# Fatigue damage of automotive LEDs: Experimental approach and thermomechanical model

Khalil Maarouf, Christine Roucoules, Kouadio Joseph Akrou, Sergio Sao Joao, Helmut Klöcker

► To cite this version:

Khalil Maarouf, Christine Roucoules, Kouadio Joseph Akrou, Sergio Sao Joao, Helmut Klöcker. Fatigue damage of automotive LEDs: Experimental approach and thermomechanical model. Microelectronics Reliability, 2025, 171, pp.115799. 10.1016/j.microrel.2025.115799. emse-05121300

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Submitted on 19 Jun 2025

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Research paper

# Fatigue damage of automotive LEDs: Experimental approach and thermomechanical model

Khalil Maarouf<sup>a, b</sup>, Christine Roucoulies<sup>a</sup>, Kouadio Joseph Akrou<sup>a</sup>, Sergio Sao-Joao<sup>b</sup>, Helmut Klöcker<sup>b, *</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Keywords:**

Solder Joints

FEA

Thermal fatigue

Damage model

Thermal cycling

## ABSTRACT

The automotive lighting industry continues to experience significant growth as it embraces new trends focused on higher performance and smarter functionalities.

Any new products in automotive must undergo severe accelerated tests in order to ensure its reliability under the various conditions that it may be confronted with during its lifetime.

Due to the coefficient of thermal expansion mismatch between the LED package and the PCB substrate, the solder joint fatigue failure was revealed to be one of the major failure modes during accelerated thermal cycling.

The present work focuses on analyzing three LEDs (2-pads, 3-pads and 4-pads) configurations subject to thermal cycling test. First, the damage in the solder joints during tests is observed with dye penetration at different stages of cycling. During the tests, monitoring of the variation of ΔV<sub>F</sub> was made to follow the performance evolution of LED as a function of cycles. The dye penetration observations were analyzed to follow the evolution of the damage. On the 3 configurations of LEDs (2-pads, 3-pads and 4-pads) a model predicting the damage as function of the ΔV<sub>F</sub> was defined and used to establish a damage law.

The second part is focusing on a thermomechanical modeling of the strains on the solder SAC305 joint occurring during thermal cycles for the 3 configurations of LEDs mounted on the type of IMS PCB.

Finally, a fatigue analysis is addressed based on the 3 configurations of LEDs on the time to failure in the thermal cycle test. A comparison between three configurations is made and a correlation with test results is performed to evaluate the accuracy of the prediction.

## 1. Introduction

Automotive lighting has advanced to incorporate smart features like near-field projection and interior lighting, alongside traditional functions such as low/high beams, daytime running lights, and turn indicator signals, all while meeting regulatory and manufacturer standards. LEDs, known for their energy efficiency, durability, and superior performance over halogen and xenon lamps, have become a cornerstone of automotive lighting, driving advancements in LED matrices and pixelization since 2007 and accounting for 16.1 % of the global LED market by 2020 [1-4]. European automotive lighting is governed by EU regulations [5,6]. Lighting module failures may involve reduced output, color shifts, or changes in light shape. Key LED parameters and their interrelationships are explored in [7], with interactions illustrated in [8].

In LEDs, electrons and holes recombine either radiatively (producing

photons) or non-radiatively (generating self-heating). Non-radiative recombination increases with temperature, leading to reduced efficiency and more heat generation [9]. The LED's luminous flux, determined by radiative recombination efficiency, decreases with rising temperatures, which also affect color output, such as shifting white LEDs toward yellow [10,11]. LED thermal measurements are performed using a T3Ster (Mentor Graphics, Siemens) bench test, adhering to the JEDEC-51 standard, with measurements taking only a few seconds per LED after initial calibration [8,12]. The LED's optical, electrical, and thermal parameters are interdependent and quantified through electrical measurements, as explained in [13]. During testing, a heating current matching the LED's nominal forward current is applied for 1 s to achieve steady-state conditions, followed by a reduction to a lower value (1-10 mA) to minimize heat generation. As the LED is switched off, the junction temperature decreases and the forward voltage increases (ΔV<sub>F</sub> =

<footnote><sup>a</sup> Valeo Lighting Systems, 93000 Bobigny, France</footnote>

<footnote><sup>b</sup> Mines Saint-Etienne, Univ Lyon, CNRS, UMR 5307 LGF, Centre SMS, F - 42023 Saint-Etienne, France</footnote>

<footnote>* Corresponding author at: Mines Saint Etienne, 158 Cours Fauriel, France.</footnote>

<footnote>E-mail address: klocker@emse.fr (H. Klöcker).</footnote>
$V_{Ff}$ – $V_{Fi}$), with the junction temperature and forward voltage relationship quantified by the k-factor (K/mV) as described in [7].

Automotive lighting modules are designed to last 15 years without performance degradation, enduring harsh environmental conditions, including temperature variations from –15 °C in winter to 40 °C in summer [14], and heat generated by high currents or frequent switching of LED chips, with engine temperatures around 90 °C. Thermal loadings can lead to failures in electronic components like semiconductors and LEDs. The LED assembly, a multi-layer structure with materials having different thermal expansion coefficients (CTEs), experiences constrained expansion due to layer connections, with a significant CTE mismatch between ceramic (4.5 ppm/°C) and aluminum in PCB substrates (25 ppm/°C), causing thermal expansion to damage solder joints, which are responsible for 70 % of electronic component failures, primarily due to thermal stresses and fatigue, leading to cracks that degrade light flux in LEDs during reliability tests [15,16].

Solder damage induced by thermal fatigue is controlled by the LED architecture (the number of pads), the substrates used, the solder material and the reflow process. Cracks in solder joints reduce the contact area between the LED and its structure, leading to increased thermal resistance, which worsens as the cracks propagate. A study by [17] found that thermal resistance increased with the number of cycles, correlating with the observed crack growth. Further studies by [18,19] explored the relationship between crack size and thermal resistance in LED modules, offering insights into damage locations by analyzing the thermal path.

Solder joint materials have evolved through three phases: 1) Tin-lead (Sn—Pb) alloys were widely used until July 2006 but phased out due to environmental and health concerns [20,21]; 2) Lead-free Sn-Ag-Cu alloys became the preferred alternative, though they face challenges in high-temperature automotive applications [22]. 3) Research now focuses on doping Sn-Ag-Cu alloys with elements like Bi, Sb, or Ni to improve their performance over Sn—Pb alloys.

In the reflow soldering process, solder paste and flux are applied to the LED pads on the IMS-PCB, and the LEDs are precisely positioned before being heated in a reflow oven, where a thermal profile melts the paste and forms a metallurgical bond between the LED and PCB [23,24]. The process includes four stages: 1) Preheating: the temperature rises to 120–150 °C at 1–3 °C/s; 2) Soak: temperature increases to the solder alloy’s melting point (183–217 °C); 3) Reflow: assembly is kept at temperatures above the melting point (235 °C–250 °C) for 45–90 s; 4) Cooling: temperature is reduced to solidify the solder at a rate of 1–4 °C/s [25]. The reflow process can lead to porosity, incomplete soldering and thermal stress in solder joints [26,27].

