Degradation Progress of Metallized Silicon Nitride Substrate Under Thermal Cycling Tests by Digital Image Correlation

Abstract

Thermal cycling test is one of the reliability tests, which are important for metal-ceramic layered composites (metallized ceramic substrates), a part in power modules. Since thermal cycles are within a large range of temperature, the test has only been performed using a thermal chamber. It limited the understanding of degradation mechanism in metallized ceramics substrates. Among NDE techniques, Digital Image Correlation (DIC) is a simple and effective method, enhanced by modern digital imaging technologies, enabling precise measurements of displacement, strain, deformation, and defects with a simple setup. In this paper, we combined some of our previous work to make a review to present a full analysis of a silicon metallized substrate under thermal cycling test (from beginning to fail) using DIC method. The main content is the application of DIC in evaluating the reliability of metallized silicon nitride (AMB-SN) substrates under thermal cycling with temperatures from −40 °C to 250 °C. Three key aspects of the AMB-SN substrate are presented, including (i) thermal strain characteristics before and after delamination, (ii) warpage and dynamic bending behavior across damage states, and (iii) stress–strain behavior of constituent materials. The review provides insights into degradation progress of the substrate and the role of Cu in substrate failure, and highlights DIC’s potential in ceramic composites, offering a promising approach for improving reliability test simulations and advancing digital transformation in substrate evaluation, ultimately contributing to enhanced durability in high-power applications.

1. Introduction

The rapid advancement of robotics, artificial intelligence, and the electric vehicle industry, all of which rely heavily on electricity, has led to a substantial increase in the demand for semiconductors [1,2,3]. This trend further necessitates the development of new types of semiconductors with higher switching speed and greater efficiency [4,5,6,7,8]. Furthermore, efforts are being made to reduce CO₂ emissions by utilizing green energy sources such as solar, wind, and hydrogen for electricity generation [9,10,11,12,13,14,15]. As a result, devices that currently rely on fossil fuels are increasingly being replaced by electrically powered alternatives [16,17]. This transition presents new challenges in the field of ceramics, as ceramic substrates play a crucial role in ensuring the reliability of power devices, particularly in electric vehicles and power conversion systems [18,19,20,21].

In power modules, the metallized ceramic substrate, as shown in Figure 1, consists of a ceramic layer functioning as an insulator between two metal plates on both sides. One metal layer is used to form a circuit connecting electronic components, while the other layer facilitates heat dissipation by transferring heat from the circuit to the heat sink [18,22]. During operation, the high current density and large voltage amplitude in power modules generate significant amounts of heat. Frequent temperature fluctuations can cause fractures in the ceramic substrate, leading to circuit failure. This failure is attributed to the mismatch in the coefficients of thermal expansion (CTE) among the different materials in the composite under temperature changes. The CTE of Cu is substantially larger than that of ceramic materials like Al₂O₃, AlN, Si₃N₄. The issue is particularly severe in electric vehicles, where operating conditions may range from −40 °C to 250 °C. The mechanism of failure during thermal cycling is illustrated in Figure 2.

Therefore, the reliability of ceramic substrates in power modules is a crucial topic for real-world applications. Numerous studies have investigated the reliability of metallized ceramic substrates under thermal cycling [23,24,25,26,27,28,29] and power cycling conditions [30,31,32]. However, in situ measurements during reliability tests remain limited. Non-destructive evaluation (NDE) testing [33] is an ideal method for evaluating reliability because it can identify ceramic defects without damaging the structure of the tested samples. NDE techniques include penetration testing [34], ultrasonic testing [35], radiographic testing [36], infrared thermography [37], acoustic emission [38], laser emission, X-ray [39], machine vision, and digital image correlation (DIC) [40]. The working principles of these techniques have been thoroughly reviewed by Zhao [41]. Among these methods, DIC is one of the most promising techniques for studying reliability under thermal cycling conditions. Advances in camera technology and algorithms for image analysis have significantly improved the accuracy of DIC measurements. The development and evolution of DIC have been comprehensively reviewed by Blikharskyy et al. [42]. DIC method was developed in the 1980s and has been widely applied in characterizing material properties [43,44,45,46,47,48,49,50,51,52,53].

