Nice, Côte d’Azur, France, 27-29 September 2006
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
THERMOS3, A TOOL FOR 3D ELECTROTHERMAL SIMULATION OF SMART POWER
MOSFETS
Giovanni Buonaiuto, Andrea Irace, Giovanni Breglio, Paolo Spirito
University of Naples Federico II,
Department of Electronic and Telecommunication Engineering, Italy.
ABSTRACT
In this work we present a novel 3D simulation tool
capable of taking into account also particular driving
strategies of the electron device as it may be the case of
Smart Power MOSFETs where a control logic interacts
with the power section and controls its dissipated power
and temperature. As an example a thermal shutdown
circuit, capable of reading the temperature on chip and
switching the device off if the latter reaches dangerous
values is usually embedded within Smart Power devices
used in automotive applications to drive direction light or
small motors/actuators.
1. INTRODUCTION
The simulation of power electron devices is a complex
numerical problem and it has been faced in many
different ways in the recent past as the issue of power
dissipation together with the knowledge of electro-
thermal interactions in MOSFETs has become relevant.
Being coupled, but on a different timescale with respect
to the thermal problem, the electrical problem is usually
reduced to few DC equation that are sufficient to model
the temperature dependent static behavior of the single
cell. The time-dependent heat equation is solved,
numerically or analytically, in a way such as to take into
account layout geometries, boundary conditions and
heatsink influence.
The THERMOS3 simulator we propose, entirely written
in MATLAB, is based on a forward iterative finite
difference time domain scheme [1] where the electrical
equivalent of the thermal problem and the electrical
quantities (drain current, source voltages) are solved self-
consistently at each discrete time step. Non linearity in
the thermal conductivity together with voltage
depolarization due to finite resistance of the source
metallization is taken into account. The
ID=f(VGS,VDS,T) behavior of the unit cell is modeled
considering temperature dependence of the threshold
voltage, mobility and MOSFET internal resistances.
Convection on the surface and sides and isothermal
boundary condition at the heatsink have been used.
As an exhaustive example of the capability of this new
tool we present the simulation of a smart power device
produced by STMicroeletronics (Fig.1). This device is
protected during permanent short circuit by a current
feedback loop which keeps the dissipated power inside
the SOA together with a thermal shutdown circuit which
shuts the device of if temperature on chip exceeds a
reference value. Dynamic temperature behaviour of this
device has been fully characterized by fast transient
infrared imaging [2] therefore a quantitative comparison
with the simulation is available for validation. One main
issue is the optimization of timestepping since the overall
behaviour of the device has to be observed in the 100ms
(or longer) timescale while sensitive information such as
fast temperature transients can be as short as 100µs. In
our approach an adaptive timstepping strategy together
with switching event prediction and detection has been
implemented.
Fig. 1 Optical picture of the two channels monolithic smart
Power MOSFET implemented with M0 technology
(VND830SP).
2. THE SIMULATOR
A multicellular power VDMOS can be treated as a
number of equivalent single cells all of them sharing the
same voltage on the drain and gate terminal and with the
sources connected through a metal layer with a finite
resistivity. Therefore both VDS and VGS are dependent not
only on temperature (the resistivity of the metal layer is
G. Buonaiuto, A. Irace, G. Breglio, P. Spirito
Thermos3, a Tool for 3D Electrothermal Simulations of Smart Power MOSFET
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
itself a function of temperature) but on the layout of the
device and position of the source bond wires. The single
cell is modelled by the following set of equations which
are a version of the SPICE LEVEL 1 model modified to
take explicitly into account temperature dependence of
the threshold voltage and mobility. All the internal
capacitances are neglected because the transient problem
is observed on a different timescale, and also the other
devices (drain-body diode etc.) which are usually
considered in power MOSFET models since we are
interested in the behaviour of the device when it is driven
in its triode or pinch-off region. Therefore for the generic
cell we have:
00
0
0
()
1() ()
2
()
?
µ
µµ
?
=? ?
=
??=
????
TT
ox
m
VV TT
WKT TC
L
TT
T
(1)
()
()
2
2
0
2 DS
GS T
D GS T DS GS T DS GS T
GS T GS T DS GS T
if V V
I K V V V V if V V and V V V
K V V if V V and V V V
? ?
??
??? ??? ??
? ?? ??
??