This research aims to investigate the fatigue life of solder joints in high-power LEDs used in automotive applications during thermal reliability testing, with a focus on improving product reliability and reducing development costs. The specific objectives are as follows:

* Develop models for solder joint fatigue and modify existing failure criteria.

* Use the $\Delta V_F$ parameter (change in forward voltage) as an experimental damage indicator.

* Incorporate design parameters of high-power LEDs into the analysis.

* Analyze cumulative damage in solder joints due to thermal cycling and thermal shock loadings.

In the following section the experimental set-up is described. The different LEDs and corresponding loadings are described in detail.

## 2. Experimental set-up

Thermal Cycling tests evaluate the ability of components and solder interconnects to withstand mechanical stresses from alternating high and low temperatures. The temperature transitions gradually in a single-chamber oven with forced convection, unlike the rapid transitions in

thermal shock tests. The temperature range is similar (max 150 °C, min –65 °C), with a minimum dwell time of 15 min. The key difference from thermal shock is the longer transition time, which avoids thermal gradients in the assembly. This test simulates real-life temperature changes more closely and is used to validate component reliability [28,29].

Thermal Shock tests assess a component's ability to endure sudden and extreme temperature changes and repeated exposures to these extremes. The test involves transitioning components between hot and cold chambers, with the transition time not exceeding 20 s. The temperature extremes can range from 150 °C (max) to –65 °C (min), with the dwell time sufficient to ensure temperature uniformity across the structure, verified using thermocouple measurements. Failure criteria and specific conditions for each design are provided by [30].

### 2.1. Tested LED configurations

The thermal dissipation and hence the potential damage in solder joints depends on the LED architecture, the solder material, the reflow process, the substrate and the loading. In present work, two solder materials are analyzed: a reference solder SAC305 (D) and a new solder material (A). Two PCBs were considered. AA5052 and CTEII. Indeed, Aluminum Insulating Metal Substrates (IMS), combining the electrical properties of a metal base with the insulating characteristics of a dielectric layer, are ideal for applications requiring heat dissipation and electrical insulation, such as automotive front lighting with high-power LEDs, and typically consist of three layers: a metal base, dielectric layer, and conductive copper layer [15]. For each combination of PCB and solder material, two reflow conditions were tested (Table 1). ‘V’ corresponds to reflow under vacuum condition and ‘N’ corresponds to reflow under ambient conditions. In the current study, three LED references are considered.

LED samples were assembled in panels. Each panel contained 6 PCBs. And each PCB had 8 LEDs of the same reference, resulting in a total of 6 different LED references being tested per panel. A connector is placed in the center of each PCB to ensure electrical connections from the power device (Fig. 1). In this paper the analysis will focus on three LEDs, 2-pads, 3-pads and 4-pads LEDs, mounted on IMS PCB corresponding respectively to ‘PCB 1’, ‘PCB 3’ and ‘PCB 5’ in Fig. 1(b).

The impact of the number of pads (Fig. 2) and the package geometry (Table 1) was evaluated, along with the influence of other parameters (Table 2), on the time to failure during thermal cycle testing. For this study, the three different LED package types were subjected to various thermal cycles to develop a new simulation model for more accurate predictions of the time to failure. The 3-pads LED package has pads with a surface area 27 % larger than those of the 2-pads LED package, while the 4-pads LED package features pads that are seven times larger than those of the 2-pads LED package. Each pad contains a copper layer above the solder. The thicknesses of these layers vary between 10 µm for the 2-pad LED and 60 µm for both 3 and 4-pad LEDs (Fig. 3(a)). The LEDs are soldered to IMS-PCB by the means of solder joints with a 50 µm thickness.

### 2.2. Thermal cycling testing conditions

Literature results indicate that fatigue damage predominantly occurs in the solder joints of LEDs. The goal of the present work is to simulate the thermomechanical fatigue of the LED assembly and the consequent damage development in their solder joints. The thermal cycle test was performed with the same temperature range ($T_{min}, T_{max}$) on a large number of samples (Fig. 3). Before launching the test, the voids status was evaluated on each LED. The characterization of the initial variation of forward voltage $\Delta V_F$ was performed. During the test, measurement of $\Delta V_F$ was done at specified cycles. Finally, some PCB were extracted for Dye penetrant analysis to check the proportion of damage at specific cycles.
<caption>**Table 1**</caption>

Configurations tested. All mentioned LEDs were tested under thermal shocks (TS) and thermal cycling conditions (TC). Two different PCBs were considered: AA5052 and Aluminum CTE II. Two solder materials were tested. The reference solder SAC305 (D) and a new solder material (A). For all combinations of solder material and PCB two reflow conditions were tested: vacuum (V) and non-vacuum oven (N). The table indicates the number of LEDs tested for each condition.

<table><thead><tr><th rowspan="2">PCB<br>Reflow</th><th colspan="2">2-Pads<br>AA5052</th><th colspan="2">CTE</th><th colspan="2">3-Pads<br>AA5052</th><th colspan="2">CTE</th><th colspan="2">4-Pads<br>AA5052</th><th colspan="2">CTE</th></tr><tr><th>N</th><th>V</th><th>N</th><th>V</th><th>N</th><th>V</th><th>N</th><th>V</th><th>N</th><th>V</th><th>N</th><th>V</th></tr></thead><tbody><tr><td>A</td><td>128</td><td>128</td><td>128</td><td>128</td><td>128</td><td>128</td><td>128</td><td>130</td><td>128</td><td>128</td><td>128</td><td>128</td></tr><tr><td>D</td><td>32</td><td>32</td><td></td><td></td><td>32</td><td>32</td><td></td><td></td><td>32</td><td>32</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Thermal cycle tests. Panel a shows the rack with 6 panels put in the climatic chamber. Panel b gives the detail of a typical panel. Each panel corresponds to 6 test configurations. On each test configuration 8LEDS are mounted on a particular PCB (PCB1-PCP6). The connector in the center of the panel allows to power independently each LED.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Schematic representation of the LED architectures tested. (a) 2 electrical pads (2-pads hereafter), (b) 2 electrical and 1 thermal pad (3-pads hereafter), (c) 4 electrical pads (4-pads hereafter).</figcaption></figure>

<caption>**Table 2**</caption>

Performance of the LEDs under a 1000 mA forward current.

