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Article

Stress Compensation in TiO2/SiO2 Optical Coatings by Manipulating the Thickness Modulation Ratio

by
Bo Wang
1,2,
Taiqi Wu
1,2,
Weidong Gao
1,2,
Gang Hu
1,2 and
Changjun Wang
1,2,3,*
1
State Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China
2
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China
3
Chinese Academy of Sciences, Beijing 100039, China
*
Author to whom correspondence should be addressed.
Coatings 2025, 15(7), 848; https://doi.org/10.3390/coatings15070848 (registering DOI)
Submission received: 30 June 2025 / Revised: 15 July 2025 / Accepted: 17 July 2025 / Published: 19 July 2025
(This article belongs to the Section Thin Films)
Browse Figures
Versions Notes

Abstract

With the rapid advancement of high-precision optical systems, increasingly stringent demands are imposed on the surface figure accuracy of optical components. The magnitude of residual stress in multilayer films directly influences the post-coating surface figure stability of these components, making the control of multilayer film stress a critical factor in enhancing optical surface figure accuracy. In this study, which addresses the process constraints and substrate damage risks associated with conventional annealing-based stress compensation for large-aperture optical components, we introduce an active stress engineering strategy rooted in in situ deposition process optimization. By systematically tailoring film deposition parameters and adjusting the thickness modulation ratio of TiO2 and SiO2, we achieve dynamic compensation of residual stress in multilayer structures. This approach demonstrates broad applicability across diverse optical coatings, where it effectively mitigates stress-induced surface distortions. Unlike annealing methods, this intrinsic stress polarity manipulation strategy obviates the need for high-temperature post-processing, eliminating risks of material decomposition or substrate degradation. By enabling precise nanoscale stress regulation in large-aperture films through controlled process parameters, it provides essential technical support for manufacturing ultra-precision optical devices, such as next-generation laser systems and space-based stress wave detection instruments, where minimal stress-induced deformation is paramount to functional performance.

1. Introduction

Optical films, as critical components in laser systems, optical instruments, and microelectronic devices, are fundamental to the stable and reliable operation of complex optoelectronic systems [1,2]. Among the key factors governing their durability and functional integrity, residual stress [3,4], encompassing thermal and intrinsic stress, plays a pivotal role. These stresses not only induce substrate deformation, thereby perturbing light wave transmission characteristics and compromising system performance, but also instigate detrimental phenomena such as cracking and delamination, leading to catastrophic film failure [5,6,7]. Consequently, the systematic investigation of optical film stress is essential for enhancing coating reliability, driving advancements in optical engineering, and enabling their broader integration into industrial applications. Such research underpins the development of high-performance optical technologies, ensuring their suitability for demanding environments in modern optoelectronic systems.
In recent decades, researchers have conducted extensive research on film stress. Nishikawa [8] and Robic [9] employed ion-assisted deposition (IAD) [10,11] to characterize the stress behavior of SiO2 and TiO2 films, respectively, identifying dominant compressive stress that posed significant challenges for regulation. Zhang Jinsheng et al. [12] systematically analyzed the influences of SiO2 film thickness and deposition rate on residual stress. Shao Shuying [13,14] innovatively integrated macroscopic stress measurement with microscopic structural analysis to investigate the origins of stress in ZrO2/SiO2 single-layer systems. Scholars such as Shen Yanming [15,16,17,18] explored the microstructural mechanisms of materials, including HfO2, SiO2, and ZrO2, revealing correlations between process parameters (e.g., packing density, oxidation degree, crystallinity) and stress behavior. They achieved precise control of multilayer stress by optimizing the HfO2/SiO2 thickness modulation ratio and oxygen partial pressure.
Additionally, prior studies exploited the opposing stress responses of Ta2O5 (tensile) and SiO2 (compressive) after annealing, achieving stress balance in multilayer Ta2O5/SiO2 by alternating tensile–compressive stress layers [19,20,21]. However, this annealing-dependent approach is impractical for large-aperture components: elevated temperatures may induce material decomposition, oxidation, or irreversible substrate damage. In situ tuning of stress polarity via deposition parameter optimization could be a more promising strategy [22,23,24], eliminating the need for post-deposition thermal treatment. By adjusting deposition parameters (such as substrate temperature and deposition rate), stress with opposite polarities can be induced in high- and low-refractive-index materials. Furthermore, by tuning the thickness ratio of the materials, alternating stress-compensating structures can be constructed [25,26,27,28,29,30,31]. This non-thermal approach circumvents the thermal risks associated with large-scale components, offering a scalable solution for achieving engineering-level stress uniformity. This hinges on deciphering the quantitative relationship between processing parameters and stress behavior to establish a predictive, non-thermal, stress regulation framework, thereby expanding the applicability of multilayer stress management across diverse optical systems [32,33,34].
In this study, we investigated the effects of process parameters on the residual stress of SiO2 and TiO2 films. Leveraging the complementary stress polarities (compressive vs. tensile) inherent in these materials, we developed a systematic optimization framework for deposition conditions to design the stress profiles of single-band TiO2/SiO2 high-reflection films. Specifically, through precise adjustment of the thickness modulation ratio between high- and low-refractive-index materials, we successfully fabricated low-stress, high-reflectivity coatings. Subsequent investigations into multi-band film systems further validated the transferability and reproducibility of these stress modulation ratios across diverse optical configurations. Addressing the process limitations and substrate damage risks associated with the traditional annealing stress compensation method in the application of large-aperture optical components, as well as the issue where backside coating for stress compensation is not permissible on certain substrates, this paper presents an active stress regulation strategy based on preparation process optimization. Dynamic compensation of residual stress is achieved through systematic optimization of thin-film deposition conditions.

