OUTLINE

1
Lecture 30

• OUTLINE
• The MOS Capacitor
• Electrostatics
• Reading Chapter 16.3

2
Bulk Semiconductor Potential, fF

• p-type Si
• n-type Si

Ec
Ei
qfF
EF
Ev
Ec
EF
qfF
Ei
Ev
3
Voltage Drops in the MOS System

• In general,
• where
• qVFB FMS FM FS
• Vox is the voltage dropped across the oxide
• (Vox total amount of band bending in the oxide)
• fs is the voltage dropped in the silicon
• (total amount of band bending in the
  silicon)
• For example When VG VFB, Vox fs 0
• i.e. there is no band bending

4
MOS Band Diagrams (n-type Si)
Decrease VG (toward more negative values) -gt
move the gate energy-bands up, relative to the Si
decrease VG
decrease VG

• Inversion
• VG lt VT
• Surface becomes p-type

• Accumulation
• VG gt VFB
• Electrons accumulate at surface

• Depletion
• VG lt VFB
• Electrons repelled from surface

5
Biasing Conditions for p-type Si
increase VG
increase VG
VG VFB
VG lt VFB
VT gt VG gt VFB
6
Accumulation (n poly-Si gate, p-type Si)
M
O
S
VG lt VFB
3.1 eV
qVox
Ec EFM
Ev
GATE
qVG
qfS is small, ? 0

Ec
VG
_
p-type Si
4.8 eV
EFS
Ev
Mobile carriers (holes) accumulate at Si surface
7
Accumulation Layer Charge Density
VG lt VFB
From Gauss Law
GATE
xo

VG
_
Qacc (C/cm2)
p-type Si
(units F/cm2)
8
Depletion (n poly-Si gate, p-type Si)
M
O
S
VT gt VG gt VFB
qVox
W
Ec
EFS
GATE
qfS
Ev
3.1 eV
qVG

VG
Ec EFM
_
p-type Si
Ev
4.8 eV
Si surface is depleted of mobile carriers
(holes) gt Surface charge is due to ionized
dopants (acceptors)
9
Depletion Width W (p-type Si)

• Depletion Approximation
• The surface of the Si is depleted of mobile
  carriers to a depth W.
• The charge density within the depletion region is
• Poissons equation
• Integrate twice, to obtain fS

To find fs for a given VG, we need to consider
the voltage drops in the MOS system
10
Voltage Drops in Depletion (p-type Si)
From Gauss Law
GATE

VG
_
Qdep (C/cm2)
Qdep is the integrated charge density in the Si
p-type Si
11
Surface Potential in Depletion (p-type Si)

• Solving for fS, we have

12
Threshold Condition (VG VT)

• When VG is increased to the point where fs
  reaches 2fF, the surface is said to be strongly
  inverted.
• (The surface is n-type to the same degree as the
  bulk is p-type.)
• This is the threshold condition.
• VG VT

13
MOS Band Diagram at Threshold (p-type Si)
M
O
S
qVox
WT
qfF
Ec
EFS
qfF
qfs
Ev
qVG
Ec EFM
Ev
14
Threshold Voltage

• For p-type Si
• For n-type Si

15
Strong Inversion (p-type Si)
As VG is increased above VT, 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 W WT
r(x) M O S
WT
GATE

VG
x
_
p-type Si
Significant density of mobile electrons at
surface (surface is n-type)
16
Inversion Layer Charge Density (p-type Si)