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A detailed sensitivity study was carried out on various key parameters from a high precision numerical model of a microelectronic package cooled by natural convection, to provide rules for the thermal modeling of microelectronic packages subjected to natural convection heat transfer. An accurate estimate of the junction temperature, with an error of less than 1˚C, was obtained compared to the experimental data for the vertical and horizontal orientations of the test vehicle in the JEDEC Still Air configuration. The sensitivity study showed that to have an accurate estimate of the temperature, the following elements should be present in the thermal model: radiation heat transfer in natural convection cooling; a computational fluid dynamics analysis to find realistic convection coefficients; detailed models of the high conductivity elements in the direction of the heat flow towards the environment; and finally precise values for the thicknesses of layers and the thermal properties of the substrate and the printed circuit board.

The performance of microelectronic systems deteriorates rapidly when their temperature exceeds a certain limit. For some JEDEC standards used in qualification and reliability tests, operating temperature limits are set, for example, to 125˚C for processors and 85˚C for memory chips. The purpose of thermal management is to maintain throughout the equipment a temperature distribution with limited variations above the recommended limits. The advancement in IC package development driven by the increase of transistor density and miniaturization makes the task of the packaging designer more challenging.

The key to successful thermal management is the ability to obtain complete and accurate temperature data under realistic operating conditions. Collecting temperature data by direct measurements (e.g. thermocouples) is the most commonly used method, but it is limited by the number of measurement points and the small size of the components. Infrared Thermal Imaging (IR) alleviates some of these problems by providing complete external temperature mappings. However, this approach can be time-consuming and can only be applied after the design is complete and the parts have been fabricated. It is therefore important to have thermal models and numerical simulation tools that can provide the temperature profile of the chips to achieve high-quality designs before prototyping or manufacturing.

Several studies have been conducted to thermally model microelectronic packages [

The objective of this study was to perform a sensitivity analysis on our coupled (conjugate) methodology between a highly accurate conduction model and a computational fluid dynamics (CFD) model, which was reported in [

We present in this paper a method that enables an accurate prediction of the temperature field in a microelectronic package mounted on a printed circuit board (PCB) when it is cooled by natural convection to a thermal steady state. This configuration allows the estimate of the standard junction-to-ambient (θJA) thermal resistance in natural convection, which is useful to evaluate the relative thermal performance of microelectronic packages [

The paper is divided into eight sections. A review of the literature on the sensitivity studies around thermal issues in microelectronics packaging is presented in Section 2. Section 3 describes the detailed methodology of the two-way coupling between the conduction model and the fluid flow model. The acquisition of experimental data for the validation of the methodology is presented in Section 4. The results from the detailed numerical models are discussed in Section 5. Section 6 presents the validation of the numerical models, by comparing the results of the simulations from Section 4 with the experimental data from Section 5. The sensitivity analysis is discussed in Section 7 (key parameters) and in Section 8 (results and discussion).

Sensitivity studies have been carried out by some authors for thermal issues in microelectronic packaging, but the list of parameters studied is not as exhaustive as what is targeted in the present study. Reference [^{2}K) and the bottom of the substrate (10 W/m^{2}K), neglecting edge effects and fluid velocity fluctuations on surfaces.

The heat dissipation of a microelectronic device mounted on a four-layer PCB cooled by natural convection was studied in references [

Reference [

Reference [

These studies show that some parameters (such as the number of copper layers, and the presence of thermal vias) have a much larger impact on the estimated thermal resistance than other parameters. While leaving important details out of the simulations can reduce accuracy considerably, adding unnecessary details consume more computing resources, sometimes with minimal benefits on accuracy. Therefore, there is a need for identifying key features for the construction of precise thermal models, which is the main goal of our study.

