### A Modified MODPLEX Model for MOSFET and Parameter Optimization Using Excel-Based Genetic Algorithm

```A Modified MODPEX Model for MOSFET and
Parameter Optimization Using Excel-based
Genetic Algorithm
Zhiyang Chen
Richard Lindeman
Automotive & Power Group
ON Semiconductor
Phoenix AZ USA
[email protected]
Automotive & Power Group
ON Semiconductor
Phoenix AZ USA
Abstract—MODPEX is widely used in industry and universities
to produce Pspice model for power semiconductor devices,
including MOSFETs. However, the model generated by
MODPEX for MOSFETs does not include channel charge at
strong inversion condition. This paper presents a modified
MODPEX model for MOSFETs, which includes channel
charge at strong inversion condition. A process based on
genetic algorithm (GA) implemented in Microsoft Office Excel
is developed to optimize parameters of the modified MODPEX
model. Static and dynamic validation proves that the modified
MODPEX model improves simulation accuracy in both
switching loss and driver loss.
I.
Whenever a MODPEX MOSFET model is modified,
parameters for the MOSFET model must be re-extracted and
optimized. There are basically two methods to extract
parameter for spice models. One is calculus-based method,
in which derives are used, the other is guided random search
technique. Comparing with the calculus-based method,
guided random search technique is more robust and can
search global optimization solution [2].
Genetic Algorithm (GA) is one of the random search
techniques. Genetic algorithm directly searches the best
solution in all the solution space. It is easy to understand, and
has clear calculation flow and is easy to program in
mathematical software, like MS Office Excel. Simple genetic
algorithm is used in this paper.
Figure 1 shows the structure of traditional MODPEX MOSFET model [3]
[4].
RD
FI2 (VFI2)
9
FI1 (VFI1)
GATE
RG
M1
(MM)
7
D1
(MD)
RDS
8
RS
INTRODUCTION
MODPEX has been used in generating spice models for
various
power
semiconductor
devices,
including
MOSFETs[1]. It has been widely used in industry and
research by electrical engineers to build simulation models
for semiconductor devices. However, the models generated
by MODPEX have no flexibility to change structure or
components to include various physics, like channel charge
at strong inversion condition. To include channel charge at
strong inversion condition, traditional MODPEX models for
MOSFETs have to be modified.
II.
DRAIN
SOURCE
Figure 1: Structure Of traditional MODPEX MOSFET model
In Figure 1, M1 is the main MOSFET. Voltage
dependant capacitances are not included in M1. Only
parasitic capacitances, such as gate-source overlay
capacitance CGSO and gate-drain overlay capacitance
CGDO, are included in M1.
In Figure 1, D1 is the MOSFET body diode. Both diode
reverse recovery loss and power loss operating in the third
quadrant are captured by the diode. The structure of body
diode model is shown in [3]. Capacitance of D1 in Figure 1
and D2 in Figure 2 are shown in equation (1)[5].
V AK ≤ FC ⋅ VJ
⎛ V ⎞
C D = CJ 0 ⋅ ⎜⎜1 − AK ⎟⎟
VJ ⎠
⎝
V AK > FC ⋅ VJ
−M
(1)
V ⎤
⎡
C D = CJ 0 ⋅ (1 − FC )− (1+ M ) ⋅ ⎢1 − FC ⋅ (1 + M ) + M ⋅ AK ⎥
VJ ⎦
⎣
here, FC, VJ, CJ0, and M are model parameters.
In Figure 1, RDS is the MOSFET body resistance. RD is
the drain resistance, RS is the source resistance, and RG is
gate resistance.
Figure 2 is the control circuit of the controlled current
sources FI1 and FI2 in Figure 1. The current of controlled
current source FI1 is the current flowing through zerovoltage source VFI1; the current of controlled current source
FI2 is the current flowing through zero-voltage source VFI2.
