B. Vermeersch

Thermal impedance plots of micro-scaled devices

The complex thermal impedance Zth of a microelectronic heat source on the surface of a silicon wafer has been calculated semi-analytically as a function of the frequency. By representing the results in a Nyquist plot, almost perfect circular curves are obtained. This result is analogous to complex loci of the dielectric constant obtained for some materials.

A Fixed-Angle Heat Spreading Model for Dynamic Thermal Characterization of Rear-Cooled Substrates

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.

Generation of reduced dynamic thermal models of electronic systems from time constant spectra of transient temperature responses

This paper concerns the problem of generating reduced dynamic thermal models whose elements have physical interpretation. The compact models of an electronic system are generated here based on the analysis of the time constant spectra of system transient thermal responses. The proposed method is illustrated on a practical example of an integrated power amplifier with a heat sink. The experiments demonstrate the influence of contact resistance and cooling conditions on the resulting values of thermal model elements.

Evaluation of the Heat Transfer Coefficient in Microcircuits From the Frequency Analysis of the Thermal Transient Response

In this paper, it is outlined how thermal AC measurements can be carried out on a resistor deposited on an electronic substrate. The AC approach enables us to limit ourselves to phase measurements which can be carried out with a much higher precision than amplitude measurements. It will also be demonstrated how the phase measurements at a well-chosen frequency can be used to measure the heat transfer coefficient.

Dynamic thermal modelling of a power integrated circuit with the application of structure functions

This paper presents dynamic thermal analyses of a power integrated circuit with a cooling assembly. The investigations are based on the examination of the cumulative and differential structure functions obtained from the circuit cooling curves recorded during transient circuit temperature measurements. The experiments carried out and the comprehensive study of the computed structure functions rendered possible determination of the interface contact resistance and the heat transfer coefficient values necessary for numerical thermal simulations illustrating the influence of these thermal model parameters on circuit temperature.

Chimney Effect on Natural Convection Cooling of a Transistor Mounted on a Cooling Fin

The thermal impedance Z(th)(j omega) has been measured for the junction of a transistor mounted on a cooling fin. The setup was put inside a chimney in order to enhance the natural convection cooling. From the thermal impedance Z(th)(j omega) the influence of the chimney on the reduction in thermal resistance R-th=Z(th)(j omega=0) is clearly visible. A maximum improvement of almost 20% has been observed experimentally. Measuring the thermal impedance as a function of the angular frequency omega provides specific information about the thermal path being influenced by the chimney.

A Fixed-Angle Dynamic Heat Spreading Model for (An)Isotropic Rear-Cooled Substrates

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.

Application of Advanced Thermal Analysis Method for Investigation of Internal Package Structure

This paper presents an application of thermal analysis methods for the investigation of the internal structure of electronic device packages. The problem is illustrated based on the example of two silicon carbide power diodes. These diodes provided by different manufacturers have the same ratings and package type but one of the diodes exhibits oscillatory behaviour when used in a power converter. The presented results of thermal tests and analyses confirmed that there exist important differences between the two devices in their internal structures, possibly indicating the presence of some imperfections in the die attach or the wire bonds. These faults, in turn, have negative impact on their electrical performance in the investigated circuit.

Determining Thermal Simulation Data from Transient Measurements

This paper illustrates how the information obtained from dynamic thermal measurements can be used directly for the determination of certain unknown thermal data necessary for simulation purposes. Experimental heating curves of a hybrid power amplifier are processed further to compute the time constant spectra of the thermal responses and to construct their corresponding structure functions. From these functions, the values of selected thermal model parameters, such as the heat transfer coefficient or the contact resistance are determined. Owing to this approach, it is possible to eliminate certain time consuming parameter optimization procedures.

Application of structure functions for the investigation of forced air cooling

This paper presents thermal analyses of a power amplifier placed in a wind tunnel. All the investigations are based on the transient temperature measurements performed during the circuit cooling process. The measured cooling curves were used to compute the cumulative and differential structure functions for the circuit with a heat sink. These functions helped to determine the optimal values of circuit model parameters necessary for numerical thermal simulations. The experiments demonstrated the influence of the wind speed on the value of the heat transfer coefficient and consequently on the temperature of the entire structure.