Thermal-structural Modeling of power electronic package: effects of deposition geometry and dry spot on the stress distributions

A Power Electronics package is a heterogeneous system made of semiconductor devices (dies), metallic-ceramic substrate, baseplate and encapsulating material. The electronic devices can be MOSFETs (Metal Oxide Semiconductors Field Effect Transistors), diodes, IGBTs (Insulated Gate Bipolar Transistors) and passive components such as capacitors, resistors and sensors integrated on support circuit; the complete set of semiconductor devices installed on a package form the so-called “power modulus”. These devices play an important role in the transmission and conversion of energy in electric and hybrid vehicles. Due to the elevated currents and, consequently, the elevated temperatures at which these systems work, and due to the mismatch of the thermal-mechanical properties of the materials from which they are made, stresses and strains develop within the devices. Such stresses can be locally concentrated and amplified, depending on the deposition geometry of the various layers constituting the semiconductor device. Edge termination structures are essential to decrease the electric field at die’s edges, and, including brittle compounds in their composition, like Si3N4 or SiO, they are quite sensitive to mechanical stress. Another reason that may cause the stresses concentrations is the presence of dry spots. Dry spots are areas of various size, located at the interface between die or leadframe and the encapsulating resin, where there is a total or partial lack of adhesion. The aims of this work are, mainly, two. At first, four linear finite element analyses have been performed in order to evaluate the stresses concentrations at the corners of edge termination structure. The first case concerns sharp corners and the other cases concern differently filleted corners. In the second part of this work, it has been analysed the dry spot effect on stress distributions. Due to the small size of the defect with respect to the whole package, a Global-Local FEM approach has been used, creating a local subdomain where the mesh is denser than the global domain and a running a further separate numerical analysis which takes its boundary conditions from the global analysis, so delivering reliable small-scale stress and strain gradients. This approach permits to achieve accurate analyses focused on zones of interest of the global domain, limiting the increase of the computational cost of the modelling.


Introduction
Power Electronics package is a heterogeneous system that comprises several components, including semiconductor devices (dies), passive components like resistors or capacitance, copper frame, metallicceramic substrate, baseplate, and encapsulating material.The dies are the active components of an electronic device, such as a transistor or a diode.They are usually very small, typically a few millimeters in size, and are mounted onto a substrate using brazing, sintering, wire bonding or flip-chip technology [1,2].Dies, and eventual passive components such as capacitors, resistors and sensors, can be integrated on support circuit; the complete set of semiconductor devices installed on a package form the so-called "power modulus" [3].Transistors are mainly MOSFETs (Metal Oxide Semiconductors Field Effect Transistors) or IGBTs (Insulated Gate Bipolar Transistors), they are made by silicon (Si) and wideband gap (WBG) compounds like silicon carbide (SiC) and gallium nitride (GaN).Nowadays, SiC-based and GaN-based power MOSFETs play an important role on the transmission and conversion of the energy.They are gaining more and more attention thanks to their excellent properties in terms of electric resistance and capacitance, withstanding high temperature and voltage [4][5][6].WBG compounds are enabling factors to boost performance and efficiency of current and next converters' technology, which plays a key role in industry and automotive frameworks.For example, converters and, more in general, Power Electronics are deployed in several functions of electric and hybrid vehicles, such as on-board charger, DC-DC converter, and traction inverters [7].The spreading of such technologies pushes the improvement of power semiconductors devices and packages reliability, required to fit the string requirements from the market.A key aspect is the design and reliability of passivation structures of dies.Passivation scheme is made by one or more thin films, which are deposited on the surface of the device.Its function is to protect the surface of the device from environmental factors such as moisture, dust, and other contaminants.Passivation can also improve the electrical properties of the device by reducing surface recombination and leakage currents.They also support the function of edge termination to reduce of electric field close to die edges, avoiding undesired avalanche breakdown [8].Some compounds that ensure passivation are silicon nitride (Si3N4) or silicon dioxide (SiO2).They behave like brittle materials, being quite sensitive to mechanical stress.
On the contrary, other elements of the package like the copper baseplate and the encapsulating resin may behave in a rather ductile or viscoplastic way, with lower stress sensitivity and with the possibility of accommodating larger, possibly permanent strains.The above elements of a package may also exhibit significantly different coefficients of thermal expansion.The above mismatch between thermal and mechanical properties implies that semiconductor packages are stressed and deformed whenever temperature variations occur within the package [9], which can either be induced by the whole packaging processes , such as the molding compound injection or wire boding process [10], or by the temperature swings typical of their operating conditions in common applications [11].Stress gradients at weaker interface could lead the degradation of the bonding between two layers, causing delamination or damage induced by thermal-fatigue.All these phenomena may affect the reliability of the whole system.The experimental assessment of thermal stresses and failure modes in power electronics packages is very difficult to perform due to the complex configuration of the integrated devices and their microscopic dimensions, which require precise instruments for destructive and non-destructive testing [12,13].In recent years, Finite Element and Multi-physics simulations are used from industry and researchers as power tools for the prediction and the evaluation of stresses and damage in these systems, combining structural, thermal and electromagnetic effects [14][15][16][17] .The stresses generated by the temperature changes in non-homogeneous packages can be locally concentrated and amplified, depending on the deposition geometry of the various layers constituting the semiconductor device.
Another reason that can induce local stress magnification is the presence of dry spots.Dry spots are areas of various dimensions, located at the interface between die or leadframe and the encapsulating resin, where a total or partial lack of adhesion occurs.Due to the small size of the defect with respect to the whole package, a Global-Local FEM approach has been used, creating a local subdomain where the mesh is denser than the global domain and a running a further separate numerical analysis which takes its boundary conditions from the global analysis, so delivering reliable small-scale stress and strain gradients [18][19][20].

