Analysis of Power Modules Including Phase Change Materials in the Top Interconnection of Semiconductor Devices

Abstract

Power modules can occasionally be exposed to brief power peaks, causing overheating and premature failure of the power semiconductor devices. In order to overcome this issue without oversizing the module or its cooling system, this study aims to design a new class of power modules with integrated Phase Change Material (PCM) in a container serving as a top device interconnection. Simulations and experiments are performed with two organic PCMs, and the interest in adding copper foam is discussed. Under various test conditions, the results show that the simulations agree well with the experiments. Hence, virtual prototyping can be very useful for sizing containers based on a specific mission profile. For a constant selected PCM volume (around 1 cm³/device) and with a convection heat transfer coefficient value of 800 W.m⁻².K⁻¹, the solution allows achieving a junction temperature reduction of about 35 °C (erythritol and 90% porosity copper foam) compared to a wire-bonded conventional technique. Repetitive power cycles can be achieved with both materials, but the selection of the PCM should be conducted cautiously based on the mission profile. The two selected organic PCMs show degradation of their latent heat of fusion and mass loss during high-temperature isothermal aging in air above 130 °C. By assuming as endpoint criterion the reduction of energy storage by 50% compared to the initial state, the lifetime of erythritol and RT100 is evaluated to be about 100 and 340 h, respectively, during aging at 150 °C.

1. Introduction

The current trend in aeronautics is to develop More Electrical Aircraft (MEA) and More Electric Propulsion (MEP) with electrical and electronic systems on board. The main goals are to reduce equipment weight, fuel consumption, maintenance cost, and duration [1]. Accordingly, the use of highly reliable electrical converters is increasing, and among the most critical components, power modules can be exposed to harsh environmental conditions in some aircraft areas. Most of the time, power modules operate at their rated capabilities for long periods, and efficient cooling systems are used to dissipate the heat flux. However, in some applications, power modules can occasionally be exposed to brief power peaks (a few seconds to several tens of seconds), causing overheating and premature failure of power semiconductor devices. In order to address heat management during power peaks, the common solution consists of oversizing the power modules and/or their cooling system. The other option is to move the power modules toward colder areas. Such solutions are controversial, with the constant trend toward high power density and integrated modules pushed by the development of devices using wide band gap semiconductors (SiC, GaN, Diamond, etc.) [2,3,4]. Therefore, developing alternative solutions enabling the cooling of power modules during short power peaks is necessary to meet the weight and volume reduction needs for electric transportation and, more specifically, for the aeronautic sector.

Phase Change Materials (PCMs) have already demonstrated their advantages for energy storage in various applications like building materials, solar energy storage, shipping containers, packaging for temperature-sensitive devices, anti-acing systems, and human wear for heat and cold protection [5]. PCMs rely on the absorption and release of heat as the material undergoes a phase change within a defined temperature range (solid–solid, solid–liquid, solid–gas, or liquid–gas). Solid–solid PCMs present the advantage of conserving a solid phase, and consequently, they do not require encapsulation. However, they suffer from low latent heat storage [6]. Solid–gas or liquid–gas PCMs have a high heat of transformation, but they undergo enormous volume changes during evaporation. Consequently, for applications where multiple cycles are required, expensive and complex hermetic packaging sealing should be used to avoid any leakage of the gas [7]. Solid–liquid PCMs, also called Latent Heat Storage (LHS) materials, present little volume change and have the capacity for a high amount of heat storage over a narrow temperature range [8]. Thanks to their high heat storage capacity and the relative simplicity of their encapsulation, this paper will focus on LHS materials.

