Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET...
Transcript of Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET...
![Page 1: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/1.jpg)
MOS Cap
Session 9: Solid State Physics
1
![Page 2: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/2.jpg)
1.
2.
3.
4.
5.
Outline
� A� B
� C
� D
� E
� F� G
� H
� I
� J
2
![Page 3: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/3.jpg)
1.
2.
3.
4.
5.
MOS!
3
Metal:
Oxide:
Semi Conductor:
Al, …, Poly Si (n++,p++), ρ���� � 0.1�Ω �SiO2 (reason why Si beat GaAs)
Si
CMOS is the dominant technology in integrated circuits
Heart of a MOSFET is MOS-cap
p-type bulk � nMOS
n-type bulk � pMOS
(n/p)MOS � CMOS
����
p-type Si (bulk)
SiO2 (oxide)� High k
Al (metal)
~0.1��
~5�����
��� � 11.9, ~3 � ����� � 3.9
![Page 4: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/4.jpg)
1.
2.
3.
4.
5.
Bulk Semiconductor Potential , ϕF
4
!"
#"
$" !�
#� $�
Definition:
p-type n-type
%&$ ≡ � ( $ � � )*�+ ( $
&$ � ,-% ln 01�� 2 0 &$ � (,-% ln 03�� 4 0
%&$%&$
![Page 5: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/5.jpg)
1.
2.
3.
4.
5.
MOS –Special Case
5
!
# $5 $6
7
%8%&5%&6
Special case: &6 � &5
metal Si, p-typeSiO2
!
#
9
%8�
![Page 6: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/6.jpg)
1.
2.
3.
4.
5.
MOS –Special Case
6
!
# $5
7
%8%&5%&6
Special case: &6 � &5 %8�
����
p-type Si (bulk)
SiO2 (oxide)� High k
Al (metal)
~0.1��
~5�����
A
A’
SiO2 Si, p-typemetal
![Page 7: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/7.jpg)
1.
2.
3.
4.
5.
M (Al) , O (SiO2) , S (Si)
7
!
# $5
$6
7
%8 � 4.05�;%&5 � 4.9�;
%&6<= � 4.1
metal Si, p-typeSiO2
!
#
9 � 9�;
0.95
? $
![Page 8: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/8.jpg)
1.
2.
3.
4.
5.
Flat Band Voltage
8
!
# $5
$6
7
%8 � 4.05�;%&5 � 4.9�;
%&6<= � 4.1
metal Si, p-type
0.95
%;9%;9 � %&6 ( %&5;$? ≡ &6 ( &5 � &65;$? � (0.8;
![Page 9: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/9.jpg)
1.
2.
3.
4.
5.
Voltage Barrier
9
! # $5
$6
7
%8 � 4.05�;%&6<= � 4.1
metal Si, p-type
0.95
%;9
;9 � ;$? � (0.8;
%&5 � 4.9�;3.1�;3.15�;
No way electrons might pass the voltage barrier!
![Page 10: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/10.jpg)
1.
2.
3.
4.
5.
No Gate Voltage
10
! # $5 $6
7
%8 � 4.05�;%&6<= � 4.1�;
metal Si, p-type
0.95
;9 � 0;
%&5 � 4.9�;3.1�;3.15�;
0.8; ? ?
![Page 11: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/11.jpg)
1.
2.
3.
4.
5.
Boundary Condition
11
�A�B CB"
CA"CB" ( CA" � D5*EFGHHI
D5*EFGHHI � 0�AJA � �BJB��� K ��KL M
�"N� ��� K ��KL M�"N
K ��KL M�"N
≅ 3K ��KL M�"N
![Page 12: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/12.jpg)
1.
2.
3.
4.
5.
M (PolyGate) , O (SiO2) , S (Si)
12
! # $5
7
%8 � 4.05�;%&5 � 4.9�;
n+ poly Si, p-typeSiO2
!