<table><thead><tr><th>Characteristics</th><th>2-Pads</th><th>3-Pads</th><th>4-Pads</th></tr></thead><tbody><tr><td>Package (mm)</td><td>1.5 * 1.85 *</td><td>1.9 * 1.5 *</td><td>3.75 * 3.50 *</td></tr><tr><td>Nominal forward voltage V<sub>F</sub><br>(V)</td><td>0.8</td><td>0.73</td><td>0.7</td></tr><tr><td>Heat power (W)</td><td>3.3</td><td>3.25</td><td>6.5</td></tr><tr><td>Thermal resistance (K/W)</td><td>2.31</td><td>2.4</td><td>7.6</td></tr><tr><td></td><td>5.8</td><td>6.7</td><td>3.3</td></tr></tbody></table>

# 3. Experimental results

## 3.1. Voids present after reflow

After reflow each one of the three LED configurations were characterized by X-ray to evaluate the voids. X-ray data images generated to analyze the pads after reflow of all DoE samples represent 1728 images in the shape of (1004 × 1004 pixels), similar to the ones illustrated in Fig. 4.
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) Thermal cycling test setup (b) temperature cycling profile.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. X-ray generated images (a) 2-pads (b) 3-pads (c) 4-pads.</figcaption></figure>

X-ray imaging is commonly used to inspect voids in solder joints due to its non-destructive capability. X-ray absorption correlates with the atomic number of materials, generating grayscale images that reflect the density and material thickness. X-ray inspection can be automated for high throughput, but void ratio assessment often relies on time-consuming manual inspection and segmentation hence limited quantitative analysis on few samples. Image segmentation methods like thresholding and statistical algorithms (e.g., k-means) have been used for void detection, but these methods are not suitable for solder joints of arbitrary shapes [31].

Since 2014, convolutional neural networks (CNNs) for image segmentation, such as U-net algorithms, have shown promising results for void ratio segmentation [32]. A fully convolutional network developed in [32] enables automatic void segmentation in X-ray images of LED solder joints. Additionally, [33] combined two CNN models, one for

solder joint segmentation and another for void segmentation, allowing for the calculation of void ratios in each solder pad.

The U-Net model is a type of convolutional neural network (CNN) designed primarily for biomedical image segmentation. The model was trained to detect voids and pads for each image using the dataset of 96 images where each image corresponds to one specific LED and six LED references are involved in the dataset which help avoid overfitting on a specific LED. For each LED reference 16 LEDs were considered (16 (LEDs) × 6(LED references) = 96 X-ray images).

The dataset was divided into 76 training images and 20 validation images mentioned in the previous paragraphs. The accuracy was measured on the validation dataset, meaning that for each pixel prediction, the likelihood of making a correct prediction is 95.17 % for void detection and 93.85 % for pad detection (Fig. 5).

Table 3 resumes the void ratio in the different configurations. LEDs

<figure><img src="image_7.png" /><figcaption>Fig. 5. Model predictions (a) original image (b) cropped image (c) voids detection (d) pads detection.</figcaption></figure>
<table><caption>**Table 3**
Void ratio in solder joint per design configuration.</caption><thead><tr><th rowspan="2">PCB</th><th rowspan="2">Pads/LED</th><th colspan="2">Solder type</th></tr><tr><th>A</th><th>D</th></tr></thead><tbody><tr><td rowspan="5">5052_N</td><td>2-Pads</td><td>3 %</td><td>3 %</td></tr><tr><td>3-Pads</td><td>14 %</td><td>10 %</td></tr><tr><td>4-Pads</td><td>23 %</td><td>20 %</td></tr><tr><td>2-Pads</td><td>0 %</td><td>0 %</td></tr><tr><td>3-Pads</td><td>1 %</td><td>1 %</td></tr><tr><td rowspan="5">5052_V</td><td>4-Pads</td><td>2 %</td><td>2 %</td></tr><tr><td>2-Pads</td><td>2.8 %</td><td></td></tr><tr><td>3-Pads</td><td>11.4 %</td><td></td></tr><tr><td>4-Pads</td><td>22.4 %</td><td></td></tr><tr><td>2-Pads</td><td>0.2 %</td><td></td></tr><tr><td rowspan="2">CTE_N</td><td>3-Pads</td><td>1.0 %</td><td></td></tr><tr><td>4-Pads</td><td>2.2 %</td><td></td></tr><tr><td rowspan="2">CTE_V</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr></tbody></table>

assembled in vacuum ovens exhibit very small void surface fractions in their solder joints, (ranging from 0.5 % to 2 %) compared to the samples gone through the reflow without vacuum (void surface fractions ranging from 2.8 % to 25 %). The type of PCB does not appear to affect void generation in these joints. We also see that the void ratio is higher in 4-pads LEDs than in 3-pad LEDs and 2-pads LEDs especially when reflow in normal atmosphere. The 4-pad LEDs have a pad size approximately 5 times larger than the 2- and the 3-pad LEDs. Larger pad sizes lead classically to increased void volume fractions under normal atmosphere reflow conditions. However, when making the reflow in vacuum the voids proportion is less sensitive to the size of the pads.

## 3.2. ΔV<sub>F</sub> analysis

To enhance the detection of failure during thermal cycle tests, the forward voltage differential (ΔV<sub>F</sub>) [12] was measured across different cycles. This measurement is commonly adopted for LED transient thermal characterization methods. The progression of damage during thermal shocks and thermal cycling has been observed to affect the heat transfer path, as evidenced by changes in structure function measurements. This indicates that the thermal resistance of the LED module increases with the number of cycles, as shown by analyzing the relationship between the thermal resistance of an LED module and the crack size in the solder joint [2,3]. This raises the question: can an evolution of ΔV<sub>F</sub> a reliable metric for monitoring damage progression?

In our study, ΔV<sub>F</sub> was measured across varying numbers of cycles during both Thermal Shocks (TS) and Thermal Cycling (TC) to monitor its progression, however in this paper we will focus mainly on TC results. Table 4 provides a summary of the configurations, including the number of LEDs and the cycle counts at which ΔV<sub>F</sub> measurements were taken during TC. It is worth mentioning that when analyzing the evolution of Δ(ΔV<sub>F</sub>) as a function of the number of cycles during thermal cycling on 12 LEDs under the same configurations as the thermal shock tests, a similar trend was observed in both Thermal Cycling and Thermal Shocks.

The variation of ΔV<sub>F</sub>, i.e. (Δ(ΔV<sub>F</sub>)) increases for LEDs mounted with both solder types D and A as a function of the number of cycles on 2-pads. A similar trend is observed for LEDs with 3-pads and 4-pads using solder types D or A during thermal cycling. This behavior exhibits a pattern of slow initial growth followed by a rapid increase, as shown in Fig. 6. This increase comes also with an increase in the

<table><caption>**Table 4**
Number of thermal cycles (TC) at which ΔV<sub>F</sub> measurement per configuration were made.</caption><thead><tr><th>Configuration</th><th>Number of LEDs</th><th>Measurement cycles</th></tr></thead><tbody><tr><td>5052 VA</td><td>16</td><td>[0, 500, 800, 900, 1000, 1700, 2000]</td></tr><tr><td>CTE VA</td><td>24</td><td>[0, 500, 800, 900, 1000, 1700, 2000]</td></tr><tr><td>5052 VD</td><td>20</td><td>[0,250, 500, 800, 900, 1500, 1700, 1800]</td></tr></tbody></table>

dispersion of the measurement suggesting that the increase rate in the ΔV<sub>F</sub> can be different from one LED to another.