2. Materials and Methods

All films were deposited on fused silica substrates (φ50 mm × 2 mm) using an H4411II-1 deposition system (SDIC Nanguang Technology Co., Ltd., Chengdu, China) comprising two electron guns and a Veeco ion source. Prior to deposition, the substrates underwent sequential manual cleaning with ethanol and acetone in a standard laboratory environment, followed by argon plasma treatment via ion source within the vacuum chamber to remove residual contaminants. For SiO2 film deposition, 99.99% pure SiO2 pellets (Merck, Darmstadt, Germany) served as the evaporation material. TiO2 films were synthesized using 99.99% pure Ti3O5 particles (Merck, Darmstadt, Germany) as the evaporation source, with high-purity oxygen introduced during deposition to optimize film stoichiometry. The substrates were rotated in a planetary motion to ensure thickness uniformity [35,36], while a quartz crystal monitor enabled real-time tracking of the deposition rate and film thickness. The chamber base vacuum was maintained at ≤2 × 10−4 Pa. Detailed characteristics of the deposited SiO2 films are summarized in Table 1.
The transmittance of the SiO2, TiO2, and multilayer films was measured across the 400–1500 nm wavelength range using a PerkinElmer Lambda 1050 spectrophotometer (PerkinElmer Inc., Waltham, MA, USA). By fitting the measured transmission spectra, we obtained an excellent fitting curve that agreed well with the experimental results and also determined the thickness and refractive index of the film. The reflectance of the multilayer film was measured using a Cary 5000 UV-Vis spectrophotometer (Agilent Technologies Inc., Santa Clara, CA, USA). The surface morphology and root-mean-square (RMS) roughness of the films were characterized using a CSPM5500 atomic force microscope (AFM, Being Nano-Instruments, Guangzhou, China), with 256 × 256-point sampling over a 2 μm × 2 μm area. RMS values were obtained by averaging measurements from three randomly selected surface regions. The crystalline phase of the SiO2 and TiO2 films was analyzed using an X’Pert3 Powder X-ray diffractometer (XRD, PANalytical, Almelo, The Netherlands). Measurements were performed in the 2θ range of 10–70°, with a 0.1° step size, using Ni-filtered Cu Kα radiation (λ = 0.154178 nm, 30 kV, 30 mA). Finally, the film stress of TiO2 and SiO2 was evaluated using a TYYGO laser interferometer (TYGGO Optoelectronic Technology Co., Ltd., Chengdu, China) by measuring substrate curvature variations before and after deposition at the He-Ne laser wavelength (632.8 nm). The interferometer achieved a surface flatness measurement accuracy better than λ/100.