#
9 � 9�;
0.95
? $ ! #
$
%8 � 4.05�;
;$? � &6 ( &5 � (0.85;
![Page 13: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/13.jpg)
1.
2.
3.
4.
5.
No Gate Voltage –Poly Gate
13
! # $5 $6
7
%8 � 4.05�;
metal Si, p-type
0.95
;9 � 0;
%&5 � 4.9�;3.1�;3.1�;
! #
%8 � 4.05�;
![Page 14: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/14.jpg)
1.
2.
3.
4.
5.
No Gate Voltage
14
! # $5 $6
7
%8 � 4.05�;%&6<= � 4.1�;
metal Si, p-type
0.95
;9 � 0;
%&5 � 4.9�;3.1�;3.15�;
![Page 15: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/15.jpg)
1.
2.
3.
4.
5.
No Gate Voltage
15
! # $5
$
;9 ( ;$? � ;���PI Q ;��
%&5 � �)*�+ ( �5*EFGHI
%;9
� ;�� Q &5
%&5
;9 ( ;$? � ;�� Q &5As important as KVL
%;��
![Page 16: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/16.jpg)
1.
2.
3.
4.
5.
Flat Band
16
! # $
$%;$?
;9 � ;$?
D
J
L
L
![Page 17: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/17.jpg)
1.
2.
3.
4.
5.
Accumulation
17
! # $
$%;$?
;9 4 ;$?
D
J
L
L
QR
(R
![Page 18: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/18.jpg)
1.
2.
3.
4.
5.
Flat Band
18
! # $
$%;$?
;9 � ;$?
D
J
L
L
![Page 19: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/19.jpg)
1.
2.
3.
4.
5.
Depletion (Weak Inversion)
19
! # $ $ %;$?
;S 2 ;9 2 ;$?
D
J
L
L
TPI��QRPI��(%01
J�� AUJ��
![Page 20: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/20.jpg)
1.
2.
3.
4.
5.
(Strong) Inversion
20
! # $ $ %;$?
;9 2 ;S
D
J
L
L
TPI��QRPI��(%01
QR�"V
(R�"V
![Page 21: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/21.jpg)
1.
2.
3.
4.
5.
Depletion (Weak Inversion)
21
! # $
$ %;$?
;S 2 ;9 2 ;$? TPI��
%&5
KJKL �
D��� �
(%01��� � KB&KLB
%;9→&5 � %01LB2��� → TP � 2���%01 &5
J�� � (RPI����
RPI� � (%01TP � 2%01���&5
→ ;�� � (���RPI���� � (RPI�Y��Y �B⁄[ �B⁄
;9 � ;$? Q ;�� Q &5 → ;9 � ;$? Q &5 Q 1Y�� 2%01���&5 p-type Si (nMOS)
In Depl
&5 4 0 ;9 � ;$? Q &5 ( 1Y�� 2%01��� &5 n-type Si (pMOS)
In Depl
![Page 22: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/22.jpg)
1.
2.
3.
4.
5.
Threshold Voltage –Definition!
22
����
p
SiO2
\]^_ � C_�`�n+ n+
A A’ !
#
$C_�`�\]^_ �
;9 � 0;9 2 0;9 � ;S
![Page 23: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/23.jpg)
1.
2.
3.
4.
5.
Threshold Voltage
23
! # $
$ %;$?
;9 � ;S TPI��
%&5;S � ;9abcdBbe
%;9f)*�+ � 01
2���%01 g2&$hT6G� � TPI��ibcdBbe �
;S � ;9abcdBbe � ;$? Q 2&$ Q 1Y�� 2%01���g2&$h
Definition of Threshold voltage:
;9 � ;$? Q 2&$ ( 1Y�� 2%01��� 2&$
n-type
�5*EFGHI � 01
p-type
%&$ � ,-% ln 01�� 2 0
%&$ � (,-% ln 03�� 4 0
![Page 24: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/24.jpg)
1.
2.
3.
4.
5.