The slow growth phase of Δ(ΔV<sub>F</sub>), followed by a rapid increase, is typically associated with exponential damage progression. This trend was also observed on another PCB, referred to as CTE, using solder type A. The low dispersion in the measurement in the first phase can be attributed to the preserved structural integrity of the assembly. In the second phase, the increase rate in ΔV<sub>F</sub> differs from one LED to another suggesting changes in the thermal paths hence in the structural integrity of the LED. This is interpreted mainly as a development of a fatigue damage in the solder joints during testing. These Δ(ΔV<sub>F</sub>) trends are utilized in the subsequent analysis of damage evolution as a function of ΔV<sub>F</sub>.

## 3.3. Dye penetrant observations

A first analysis of thermal shock samples with dye penetrant showed that the damage was starting from the external edges in thermal shocks [4]. The damage analysis was extended to thermal cycles damage analysis to the three LED configurations mounted with solder D and presented in Fig. 7 below. The comparison between thermal shock and thermal cycles damage confirms that on the three LED configurations the damages are starting from the external edges of the pads and extending toward the center of the LED. Dye Penetrant on LED subject to 1400 TS cycles, and 1800 TC cycles show similar patterns.

All dye penetrant images were analyzed to measure the total crack surface fraction, which was then normalized by the total pad surface area. By examining the increase in damage as a function of cycles, which correlates with the evolution of the variation in ΔV<sub>F</sub>, a relationship between damage (represented as the reduction in area) and the variation in ΔV<sub>F</sub> was evaluated. This approach provides a means to quantify the statistical progression of damage without requiring cross-sectional analysis or further dye penetrant testing.

## 3.4. Relation between crack surface and final ΔV<sub>F</sub> measurement

The study was initially conducted using LEDs with 2-pads and 3-pads, and the findings were later verified on LEDs with 4-pads. Similar trends in evolution were observed for LEDs with two and three pads (Fig. 8). Data from solder type A on the 2-pads and 3-pads configurations was utilized to develop a model linking damage, represented as the fraction of damaged surface area relative to the total pad surface area, to the variation in ΔV<sub>F</sub>.

This model was further linked to thermal resistance, with both the thermal resistance (R<sub>th-ja</sub>) and the variation in forward voltage (ΔV<sub>F</sub>) being considered linearly proportional to the junction temperature variation ΔT<sub>j</sub>, as described in Eqs. (1) and (2). The increase in thermal resistance R<sub>th-ja</sub> with crack surface fraction f led to the derivation of Eq. (3). Here, f is defined as the ratio of cracked surface area to initial pad area (A<sub>ci</sub>), and β* is an empirical fitting parameter.

$$R_{th-ja} = \frac{\Delta T_j}{P_h} \qquad (1)$$

$$\Delta T_j = K \cdot \Delta V_F \qquad (2)$$

$$f = 1 - \frac{\beta^*}{\beta^* + A_{ci} \Delta V_F} \qquad (3)$$

The relation Δ(ΔV<sub>F</sub>)(f) between the crack surface fraction f and the relative increase in the forward voltage differential Δ(ΔV<sub>F</sub>) established in the section above, is illustrated in Fig. 8(a, b, c) for the LEDs configurations with solder type “A” and “D” are plotted; on the x-axis Δ(ΔV<sub>F</sub>) of the LED and on the y-axis the observed crack surface fraction (f). It shows that the damage in the solder joints is proportional to the increase of the ΔV<sub>F</sub> measured either for the 2-pads LED, the 3-pads LED
<figure><img src="image_8.png" /><figcaption>Fig. 6. Evolution of Δ(ΔVF) function of cycles.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Dye penetrant observation on LEDs subject to thermal shock and thermal cycling.</figcaption></figure>

and the 4-pads LED.

The model representing the fraction of damage (f) as a function of the difference in (ΔVF) between cycle (N) and cycle 0 (Eq. (3)) was developed based on LEDs with 2-pads and 3-pads using solder type A, as illustrated in Fig. 9. This model is developed under the assumption that the damage during thermal shock and thermal cycling is located in the solder joint. The relation between the two damage variables (Δ(ΔVF)

and (f) is independent of the testing condition. Fig. 8 depicts results obtained by TS and TC tests. This hypothesis is based on previous testing and literature results. Besides, dye penetrant observations illustrated solder joint fatigue damage as the predominant failure mode during these tests. Hence, damage occurring in other locations than the solder interconnection is undermined.

The damage quantification process is inherently affected by the
<figure><img src="image_10.png" /><figcaption>Fig. 8. Scatter of point represents the (Δ(ΔVF), f) with respect to applied test.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Fitting the experimental data to the proposed law.</figcaption></figure>

variability in ΔVF measurements and damage estimation methods. This uncertainty was systematically evaluated across damage levels (Table 5), with the standard deviation of the predicted damage providing a practical metric to assess the range of potential ΔVF criteria. For damage levels above 80 %, randomness Δ(ΔVF) is accentuated and translated in higher standard deviations.

The progression of damage as a function of the number of cycles can be observed through the variation in ΔVF, corresponding to damage ranging from 25 % to 90 % of the cracked surface. The relationship between the number of cycles N and ΔVF was determined at fixed damage levels for each tested LED. Now, we know the relation Δ(ΔVF) (N). This relation was combined with Δ(ΔVF)(f) represented in Fig. 8. The combination of Δ(ΔVF)(N) and Δ(ΔVF)(f) allows to define Weibull

<table><caption>**Table 5**
Uncertainty estimation of the developed model.</caption><thead><tr><th></th><th>LED 2-pads</th><th>LED 3-pads</th><th>LED 4-pads</th></tr></thead><tbody><tr><td>RMSE</td><td>0.142</td><td>0.110</td><td>0.139</td></tr><tr><td>Δ(ΔVF)(80 %)</td><td>43 % mini<br>354 % maxi</td><td>75 % mini<br>270 % maxi</td><td>43 % mini<br>154 % mini</td></tr><tr><td>Δ(ΔVF)(50 %)</td><td>12.7 %<br>40.1 %</td><td>17.6 %<br>43.2 %</td><td>12 %<br>37.8 %</td></tr></tbody></table>

curves of failure, as shown in Fig. 10. However, deviations from the Weibull curve are noticeable for failure probabilities below 30 %, suggesting a possible change in the failure mode for LEDs with 3-pads and 4-pads. The Weibull distributions were determined only for LEDs submitted to TC tests.

Among all the Δ(ΔVF)(N)-relations determined experimentally, some exhibited very low R²-values. These measurement issues may correspond to negative variations in ΔVF, or zero ΔVF due to failure on 2-pad LEDs. The corresponding Δ(ΔVF)(N)-curves (with R²-value lower than 0.8) were not used to construct the Weibull curves. This approach ensures a more accurate representation of the Weibull model, based on reliable ΔVF variations. Resulting in 5 LED samples considered for the 2-pad LED and 12 LED samples considered for both 3-pad and 4-pad LEDs. On Fig. 10, damage evolution in the 2-pad LED leads to a straight line for the Weibull distribution. Hence, this refinement allows for a more precise analysis of damage progression and failure probabilities (Fig. 11).