Sharp Edge Model
The aim of this work is an advanced Finite Element modelling of a power electronics package subjected to a quasi-static heating from -65 °C to 150 °C.Under this condition, it is reasonable to assume that thermal equilibrium is ensured instant by instants, for each bodies belonging to the model.Then, thermal transients are neglected and uniform temperature distribution is imposed on all points.
Looking the whole package from the bottom to the top, the layers constituting it are following: the copper layer having the function to form the electrical circuitry for the semiconductor devices (dies) installed on it, the solder layer (typically PbSnAg alloy) which ensures the connection between copper and dies, the Silicon Carbide (SiC), Tetraethyl Orthosilicate (TEOS), and Silicon Nitride (Si3N4) layers.
In order to protect the materials sensitive to thermal oxidative phenomena and guarantee the electrical insulation of the electronic components, a thermosetting resin filled with silica particles (Epoxy Molding Compound or EMC) encapsulates the entire system described before.
For the modelling of the thermal-mechanical behavior of the materials, the assumption of linearelastic-isotropic response was adopted.The thermal-mechanical properties of each materials are reported in the following Table 1.The entire modeled package has the following dimensions: 14.5 mm x 10 mm x 5 mm.Taking as reference the isometric view of the model (see Figure 1) , the extended surfaces of each layers are parallel to the x-y plane of the fixed cartesian reference system, while the thicknesses are parallel to the z direction.The in-plane dimensions and the thicknesses of the various layers are reported in the following Table 2 .2, that the proportions between the in-plane dimensions and thicknesses, for TEOS and Si3N4 layers, are about 2000:1 and 3600:1 respectively.Then, in the Finite Element modelling of the whole package, the mesh of the "thick" layers is realized with hexaedric 8-nodes elements, while "thin" layers are discretized with planar quadrilateral 4-nodes elements with thin shell formulation.The commercial software used for the simulations performed for this work is MSC MARC Mentat ®.
The package is supposed to be free to expand and warpage in all directions, as should happen if it was placed and heated on a bench into a climatic chamber.Therefore, two orthogonal roller constrains in x-y plane and a spherical hinge constrain have been imposed on three vertex nodes of the package's base.
For each interface within the package, the bonding between two layers is supposed to be infinite rigid.Glued contact has been implemented both for the contact between solid element/solid element interfaces and planar element/solid element interfaces.Rigid links type n to n have been adopted for the contact between planar/planar elements since they do not support the glued interaction both on top and bottom face.
All the analyses for this work have been performed under the hypothesis of "large displacements", then geometric non-linearities have been taken into account.