Threshold Voltage vs. Bulk Doping
24
;S
ln01
;S
ln03
;$?
;$?
↘ ���p-type
n-type
![Page 25: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/25.jpg)
1.
2.
3.
4.
5.
MOS Band Diagram (n-type Bulk)
25
Decrease VG (toward more negative values)
� move the gate energy-bands up, relative to the Si
decrease VG
decrease VG
• Accumulation
– ;9 2 ;$?– Electrons
accumulate at surface
• Depletion
– ;9 4;$?– Electrons repelled
from surface
• Inversion
– ;9 4;S– Surface
becomes p-type
![Page 26: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/26.jpg)
1.
2.
3.
4.
5.
Accumulation, Poly Gate
26
;9 4 ;$?
p
Mobile carriers (holes) accumulate at Si surface
n+ Poly Gate
+- !
# $
$
;9 ≅ ;$? Q ;��
%&5≅ 0 !
# %;9
%;��M O S
;94.8�;
3.1�;
![Page 27: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/27.jpg)
1.
2.
3.
4.
5.
Accumulation, Layer Charge Density
27
;9 4 ;$?
p
From Gauss’ Law:Gate
+- ;9 RGHH
���
Y �B⁄
;�� ≅ ;9 ( ;$?
J�� � (RGHH �����⁄;�� � ���J�� � (RGHH Y��⁄
where Y�� ≡ ����� ���⁄ [ �B⁄
→ RGHH � (Y�� ;9 ( ;$? 2 0
![Page 28: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/28.jpg)
1.
2.
3.
4.
5.
Depletion, Poly Gate
28
;9 4 ;$?
p
Si surface is depleted of mobile carriers (holes)
=> Surface charge is due to ionized dopants
(acceptors)
+-
! # $ $
%&5 !
#
%;9
%;��M O S
;9
n+ Poly Gate
4.8�;
3.1�;
T
T
;9 � ;$? Q ;�� Q &5
![Page 29: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/29.jpg)
1.
2.
3.
4.
5.
Depletion (Weak Inversion)
29
! # $ $
;S 2 ;9 2 ;$? TP
%&5
KJKL�
(%01��� � KB&KLB
%;9
→&5 � %01LB2���
→ TP � 2���%01 &5
RPI� � (%01TP � ( 2%01���&5
;�� � (RPI�Y��
;9 � ;$? Q ;�� Q &5 → ;9 � ;$? Q &5 Q 1Y�� 2%01���&5
Solving for &5 :
&5 � %01���2Y��B 1 Q 2Y��B%01��� ;9 ( ;$? ( 1B
![Page 30: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/30.jpg)
1.
2.
3.
4.
5.
Strong Inversion
30
;9 2 ;S
p
Significant density of mobile electrons
at surface (surface is n-type)
+- ;9
Gate
TS
As ;9 is increased above ;S, the negative charge in the Si
is increased by adding mobile electrons (rather than by
depleting the Si more deeply), so the depletion width
remains ~ constant at T �TS
&5 ≅ 2&$;9 � ;$? Q &5 Q ;��
∴ R�"V � (Y�� ;9 ( ;S;9 � ;S ( R�"VY��
→ T ≅ TS � 2���%01 g2&$h
� ;$? Q 2&$ ( RPI� Q R�"VY��� ;$? Q 2&$ ( 2%���01g2&$hY�� ( R�"VY��
![Page 31: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/31.jpg)
1.
2.
3.
4.
5.
ϕsand W vs. VG
31
&5:
T:accumulation depletion inversion ;9;$? ;S0
2&$&5 &5 � %01���
2Y��B 1 Q 2Y��B%01��� ;9 ( ;$? ( 1Bg;$? 4 ;9 4 ;Sh
accumulation depletion inversion ;9;$? ;S0
TS
T T � ���Y�� 1 Q 2Y��B%01��� ;9 ( ;$? ( 1 g;$? 4 ;9 4 ;Sh
TS � 2���g2&$h %01⁄
![Page 32: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/32.jpg)
1.