Parameters | Nominal value | Relative variation of thermal resistance | References |
---|---|---|---|

PCB copper layers | 2 vs. 4 layers | 54% | [ |

PCB thermal vias | On-off | 14% | [ |

Flow velocity | 2 m/s | 9.4% | [ |

Underfill/C4 (between the two chips) thermal resistivity | 50 mm^{2}K/W | 9.1% | [ |

Operating power | 40 W | 7% | [ |

TIM thermal resistivity | 10 mm^{2}K/W | 5.3% | [ |

Flow angle | 0˚ | 5% | [ |

CFD | On-off (empirical formulas) | 2% | [ |

Enclosure width | 60 mm | 2% | [ |

Distance between the heat sink and the enclosure | 5.5 mm | 1.1% | [ |

PCB thermal BGA | On-off | 1% | [ |

Substrate thermal resistivity | 60 mm^{2}K/W | 0.7% | [ |

Heatsink conductivity | 151 W/mK | 0.34% | [ |

Underfill/C4 (between the lower chip to substrate) thermal resistivity | 75 mm^{2}K/W | negligible | [ |

Sealband thermal resistivity | 600 mm^{2}K/W | negligible | [ |

Our study uses the finite element method (FEM) for the heat conduction inside the package and the finite volume method (FVM) for the air convection in the volume surrounding the package. The FEM enables more precise solutions by increasing the order of the elements and by refining the mesh locally, while the FVM is robust for solving the non-linear conservation laws which appear in fluid transport problems.

The full heat transfer problem was simulated using a two-way (conjugate) coupling methodology between a FEM conduction model and an FVM fluid model. The detailed numerical models are presented in Section 5. The interaction between the two models was implemented through exchanges of temperature fields and convection coefficients at the boundaries between the solid domain and the fluid domain.

The two-way coupling methodology involved iterating through the following steps: first, the heat transfer in the conduction model was solved with Ansys APDL [_{tot} was calculated using

h tot = q wall T element − T ambient (1)

where q_{wall} is the total heat flux including convection and radiation, T_{element} is the temperature of each element at the solid-fluid interface and T_{ambient} is the fluid temperature at infinity. The heat transfer coefficients were transferred to the FEM model (see below). Third, the heat transfer coefficients were applied to all elements in the conduction model, which was solved again. Several iterations of the second and third steps were executed, until the calculation was terminated after the third step when the difference of the maximum temperature between two successive iterations was less than 0.2 K.

The FEM and FVM meshes were non-conformal. We found that an effective way of transferring the temperature field from FEM to FVM was to fit the temperature distribution on each surface with a Gaussian function. The fitting equation of the FEM temperature field for each surface was

T ( x , y ) = A i e − ( ( x − x 0 i ) 2 2 σ x i 2 + ( y − y 0 i ) 2 2 σ y i 2 ) + B i (2)

where A i , B i , x 0 i , y 0 i and σ x i and σ y i are the fit constants for each surface i (the top of the lid and the top and the bottom of the PCB).

The FVM convection coefficients were transferred to the FEM by projecting

the convection coefficients from the FVM mesh to the FEM mesh at the solid-fluid interfaces using linear interpolation, by using a Delaunay triangulation of the FVM data, and performing linear barycentric interpolation at each FEM nodes.

The validation of our calculation methodology was performed using experimental data obtained under the Integrated Circuits Thermal Test Method Environmental Conditions-Natural Convection (Still Air) (JEDEC JESD51-2) [^{3}. The 6.35 mm thick plastic walls were fabricated from transparent acrylic with low thermal conductivity and high emissivity. The chamber included a fixed thermocouple probe for measuring the internal air temperature. The standard JESD51-2 recommends an increase of the box volume if during the tests the temperature in the chamber increases by 10% or if the power exceeds 3 W, which was the case in our tests. This recommendation is justified by the fact that there could be convection on the exterior surfaces of the box impacting the thermal characterization. To verify this, type-T thermocouples were bonded internally to the corners of the box and at the center of each wall of the box to measure an eventual heat flux outside the box for heating powers above 3 W. Based on these results, it was decided to increase the domain of the CFD model to take into account the air volume outside of the box.

