-field signals observed at the indentation sites are due to densification, and the near-field phase is the important factor in accurately reflecting the densification changes. A quantitative relationship between the near-field signal and the degree of densification is established, achieving high-resolution characterization with a lateral resolution of tens of nanometers. This approach provides a novel, high-resolution, non-destructive method for detecting structural changes in fused silica, offering valuable insights for optimizing its manufacturing processes.

Author contributions

The project was conceived and co-ordinated by Ying Yan and Bo Jiang. s-SNOM data were acquired and analyzed by Bo Jiang. The calculations were performed by Qing Mu. The data were analyzed by Ping Zhou and Bo Jiang. All authors discussed the results and contributed to writing the manuscript.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article. The raw data are available from the corresponding author upon reasonable request.

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

The authors appreciate the financial support from the National Key Research and Development Program of China (No. 2019YFA0709102, 2020YFA0714502).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4nr05309e

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