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G. De Mey - One of the best experts on this subject based on the ideXlab platform.

  • a shortcut to inverse fourier transforms approximate reconstruction of transient heating curves from sparse frequency domain data
    International Journal of Thermal Sciences, 2010
    Co-Authors: B Vermeersch, G. De Mey
    Abstract:

    Abstract Frequency domain (AC) analysis, and associated Phasor Notation, offers a powerful and systematical way for dynamic thermal characterisation. The complex thermal impedance Zth(jω) plays a central role and can be obtained from analytical calculation, numerical simulation and experimental measurements. Relevant associated time domain information, such as the transient heating curve, can be derived through inverse Fourier transform (IFT). However, IFT is known to suffer from aliasing, instabilities and other artifacts. In this work we propose an alternative method that bypasses the IFT but still allows approximate reconstruction of the heating curve based on the impedance spectrum. The technique is particularly useful in cases where only truncated or sparse (low-resolution) AC data is available. It simply consists of plotting the magnitude of the impedance |Zth(jω)| (or transfer impedance for locations outside of the active junction) versus ω−1 as time scale. Very reasonable results, with relative errors in the order of 10%, are achieved, while the transformation is extremely simple to perform. We develop a mathematical proof for increasingly complex situations, ranging from the simple case of one single thermal time constant to a generic thermal system characterised by an arbitrary continuous time constant spectrum. Additional illustration and validation of the method is provided by practical case studies. Finally, we develop an extension to the evaluation of the impulse response and related transients. In that context the proposed method produces accurate results as well, and outperforms IFT related techniques.

  • Anomalous thermal behaviour in small electronic devices: non-uniformity and overshoot in dynamic temperature distributions
    Journal of Physics D: Applied Physics, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    This paper presents a theoretical investigation of the temperature distributions generated by a small heat source mounted on or embedded in semiconductor material. The dynamic thermal behaviour of the structures is studied in the frequency domain using Phasor Notation for the temperature and heat flux fields. Both classical and hyperbolic thermal conductions are considered. The latter accounts for the finite heat propagation speed, which is necessary for accurately describing very fast transitions. Although a uniform power density is applied, the temperature distribution inside the source is spatially non-uniform. As is already well known, this even holds for steady state conditions. For high frequencies, however, the maximum magnitude (i.e. largest oscillations) of the temperature occurs near the edges and corners of the heat source, rather than in the centre where it could intuitively be expected. This anomalous behaviour is observed for a wide variety of configurations, ranging from a simple 1D analytical slab model to numerical results for a 3D multi-layered electronic package. The classical theory clearly underestimates the edge effect, particularly for submicrometre structures. The substantial deviation from the distributions obtained by non-Fourier theory illustrates that special care should be taken when analysing fast heat transfer in small electronic devices.

  • BEM calculation of the complex thermal impedance of microelectronic devices
    Engineering Analysis with Boundary Elements, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    This paper presents a numerical method for modelling the dynamic thermal behaviour of microelectronic structures in the frequency domain. A boundary element method (BEM) based on a Green's function solution is proposed for solving the 3D heat equation in Phasor Notation. The method is capable of calculating the AC temperature and heat flux distributions and complex thermal impedance for packages composed of an arbitrary number of bar-shaped components. Various types of boundary conditions, including thermal contact resistance and convective cooling, can be taken into account. A simple benchmark case is investigated and a good convergence towards the analytical solution is obtained. Simulation results for a thin plate under convective cooling are compared with a theoretical model and an excellent agreement is observed. In a second example a more complicated three-layer structure is investigated. The BEM is used to analyse the thermal behaviour if delamination of the package occurs, and a physical explanation for the results is given.

  • A Fixed-Angle Heat Spreading Model for Dynamic Thermal Characterization of Rear-Cooled Substrates
    Twenty-Third Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    During a period of almost 40 years already, various fixed-angle heat spreading models have been developed in the literature. These models can be used by thermal engineers as approximations for the thermal steady state resistance of a heat source on a rear-cooled substrate. In this paper an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness ts) under a fixed angle Phi. An analytical solution for the complex thermal impedance Zth(jomega) in Phasor Notation is derived. The obtained expression, in which Phi is used as a fitting parameter, is compared with exact results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness lambda = ts/a. A compact expression for the optimal heat spreading angle as a function of lambda is given. Finally the temperature response to a heat power step is investigated. A simple formula for the thermal rise time is provided, allowing a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device.

Bjorn Vermeersch - One of the best experts on this subject based on the ideXlab platform.

