York Christian Gerstenmaier

Electrothermal simulation of multichip-modules with novel transient thermal model and time-dependent boundary conditions

The ability of monitoring the chip temperatures of power semiconductor modules at all times under various realistic working conditions is the basis for investigating the limits of the maximum permissible load. A novel transient thermal model for the fast calculation of temperature fields and hot spot temperature evolution presented recently is extended to include time-dependent boundary conditions for variations of ambient temperature and surface heat flows. For this a Greens function representation of the temperature field is used. Also, general initial temperature conditions are included. The method is exemplified by application to a dc/ac converter module for automotive hybrid drives. The thermal model, which can be represented by a thermal equivalent circuit, then is combined with an electrical PSpice-metal-oxide semiconductor field-effect transistor (MOSFET) model to allow for the fully self-consistent electrothermal circuit simulation of 42-V/14-V dc/dc-converter modules. 670 converter periods with altogether 8000MOSFET switching cycles in the six-chip module can be simulated within 1-h computing time on a Pentium PC. Various simulation results are presented, which demonstrate the feasibility of the simulation method and allow for the optimization of converter losses. Short circuit modes of converter operation are investigated with a high temperature increase also revealing the thermal interaction between different chips.

Combination of thermal subsystems modeled by rapid circuit transformation

This paper will deal with the modeling-problem of combining thermal subsystems (e.g. a semiconductor module or package with a cooling radiator) making use of reduced models. The subsystem models consist of a set of Foster-type thermal equivalent circuits, which are only behavioral models. A fast algorithm is presented for transforming the Foster-type circuits in Cauer-circuits which have physical behavior and therefore allow for the construction of the thermal model of the complete system. Then the set of Cauer-circuits for the complete system is transformed back into Foster-circuits to give a simple mathematical representation and applicability. The transformation algorithms are derived in concise form by use of recursive relations. The method is exemplified by modeling and measurements on a single chip IGBT package mounted on a closed water cooled radiator. The thermal impedance of the complete system is constructed from the impedances of the subsystems, IGBT-package and radiator, and also the impedance of the package can be inferred from the measured impedance of the complete system.

Reliability analysis and modeling of power MOSFETs in the 42-V-PowerNet

This paper analyzes the operation of PowerMOSFETs in the 42-V-PowerNet and shows that very stressful conditions are encountered, which can lead to severe reliability problems. To enable thorough investigations by circuit simulations an accurate physics-based compact model of the devices is proposed: it includes all important electrothermal effects relevant to the description of the observed failure mechanisms. By means of an advanced thermal-modeling approach, multichip assemblies can be accurately described, including mutual heating effects between neighboring devices. Some properly chosen examples demonstrate the validity of the model and its usefulness for reliability investigations

Transient temperature fields with general nonlinear boundary conditions in electronic systems

Greens function representations of the solution of the heat conduction equation for general boundary conditions are generalized for the nonlinear, i.e., temperature dependent case. Temperature dependent heat transfer coefficients lead to additional terms in the Greens function representation of the temperature field. For a rectangular structure with averaged homogeneous material parameters several types of Greens functions can be chosen especially simple, because of the new representation with the possibility of differing types of boundary conditions for the temperature field and the Greens function. Exact finite closed form expressions for three-dimensional-Greens functions in the time domain using elliptic theta functions are presented. The temperature field is a solution of a nonlinear integral equation which is solved numerically by iteration. The resulting algorithm is very robust, stable and accurate with reliable convergence properties and avoids matrix inversions completely. The algorithm can deal with all sizes of volume heat sources without additional grid generation. Large and small size volume heat sources are treated simultaneously in the calculations that will be presented. Heat transfer coefficients are chosen representing radiative and convective boundary conditions. An extension of the solution algorithm to composed multilayer systems of arbitrary geometry is outlined.

Efficient calculation of transient temperature fields responding to fast changing heatsources over long duration in power electronic systems

A method is presented, which describes the evolution of the complete temperature field in electronic systems by multiplication of two low order matrices, one depending on position, the other one on time. The first matrix constitutes the model and is fitted with a linear and fast algorithm to measurement or simulation. A very fast and accurate calculation of the temperature evolution in multichip-modules (MCM) is achieved, which is beyond the practicability of finite element method (FEM)-analysis in case of high frequency power pulses over long time intervals. The problem of temperature response to arbitrarily fast heat-source changes is solved by an analytical result, which gives the steepness of the thermal impedance at time zero. The method is applied to a high frequency dc/dc-converter and a dc/ac-converter [integrated starter generator (ISG)] module both for automotive applications. A new methodology is presented for constructing thermal equivalent circuits for electrothermal simulation with a multitude of temperature dependent heat sources.

