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Determination of transient thermal characteristics for thermal electric behavioral models of integrated circuits

Drakin A. Yu, Potapov L. A., Shkolin A. N.

2020
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Bulletin of Electrical Engineering and Informatics
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In the current study, it was tried to describe a method for determining thermal characteristics of integrated micro-circuits to identify thermal parameters of multidisciplinary (thermal-electric) behavioral models. The problem is solved on the example of high-frequency pulse voltage converters. A solution was proposed to refine the minimum structure of the thermoelectric model based on an iterative least squares method using the Levenberg-M arquardt algorithm, as well as a graph of the spectral
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... aph of the spectral den-sity of time constants. This made it possible to reduce the influence of the filtering factor in the deconvolution operation when building a thermal model using the structural function of the thermal characteristic transition. Also, the results obtained can be used to build integrated circuits (IC) behavioral models, taking into account the thermal processes occurring in them. 934 frequency impulse-voltage chip circuits, taking into account the features inherent in a particular HFSVC design. This paper solves the problem of obtaining a model describing the HFSVC -thermal properties with respect to the experimentally measured thermal transient response (TTR) the dependence of the crystal (junction) temperature of the circuit on time TJ (t). LITERATURE REVIEW To determine the TTR in the standard [10], it is recommended to periodically connect the semiconductor device under test to the nominal mode with a frequency of less than 66.7 Hz, t o connect a small measuring current between pulses in the pauses of 100 µs as well as measure t he UF forward voltage at the p-n-junction. Using the UF (TJ) calibration, it is possible to obtain a set of TJk transition temperature values at the corresponding tk time points or a graph of the nonlinear TJk (tk) dependence. In the experimental TTR determination, direct measurement of the crystal temperature is impossible. The placement of the thermocouple in the instrument case (in close proximity to the crysta l) or on the case [11] leads to a distortion of the real picture of the th ermal processes taking place in the semiconductor device. In this regard, the methods of indirect determination of the crystal temperature of the device, based on the control of temperature-dependent parameters (TDP) inherent in the device under test, are actively used. The direct current voltage drop on the TJ p-n junction, the transconductance of the transistor S, reverse current (IRR) and the characteristics of the reverse pn junction recovery process (tRR, IRR,max), signal delay-propagation time tD [12] [13] [14] are usually used as IC TDP. When choosing a TDP HFPVC circuits, the following conclusions can be made. Due to the lack of connection from the external leads to the input circuit of the power transistor as part of the chip, it is not possible to use the transistor slope as the TDP. The use of tRR, IRR, max, tD dynamic parameters as a TDP makes it possible to experimentally determine the TTR of microcircuits directly in the nominal mode of the microcircuit; -the measurement of heating power requires the dynamic measurement of the microcircuit power consumption and the value of its "transit component" attributable to passive elements (choke, capacitors, external power diode) as well as load included in a typical circuit switching on HFSVC. If TJ is used as a TDP, then usually difficulties in determining the TTR in the nominal mode of the chip are also associated with the implementation of heating power dynamic measurement, and additionally with the HFSVC tss start-up time, which is fractions and millis econds and limits the resolution to select the minimum pause time during which the measuring current is applied to determine the UF at the p-n-junction. Recently, methods for determining the parameters of the electric-thermal model [15] are being developed, based on the analysis of frequency thermal characterist ics, that is, the dependence of the amplitude and phase of change of the transition temperature TJ (ω) on the frequency when the device is heated with a power varying harmonically P(t)=P0+Pmsinωt. In them, based on the calculation of the amplitudes and phases of the main harmonics of the heating power and temperature of the p -n junction, the module of transient thermal resistance (thermal impedance) and the φ phase shift between the temperature of the p-n junction and heating power is determined. Next, the dependence of the thermal impedance module on heating power modulation frequency Zthjc(ω) and the thermal circuit parameters are determined. By analogy with electrical circuits, thermal impedance is considered as a complex number Zthjc=Zthjcejφ, the real part of which determines Rthjc=Re[Zthjc ] thermal resistance. A technical solution: "Thermal Transient tester T3Ster" [16] , which implements the methods of standards [11, 17] used to control the thermal resistance of semiconductor devices and integrated circuits is known. The device provides the ability to determine the direct volt age drop at the p-n-junction at a microsecond time resolution after the end of the heating pulse. Based on these data, u sing the software, the tested chip thermal resistance as a whole and of individual links of the thermal circuit are calculated. The TTR curve analysis obtained by any method is usually performed by classical methods, for example, by analyzing the first and second derivatives [12] . Recently, when analyzing the TTR curve, the apparatus of structure functions [16, [18] [19] [20] has been often used, which allows determining thermal resistance components. In accordance with it, at the first stage, using the inverse convolution of the graph of the first TTR derivative in the logarithmic time scale z=ln(t) and the weight function wz=exp (z-exp(z)) the dependence of the spectral density of time constants (TCSD) is built. Next, it is discretized with a small dz step and a thermal model is constructed according to the Foster scheme. At the second stage, this scheme is transformed into the Cauer scheme, for example, according to the method in [2] , and on its basis a set of dependences of the heat capacities on the thermal resistances of the elements included in the resulting scheme is obtained. This dependency is called the structure function, since for a one-dimensional heat flow, it characterizes the layers that make up the design of the sample under Bulletin of Electr Eng & Inf ISSN: 2302-9285 Determination of transient thermal characteristics for thermal electric be-havioral models... (Drakin A. Yu) 935

doi:10.11591/eei.v9i3.1725
fatcat:tdjtf57uf5bv7pvfo3mrnkksg4