  • A Fixed-Angle Dynamic Heat Spreading Model for (An)Isotropic Rear-Cooled Substrates
    Journal of Heat Transfer, 2008
    Co-Authors: Bjorn Vermeersch, Gilbert De Mey
    Abstract:

    During a period of almost 40 years already, various fixed-angle heat spreading models have been developed in the literature. These models are commonly used by thermal engineers as approximations for the thermal steady-state resistance of a heat source on a rear-cooled substrate. In this paper, an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness b) under an angle phi. An analytical solution for the complex thermal impedance Zth(j*omea) in Phasor Notation is derived. The obtained expression, in which phi is used as a fitting parameter, is compared with accurate analytical results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness lambda = b / a. A compact expression for the optimal heat spreading angle as a function of lambda is given. Also the temperature response to a heat power step is investigated, and a simple formula for the thermal rise time is provided. Finally, the model can be easily extended to anisotropic media, which often appear in electronic packaging applications. Overall the proposed model allows a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device.

  • A Fixed-Angle Heat Spreading Model for Dynamic Thermal Characterization of Rear-Cooled Substrates
    2008
    Co-Authors: Bjorn Vermeersch, Gilbert De Mey
    Abstract:

    During a period of almost 40 years already, various fixedangle heat spreading models have been developed in the literature. These models can be used by thermal engineers as approximations for the thermal steady state resistance of a heat source on a rear-cooled substrate. In this paper an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness ts) under a fixed angle φ. An analytical solution for the complex thermal impedance Zth(jω) in Phasor Notation is derived. The obtained expression, in which φ is used as a fitting parameter, is compared with exact results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness λ = ts/a. A compact expression for the optimal heat spreading angle as a function of λ is given. Finally the temperature response to a heat power step is investigated. A simple formula for the thermal rise time is provided, allowing a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device

  • Anomalous thermal behaviour in small electronic devices: non-uniformity and overshoot in dynamic temperature distributions
    Journal of Physics D: Applied Physics, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    This paper presents a theoretical investigation of the temperature distributions generated by a small heat source mounted on or embedded in semiconductor material. The dynamic thermal behaviour of the structures is studied in the frequency domain using Phasor Notation for the temperature and heat flux fields. Both classical and hyperbolic thermal conductions are considered. The latter accounts for the finite heat propagation speed, which is necessary for accurately describing very fast transitions. Although a uniform power density is applied, the temperature distribution inside the source is spatially non-uniform. As is already well known, this even holds for steady state conditions. For high frequencies, however, the maximum magnitude (i.e. largest oscillations) of the temperature occurs near the edges and corners of the heat source, rather than in the centre where it could intuitively be expected. This anomalous behaviour is observed for a wide variety of configurations, ranging from a simple 1D analytical slab model to numerical results for a 3D multi-layered electronic package. The classical theory clearly underestimates the edge effect, particularly for submicrometre structures. The substantial deviation from the distributions obtained by non-Fourier theory illustrates that special care should be taken when analysing fast heat transfer in small electronic devices.

  • BEM calculation of the complex thermal impedance of microelectronic devices
    Engineering Analysis with Boundary Elements, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    This paper presents a numerical method for modelling the dynamic thermal behaviour of microelectronic structures in the frequency domain. A boundary element method (BEM) based on a Green's function solution is proposed for solving the 3D heat equation in Phasor Notation. The method is capable of calculating the AC temperature and heat flux distributions and complex thermal impedance for packages composed of an arbitrary number of bar-shaped components. Various types of boundary conditions, including thermal contact resistance and convective cooling, can be taken into account. A simple benchmark case is investigated and a good convergence towards the analytical solution is obtained. Simulation results for a thin plate under convective cooling are compared with a theoretical model and an excellent agreement is observed. In a second example a more complicated three-layer structure is investigated. The BEM is used to analyse the thermal behaviour if delamination of the package occurs, and a physical explanation for the results is given.

  • A Fixed-Angle Heat Spreading Model for Dynamic Thermal Characterization of Rear-Cooled Substrates
    Twenty-Third Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2007
    Co-Authors: Bjorn Vermeersch, G. De Mey
    Abstract:

    During a period of almost 40 years already, various fixed-angle heat spreading models have been developed in the literature. These models can be used by thermal engineers as approximations for the thermal steady state resistance of a heat source on a rear-cooled substrate. In this paper an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness ts) under a fixed angle Phi. An analytical solution for the complex thermal impedance Zth(jomega) in Phasor Notation is derived. The obtained expression, in which Phi is used as a fitting parameter, is compared with exact results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness lambda = ts/a. A compact expression for the optimal heat spreading angle as a function of lambda is given. Finally the temperature response to a heat power step is investigated. A simple formula for the thermal rise time is provided, allowing a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device.

Gilbert De Mey - One of the best experts on this subject based on the ideXlab platform.

  • A THREE LAYER MODEL FOR THE THERMAL IMPEDANCE OF THE HUMAN SKIN: MODELING AND EXPERIMENTAL MEASUREMENTS
    Journal of Mechanics in Medicine and Biology, 2015
    Co-Authors: Maria Strakowska, Gilbert De Mey, Bogusław Wiȩcek, Michał Strzelecki
    Abstract:

    In this paper a dynamic three layer model for the heat transfer in the human skin is presented. The model is solved in the Laplace domain using the Phasor Notation. In order to compare the theoretical model with experimental results, a transient heating was carried out and the time dependent skin temperature was recorded with a thermographic camera. The transient temperature could be fitted very well to an analytical function, which could easily be transformed into the Laplace domain allowing an easy comparison between the model and the experimental results. The aim of the research is to evaluate the skin thermal parameters for all layers including the blood perfusion.