Capacitance of D2 in Figure 2 is expressed by equation (1).
the model. Only overlay parasitic capacitance between gate
and source, and between gate and drain In Figure 3 are
included in M1 in Figure 1. In fact, the charge introduced by
gate bias is much more significant than parasitic overlay
capacitance when strong inversion layer forms in channel
region. Charges introduced by gate bias have strong effect on
gate-source capacitance and gate-drain capacitance, which as
a result have significant effect on switching characteristics of
MOSFET. Therefore, it is necessary to have MOSFET
model which takes into account the channel charge
introduced capacitances.
Taking intrinsic gate charge QG-CH into account,
capacitances between gate and drain, and between gate and
source are expressed by equation (3) and (4).
(3)
(4)
Figure 2: Structure of control circuit for FI1 and FI2
Voltage of node 10 is controlled by voltage difference
between node 9 and node 7, which is expressed by equation
(2).
(2)
One can see that max_Crss charges or discharges and the
nonlinear capacitor Crss is shorted by an ideal diode when
voltage V(9)<V(7). This process happens at the last instant
of MOSFET switching-on and the first intant of MOSFET
switching-off. The nonlinear capacitor Crss charges or
discharges and max_Crss is blocked by another ideal diode
when V(7)<V(9). This procedure happens when the drainsource voltage is increasing or decreasing. The capacitances
complete switching cycle.
III.
MODIFIED MODPEX MODEL FOR MOSFET
In strong inversion, by integrating gate charge along
channel, the total gate charge is obtained and expressed by
equation (5) [5].
(5)
Applying equation (5) into equation (3) and (4) gives
equation (6) and (7).
(6)
(7)
Here, VGT=VGS-VTH. Ci is the capacitance of gate oxide.
The modified MODPEX MOSFET model, in which
channel charge induced capacitance is include, is shown in
Figure 4.
Figure 3: physical structure of MOSFET
All the model components in section 2 are strictly based
on physics. However, the capacitance of MOSFET
introduced by charges in channel region is not included in
Based on the coding method, the un-coding method for
each gene is expressed by equation (9).
C
G
D
-C
H
(9)
Equation (9) shows that in order to have sufficiently
accurate solution, the solution range
must be
limited to a range as small as possible.
Figure 4: Structure of modified MODPEX model for MOSFET
The difference between traditional MODPEX model and
modified MODPEX model is that two time variant
capacitance CGS-CH and CGD-CH are inserted between gate and
source, and between gate and drain. The rest components of
modified MODPEX model is the same comparing with
traditional MODPEX model, except parameter values must
be re-optimized.
IV.
PARAMETER EXTRACTION
Due to the fact that the new model of MOSFET is
modified from original MODPEX model, a new optimization
procedure has to be developed to extract parameter values
for capacitances in the modified MODPEX model. These
components and parameters are shown in [6][7].
TABLE I.
OPTIMIZATION COMPONENTS AND PARAMETERS
Components
D1
D2
M1
CGS-CH and CGD-CH
Parameters
FC, VJ, CJ0,M
FC, VJ, CJ0,M
CGSO and CGDO
Ci
To find the optimized parameter values for the 11
parameters in table I, genetic algorithm is used. Initialization
procedures of simple GA includes: encoding solutions,
determining fitness function, determining evolution function,
determining reproduce rate and determining mutation rate.
A. Encoding and un-coding solutions
Linear coding method is used in this simple GA. A gene
is assigned 10 bits, which form a 10 bits binary number.
There are 1024 values of each gene, which is linearly
distributed in solution space. Solution space then is
discretized into 1023 sections. Therefore, the coding method
for a solution is shown in equation (8).
(8)
Here, is the value in solution space.
,
maximum and minimum limits of solution space.
the value coded in binary format, which forms a gene.
are
is
B. Determining fitness function and evaluation function
The goal of GA is to find and optimize parameter values
for the modified MOSFET model, so that the capacitances of
modified MOSFET model match the experiment C-V curves
as much as possible. The optimization process is to minimize
the difference between simulation curves and experiment
curves of Ciss, Coss, and Crss. Therefore, it is natural to
have variation of simulation curves and experiment curves as
fitness function, which is expressed by equation (10).
f =
∑ ( ΔCiss ⋅ ΔV + ΔCrss ⋅ ΔV + ΔCoss ⋅ ΔV )
N
Here,
(10)
,
,
ΔV is voltage difference of two
ΔCiss = Ciss_sim−Ciss_exp
ΔCoss = Coss_ sim − Coss_ exp
comparing points. N is experiment data point. is the area
between simulation C-V curves and experiment C-V curves
with unit “pF·V”.