Using DIC techniques, we have made significant progress in studying metallized substrates under thermal cycling tests with the metallized silicon nitride (AMB-SN) substrates [54,55,56]. Silicon nitride (SN) has been selected because of its superior mechanical properties compared with other ceramics such as aluminum nitride (AlN) or alumina (Al₂O₃), as shown in

Table 1. Summary of the popular ceramic materials used in metallized ceramic substrates. (Reproduced with permission of John Wiley and Sons. All rights reserved.).

Characteristics of Ceramic Substrates
Ceramic Material	Thermal Conductivity (W m−1K−1)	Coefficient of Thermal Expansion by DIC (ppm/°C)	Strength (MPa)	Fracture Toughness (MPam1/2)
Si3N4	140	1.5	669 ± 29	10.4
AlN	180	5.3	461 ± 62	3.2
Al2O3	30	5.8	350 ± 50	3.5

[18,54]. In our previous reports, we provided different characteristics of the AMB-SN substrate under thermal cycles. Therefore, the complete degradation process could not be included in each paper. This review paper aims to give an overview of our recent research works on unique and accurate evaluation results of the AMB-SN substrate using the DIC method under thermal cycles ranging from −40 °C to 250 °C. The paper provides a comprehensive view of the degradation process of the AMB-SN substrate throughout the entire thermal cycling test from the beginning until the substrate fails. First, an introduction to the methodology of DIC is presented. Consequently, three main technological features of the AMB-SN substrate under thermal cycling tests are discussed including (i) the thermal strain characteristics of the AMB-SN substrate during the entire consecutive cycle sequence, before and after delamination, (ii) the warpage and dynamic bending behaviors of the AMB-SN substrate relative to the number of cycles, and (iii) the analysis of the stress–strain curve in the substrate within its defect-free. Finally, we discuss the future perspectives on ceramic substrates and the role of DIC in their evaluation.

2. Fundamentals of DIC

As mentioned in the introduction, DIC is a non-contact, image-based optical method used to measure full-field displacement and deformation of objects. DIC techniques can be applied for various testing purposes, including material characterization (measuring displacement, strain, acceleration, and strain rate) [43,45,47,57], as well as identifying material parameters (Young’s modulus, Poisson’s ratio, coefficient of thermal expansion, etc.) [47,58,59]. DIC can be categorized into two main types: 2D-DIC and 3D-DIC methods [60,61,62]. In 2D-DIC, a single camera is used to measure the in-plane deformation on a planar surface. However, this method has limitations and is suitable only for specific applications, such as tensile tests with typical 2D-deformation. For non-planar samples, 3D-DIC is employed. As shown in Figure 3, 3D-DIC uses two cameras along with a specially designed light-splitting system to obtain accurate measurements of full-field 3D objects [63].

In order to use DIC, several experimental procedures are required:

• Speckle pattern fabrication: To create an effective speckle pattern on the sample surface, a spraying process is typically required. First, a layer of white paint is applied as the background. Then, black paint is sprayed to generate a stochastic contrast dot pattern. The varying shades of darkness on the surface are represented as a matrix of natural numbers, which are tracked during the monitoring process.
• Calibration: This step is essential for three-dimensional digital image correlation (3D-DIC) methods. During the calibration of stereo DIC camera sensors, the relative positions of the two cameras in space and parameters for modeling the beam path, such as lens distortion and intrinsic parameters, are defined using a calibration sample.
• Digital image acquisition: Images of the measurement surface of the sample are captured and saved on a computer for post-processing.
• Displacement and strain calculation: Using a reference image from the beginning of the test, automated image processing can be performed with various software packages, such as Vic Volume 2D/3D software (Correlated Solutions, Inc., Irmo, SC, USA [64]), Strain Master software (La-Vision, Ypsilanti, MI, USA [65]), ZEISS ARAMIS software (ZEISS Group, Carl Zeiss IQS Deutschland GmbH, Germany [66]). Several approaches exist for identifying deformed image areas. Adaptive methods, including image correlation and the least squares method, are commonly used. The primary assumption is that a causal connection exists between the original state and the deformed state.

