Parasitic Resistance
Polysilicon gate
LD
G
Drain
contact
D
S
RS
W
VGS,eff
RD
Drain
RS , D =
LS , D
W
R + RC
Short Channel Effects
Channel-Length Modulation
Equation
ID =
kn W
(VGS − VT )2
2 L
suggests that the transistor in the
saturation mode acts as a perfect current source. This is not entirely correct. The effective
length of the conductive channel is modulated by the applied VDS: increasing VDS causes the
depletion region at the drain to grow, reducing the length of the effective channel.
ID =
kn W
(VGS − VT )2 (1 + λVDS )
2 L
λ is the channel-length modulation ∝ 1/L
In short channels, the drain-junction depletion region presents a larger fraction of the channel,
and the channel-modulation effect is more pronounced. That’s why long channel transistors
are used when high-impedance current sources are designed.
Velocity Saturation in short channel devices
The behavior of transistors with very short channel lengths deviates considerably from the resistive and
saturation models just presented, mainly due to the velocity saturation effect.
Equation
υn = µn
dV states that the carrier velocity is proportional to the electrical field, where the carrier
dx
υ n (m /s)
mobility is constant. However, at high (horizontal) field strengths, the carriers fail to follow this linear model.
When the electrical field along the channel reaches a critical value ξ C, the velocity of the carriers tend to
saturate due to scattering effects (collisions suffered by the carriers). For a ξ C = 1.5V/µm, 0.5V is required for
velocity saturation in a 0.25µm device. This condition
Is very easily met in contemporary short-channel
Devices (It is easier to go into saturation
in contemporary devices).
This phenomenon has a profound impact on the
operation of the device. This is illustrated with a
first-order derivation of the device characteristics
Under velocity saturation. The velocity can be roughly
approximated by:
µ nξ
υn =
1+ ξ / ξC
= ν sat
for ξ ≤ ξ C
for ξ ≥ ξ C
υ = 105
sat
Constant velocity
Constant mobility (slope = µ)
ξ = 1.5
c
ξ (V/µm)
Velocity Saturation
The continuity requirement between the 2 regions dictates that
ζ C = 2ν sat / µ n
In the resistive region, the drain current can be expressed as:
2
µn Cox
W 
VDS 
ID =
( ) (V − VT )V DS −

1 + (VDS / ζ c L ) L  GS
2 
W 
V DS 
(
)
= kn
V
−
V
V
−
Κ (V DS
GS
T
DS
L 
2 
2
ID
)
The Κ(V) factor measures the degree of velocity saturation and is defined as Κ (V ) =
1
1 + (V / ξ C L )
Κ(V) = 1 for long channels or small V DS values. For short channels, Κ is less than 1, which
means that the delivered current is less than what would normally be expected.
When increasing V DS, the electrical field in the channel ultimately reaches the critical value, and the
carriers at the drain become velocity saturated. The saturation drain voltage V DSAT can be calculated
by equating the current at the drain under saturation conditions to the resistive current for VDS=VDSAT.
We get
I DSAT
W
= Κ (VDSAT ) µ nC ox
L
2

VDSAT 
(VGS − VT )VDSAT −

2


V
I DSAT = ν satC oxW VGS − VT − DSAT 
2

Velocity Saturation
Increasing the drain-source voltage does
not yield more current, and the transistor
current saturates at I DSAT. This leads to
two observations:
1) For a short-channel device and for large
enough values of V GS-VT, VDSAT< VGS-VT.
The device enters saturation before V DS
reaches V GS-VT. Short-channel devices
therefore experience an extended
saturation region, and tend to operate
more often in saturation conditions that
long-channels.
2) The saturation current I DSAT displays a
linear dependence with respect to V GS,
which is in contrast with the squared
dependence in the long-channel device.
This reduces the amount of current a
transistor can deliver for a given control
voltage
I
D
Long-channel device
V =V
GS DD
Short-channel device
V
DSAT
V -V
GS T
V
DS
Current-Voltage Relations
The Deep-Submicron Era
2.5
x 10
-4
VGS= 2.5 V
Early Saturation
2
VGS= 2.0 V
I D (A)
1.5
VGS= 1.5 V
1
VGS= 1.0 V
0.5
0
Linear
Relationship
0
0.5
1
1.5
VDS (V)
2
2.5
ID versus VDS
Same technology, and identical W/L ratio
-4
6
-4
x 10
VGS= 2.5 V
2.5
VGS= 2.5 V
Velocity saturation
5
2
Resistive Saturation
ID (A)
VGS= 2.0 V
3
VDS = VGS - VT
2
VGS= 2.0 V
1.5
ID (A)
4
VGS= 1.5 V
1
VGS= 1.5 V
VGS= 1.0 V
0.5
1
0
0
x 10
VGS= 1.0 V
0.5
1
1.5
2
2.5
VDS(V)
Long Channel (quadratic dependency bet. ID and V GS)
0
0
0.5
1
1.5
2
VDS(V)
Short Channel (linear dependency bet. ID and
VGS, and small V DSAT )
2.5
ID versus VGS
-4
6
-4
x 10
x 10
2.5
5
2
4
linear
quadratic
ID (A)
ID (A)
1.5
3
1
2
0.5
1
0
0
quadratic
0.5
1
1.5
VGS(V)
Long Channel
2
2.5
0
0
0.5
1
1.5
2
2.5
VGS(V)
Short Channel
Saturated devices (VDS=2.5V): Same technology, and identical W/L ratio