LHS materials can be classified into three main categories: organic, inorganic, and mixed organic-inorganic materials. Organic LHS materials include paraffin wax, sugar alcohols, fatty acids, and glycols, while inorganic materials are mainly salt hydrates, metals, and metal alloys. Paraffin waxes have suitable properties, such as intermediate latent heat of fusion, low corrosion rates, and negligible supercooling with no phase segregation [8]. The main disadvantage of paraffin waxes is their low thermal conductivity of about 0.2 W.m⁻¹.K⁻¹ and a high volume expansion of up to 15%. Fatty acids have intermediate values of latent heat of fusion that are comparable to those of paraffins. Fatty acids also show reproducible melting and freezing behaviors with no supercooling [9,10]. Their cost is about 2–2.5 times greater than that of paraffin, and they are also mildly corrosive. Polyethylene glycol (PEG) is thermally and chemically stable, non-flammable, nontoxic, cost-effective, and non-corrosive. However, similar to other organic LHS materials, they have a low thermal conductivity and latent heat of fusion comparable to paraffin waxes. Sugar alcohols have a high latent heat of fusion (as much as twice that of commonly used paraffin waxes), are of natural origin, non-flammable, nontoxic, and non-corrosive, and have an affordable cost. Sugar alcohols can be used in the medium temperature range (100–200 °C), but they suffer from supercooling [11]. Among sugar alcohols, erythritol has been extensively investigated and used in various applications owing to its high capacity to store energy (about three times higher than paraffin) and relatively high thermal conductivity (three times higher than paraffin). Regarding inorganic LHS materials, compared to paraffin, salt hydrates present a higher latent heat of fusion, a higher thermal conductivity of 0.6 W.m⁻¹.K⁻¹, negligible volume change during phase transition, favorable transition temperatures, and low cost [12,13,14]. Their main drawbacks are the corrosion of metals, incongruent melting, and supercooling below the solidification temperature [14]. Metals and metallic alloys (eutectics) offer high thermal conductivity and thermal stability. In addition, they undergo little volume change during the phase transition. Their main drawbacks are the low latent heat of fusion per unit weight (half that of paraffin) and the potential to interact with the container, mainly at high temperatures when they are in the liquid phase [15].

LHS materials have already been used to cool electronic devices. In [16], the paraffin was introduced in the heat sink in order to absorb an amount of heat once the temperature of the heat sink exceeded the melting temperature of the PCM. This solution can be easily implemented in commercially available power modules. However, the integration of the PCM in the heat sink degrades the conduction and convective heat transfer toward the cooling fluid and can have a negative impact on the cooling performance under nominal conditions. Th. Moreover, due to the relatively long distance between the device and PCM and the presence of multiple thermal insulating layers (insulated substrate, thermal interface material, etc.), the time before reaching the melting temperature of the PCM can be relatively long. Hence, the solution will not allow for an efficient reduction in the rapid increase in the junction temperature (Tj) during short power peaks of several seconds. In order to have a PCM able to melt rapidly when Tj exceeds the PCM melting temperature, Shao et al. [17] proposed a power module where a metal PCM is inserted in a metal framework in direct contact underneath the device. The distance between the heat source and the PCM is reduced, which allows it to take rapid advantage of the heat absorption ability of the PCM and to constrain Tj from rising quickly. However, this solution can alter the performance under nominal conditions due to the presence of the metal PCM, which has a relatively low thermal conductivity (20 to 50 W.m⁻¹.K⁻¹) compared to copper (400 W.m⁻¹.K⁻¹). Another approach aiming to use the PCM material as an isolating encapsulation in direct contact with the electronic device was introduced by Maxa et al. [18]. This solution does not affect the cooling under nominal conditions but induces several constraints on the PCM selection. For such a configuration, the PCM should ensure that the dielectric insulation is compatible with various electronic materials and should have high thermal conductivity. In addition, the whole packaging should be rethought in order to prevent the PCM from flowing once it melts.

In order to allow the management of short power peaks without alternating the cooling performance under nominal conditions, a potential solution based on the use of organic PCM integrated into the top metal interconnection of the power semiconductor devices is investigated in this research work. An example showing a phase-leg assembly using this concept is illustrated in Figure 1. The goal is for the PCM to melt and absorb the excessive heat only when the temperature exceeds the one at rated capabilities. In a previous paper [19], the authors used virtual prototyping in order to evaluate the impact of various parameters like the copper-to-erythritol ratio in the container, copper-to-erythritol contact area and the global thermal resistance. It was shown that, for the specified mission profile where the power peak is twice the nominal during 20 s, the dimensions of the container shown in Figure 1 are sufficient to avoid reaching the full melting of the erythritol. Moreover, the combination of erythritol with copper foam (90% porosity) offers the best compromise between Tj and weight. Based on the aforementioned recommendations, the same container filled with 90% porous copper foam and PCM is selected for this study.