The basic concepts, fundamental principles, and algorithm details of DIC have been explained in numerous technical papers [42,67,68,69]. Blikharskyy et al. reviewed the application of DIC for reinforce concrete (RC) structures [42]. However, RC structures are huge objects, the deformations are also much more significant compared with the smaller structures like metallized ceramic substrate in this paper. Therefore, the most difference is how to reduce errors during measurement to obtain the most accurate results. There are standards for preparing the speckle patterns on the sample’s surface, which can ensure the accuracy of the measurement. In ZEISS ARAMIS software, the speckle patterns need to adjust with measurement sizes [66]. Figure 4 shows the different speckle patterns according to the measurement size to maintain the accuracy of the measurement. These different patterns are also called speckle sizes.

In ZEISS ARAMIS, for tracking the displacement, setting facets on sample surface are required. A facet has standard size of 19 × 19 pixels [66]. Each pixel defines a gray value in eight bits having a value between 0 and 255. Two facets have a standard distance of 16 pixels and should have an intersection area. For the samples measured in this review, the sizes are less than 50 mm², so the speckle preparations were prepared following the reference pattern with the facet size of 19 × 19 pixels and facet distance of 16 pixels (Figure 5).

3. Thermal Strain of AMB-SN Substrate by DIC

3.1. Experimental

First, the AMB-SN substrate was prepared using an SN plate (dimensions of 40 × 10 mm and thickness of 0.32 mm) and four plates of Cu (dimensions of 17 × 8 mm and thickness of 0.30 mm) using the active metal brazing method at the brazing temperature of 790 °C with an Ag-Cu-Ti active metal filler according to the International Standard ISO 17841 “Test method for thermal fatigue of fine ceramic substrates” [70]. The configuration and structure of the SN substrate with Cu are presented in Figure 6A [54]. As mentioned in Section 2, the sample was prepared to have a suitable speckle pattern on its surface before monitoring with DIC. Figure 6B, C shows the substrate’s images before and after the praying process (speckle pattern’s preparation) [54].

In the testing process, the AMB-SN substrate underwent thermal cycles with temperatures ranging from −40 to 250 °C and was monitored by a 3D-DIC system using a commercially available DIC measurement system and software (GOM V8 SR1 Optical Measuring Techniques, Carl Zeiss GOM Metrology Co., Ltd., Braunschweig, Germany) in conjunction with a specialized thermal chamber (Mita Sangyo CORP., Tokyo, Japan), designed to achieve the desired temperature conditions. Figure 7a, b illustrates the chamber with the DIC system [54]. The chamber was heated by an integrated heater located inside and cooled by introducing liquid nitrogen through an automatic control valve during testing. Additionally, the chamber was equipped with a transparent glass, allowing the cameras to record deformation progress of the substrate. Because the AMB-SN substrate exhibits high durability under thermal cycling (delamination after more than 1000 cycles) [24], the experiment was conducted using an additional separate thermal shock test chamber (TSE-11, ESPEC CORP., Osaka, Japan) with the same temperature setting as in the DIC system. The substrate was monitored with DIC during several selected consecutive thermal cycles, ranging from 1~2 (beginning) to 2499~2501 (substrate failure), while the other alternative cycles were conducted using thermal shock testing equipment. In each thermal cycle with DIC, the temperature began at room temperature (RT), then decreased to −40 °C, where it was held for 5 min before increasing to 250 °C and being maintained for another 5 min, finally returning to RT to complete one cycle. The temperature ramp rate was 4 °C/min for both cooling and heating. One thermal cycle was completed within 155 min. After a consecutive cycle with DIC monitoring, a thermal shock chamber was used instead to subject the sample with the same temperature range from −40 to 250 °C, with each cycle lasting 36 min. The longitudinal thermal expansion of the AMB-SN substrate was measured at the centerline of the substrate for the cycles monitored by DIC, as shown in Figure 7c [54].

