Transcript 07_Abebe_MOS-AK_SF08

Compact Modeling for Symmetric and
Asymmetric Double Gate MOSFETs
Henok Abebe
The MOSIS Service
USC Viterbi School of Engineering
Information Sciences Institute
Collaborators
Ellis Cumberbatch and Hedley Morris:
CGU School of Mathematical Sciences, USA
Vance Tyree:
USC/ISI MOSIS, USA
Shigeyasu Uno:
Nagoya University, Department of Electrical and
Computer Engineering, Japan
1st International MOS-AK Meeting, co-located with CMC Meeting and IEDM
Conference, Dec.13 2008, San Francisco, CA
MOSIS
Outline
MOSIS
• 1-D symmetric undoped DG MOSFET modeling.
• 2-D asymmetric and lightly doped DG MOSFET
modeling.
• Mid-section electrostatic potential approximation.
• Long channel mobile charge and current models for
asymmetric DG MOSFET.
• Preliminary simulation results and comparison with
numerical 2-D data.
2
1-D symmetric undoped DG MOSFET modeling
•
•
•
•
MOSIS
Undoped and symmetric.
Relatively small silicon thickness (eg. tsi=5nm).
Two gate voltages are taken to be the same.
Thin gate oxide (eg. tox=1.5nm).
3
1-D symmetric DG (continued)
• Poisson equation
• Boundary conditions
x 0
tox
t si
MOSIS
d 2
q
q ( V ) / kT

n
e
i
dx2  si
d
| x 0  0
dx
2. x  0   0
1.
3. Cox (Vg   
 t si
)    si
/2
d
dx
where Cox   ox / t ox
x   t si / 2
4
1-D symmetric DG (continued)
MOSIS
• Exact solution using the first two boundary conditions:
q 2 ni q 0 / 2 kT
2kT
 ( x)  V  0 
ln[cos(
e
x)]
q
2 si kT
• Surface potential:
 s 
t si / 2
5
1-D symmetric DG (continued)
• Interface boundary condition
MOSIS
equation for β:
ln   ln(cos  )  2 r  tan   
 
q (Vg    V )
2 kT
t si
where  
2
 ln(
2
t si
2 si kT
)
2
q ni
q 2 ni q 0 / 2 kT
 si tox
e
and r 
2kT  si
 ox t si
6
1-D symmetric DG (continued)
MOSIS
• Total mobile charge per unit gate area:
Q  2 si (d / dx) xtsi / 2  2 si (2kT / q)(2 / t si ) tan
• Channel current:
I ds
1 2
S
2
2
 I ds 0 [  tan     r tan  ]  D
2
where I ds 0
W 4 si 2kT 2

(
)
L t si
q
and 0     / 2
7
Summary of the 1-D symmetric DG MOSFET
MOSIS
• For charge and current calculations,  equation
needs solving at source and drain only.
• Have efficient iteration algorithm to solve for  .
• Results are very accurate (see WCM proceedings
Vol. 3, pp. 849, June 1-5, (2008), Boston)
8
2-D asymmetric and doped DG MOSFET modeling
MOSIS
VGF
TOXF
Y
d 2 d 2
q
q ( V ) / kT


n
e
 Na
i
2
2
dX
dY
 si


X
TOXB
Scaling
VGB
X  xLd ln  /  ,
Na
where  
,
ni
Y  Ly,
( ,V )  (w, v)Vth ln 
Vth si
Vth  KbT/q and Ld 
ni q
9
MOSIS
2-D asymmetric (continued)
2
2w

w 1 ( wv ) ln
2

 e
1
2
2
x
y

Ld
where  
L
ln 

Parabolic potential approximation:
w( x, y)  a( y)  b( y) x  c( y) x
2
10
2-D asymmetric (continued)
MOSIS
Boundary conditions:
(vgf  wsf   f )
w
1.  si
  ox
x x  t si
toxf
2
(vgb  wsb   f )
w
2.  si
  ox
x x   t si
toxb
2
3. w( x, y ) x 0  w0  a( y )
 ox vgf  wsf   f vgf  wsb  b
b( y ) 
(

)
2 si
toxf
toxb
 ox vgf  wsf   f vgf  wsb  b
c( y ) 
(

)
2t si  si
toxf
toxb
11
2-D asymmetric (continued)
MOSIS
Surface potentials:
2
si
t si
t
wsf  w0  b  c
2
4
t si
t si2
wsb  w0  b  c
2
4
Explicit solutions can be calculated for wsf and wsb.
12
Mid-section electrostatic potential approximation
MOSIS
2
d
w0
1 ( w0 v ) ln 
2

 Ew0  e
K 0
2
dy

where E  f (toxf , toxb , tsi ) and K  f (toxf , toxb , tsi , vgf , vgb )
Long channel approximation:
 0
2
w0  w0*  w0
where  is a correctionfactor.
13
Mid-section (continued)
Ew 
*
0
1

e
( w0*  v ) ln 
MOSIS
K 0
 ln  (  E v ) ln 
Lam bertW(
e
)
K
E
w0*  

ln 
E
K
 ln  (  E v ) ln 
where (
e
)0
E
K
14
MOSIS
Long channel mobile charge and current models for
asymmetric DG MOSFET
Total mobile charge per unit gate area:
 (VGF  SF  F ) (VGB  SB  F ) 