The aim of this paper is to go further in the investigation and to address three main topics:

• To experimentally validate the previous models by using two types of PCMs and by closely reproducing the test conditions in simulations in order to be confident in the virtual prototyping results.
• To evaluate the ability of the solution to be used under repetitive power cycles for two potential PCM candidates showing different behaviors during cooling.
• To evaluate the reliability and the lifetime of the two PCMs under isothermal accelerated aging conditions in the temperature range between 130 °C and 150 °C. This can correspond to the temperature range encountered in real applications.

2. Materials and Methods

2.1. Samples Preparation and Characterization Techniques

For simplicity reasons, a single switch of the phase-leg module is fabricated. Two 180 µm thick SiC MOSFET devices (1200 V–98 A) from Wolfspeed (Durham, NC, USA) with an area of 6.44 × 4.04 mm² are used in this study. Direct Bonded Aluminum DBA substrates were manufactured using 1 mm thick AlN ceramic and a 400 µm thick Al metal layer on each side. A Ni Layer of 6 µm thick was chemically plated on the Al layer in order to be suitable for the soldering process. SiC MOSFETs are soldered on a DBA substrate using a 50 µm Au₈₀Sn₂₀ preform in an oven under vacuum in order to limit the voids in the solder. During the same reflow process, the AuSn preform is also used to attach the Mo₆₀Cu₄₀ interposers to the top of the SiC MOSFETs and to the substrate (Figure 1b). The main role of interposers is to increase the distance between the container and MOSFET edges to maintain a high breakdown voltage of the devices. Interposers are also allowed to balance the height between the device and the substrate in order to place the flat container. Moreover, these interposers are selected with an intermediate coefficient of thermal expansion (CTE) of 8.8 ppm/°C (part per million/°C) between the SiC (4.5 ppm/°C) and the copper (17 ppm/°C). Accordingly, they can play the role of a buffer layer and allow the reduction of the mechanical stress between the device and the copper container. The container was manufactured from a Cu bulky block using a milling machine. The outer dimensions of the container are 3 × 1.1 × 1 cm³, and the inner dimensions are 2.9 × 1 × 0.9 cm³. In some cases, copper foam was soldered inside the container. The Cu foam was manufactured by ERG Aerospace Corporation based in Sparks, NV, USA (Duocel^® foam) and has a 90–91% porosity, 0.33 mm fiber diameter, 2.55 mm pore size, and 1220 m⁻¹ specific surface area. The container is soldered to the interposers to ensure electrical interconnection between the source electrodes of both the MOSFETs and the substrate. The gate electrodes are connected to the signal circuit using ultrasonic ribbon bonding equipment. A top view of the assembly is illustrated in Figure 2a.

In order to avoid any discrepancy related to the fabrication process, thermal tests are performed on the samples without PCM using an Analysis Tech Phase 12B thermal analyzer (Wakefield, MA, USA). After that, the container is filled with PCM at 65% of the global volume, and thermal tests are performed again, allowing a fair comparison between the tests with and without PCM. The filling ratio is selected in order to avoid any leakage once the PCM melted in the open container. The backside of the substrate is thermally coupled to the cold plate by using a conformable silicone polymer filled with alumina on a fiber-glass carrier as the thermal interface material (1 mm thick, thermal conductivity 0.8 W.m⁻¹.K⁻¹) and clamping system (Figure 2b). The coolant temperature is fixed at 30 °C. In order to estimate the junction temperature Tj, the junction voltage drop Vj of the body diode of the MOSFET has been used as an electrical thermo-sensitive parameter. The sense-current was fixed at 10 mA. For the calibration of Vj(Tj), devices were heated in an oven up to 150 °C, and a Vgs of −5 V was applied to the gate-source electrodes in order to completely block the SiC MOSFET. As the temperature slowly decreases, the sense-current is applied every 5 °C, and the resulting Vj is measured and recorded. The calibration curve of Vj = f(Tj) shows a linear dependence, and the slope of this curve, known as the “k factor” is −2.4 mV/°C. Once calibrated, the device is fixed on the cold plate and heated until reaching a Tj of around 10 °C below the PCM melting temperature at a steady state. Hence, the power used to heat the device depends on the selected PCM melting temperature, and therefore, the evaluation of each PCM requires different applied powers to reach the steady-state temperature. After reaching the steady state, the power is increased toward the peak power (X times the nominal power where 1.5 < X < 2). During the whole heating phase, Tj is measured every 15 s. Repetitive power cycling tests are performed, and the durations at nominal power or with power off are changed depending on the PCM used. The fixed durations correspond to the time needed to observe full solidification at the PCM top surface.