The test vehicle consisted of a test module mounted on a JEDEC standard PCB of dimensions 127 × 139.7 mm^{2} by an array of BGA solder balls. The test module was composed of a silicon chip of dimensions 12.57 × 12.57 mm^{2}, flip-chip mounted on an organic substrate of size 55 × 55 mm^{2}. The interconnections between the chip and the substrate were a matrix of solder bumps (C4) filled with an underfill polymeric material to increase the mechanical integrity of the solder bumps. The module was stiffened by a 1 mm-thick copper lid that also served as a first-level heat sink. The lid was thermally coupled to the chip by a thin thermal interface material (TIM, approximately 15 µm thick) and attached to the substrate with a silicone adhesive (seal band). There was an excess of the TIM during the attachment process that filled the gap between the lid and the underfill (

The silicon chip had nine heating elements and six in-situ resistance temperature detectors (RTD). These RTD were located at different positions on the chip: one at each corner and two at the center of the chip (

In this paper, numerical simulations were performed using a specialized cloud software infrastructure (PACK [

x (mm) | y (mm) | x (mm) | y (mm) | ||
---|---|---|---|---|---|

Top of the package | Lid center | 0 | 0 | ||

Chip corner (over the lid) | −6 | 6 | 6 | −6 | |

Lid corner | −20 | 20 | 20 | −20 | |

PCB | −32 | 30 | 30 | −32 | |

PCB corner | −56 | 51 | 51 | −56 | |

In-situ | Die Center | −1 | 0 | 1 | 1 |

Die Corner | −4.5 | −4.5 | 4.5 | 4.5 | |

Die Corner | −4.5 | 4.5 | 4.5 | −4.5 | |

Bottom of the package | Li center(under the PCB) | 0 | 0 | ||

Chip corner (under the PCB) | −6 | 6 | 6 | −6 | |

Lid corner (under the PCB) | −20 | 20 | 20 | −20 | |

PCB | −32 | 30 | 30 | −32 | |

PCB corner | −56 | 51 | 51 | −56 |

generation of parametric numerical models that use advanced pre- and post-processing capabilities using an object-oriented programming model.

The PACK infrastructure was used to build the conduction model with the Ansys APDL finite element software [

The properties of the materials were assigned individually to each element according to the position of the element in a given volume. The C4 and BGA were modeled with a homogenized layer with equivalent thermal properties. The equivalent out-of-plane resistance of these layers was the sum of two resistances in parallel, for the interconnection and the surrounding material. In-plane, it was assumed to equal the surrounding material thermal resistance (underfill for the C4 and air for the BGA). The thermal resistances of the C4 and BGA interconnections was calculated with the flux tube formula [

R ball = ( 1 − ε ) 1.5 2 d Ball ⋅ ( 1 λ 1 + 1 λ 2 ) + 4 h Ball λ Ball π d Ball 2 , (3)

with,

ε = π d Ball 2 N 4 A (4)

where λ 1 , λ 2 and λ Ball are the thermal conductivities of the top layer, bottom layer, and the C4 or BGA, h_{Ball} is the C4 or BGA height, d_{Ball} is the C4 or BGA diameter, N is the number of C4 or BGA and A is the total area of the chip or substrate. Equation (3) is valid for 0 < ε ≤ 0.3.

Materials | Dimensions | Conductivity (W/m K) | ||
---|---|---|---|---|

in-plane | out-of-plane | |||

PCB | Prepeg | 226 μm thick | 0.8 | 0.25 |

Core | 927 μm thick | |||

Copper | 30 μm thick | 385 | ||

BGA Equivalent | 400 μm diameter 1 mm pitch 500 μm thick | 1 × 10^{−}^{3} | 6.64 | |

C4 Equivalent | 100 μm diameter 200 μm pitch | 0.7 | 5.98 | |

Substrate | Copper | 15 μm thick | 385 | |

Core | 400 μm thick | 0.65 | ||

Diel. | 33 μm thick | 0..49 | ||

Underfill | 65 μm thick | 0.65 | ||

Die (Silicon) | 785 μm thick | 148 | ||

TIM | 15 μm thick | 2.6 | ||

Sealband | 4 mm width | 3.2 | ||

Lid | 1 mm thick | 385 |

One of the key elements in the realization of the high precision conduction model was the detailed modeling of the organic substrate. Substrate layer design files were used to model accurately the copper distribution and the vias of each layer in the organic substrate by superimposing the substrate design file and the mesh. In this approach, a rectangular background grid (pixels) was constructed based on black and white images of each layer of the organic substrate. The pixel count within each finite element is used to calculate the effective isotropic material properties based on the local concentration of copper and dielectric. This, effectively, forms a map of the material properties across each layer of the organic substrate [

λ e f f , n = β n ⋅ λ Copper + ( 1 − β n ) ⋅ λ Dielectric (5)

where β n is the area fraction of element n covered by copper, λ Copper and λ Dielectric are the thermal conductivity of copper and dielectric material. This method allows for a more accurate representation of the organic substrate material distribution than the standard homogenization approach. Each layer of the PCB was modeled with homogeneous layers and the thermal vias were explicitly represented. The heat flux was applied uniformly at the bottom of the die as a source term. The simulations were performed in the steady state.

