1. The Influence of the Selected Factors on Transient Thermal Impedance of Semiconductor Devices Krzysztof Górecki, Janusz Zarębski Gdynia Maritime University Department of Marine Electronics

2. Outline Introduction Compact thermal model of semiconductor devices Algorithm of estimation parameters values of the thermal model Results of calculations and measurements Conclusions

3. Introduction (1) One of the essential phenomena influencing properties of semiconductor devices is self-heating. It appears with a rise of the device internal temperature T j and it is caused by the exchange of electrical energy dissipated in these devices into heat at not ideal cooling conditions. The rise of the device internal temperature causes changes in the course of their characteristics and strongly influences their reliability. Heat removal to the surrounding is realized by three mechanisms: conduction, convections and radiation. The efficiency of these mechanisms dependents, among others on the value on the device internal temperature and on the difference between temperature of the device case and the surrounding. Therefore, one should expect this efficiency to undergo some change connected with changes of power dissipated in these devices and changes of the manner of their mounting.

4. Introduction (2) Thermal parameters describing efficiency of removing the heat generated in the semiconductor device to the surrounding are transient thermal impedance Z(t) and thermal resistance R th. In order to take into account self-heating phenomena in computer analyses the thermal models of electronic devices in the form acceptable by the simulation software are indispensable. An essential problem is the estimation of parameters of the thermal model of semiconductor devices. In this paper the manner of estimating values of parameters of the device compact thermal model is presented and the influence of the selected factors on these parameters values of the considered model is analyzed.

5. Compact thermal model of semiconductor devices In the compact thermal model of the semiconductor device the dependence of internal temperature T j on the power dissipated in it, can be expressed by means of the convolution integral of the form where T a denotes the ambient temperature, p(v) - active power dissipated in the considered device, whereas Z′(t) is the derivative of transient thermal impedance Z(t) of this device, described usually as follows R th means thermal resistance, a i are coefficients corresponding to each thermal time constants  thi, whereas N is a number of these time constants.

6. Algorithm of estimation parameters values of the thermal model In the ESTYM software the value R th is estimated by averaging the waveform Z(t) at the steady-state (typically for the last 100 s). For the purpose of delimitation of the values of parameters a i and  thi the function y i (t) is defined Because thermal time constants considerably differ from each other, for big values of time t, the waveform of Z(t) is determined by the longissimus thermal time constant  th1 only, whereas exponential factors, corresponding to shorter time constants, are ommittably small (t>>  thi ). Then, the dependence is reduced to the linear dependence of the form

7. Algorithm of estimation parameters values of the thermal model (2) The estimation of values of parameters  thi and a i demands the use of the methods of least squares, where only the coordinates of points, lying within the range of linearity should be used in approximation. Because of big differences between the values of the following thermal time constants, it is accepted that this range comprises time from t 0 = 25% t mx to 75% t mx, whereas for i = 1 time t mx is equal to the time of the end of the measurement t max. Calculations are realized sequentially, starting from the longest thermal time constant, to shorter and shorter thermal time constants, while the parameters  thi and a i are used, which were calculated in previous steps of the evaluation of these connected parameters with longer than counted thermal time constants.

8. Algorithm of estimation parameters values of the thermal model (3) After the estimation of the values a 1 and  th1 the dependence y 2 (t) is calculated using, and the new value of the time t mx is the least number fulfilling conditions The first condition results from assumptions that any coefficient a i is higher than 0.01, whereas the second condition - from the assumption, that. This process is repeated iteratively, till the last appointed value of the time t mx is smaller than 4. t min, where t min is the time coordinate of the first measured point in the waveform Z(t).

9. Results of calculations and measurements the power MOS transistor IRF840 situated on two heat-sinks made from the shaped piece A-4240 – the first in length 60 mms (the large heat-sink) and the second in length 18 mms (the small heat-sink) as well as the operation without any heat-sink parameter transistor without any heat-sink transistor on the small heat-sink transistor on the large heat-sink R th [K/W]48.3310.85.2 a1a1 0.9760.610.66 a2a2 0.0160.230.02 a3a3 0.0080.130.28 a4a4 -0.030.04  th1 [s] 77400750  th2 [s] 0.0531514  th3 [s] 0.0010.430.4  th4 [s] -0.0040.005

10. Results of calculations and measurements (2) the examined MOS power transistor situated on the large aluminium heat-sink curve a - the transistor situated in the open plastic case 180x140x90 mm curve b - the transistor situated in the closed plastic case curve c - the transistor situated in the open metal case 170x180x80 mm curve d - the transistor situated in the closed metal case. parametercurve acurve bcurve ccurve d R th K/W]5.186.744.795.43 a1a1 0.480.4420.6640.584  th1 [s] 10961717.8690.41057.5 a2a2 0.2490.2260.050.144  th2 [s] 262.4643.917.34351.8 a3a3 0.1520.1020.0930.065  th3 [s] 0.49757.0662.014.223 a4a4 0.0680.1030.0970.136  th4 [s] 0.1460.4070.3450.39 a5a5 0.0440.0660.050.069  th5 [s] 0.02560.02470.0280.0886 a6a6 0.0070.0610.0460.002  th6 [s] 4x10 -5 9x10 -4 4x10 -5

11. Conclusions From the carried out measurements of transient thermal impedance and calculations performed with the use of ESTYM software for the considered transistors, it results that parameters of the model of Z(t) depend essentially on the manner of dissipated power, dimensions of the heat-sink and its spatial orientation, and also on dimensions and material of the equipment case. Together with an increase in the dissipated power the value of thermal resistance decreases and these changes reach even 20%. The dimensions of the heat-sink influence also time necessary to obtain the steady state in the device. For the examined transistor without any heat-sink this state appears after about 300 s, and for the transistor on the large heat-sink - after about 3000 s from the moment of turning on the power supply.

12. Conclusions (2) The tendency to shorten the longest thermal time constant together with an increase of the power dissipated in the transistor is also observed. The number of thermal time constants in the model of Z(t) of the transistor depends on the dimensions of the heat-sink. The values of the shortest thermal time constants practically do not depend on the dimensions of the heat-sink, whereas the values of the longest thermal time constants increase together with an increase of the heat-sink dimensions. In turn, the location of the device together with the heat-sink in the plastic equipment case causes an increase of thermal resistance by even about 50% and even triple extension of the longest thermal time constant in comparison to the situation, when the examined device is situated in the open metal case.