For the characterization of PCMs, Differential Scanning Calorimetry (DSC) analysis with a heating and cooling ramp of 10 °C/min is used to extract the sensitive capacity of solid phase C_ps, the sensitive capacity of liquid phase C_pl and L, and the latent heat of fusion. Volume and mass measurements are used to extract the relative density ρ, and the hot wire technique is selected to extract the thermal conductivity of the solid and liquid phases of the PCM (λs and λl, respectively). Isothermal aging of PCM materials is achieved in open cups placed in an oven under an air atmosphere at three temperatures: 130 °C, 140 °C, and 150 °C. During aging, samples areextracted after 50 h and after 100 h for analysis using visual observations, mass loss, and DSC measurements.

2.2. Transient Thermal Simulation

2.2.1. Governing Heat Transfer Equation

The liquid motion is neglected in this study. Thus, for materials having isotropic thermophysical properties independent of the temperature, the three-dimensions energy equation can be written as follows:

$${\displaystyle \frac{\delta }{\delta t}}\left(\rho C_{p}T\right)={\displaystyle \frac{\partial }{\partial x}}\left(\lambda {\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\lambda {\displaystyle \frac{\partial T}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(\lambda {\displaystyle \frac{\partial T}{\partial z}}\right)+Q$$

(1)

where Q (W/m³) is the power density generated by the heat source, ρ is the relative density, T is the temperature, C_p is the specific heat capacity, and λ is the thermal conductivity.

In the case of LHS materials, the C_p value in Equation (1) has been replaced by the value extracted from the measured partial enthalpy vs. temperature diagram, which includes the sensible heat in both the solid and liquid states as well as the latent heat of fusion.

2.2.2. Geometry and Assumptions

The transient thermal behavior is evaluated using finite element simulations on a single switch (two MOSFETs) of the phase-leg module. Figure 3 shows a 3D view and a cross-section of the simulated design. The driver circuit is not considered in these simulations.

The geometrical model is meshed using symmetric parallelepiped cells. A mesh dependence study is carried out to optimize the cell size regarding accuracy and computation cost, resulting in 0.5 × 0.5 × 0.2 mm³ parallelepiped cells in the container and PCM volume. The temperature difference between the selected mesh size and the cubic one with 0.1 × 0.1 × 0.1 mm³ was less than 0.3%, while the computing time was divided by a factor 10. For all surfaces in contact with air, natural convection with a heat transfer coefficient hc of 10 W.m⁻².°C⁻¹ has been applied. Another heat transfer coefficient he is applied on the backside of the substrate to simulate the cooling system performance. This value is extracted from the comparison between steady-state simulations and measurements. The interfaces between various materials are considered perfect. The model ignores some marginal effects like the PCM volume change during melting, natural convection between the metal and melted PCM, and radiative heat losses.

2.2.3. Material Properties

The non-PCM properties used in the simulation did not depend on the temperature (except for the AlN ceramic) and are presented in

Table 1. Properties of the non-phase change materials used in the transient thermal simulations.

	Al	Au80Sn20	Cu	AlN	SiC	Mo60Cu40
ρ [kg.m−3]	2689	11,000	8933	3260	2300	9600
λ [W.m−1.K−1]	237.5	57	380	Linear dependence vs. temperature 170@20 °C; 140@150 °C	300	220
Cp [J.kg−1.K−1]	951	385	385	740	700	310

. For the PCM, paraffin (RT100) and sugar alcohol (erythritol) are evaluated, and their properties areused as input data in the simulations (Figure 4). In addition to the PCM, the container can also include Cu foam. In order to avoid complex and time-consuming simulations, an equivalent thermal model for the PCM/foam composite is used. The equivalent heat capacity (Ceq) of the foam filled with PCM is calculated using the following equation:

$$Ceq={\displaystyle \frac{\left(1-\epsilon \right){.\rho }_{\mathrm{C}\mathrm{u}}.C_{p\mathrm{C}\mathrm{u}}+\epsilon .{\rho }_{\mathrm{P}\mathrm{C}\mathrm{M}}.C_{p\mathrm{P}\mathrm{C}\mathrm{M}}}{\left(1-\epsilon \right){.\rho }_{\mathrm{C}\mathrm{u}}+\epsilon .{\rho }_{\mathrm{P}\mathrm{C}\mathrm{M}}}}$$