Considering the variation of ΔVF at 90 % or 100 % damage results in an unrealistic Mean Time To Failures (MTTF), as the samples have already failed, leading to null ΔVF values for the remaining LEDs after removal. Due to uncertainties between 80 % and 100 % cracks, the modeling of ΔVF for some LEDs shows low R² values. The MTTF at 90 % cracks does not provide a realistic estimate of damage, as it corresponds
<figure><img src="image_12.png" /><figcaption>Fig. 10. Cumulative failure probability with respect to the considered damage fraction f.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Cumulative failure probability for 50 % and 90 % damage (a) 2-pads LED, (b) 3-pads LED, (c) 4-pads LED.</figcaption></figure>

to an average ΔV<sub>F</sub> variation exceeding 100 %.

Furthermore, at 80 % damage, the variation in ΔV<sub>F</sub> exhibits an exponential increase, indicating a rapid loss of functionality. To evaluate the fatigue law accurately, it is more effective to identify the MTTF based on ΔV<sub>F</sub> variations when most LEDs are still measurable, using the 80 % damage threshold to estimate the Weibull distribution for full cracking.

The 2-pads LEDs exhibit the fastest failure rate compared to the 3-
pads and 4-pads LEDs. Despite the larger package size of the 4-pads
LEDs, their Mean Time To Failure (MTTF) is 215 cycles longer than
that of the 2-pads LEDs (Fig. 12). Generally, the larger the LED package,
the faster the damage accelerates according to Engelmaier's model.
However, in our case, the 2-pad LED exhibits a higher failure rate than
the 4-pad LED. This can be explained by the difference in copper layer
thickness within the LED packages: the 2-pad LED has a 10 µm copper
layer, whereas the 4-pad LED has a 60 µm layer. This hypothesis will
later be verified through the finite element (FE) analysis of both LEDs.
Thicker copper layers allow a better redistribution of the strain due to
CTE mismatch.

The 3-pads LEDs demonstrate the best overall performance. For all
LED configurations, a change in slope is observed below a 30 % failure
probability, which will be analyzed in more detail in the next section.

Fig. 12 illustrates the differences in the scale and shape factors for

each LED, demonstrating that each LED exhibits distinct failure behav-
iors. This can also be confirmed by performing Kolmogorov-Smirnov
(KS) or Anderson-Darling tests on the Weibull data. Test Results for
50 % crack propagation is as follow:

Kolmogorov-Smirnov test (K.-S. test):

* 2-pad vs. 3-pad: Reject the null hypothesis (p = 0.000). This is strong evidence that the distributions differ.

* 2-pad vs. 4-pad: Reject the null hypothesis (p = 0.036). The K.-S. test gives evidence that the distributions differ.

* 3-pad vs. 4-pad: Fail to reject the null hypothesis (p = 0.074). The K.-S. test is insufficient to conclude at difference.

Anderson-Darling test (A.-D. test):

* 2-pad vs. 3-pad: Test statistic (5.225) exceeds all critical values. The A.-D. test strongly rejects the null hypothesis.

* 2-pad vs. 4-pad: Test statistic (0.143) is below the lowest critical value. The A.-D. test fails to reject the null hypothesis.

* 3-pad vs. 4-pad: Test statistic (1.257) falls between critical values. The A.-D. test leads to borderline significance (~10 %).

These tests shows that the 2-pad LED differs significantly from both
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Cumulative failure probability for LED 2-pads LED 3-pads LED, 4-pads LED. (a) for 50 % damage and (b) and 80 % damage.</figcaption></figure>

3-pad and 4-pad, with the strongest evidence in the 2-pad vs. 3-pad comparison. The difference between 3-pad and 4-pad is less clear: the KS test fails to reject the null hypothesis, while the Anderson-Darling test shows borderline significance.

For the 80 % crack propagation criteria:
Kolmogorov-Smirnov test (K.-S. test):

* 2-pad vs. 3-pad: Reject the null hypothesis ($p = 0.000$). Strong evidence of different distributions.

* 2-pad vs. 4-pad: Reject the null hypothesis ($p = 0.005$). Evidence of different distributions.

* 3-pad vs. 4-pad: Reject the null hypothesis ($p = 0.042$). Weaker evidence of a difference.

Anderson-Darling Test (A.-D. test):

* 2-pad vs. 3-pad: Test statistic (6.773) exceeds all critical values. The A.-D. test strongly rejects the null hypothesis.

* 2-pad vs. 4-pad: Test statistic (2.191) falls between critical values. The A.-D. test leads to moderate evidence (4.1 % significance).

* 3-pad vs. 4-pad: Test statistic (0.708) falls between critical values. The A.D. test leads to weak evidence (16 % significance).

Which shows that the 2-pad LED exhibits a strongly different failure behavior compared to the 3-pad and 4-pad, suggesting a fundamentally distinct failure mechanism. The differences between 3-pad and 4-pad are subtler, indicating similar but not identical failure patterns. The statistical analyses (Kolmogorov-Smirnov and Anderson-Darling tests) consistently demonstrate that the 2-pad LED exhibits a significantly different failure behavior compared to the 3-pad and 4-pad LEDs, particularly at higher crack propagation levels (80 %). This suggests a fundamentally distinct failure mechanism in the 2-pad design, likely influenced by its thinner copper layer (10 µm vs. 60 µm). In contrast, the 3-pad and 4-pad LEDs show more similar failure patterns, though subtle differences exist. These results highlight the critical role of package design and material properties (e.g., copper thickness) in LED reliability, with implications for optimizing durability in future iterations.

# 4. Thermomechanical modeling considerations

## 4.1. Thermomechanical model

In our approach, the LED's internal architecture is simplified for modeling purposes. Specifically, the LED chip and phosphor converter are combined into a single layer to streamline the representation. The internal LED integrated circuit and Electrostatic Discharge (ESD) protection are treated as a continuous copper layer, further reducing complexity.

The design is symmetric along both the X and Y axes. During testing, the assembly is not fixed or constrained on a rigid platform, allowing it to expand or contract freely under thermal loading, accordingly, the boundary conditions are imposed in a way to forbid rigid body motion. Therefore, in our model, we will consider a single LED and its copper layout as shown in Fig. 13. Hence, three geometric models are elaborated, each representing either a 2-pads LED, 3-pads LED or a 4-pads LED.

We use a shared topology with a coincident mesh to ensure proper contact between the layers, and quadratic elements are employed to enhance accuracy. The mesh is refined around the LED to capture finer details and improve simulation precision. For the solder joints, we recommend using 4 or 5 hexahedral (Hex20) elements along the thickness to ensure sufficient resolution and a uniform distribution of elements and nodes. Hex20 elements are also used for the copper pads and the aluminum substrate, while other layers use tetrahedral and pyramidal elements.

