lecture 17
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Lecture 17
OUTLINE• The MOS Capacitor (cont’d)– Small-signal capacitance
(C-V characteristics)
Reading: Pierret 16.4; Hu 5.6
S and W vs. VG (p-type Si)
)(for 1)(2
12
22
2 TGFBsiA
FBGox
ox
siAs VVV
qN
VVC
C
qN
VFB VT
VG
2FS:
)(for 1)(2
12 2
TGFBsiA
FBGox
ox
Si
A
SSi VVVqN
VVC
CqNW
accumulation depletion inversion0
VGaccumulation depletion inversion0
A
FSiT
)(2
qN
2εW
W:
VFB VT
EE130/230M Spring 2013 Lecture 17, Slide 2
Total Charge Density in Si, Qs(p-type Si)
invdepaccs QQQQ
VG
accumulation depletion inversion0
VFB VT
WqN AdepQ
VG
accumulation depletion inversion0
VFB VT
)( TGox VVC invQ
VGaccumulation
depletion inversion0
VFB VT
)( FBGox VVC accQ
VG
accumulation depletion inversion
0 VFB VT
Qinv
slope = -Cox
EE130/230M Spring 2013 Lecture 17, Slide 3
MOS Capacitance Measurement
G
s
G
GATE
dV
dQ
dV
dQC
vac
iac
C-V Meter
GATE
MOS Capacitor• VG is scanned slowly• Capacitive current due to vac is measured
dt
dvCi ac
ac
Semiconductor
EE130/230M Spring 2013 Lecture 17, Slide 4
MOS C-V Characteristics (p-type Si)
G
s
dV
dQC VG
accumulation depletion inversion
VFB VT
Qinv
slope = -Cox
VG
accumulation depletion inversion
VFB VT
C
Cox
Ideal C-V curve:
EE130/230M Spring 2013 Lecture 17, Slide 5
Capacitance in Accumulation (p-type Si)
oxG
acc CdV
dQC
• As the gate voltage is varied, incremental charge is added (or subtracted) to (or from) the gate and substrate. The incremental charges are separated by the gate oxide.
M O SQ
Q
Q
-Q
Cox
EE130/230M Spring 2013 Lecture 17, Slide 6
Flat-Band Capacitance(p-type Si)
• At the flat-band condition, variations in VG give rise to the addition/subtraction of incremental charge in the substrate, at a depth LD
– LD is the “extrinsic Debye Length,” a characteristic screening distance, or the distance where the electric field emanating from a perturbing charge falls off by a factor of 1/e
Si
D
oxFB
L
CC
11
A
SiD Nq
kTL
2
Cox CDebye
EE130/230M Spring 2013 Lecture 17, Slide 7
Capacitance in Depletion (p-type Si)
Sioxdepox
W
CCCC
1
111
• As the gate voltage is varied, the depletion width varies. Incremental charge is effectively added/subtracted at a depth
W in the substrate.
M O SQ
Q
Q-Q
Cox
W
Cdep
SiA
FBG
oxG
dep
qN
VV
CdV
dQC
)(21
2
EE130/230M Spring 2013 Lecture 17, Slide 8
Capacitance in Inversion (p-type Si)
CASE 1: Inversion-layer charge can be supplied/removed quickly enough to respond to changes in gate voltage.
Incremental charge is effectively added/subtracted at the
surface of the substrate.
M O SQ
Q
Cox
WT
oxG
inv CdV
dQC
Time required to build inversion-layercharge = 2NAo/ni , where o = minority-carrier lifetime at surface
EE130/230M Spring 2013 Lecture 17, Slide 9
Capacitance in Inversion (p-type Si)
CASE 2: Inversion-layer charge cannot be supplied/removed quickly enough to respond to changes in gate voltage.
Incremental charge is effectively added/subtracted at a depth WT in the substrate.
M O SQ
Q
WT
min
1)2(21
1
111
CqNC
W
C
CCC
SiA
F
ox
Si
T
ox
depox
Cox Cdep
EE130/230M Spring 2013 Lecture 17, Slide 10
Supply of Substrate Charge (p-type Si)
Accumulation: Depletion:
Inversion: Case 1 Case 2
EE130/230M Spring 2013 Lecture 17, Slide 11
MOS Capacitor vs. MOS Transistor C-V(p-type Si)
VGaccumulation depletion inversion
VFB VT
C MOS transistor at any f,MOS capacitor at low f, orquasi-static C-V
MOS capacitor at high fCmin
Cmax=Cox
CFB
EE130/230M Spring 2013 Lecture 17, Slide 12
Quasi-Static C-V Measurement(p-type Si)
The quasi-static C-V characteristic is obtained by slowly ramping the gate voltage (< 0.1V/s), while measuring the gate current IG with a very sensitive DC ammeter. C is calculated from IG = C·(dVG/dt)
VGaccumulation depletion inversion
VFB VT
C
Cmax=Cox
Cmin
CFB
EE130/230M Spring 2013 Lecture 17, Slide 13
Deep Depletion(p-type Si)
• If VG is scanned quickly, Qinv cannot respond to the change in VG. Then the increase in substrate charge density Qs must come from an increase in depletion charge density Qdep
depletion depth W increases as VG increases
C decreases as VG increases
VG
VFBVT
CCox
Cmin
EE130/230M Spring 2013 Lecture 17, Slide 14
MOS C-V Characteristic for n-type Si
EE130/230M Spring 2013 Lecture 17, Slide 15
VGaccumulation depletion inversion
VT VFB
CMOS transistor at any f,MOS capacitor at low f, orquasi-static C-V
MOS capacitor at high fCmin
Cmax=Cox
CFB
Examples: C-V Characteristics
Does the QS or the HF-capacitor C-V characteristic apply?
(1) MOS capacitor, f=10kHz
(2) MOS transistor, i=1MHz
(3) MOS capacitor, slow VG ramp
(4) MOS transistor, slow VG ramp
VG
VFBVT
C
Cox
QS
HF-Capacitor
EE130/230M Spring 2013 Lecture 17, Slide 16
Example: Effect of Doping• How would the normalized C-V characteristic below change if
the substrate doping NA were increased?
– VFB
– VT
– Cmin
VFBVT
C/Cox
1
EE130/230M Spring 2013 Lecture 17, Slide 17
Example: Effect of Oxide Thickness• How would the normalized C-V characteristic below change if
the oxide thickness xo were decreased?
– VFB
– VT
– Cmin
EE130/230M Spring 2013 Lecture 17, Slide 18
VFBVT
C/Cox
1
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