### A MOSFET parameter extraction tool using EKV model

```The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010)
275
A MOSFET parameter extraction tool using
EKV model and Matlab
Le Duc Hung, Vo Thanh Tri, Nguyen Thi Thien Trang
Faculty of Electronics and Telecommunications
University of Science – VNUHCM
Abstract—This paper presents a MOSFET parameter
extraction tool using Matlab. The purpose of this tool is to
extract parameters to characterize CMOS devices.
Parameter extraction is implemented in behavior of
transistors in conditions which consist of long-wide devices,
short-wide devices and long-narrow devices. The program
has GUI interface, easy-to-use. It can import measurements
data, manage and save MOSFET parameters, display
voltage – current characteristics, etc.
Keywords: parameter extraction, MOSFET, Matlab, Gui
interface
1. INTRODUCTION
There are a lot of parameter extraction tools for MOSFET
devices, however most of them are too expensive to own.
The popular parameter extraction tools can be listed as
IC-CAP, UTMOST, etc. The objective of our project is
developing an automated parameter extraction tool which
is made in Vietnam. Our program will have low cost
meanwhile we can also understand a whole parameter
extraction process.
Initially, we developed a core program and parameter
extraction modules for MOS Level 1, 2, 3. All routines of
the program have been based on Matlab. With the
advantage of MATLAB in mathematics and computing,
especially in numerical computation, statistics, we can
develop our tool rapidly and effectively. The program can
apply the most popular MOSFET models such as MOS
level 1, 2, 3 and EKV. We also upgrade the PSP and
BSIM models in the future.
I ds 
Weff Cox
2 Leff
(Vgs  Vt )2  (1  Vds )


2.2. MOSFET level 2
This model is identical to MOS level 1, except for DC
current formulation and addition of sub-threshold region.
This model also improves linear-to-saturation current
characteristics.
2.3. MOSFET level 3
MOSFET level 3 describe the first- and second-oder
effects:
- The short, narrow channel and Drain induced barrier
lowering effect the threshold voltage.
- Carrier mobility dependence (degradation) on both the
transversal and longitudinal components of the electric
field.
- Saturation of carrier’s velocity.
- Channel length modulation.
- Weak inversion conduction.
- The effect of temperature.
2.3.1. Threshold voltage
Threshold voltage is defined as,
2. MODELS
VTH VFB 2F V . fs 2F VBS  fn(2F VBS )
2.1. MOSFET level 1
MOSFET level 1 or Shichman-Hodges FET model
provides square-law characteristic and includes two gate
junction capacitances. Equation of drain current in linear
region is given as,
I ds ,lin 
And in saturation region:
Weff C ox 
Leff
Vds 2 
 (V gs  Vt ).Vds 

2 

VFB 2F VTO. 2F
With V  ETA.
5.15E  22
.VDS is the increase threshold
Cox.L3
voltage by DIBL effect (Drain-Induced
Lowering).
γ is body factor effect.
Fs = correction factor of short channel effect.
Barrier
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The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010)
1
fs  1 
Leff
If VMAX is not specified, Vdsat is written as follow:
1/ 2



Wp 2 
(Wc  LD) 1  (
)   LD 
Xj

W


p




V D SA T 
V gs  V T H
1  FB
fn = correction factor of narrow channel effect.
fn  DE LT A
2.3.6 Channel Length Modulation
 si
2 C oxW ff
LD is the lateral diffusion length, ETA, XJ, DELTA are
model parameters. VTO is threshold voltage at Vbs = 0V.
L 
2.3.2. Drain current equation
Model’s author proposed a unique Ids equation for all
MOSFET operation regions. It is formulated as:
1  FB


I DS   VGS  VTH 
VDS  VDE
2


W
L
a
VDSAT
(V  V ) V
 KAPPA. DS DSAT  DSAT
2.a.Leff
a
2.a.Leff
q.NUSB
2. Si
NSUB is substrate doping parameter which is extracted
from body-factor effect. KAPPA is also a model
parameter.
With
  eff Cox
When VDS become greater than VDSAT, channel length
will be reduced. The channel length reduction, ΔL, is
formulated as follow:
If VMAX is not specified, channel length reduction is
written as:
VDE  MINV
( DS,VDSAT )
1
 . fS
FB 
 fn
4 2F VBS
 KAPPA.(Vds Vdsat ) 2
L  

a


Finally, the full Ids equation is rewritten as:
2.3.3 Mobility modulation by the gate voltage
In MOSFET level 3 model, model’s author proposed a
simple equation to explain the decrease of carrier
mobility by vertical electric field.
U0
s 
(*)
1  THETA(Vgs  VTH )
UO is carrier mobility at low electric field. THETA is a
model parameter.
e ff


s

 s .V D E
1 

V M A X . L e ff

2.3.7 Weak inversion conduction
In the weak inversion region, model level 3 proposed an
equation which provides both the continuity of the drain
current, the proper bias dependence and sufficient
computational efficiency.
Von  Vt  n.



VMAX is mode parameter, must be extracted from
experimental values. µs is calculated as previous
equation, VDE = min (VDS, VDSAT). If VMAX is not
specified, µeff = µs.