3. Results and Discussion

3.1. SiO2 Single-Layer Coatings

We first investigated the influence of SiO2 film thickness on residual stress. Figure 1a displays the XRD patterns of the SiO2 films with varying thicknesses. No distinct diffraction peaks were observed, indicating that the IAD-prepared SiO2 films exhibit an amorphous structure at the substrate temperature of 150 °C [37]. XRD patterns for the SiO2 films under alternative deposition conditions and the single-layer TiO2 films are provided in Supplementary Material S1, all of which also confirm amorphous characteristics. Figure 1b shows the transmission spectra of the SiO2 films with different thicknesses. Surface topography measurements of the samples were subsequently conducted. According to the Stoney formula:
σ residuary = E s 6 ( 1 − ν s ) t s 2 t f ( 1 R 2 − 1 R 1 ) = 4 E s 3 ( 1 − ν s ) t s 2 Δ P o w e r t f D s 2
we calculated the residual stress of the SiO2 single-layer, in which E s and ν s are the Young’s modulus and Poisson’s ratio of the substrate [38]; t s and t f are the thicknesses of the substrate and film; R 1 and R 2 are the radii of curvatures of the substrate before and after coating, Δ P o w e r is the difference in power reflected wave-front mapping before and after coating, and D s is the diameter of the substrate. In our experiment, fused silica substrates with a thickness of 2 mm and a diameter of 50 mm were employed. The large diameter-to-thickness ratio of the substrates amplified the measurable curvature changes, enhancing experimental sensitivity. The Young’s modulus and Poisson’s ratio of the fused silica were fixed at 72 GPa and 0.17, respectively.
It is worth noting that films deposited via electron beam evaporation typically exhibit columnar microstructures, where voids between columnar grains allow atmospheric water molecules to penetrate the film’s interior and adsorb onto column surfaces, inducing time-dependent stress evolution [39,40,41]. To account for this, samples were stored in a controlled laboratory environment for at least 1 month prior to stress measurements. All stress data reported herein correspond to the stabilized state.
Figure 1c illustrates the variation in residual stress of the SiO2 films with thickness. All samples exhibited negative (compressive) stress, with the magnitude decreasing as film thickness increased. This trend can be attributed to microstructural evolution during deposition: at initial film growth, the interface with the substrate dominates, characterized by high defect density, small grain size, and strong substrate-induced constraints, leading to elevated interfacial and growth-related compressive stress. As deposition progresses, grain coarsening occurs, and the influence of the substrate interface diminishes, allowing stress relaxation through reduced structural constraints. Consequently, the gradual thickening of the film correlates with a decreased stress magnitude, reflecting a transition from interface-dominated to growth-dominated stress mechanisms [42,43,44].
To validate the aforementioned hypothesis relating film thickness to stress evolution, atomic force microscopy (AFM) was used to characterize the surface morphologies of samples with varying SiO2 thicknesses, as depicted in Figure 2. For the 100 nm thick SiO2 film, the microstructure exhibits smaller grain sizes, whereas progressive thickening of the film correlates with gradual grain coarsening, as evident from the AFM images (Figure 2a for 100 nm; Figure 2b for 300 nm and Figure 2c for 800 nm). A quantitative analysis of surface roughness, summarized in Figure 2d, reveals that the RMS roughness of the single-layer SiO2 films increases monotonically with thickness: from 0.84 nm for the 100 nm thick film to 2.08 nm for the 1000 nm thick film. These observations are in good agreement with the stress measurement results. As thickness increases, the grain size grows and roughness increases, which indicates that the reduction in interfacial constraints and the enhancement in structural relaxation lead to a decrease in compressive stress.
Subsequently, similar tests were conducted on SiO2 films with varying substrate temperatures and deposition rates. Figure 3a,d present the residual stress data for the SiO2 films as functions of substrate temperature and deposition rate, respectively. Notably, the compressive stress in the SiO2 films increases with rising substrate temperature. This phenomenon is primarily attributed to the enhanced surface mobility of incident particles at higher temperatures, which improves film packing density. Generally, a positive correlation exists between film packing density and compressive stress: the higher the packing density, the greater the compressive stress. As documented in the literature, the packing density q of a film exhibits a linear relationship with its refractive index n , described by [45]:
n = n g + q ( n s − n g )
where n g is the refractive index of the void part of the film and n s is the refractive index of the solid part of the film. Spectroscopic ellipsometry was used to measure the refractive index of the samples at different temperatures. The results show a monotonic increase in the refractive index with deposition temperature, as shown in Figure 3b, indicating that higher-temperature deposition yields SiO2 films with greater packing density. This conclusion is further supported by the AFM roughness measurements in Figure 3c, as the films deposited at higher temperatures exhibit lower surface roughness.
The residual stress of the SiO2 films shows significant dependence on the deposition rate. As shown in Figure 3d, compressive stress decreases monotonically with an increasing deposition rate. This behavior arises from differences in atomic migration dynamics and structural evolution during film growth: at low deposition rates, the mobility of adsorbed atoms on the substrate surface is limited, allowing a higher influx of ambient oxygen molecules into the growing film. A sufficient reaction between deposited Si atoms and oxygen leads to a disordered, amorphous structure with a smooth, dense surface morphology, which are conditions that promote significant compressive stress due to restricted atomic rearrangement. As the rate increases moderately, the film transitions to a shaggy state, accompanied by a roughened surface and a notable decrease in packing density. The reduced atomic interdiffusion and looser structural packing result in a decline in compressive stress, as the lattice accommodates fewer trapped oxygen species, which is consistent with the results of refractive index shown in Figure 3e. Further increasing the deposition rate maintains the film’s stress; the stress values stabilize and become rate-insensitive, consistent with the AFM measurements of surface roughness in Figure 3f, which show minimal variation under high-rate deposition.