3.2. Substrate Delamination Inspected by SAM

To check the delamination between the SN and Cu layers on the substrate, a scanning acoustic microscope (SAM) was utilized to inspect the sample after a specific number of thermal cycles including states of before testing, after 1000, 1501, 2001, and 2501 cycles. The inspection results are shown in Figure 8, the observation on both sides of the sample. The SAM observations revealed an identical pattern on the substrate at the beginning and after 1000 thermal cycles, indicating the non-delaminated state. A small delamination was detected at the joint corners between SN and Cu after 1501 cycles; then gradually increased as after 2001 cycles. However, it became significant after 2501 cycles, which was marked as the sample failure state. On the backside of the sample, light spots were observed after 2001 and 2501 cycles. However, it was confirmed that these originated from the delamination on the front side, as later shown through visual inspection in the next paragraph. From the SAM observation data at the several checkpoints, the degradation of the AMB-SN substrate could be distinguished for analysis, which was divided into before and after delamination. Consequently, the thermal strain of the substrate measured by DIC was analyzed according to the SAM results.

Besides SAM observation, a visual inspection was also conducted at the same time. However, the change in the substrate could not be recognized for the states after 1000 and 1501 cycles. Therefore, the sample pictures before testing, after 2001 cycles, and after 2501 cycles were selected for the comparison, shown in Figure 9 [55]. The Cu surface without spraying became more scabrous with increasing cycle numbers; this was explained by the growth of the Cu crystal at high temperature, as reported elsewhere [71]. The delamination was observed on the substrate only on the sprayed side, and the delamination was critical and clear after 2501 cycles. However, when the delamination was small, such as after 2001 cycles, it could not be detected by the digital microscope.

3.3. Thermal Strain Before the Delamination

Based on the SAM observations, DIC measurements were selected for analysis. The longitudinal thermal strain of the AMB-SN substrate was measured at various states, including before and after the delamination. Figure 10 shows the thermal strain of several consecutive thermal cycles of 1~2, 11~12, 99~100, and 999~1000, which present the substrate states before delamination. The evolution of the thermal strain exhibited distinct hysteresis characteristics, and its amplitude expanded with an increase number of cycles.

To understand the formation of the hysteresis curve and its evolution, the strain curves of each consecutive thermal cycle were analyzed and are shown in Figure 11. The CTEs of SN and AMB-SN (calculated from the measured CTEs of Cu and SN within elastic deformation range of Cu) were plotted to track how the curve changes compared to these CTE lines. In every strain curve, at the beginning of heating from −40 °C and cooling from 250 °C, the strain curve was close to the calculated CTE of the AMB-SN substrate. However, at a certain temperature, the curve deviated from the AMB-SN CTE toward a lower slope curve and eventually reached the CTE of SN at the end of the heating and cooling processes at 250 °C and −40 °C, respectively. The deviation points during heating and cooling varied according to the number of cycles showed in Figure 12. It was realized that the deviation became almost stable after 100 thermal cycles. The alignment of the strain curve with the calculated AMB-SN CTE indicated the elastic deformation range of Cu on the substrate. However, the deviation from the AMB-SN’s CTE implied the onset of plastic deformation of Cu plates. When plastic deformation occurred in Cu, it contributed to the reduction in strain of the AMB-SN substrate, resulting in a lower slope of the overall substrate strain curve.

The development of the thermal strain and deviation points was attributed to the work hardening of Cu on the substrate [72,73,74,75,76]. This phenomenon can be explained by the cyclic hardening effect [32], which occurs in Cu under repeated strain cycles. Initially, the Cu on the AMB-SN substrate was at its softest state, having not undergone any plastic deformation. In the later cycles, the Cu underwent plastic deformation during both heating and cooling. These plastic deformations caused Cu to become harder. Therefore, higher stress from SN substrate was required to induce plastic deformation in Cu at later cycles. This shift in stress caused the deviation points to move to higher temperatures during heating and lower temperatures during cooling, leading to an expansion in the strain curve’s amplitude as the number of cycles increased [54]. The expansion of strain amplitude is summarized in Figure 13.