(2)
Depolarization effects due to finite resistance of the
source metal layer can be taken into account by solving
the linear problem:
)E = (3)
where YE is the admittance matrix (where temperature
dependence of the metal resistivity is taken into account)
which defines the electrical network modelling the metal
layer, V is the vector of the voltages at each node and I
are the current flowing into each node (that is the drain
current of the active MOSFET cells).
Given the temperature field T(x,y) on the surface of our
domain, both VDS and ID are known at each cell and
therefore it is know the dissipated power at the particular
location, that is the heat flux field Q(x,y) according to the
equations:
(, ) (, )(, ) DS D xyQxy
A= (4)
Since we discretize the domain in x and y directions the
equation (4) reduces to its discrete form which gives us
the discrete heat sources needed to solve the thermal
problem
,,
,
,
ij ij
ij
ij
VIQ
A= (5)
The power device is treated as a surface heat source,
being the heat flux equal to the power dissipated by joule
heating within the device, while the solder and heat sink
are modelled through simple RC networks.
Convection/Radiation from the top and side surfaces are
also taken into account.
By writing heat balance at each node of the domain we
can completely describe our problem by its matrix form
)T = (6)
where the admittance matrix YT is a sparsely populated
matrix, T is the vector which defines temperatures at each
node of the domain and Q is the vector which takes into
account the heat flux injected into the domain as a
consequence of the dissipated power by the power device.
The solution strategy we propose, entirely implemented
in MATLAB, is based on a forward iterative finite
difference time domain scheme [3] where the electrical
equivalent of the thermal problem as described by eq.4
and the electrical quantities (drain current, source
voltages) of eq.3 are solved iteratively at each discrete
time step until a number desired convergence criteria is
reached. Before entering the details of the simulation
results few words regarding driving strategies of Smart
Power Devices and consequent meshing and time
stepping solutions have to be spent.
In our case the single unit cell is too small to be
considered as a good elementary cell to discretize our
domain. Therefore we decide to group a number of single
devices and treat them as a macro cell with the current
scaled by its area. We usually start with a 50µm x 50µm
cell although, during the transient simulation, an adaptive
remeshing strategy is used to refine the mesh where the
temperature gradients are higher. In the case of the
VND800PEP, which is about 2mm x 2mm the starting
grid results in 40x40 elementary cells. During the
transient solution the number of nodes is kept constant
whereas their location is moved in the region where
temperature gradients are higher.
Regarding time stepping strategy, the issue is slightly
different. We have already described the driving strategy
of this kind of devices and, in general, as we will deal
with smart power devices, where dynamics can happen
with very different dynamics and timescales, a fixed time
step strategy can increase the computational time to non
practicable solutions. We therefore choose an adaptive
time stepping strategy where the time step shortens as
temperature and voltage derivatives increase. This on its
turn poses a problem when the control logic switches the
G. Buonaiuto, A. Irace, G. Breglio, P. Spirito
Thermos3, a Tool for 3D Electrothermal Simulations of Smart Power MOSFET
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
power on and off being at this time instant the VGS
derivative is theoretically infinite demanding for a time
step which approaches to zero. We choose in this case an
event-driven predictive algorithm in order to foresee the
instant when the condition for commutation will be
verified and adjust the time step accordingly.
This is a quite new approach in the solution of electrical
network with a high number of switches and it can be
also implemented in this case where all the unit cells can
be treated as a single switch.
3. THE FAST TRANSIENT INFRARED IMAGING
The detection of the temperature distribution across the
area of the device in transient conditions has been made
possible by the use of a custom developed radiometric 2D
measurement system that allows acquiring the transient
temperature maps of the device surface [2]. We use a fast
(actual time resolution is less than 2 µs) single cooled Cd-
Mg sensor mounted in a microscope optical chain that has
an equivalent spot size of about 10 µm with a working
distance of 2.5 mm. In order to perform a 2D scanning of
the surface to be mapped, we use an x-y step motor stage
controlled via a motor control card installed in a PC
which controls device biasing and data acquisition. In
such way, the device under test is shifted with respect to
the microscope spot, and it is possible to cover the entire
surface under observation.
The step by step acquisition of the radiometric waveforms
coming from the sensor is performed by means of a
5MS/s 12bit A/D converter card that connected via the
PCI bus into the PC converts and elaborates the output
detected signal. The acquisition software also performs
the pre-filtering of the detected signal by using an
averaging procedure to increase the signal to noise ratio.