3.2. TiO2 Single-Layer Coatings

We further investigated the factors influencing stress in TiO2 monolayer films. TiO2 films were fabricated under varying substrate temperatures and deposition rates, their surface morphologies were characterized, and film stress values were calculated using the Stoney formula, as shown in Figure 4a,b. Unlike the SiO2 films, which inherently exhibit compressive stress, the stress of the TiO2 films deposited on quartz substrates could be tuned to tensile stress through the optimization of deposition conditions.
It is obvious that the TiO2 film displays compressive stress at a deposition rate of 1 Å/s; as the rate increases to 2 Å/s, the stress transitions to tensile and increases monotonically with further rate elevation—a behavior analogous to the stress evolution in the SiO2 films (Figure 3d). This trend arises from structural densification effects: lower deposition rates facilitate more complete atomic rearrangement, yielding denser films with higher compressive stress due to constrained lattice expansion. Conversely, increasing the evaporation rate reduces atomic mobility, leading to a gradual decrease in film packing density. This structural loosening diminishes compressive stress and eventually induces tensile stress as kinetic limitations disrupt ideal stoichiometric bonding and lattice coherence.
The temperature-dependent stress behavior of the TiO2 films differs markedly from that of the SiO2 films. As illustrated in Figure 4b, at a deposition temperature of 100 °C, the film exhibits 79 MPa of residual tensile stress. Increasing the temperature to 150 °C drives a gradual rise in tensile stress to 120 MPa, whereas further heating to 200 °C reduces the stress to 42 MPa. This non-monotonic response implies the coexistence of two competing stress-generating mechanisms: thermal stress and densification-induced stress.
Thermal stress arises from the coefficient of thermal expansion (CTE) mismatch between the film and substrate, while densification-induced stress stems from atomic packing efficiency during growth. For TiO2 films, thermal stress manifests as tensile stress due to TiO2’s higher CTE (∼9 × 10−6 K−1) [46] compared to quartz (∼0.55 × 10−6 K−1). Below 150 °C, the increase in tensile stress with temperature reflects thermal stress dominance; elevated temperatures amplify the CTE mismatch, exacerbating tensile stress from differential thermal contraction upon cooling.
Conversely, above 150 °C, the decline in tensile stress indicates a shift to densification-induced compressive stress dominance. Higher temperatures enhance atomic surface mobility, promoting denser film packing and reduced defect density. This structural densification introduces compressive stress, which progressively counteracts the thermal tensile component. The inflection at 150 °C marks the crossover point where densification effects surpass thermal stress contributions. This temperature–stress inflection is absent in the SiO2 films because their thermal stress is practically negligible (owing to SiO2’s lower thermal expansion coefficient relative to quartz), overshadowed by densification effects across the studied temperature range. These results are corroborated by the surface morphology and roughness measurements of the TiO2 samples, with detailed data presented in Supplementary Material S2.