3.4. Thermal Strain After the Delamination

A light delamination in the AMB-SN substrate was observed after 1501 thermal cycles at the edges of Cu plates. The delamination did not occur evenly across the substrate but only in specific areas. To track the strain on the substrate and understand how delamination affects thermal strain, the average longitudinal strain of the entire sample was measured instead of measuring the longitudinal strain at the substrate center, as was performed in the non-delaminated states in Section 3.3. The measurement area is shown along with the thermal strain results in Figure 14 [55]. The tendency of the strain curve in Figure 14a was similar to that in Section 3.3. The difference in strain range can be explained by the different measuring area on the substrate.

In Figure 14b, the strain of AMB-SN substrate from 1499~1501 was almost identical to the strain curve of 999~1000 cycles. This implies that minor delamination did not show a significant effect on the strain curve under thermal cycles. After 2001 cycles, the delamination slightly expanded, as observed in the SAM results. However, a significant change in the strain curve was detected. In Figure 14c, the strain curve during the 1999th cycle remained close to the strain curve from cycles of 1499~1501, exhibiting a hysteresis loop with deviation points during heating and cooling. However, in the following cycle (the 2000th), the strain curve shifted in the negative direction, and the hysteresis loop became asymmetrical between heating and cooling. Then, in the next thermal cycle (the 2001st), the entire strain curve compressed and sharply decreased in amplitude at high temperatures. It was assumed that in period from 2000 to 2001 thermal cycles, a large delamination occurred, making a critical change in the thermal strain. During heating, Cu expands more than the ceramic, exerting a tensile force on the entire substrate. However, when delamination occurs, the Cu suddenly detaches from the ceramic substrate, leading to a reduction in the overall deformation (strain) of the substrate due to the loss of tensile force from Cu. During cooling, the strain curve appears closer to a straight line with a smaller slope, which may indicate the reduced influence of Cu on the entire substrate. As the bonded Cu area decreases, the composite’s overall CTE also becomes smaller.

The delamination became significant after 2501 cycles, as observed in the SAM results. However, we obtained uniform strain curves during consecutive cycles from 2499 to 2501. The strain curves expanded in a negative direction compared to the curves before delamination or with a minor delamination (during 1499~1501 cycles and during 1999~2001 cycles). On the other hand, the hysteresis still presented but became very narrow, and the strain curves were close to a linear line, with a slope of 7.1 ppm/°C, which was higher than the calculated CTE of AMB-SN substrate. However, it is noted that once delamination occurs, the calculated CTE of AMB-SN is no longer applicable. Upon inspecting the substrates, delamination of the Cu layer occurred only on one side (sprayed/front surface), while on the other side, the Cu remained firmly bonded to the SN substrate. This suggests that the asymmetry develops when Cu peels off on one side, leading to a greater influence of the intact Cu layer on the overall substrate deformation during the temperature changes. As a result, the total substrate deformation increases, producing a steeper strain curve. Furthermore, in the presence of large-scale delamination, the expansion and contraction of Cu on the SN substrate are reduced during heating and cooling. This lowers residual stress on the substrate, keeping it below Cu’s yield point, and results in an almost linear strain curve, behaving like the natural expansion of a material. It is important to distinguish between minor and significant delamination. With minor delamination, residual stress on SN is influenced by Cu on both sides, making it larger across the AMB-SN substrate. However, with significant delamination, residual stress is dominated by Cu layer on intact side, causing a reduction in overall residual stress but making SN substrate more susceptible to the deformation within its elastic range.

4. In Situ Observation of Warpage and Dynamic Bending Behaviors of the AMB-SN by DIC

In addition to monitoring the thermal strain, the DIC method was also employed for in situ observation of warpage, deformation, and dynamic bending behavior of the substrate during thermal cycling tests, which were challenges in traditional research. This section presents the results of these key observations.

