Lecture 15
OUTLINE
• The MOS Capacitor
– Energy band diagrams
Reading: Pierret 16.1-16.2, 18.1; Hu 5.1
MOS Capacitor Structure
MOS capacitor
(cross-sectional view)
GATE
VG +_
Semiconductor
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• Most MOS devices today employ:
o degenerately doped polycrystalline
Si (“poly-Si”) as the “metallic” gateelectrode material
 n+-type for “n-channel” transistors
xo
 p+-type, for “p-channel” transistors
o SiO2 as the gate dielectric
 band gap = 9 eV
 er,SiO2 = 3.9
o Si as the semiconductor material
 p-type, for “n-channel” transistors
 n-type, for “p-channel” transistors
Lecture 15, Slide 2
Bulk Semiconductor Potential, fF
qfF  Ei (bulk )  EF
• p-type Si:
kT
fF 
ln( N A / ni )  0
q
Ec
EF
qfF
Ev
• n-type Si:
kT
fF   ln( N D / ni )  0
q
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Lecture 15, Slide 3
EF
Ei
Ec
|qfF|
Ei
Ev
Special Case: Equal Work Functions
FM = FS
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R. F. Pierret, Semiconductor Device Fundamentals, Fig. 16.2
Lecture 15, Slide 4
General Case: Different Work Functions
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 18.1
E0
E0
E0
E0
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Lecture 15, Slide 5
MOS Band Diagrams: Guidelines
• Fermi level EF is flat (constant with x) within the semiconductor
– Since no current flows in the x direction, we can assume that equilibrium
conditions prevail
• Band bending is linear within the oxide
– No charge in the oxide => dE/dx = 0 so E is constant
=> dEc/dx is constant
• From Gauss’ Law, we know that the electric field strength in the
Si at the surface, ESi, is related to the electric field strength in
the oxide, Eox:
Eox 
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ε Si
E Si  3 E Si
ε ox
so
dEc
dx
Lecture 15, Slide 6
 3
oxide
dEc
dx
Si ( at the surface)
MOS Band Diagram Guidelines (cont’d)
• The barrier height for conduction-band electron flow from the
Si into SiO2 is 3.1 eV
– This is equal to the electron-affinity difference (cSi and cSiO2)
• The barrier height for valence-band hole flow from the Si into
SiO2 is 4.8 eV
• The vertical distance between the Fermi level in the metal,
EFM, and the Fermi level in the Si, EFS, is equal to the applied
gate voltage (assuming that the Si bulk is grounded):
qVG  EFS  EFM
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Lecture 15, Slide 7
MOS Equilibrium Band Diagram
metal oxide semiconductor
n+ poly-Si
SiO2
EC
p-type Si
EC=EFM
EV
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Lecture 15, Slide 8
EFS
EV
Flat-Band Condition
• The flat-band voltage, VFB, is the applied voltage which results
in no band-bending within the semiconductor.
– Ideally, this is equal to the work-function difference between the gate
and the bulk of the semiconductor: qVFB = FM  FS
EE130/230A Fall 2013
Lecture 15, Slide 9
Voltage Drops in the MOS System
• In general,
VG  VFB  Vox  fs
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)
qfS  Ei (bulk )  Ei ( surface)
• For example:
When VG = VFB, Vox = fs = 0, i.e. there is no band bending
EE130/230A Fall 2013
Lecture 15, Slide 10
MOS Operating Regions (n-type Si)
Decrease VG toward more negative values
 the gate electron energy increases relative to that in the Si
decrease VG
• Accumulation
– VG > VFB
Electrons accumulated
at Si surface
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decrease VG
• Depletion
– VG < VFB
Electrons depleted
from Si surface
Lecture 15, Slide 11
• Inversion
– VG < VT
Surface inverted to
p-type
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 16.5
MOS Operating Regions (p-type Si)
increase VG
VG = VFB
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VG < VFB
increase VG
VT > VG > VFB
Lecture 15, Slide 12
R. F. Pierret, Semiconductor Device Fundamentals, Fig. 16.6