091498_lecture9
TRANSCRIPT
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EECS 105 Fall 1998
Lecture 9
MOS Capacitor in Depletion
Now we make VGB> VFB. Note that thermal equilibrium falls into this range of
applied bias.
Surface potential at oxide/silicon interface is now positive --> n-type
(slightly, ns= 1013cm-3).
(x)
-tox
Xd
x-qNa
-tox Xd x
E(x)
0
0
QG
-tox Xd
x
(x)
0s= 185 mV
VGB+ n+
-500 mV
500 mV
1 V
chargedensity
electricfield
potentialVGB
9
EECS 105 Fall 1998
Lecture 9
The Threshold Voltage VTn
Keep increasing VGB--> surface potential keeps increasing. At some point, the
surface is n-type (i.e., we say that it isinverted)
The gate-bulk potential at the onset of inversion is called the threshold voltage,
VTn. To find the threshold voltage, we need to consider the electrostatics in
depletion (no electrons at the surface at the onset of inversion) -- with the surface
potential equal to the opposite of the bulk potential:
s max, p=
-toxXd,max
x
(x)
0
s,max= - p = 420 mV
VTn + n+
-500 mV
500 mV
1 V
1.5 V
Vox
VB,max
VTn- VFB
- p
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EECS 105 Fall 1998
Lecture 9
Threshold Voltage Expression
We can solve for the threshold voltage:
The drop across the depletion region is
The drop across the oxide for VGB= VTnis
Substituting for the bulk charge (found from the potential drop across the
depletion region, we find
VT
VFB
Vox VB max,+=
VB max, s max, p p p 2p= = =
Vox Eox tox
QB max,ox
----------------------
tox
QB max,
Cox
----------------------= = =
VTn
VFB
2 p
1
Cox
--------- 2qsN
a2
p( )+=
EECS 105 Fall 1998
Lecture 9
The Inverted MOS Capacitor (VGB>VTn)
We consider the surface potential as fixed (pinned) at s,max = - 2p
Inversion charge QNat SiO2- silicon surface balances extra + charge on gate as
VGBincreases
- tox
Xd,max x
(x)
0
500 mV
- 500 mV
1.0 V
1.5 V
s,max = 420 mV
Vox
VGB- VFB
2 p
QN
Cox
VGB
VTn
( )=
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EECS 105 Fall 1998
Lecture 9
Charge Storage in the MOS Structure
Three regions of operation:
Accumulation: qG= Cox(vGB- vFB) ... parallel plate capacitor
Depletion: qG= - qB(vGB), with the bulk (depletion) charge in the
silicon being a nonlinear function of vGB
Inversion: qG= - qN- qB,max, where qB,max= qB(vGB= VT) is thedepletion charge at the onset of inversion and
Sketch of the gate charge as a function of gate-bulk voltage:
qG[C/cm2]
VGB[V]VFB VTn
EECS 105 Fall 1998
Lecture 9
MOS Capacitance
The capacitance of the MOS structure is defined as
From sketch, determine the slope and plot as the capacitance
Cdq
G
dvGB
-------------
VGB
=
C [C/cm2]
VGB[V]VFB VTn
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EECS 105 Fall 1998
Lecture 9
Physical Interpretation of MOS Capacitance
Accumulation: parallel plate capacitor --> C= Cox
Depletion: increment in gate charge is mirrored at bottom of depletion region, so
capacitance model is Coxin series with the depletion region capacitance Cb
Inversion: bulk charge is no longer changing with VGB--> an increment in
gate charge is mirrored in the inversion layer under the gate.
The capacitance is therefore the same as in accumulation --> C= Cox
Cox
ox
tox
--------=
Cb
s
Xd
------=
gate
Si/SiO2 surface
bulk
Note thatXdisa function of VGB
C Cox
Cb
=
EECS 105 Fall 1998
Lecture 9
MOS Field Effect Transistors
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deposited
oxide
field
oxide
n+ drain diffusion
drain
interconnect
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p+
[ p-type ]
bulk
interconnect
Ldiff
gate contact
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A
drain
contacts
bulk
contact
n+polysilicon gate
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active area (thin
oxide area)
polysilicon gate
contact
metal
interconnect
n+source diffusion
edge of
active area
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source
interconnect
(b)
L
n+polysilicon gate
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gate oxide
gate
interconnect
source contacts
drain
interconnectsource
interconnect
A
W
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EECS 105 Fall 1998
Lecture 9
MOSFET Circuit Symbols
Two complementary devices (each with two symbols): both are very useful
p-substrate (n-type channel under gate oxide)
n-substrate (p-type channel under gate oxide)
Fourelectrical terminals: source (lowest potential for n-channel, highest for p-
channel), drain, gate, and bulk.
Basic concept: inversion layer (called the channel) formed under gate betweensource and drain enables drift current
n+
n+
p Bulk or
Body
Drain
Source
Gate
(a) n-channel MOSFET
D
G
IDp
B
p+
p+
n Bulk or
Body
Drain
Gate
(b) p-channel MOSFET
Source
+
_ VSG
D
S
G
+
+
_
VGS
IDn IDn
B
VSD>0
VDS >0
+
_VBS
+
_VSB
D
GB
S
S S
B
D
G
IDp
EECS 105 Fall 1998
Lecture 9