Lecture 22
OUTLINE
The MOSFET (cont’d)
• Velocity saturation
• Short channel effect
• MOSFET scaling approaches
Reading: Pierret 19.1; Hu 7.1, 7.3
MOSFET Scaling
• MOSFETs have been steadily miniaturized over time
– 1970s: ~ 10 mm
– Today: ~30 nm
• Reasons:
– Improved circuit operating speed
– Increased device density --> lower cost per function
EE130/230M Spring 2013
Lecture 22, Slide 2
Benefit of Transistor Scaling
As MOSFET lateral dimensions (e.g. channel length L) are reduced:
• IDsat increases  decreased effective “R”
• gate and junction areas decrease  decreased load “C”
 faster charging/discharging (i.e. td is decreased)
EE130/230M Spring 2013
Lecture 22, Slide 3
Velocity Saturation
Velocity saturation limits IDsat in sub-micron MOSFETS
Simple model:
v
m

1

sat
v  vsat
for  < 
for   sat
Esat is the electric field at velocity saturation:
vsat
EE130/230M Spring 2013
sat

8 106 cm/s for electr ons in Si

6
6

10
cm/s for holes in Si

Lecture 22, Slide 4
sat

2vsat
m
MOSFET I-V with Velocity Saturation
In the linear region:
W
m


Coxe meff VGS  VT  VDS VDS
L
2


ID 
VDS
1
 sat L
long  channel I D
ID 
VDS
1
 sat L
EE130/230M Spring 2013
Lecture 22, Slide 5
Drain Saturation Voltage, VDsat
• If satL >> VGS-VT then the MOSFET is considered
“long-channel”. This condition can be satisfied when
– L is large, or
– VGS is close to VT
1
VDsat
EE130/230M Spring 2013
m
1


VGS  VT  sat L
Lecture 22, Slide 6

sat

2vsat
m
Example: Drain Saturation Voltage
Question: For VGS = 1.8 V, find VDsat for an NMOSFET
with Toxe = 3 nm, VT = 0.25 V, and WT = 45 nm, if L =
(a) 10 mm, (b) 1 mm, (c) 0.1 mm (d) 0.05 mm
Solution: From VGS , VT and Toxe, meff is 200 cm2V-1s-1.
Esat= 2vsat / meff = 8 104 V/cm
m = 1 + 3Toxe/WT = 1.2
VDsat
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 m
1 

 

 VGS  VT  sat L 
Lecture 22, Slide 7
1
(a) L = 10 mm: VDsat= (1/1.3V + 1/80V)-1 = 1.3 V
(b) L = 1 mm:
VDsat= (1/1.3V + 1/8V)-1 = 1.1 V
(c) L = 0.1 mm: VDsat= (1/1.3V + 1/.8V)-1 = 0.5 V
(d) L = 0.05 mm: VDsat= (1/1.3V + 1/.4V)-1 = 0.3 V
EE130/230M Spring 2013
Lecture 22, Slide 8
IDsat with Velocity Saturation
Substituting VDsat for VDS in the linear-region ID equation gives
I Dsat
W
2
Coxe meff VGS  VT 
long  channel I Dsat
2
mL