Filleted edge Models
The main objective of this work is the assessment of the effect of the deposition geometry of TEOS and Si3N4 layers on stresses distributions around the edge termination structures.The design of the edge termination structures play a crucial role in the mitigation of the electrical field intensity at the die's edge, increasing the energy efficiency of the electronic devices.Also stresses can be locally concentrated and amplified depending on the geometry of these regions.Then, four Finite Element simulations have been performed in order to compare the stresses distributions along paths extracted at representative interfaces between two adjacent layers, for sharp edge geometry and filleted edge geometry.
Looking at one corner of the TEOS (or Si3N4) frame (Figure 2), three values of the frame external boundary's fillet radius Rext have been chosen: 0.1 mm, 0.25 mm, and 0.32 mm, while the frame internal boundary's fillet radius Rint are respectively: 0.05 mm, 0.125 mm, and 0.16 mm.
The procedure for the modelling described before is suitable for each filleted model.

Global-Local approach for the effect of dry spots on stresses distributions
The second objective of this work is the modelling of the package when an artificial defect, in terms of de-bonded area, has been introduced at the Si3N4/Resin interface reproducing a so-called "dry spot".During the process in which the thermosetting resin is injected into a mold containing the metallicceramic layers, partial or total lack of adhesion may occur between this one and die or copper leadframe.The de-bonded areas have small dimensions (an average about of 100 m x 100 m) with respect to the in-plane dimension of Si3N4 frame, so the modelling of these critical interfacial regions requires more finer mesh than other parts of the package.Then, the Global-Local Finite Element Analysis has been used in order to investigate more accurately the stresses distributions near the discontinuity induced by the dry spot.
The Global-Local approach consists on the modelling of two physical domains: the so-called "global" one which is the whole model discretized with a coarse mesh, and a "local" one representing a spatial sub-domain belonging to the global domain.From the analysis on global model, the displacement field is determined for each points with a certain degree of accuracy, depending on spatial and temporal discretization.Then, the global displacements and corresponding nodal forces are assigned to the nodes belonging to the local domain's boundary.
In this work, a dry spot with size of 0.128 mm x 0.332 mm has been modelled in the middle region of the Si3N4 frame, sufficiently far from the two corners, neglecting other edge effects.The representative volume element chosen for the analysis has the following dimensions: 0.5 mm x 0.17 mm x 0.0426 mm (see Figure 3).A portion of resin lying on the two lateral sides of the TEOS and Si3N4 frames has been included in the local model in order to capture the in-plane transition from a layer to the encapsulating resin.For the modelling of the dry spot, the elements belonging to the Si3N4 contact body at the interface with resin elements have been excluded from the glued interaction.

Stresses distributions on sharp edge model
Given the geometry, constrains and thermal loads described in section 2, the modelled system has two symmetry planes as shown in Errore.L'origine riferimento non è stata trovata.. Due to these symmetries, Equivalent Von Mises stress distributions along each corner's diagonal path are perfectly coincident.For the layers discretized with shell elements, information about interlaminar shear stress are not available at the interfaces with other materials.Therefore, the components of the stress tensor chosen for the following comparisons are: normal stress along x direction, normal stress along y direction, and tangential stress on x-y plane.All these components are extracted at maximum temperature (T=150 °C).
For the "sharp edge" package, stresses distributions are shown in Figure 6.From these diagrams, it is possible to appreciate the effect of stresses concentrations induced by sharp edge configuration particularly on SiC/TEOS interface and Si3N4 middle plane.Stress components increase along the path extracted at the four levels defined before, from a minimum value reached "far" from sharp edge to a maximum one near the edge termination, excepted for normal components of stress at SiC/TEOS interface which present the maximum on a point 0.1 mm distant from the sharp termination.