2.
3.
4.
5.
Total Charge Density in Si, QS
32
RGHH:
accumulation depletion inversion
;9;$? ;S
RGHH � (Y�� ;9 ( ;$?
RPI�:accumulation depletion inversion
;9;$? ;S
R5 � RGHH Q RPI� Q R�V"
R�"V:accumulation depletion inversion
;9;$? ;S
R5:
accumulation depletion inversion
;9;$? ;SRPI� � (%01T
R�"V � (Y�� ;9 ( ;S
R�"VSlope = (Y��
![Page 33: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/33.jpg)
1.
2.
3.
4.
5.
MOS C-V Characteristics
33
Y � KRmGNIK;9 � KR5K;9R5:accumulation depletion inversion
;9;$? ;S
R�"VSlope = (Y��
accumulation depletion inversion
;9;$? ;S
YY��
![Page 34: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/34.jpg)
1.
2.
3.
4.
5.
Debye Length
34
• As the gate voltage is varied, incremental charge is added/subtracted to/from the
gate and substrate.
• The incremental charges are separated by the gate oxide.
M O S
R(R
∆R
(∆RY
Y � KRGHHK;9 � Y��
S
o3
KB&KLB � (D� �
%� 03 ( 01 Q f ( �
n-type bulk:KB&KLB �
%� 03 ( �
KB&KLB �
%� 03 ( ���p bqpb brs⁄
� %� 03 1 ( �b brs⁄
≅ %� 03
&&Nt �
&o3B
o3 � �,-%B03
![Page 35: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/35.jpg)
1.
2.
3.
4.
5.
o3
Flat-Band Capacitance
35
TPI�
p
Gate
p
Gate
Y��Y$?Y��YPI�
Y$? � Y��Y3Y�� Q Y3→ 1Y$? �
������ Qo3���
;9;$?
Y Y��Y$?1Y �
������ QTPI����
![Page 36: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/36.jpg)
1.
2.
3.
4.
5.
Capacitance in Inversion
36
CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond
to changes in the gate voltage.
M O S
∆R
(∆R
Y��Y � KR�"VK;9 � Y��
� Incremental charge is effectively
added/subtracted at the surface of the substrate.
TSTime required to build inversion-layer
charge = 201u7/�� , where u7 = minority-carrier
lifetime at the surface
![Page 37: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/37.jpg)
1.
2.
3.
4.
5.
Capacitance in Inversion
37
CASE 2: Inversion-layer charge can not be supplied/removed quickly enough to
respond to changes in the gate voltage.
M O S
∆R
(∆R
Y��
� Incremental charge is effectively
added/subtracted at depth WT in the substrate.
TS
YPI�
� 1Y�� Q
TS���
1Y �
1Y�� Q
1YPI�
� 1Y�� Q
2 2&$%01��� ≡ 1
Y6�"
![Page 38: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/38.jpg)
1.
2.
3.
4.
5.
Supply of Inversion Charge
38
Accumulation:
Depletion:
Inversion:
Case 1
p
Gate
Y��
p
Gate
Y��YPI�
p
Gate
Y��YPI�
p
Gate
Y��n+
Case 2
![Page 39: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/39.jpg)
1.
2.
3.
4.
5.
Boundary Condition
39
accumulation depletion inversion
;9;$? ;S
YY��Y$?
MOS capacitor at high fY6�"
MOS capacitor at low f, or
quasi-static C-V
MOS transistor at any f,
![Page 40: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/40.jpg)
1.
2.
3.
4.
5.
Deep Depletion
40
accumulation depletion inversion
;9;$? ;S
YY��Y$?
Y6�"
If VG is scanned quickly, Qinv cannot respond to the change in VG. The increase
in substrate charge density Qs must then come from an increase in depletion
charge density Qdep⇒ depletion depth W increases as VG increases⇒ C decreases as VG increases
![Page 41: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/41.jpg)
1.