(2)

where ρ is the density, C_p is the specific heat capacity, and ɛ is the foam porosity. The equivalent thermal conductivity was deduced from the experimental and simulation results of various studies on Cu foam/paraffin PCM composites summarized in the literature [20]. For a copper foam porosity of 90%, the estimated equivalent thermal conductivity was around 15 W.m⁻¹.K⁻¹.

3. Results and Discussions

3.1. Thermal Experiments and Model Validation

In order to evaluate the impact of RT100 as a PCM on Tj during the power peak, the following procedure is applied. A nominal power Pn of 72 W is dissipated in the two MOSFETs for 120 s, which allowed the quasi-static regime to be attended. This Pn value is in order to reach a Tj of about 90 °C, which is 10 °C below the melting temperature of the RT100. According to the DSC curve of RT100 presented in Figure 4, a part of the latent heat of storage (L) is already consumed at 90 °C, and the remaining L value between 90 and 116 °C is about 145 J.g⁻¹. For the simulations, an equivalent he of 700 W.m⁻².K⁻¹ is applied on the backside of the substrate. This value corresponds to the contribution of the TIM and the cooling system, and has been selected to have the same Tj at a steady state from experiments and simulations. After reaching the steady-state regime, the power is increased up to 2 × Pn. During the transient phase, this hc value is kept constant, and a power profile similar to the experimental one is applied in the simulations. Figure 5a presents the measured and simulated Tj values in the transient phase as a function of time. It includes samples in which the containers are empty, filled with RT100, and filled with RT100 and copper foam. The comparison between the two containers filled with PCM with and without copper foam highlights the impact of improving the thermal conductivity by using a metal/PCM composite on the transient thermal response during short periods of several tens of seconds. A comparison between the simulation and measured curves (lines and markers, respectively) in Figure 5a shows that the developed model can accurately predict the junction temperature as a function of time for different configurations. For experimental data, in the case where the container has not been filled with PCM (orange curve), the heat is dissipated by natural air convection for the parts in contact with air and by the cold plate. After 30 s of the application of the power peak, Tj reaches a value of 150 °C followed by a quasi-stabilization of the temperature. For the case where RT100 is used as a filler, the curve presents a similar trend as the empty container, but with slightly lower temperatures. For the case where the container was filled with copper foam with RT100, in the range of 5 to 15 s, Tj is about 12 °C lower than the case without PCM and 7 °C lower than the case with PCM but without copper foam. This reduction in temperature during the first 15 s is due to the large amount of melted PCM and, consequently, the large amount of absorbed heat. Based on finite element simulations, a comparison of the calculated volume ratio of the PCM above the melting temperature with and without copper foam is presented in Figure 5b. While 10 s is sufficient to reach full melting of the PCM in the case of the use of copper foam, more than 120 s are needed for the PCM without Cu foam. The calculated ratio of the melted PCM is consistent with the observations presented in Figure 6, where the color of the melted PCM becomes translucent. When the PCM is used with copper foam, full melting is almost achieved after 10 s, unless some small partsare still floating at the surface of the liquid PCM. After the full melting of the PCM, Tj continues increasing until the two curves (empty container and container filled with RT100 and Cu foam) are superposed after 60 s. For the case without copper foam, a small volume of the PCM remains in a solid phase in the middle of the container after 120 s. The results are consistent with those of a previous study focusing on the impact of metal foam porosity and pore density on the thermal behavior [21].