3.3. Multilayer Coatings

Through the above experiments, we determined the stress response of single-layer SiO2 and TiO2 films to deposition temperature and rate. The SiO2 films consistently exhibit compressive stress, whereas the TiO2 films display tensile stress under the tested conditions. For optical coatings composed of alternating high- and low-refractive-index materials (such as high-reflection or anti-reflection films), this complementary stress polarity enables systematic stress compensation in multilayer structures.
However, the residual stress in a multilayer film is not merely the simple algebraic sum of the stress in its constituent layers, which include growth stress and thermal stress. Fundamentally, it arises from interlayer mechanical constraints and interface coupling [47,48,49], as detailed below. Firstly, during the deposition of each individual layer, growth stress is generated. This includes intrinsic stress caused by lattice mismatch or defects. In a multilayer system, this stress is subject to “reverse constraints” from adjacent layers. For example, when lattice mismatch induces compressive stress in one layer, it will trigger tensile stress in the adjacent layer to maintain the mechanical equilibrium of the entire system. This “stress induction” phenomenon makes the stress of all layers interdependent rather than independent entities. Secondly, the physicochemical state of the interface, which includes diffusion, interfacial phases, and roughness, plays a crucial role in modulating the efficiency of stress transfer. In the case of a strongly bonded interface, such as an epitaxial interface, stress can be directly transmitted across it, resulting in strong interlayer coupling. On the contrary, if there is a loose layer or a diffusion zone at the interface, stress transfer is weakened, and the stress of each layer tends to behave more independently. In conclusion, the stress state of a multilayer film is determined by the stress of individual layers, the thickness of each layer, and the structural combination of its constituent layers. Through the selection of appropriate process parameters and the optimization of the layer thickness ratio, among other factors, it is possible to tailor the multilayer film to achieve zero or minimal stress.
To achieve this objective, we aimed to minimize the compressive stress of the SiO2 films while maximizing the tensile stress of the TiO2 films. Through comprehensive parameter optimization, we identified the optimal conditions: the TiO2 films exhibited peak tensile stress at a deposition temperature of 150 °C and a rate of 3 Å/s, whereas the SiO2 films achieved minimal compressive stress at 150 °C and 4 Å/s, as shown in Table 2. Figure 4c,d show the surface figure of the SiO2 and TiO2 films under these two deposition conditions, with corresponding stress values of −166 MPa and 120 MPa.
Under these conditions, we deposited a standard high-reflection film centered at 633 nm, following the layer structure G|(HL)∧10|A (where G denotes the fused silica substrate, A denotes the ambient air, and H and L are the TiO2 high-refractive-index layer and SiO2 low-refractive-index layer). The stack featured TiO2 and SiO2 layers with thicknesses of 69 nm and 107 nm, respectively, yielding a thickness modulation ratio (H/L) of 0.65. Post-deposition characterization of the sample’s surface figure (Figure 5a) revealed net compressive stress in the film. Leveraging insights from single-layer stress behavior, we hypothesized that increasing the proportion of the TiO2 layer thickness could dynamically compensate for the cumulative compressive stress in the multilayers.
Through systematic adjustment of the modulation ratio, we achieved optimal stress compensation at a ratio of about 1.3, as shown in Figure 5b. At this optimized ratio, the multilayer film demonstrated exceptional surface figure accuracy: the post-coating optical surface deviation remained nearly identical to that of the uncoated substrate, signifying remarkable stress compensation through strategic layer thickness engineering.
Figure 5c plots the residual stress of the multilayer film as a function of the thickness modulation ratio. At a modulation ratio of 0.65, the film exhibits a residual stress of approximately −63 MPa (compressive). As the ratio increases, the residual stress decreases gradually and follows an approximately linear trend, reaching 0.3 MPa near 1.3. This linear correlation demonstrates that multilayer film stress can be effectively compensated for by adjusting the thickness modulation ratio, leveraging the complementary stress polarities of TiO2 and SiO2. Additionally, we simulated our experimental results using COMSOL Multiphysics 6.2. First, the Equivalent Reference Temperature (ERT) [50,51] model was employed to simulate single-layer SiO2 and TiO2 films fabricated under optimal deposition conditions, aiming to derive their ERT values. The simulations yielded an ERT of −3070 K for SiO2 and 343 K for TiO2. The same ERT model was then applied to simulate residual stress predictions for SiO2/TiO2 multilayer structures under varying thickness modulation ratios. A comparison between the ERT model predictions and experimental data is shown in Figure 5c. As depicted, the simulated residual stress values closely align with the experimental