4.1. Substrate Warpage During Thermal Cycling Test

Warpage is a phenomenon, in which a material undergoes uneven expansion or contraction leading to bending, twisting, or other shape distortions [77,78,79,80]. In the AMB-SN substrate, which has a symmetric structure, the warpage phenomenon does not occur as long as there are no defects such as cracks or delamination. Therefore, monitoring the warpage provides a valuable indicator of the substrate’s damage. According to the SAM observations, warpage was observed at different states: before delamination during the 1000th cycle, with minor delamination during the 2001st cycle, and with significant delamination during the 2501st cycle. The 3D contour maps of the warpage in these states are presented in Figure 15 [55]. During the 1000th cycle, identical contour maps were obtained at different temperatures of 30 °C, −40 °C and 250 °C with almost a constant in height at any position on the substrate. The result confirmed that the AMB-SN substrate remained defect-free after 1000 thermal cycles [54]. However, as shown in Figure 15b, warpage appeared on substrate at 30 °C and −40 °C during the 2001st cycle. The contour map indicated a raised center area of the AMB-SN substrate. According to SAM observations, delamination was more pronounced at the Cu edge near the center. This suggests that the warpage at the center was a direct result of the delamination affecting the substrate’s deformation. Finally, in Figure 15c, the warpage of the substrate during the 2501st cycle followed the same trend as observed during the 2001st cycle. However, the warpage was significantly more pronounced in height, which aligns well with the SAM observation results. When large delamination occurs on one side of the substrate, the overall deformation is dominated by the Cu layer that remains bonded on the opposite side, leading to substantial warpage. Interestingly, the warpage was not obtained at 250 °C, the highest temperature point, in any of the measured states. This phenomenon can be explained by considering the brazing temperature between Cu and SN, which was 790 °C. As the substrate cools from 790 °C to room temperature, the Cu undergoes compression. When delamination occurs on one side, the remaining Cu layer on the other side induces stress, bending the substrate even at room temperature (as seen at 30 °C during the 2001st and 2501st thermal cycles). However, at higher temperatures, such as 250 °C, the compressive stress in Cu is relieved, allowing it to return to its natural state, which in turn causes the substrate to become non-warped.

4.2. Dynamic Bending Behaviors of the AMB-SN by DIC

The warpage observation provided an overall view of the substrate deformation during thermal cycles at different delamination states. However, they do not clearly explain how each constituent material contributes to the substrate degradation. When defects occur, the asymmetric structure of the substrate induces dynamic bending due to uneven distribution of the residual stress on two sides of the substrate. Therefore, analyzing the bending behavior of the substrate can help us better understand its deformation mechanisms. Figure 16 presents an in situ cross-sectional observations of Cu and SN on the AMB-SN substrate. The green section represents the cross-section through only SN substrate, while the red section corresponds to the cross-section through the central area covered by Cu. Observations were conducted at three presentative temperatures (30 °C, −40 °C, and 250 °C), matching the warpage measurement points. During the 1000th cycle, the height of Cu and SN remained constrained throughout the thermal cycle, and no bending was observed. However, during the 2001st cycle in Figure 16b, negative bending appeared at 30 °C, forming a curve at the center of the substrate. The bending curve increased slightly at −40 °C but returned to a non-bent state at 250 °C. Despite the height at the center lifting from 0.5 to 0.1 mm, the total height from the SN layer to the Cu surface remained approximately 0.3 mm. It was assumed that microcracks formed in the SN layer beneath the Cu at the delaminated center area, reducing the compressive force from Cu and allowing bending at low temperatures. However, these microcracks were not visible on the sample surface. Bending behavior became more pronounced during the 2501st cycle. At 30 °C and −40 °C, significant negative bending occurred, with the center height increasing from 0.2 to 0.4 mm. The height from the SN layer to the Cu surface was from 0.40 mm at 30 °C to 0.45 mm at −40 °C. Additionally, at 250 °C, positive bending was observed.

