Transcript Nieizotermiczne charakterystyki impulsowych układów zasilających

The Influence of the Selected
Factors on Transient Thermal
Impedance of Semiconductor
Devices
Krzysztof Górecki, Janusz Zarębski
Gdynia Maritime University
Department of Marine Electronics
Outline
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Introduction
Compact thermal model of semiconductor
devices
Algorithm of estimation parameters values of
the thermal model
Results of calculations and measurements
Conclusions
Introduction (1)
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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)
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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
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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
T  T  Z ' t  v   pv   dv
t
j
a

0
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

 t 
N

Z (t )  Rth  1   ai  exp  
 t thi 
 i 1
Rth means thermal resistance, ai are coefficients corresponding to
each thermal time constants tthi, whereas N is a number of these
time constants.
Algorithm of estimation parameters
values of the thermal model
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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
tthi the function yi(t) is defined
 Z (t ) i 1
 t 

yi t   ln 1 
  a j  exp  



Rth
j 1
 t thj  

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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 tth1 only, whereas
exponential factors, corresponding to shorter time constants, are
ommittably small (t>>tthi).
Then, the dependence is reduced to the linear dependence of the
form
yi t    t t thi  ln ai 
Algorithm of estimation parameters
values of the thermal model (2)
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The estimation of values of parameters tthi 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 tthi 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)
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After the estimation of the values a1 and tth1 the dependence
y2(t) is calculated using, and the new value of the time tmx is
the least number fulfilling conditions
t mx  t thi 1 4
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y2 t mx   4.5
The first condition results from assumptions that any
coefficient ai is higher than 0.01, whereas the second
condition - from the assumption, that t thi 1 t thi  1 .
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).
Results of calculations and
measurements
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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
60
parameter
IRF840
transistor without any heat-sink
Z(t) [K/W]
50
40
30
20
transistor situated on the big heat-sink
transistor situated
on the small heat-sink
10
0
0,001
0,01
0,1
1
10
t [s]
100
1000
10000
transistor
without
any heat-sink
transistor on the transistor on the
small heat-sink 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
tth1 [s]
77
400
750
tth2 [s]
0.053
15
14
tth3 [s]
0.001
0.43
0.4
tth4 [s]
-
0.004
0.005
Results of calculations and
measurements (2)
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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.
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
6
tth1 [s]
1096
1717.8
690.4
1057.5
5
a2
0.249
0.226
0.05
0.144
tth2 [s]
262.4
643.9
17.34
351.8
3
a3
0.152
0.102
0.093
0.065
2
tth3 [s]
0.4975
7.066
2.01
4.223
1
a4
0.068
0.103
0.097
0.136
tth4 [s]
0.146
0.407
0.345
0.39
a5
0.044
0.066
0.05
0.069
tth5 [s]
0.0256
0.0247
0.028
0.0886
a6
0.007
0.061
0.046
0.002
tth6 [s]
4x10-5
9x10-4
4x10-5
4x10-5
8
7
Zth(t) [K/W]
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b
IRF530 on heat-sink
p = 17.5 W
d
4
0
0,0001
a
c
0,001
0,01
0,1
1
t [s]
10
100
1000
10000
Conclusions
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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)
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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.