Q(V )   ox 

TOXF
TOXB


Channel current:
I ds 
 0W
L
Vds
 Q(V )dV
0
15
MOSIS
Preliminary simulation results and comparison with
numerical 2-D data
Na/ni=105, Ts =5nm, TOXF=1.5nm, TOXB=3nm and VGB=-1V
Na/ni=105, Ts =5nm, TOXF=1.5nm, TOXB=3nm and VGB=-1V
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0 [V]
0.1
*
*
0 [V]
0.2
0
0
-0.1
-0.1
-0.2
-0.2
-0.3
-0.4
0.1
-0.3
1
1.5
2
2.5
(VGF-VGB) [V]
3
3.5
4
-0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(SF-SB) [V]
0.9
1
1.1
1.2
Mid-section potential versus relative gate voltage and relative surface
potential with 5nm silicon thickness (lightly doped asymmetric DG MOSFET)
16
MOSIS
Preliminary simulation (continued)
Vgs - =1V, TOXF=TOXB=1.5nm
Na/ni=105, Ts =5nm, TOXF=TOXB=1.5nm
0.58
0.7
0.57
0.6
0.56
0.5
*0 [V]
0.4
*
0 [V]
0.55
0.54
0.3
0.53
0.2
0.52
0.1
0
0.51
0
0.2
0.4
0.6
0.8
1
Vgs - [V]
1.2
1.4
1.6
1.8
2
0.5
0.4
0.6
0.8
1
1.2
Ts [m]
1.4
1.6
1.8
2
-8
x 10
Mid-section potential versus relative gate voltage and silicon thickness with
1.5nm oxide thickness (lightly doped symmetric DG MOSFET)
17
MOSIS
Preliminary simulation (continued)
-3
7
-3
L=W=200nm
x 10
9
Simulation
Numerical data
6
L=W=200nm
x 10
Simulation
Numerical data
8
7
5
Vgs  2V
[A/V]
4
6
ds
g
I
ds
[A]
  1.25
3
5
4
3
2
2
1
0
1
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
0
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
Channel current and output conductance versus source-drain voltage with
5nm silicon and 1.5nm oxide thicknesses (lightly doped symmetric DG
MOSFET)
18
MOSIS
Preliminary simulation (continued)
-3
-4
Simulation
Numerical data
6
Simulation
Numerical data
-5
(log scale)
-6
5
Vds  2V
4
I
ds
[A]
  1.25
g [A/V]
7
L=W=200nm
L=W=200nm
x 10
-8
m
3
-7
-9
2
-10
1
0
0.2
-11
0.2
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
Channel current and tansconductance versus gate voltage with 5nm silicon
and 1.5nm oxide thicknesses (lightly doped symmetric DG MOSFET)
19
MOSIS
Preliminary simulation (continued)
-3
-3
7
L=W=118nm
x 10
9
Simulation
Numerical data
6
L=W=118nm
x 10
Simulation
Numerical data
8
7
4
  1.25
6
I
g
ds
ds
[A/V]
Vgs  2V
[A]
5
3
5
4
3
2
2
1
0
1
0
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
Channel current and output conductance versus source-drain voltage with
5nm silicon and 1.5nm oxide thicknesses (lightly doped symmetric DG
MOSFET)
20
MOSIS
Preliminary simulation (continued)
-3
L=W=118nm
L=W=118nm
-4
Simulation
Numerical data
6
Vds  2V
4
  1.25
-6
-7
I
ds
[A]
5
Simulation
Numerical data
-5
(log scale)
7
x 10
-8
m
g [A/V]
3
2
-9
1
0
0.2
-10
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
-11
0.2
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
Channel current and tansconductance versus gate voltage with 5nm silicon
and 1.5nm oxide thicknesses (lightly doped symmetric DG MOSFET)
21
MOSIS
Preliminary simulation (continued)
-3
7
-3
L=W=90nm
x 10
9
Simulation
Numerical data
6
L=W=90nm
x 10
Simulation
Numerical data
8
7
5
ds
[A]
ds
I
  1.25
3
g
Vgs  2V
4
[A/V]
6
5
4
3
2
2
1
0
1
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
0
0
0.2
0.4
0.6
0.8
1
Vds [V]
1.2
1.4
1.6
1.8
2
Channel current and output conductance versus source-drain voltage with
5nm silicon and 1.5nm oxide thicknesses (lightly doped symmetric DG
MOSFET)
22
MOSIS
Preliminary simulation (continued)
-3
7
L=W=90nm
L=W=90nm
x 10
-4
Simulation
Numerical data
6
Simulation
Numerical data
-5
-6
Vds  2V
3
  1.25
-7
-8
m
I
ds
[A]
4
g [A/V]
(log scale)
5
-9
2
-10
1
0
0.2
-11
0.2
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
0.4
0.6
0.8
1
1.2
Vgs [V]
1.4
1.6
1.8
2
Channel current and tansconductance versus gate voltage with 5nm silicon
and 1.5nm oxide thicknesses (lightly doped symmetric DG MOSFET)
23
University of Southern California (USC)
Viterbi School of Engineering
Information Sciences Institute (ISI)
The MOSIS Service
Marina del Rey, California
MOSIS
7th floorof theMarina
south tower.
USC main campus