COMP 103
Lecture 04: MOS Transistor
short channel and scaling effects
Reading: Section 3.3 up to page107, Sec 3.5
[All lecture notes are adapted from Mary Jane Irwin, Penn State, which were adapted
from Rabaey’s Digital Integrated Circuits, ©2002, J. Rabaey et al.]
COMP 103.1
MOS – Long Channel Equations
‰
When VGS > VT, MOS is ON
‰
Linear: When VDS is small: VDS ≤ VGS – VT
ID = k’n W/L [(VGS – VT)VDS – VDS2/2]
‰
When VDS is large: VD ≥ VGS – VT
ID’ = k’n/2 W/L [(VGS – VT) 2]
‰
Linear or quadratic dependence on VGS
COMP 103.2
Long Channel I-V Plot (NMOS)
X 10-4
VGS = 2.5V
VDS = VGS - VT
5
4
ID (A)
VGS = 2.0V
3
Linear
Saturation
2
VGS = 1.5V
1
VGS = 1.0V
Quadratic dependence
6
0
cut-off
0
0.5
1
1.5
2
2.5
VDS (V)
NMOS transistor, 0.25um, Ld = 10um, W/L = 1.5, VDD = 2.5V, VT = 0.4V
COMP 103.3
Short Channel Effects
z
υsat =105
Constant
velocity
5
υn (m/s)
10
Behavior of short channel device mainly due to
Constant mobility
(slope = µ)
0
0
ξc= 1.5
Velocity saturation
– the velocity of the
carriers saturates due
to scattering (collisions
suffered by the
carriers)
z
3
ξ(V/µm)
For an NMOS device with L of .25µm, only a couple of volts
difference between D and S are needed to reach velocity
saturation
z
COMP 103.4
Voltage-Current Relation: Velocity Saturation
For short channel devices
‰
Linear: When VDS ≤ VGS – VT
ID = κ(VDS) k’n W/L [(VGS – VT)VDS – VDS2/2]
where
κ(V) = 1/(1 + (V/ξcL)) is a measure of the degree of
velocity saturation
For large L or small VDS, κ approaches 1.
‰
Saturation: When VDS = VDSAT ≥ VGS – VT
IDSat = κ(VDSAT) k’n W/L [(VGS – VT)VDSAT – VDSAT2/2]
COMP 103.5
Velocity Saturation Effects
10
VGS = VDD
Long
channel
devices
Short
channel
devices
0
VDSAT
VGS-VT
For short channel devices
and large enough VGS – VT
VDSAT < VGS – VT so
the device enters
saturation before VDS
reaches VGS – VT and
operates more often in
saturation
z
IDSAT has a linear dependence wrt VGS so a reduced
amount of current is delivered for a given control
voltage
z
COMP 103.6
Short Channel I-V Plot (NMOS)
2.5
X 10-4
Early Velocity
Saturation
VGS = 2.5V
VGS = 2.0V
1.5
Linear
1
Saturation
VGS = 1.5V
VGS = 1.0V
0.5
Linear dependence
ID (A)
2
0
0
0.5
1
1.5
2
2.5
VDS (V)
NMOS transistor, 0.25um, Ld = 0.25um, W/L = 1.5, VDD = 2.5V, VT = 0.4V
COMP 103.7
MOS ID-VGS Characteristics
Linear (short-channel)
versus quadratic (longchannel) dependence of
ID on VGS in saturation
z
ID (A)
X 10-4
6
5
4
3
2
1
0
long-channel
quadratic
Velocity-saturation
causes the shortchannel device to
saturate at substantially
smaller values of VDS
2.5 resulting in a substantial
drop in current drive
short-channel
linear
0
0.5
1
1.5
VGS (V)
(for VDS = 2.5V, W/L = 1.5)
COMP 103.8
2
z
Short Channel I-V Plot (PMOS)
z
All polarities of all voltages and currents are reversed
VDS (V)
-2
-1
0
VGS = -1.0V
-0.2
VGS = -1.5V
-0.4
-0.6
ID (A)
0
VGS = -2.0V
-0.8
VGS = -2.5V
-1 X 10-4
PMOS transistor, 0.25um, Ld = 0.25um, W/L = 1.5, VDD = 2.5V, VT = -0.4V
