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Lundstrom ECE 305 F15
ECE-305: Spring 2015
MOSFETs: An Energy Band Treatment
Professor Mark Lundstrom
Electrical and Computer Engineering Purdue University, West Lafayette, IN USA
lundstro@purdue.edu
4/8/15
Lundstrom’s lecture notes: Lecture 3
understanding MOSFETs
VGS >VT VD 0
p-Si
n-Si n-Si
To understand any device, we should first draw an Energy Band Diagram.
Lundstrom ECE 305 F15
x
normal to the channel
3
EC
EV
Ei
EF
Si
metal
φS
ΔVOX
EFM
x
understanding MOSFETs
VGS >VT VD 0
p-Si
n-Si n-Si
y
To understand this device, we should first draw an Energy Band Diagram.
Lundstrom ECE 305 F15
x
equilibrium E-band diagram: 3 separate pieces
VGS 0 0
p-Si
n-Si n-Si
y
x
EF
EC
EV
source
EF
channel
EV
EC
EF
drain Lundstrom ECE 305 F15
equilibrium E-band diagram: 3 separate pieces
EF
EV
EC
EF EF
EC
EV
source channel drain
1) Equilibrium: Fermi level is constant
2) Changes in electrostatic potential, change the electron’s energy.
EC y( ) = EC0 − qφ y( ) EV y( ) = EV 0 − qφ y( )
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putting the 3 pieces together (equilibrium)
EC y( ) = EC0 − qφ y( ) EV x( ) = EV 0 − qφ y( )
y
EF EC
EV
source channel drain
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final result: one semiconductor with 3 regions
EC y( ) = EC0 − qφ y( ) EV y( ) = EV 0 − qφ y( )
y
EF EC
EV
E
source channel drain
Now, what effect does a gate voltage have?
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equilibrium energy band diagram
VGS 0 0
p-Si
n-Si n-Si
y
x
A positive gate voltage will increase the electrostatic potential in the channel and therefore lower the electron energy in the channel.
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the transistor as a barrier controlled device
Lundstrom March 5, 2015 y
E
EF
EC
VG
source drain channel
ß low gate voltage
ß VD = VS = 0 EF
EC
the transistor as a barrier controlled device
Lundstrom March 5, 2015
y
E
EC
VG
ß low gate voltage
source drain channel
E = −qV
ß high drain voltage Fn
Fn
the transistor as a barrier controlled device
Lundstrom March 5, 2015
y
E
FnEC
VG
ß high gate voltage
source
E = −qV
ß high drain voltage Fn
effect of gate voltage first
y
E
EF
EC
VG
ß low gate voltage
ß high gate voltage
EC = EC0 − qφs
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Now add a small drain voltage
y
E EC
VG
What if we apply a small positive voltage to the drain?
1) The Fermi level in the drain is lowered.
2) The conduction band is
lowered too, but the electron density stays the same.
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Fn
constant electric field substantial electron density
how transistors work
2007 N-MOSFET
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
VGS
EC
EC
VGS
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understanding DIBL
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VGS
↑ID
mA µm( )
VDD
VDS = 0.05 V
VDS = VDD
VTSAT VTLIN
threshold voltage
IONVT VDS( )
understanding DIBL
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VGS
↑log10 IDmA µm( )
VDD
transfer characteristics:
ION
VDS = 0.05 V
VDS = VDD
DIBL ≡ ΔVGSΔVDS
mV V( )
VTSAT VTLIN
understanding DIBL
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y
E
EC
VG
source drain channel
FnFn low VDS( )
Fn high VDS( )
DIBL
understanding DIBL
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VGS
0
p-Si
n-Si n-Si
y
VDS > 0
E y
2D energy band diagrams
VGS >VT VD 0
p-Si
n-Si n-Si
x
y
We have been discussing energy band diagrams from the source to the drain along the top of the Si, but more generally, we should look at the 2D energy band diagram.
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2D energy band diagram on n-MOSFET
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(a)
(b)
(c)
(d)
S.M. Sze, Physics of Semiconductor Devices, 1981 and Pao and Sah.
a) device b) equilibrium (flat band) c) equilibrium (ψS > 0) d) non-equilibrium with VG and VD > 0
applied FN
essential physics of a transistor
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A MOSFET (and most transistors) are barrier-controlled devices.
limits to barrier control: quantum tunneling
from M. Luisier, ETH Zurich / Purdue
1) 2)
3) 4)
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