The Influence of the Selected Factors on Transient Thermal Impedance of Semiconductor Devices

Krzysztof Górecki, Janusz Zarębski

Gdynia Maritime UniversityDepartment of Marine

Electronics

Outline Introduction Compact thermal model of semiconductor

devices Algorithm of estimation parameters

values of the thermal model Results of calculations and

measurements Conclusions

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 Tj

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.

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 Rth.

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.

Compact thermal model of semiconductor devices

In the compact thermal model of the semiconductor device the dependence of internal temperature Tj on the power dissipated in it, can be expressed by means of the convolution integral of the form

where Ta 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

Rth means thermal resistance, ai are coefficients corresponding to each thermal time constants thi, whereas N is a number of these time constants.

dvvpvtZTTt

aj 0

'

N

i thiith

taRtZ

1

exp1)(

Algorithm of estimation parameters values of the

thermal model In the ESTYM software the value Rth 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 ai and thi the function yi(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

1

1

exp)(

1lni

j thjj

thi

ta

R

tZty

ithii atty ln

Algorithm of estimation parameters values of the

thermal model (2) The estimation of values of parameters thi and ai 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 t0 = 25% tmx to 75% tmx, whereas for i = 1 time tmx is equal to the time of the end of the measurement tmax.

Calculations are realized sequentially, starting from the longest thermal time constant, to shorter and shorter thermal time constants, while the parameters thi and ai are used, which were calculated in previous steps of the evaluation of these connected parameters with longer than counted thermal time constants.

Algorithm of estimation parameters values of the

thermal model (3) After the estimation of the values a1 and th1 the

dependence y2(t) is calculated using, and the new value of the time tmx is the least number fulfilling conditions

The first condition results from assumptions that any coefficient ai 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 tmx is smaller than 4.tmin,

where tmin is the time coordinate of the first measured point in the waveform Z(t).

5.42 mxty

11 thiith

41 ithmxt

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

0

10

20

30

40

50

60

0,001 0,01 0,1 1 10 100 1000 10000

t [s]

Z(t

) [K

/W]

IRF840 transistor without any heat-sink

transistor situated on the small heat-sink

transistor situated on the big heat-sink

parameter transistor withoutany heat-sink

transistor on the small heat-sink

transistor on the large heat-sink

Rth [K/W] 48.33 10.8 5.2

a1 0.976 0.61 0.66

a2 0.016 0.23 0.02

a3 0.008 0.13 0.28

a4 - 0.03 0.04

th1 [s] 77 400 750

th2 [s] 0.053 15 14

th3 [s] 0.001 0.43 0.4

th4 [s] - 0.004 0.005

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.

0

1

2

3

4

5

6

7

8

0,0001 0,001 0,01 0,1 1 10 100 1000 10000

t [s]

Zth

(t)

[K

/W]

IRF530 on heat-sinka

b

c

p = 17.5 W d

parameter curve a curve b curve c curve d

Rth K/W] 5.18 6.74 4.79 5.43

a1 0.48 0.442 0.664 0.584

th1 [s] 1096 1717.8 690.4 1057.5

a2 0.249 0.226 0.05 0.144

th2 [s] 262.4 643.9 17.34 351.8

a3 0.152 0.102 0.093 0.065

th3 [s] 0.4975 7.066 2.01 4.223

a4 0.068 0.103 0.097 0.136

th4 [s] 0.146 0.407 0.345 0.39

a5 0.044 0.066 0.05 0.069

th5 [s] 0.0256 0.0247 0.028 0.0886

a6 0.007 0.061 0.046 0.002

th6 [s] 4x10-5 9x10-4 4x10-5 4x10-5

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.

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.