It is important to remember that radiometric systems are
able to perform absolute thermal measurement only if the
target emissivity coefficient is known. Unfortunately, the
surface of power devices is often composed of different
materials (i.e. aluminum, passivation, silicon oxide, etc.)
that are characterized by different emissivity coefficients.
Hence, in our thermal mapping procedure, a preliminary
characterization step is also performed in order to
determine the emissivity coefficients of the points that
define the acquisition grid.
The temperature map is reconstructed by acquiring the
emissivity signals synchronized with the electrically
switching and after that the numerical processing of the
radiometric transient signals starts.
First of all, the stored dynamic radiometric signals are
properly corrected by using the emissivity coefficient of
the corresponding grid point and converted into the true
dynamic temperature signal. Then, the temperature array
data manipulated to obtain the time frames of the
temperature distribution on the DUT.
By means of this equipment and following the previously
described procedure we have obtained the thermal
transient analyses used to optimize the performances of
the devices described in this work.
4. THE VDN SMARTH POWER MOS AND ITS
PROTECTION STRATEGY
Figure 1 shows a smart power MOSFET made with
M0TM technology integrating a DMOS and its control
part in a monolithic chip solution. To comply with
automotive requirements this class of devices includes
several protections that are described in fig. 2.
4.1. Short circuit protection
The more restricting rule driving the protection strategy
of the Power actuator is to avoid false short circuit
detections in the harsh and very noisy automotive
environment. Beside a high level of electromagnetic
susceptibility the devices should not turn off either for an
inrush condition either for intermittent short circuit. The
short circuit protection is implemented using only
negative feedback method to ensure stability and to
maintain the device in a predictable status in every
condition.
A Current limitation combined with thermal shut down
intervention protects the power device during short circuit
operation. The integrated current feedback fixes the
working point in the active area of the Power stage.
The resulting high power dissipated equal to battery
voltage multiplied by Drain current leads to a fast
increase of the thermal sensor temperature and to the
intervention of thermal shut down block.
Logic
Undervoltage
Gate drive
Gate clamp
Vcc-Output
clamp
Vcc-GND
clamp
Overvoltage
Current
Limiter
Thermal
shutdown
Open load
ON state
Open load
OFF state /
Output-Vcc
short
Input
Status or
Current Sense
GND
Output
Fig. 2. Functional block diagram of the smart Power
MOSFET
4.2 Current density versus technology evolution
The balance of power dissipation due to joule effect
(Pd = Ron * I2) and the ability to extract the heat
(Pd = RTH * (TJ – TAMB)) establish the current rating of a
Power device. In actual automotive junction boxes Smart
Power are surface mounted and the heat is dissipated via
G. Buonaiuto, A. Irace, G. Breglio, P. Spirito
Thermos3, a Tool for 3D Electrothermal Simulations of Smart Power MOSFET
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
the cupper traces of a PCB in FR4. With this boundary
condition the die size reduction does not affect
significantly the thermal resistance junction ambient so it
is the on resistance of the device that manly sets the
current rating.
Scaled technology permitted a significant die size
reduction and the Ron*mm2 has decreased by a factor 10
in the last 10 years. As a result the size of the silicon can
be reduced significantly for the same targeted load.
On the other hand the short circuit current of the device
cannot be reduced because this value needs to be higher
than the inrush current of the targeted loads. The result is
that also the power density generated in the device during
short circuit increased also by a factor 10.
The protection strategy is very simple (Fig.3): as
temperature at sensor location reaches a high threshold
value (Tshutdown) drain current is switched off and the
device is left to its free thermal evolution; when
temperature then reaches a low threshold value (Treset)
drain current is switched on again. In this way power is
controlled, the device is kept well inside the SOA and
failures are prevented (although reliability problems due
to metal fatigue can occur [2]).
At this point the temperature is toggling between max
temperature fixed and fixed temperature reset. The device
returns automatically to nominal operation when the short
circuit disappears so the device continues to operate
properly.
Fig. 3 The sketched representation of the protection
strategy of the device under short circuit conditions: Time
plots in milliseconds scale of the whole dissipated power
and temperature of the embedded thermal sensor.
