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is used to model the forward polarization capacitor.
7-9 October 2009, Leuven, Belgium
The current source I ds is responsible of the linear and saturation
state of the transistor,
I
I
DS
DS
⋅ ( Vcom
− Vth
) − ⋅VI DS
) ⋅VI
DS
( V −V
) 2
= Kp
1 (2)
2
= ⋅
(3)
Kp
2 com th
Fig. 3. The forward polarization of the body diode
I
J c
= K.
V L
(1)
This current “(1),” depends of the drop voltage of the
inductance L and magnified by a constant K, during the
transient blocking stage of the diode the inductance L energy
will discharge in the resistor R L , and the current source Jc will
deliver a reverse current simulating the reverse state current of
this diode, an example of this reverse current simulation is
shown on “Fig.4.”, in this paper we will show only a
simulation of the reverse current because the body diode of our
MOSFET DUT is a very fast one, it have a very low reverse
current, and it doesn’t vary in a significant matter with
temperature.
Fig. 4.Simulation of the diode current during commutation for two given
temperature, the dotted curve(blue) is at 150°C and the normal one is at
25°C
By using this model as a body diode we have a complete power
MOSFET electrical model “Fig.5.”. We should mention that
the C ds capacitor is the reverse polarization capacitor of the
diode model play the role of the drain-source capacitor and this
capacitor is a non linear with voltage as mentioned above.
Fig. 5. Power MOSFET electrical & thermo-sensible model for switching
circuits.
“(2),” describe the linear phase knowing that
I DS
is the drop
voltage of the current source Ids and V com is the command
voltage. “(3),” describe the saturation phase
B. Temperature dependents parameters
The expansion of the electrical model into a thermal sensible
one is done by introducing the temperature as a variable into
the equations of the electrical parameters in the electrical
model. The first step is to identify the electrical parameters
influenced by the temperature in a way that the electrical
behavior of the MOSFET is changed. These parameters are
(Kp, V th , R sub , R g , R s , R on , I ss , V knee ) where Kp is the
transconductance parameter and V th is the threshold voltage,
R epi , R sub , R g , R s are the epitaxial resistor, substrate resistor,
gate resistor, source resistor of the MOSFET. Ron is the
forward phase resistor, I ss is the leakage current, and V knee is
the threshold voltage of the diode. We don’t need to include
the capacitors as temperature dependent because it doesn’t
vary much with temperature [6]. The extraction of the
temperature dependent parameters has been done by
electrical characterization of a power MOSFET and the body
diode under different temperature imposed by the air flux of
the thermo stream.
III. MODEL’S PARAMETER EXTRACTION AND VALIDATION
A. Parameter extraction
The model parameters were carefully identified based on
simulations and an automatic experimental acquisition method
developed in our laboratory which is sufficiently general to be
applied to Power MOSFET devices. The experimental
measurements are done under different temperature using the
thermo-stream (25°C, 50°C, 75°C…175°C), We faced a
serious problem for temperature above 175°C; the
experimental dispositive melted down cause’s short circuit, so
the temperature dependent equations are valid between 25°C
and 175°C. The determination of the static parameters Kp
“(4),” transconductance parameter, the threshold voltage V th
“(5),” and the series resistor R ON “(6),” is done by measuring
the transfer characteristics and the output characteristics using
the Agilent HP4142.
Kp = 244 − 0.7( T − 25) (4)
−3
V th
= 2.6 − 3.3e
( T − 25) (5)
−6
3 −4
2 −4
R on
= 1.0e
( T −25)
−2.0e
( T −25)
+ 1.9e
( T −25)
+ 1.97 (6)
For the diode parameters, they are represented by the following
equations,
−3
V Knee
= 0.7 − 2.0e
( T − 25) (7)
V
©EDA Publishing/THERMINIC 2009 88
ISBN: 978-2-35500-010-2