Ansys Fluent was used to build the FVM model [

A surface-to-surface radiation model [

The validation of our numerical model was done by comparing the results of the simulations with the experimental data (

The results presented in

In order to contribute to the definition of best practices in the modeling of packages cooled by natural convection, a sensitivity study was performed on key parameters of our numerical model in order to evaluate their impact on the accuracy of the simulation results. These parameters can be classified into two types: continuous parameters where the impact of a variation of +10% of their nominal value was evaluated (e.g. variations in thickness and thermal conductivity) and discrete parameters where the impact of their taking into account or not in the simulations was evaluated (e.g. the presence of vias and the use of copper distributions). See

The “Underfill flux tube” parameter refers to taking into consideration or not the heat flux contraction in the calculation of the equivalent resistance of the underfill layer (Equation (3)). “Laminated substrate copper distribution” refers to the modeling of the copper distribution on the thermal properties of the substrate (Equation (5)). The parameters “Substrate core PTH”, “Substrate dielectric vias”, and “PCB thermal vias” evaluate the taking into account the presence of these structures in numerical models. When not included, a homogenized layer with uniform thermal properties was modeled. The use of empirical formulas for convection modeling and the consideration of radiation heat exchange are evaluated in the “CFD” and “Radiation” parameters, respectively. Finally, the impact of still air chamber inclination is also evaluated in the “Still air chamber inclination” parameter. The impact of all these parameters on the temperature was evaluated at different locations (junction, top lid, bottom PCB and corner PCB) and in the two configurations (horizontal and vertical orientations).

Parameters | Nominal | Variation |
---|---|---|

Lid conductivity | 385 W/mK | +10% |

TIM thickness | 30 µm | +10% |

TIM conductivity | 2.6 W/mK | +10% |

Underfill conductivity | 0.65 W/mK | +10% |

Underfill flux tube | On | On - off |

Substrate thermal resistance | 0.022 K/W | +10% |

Laminated substrate copper distribution | On | On - off |

Substrate core conductivity | 0.8 W/mK | +10% |

Substrate core PTH | On | On - off |

Substrate dielectric conductivity | 0.49 W/mK | +10% |

Substratte dielectric vias | On | On - off |

BGA conductivity | 57 W/mK | +10% |

PCB thermal resistance | 0.047 K/W | +10% |

PCB Emissivity | 0.85 | +10% |

PCB FR4 in-plane conductivity | 0.8 W/mK | 10% |

PCB FR4 out-of-plane conductivity | 0.25 W/mK | +10% |

PCB thermal vias | On | On - off |

Box emissivity | 0.91 | +10% |

CFD | On | On - off |

Radiation | On | On - off |

Still air chamber inclination | 0 º | ±5˚ |

The parameters were classified according to four categories: those that we consider negligible (maximum variation of less than 1% on the temperature at either the junction of the chip, the top of the lid, the bottom of the PCB, or the corner of the PCB); influential (variations between 1% and 5%) and critical (variations of more than 5%). Three parameters have been identified as critical: “Radiation”, “CFD” and “substrate dielectric vias”. In many thermal studies in microelectronics, radiation heat transfer is neglected because of the underestimation of its importance in the cooling of electronics. Some authors neglect its

Parameters | Relative variation of temperature | ||||||||
---|---|---|---|---|---|---|---|---|---|

Horizontal Orientation | vertical Orientation | ||||||||

Die junction center | Lid top center | PCB bottom center | PCB bottom corner | Die junction center | Lid top center | PCB bottom center | PCB bottom corner down | PCB bottom corner up | |