2.
3.
4.
5.
Boundary Condition
41
![Page 42: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/42.jpg)
1.
2.
3.
4.
5.
Oxide Charges
42
p
In the oxide:Gate
���
SiO2
K+
Na
+
+ + +
e- e- e- e-
In real MOS devices, there is always some charge in the oxide and at the Si/oxide interface.
1. Trapped charge Qox
High-energy electrons and/or holes injected
into oxide
2. Mobile charge QM
Alkali-metal ions, which have sufficient mobility
to drift in oxide under an applied electric field
At the interface:
1. Fixed charge QF
Excess Si (+)
2. Trapped charge QIT
Dangling bonds
![Page 43: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/43.jpg)
1.
2.
3.
4.
5.
Effect of Oxide Charges
43
M O S
R
(R D��gLh
In general, charges in the oxide cause a shift in the gate
voltage required to reach the threshold condition:
∆;S � ( 1����B x LD7� L KL
Nyz
7(x defined to be 0 at metal-oxide interface)
In addition, they may alter the field-effect mobility of
mobile carriers (in a MOSFET) due to Coulombic scattering
![Page 44: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/44.jpg)
1.
2.
3.
4.
5.
Fixed Oxide Charges QF
44
! # $
$;$? � &65 ( R$Y�� !
# %;$?
%R$ Y��⁄M O S
4.8�;
3.1�;
![Page 45: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/45.jpg)
1.
2.
3.
4.
5.
Parameter Extraction from C-V
45
From a single C-V measurement, we can extract much information about the
MOS device.
Suppose we know that the gate-electrode material is heavily doped n-type
poly-Si (&{=4.05eV), and that the gate dielectric is SiO2 (�E � 3.9):
o From Y6G� � Y��we determine the oxide thickness L7o From Y6�" and Y�� we determine substrate doping (by iteration)
o From substrate doping and Y�� we calculate the flat-band capacitance Y$?o From the C-V curve, we can find
o From &{, &�, Y��, and ;$? we can determine R$
![Page 46: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/46.jpg)
1.
2.
3.
4.
5.
Determination of ϕMand QF
46
Measure C-V characteristics of capacitors with different oxide thicknesses.
Plot ;$? as a function of L7:
0
–0.15V
–0.3V
Tox
Vfb 10 nm 20 nm 30 nm
;$? � &65 ( R$����� ���
p
Gate Gate
Gate
![Page 47: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/47.jpg)
1.
2.
3.
4.
5.
Mobile Ions
47
Odd shifts in C-V characteristics were once a mystery:
Source of problem: Mobile charge moving to/away from interface,
changing charge centroid
Before bias Temp
After +12V bias
100°C 70min
After -30V or 0V
bias 200°C 60min
;9
YY7
∆;$? � (79;
∆;$? � ( R{Y��
![Page 48: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/48.jpg)
1.
2.
3.
4.
5.
Interface Traps
48
Traps cause “sloppy” C-V and also
greatly degrade mobility in channel
Before
no annealing
After
;9
YY7
∆;9 � (R}S &5Y��
H2 annealing
! # $
%&5
! # $
!
# $
!
# $
![Page 49: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/49.jpg)
1.
2.
3.
4.
5.
Poly-Si Gate Depletion
49
A heavily doped film of polycrystalline silicon (poly-Si) is typically employed
as the gate-electrode material in modern MOS devices.
p-type Si
n+ poly Si
n-type Si
p+ poly Si
NMOS PMOS
There are practical limits to the electrically active dopant concentration
(usually less than 1x1020 cm-3 )
⇒ The gate must be considered as a semiconductor, rather than a metal
![Page 50: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/50.jpg)
1.
2.
3.
4.
5.
%&5
MS Junction (Poly Gate)
50
! # $
$
;9 2 ;S TS
! # $
%;9%;����
T����p-type Sin+ poly Si gate
Si biased to inversion:
VG is effectively reduced:
R�"V � Y�� ;9 ( ;���� ( ;S
T���� � 2���;����%0����
How can gate depletion
be minimized?