  • A Fixed-Angle Dynamic Heat Spreading Model for (An)Isotropic Rear-Cooled Substrates
    Journal of Heat Transfer, 2008
    Co-Authors: Bjorn Vermeersch, Gilbert De Mey
    Abstract:

    During a period of almost 40 years already, various fixed-angle heat spreading models have been developed in the literature. These models are commonly used by thermal engineers as approximations for the thermal steady-state resistance of a heat source on a rear-cooled substrate. In this paper, an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness b) under an angle phi. An analytical solution for the complex thermal impedance Zth(j*omea) in Phasor Notation is derived. The obtained expression, in which phi is used as a fitting parameter, is compared with accurate analytical results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness lambda = b / a. A compact expression for the optimal heat spreading angle as a function of lambda is given. Also the temperature response to a heat power step is investigated, and a simple formula for the thermal rise time is provided. Finally, the model can be easily extended to anisotropic media, which often appear in electronic packaging applications. Overall the proposed model allows a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device.

  • A Fixed-Angle Heat Spreading Model for Dynamic Thermal Characterization of Rear-Cooled Substrates
    2008
    Co-Authors: Bjorn Vermeersch, Gilbert De Mey
    Abstract:

    During a period of almost 40 years already, various fixedangle heat spreading models have been developed in the literature. These models can be used by thermal engineers as approximations for the thermal steady state resistance of a heat source on a rear-cooled substrate. In this paper an extension of these models to dynamic (time-dependent) phenomena is proposed. The heat dissipated by a square source (side a) is assumed to spread out into the substrate (thickness ts) under a fixed angle φ. An analytical solution for the complex thermal impedance Zth(jω) in Phasor Notation is derived. The obtained expression, in which φ is used as a fitting parameter, is compared with exact results. A very good agreement is observed (average relative error less than 6%) for a wide range of the normalized thickness λ = ts/a. A compact expression for the optimal heat spreading angle as a function of λ is given. Finally the temperature response to a heat power step is investigated. A simple formula for the thermal rise time is provided, allowing a thermal designer to make quick yet accurate estimations about the dynamic behavior of the device

B Vermeersch - One of the best experts on this subject based on the ideXlab platform.

  • a shortcut to inverse fourier transforms approximate reconstruction of transient heating curves from sparse frequency domain data
    International Journal of Thermal Sciences, 2010
    Co-Authors: B Vermeersch, G. De Mey
    Abstract:

    Abstract Frequency domain (AC) analysis, and associated Phasor Notation, offers a powerful and systematical way for dynamic thermal characterisation. The complex thermal impedance Zth(jω) plays a central role and can be obtained from analytical calculation, numerical simulation and experimental measurements. Relevant associated time domain information, such as the transient heating curve, can be derived through inverse Fourier transform (IFT). However, IFT is known to suffer from aliasing, instabilities and other artifacts. In this work we propose an alternative method that bypasses the IFT but still allows approximate reconstruction of the heating curve based on the impedance spectrum. The technique is particularly useful in cases where only truncated or sparse (low-resolution) AC data is available. It simply consists of plotting the magnitude of the impedance |Zth(jω)| (or transfer impedance for locations outside of the active junction) versus ω−1 as time scale. Very reasonable results, with relative errors in the order of 10%, are achieved, while the transformation is extremely simple to perform. We develop a mathematical proof for increasingly complex situations, ranging from the simple case of one single thermal time constant to a generic thermal system characterised by an arbitrary continuous time constant spectrum. Additional illustration and validation of the method is provided by practical case studies. Finally, we develop an extension to the evaluation of the impulse response and related transients. In that context the proposed method produces accurate results as well, and outperforms IFT related techniques.

Michał Strzelecki - One of the best experts on this subject based on the ideXlab platform.

  • A THREE LAYER MODEL FOR THE THERMAL IMPEDANCE OF THE HUMAN SKIN: MODELING AND EXPERIMENTAL MEASUREMENTS
    Journal of Mechanics in Medicine and Biology, 2015
    Co-Authors: Maria Strakowska, Gilbert De Mey, Bogusław Wiȩcek, Michał Strzelecki
    Abstract:

    In this paper a dynamic three layer model for the heat transfer in the human skin is presented. The model is solved in the Laplace domain using the Phasor Notation. In order to compare the theoretical model with experimental results, a transient heating was carried out and the time dependent skin temperature was recorded with a thermographic camera. The transient temperature could be fitted very well to an analytical function, which could easily be transformed into the Laplace domain allowing an easy comparison between the model and the experimental results. The aim of the research is to evaluate the skin thermal parameters for all layers including the blood perfusion.