Due to the fact that optimization is to find the minimum
value for fitness function, it is straightforward to choose the
reciprocal of fitness function as evaluation function.
In GA reproduce rate, which is between 0.4 and 1, is
chosen to be 0.6. Mutation rate, which is between 0.001 and
0.1, is chosen to be 0.01. For simplicity, single point
crossover operation is used in the genetic algorithm.
In Excel, each row forms a chromosome and each cell
forms a bit in the chromosome. Because there are 10 bits for
each parameter, the length of a chromosome is 110 bit,
therefore, is 110 cells. Because the population is set to be 80,
there are 80 rows of chromosome. As a result, in excel there
is a matrix of 80x110, in which each cell is a binary number.
The calculation procedure of simple genetic algorithm in
Excel is the following:
•
At first, Excel randomly generates 0 or 1 for each
cell in the 80x110 matrix.
•
Then decode each chromosome to 11 values based
on the boundary values of parameters.
•
Use the 11 decoded values to simulate the C-V
curves for modified MODPEX model.
•
Then compare simulation results with experiment
data and extract errors. Each chromosome has an
error and each generation have 80 error values.
•
Then use the reciprocal of error value as evaluation
function. Chromosomes with evaluation values that
are higher than average values are copied to next
generation.
•
A single point crossover operation follows step 5.
•
The last step is to randomly change values of some
cells from 1 to 0 or from 0 to 1 based on a mutation
rate, which is a possibility between 0.001 and 0.1. It
is 0.01 for devices parameter optimization for this
paper.
•
Copy population of first generation to second
generation and repeat step 2 to 7 for next generation.
V.
EXPERIMENT VALIDATION
A. Static validation
The modified MOSFET model has been applied to
MOSFET NTD4815, a product of ON Semiconductor
Company. C-V curves are measured with Hewlett Packard
4284A.
Experiment C-V curves and simulation curve of
traditional MODPEX model are shown in Figure 5.
Figure 5: Ciss, Coss and Crss curves Comparison between experiment and
simulation of (Dashed lines with marks are experiment curves, solid lines
are simulation curves)
Experiment curves and modified MODPEX model are
shown in Figure 6.
Figure 6: Ciss, Coss and Crss curves Comparison between experiment
and simulation (Dashed lines with marks are experiment curves, solid
lines are simulation curves)
B. Dynamic validation
Resistive switching experiment has been done to
compare the traditional model and new model. Figure 7
shows the experiment setup, in which three boards are
included: driver board, test board and mother board. Driver
used in test is NCP5911, a 5V driver of ON semiconductor.
Figure 7: Resistive switching experiment setup
Schematic circuit of experiment setup is shown in Figure
8. To take the full advantage of existing experiment setup,
load resistance is connected to source of MOSFET
NTD4815.
Resistive Turn-off
20
Voltage (V) / Current (A)
IDS
VDS
15
10
model
-6.E-08
-4.E-08
Modified
model
5
-2.E-08
0
-2.E-22
2.E-08
4.E-08
6.E-08
Experiment
-5
Time (s) (20ns/div)
Figure 8: Resistive switching circuit
Resistive Turn-on
20
Experiment
15
IDS
Resistive Turn-on
VDS
0
-6.00E-08 -4.00E-08 -2.00E-08 -2.00E-22 2.00E-08
model
-2.E-08
Experiment
5
0
2.E-23
-5
Modified
model
4.00E-08
Modified
model
10
-4.E-08
5
IDS
15
10
model
25
20
2.E-08
4.E-08
6.E-08
8.E-08
Time (s) (20ns/div)
Figure 11: 20V20A resistive switching on validation
6.00E-08
Resistive Turn-off
-5
Time (s) (20ns/div)
25
IDS
VDS
20
Figure 9: 12V12A resistive switching on validation
Voltage (V) / Current (A)
Voltage (V) / Current (A)
VDS
Figure 10: 12V12A resistive switching off validation
Voltage (V) / Current (A)
Figure 9 to Figure 12 are comparison of resistive
switching experiment results and simulation results of
modified MODPEX model and conventional MODPEX
model. Driver waveforms are not shown in these figures.