For the silicon (Si) and aluminum nitride (AlN) layers, we assume linear, temperature-independent isotropic material behavior. However, the elastic modulus of the dielectric material decreases with increasing temperature, particularly as it approaches its glass transition temperature, leading to a significant reduction in its values. The mechanical properties used in the simulations are summarized in Table 6.

Thermal Cycle (TC) tests are addressed using static thermomechanical models, which exclude viscosity effects from our analysis. Instead, we will use stress-strain data with temperature dependencies from viscoplastic Anand models, without incorporating the Anand viscosity parameters directly. The engineering stress strain curves for solder 'A' and solder 'D' are shown in Fig. 14.
<figure><img src="image_15.png" /><figcaption>Fig. 13. LED configurations architectures.</figcaption></figure>

<table><caption>**Table 6**

Mechanical material properties.</caption><thead><tr><th>Material</th><th>E (GPa)</th><th>CTE (10<sup>-6</sup>·°C<sup>-1</sup>)</th></tr></thead><tbody><tr><td>Si. chip</td><td>130</td><td>2.6</td></tr><tr><td rowspan="2">Cu</td><td>-50 °C</td><td>132.2</td><td>100 °C</td><td>16.9</td></tr><tr><td>100 °C</td><td>125.6</td><td>200 °C</td><td>17.3</td></tr><tr><td rowspan="2">Dielec.</td><td>25 °C</td><td>13</td><td>25 °C</td><td>34</td></tr><tr><td>160 °C</td><td>0.5</td><td>135 °C</td><td>88</td></tr><tr><td>AA 5052</td><td>25 °C</td><td>68.8</td><td>-50 °C</td><td>22.1</td></tr><tr><td>AlN</td><td>150 °C</td><td>63.4</td><td>100 °C</td><td>23.8</td></tr><tr><td></td><td>300</td><td></td><td>4.6</td><td></td></tr></tbody></table>

Our study utilizes static structural simulations, where the results at each time step are independent of previous steps. Thermal Cycles (TC) are modeled by applying a uniform temperature to simulate extreme conditions. This approach excludes dwell time and viscosity effects, focusing solely on the impact of extreme temperatures which is the main root cause of failure with memory and time effectiveness. Fig. 15 shows a typical temperature profile for TC tests, with simulations conducted for branches 1 and 2.

<figure><img src="image_16.png" /><figcaption>Fig. 14. Engineering stress-strain (a) solder D (b) solder A.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Fig. 15. Thermal cycling temperature profiles.</figcaption></figure>

## 4.2. Plastic strain analysis

Some common multiaxial criteria in the literature use equivalent plastic strain [34,35]. However, this paper proposes the use of principal strains, focusing on the principal directions, to predict the fatigue life of solder joints. This approach better reflects the physics of the loadings by accounting for the tensile or compressive nature of the loading as cracks mainly propagates perpendicular to the maximum principal direction.

Fig. 16 illustrates the distribution of the maximum principal plastic strain in the solder joint at the high temperature $T_{max}$. It shows that the highest strains occur closer to the solder/LED interface, regardless of whether it is a 2-pads, 3-pads, or 4-pads LED. Positive strain values indicate tensile strain.

Fig. 17 depicts the minimum principal plastic strain at the low temperature $T_{min}$, also showing that the highest strains (absolute value) occur near the solder/LED interface for the 2-pads, 3-pads, and 4-pads LEDs. Negative strain values indicate compressive strain.

When analyzing the principal directions, we observed that the maximum principal direction at $T_{max}$ corresponds to the minimum principal direction (maximum absolute value) at $T_{min}$. This suggests that the maximum loading direction alternates between tension and compression during the thermal cycling test, influencing the behavior of the solder joint. Solder joint damage may be analyzed with a standard low cycle fatigue Manson-Coffin relation. Indeed, we consider power law relation between the number of cycles to failure N and the plastic strain range $\Delta\epsilon_p$. However, in present work, the plastic strain measure used in Manson-Coffin is thus defined as follows:

$$ \Delta\epsilon_p = \epsilon_{p\_max} - \epsilon_{p\_min} \quad (4) $$

where $\epsilon_{p\_max}$ and $\epsilon_{p\_min}$ are respectively the maximum and minimum principal plastic strains.

## 4.3. Damage criterion based on the plastic strain distribution

As cracks in the solder joints develop in the solder joint sectional plane as illustrated in the dye penetrant observation, a sectional plan closer to the LED interface is considered to depict the plastic strain range during thermal cycling.

In the sectional plane, the plastic strain range is maximized at the

exterior corners and decreases toward the center of the LED (Fig. 18). This indicates that the lowest strain values are found at the center of the LED. Consequently, cracks are expected to initiate at the corners and propagate toward the center of the LED during cyclic thermal loading. When averaging the plastic strain on the total pads surface, the minimum average plastic strain is observed for the 3-pads LED, while the maximum average plastic strain is found in the 2-pads LED. However, when only focusing on the corners the maximum plastic strain is found on the 4-pads LED. The small copper thickness of the 2-pad LED (Fig. 3 (a)) explains the higher strains in the 2-pad LED compared to the other LEDs. On the other hand, the larger size of the 4-pad LED compared to the 3-pad LED can explain its higher strain values. Small copper layers lead to larger strains in the solder joints and larger pad sizes also lead increased strains.

To establish a failure criterion for 50 % crack damage, we propose calculating the average maximum plastic strain over 50 % of the surface, starting from the external edges (Fig. 19). This allows for a comparison of the average maximum plastic strain with the Mean Time To Failure (MTTF) for 50 % damage, evaluated using the Weibull curve based on the variation in $\Delta V_F$.

In this analysis, the minimum average plastic strain is observed for the 3-pads LED, while the maximum average plastic strain is found in the 4-pads LED. This observation illustrates the high plastic strain in the 4-pads compared to the 2-pads in the corners but also its lower values in the center of the LED highlighting the different strain distribution for the different LEDs. This conclusion can be interpreted by the fact that the 4-pad LED reaches its 50 % crack before the 2-pads LED however and for a full crack criterion the 2-pads LED may reach the failure before the 4-pads LED.

However, when comparing this with the MTTF evaluated from the Weibull curve based on $\Delta V_F$, the experimental evaluation shows that the highest MTTF corresponds to the 3-pads LED, while the 2-pads LED has the lowest MTTF, and the 4-pads LED does not exhibit the expected trend.

This approach provides a more comprehensive understanding of how plastic strain accumulates and varies across different solder joint designs subjected to thermal cycling conditions. The integral of the strain on a path with a criterion of 10 % [35] on the equivalent plastic was used in the past to calculate the variation of the plastic strain. It showed an overestimation of life prediction [36] on LED first estimation due to the positive values of plastic strains at cold conditions. The integral criteria of 10 % on the path was changed to 30 % on BGA [37]. Here the variation from the maximum and minimum plastic strains are calculated on the average surface of the electrical and thermal pads for all three LED configurations. The highest plastic strain variation is observed in the 2-pad LED, which has the largest package size, while the lowest variation is seen in the 3-pad LEDs. The evolution of the average plastic strain is consistent with the Mean Time To Failure (MTTF) evolution, as indicated by the variation in $\Delta V_F$.