VGS  VT
VGS  VT
1
1
m sat L
m sat L
For very short L:
I Dsat

sat
L  VGS  VT  / m
W
  satCoxe m eff VGS  VT   WvsatCoxe VGS  VT 
2
• IDsat is proportional to VGS–VT rather than (VGS – VT)2
• IDsat is not dependent on L
EE130/230M Spring 2013
Lecture 22, Slide 9
V gs = 1.0V
0.0
Short- vs. Long-Channel NMOSFET
V (V)
0
1
2
2.5
ds
0.4
L = 0.15 mm
Vt = 0.4 V
I ds (mA/mm)
L = 2.0 mm
V gs = 2.5V
Vgs = 2.5V
Vt = 0.7 V
0.3
0.02
Ids (mA/mm)
(a)
0.03
(b)
V gs = 2.0V
0.2
V gs = 1.5V
0.1
Vgs = 2.0V
0.01
Vgs = 1.5V
V gs = 1.0V
Vgs = 1.0V
0.0
0.0
0
1
2
2.5
V ds (V)
Short-channel
NMOSFET:
0.03
Vto
2.5V-V rather than (V -V )2
L =is
2.0proportional
mm
gs =V
• IDsat
GS Tn
GS Tn
Vt = 0.7 V
• VDsat is lower than for long-channel MOSFET
0.02
• Channel-length modulation is apparent
/mm)
(b)
Vds (V)
EE130/230M Spring 2013
Vgs = 2.0V
Lecture 22, Slide 10
Velocity Overshoot
• When L is comparable to or less than the mean free
path, some of the electrons travel through the channel
without experiencing a single scattering event
 projectile-like motion (“ballistic transport”)
 The average velocity of carriers exceeds vsat
e.g. 35% for L = 0.12 mm NMOSFET
 Effectively, vsat and sat increase when L is very small
EE130/230M Spring 2013
Lecture 22, Slide 11
The Short Channel Effect (SCE)
“VT roll-off”
• |VT| decreases with L
– Effect is exacerbated by
high values of |VDS|
• This effect is undesirable (i.e. we want to minimize it!)
because circuit designers would like VT to be invariant
with transistor dimensions and bias condition
EE130/230M Spring 2013
Lecture 22, Slide 12
Qualitative Explanation of SCE
• Before an inversion layer forms beneath the gate, the
surface of the Si underneath the gate must be
depleted (to a depth WT)
• The source & drain pn junctions assist in depleting the
Si underneath the gate
– Portions of the depletion charge in the channel region are
balanced by charge in S/D regions, rather than by charge on
the gate
 Less gate charge is required to invert the semiconductor
surface (i.e. |VT| decreases)
EE130/230M Spring 2013
Lecture 22, Slide 13
The smaller L is, the greater the percentage of
depletion charge balanced by the S/D pn junctions:
depletion
charge
supported
by gate
(simplified
analysis)
VG
n+
n+
p
D
S
D
Depletion charge
supported by S/D
Depletion charge
supported by S/D
EE130/230M Spring 2013
depletion region
Small L:
Large L:
S
rj
Lecture 22, Slide 14
First-Order Analysis of SCE
• The gate supports the depletion charge in the trapezoidal region.
This is smaller than the rectangular depletion region underneath
the gate, by the factor
L  L
1
2L
WT
• This is the factor by which the depletion charge Qdep is reduced
from the ideal
• One can deduce from simple geometric analysis that
EE130/230M Spring 2013
Lecture 22, Slide 15


2WT
L  L  2 r j  1 
 1
rj


VT Roll-Off: First-Order Model
VT  VT (longchannel)

 qN AWT rj 
2WT
 VT 
1
 1

Coxe
L 
rj

Minimize VT by
• reducing Toxe
• reducing rj
• increasing NA
(trade-offs: degraded meff, m)
 MOSFET vertical dimensions should be
scaled along with horizontal dimensions!
EE130/230M Spring 2013
Lecture 22, Slide 16
MOSFET Scaling: Constant-Field Approach
• MOSFET dimensions and the operating voltage (VDD) each are
scaled by the same factor k>1, so that the electric field
remains unchanged.
EE130/230M Spring 2013
Lecture 22, Slide 17
Constant-Field Scaling Benefits
• Circuit speed
improves by k
• Power dissipation
per function
is reduced by k2
EE130/230M Spring 2013
Lecture 22, Slide 18
• Since VT cannot be scaled down aggressively, the operating
voltage (VDD) has not been scaled down in proportion to the
MOSFET channel length:
EE130/230M Spring 2013
Lecture 22, Slide 19
MOSFET Scaling: Generalized Approach
• Electric field intensity increases by a factor a>1
• Nbody must be scaled up by a to suppress short-channel effects
• Reliability and
power density
are issues
EE130/230M Spring 2013
Lecture 22, Slide 20