The bending behavior of Cu and SN was also examined across the substrate width, as shown in Figure 17. No noticeable bending was observed in the states without delamination (during the 1000th cycle) and with minor delamination (during the 2001st cycle). However, in the case of large-scale delamination during the 2501st cycle, bending was clearly observed. At 30 °C and −40 °C, Cu and SN exhibited opposite bending behaviors, while at 250 °C, both Cu and SN underwent negative bending across the entire cross-section. The bending behaviors were primarily observed on the delaminated (sprayed/front) side of the substrate. On the non-delaminated (non-sprayed/back) side, Cu remained firmly bonded to SN. This suggests that the bending behavior of Cu on the non-delaminated side is similar to that of SN, as the structure remains intact.

5. Stress–Strain Analysis of Cu on Metallized Ceramics Substrate by DIC

In Section 3, the thermal strains and deformation of metallized ceramic substrates were analyzed during thermal cycling tests using the DIC method. However, due to the non-equivalent structures of Cu and ceramic substrates, calculating thermal stress directly from the measured thermal strains was complex. To simplify the considered parameters and calculations, it was hypothesized that an equivalent structure of the metallized silicon nitride substrate would provide for a more straightforward approach to predict the thermal stress on the substrate. To make progress this hypothesis, an equivalent Cu and SN substrate was prepared and tested under thermal cycling conditions the same as in Section 3. In this section, thermal stress was analyzed under the assumption that no defects were on the substrate. Figure 18 illustrates the structure of the AMB-SN substrate (a) and depicts the thermal strain evolution over several consecutive thermal cycles, ranging from 1~2 to 199~200 cycles, with temperatures varying from −40 °C to 250 °C. The experimental process followed the methodology described in Section 3.1 [54,56].

The measured strain results were utilized to calculate the thermal stress of Cu and SN on the substrate. Details of these calculations are provided in Ref [56]. In Figure 18b, the intersection of the CTE lines of Cu, SN, and the composite CTE was considered the reference point for the stress calculation. The composite CTE represents the calculated CTE of the AMB-SN substrate, derived from experimental thermal expansion data of plain SN and Cu by applying the Tuner model in Equation (1) [54,56,81,82], under the assumption that Cu undergoes only elastic deformation.

$$CT{E}_{\mathrm{A}\mathrm{M}\mathrm{B}\text{-}\mathrm{S}\mathrm{N}}={\displaystyle \frac{CT{E}_{\mathrm{C}\mathrm{u}}\times V_{\mathrm{C}\mathrm{u}}\times E_{\mathrm{C}\mathrm{u}}+CT{E}_{\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4}\times V_{\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4}\times E_{\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4}}{V_{\mathrm{C}\mathrm{u}}\times E_{\mathrm{C}\mathrm{u}}+V_{\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4}\times E_{\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4}}}$$

(1)

where CTE, V, and E are the coefficient of thermal expansion, volume fraction, and Young’s modulus, respectively. Subscripts, Cu and SN indicate the material.

The measurement results indicate that the thermal strain curves closely align with those presented in Section 3.1. However, the strain curves exhibited greater symmetry during heating and cooling. SAM analysis confirmed that the sample had no delamination up to 200 thermal cycles [56]. This symmetry can be attributed to the structural uniformity of the substrate and the equivalent yield stress of Cu during both heating and cooling. After thorough consideration and calculation, the stress–strain curves for Cu and SN on the substrate were obtained, as presented in Figure 19a [56].

The amplitude of stress in Cu increases with the number of thermal cycles, exhibiting a hysteresis effect with respect to the strain. Notably, the stress in Cu saturates after 50 thermal cycles. However, as the stress increases, the thermal strain in Cu slightly decreases. This phenomenon has been discussed in detail in the original work [56]. Due to the absence of deformation and delamination in the substrate, the stress–strain curve of SN appears as a straight line. The stress and strain of SN also increase with the rising stress in Cu during thermal cycling. Figure 19b presents a summary of the maximum stress and strain of Cu on the substrate. The maximum stress increases during both cooling and heating; however, the maximum strain decreases. The relationship between stress and strain reverses as the number of thermal cycling progresses from the beginning up to the 50th thermal cycle. It is understood that during thermal cycling, the thermal expansion of the substrate is a natural phenomenon, with temperature being a fixed parameter. Consequently, when material properties change due to thermal cycling, their expansion within the same temperature range can be affected. Therefore, the observed reversibility of stress and strain is explainable. The stress–strain curve obtained from the DIC method was compared with results from bending tests and showed good agreement [56].