measurements and exhibit identical trends: both transition from compressive to compensatory stress as the thickness modulation ratio increases. This consistency validates the methodological soundness and selected ratio, underscoring the reliability of our approach. Figure 5d presents the optical reflectance spectra of samples with different modulation ratios. The sample with a modulation ratio of 0.65 achieves reflectivity >99% across the 560–710 nm spectral band, consistent with the standard high-reflection design. While increasing the modulation ratio introduces deviations from the ideal layer thicknesses, the sample with a modulation ratio of about 1.3 retains reflectivity of >99% within the 590–690 nm band, despite a slight reduction in bandwidth. These results confirm that stress compensation via thickness modulation ratio optimization can be achieved with minimal compromise to optical performance in the target spectral region.
Subsequently, COMSOL Multiphysics simulation was employed to assess the applicability of this stress control technique for large-aperture optical films [52]. Maintaining a thickness ratio of 1.33, we established the same substrate–multilayer film model as in prior studies. The ERT model was applied to each film layer to compute the deformation of the multilayer films induced by residual stress. The obtained deformation data were then substituted into the Stoney formula to derive the stress of the multilayer films. Initially, the film diameter-to-thickness ratio was fixed to match the experimental parameters. Simulations were conducted to analyze the correlation between film stress and substrate aperture under an identical diameter-to-thickness ratio. As shown in Figure 6a, negligible stress variation was observed with changing aperture; the minor stress fluctuations in the simulations were primarily attributed to meshing errors. Furthermore, simulations were performed to evaluate film deformation due to residual stress on a substrate with a 2000 mm aperture. As illustrated in Figure 6b, when the substrate thickness exceeded 100 mm, the film surface peak–valley (PV) remained below 20 nm, demonstrating the extendability of our experimental findings to large-aperture primary mirrors and other optical components. Figure 6c depicts the surface figure of the multilayer film deposited on a φ2000 mm × 200 mm substrate, where the maximum deformation was approximately 4 nm, significantly below the surface profile requirements for engineering applications.
To validate the universality of the optimized thickness modulation ratio, we extended our analysis to multi-band reflective coatings. We implemented the layer structure a*(b(2.06H L)10 c(2.06H L)10), where a, b, c are scaling parameters, H and L denotes the TiO2 and SiO2 thickness. By tuning these parameters and the central wavelength, we designed multi-band systems adhering to the stress-compensating ratio. For example, a dual-band high-reflection coating with a central wavelength of 633 nm and parameter values of a = 0.92, b = 1.12, and c = 0.64 achieved high reflectivity at both 633 nm and 1064 nm.
Figure 7 a,b show the surface figure and reflectance spectrum of this multilayer film. The coating exhibited exceptional surface flatness, with post-deposition optical surface deviation nearly identical to the uncoated substrate, indicating effective stress compensation. Quantitative stress analysis revealed a residual stress of –1.5 MPa. Spectroscopic characterization confirmed >99% reflectivity across the 560–680 nm and 950–1150 nm bands, with reflectivity of 99.9% at the target wavelengths (633 nm and 1064 nm). Supplementary Material S3 provides stress and spectral data for a broadband high-reflection coating, further demonstrating the robustness of low-stress, high-reflectivity performance across diverse optical configurations. These results validate the general applicability of the modulation ratio in designing high-reflection film systems, regardless of band count or spectral spacing.
To assess the modulation ratio’s applicability beyond regular layer configurations, we investigated stress behavior in anti-reflective (AR) coatings. Using Optilayer 15.12, we designed a 600–900 nm AR coating by fixing the average thickness modulation ratio of TiO2/SiO2 while allowing individual layer thicknesses to vary. This yielded a 30-layer multilayer structure (total thickness: 1597 nm; TiO2: 912 nm; SiO2: 685 nm), with the layer thickness distribution detailed in Figure 8a.
The single-sided AR film deposited on fused silica exhibited a low residual stress of ~0.62 MPa (Figure 8b), demonstrating stress compensation even in irregular layer stacks. The transmission spectrum (Figure 8c) showed an average transmittance of >96% across the 600–900 nm band. Depositing an identical film on the substrate’s reverse side created a double-sided AR coating with an average transmittance of >99%. We also deposited an AR film within the same wavelength band (total thickness: 931 nm; TiO2: 274 nm; SiO2: 657 nm) without imposing constraints on the thickness modulation ratio. Although its transmittance was higher (double-sided coating transmittance exceeding 99.6%), the single-sided coated film exhibited a notably larger compressive stress of approximately −90 MPa, with stress-induced deformation approaching 3λ/4.