Radiation | 42.1% | 42.3% | 49.4% | 80.6% | 42.7% | 43% | 49.8% | 65.7% | 97.6% |

CFD | 8.6% | 8.7% | 8.5% | 12.6% | 9.4% | 9.5% | 10.2% | 5.8% | 25.7% |

Substrate dielectric vias | 5.4% | 5.4% | 1.4% | 0.4% | 5.6% | 5.6% | 1.3% | 0.3% | 0.3% |

Substrate core PTH | 2.4% | 2.4% | 0.7% | 0.07% | 2.5% | 2.5% | 0.7% | 0.1% | 0.2% |

PCB thermal resistance | 2% | 2% | 2.2% | 1.8% | 1% | 1% | 1% | 5.2% | 1.8% |

PCB Emissivity | 1.9% | 1.9% | 2.3% | 2.9% | 1.5% | 1.5% | 1.8% | 2.2% | 3.4% |

Substrate thermal resistance | 1.5% | 1.5% | 0.8% | 0.3% | 1.5% | 1.5% | 0.8% | 0.2% | 0.04% |

PCB FR4 vertical conductivity | 0.7% | 0.7% | 0.3% | 0.03% | 0.7% | 0.7% | 0.3% | 0.02% | 0.1% |

Still air chamber inclination | 0.7% | 0.7% | 0.3% | 3.6% | 0.04% | 0.04% | 0.05% | 0.06% | 0.2% |

Laminated substrate copper distribution | 0.4% | 0.4% | 0.4% | 0.05% | 0.4% | 0.4% | 0.5% | 0.1% | 0,01% |

Substrate dielectric conductivity | 0.4% | 0.4% | 0.03% | 0.01% | 0.4% | 0.4% | 0.1% | 0.1% | 0.02% |

Lid conductivity | 0.3% | 0.3% | 0.01% | 0.05% | 0.26% | 0.29% | 0.13% | 0.03% | 0.02% |

Substrate core conductivity | 0.2% | 0.2% | 0.01% | 0.04% | 0.2% | 0.2% | 0.01% | 0.01% | 0.03% |

Box emissivity | 0.2% | 0.2% | 0.2% | 0.4% | 0.3% | 0.3% | 0.3% | 0.6% | 0.6% |

PCB FR4 in-plane conductivity | 0.1% | 0.1% | 0.12% | 0.07% | 0.10% | 0.10% | 0.12% | 0.07% | 0.01% |

TIM thickness | 0.1% | 0% | 0.03% | 0.01% | 0.07% | 0.02% | 0.03% | 0.01% | 0% |

BGA conductivity | 0.1% | 0.1% | 0.03% | 0.04% | 0.03% | 0.03% | 0.01% | 0.01% | 0.01% |

PCB thermal vias | 0.1% | 0.1% | 0.2% | 0.01% | 0.01% | 0.01% | 0.16% | 0.04% | 0.2% |

TIM conductivity | 0.01% | 0.01% | 0.01% | 0% | 0.04% | 0.01% | 0.03% | 0.03% | 0.05% |

Underfill conductivity | 0.01% | 0.01% | 0.05% | 0.02% | 0.01% | 0% | 0.04% | 0.05% | 0.05% |

Underfill flux tube | 0.01% | 0.01% | 0.05% | 0.02% | 0.01% | 0% | 0.04% | 0.05% | 0.05% |

importance in conditions where the difference in temperature is small enough to simplify their analysis. In our setting, this would lead to errors of more than 40% at the junction of the chip and up to 80% at the corners of the test card because of its high emissivity (0.85). For a more detailed investigation on the importance of radiation heat transfer in simulations, the contribution of radiation compared to that of convection in natural convection heat transfer as a function of the power dissipated in the horizontal and vertical configurations is shown in

It can be seen in both the horizontal and vertical configurations that the radiation heat transfer is responsible for more than half of the total heat flux dissipated, especially at the lower power levels, where up to 60% of the heat can be dissipated by radiation. Radiation heat transfer is therefore very important in natural convection cooling and must not be neglected.