COMP 103.9
The MOS Current-Source Model
ID = 0 for VGS – VT ≤ 0
G
ID
S
D
ID = k’ W/L [(VGS – VT)Vmin–Vmin2/2](1+λVDS)
for VGS – VT ≥ 0
with Vmin = min(VGS – VT, VDS, VDSAT)
B
Determined by the voltages at the four terminals and
a set of five device parameters
z
NMOS
PMOS
COMP 103.10
VT0(V)
0.43
-0.4
γ(V0.5)
0.4
-0.4
VDSAT(V)
0.63
-1
k’(A/V2)
115 x 10-6
-30 x 10-6
λ(V-1)
0.06
-0.1
The Transistor Modeled as a Switch
7
x105
Req (Ohm)
6
Modeled as a switch with
infinite off resistance and a
finite on resistance, Ron
VGS ≥ VT
5
4
Ron
S
D
3
2
1
Resistance inversely
proportional to W/L (doubling
W halves Ron)
z
For VDD>>VT+VDSAT/2, Ron
independent of VDD
z
0
0.5
1
(for VGS = VDD,
VDS = VDD →VDD/2)
VDD(V)
NMOS(kΩ)
PMOS (kΩ)
1.5
2
VDD (V)
1
35
115
1.5
19
55
2.5
z Once VDD approaches VT,
Ron increases dramatically
2
15
38
2.5
13
31
Ron (for W/L = 1)
For larger devices
divide Req by W/L
COMP 103.11
Other (Submicon) MOS Transistor Concerns
‰
Velocity saturation
‰
Subthreshold conduction
z
‰
Transistor is already partially conducting for voltages below VT
Threshold variations
z
z
COMP 103.12
In long-channel devices, the threshold is a function of the length
(for low VDS)
In short-channel devices, there is a drain-induced threshold
barrier lowering at the upper end of the VDS range (for low L)
Subthreshold Conductance
Transition from ON to
OFF is gradual (decays
exponentially)
z
10-2
Linear region
Quadratic region
Current roll-off (slope
factor) is also affected by
increase in temperature
ID (A)
z
Subthreshold
exponential
region
VT
10-12
0
Has repercussions in
dynamic circuits and for
power consumption
z
0.5
1
1.5
2
2.5
VGS (V)
COMP 103.13
Threshold Variations
VT
VT
Long-channel threshold
L
Threshold as a function of
the length (for low VDS )
COMP 103.14
Low VDS threshold
VDS
Drain-induced barrier lowering
(for low L)
Scaling Analysis
‰
Manufacturing allows constant reduction in transistor channel length
‰
A reduction of 13% per year, halving every 5 years.
‰
Scaling analysis: how reduction in feature size influences the
operating characteristics and properties of MOS transistors
‰
Three different models are assume:
z
z
Full Scaling: everything scales by 1/S
Fixed-Voltage scaling: everything scales by 1/S except voltages
(supply voltage, threshold voltage)
- Integration issues: 5V was standard, and now 3.3V and 2.5V
- Silicon bandgap and built-in junction potentials are material parameters
- Scaling Vt is limited: can’t turn device 100% off – Bad Leakage problems
- No more benefits for shorter transistors
z
General Scaling:
- Device features scale by 1/S
- Voltages scale by 1/U
COMP 103.15
Scaling Examples
Parameter
Relation
Full Scaling
General
Scaling
W, L, tox
1/S
1/S
Fixedvoltage
scaling
1/S
Vdd, Vt
1/S
1/U
1
Area of
device
Cox
W*L
1/S2
1/S2
1/S2
1/tox
S
S
S
Cgate
Cox WL
Isat
Cox WV
Ron
V/Isat
Delay
Ron Cgate
P
Isat V
COMP 103.16