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
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
Lundstrom ECE 305 F15
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.
Lundstrom ECE 305 F15
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
Lundstrom ECE 305 F15
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
Lundstrom ECE 305 F15
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)