Once erythritol was used as the PCM in addition to the copper foam, a nominal power Pn of 95 W was dissipated in the two MOSFETs for 120 s. At the end of this phase, the quasi-static regime with a Tj of about 110 °C (10 °C below the melting temperature of erythritol) is reached. After the steady state, two different power peaks of 1.5 × Pn and 1.8 × Pn are applied. For the RT100 case, an equivalent hc of 700 W.m⁻².K⁻¹ is applied on the backside of the substrate. Figure 7 presents the measured and simulated Tj under 1.5 × Pn and 1.8 × Pn as a function of time for a sample tested before and after filling the container with PCM. For comparison, the simulated curve for a wire-bonded conventional structure is added to the graph. For RT100, a good agreement is obtained between the simulation curves and the measured points. Before filling the container with PCM, Tj reaches a value of 150 °C and a value higher than 175 °C after 30 s under power peaks of 1.5 × Pn and 1.8 × Pn, respectively. Once the junction temperature is above 175 °C, the power is switched off automatically in order to avoid the thermal degradation of the device under test. For the case with erythritol and copper foam (green curve), three phases can be distinguished on the graphs for the highest peak power delimited by green dashed lines. The first phase occurs during the first 2 s, when the PCM is in a solid phase and absorbs only sensible heat. During the second phase, between 2 s and 30 s, the curve with the PCM diverges from that without the PCM because the PCM starts melting and absorbs latent heat. In the range of 10 s to 30 s, Tj is about 20 °C lower than the case without PCM. The larger reduction in temperature in the case of erythritol compared to RT100, both used with copper foam, is related to the larger amount of heat that can be absorbed by erythritol due to its higher latent heat of fusion and higher density. Finally, in phase 3, the PCM is fully melted and no longer absorbs large amounts of heat. Tj increases rapidly again, and both curves are superimposed after 100 s. Compared to wire-bonded modules simulated under the same conditions, the container filled with erythritol and copper foam allows a temperature decrease of about 35 °C after 10 to 30 s of power peak application (1.8 × Pn). This temperature reduction is due to the spreading effect of the copper container and heat absorption by the PCM. Moreover, for the containers with or without erythritol (green and orange, respectively) and for a power of 1.5 × Pn, the difference of the surface covered by each curve during the first 30 s can reflect that around 50% of the peak energy (47.5 W × 30 s) is absorbed by the PCM and the other 50% is dissipated via the cooling system. For SiC MOSFETs under power cycles, it was shown that the reduction in Tj variation (ΔTj) from 80 °C to 70 °C allows an increase of about two times the number of cycles until failure. The lifetime is about four times higher if ΔTj is reduced by 20 °C [22]. Moreover, compared to a wire bonding solution, using a copper plate as the metal top device interconnection (also called Direct Lead Bonding DLB) allows an increase in the lifetime of packaged Si IGBT by a factor of 10 under power cycles (with a ΔTj of 100 °C) [23]. Accordingly, due to the wire bond replacement and the temperature decrease during peak powers, one can expect that the use of PCM in the container as top device interconnection can contribute to significantly improving the lifetime of the module.

3.2. Behavior under Repetitive Power Cycles

As shown in the DSC measurement presented in Figure 4, the solidification temperature during cooling at a rate of 10 °C/min is much lower for erythritol (40 °C) than for RT100 (90 °C). This behavior will impact the power cycle profile that can be applied for each PCM. Two preliminary tests is performed on the samples with copper foam and PCMs (Figure 8a). Preliminary test 1 consists of applying a nominal power Pn for 3 min (steady state) followed by a peak power of 2 × Pn for RT100 and 1.8 × Pn for erythritol during 1 min (fully melted PCM). After the power peak, the power decreases again to Pn. The latter power is maintained until full solidification of the top surface of the PCM is observed. Under these conditions, 180 s were needed to observe the RT100 solidification, while more than 3600 s were needed for the erythritol (the test is stopped after 3600 s without solidification). Preliminary test 2 is performed by turning off the power after the power peak. In this test, solidification of RT100 was observed after 20 s, while for erythritol, it took 90 s. Based on these results, it can be concluded that, unlike RT100, erythritol is not suitable for repetitive power cycles if the device temperature is not significantly reduced below the nominal temperature for a long period after each power cycle. Based on the preliminary results and in order to evaluate the ability of the PCM to withstand repetitive power cycles, a suitable power profile was selected for each of the PCMs, as presented in Figure 8b.