Driver loss comparison of modified MODPEX model,
conventional and experiment on driver loss prediction is
shown in Figure 13.
-6.E-08
15
model
10
Modified
model
5
-4.E-08
-2.E-08
Experiment
0
-1.E-22
2.E-08
4.E-08
-5
-10
Time (s) (20ns/div)
Figure 12: 20V20A resistive switching off validation
6.E-08
[email protected]
35
30
PowerLoss (mW)
25
20
15
10
5
0
OldModel
NewModel
Experiment
Figure 13: Driver loss at 5V
The overall variation between experiment curves and
simulation curves of each generation as a function of
generations is in Figure 14. The mutation rate is 0.001, 0.01,
and 0.1, respectively.
Figure 15: Simple GA calculation results at crossover frequency 0.2, 0.4,
0.6 and 0.8
VI.
DISCUSSION
Comparing with traditional MODPEX model, the
modified MODPEX model has better simulation accuracy,
especially for gate source capacitance CGS when VGS is
greater than zero. Figure 6 clearly shows that the accuracy of
Ciss, Coss, and Crss are improved in both region of VGS>0,
VDS=0 and VGS=0, VDS>0. Area between simulation and
experiment of C-V curves are reduced from around 9000
pF·V of traditional MODPEX model to around 5100 pF·V of
modified MODPEX model.
Dynamic validation shows that modified MODPEX
model has better match with experiment voltage and current
than conventional MODPEX model, as is shown in from
Figure 9 to Figure 12. Due to the better modeling of channel
charge in strong inversion, modified MODPEX model has
better simulation accuracy in switching time, and therefore
switching loss.
Figure 14: Simple GA calculation results at mutation rate 0.001, 0.01 and
0.1
The overall variation between experiment curves and
simulation curves of each generation as a function of
generations at various crossover rates is in Figure 15. The
crossover operation rate is 0.2, 0.4, 0.6, and 0.8, respectively.
Driver loss is also improved in modified MODPEX
model. Experiment shows that driver loss for NTD4915 at
5V driver is 30.4mW. Conventional MODPEX model
predicts drive loss to be 20.5mW, only 67% of total driver
loss. Modified MODPEX model predicts 31.2mW, which
give simulation accuracy of 97.4%.
Figure 14 shows the solution evolution of genetic
algorithm as a function of generation. Solutions are quickly
converged to optimized minimum value in the first 100
generations. After 100 generations, no significant
improvement is observed. To save simulation resources,
genetic algorithm could be limited to 100 generations.
Mutation rate has significant effect on final solutions of
genetic algorithm. Higher mutation rate has faster
convergence speed. However, mutation rate higher than 0.01
results in slower convergence speed. Three optimization
results vs generation curves at mutation rate 0.001, 0.01 and
0.1 are shown in Figure 14. It is clearly shown that
convergence speed with mutation rate 0.01 is highest among
three situations.
Crossover rate is another factor that affects the
convergence speed. Crossover frequency that is greater or
smaller than 0.6 will reduce the convergence speed of
genetic algorithm, which is shown in Figure 15. In Figure 15,
it takes about 60 generations to converge for the case with
crossover frequency 0.6 to optimized vale, while it takes
about 130 and 140 generations for cases with crossover
frequency 0.2 and 0.8, respectively.
VII. CONCLUSIONS
A modified MODPEX model for MOSFETs is proposed.
This model includes channel charge induced capacitances,
which is the key capacitance during turn-on and turn-off
intervals.
Genetic algorithm is designed to optimize
capacitances in the model. Improvements are validated by
simulation and experiment.
REFERENCES
[1] “MODPEX Modeling Tool”, http://www.symmetry.com/
[2] D. Goldberg (1989), Genetic Algorithms in Search, Optimization,and
[3]
Description
of
ONSemiconductor
MOSFET
Model
www.onsemi.com/pub/Collateral/AND9033-D.PDF