2.3.5 Saturation voltage
The saturation voltage of short-channel MOSFET is
defined as the Drain voltage at which the carriers reach
the maximum velocity. The LEVEL 3 model determines
the saturation voltage (VDSAT) due to the channel pinchoff at the drain side. The VMAX parameter specifies the
reduction of the saturation voltage due to the carrier
velocity saturation effect.
2
VDSAT 
W 
1 FB 
VGS VTH 
VDS VDE

L L 
2

I ds  Ione
2.3.4 Velocity saturation
Velocity saturation affects carrier mobility as follow:

IDS  eff Cox
2
VGS VTH VMAX.L VGS VTH  VMAX.L 

 
 

1 FB
S
 1 FB   S 
q (Vgs Von )/ nkbT
kb .T
q
1/2
q.NFS 1  fs . .(2 f Vbs )  fn.(2 f Vbs ) 
n 1
 

Cox Cox 
2(2 f Vbs )

NFS is also a model parameter.
2.3.8 Temperature effect
Model level 3 provides the effect of temperature on
carrier mobility. At the higher temperature, mobility
decreases. As the result, the drain current is also reduced.
The relationship between temperature and mobility is
formulated as follow:
 T 
 (T )   (Tnorm ). 

 Tnorm 
BEX
In this equation, Temperature is measure on Kelvin
absolute temperature scale and Tnorm is the room
The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010)
temperature. µ(Tnorm) is carrier mobility which is
measured at Tnorm. BEX is a model parameter that default
value is -1.5.
277
simulating and compare with experimental values: IDSVGS, IDS-VDS, gm, gDS. With simulation function, we can
check the error between simulated value and experimental
values one by one.
3. MODEL IMPLEMENTATION USING MATLAB GUI
This senior project focuses on developing software which
the main function is to extract model parameters
automatically. We base on MOSFET level 1, 2, 3
models. Based on this result, we can upgrade for other
models such as EKV, BSIM, etc.
You can image the function of the software as following
figure:
With Matlab, we easily build a simple but effective
graphic user interface (GUI). The program is flexibility
with the database system and results of each parameter
extraction methodology can be compared to the default
result for each model.
Extracted parameter values are showed in table below as
using MOSFET level 3 model:
Default
value
Extracted
value
0.848
0.686
V
600
627.3
2
cm /V.s
THETA
0
0.032
V-1
DELTA
0
1.161
XJ
0
0
M
NSUB
1E+15
6.67E+15
cm-3
VMAX
0
8.596E+4
m/s
ETA
0
0.006
0.2
0.341
V-1
NFS
0
6.927E+11
cm-2
BEX
-1.5
-1.5
Name
VTO
UO
KAPPA
Unit
4. RESULT
The main GUI is the following figure:
Figure 4.2 shows the transfer characteristics ID vs.
V G , ID vs. V D, g m vs. V GS, g ds vs. VDS with longwide-channel device. The transfer characteristics
shown on Figure 4.3 demonstrate the influence of
short channel effects.
Figure 4.1. Main GUI
Providing three data input files, wide- long-channel
device, narrow- long-channel device and wide- shortchannel device respectively, the program can plot the
diagrams which manifest relationship between values, or
calculate and show automatically extracted parameters
which describe the behavior of devices.
To obtain model parameters, the software use a lot of
algorithms, such as regression, interpolate, extrapolate,
etc. which based on extraction methods.
After extracting all model parameters, the software
permits us to export them to text file or database. The
software can implement simultaneously many tasks
corresponding to different samples of devices by database
system. We also use these extracted parameters for
Figure 4.2. W/L = 50µm/50µm
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The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010)
Figure 12.4.1 W/L = 50µm/0.7µm
The simulation results is quite accurate with a small error
(see Figure 4.2). When channel length becomes smaller,
however, the simulation results do not maintain the
accuracy (see Figure 4.2). In that case, the simulation
values is smaller the experimental values. This is the
constraint of MOSFET Level 3.
5. CONCLUSION
The paper presents characteristics and behavior based on
the MOSFET models using open source Matlab
implementation of the program code.
The simulation results of the modeled characteristics
show good accuracy in all operational regions. The
applicability, flexibility and usefulness of this tool is
clearly demonstrated.
6. REFERENCES
[1] Daniel Foty, “MOSFET Modeling with SPICE:
Principles and Practice”, Prentice Hall, 1997.
[2] Y. P. Tsividis, “Operation and Modeling of the
MOS Transistor”, McGraw-Hill, 1987.
[3] H. G. Lee, S. Y. Oh and g. Fuller, “A simple and
accurate Method to Measure the Threshold Voltage
of an Enhancement-Mode MOSFET”, Trans. On
Elec. Device, Vol. ED-29, No.2, 1982.
[4] Y. Tsividis and K. Suyama, “MOSFET Modeling
for Analog Circuit CAD: Problems and Prospects”,
JSSC, Vol. 29, No. 3, 1994
[5] A.I.A. Cunha, M.C. Schneider and C. Galup-Montoro,
“An explicit physical model for the long channel MOS
transistor including small-signal parameters”, SolidState Electronics 1945-1952, 1995.
[6] “HSPICE User's Manual: Elements and Device
Models, Volume II”, Meta-Software Inc., pp. 16103–16-113, 1996
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