During the 20 applied repetitive cycles, when power is applied for RT100 and erythritol, both with copper foam, the evolution of Tj is illustrated in Figure 9. During the power peaks applied for 60 s, both PCMs do not show any significant degradation tendency on the thermal performance. Hence, if a suitable power cycle profile is used (allowing solidification of the PCM after the power peak), both erythritol and RT100 show reproducible results for at least 20 tested cycles.

3.3. Isothermal Accelerated Aging of PCM

3.3.1. Thermophysical Properties Variation during Aging

Figure 10a and b show the DSC curves before and after 100 h of isothermal aging in air at 130 °C, 140 °C, and 150 °C for RT100 and erythritol, respectively. Both materials present a decrease in the L value after 100 h of isothermal aging, and this decrease is accelerated by the increase in aging temperature. After 100 h at 150 °C, the variation in the latent heat of fusion is more significant for erythritol (41% decrease) than for RT100 (16% decrease). In addition, a shift in the melting temperature Tm toward a lower temperature is observed for both PCMs. After 100 h at 150 °C, the Tm variation is more significant for RT100 (about 20 °C) than erythritol (about 5 °C).

Previous papers have already shown a decrease in the L for sugar alcohols after high-temperature aging [24,25]. It has been suggested that the hydrogen bonding structure and its concentration in sugar alcohol are the main contributors to the stored energy [26,27]. Hydrogen bonding can be weakened and eventually broken by heat, which in turn may cause a decrease in the L value [28,29]. In addition to the decrease in their L value, sugar alcohols have also shown a slight shift (<10 °C) in their Tm toward lower values with increasing aging duration and aging temperature [25]. It was also reported that the molecular structure and properties, such as the melting point, are related to hydrogen bonding [29]. Thus, the melting point can be reduced by weakening the hydrogen bonding when heating the materials [30]. The paraffin RT100 also presents a significant shift in the Tm peak after isothermal aging, and this shift is accelerated by temperature. This can be attributed to the chemical modification of the paraffin-based materials. In fact, the Tm of PCM is dependent on the number of carbon atoms in the chain. A lower carbon number induces a lower melting temperature [31]. Oxidative aging at high temperatures can induce chain scission and reduce the carbon number in the chain. Both the Tm and L show a decrease by reducing chain length [8]

Visual observations presented in Figure 11a pointed out that erythritol under air gradually became brown with increasing temperature and aging time, while RT100 did not show a significant change in color (white) during 100 h of aging at 130 °C and 140 °C. It has been reported that erythritol browning is related to the formation of conjugated carbonyl compounds when it oxidizes/dehydrates rather than to the caramelization process [30]. The mass is also monitored during aging. For both PCMs, the mass loss ratio evolution depicts a linear variation during the 100 h of aging in the tested temperature range. The mass loss ratio is illustrated in Figure 11b. It is clear that the mass loss ratio values are much more significant for erythritol than RT100. It is assumed that erythritol may undergo oxidation and dehydration reactions. In the presence of oxygen, the degradation mechanism of erythritol can occur through hydrogen abstraction either from carbon chains or hydroxyl groups. Fragmentation via C-C bond scission produces low-molecular-weight products with high vapor pressures, which may then evaporate and contribute to mass loss [30]. In addition, the dehydration of erythritol yields 1,4-erythritane, which can be further dehydrated to form carbonyl compounds, also affecting the mass loss ratio. For RT100, the mass loss observed mainly at 150 °C (1.6% after 100 h of aging) can be due to chain scission of usually linear hydrocarbon chains C_nH_2n+2, producing volatile low-molecular-weight by-products.

3.3.2. Kinetic Model

The thermal degradation characteristics of the two PCMs were evaluated using a first-order reaction rate equation based on the degradation of the latent heat of fusion measurement, as already shown for various sugar alcohols [32]. The degradation level α was defined to depend on the ratio between the latent heat of fusion variation before and after isothermal storage as follows:

$$\alpha =1-{\displaystyle \frac{L_t}{L_0}}$$

(3)

where L₀ is the initial value of the latent heat of fusion, and L_t is the value of the latent heat of fusion after the aging time t.