From these results, the thermal stress–strain characteristics of Cu and SN on the AMB-SN substrate were defined. Thermal stress is a critical parameter for assessing material reliability under thermal cycling conditions. The accurate characterization of stress in Cu is essential for studying substrate failure. Furthermore, it serves as an important parameter for improving simulation models to predict the reliability of metallized ceramic substrates, as will be mentioned later in Section 6. However, local stress plays a significant impact on the degradation of the substrate; therefore, it should be studied in detail in subsequent investigations.

6. Prospectives of DIC in Reliability Test of Ceramic Substrate

The DIC method has undergone multiple stages of development to achieve high-precision technology and is widely utilized today. The primary applications of DIC include defect detection, stress–strain analysis, and deformation monitoring. With advancements in camera configurations and improvements in image processing algorithms, DIC can be employed for extreme experiments involving high deformation rates or long-term automated monitoring tests. The application of DIC has significantly expanded in both practical applications and research. Through this review of using DIC to evaluate the metallized silicon nitride substrates with a large range of temperature for thermal cycling, the DIC method demonstrated notable advantages in minimizing the influence of external temperature and atmospheric factors, thereby providing highly accurate measurement results compared to other non-destructive testing methods.

Despite the numerous advantages of DIC for various applications, this study focuses on its role in enhancing the reliability evaluation of metallized ceramic substrates used in the next generation of power modules. At this stage, thermal strain, warpage, dynamic bending behavior, and stress–strain behavior of the AMB-SN have been investigated. To the best of our knowledge, these in situ measurement results represent the first report on the thermal cycling test with temperature range from −40 to 250 °C. These findings contribute to a deeper understanding of failure mechanisms during thermal cycling of the AMB-SN substrate. Consequently, our next step is to leverage these DIC data to improve standard models in simulations, thereby enhancing predictions of the reliability of ceramic substrates under thermal cycling tests. Detailed mechanical information regarding the substrate throughout the entire thermal cycle can provide precisely defined parameters for the simulations. Furthermore, the timing and location of deformation can be incorporated into the simulation. By this way, DIC can serve as a method that promotes digital transformation technology (DX) and can be applied in the lifetime prediction of ceramic materials and metalized ceramic components.

However, there are several challenges facing DIC in the future. For instance, while the currently applied spray paint on the surface is suitable for existing temperature ranges, significantly higher or lower temperatures necessitate the use of more robust spray paints or the development of alternative methods to create better speckle patterns on the surface for the measurement process. On the other hand, the applications of DIC for inspection process in manufacturing is not popular yet. If the advantages of DIC can be utilized to develop a new DX technology, it can become a strong tool for inspection in quality management process. In addition, the DIC can be integrated with other techniques to become an advanced evaluation testing method.

7. Conclusions

This review paper is an overview of DIC method used as non-destructive method in evaluation of metallized silicon nitride substrates under its thermal cycling test. This work focuses on the degradation progress of the substrate according number of thermal cycles, including: (1) thermal strain evolution of the metallized Si₃N₄ substrate under thermal cycling before and after the formation of delamination, (2) in situ observations of warpage and deformation throughout the life cycle of the substrate, and (3) the stress–strain behavior of Cu on the substrate, considering at the non-defective state of the substrate. The review provided a completed degradation progress of the metallized Si₃N₄ substrate within its whole lifetime. The work not only advances the understanding of metallized Si₃N₄ substrate behavior under thermal cycling but also provides the potential of DIC for both research and industrial applications.