4. Conclusions

In this study, we systematically investigated the effects of process parameters, including film thickness, substrate temperature, and deposition rate, on the residual stress of single-layer SiO2 and TiO2 films. We observed that SiO2 films consistently exhibit compressive stress, whereas TiO2 films predominantly display tensile stress under the tested conditions. The deposition rate influences film stress primarily by altering packing density: higher rates reduce atomic mobility, leading to looser packing and decreased compressive stress (for SiO2) or increased tensile (for TiO2) stress. The substrate temperature impacts stress through two mechanisms: thermal stress (arising from thermal expansion mismatch) and densification-induced stress. The former dominates at lower temperatures, and the latter becomes significant at higher temperatures. Leveraging these stress polarity differences, we optimized deposition conditions and tuned the thickness modulation ratio of TiO2 and SiO2 to engineer stress-compensated multilayer films. For a 633 nm high-reflection coating, we demonstrated that increasing the TiO2/SiO2 thickness modulation ratio reduces net residual stress, achieving optimal compensation at a ratio of about 1.3, where the tensile stress from TiO2 layers balances the compressive stress from SiO2 layers. This strategy was validated across diverse optical systems, namely, multi-band high-reflective films and irregular anti-reflective coatings, both of which exhibited low residual stress and high optical performance. This method achieves stress compensation by tuning the intrinsic stress polarity of materials, effectively avoiding the risks of material decomposition and substrate damage associated with high-temperature processes. The ability to achieve nanoscale stress control in large-aperture films provides critical advancements for manufacturing ultra-precise optical devices, including space-based interferometric sensors and high-stability optical components. Its broad applicability across regular and irregular film architectures underscores its potential to redefine stress engineering in complex optical coating design, offering a scalable solution for balancing mechanical integrity and optical performance in advanced photonic systems.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/coatings15070848/s1, Figure S1: XRD measurements of single-layer SiO2 and TiO2 films under different deposition conditions; Figure S2: Surface morphologies and RMS roughness of PIAD-prepared TiO2 films; Figure S3: Discussion on the verification of the thickness modulation ratio in broadband high-reflection films.