The kinetic model G(α) can be expressed according to the following expression:

$$G\left(\alpha \right)=k.t$$

(4)

it was shown that the degradation of L for sugar alcohol was fitted to the first-order rate equation from the initial time. As a result, G(α) is expressed as −ln(1 − α). In Equation (4), k is the reaction rate constant described by the Arrhenius expression:

$$k=A.e^{{\displaystyle \frac{-E_a}{RT}}}$$

(5)

where E_a is the activation energy, A is the Arrhenius prefactor, T is the temperature in K, and R is the Boltzmann constant equal to 8.31 J.mol⁻¹.K⁻¹.

Figure 12a,b show plots of ln(L_t/L₀) vs. aging time for RT100 and erythritol, respectively. For each temperature, the data points show linear fitting, and the slopes were obtained as the mean k. Figure 13 shows the Arrhenius plots of the reaction rate constants of the PCMs. Likewise, the data points were subjected to least-squares fitting, where the slope corresponds to E_a and the intercept corresponds to the logarithmic value of the pre-exponential factor A.

3.3.3. Lifetime Estimation

Once the kinetic models are established, the variation of L with time can be calculated. In practical applications, a PCM is used above T_m and below Tjmax for heat storage and release; therefore, the relationship between the L value and the aging duration was calculated for both PCM in the temperature range between 130 °C and 160 °C according to Equation (6), and the results are presented in Figure 14:

$$t={\displaystyle \frac{-1}{e^{(\ln \left(A\right)-\frac{E_a}{RT})}}}\times \mathrm{l}\mathrm{n}\left({\displaystyle \frac{L_t}{L_0}}\right)$$

(6)

At the end of the phase change, the global energy absorbed by the PCM is related to the product of the L value and its mass. By assuming the loss of a percentage of the energy storage capacity as the life criterion, the lifetime for a targeted aging temperature can be extracted by considering the decrease in the L value as well as the mass losses. For example, the variation in the energy storage ratio as a function of aging time at 150 °C is presented in Figure 15 for both erythritol and RT100. It should be noted that the atmosphere impact on the aging of erythritol was evidenced, and it was shown that replacing air with argon during isothermal aging at 141 °C allows for a decrease in the weight loss ratio by a factor of three [30]. Accordingly, an improvement in the lifetime of the PCM can be expected if a hermetically closed container is used under an inert atmosphere or with a low oxygen concentration.

4. Conclusions

The solution aims to use a container filled with PCM and Cu foam as the device top interconnection in a complementary way with the conventional cooling systems shown to be efficient in limiting the increase in Tj during transient power peaks. It presents a specific interest for aeronautic applications where the footprint of power modules should be reduced in order to increase the electric system integration, and power module robustness should be increased. Experimental data are in good accordance with simulation results. Hence, virtual prototyping can be very useful for designing containers and their fillers for a specific mission profile.

Under repetitive cycles due to the supercooling effect, erythritol is not suitable for repetitive power cycles if the device temperature is not reduced significantly below the temperature obtained under nominal power after each power cycle. For repetitive power cycles where Tj during nominal power is around 10 °C below the melting temperature of the PCM, paraffin-based materials like the one RT100 should be used. In all cases, to obtain repeatable results for various power cycles, a minimal duration allowing full solidification of the PCM should be defined between two power peaks.

The thermal degradation characteristics were evaluated under isothermal conditions in air. The lifetime for a targeted aging temperature can be extracted simply by considering the degradation kinetic model of the latent heat of fusion as well as the mass losses. The performed aging tests are considered accelerated aging since aging is performed in the presence of oxygen at high homogenous temperatures. However, for real application conditions and in order to accurately evaluate the lifetime of PCMs, additional parameters like the shift of the latent heat of fusion toward a lower temperature (mainly observed for RT100), the oxygen presence as well and the temperature gradient in the PCM should be considered.

Despite the interest in the proposed solution to reduce the temperature during power peaks, several considerations should be carefully addressed before its use for industrial applications. In fact, the filling of the container should not exceed 85% of the global volume in order to allow the expansion of the PCM during the phase change. Erythritol, like other sugar alcohols, suffers from supercooling since its solidification temperature is much lower than its melting temperature. This can be an issue if successive power peaks are desired. In this case, other PCMs with low supercooling effects are preferred. Finally, unlike conventional wire-bonded devices, the absence of the wire-fuse-effect in the case of extreme failure requires rethinking fail-safe and fault-tolerant strategies for critical converters.