![Page 51: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/51.jpg)
1.
2.
3.
4.
5.
Gate Depletion Effect
51
p
n+ Poly Gate
TS
Y��Y����
Gauss’s Law dictates:
� �������� Q AUT����
T���� � ���~��%0������� is effectively increased:
Y � 1Y�� Q
1Y����
pA� �������� Q
T�������pA
R�"V � Y�� ;9 ( ;���� ( ;SR�"V � �������� Q AUT����
;9 ( ;S
![Page 52: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/52.jpg)
1.
2.
3.
4.
5.
Inversion Layer Thickness Tinv
52
-50 -40 -30 -20 -10 0 10 20 30 40A
50
Si
%&5 ! # $
$
;9 2 ;S TS
! # $
%;9%;����
T����
7 A
T���� ���
Electron density
QM theory
Poly Si SiO2
Physical
-���effective
-�"V
The average inversion-layer location
below the Si/SiO2 interface is called
the inversion-layer thickness, -�"V .
![Page 53: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/53.jpg)
1.
2.
3.
4.
5.
Effective Oxide Thickness , TOxe
53
-��� � ��� Q AUT���� Q AU-�"V@;9 � ;33
g;9 Q ;Sh/-��can be
shown to be the
average electric field in
the inversion layer. Tinv
of holes is larger than
that of electrons
because of the
difference in effective
masses.
![Page 54: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/54.jpg)
1.
2.
3.
4.
5.
Effective Oxide Capacitance , COxe
54
-��� � ��� Q AUT���� Q AU-�"VR�"V � Y��� ;9 ( ;S
Basic CV
with poly-depletion
with poly-depletion and charge-layer thickness
measured data
Y���Y��
;9
![Page 55: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/55.jpg)
1.
2.
3.
4.
5.
MOS Cap:
Equivalent Circuit in Depletion & Inversion
55
Y��Y����
YPI� Y�"V
Y��YPI�
Y��Y����
Y�"V
���� ����Y��
YPI� Y�"V
���� ����
General case for
both depletion and
inversion regions.
In the depletion
regions;9 ≈;S Strong inversion
![Page 56: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/56.jpg)
1.
2.
3.
4.
5.
VTAdjustment by Ion Implantation
56
In modern IC fabrication processes, the threshold
voltages of MOS transistors are adjusted by ion
implantation:
• A relatively small dose NI (units: ions/cm2) of
dopant atoms is implanted into the near-surface
region of the semiconductor
• When the MOS device is biased in depletion or
inversion, the implanted dopants add to the dopant-
ion charge near the oxide-semiconductor interface.
∆;S � (%0}Y��0} 2 00} 4 0
for donor atoms
for acceptor atoms
![Page 57: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/57.jpg)
1.
2.
3.
4.
5.
Dynamic VTAdjustment Bulk Voltage
57
! # $ $
;9 2 ;S TPI��
%&5%;9
;S � ;$? Q 2&$ Q RPI��Y��
p
\ Cn+ n+
;9� 2 ;S ;3� � 0
;?
�0 ;HD
$
! # $
%; ?!
%;?!Q2
& $
;S � ;$? Q ;! Q 2&$ Q RPI��Y��RPI�� � 2%01��� ;?! Q 2&$
![Page 58: Session 9: Solid State Physics MOS Capee.sharif.edu/~sarvari/25772/PSSD008.pdf · Heart of a MOSFET is MOS-cap p-type bulk nMOS n-type bulk pMOS (n/p)MOS CMOS p-type Si (bulk) SiO2](https://reader035.fdocuments.net/reader035/viewer/2022062606/5fe49f90811aa75e5f5c1010/html5/thumbnails/58.jpg)
1.
2.
3.
4.
5.
CCD Imager and CMOS Imager
58
Deep depletion, Qinv
= 0 Exposed to light