6. RESULTS, COMPARISONS AND COMMENTS.
The device has been discretized in Nx × Ny × Nz unit
cells each with its own thermal parameters and operated
in short circuit to the usual battery voltage Vbat=12V.
Current feedback fixes the total current at Ilim=10A. In
Fig.4 we report a comparison between experimentally
detected temperature distribution and the result of the
simulation. As we can note a good quantitative agreement
is obtained both in shape and in peak temperature value.
14710131619
S1
S3
S5
S7
S9
S11
S13
S15
S17
S19
S21
S23
S25
S27
S29
240-250
230-240
220-230
210-220
200-210
190-200
180-190
170-180
160-170
Fig.4: Temperature distribution on chip: experimental
(up) and simulated (down)
To further investigate the features of the simulator we
would like to underline that a well designed thermal
shutdown strategy relies on the optimal position of the
thermal sensor on the device surface. If this should not be
the case, temperature difference between the sensor and
the maximum temperature reached on chip can be
observed and reliability of the device can be eventually
impaired as temperature fatigue of the metals and
soldering joint might increase the Ron of the device. In
Fig.5 we report a simulation where the temperature sensor
has been deliberately placed far from the region where
temperature reaches its maximum, we notice how, even if
the sensor is correctly switching the device, the maximum
5 10 15 20 25 30
5
10
15
20
25
30
35
40
160
170
180
190
200
210
220
Tj
Iout
Pd = ILim * Vbat
Vin
T shut down
T
T
ms range
time
time
time
G. Buonaiuto, A. Irace, G. Breglio, P. Spirito
Thermos3, a Tool for 3D Electrothermal Simulations of Smart Power MOSFET
©TIMA Editions/THERMINIC 2006 -page- ISBN: 2-916187-04-9
temperature on chip reaches values higher than
Tshutdown.
From Fig.5 and Fig. 6 the PWM modulation of the
dissipated power and the timestepping strategy can also
be observed. In particular (see Fig. 6) it is noticeable that
as temperature at the sensor location reaches the
shutdown threshold timestepping is reduced thanks to the
predictive event detection algorithm and the same
happens when temperature reaches the reset value with a
negative slope.
0 5 10 15 20300
350
400
450
500
Temperature [K]
0 5 10 15 200
50
100
150
200
Time [ms]
Dissipated power [W]
Tsensor
Tcase
0 5 10 15 20300
350
400
450
500
Temperature [K]
0 5 10 15 200
50
100
150
200
Time [ms]
Dissipated power [W]
Tsensor
Tcase
Fig.5 Simulation of the permanent short circuit protection
on a VND800PEP device
0 1 2 3 4
450
455
460
465
470
475
480
485
490
Time [ms]
T [K]
Tmax
Tsensor
Tshutdown
Treset
0 1 2 3 4
450
455
460
465
470
475
480
485
490
Time [ms]
T [K]
Tmax
Tsensor
Tshutdown
Treset
Fig. 6 A detail of a single heating-cooling transient with
comparison between the maximum temperature on chip
and temperature detected by the thermal sensor
The value of such a tool in the design stage of a smart
power device is straightforward as it can be used to
optimize the whole design, influence of layout (i.e.
position of temperature sensors, bond pads location etc.)
and to investigate the performances of different
protection strategies.
7. FURTHER IMPLEMENTATION
In our study on these kind of devices and in all the
experienced acquired in the electro-thermal simulation of
power devices, we have understood that not only the
localization of the bond wires is important in simulations
but also a proper electro-thermal description of these
components must to be taken into account.
Into the next new version of the THERMOS3 simulation
tool will be inserted also the possibility to well simulate
and describe how the power bond wires, described in
terms of position contact area with the device, thick and
length, of power MOS can affect the electro-thermal
behavior of the whole device.
8. REFERENCES
[1] G. Breglio and P. Spirito “Experimental detection of time
dependent temperature maps in power bipolar transistors”,
Microelectronics Journal, Volume 31, Issue 9-10, October 2000,
pp. 735-739
[2] A. Irace, G. Breglio, P. Spirito, R. Letor, S. Russo,
“Reliability enhancement with the aid of transient infrared
thermal analysis of smart Power MOSFETs during short circuit
operation”, Microelectronics Reliability, Volume: 45, Issue: 9-
11, September - May, 2005, pp. 1706-1710
[3] A.F. Mills, Heat and mass transfer, Richard D. Irwin
ed.,1995.