Also, using empirical formulas to calculate convection and radiation heat transfer coefficients leads to errors of more than 8% at the junction of the chip and up to 25% at the corners of the test card in the vertical configuration. The approximations introduced by the empirical relations (for example, neglecting the non-uniformity of the velocity on the interfaces) can explain these errors. In this regard and in order to better understand the differences in temperatures agreement between the CFD and the empirical relations method, a comparison between their corresponding heat transfer coefficients has been performed in references [

In our previous studies [

Four parameters were found to be influential (variation between 1% and 5%). Like the vias in the dielectric layers, the PTH in the core layer of the substrate also plays the role of thermal bridges. Their presence leads to an increase by 3 times on the effective conductivity of the substrate core. The thermal resistances of the substrate and of the PCB also had an impact on the validity of the simulations results. As shown above, radiation is important in natural convection heat transfer, as confirmed by the impact of the PCB Emissivity. It can be concluded that a good characterization to find their precise values is necessary for these four parameters.

Negligible parameters (variation less than 1%) include the copper distribution in the substrate, the inclination of the still air chamber, the thermal vias in PCB (~0.7% of the PCB thermal resistance), the thermal conductivity of the dielectric layers, core layer, lid, underfill, BGA layer, layers of FR4 in the PCB, and the thickness and thermal conductivity of the TIM, as well as the emissivity of the still air chamber (which has a temperature that is close to ambient). Not taking them into account or varying their nominal value up to 10% did not affect much the accuracy of our simulations.

An accurate estimate of the temperature field, with an error of less than 1˚C compared to experimental measurements for the vertical and horizontal orientations of the test vehicle, was obtained through a conjugate methodology that combines a high-resolution conduction model and a CFD-based model to more precisely simulate the natural convection and radiation heat transfers in microelectronic packages. A sensitivity study was performed using this high precision model for various parameters. The sensitivity study has revealed that in order to have an accurate solution for the temperature field, the following features must be incorporated into the model:

Using CFD to find realistic convection coefficients: the use of empirical formulas to calculate heat transfer coefficients can lead to large errors (8% at the junction of the chip and 25% at the corners of the test card in the vertical configuration). These error results are mainly from the assumptions of a uniform velocity field, which is not observed when edge effects and fluid flow in a confined box are present.

Including radiation heat transfer: radiation can be responsible for more than half of the total heat flux dissipated in the studied natural convection cooling configuration, even at low power. In our case, almost all of the radiation heat transfer passes through the PCB (98%) because of its high emissivity (0.85), which is 17 times greater than that of the lid (0.05), and its surface which is 8 times larger than the surface of the lid. Given the importance of radiation in natural convection heat transfer, proper knowledge of the precise values of the emissivity of the PCB and the still air chamber walls is also important.

Model the vertical interconnections along the heat dissipation path: the heat being dissipated mainly through the PCB in the two orientations (86% for horizontal, 84% for vertical), the vias in the dielectric layers as well as the PTH in the substrate core play the role of thermal bridges and can increase significantly the substrate out-of-plane conductivity.

Obtain the correct thicknesses and thermal properties for the substrate and the PCB: the thermal resistance of the substrate and of the PCB can have a significant impact on the simulation results. Variations that may come from manufacturing tolerances should be properly understood.

Other parameters could vary by up to ±10% or not be taken into account and not affect the calculated temperatures by more than 1%. These parameters include the copper distribution mapping in the substrate, the inclination of the still air chamber, the thermal vias in PCB, the thermal conductivity of the dielectric layers, the core layer, lid, underfill, BGA layer, layers of FR4 in the PCB, and the thickness and thermal conductivity of the TIM, as well as the emissivity of the still air chamber.

The authors thank Éric Duchesne, Benoît Foisy, and Michel Levesque from the IBM Corporation for useful discussions, technical support, as well as the provision and maintenance of the laboratory equipment.

This project was financially supported by the IBM Corporation, the Natural Sciences and Engineering Research Council of Canada and Prompt.

The authors declare no conflicts of interest regarding the publication of this paper.

Touré, M.K., Souaré, P.M. and Sylvestre, J. (2021) Best Practices for Thermal Modeling in Microelectronics with Natural Convection Cooling: Sensitivity Analysis. Journal of Electronics Cooling and Thermal Control, 10, 15-33. https://doi.org/10.4236/jectc.2021.102002