This representation of evolution of damage during cycling in a plane is offering a more physically meaningful representation than analyzing distributions along paths in the solder joint for 1800 cycles. Yet the hypothesis of the average plastic strain is assuming an equivalent

<figure><img src="image_18.png" /><figcaption>Fig. 16. Maximum principal plastic strain distribution in the solder joints at hot condition ($T_{max}$).</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Fig. 17. Minimum principal plastic strain distribution in the solder joints at cold condition (T<sub>min</sub>).</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 18. Plastic strain range distribution in the section plan.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 19. Highest plastic strain range distribution in the section plan.</figcaption></figure>

propagation from each edge of the damage. This seems to be well supported from the Weibull curve and the dye penetrant (Fig. 20).

However, for the Weibull curve, while it fits well for most of the data, the deviation at lower damage levels may indicate a less homogeneous failure at the beginning of the damage process, which is not captured in the simulation. This behavior can also be observed in some dye penetrant images at 600 cycles, where damage initiates preferentially on one side of the pads rather than uniformly across all pads.

This localized behavior could influence the prediction of the failure probability at 1 %, as the slope of the Weibull curve changes below 30 % probability. It suggests a shift from slow, localized damage growth to a rapid, generalized damage increase across all pads. A difference of behavior was also reported using a thermal resistance solder change criteria and a LED thermal resistance change criteria in the Weibull

curve [38].

## 5. Fatigue thermal cycle prediction

Despite this gap, the average maximum and minimum plastic strain in the plane was used to define a new fatigue law for cycles between 100 % and 50 % damage, based on the 2-pads and 3-pads LEDs with solder D. The root mean square error was used to quantify the uncertainty of the prediction. The new fatigue law [36] was validated by predicting the thermal cycle time to failure for the 4-pads LED.

The prediction of the Mean Time To Failure (MTTFF) for 100 % crack damage is within 4.4 % of the experimental result, while the prediction for 50 % surface crack damage is 22.2 % lower than the test data. The smaller MTTFF predicted for 50 % cracks could be attributed to the small
<figure><img src="image_22.png" /><figcaption>Fig. 20. Cracks evolution from the exterior edges to the interior observed by dye penetration.</figcaption></figure>

number of ΔV<sub>F</sub> measurements between 600 and 1200 cycles. We insist that the new criterion is conservative for LED design at 50 % failure (Table 7).

## 6. Conclusions

This study investigated the mechanisms of damage in LED packages and proposed a comprehensive approach to monitoring, analysis, and modeling to improve understanding and prediction of failure modes. Three different architectures—corresponding to 2-, 3-, and 4-pads LEDs—were evaluated. The effects of reflow processes under both “normal” and vacuum conditions were analyzed. Additionally, two solder materials and two types of PCBs were tested.

All configurations underwent thermal cycling (TC) loading, with forward voltage monitored throughout the tests. Selected samples from each configuration were further analyzed using dye penetrant testing. A thermomechanical model, based on finite element (FE) simulations, was employed to study plastic strain accumulation during the TC tests. This model was used to correlate experimentally observed damage from dye penetrant testing and the reductions in area caused by damage. Furthermore, the area reductions due to damage were correlated with variations in forward voltage. The key findings are summarized as follows:

### ► ΔV<sub>F</sub> as Damage Indicator (Measure)

The forward voltage differential (ΔV<sub>F</sub>) can be considered a good

indicator for tracking damage progression in LEDs subjected to thermal or mechanical stresses. Indeed, the criterion based on ΔV<sub>F</sub> has:

* **Been validated** on 3 different LED configurations
Analyzing ΔV<sub>F</sub> across different LED configurations confirmed its effectiveness in characterizing degradation across various designs.

* **Been verified** via Dye Penetrant Testing
Observations from dye penetrant testing validated the damage progression and crack propagation identified through ΔV<sub>F</sub> monitoring, establishing a strong correlation between electrical and visual inspection methods.

* **Allowed the formulation of Damage Laws** as a Function of ΔV<sub>F</sub>
A damage law linking ΔV<sub>F</sub> to crack propagation was successfully developed for each LED package, providing a predictive framework for evaluating reliability.

### ► Thermomechanical Model and Damage Measure based on Plastic Cumulative Strain

* **Strain localization**

Finite element simulations identified zones of highest plastic deformation near the solder/LED interface, with strain higher at the package's exterior and lower at the center.

* **Crack path observed by Dye penetrant**

Dye penetrant observations across different thermal cycle counts enabled correlation of the observed crack path with plastic strain accumulation and supported the adoption of a new damage criterion based on the maximum difference between plastic eigenstrains.

### ► Model for Low Cycle Thermal Fatigue

Based on these findings, the study proposes adopting a low-cycle fatigue (LCF) model corresponding to a sectional plane rather than averaging plastic strains. This approach demonstrated accurate predictions for 100 % crack propagation and holds promise for partial crack predictions, such as 50 %.

<table><caption>**Table 7**
Fatigue model prediction with different failure criteria: Full crack and 50 % cracked surface.</caption><thead><tr><th>4-Pads</th><th>(100 % surface)</th><th>(50 % surface)</th></tr></thead><tbody><tr><td>Δε<sub>p</sub></td><td>0.006912</td><td>0.011212</td></tr><tr><td>Predicted MTTF(63.2%)</td><td>1971 ±115 cycles</td><td>925 + -90 cycles</td></tr><tr><td>Test MTTF(63.2%)</td><td>1888 cycles</td><td>1189 cycles</td></tr></tbody></table>
This work underscores the importance of integrating electrical, me-
chanical, and visual diagnostic tools with advanced modeling tech-
niques to enhance reliability and predictive capabilities in LED package
design. Future research should aim to refine these methods for broader
applicability across diverse LED configurations and operating
conditions.

Prediction of 50 % crack, needs a closer definition of the Weibull
distribution. Indeed, the presence of two distinct slopes in the distri-
bution might reveal the existence of two active failure mechanisms.

In present work, reflow under atmospheric pressure and vacuum was
tested. Clearly vacuum reflow leads to a reduced presence (absence) of
initial voids. From an industrial point of view determining the highest
allowable pressure could be interesting.

CRediT authorship contribution statement

**Khalil Maarouf:** this work represents a part of results from Khalil Maarouf's PhD.

**Christine Roucoules:** is in charge of thermo-mechanical fatigue at
Valeo and contributed in writing the paper.

**Kouadio Joseph Akrou:** helped during his internship with 4-pad
LED analysis.

**Sergio Sao-Joao:** In charge of Sem observation and supervisor of
Khalil Maarouf's PhD.

**Helmut Klöcker:** directed Khalil Maarouf's PhD.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Data availability

The authors do not have permission to share data.

