Lundstrom ECE 305 S16
ECE-305: Spring 2016
MOS Fundamentals
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA [email protected]
3/29/16
Pierret, Semiconductor Device Fundamentals (SDF) pp.563-567
MOS Fundamentals
2
1) MOSFETs and MOS capacitors 2) E-bands and workfunctions
Lundstrom ECE 305 S16
Pep talk
3
“I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.’” -Muhammad Ali http://www.brainyquote.com/quotes/quotes/m/muhammadal148629.html.
Pep talk
4
A dog weighing 10.0 lb is standing on a flatboat so that he is 20 ft from the shore. He walks 8.0 ft on the boat towards shore and then halts. The boat weighs 40 lbs, and one can assume that there is no friction between the it and the water. How far is he from shore at the end of this time? (Hint: The center of mass of boat + dog does not move. Why?) The shoreline is also to the left in Fig. 9-15.
Halliday and Resnick, Physics, 1966
MOSFETs
5
source drain
SiO
2 silicon
G S D
(Texas Instruments, ~ 2000)
gate oxide EOT ~ 1.1 nm
channel ~ 20 nm
gate
electrode
MOSFET (off)
6
VD
0
L
p-Si
n+-Si n+-Si
VG < VT ID = 0
Lundstrom ECE 305 S16
MOSFET (on)
7
VD
0
L
p-Si
n+-Si n+-Si
VG > VT ID > 0
Lundstrom ECE 305 S16
MOSFET and MOS C
8
p-Si
n+-Si n+-Si
MOS capacitor
MOS capacitor
9
VG
p-Si or n-Si
metal or
heavily doped “polysilicon”
SiO2
tox ≈1− 2 nm
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oxide scaling
10
MOS Fundamentals
11
1) MOSFET and MOS capacitors 2) E-bands and workfunctions
Lundstrom ECE 305 S16
EC
EV
Ei
SiO2
EG ≈ 8.9eV
χi
e-band diagram
12
EC
EV
Ei
EF
EG = 1.12eV
Si
metal
EFM
ΦM
E0
χS
recall the MS junction
13
EC
EVEFP
Ei
aluminum
EFM
E0
ΦM = 4.08 eVΦS
χS = 4.05 eV
Lundstrom ECE 305 S16
built-in potential
14
EC
EVEFS
Ei
aluminum
EFM
E0
ΦM = 4.08 eVΦS
χS = 4.05 eV
qVbi = EFM − EFS( ) = ΦS −ΦM( ) = − ΦM −ΦS( ) = −ΦMS
potential =VbiVbi =
−ΦMS
q= −φms
example:
15
Aluminum metal and p-type Si
NA = 1016 cm-3
p0 = NVeEV −EFS( )/kBT cm-3
EFS − EV = kBT lnNV
NA
⎛⎝⎜
⎞⎠⎟
NV = 2mp*kBT( )2π!2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
3/2
= 1.83×1019 cm-3
EFS − EVq
= 0.2
ΦM = 4.08 eV
ΦS = χS + EG − EFS − EV( ) q
ΦS = 4.97 eV
φms =ΦM − ΦS( )
q= −0.9 V
Vbi = −φms = +0.9 V
now the band diagram
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EC
EVEFS
Ei
metal
EFM
E0
ΦM = 4.5
Lundstrom ECE 305 S16
ΦS
the band diagram
17
EC
EVEF
Ei
metal
EF
qVbi
Lundstrom ECE 305 S16
MOS e-band diagram
18
EC
EV
Ei
SiO2
EG ≈ 8.9eV
EC
EV
Ei
EF
EG = 1.12eV
Si
metal
EFM
ΦM
E0
χS
χi
MOS e-band diagram
19
1) Built-in potential is exactly the same. 2) But part of the voltage drop now occurs across the
semiconductor and part across the oxide.
Lundstrom ECE 305 S16
equilibrium e-band diagram
20
EC
EV
Ei
EF
metal
ΔVS
ΔVox
Vbi = −φms φ x( ) = 0 in the bulk
φ x = 0( ) = φS surface potential
V metal( ) = ΔVox +φS
φS
V metal( ) =Vbi
equilibrium e-band diagram
21
EC
EV
Ei
EF
metal
V metal( ) =Vbi
Applied gate voltage = 0
Energy bands are bent.
e-band under “flat band” conditions
22
EC
EV
Ei
EF
Si
metal
What happens if we apply a negative voltage = ? φms
VG = −Vbi
MOS–C at the flat band voltage.
VG =VFB =ΦM −ΦS( )
q= φms
“ideal” MOS structure
23
EC
EV
Ei
SiO2
EG ≈ 8eV
EC
EV
Ei
EF
EG = 1.12eV
Sihypothetical
metal
EFM
ΦM
E0
χS
χi
Vbi = 0
flat band conditions
24
For an ideal MOS structure, flat band occurs for: For a real MOS structure, flat band occurs for:
VG =VFB = 0
VG =VFB = φms
′VG =VG −VFB
VFB = φms
Lundstrom ECE 305 S16
in Chapter 16 of SDF by Pierret
25
VG means V’G; i.e. an ideal MOS structure with NO metal-semiconductor workfunction difference is assumed.
Lundstrom ECE 305 S16