Effect of filleted corners on stress distributions
For the assessment of the effect of layer's deposition geometry on in-plane stresses distributions, diagonal paths on Si3N4 and TEOS middle planes are chosen (results in Figure 7).Moreover, taking as a reference Figure 5, additional path along a straight line passing through the middle point of the corner's diagonal and orthogonal to the x-y plane is proposed, in order to observe stresses gradients through the thickness.This last path starts from a point 5 m above Si3N4/Resin interface (inside encapsulating resin) and finishes 11.6 m below SiC/TEOS interface (inside SiC layer).The obtained results are shown in Figure 8, where colored rectangles have been added in the diagrams in order to remark the changing of the materials along the arc length: red for resin, green for Si3N4, blue for TEOS, and orange for SiC.Looking at the stresses distributions in Figure 7, the filleted and sharp configurations lie on the same curve.Only the maximum values of stresses differ depending on the external fillet radius.
Having this useful information, by a single simulation on sharp edge model is possible to predict the maximum stresses on filleted layers model.
If path along the thickness pass through the middle point of the corner's diagonal, any effect of fillet radius is observed on stresses components (see Figure 7 and Figure 8) .However, these diagrams show the amplitude of the stresses discontinuities due to the transition from one layer to the adjacent one.Taking as reference the component sigma y, stress gradient is 550 MPa at Resin/Si3N4 interface, 400 MPa passing from Si3N4 middle plane to TEOS middle plane, and about 450 MPa at SiC/TEOS interface.
For the component tau xy, stress gradients assume these following values: 90 MPa at Resin/Si3N4 interface, 75 MPa along the transition from Si3N4 middle plane to TEOS middle plane, and about 110 MPa at SiC/TEOS interface.
These huge discontinuities are caused by the high mismatch between the thermal-mechanical properties of the materials constituting the model.It is important to remark that performed analyses are linear and elastic and these predicted stresses could be overestimate the real ones since plasticity or damage effects have not been taken into account.The effect of this defect is negligible if we observe the component of stress sigma x.Indeed, the mean value of the difference between stress in presence and in absence of dry spot (delta sigma reported in secondary axis) is about 15 MPa compared with the mean value of sigma x of 600 MPa (difference of 2.5 %).Local peaks of stress of 25 MPa and 80 MPa are located, respectively, at arc length 0.024 mm and 0.147 mm, where there is the in-plane transition from the "glued zone" to the de-bonded one.A more relevant stress amplification effect is observed on the tau yz stress distribution.Within the dry spot region, far from the boundary edges, the interlaminar shear passes from a mean value of -50 MPa to zero MPa.Also in this case, the peak stresses of -350 MPa and -400 MPa occur at the glued-dry spot transition.As expectable, the presence of the fillets and the change of their radii do not induce any change in the predicted through-the-thickness distributions of stresses, as the whole path is taken at the midpoint of the 300 microns-wide track of TEOS and Si3N4 (see Figure 3).

