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Chapter 18. NONIDEAL MOS
NONIDEAL MOS
Sung June Kimkimsj@snu.ac.kr
http://helios.snu.ac.kr
Chapter 18.
Chapter 18. NONIDEAL MOS
CONTENTS
• Metal-Semiconductor Work function Difference• Oxide Charges• MOSFET Threshold Considerations
Chapter 18. NONIDEAL MOS
Physics of Non-ideal MOS-C
1 fms ¹ 0
2 charges exist in SiO2
“ real ”
Chapter 18. NONIDEAL MOS
Workfunction Difference
• Workfunction :– the minimum energy required to bring an electron
from the Fermi level to the vacuum level.– for Al, qf
m= 4.3 eV.
• Electron affinity :– the energy difference between conduction band edges
of the semiconductor and the vacuum level.– for silicon, qc = 4.05 eV.
Chapter 18. NONIDEAL MOS
Equilibrium
EF
eV3.4q m =f
Silicon
eV05.4q =c
sqf
Al
sm ff ¹
msqf
msFBV f=
Chapter 18. NONIDEAL MOS
Heavily-doped polysilicon gate
gate bulk
EF = EC
at equilibrium
Chapter 18. NONIDEAL MOS
Heavily-doped polysilicon gate
Gate SiliconOxide
Chapter 18. NONIDEAL MOS
÷÷ø
öççè
æ--=
--=
i
Ag
g
nNln
qkT2/E
2/EFms
ff
~ 560mV ~ 350mV
약 -900 mV
Chapter 18. NONIDEAL MOS
Oxide Charges and Traps
• Qtot : total oxide charges (per unit area)
Si
SiOx
SiO2
metal
Chapter 18. NONIDEAL MOS
( )ò-= ox0 ox
ooT dxxx
K1V re
D
Chapter 18. NONIDEAL MOS
Mobile Ionic Charges
• Na+, K+
• Very high diffusivities in the oxide even below 200 °C– VT instability
Chapter 18. NONIDEAL MOS
• Test : MOS-C CV
High T High T
- VGB + VGB
VG
C
after +BT stress
after -BT stress
ox
mCQV =D
Chapter 18. NONIDEAL MOS
Fixed Oxide Charge
1. Located very close to the interface2. Associated with the structure of the interfacial between Si and
SiO2
3. Function of substrate orientation, oxidation temperature (anneal condition)
Chapter 18. NONIDEAL MOS
( ) ( ) mV 2.5 =´
´´-= -
--
29
21019
T F/cm10690cm101 C106.1VD
2nF/cm cm
F/cm , 6901050
10854.89.3t
KC50t)100( 8
14
ox
ooxoxox =
´´´
=== -
-e
(111) > (110) > (100)
1´1010 cm-2 \ (100) wafers are used for MOS IC
ox
f
ox
fT C
qNCQ
V-
=-
=D
Å
Chapter 18. NONIDEAL MOS
Interface Trapped Charge1. Arises from allowed energy states in the forbidden gap of
the Si, very close to Si-SiO2 interface.2. Physical origin unknown yet.
® “dangling bond” (?)Dangling bond
surface
electron can be trapped
O O OSi
Si
Chapter 18. NONIDEAL MOS
3. The surface state acts like a recombination center.4. Function of VGB ®가장나쁜 charge.5. Distributed throughout the entire band gap
Filled Empty
donor-like traps “0” “+” below Ei
acceptor-like traps “-” “0” above Ei
filled
empty
Interfacialtraps
Ev
Ec
EF
Chapter 18. NONIDEAL MOS
- accumulation : mostly empty
Qit
+3
- inversion :mostly filled
donor-like
acceptor-like
Qit
-3
Chapter 18. NONIDEAL MOS
6. Distribution of trap level vs. energy
7. (111) > (110) > (100) , Dit(111) : Dit(100) » 3:1
Nit( #/cm2 )
Ev
Ei
Ec
E
Chapter 18. NONIDEAL MOS
8. Annealing with hydrogen at relatively low temperature (£500 °C) minimize Dit.
0.1 mm´ 0.1 mm® 1 trap
1010 traps/cm2 ® 100 traps/mm2
D S[H] diffusion
Chapter 18. NONIDEAL MOS
Oxide Trapped Charge Qot
• Due to holes and electrons trapped in the bulk of oxide.
Chapter 18. NONIDEAL MOS
Effect of Oxide Charge on VT
) interface at the Q If ( totox
totT C
QV -=D
Chapter 18. NONIDEAL MOS
Threshold Voltage Equation
• Flat band voltage º VFB ºox
totms C
Q-f
ox
FA0sFFBT C
NqK42VV
fef
++= ~ 0.6 V
potential drop in Si potential drop in oxide
Chapter 18. NONIDEAL MOS
Back Biasing• Body effect: Reverse biasing the back contact relative to
the source Ô VT change
If VBS=0, inversion occurs when fs=2fF
If VBS<0, inversion layer carriers migrate laterally into the S/D. The inversion occurs when fs=2fF+|VBS|.The maximum depletion width
( )A
BSFosT qN
|V|2K2W +=
fe
Chapter 18. NONIDEAL MOS
• At threshold,
( )
ox
BSFAosBSFFBGB C
|V|2NqK2|V|2VV
++++=
fef
( )
( )FBSFox
AosBST
ox
BSFAosFFBBSGBGS
2|V|2C
NqK2)0(VV
C|V|2NqK2
2VVVV
ffe
fef
-++==
+++=+=\
=
VT
Body Factor
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