Combination of thermal subsystems by use of rapid circuit transformation and extended two-port theory

This paper deals with the modeling problem of combining thermal subsystems (e.g. a semiconductor module or package with a cooling radiator) making use of reduced models. The subsystem models consist of a set of Foster-type thermal equivalent circuits, which are only behavioral models. Fast algorithms are presented in concise form by use of recursive relations for transforming (in both directions) unphysical Foster-type circuits in Cauer-circuits, which have physical behavior and therefore allow for the construction of the thermal model of the complete system. The R, C elements in the circuit can have negative values contrary to conventional network theory. Therefore the transformation methods have to be investigated under relaxed conditions concerning positive realness and passivity of the impedances. The method is exemplified by modeling and measurements on a single-chip IGBT package mounted on a closed water-cooled radiator. The thermal impedance of the complete system is constructed from the impedances of the subsystems, IGBT-package and radiator, and also the impedance of the package can be inferred from the measured impedance of the complete system. For modules or packages with large thermal contact area of largely inhomogeneous temperature a multi-port description is presented, which can be viewed as an extended two-port theory. In case of real two-ports the presented recursive analytic calculation methods for the impedances/admittances give an easy-to-use description for high calculation speed for all boundary conditions of the Cauer-network.

Efficiency of Thermionic and Thermoelectric Converters

Thermoelectric and thermionic converters — also in micro‐ and nano‐meter design — are considered for power generation and cooling applications. The potential of thermionic vacuum gap converters is investigated precisely by a new advanced theory with inclusion of backward currents from the 2nd electrode, losses due to thermal radiation and ohmic resistance in the electrodes, tunneling through the gap, image forces, and space charge effects. The efficiency of nano‐meter gap thermionic converters is by far higher than for thermoelectric devices (including nano‐structured superlattices) for operating temperatures above 800°K, however, there is no chance of realization with today’s technology. For a vacuum gap width of about 1 μm the performance is higher than for hypothetical bulk‐ thermoelectric generators (TEGs) with ZT = 1 for T > 1000°K and also higher than for hypothetical nano‐structured superlattices (ZT = 2.4) for T > 1200°K. A thermionic converter with gap width of 5μm has lower performance than a TE...

Theory of abnormal thyristor forward voltage behavior

The on-state current-voltage characteristic of thyristors is investigated by numerical simulation. For sufficiently high p-base concentration-as already known-an abrupt increase in on-state voltage is observed above a critical current density. Driving the device to higher currents results in a reduction of on-state voltage. Similar results are obtained for thyristor profiles with very shallow emitters. An analytic model that explains the described phenomena from first principles and leads to a simple criterion for current limiting in terms of Gummel numbers and carrier mobilities is presented. >

Rigorous theory of graded thermoelectric converters including finite heat transfer coefficients

Maximization of thermoelectric (TE) converter performance with an inhomogeneous material and electric current distribution has been investigated in previous literature neglecting thermal contact resistances to the heat reservoirs. The heat transfer coefficients (HTCs), defined as inverse thermal contact resistances per unit area, are thus infinite, whereas in reality, always parasitic thermal resistances, i.e., finite HTCs, are present. Maximization of the generated electric power and of cooling power in the refrigerator mode with respect to Seebeck coefficients and heat conductivity for a given profile of the materials TE figure of merit Z are mathematically ill-posed problems in the presence of infinite HTCs. As will be shown in this work, a fully self consistent solution is possible for finite HTCs, and in many respects, the results are fundamentally different. A previous theory for 3D devices will be extended to include finite HTCs and is applied to 1D devices. For the heat conductivity profile, an i...

Fast solution of thermoelectric equation for inhomogeneous devices

Computation speed is important in the optimization of systems which include several TE-modules at different temperatures and el. currents. Typically for maximum power generation or maximum efficiency the individual module currents and leg-lengths in the modules have to be optimized. Also optimization of inhomogeneous material distribution within TE-legs is an issue. This work will demonstrate that by making use of the continuity conditions for heat current and temperature, the general nonlinear problem with position-and temperature-dependent material properties can be solved quickly and precisely in one-dimensional TE-legs. Different algorithms are presented with calculation times of typically 0.2 s on a 3GHz single core PC. The nodal methods presented are robust also in case of material discontinuities, where differential equation solvers can have problems. It is important to include thermal contact resistors to the heat reservoirs in the calculation, which can be done easily by setting the Seebeck S equ...