Author Contributions

Conceptualization, B.W. and C.W.; methodology, B.W., T.W. and W.G.; software, B.W.; validation, B.W. and T.W.; formal analysis, G.H. and B.W.; investigation, B.W. and T.W.; resources, C.W.; data curation, B.W. and C.W.; writing—original draft, B.W.; writing—review and editing, B.W., G.H. and C.W.; visualization, B.W. and T.W.; supervision, B.W. and T.W.; project administration, C.W.; funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by an independent project of the Chinese Academy of Sciences (A19K011-3 and H19A007-7). The Article Processing Charge was funded by the independent project of the Chinese Academy of Sciences(H19A007-7).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are contained within this article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. (a) XRD spectra of SiO2 films with different thicknesses. (b) Transmittance spectra of SiO2 films. (c) Residual stress of IAD-prepared SiO2 films plotted against thickness.
Figure 1. (a) XRD spectra of SiO2 films with different thicknesses. (b) Transmittance spectra of SiO2 films. (c) Residual stress of IAD-prepared SiO2 films plotted against thickness.
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Figure 2. Surface topography of TiO2 films with thicknesses of (a) 100 nm, (b) 300 nm, and (c) 800 nm. (d) RMS roughness of SiO2 films as a function of thickness.
Figure 2. Surface topography of TiO2 films with thicknesses of (a) 100 nm, (b) 300 nm, and (c) 800 nm. (d) RMS roughness of SiO2 films as a function of thickness.
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Figure 3. Residual stress of IAD-prepared SiO2 films plotted against (a) substrate temperature and (d) deposition rate. The refractive index of SiO2 films with different (b) substrate temperatures and (e) deposition rates, with the wavelength ranging from 300 to 1400 nm. RMS roughness of SiO2 films as a function of (c) substrate temperature and (f) deposition rate.
Figure 3. Residual stress of IAD-prepared SiO2 films plotted against (a) substrate temperature and (d) deposition rate. The refractive index of SiO2 films with different (b) substrate temperatures and (e) deposition rates, with the wavelength ranging from 300 to 1400 nm. RMS roughness of SiO2 films as a function of (c) substrate temperature and (f) deposition rate.
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Figure 4. Stress of IAD-prepared TiO2 film as a function of (a) deposition rate and (b) substrate temperature. (Negative and positive values correspond to compressive and tensile stress, respectively.) The surface figure of (c) SiO2 and (d) TiO2 films under the optimized deposition conditions.
Figure 4. Stress of IAD-prepared TiO2 film as a function of (a) deposition rate and (b) substrate temperature. (Negative and positive values correspond to compressive and tensile stress, respectively.) The surface figure of (c) SiO2 and (d) TiO2 films under the optimized deposition conditions.
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Figure 5. Surface figures of TiO2/SiO2 multilayer films with the modulation of (a) 0.65 and (b) 1.3 fabricated by IAD. (c) Stress of IAD-prepared TiO2/SiO2 films as a function of the modulation ratio. (d) Reflectance spectrum of TiO2/SiO2 multilayer films with different modulation ratios, with the wavelength ranging from 400 to 900 nm.
Figure 5. Surface figures of TiO2/SiO2 multilayer films with the modulation of (a) 0.65 and (b) 1.3 fabricated by IAD. (c) Stress of IAD-prepared TiO2/SiO2 films as a function of the modulation ratio. (d) Reflectance spectrum of TiO2/SiO2 multilayer films with different modulation ratios, with the wavelength ranging from 400 to 900 nm.
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Figure 6. (a) Film stress as a function of substrate aperture under an identical diameter-to-thickness ratio. (b) The film deformation due to residual stress for substrates with different thicknesses. (c) The simulated surface figure of TiO2/SiO2 coatings on a φ2000 mm × 200 mm substrate.
Figure 6. (a) Film stress as a function of substrate aperture under an identical diameter-to-thickness ratio. (b) The film deformation due to residual stress for substrates with different thicknesses. (c) The simulated surface figure of TiO2/SiO2 coatings on a φ2000 mm × 200 mm substrate.
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Figure 7. (a) Surface figure of TiO2/SiO2 multi-band reflective coatings. (b) Reflectance spectrum of as-deposited multi-band reflective coatings.
Figure 7. (a) Surface figure of TiO2/SiO2 multi-band reflective coatings. (b) Reflectance spectrum of as-deposited multi-band reflective coatings.
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Figure 8. (a) Layer-thickness profile of AR coating. (b) Surface figure of TiO2/SiO2 AR coatings. (c) Transmittance spectra of as-deposited AR coatings.
Figure 8. (a) Layer-thickness profile of AR coating. (b) Surface figure of TiO2/SiO2 AR coatings. (c) Transmittance spectra of as-deposited AR coatings.
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Table 1. List of the different conditions surveyed in the IAD of SiO2 thin films.
Table 1. List of the different conditions surveyed in the IAD of SiO2 thin films.
SampleTemperature (℃)Deposited Rate (Å/s)O2 Flue (sccm)Thickness (nm)
S11002.028108.8
S21002.028213.3
S31002.028422.3
S41002.028616.8
S51002.028826.3
S61002.0281035.7
S71001.028386.6
S81003.028442.4
S91004.028465.9
S101502.028405.1
S111002.028392.8
S122302.028374.1
Table 2. The optimized deposition parameters of the TiO2 and SiO2 thin films.
Table 2. The optimized deposition parameters of the TiO2 and SiO2 thin films.
MaterialSubstrate Temperature
(°C)		Deposited Rate
(Å/s)		Bias
Voltage
(V)		Neutralizer
Current
(mA)		Ar Flue
(sccm)		O2 Flue
(sccm)
SiO21504.01701201228
TiO21503.01701201228
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Wang, B.; Wu, T.; Gao, W.; Hu, G.; Wang, C. Stress Compensation in TiO2/SiO2 Optical Coatings by Manipulating the Thickness Modulation Ratio. Coatings 2025, 15, 848. https://doi.org/10.3390/coatings15070848

AMA Style

Wang B, Wu T, Gao W, Hu G, Wang C. Stress Compensation in TiO2/SiO2 Optical Coatings by Manipulating the Thickness Modulation Ratio. Coatings. 2025; 15(7):848. https://doi.org/10.3390/coatings15070848

Chicago/Turabian Style

Wang, Bo, Taiqi Wu, Weidong Gao, Gang Hu, and Changjun Wang. 2025. "Stress Compensation in TiO2/SiO2 Optical Coatings by Manipulating the Thickness Modulation Ratio" Coatings 15, no. 7: 848. https://doi.org/10.3390/coatings15070848

APA Style

Wang, B., Wu, T., Gao, W., Hu, G., & Wang, C. (2025). Stress Compensation in TiO2/SiO2 Optical Coatings by Manipulating the Thickness Modulation Ratio. Coatings, 15(7), 848. https://doi.org/10.3390/coatings15070848

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