Conclusions
The present work deals with the prediction of the stress distributions induced within a power electronics package by a reference temperature change, focusing at the interfaces of resin/silicon nitride, TEOS/silicon carbide and within the layers of TEOS and silicon nitride.
The sensitivity of the stress distributions to the deposition layout of the layers has been assessed by numerical analyses performed with different corner's geometric configurations, namely a sharp-edges reference configuration one and three derived configurations with different radii fillets.
The whole package geometry initially modelled in the sharp edge configuration exhibited a double symmetry in the plan view together with its thermomechanical loading system, which successively allowed to model a quarter/corner of the entire system to evaluate the mitigation effect of the fillet radii on the stress maps.
For the sharp edge model, the x, y and xy components of the stress tensor were analysed along four diagonal paths at different heights within the model, in order to assess the reference effect of stress concentrations at the corners of the deposition layout which is likely the critical location where mechanical damage may occur.
The same stresses predicted by models with filleted edge deposition layouts shown a relevant role of the filled radius in the reduction of the maximum stresses.
More in detail, the overall stresses distributions are nearly unaffected by the radii which, instead, tend to truncate such distributions at their outer ends where the increasing spatial trends deliver the higher values: the larger is the fillet radius, the longer is the segment of increasing stress distribution trimmed-out with respect to the sharp-edge configuration.This finding potentially allows to decide the fillet radius to be realized depending on the maximum acceptable stress level, simply based on the stress distributions of the sharp-edge configuration, with no need for further time-consuming finite elements analyses.
The distributions through the thickness of x, y and xy stresses have also been shown in order to quantify stresses gradients and discontinuities along the transition zones between adjacent layers.
The second part of this work concerned the modelling of a de-bonded area located at Resin/Si3N4 interface which is called "dry spot".Since the dimension of this defect are too much small compared with the whole model, a global-local approach has been implemented for this task, in order to discretize a portion (local domain) of the entire system (global domain) with a finer mesh, performing a dedicated finite elements analysis with without further increasing the computational cost of the analysis.
Two orthogonal paths, lying in the x-y plane and passing through the centre of the dry spot have been taken to compare the stress distributions with and without this defect.The dry spot exhibited an irrelevant influence on the normal components of stress: sigma x and sigma y, while it nullifies interlaminar shear stress tau yz on the inner region of the dry spot, far from its boundary edges.Peaks of shear stress occur in the proximity of the in-plane transition zone between glued interface and de-bonded elements.

Figure 1 :
Figure 1: Exploded isometric view of the layers constituting the electronic package

Figure 3 :
Figure 3: Two axonometric views of the global (on the right) and local (on the left) physical domains

Figure 4 :
Figure 4: Equivalent Von Mises stress distribution on die at Tmax=150 °C and symmetry planes

Figure 5 :
Figure 5: Schematic in-plane (left) and exploded axonometric (right) views of a representative corner of the package and path plot's extremes

9 Figure 6 :
Figure 6: Stress distributions extracted along sharp edge corner's diagonal, at four levels and Tmax=150 °C

Figure 7 :
Figure 7: Comparisons between in-plane stresses distributions along corner's diagonal in sharp edge and filleted edge configurations

Figure 8 :
Figure 8: Components sigma y and tau xy through the layers' thickness: comparisons between sharp edge and filleted edge corner 3.3.Global-Local approach: Effect of dry spot on stress distribution Taking as reference the local model shown in Figure 3, three orthogonal path's directions passing through the centre of the dry spot have been chosen for the evaluation of this de-bonded area on stresses amplifications.The components of stress tensor used for the comparisons are the same of the previous case (subsection 3.1 and 3.2), excepted for the shear stress tau yz which substitutes tau xy since this last one assumed values closed to zero.The obtained results are shown in Figure 9, where the arc length interval between the two dashed lines indicates the region where dry spot is present.The effect of this defect is negligible if we observe the component of stress sigma x.Indeed, the mean value of the difference between stress in presence and in absence of dry spot (delta sigma reported in secondary axis) is about 15 MPa compared with the mean value of sigma x of 600 MPa (difference of 2.5 %).Local peaks of stress of 25 MPa and 80 MPa are located, respectively, at arc length 0.024 mm and 0.147 mm, where there is the in-plane transition from the "glued zone" to the de-bonded one.A more relevant stress amplification effect is observed on the tau yz stress distribution.Within the dry spot region, far from the boundary edges, the interlaminar shear passes from a mean value of -50 MPa to zero MPa.Also in this case, the peak stresses of -350 MPa and -400 MPa occur at the glued-dry spot transition.

Figure 9 :
Figure 9: Effect of dry spot on in-plane stresses distributions

Table 1 :
Thermal-mechanical properties of the materials used in the package

Table 2 :
In-plane dimensions and thicknesses for each layers Furthermore, TEOS and Si3N4 layers have a square inner cavity of side 2.85 mm.It is very important to notice, from Table