References

[1] Annaniah, L., Saheed, M. and Jose, R. Led packaging technologies: design, manufacture and applications. Wiley VCH.

[2] Yole Développement, "Lighting for Automotive 2022 Market and Technology Report Product Brochure," in Yole, 2022.

[3] S.Beddar, J-B.Millet and Y.Alayli, "Pixelated-LEDs Car Headlight Design for Smart Driving and CO2," CO2 Reduction for Transportation Systems Conference, 2020.

[4] Frost and Sullivan, 2020 anual update for global LED lighting market, 2020.

[5] M. Krames, O. Shchekin, R. Mueller-Mach, G. Mueller, L. Zhou, G. Harbers, M. Craford, Status and future of high-power light-emitting diodes for solid-state lighting, J. Disp. Technol. 3 (2007) 160-175.

[6] Chang M-H Das D. Varde P. Pecht M. Light emitting diodes reliability review Microelectron. Reliab. Volume 52 762 782 2012.

[7] C. Lasance, A. Popp, Thermal management for LED applications. Springer, 2014.

[8] JEDEC JESD51-51, "Implementation of The Electrical Test Method for The Measurement of Real Thermal Resistance and Impedance of Light-Emitting Diodes with Exposed Cooling," JEDEC.

[9] J. Li, Z.J. Wang, A. Poppe, Solid State Physics Fundamentals of LED Thermal Behavior, in: Thermal management for LED applications, Springer, New York, 2013, pp. 15-52.

[10] Huang, J., Golubović, D.-S., Koh, S., Yang, Da., Li, X., and Fan, X. Degradation mechanisms of mid-power white-light LEDs under high-temperature-humidity conditions. IEEE Trans. Device Mater. Reliab., Volume: 15, 220-228, 2015.

[11] M. Mehr, A. Bahrami, W. Driel, X.J. Fan, J.L. Davis, G.Q. Zhang, Degradation of optical materials in solid-state lighting systems, Int. Mater. Rev. (2020) 102-128.

[12] JEDEC JESD51-14, "Transient Dual Interface Test Method for the Measurement of Thermal Resistance Junction-to-Case of Semiconductor Devices with Heat Flow Through a Single Path," JEDEC.

[13] G. Farkas, Q. Vader, A. Poppe, G. Bognar, Thermal investigation of high power optical devices by transient testing, IEEE Trans. Components Packag. Technol. (2005) 45-50.

[14] Weather Spark, https://weatherspark.com/, Cedar Lake Ventures, Inc., [Online].
Available: https://weatherspark.com/. [Accessed 2024].

[15] D. Mauve, R. Art, The printed circuit designer's guide to: thermal management with insulated metal substrates, BR Publishing, 2018.

[16] R. Tilgner, Physics of failure for interconnect structures: an essay, Springer, 2009.

[17] L. Mitterhuber, S. Defregger, J. Magnien, J. Rosc, R. Hammer, L. Goullon, M. Hutter, F. Schrank, S. Hörth, E. Kraker, Thermal transient measurement and modelling of a power cycled flip-chip LED module, Microelectron. Reliab. 81 (2018) 373-380.

[18] G. Elger, A. Hanss, M. Schmid, T. Wipiejewski, Application of Thermal Analysis for the Development of Reliable High Power LED Modules, China International Forum on Solid State Lighting, 2014.

[19] G. Elger, S.V. Kandaswamy, R. Derix, J. Wilde, Transient thermal analysis as a highly sensitive test method for the reliability investigation of high power LEDs during temperature cycle tests, J. Microelectron. Electron. Packag. (2014) 51-56.

[20] RoHS Directive 2002/95/EC, "European Parliament and the council of the restriction of the use of certain hazardous substances in electrical and electronic equipment," 2003.

[21] W. D. 2002/96/EC, European parliament and the council on waste electrical and electronic equipment, 2003.

[22] T. B, C.-U, H.T.-K. Lee, Fundamentals of lead-free solder interconnect technology, Springer, 2015.

[23] JEDEC J-STD-020F, "Moisture/Reflow sensitivity classification for nonhermetic solid state surface mount devices".

[24] Valeo Standards, "Guide for reflow soldering".

[25] J.S.J. Bath, Lead-Free Surface Mount Technology, Wiley, 2011.

[26] W. Seo, Y.-H. Ko, Y.-H. Kim, S. Yoo, Void fraction of a Sn-Ag-Cu solder joint underneath a chip resistor and its effect on joint strength and thermomechanical reliability, J. Mater. Sci. Mater. Electron. 30 (2019) 15889-15896.

[27] S. Noçairi, Mechanical Analysis and Experimental Characterization of an Automotive High-Definition LED, Mines de Saint-Etienne, 2021.

[28] JEDEC JESD104C, "Temperature Cycling," JEDEC.

[29] AEC-Q102, Failure mechanism based stress test qualification for discrete optoelectronic semiconductors in automotive applications, in: Automotive Electronics Council, 2017.

[30] SAE/USCAR-33, "Specification for testing automotive LED modules," SAE International.

[31] Ronneberger, O., Fischer, P., and Brox, T. U-net: convolutional networks for biomedical image segmentation. Medical Image Computing and Computer-Assisted Intervention, p. 234-241, 2015.

[32] K. Schmidt, N. Thielen, C. Voigt, R. Seidel, J. Franke, Y. Milde, Enhanced X-Ray Inspection of Solder Joints in SMT Electronics Production Using Convolutional Neural Networks, International Symposium for Design and Technology in Electronic Packaging, 2020.

[33] J. Zhou, G. Li, R. Wang, R. Chen, S. Luo, A novel contrastive self-supervised learning framework for solving data imbalance in solder joint defect detection, Entropy 25 (2023) 268-287.

[34] M. Roellig, R. Dudek, S. Wiese, B. Boehme, B. Wunderle, K. Wolter, B. Michel, Fatigue analysis of miniaturized lead-free solder contacts based on a novel concept, Microelectron. Reliab. (2007) 187-195.

[35] M. Shaygi, M. Li, K.J. Lang, H. Laux, B. Wunderle, Finite Element -Based Lifetime Modelling of SAC Solder Joints II LED Applications, EuroSimE, 2021.

[36] K. Maarouf, "Finite Elements Analysis of LED's Solder Joints During Power Thermal Cycling" in estc 2022, Sibiu Romania.

[37] M.Z. Akhtar, A. Zippelius, C. Kreiner, U. Tetzlaff, M. Schmid, G. Elger, Fully, Connected Neural Network (FCNN) based Validation Framework for FEA Post Processing to Improve SAC Solder Reliability Analysis, 2024 IEEE 10th Electronics System-Integration Technology Conference (ESTC).

[38] A. Zippelius, A. Hanß, M. Schmid, J. Perez-Velazquez, G. Elger, Reliability analysis and condition monitoring of SAC+ solder joints under high thermomechanical stress conditions using neuronal networks, Microelectron. Reliab. 129 (5) (2022) 114461.