Scaling

```Scaling II
• Textbook I, Chapter 2
• Textbook II, Section 3.5, Section 4.5.3,
Section 5.6
CMOS Scaling
• Basic MOS rule: L↓  gm↑, C ↓
• Short channel effect + Lithography limits
L
• The worst SCE: reduction in gate Vt where
MOS turns on, especially at high VDS
• Process needs to keep SCE under control
Constant Field Scaling
• To scale vertical and
horizontal dimensions at
the same proportions
– Gate insulator, junctions
depth, etc.
– Doping concentration ↑ 
Depletion width ↓
• Decreasing the applied
voltage
•  Size 1/k, voltage 1/k
E constant
•  Hot carrier injection is
not worse than the original
device
Scaling of MOS and circuit
parameter
Scaling of MOS and circuit
parameter
• R of the MOS remains unchanged (I and V
scale together)
• Delay ~ R x C  1/K
• Power ~ V x I  1/K^2
• Power x Delay  1/K^3 
• Power density ~ Power / Area  1
2-D effects (Deep sub-micron)
• Poisson equation:
• Increasing the doping keeps E unchanged
over X axis
• Boundary cond. function of built-in p-n
potential  Do not scale
• When V~1V (bandgap) the second order
effects kick-in
2-D effects (Deep sub-micron)
• Maximum gate depletion width: Wdm (no
carriers under the gate)
• If horiz. side is twice as long as vertical side,
long-channel device with good short-channel
behavior
• Else, source channel potential (critical for setting
threshold condition) is influenced by drain
voltage (SCE)  No small Vt is possible
2-D effects (Deep sub-micron)
• There are oxide and silicon
• Boundary cond. at interface
• Depth of oxide region
equivalent to
In silicon
• So the total vertical side
• L min ~= 2(Wdm+3tox)  both
tox and Wdm has to be scaled
proportionally
Power-supply and threshold
voltage scaling
• Power supply usually
do not scale as much
– Subthreshold diffusion
current not scaled
– Previous generation
voltages are of interest
• Problems:
– High electric field 
Hot carrier injection to
the gate,
electromigration
– Power consumption
(100W)
Power-supply and threshold
voltage scaling
• In subthreshold the leakage drops
exponentially proportional to kT
• I0~0.1uA/um for a 0.1um device
• Even if Vt is kept constant, the
leakage increases in proportion to
1/tox and Wtot/L because the
current at threshold is proportional
to Qi ~ 1.5 kT/q Cox
• Every 0.1V decrease in Vt  10x
more leakage
• For a 100million T chip, the
average leakage current <10nA
• Minimum bound for Vt ~ 0.2V
Power-supply and threshold
voltage scaling
• Vt/Vdd ↑  performance ↓:
• Performance ~ 0.7-Vt/Vdd ;
stronger than Ion because
of the finite rise time at the
input
• With Vt bound to 0.2, Vdd
less than 1V will not buy
us a lot of performance
Power-supply and threshold
voltage scaling
• Performance gain
– Lower Vt, higher stand-by
power (high Vt for low
power designs)
– Higher Vdd, higher
dynamic power (high
performance processes)
Power-supply and threshold
voltage scaling
• A 0.1um CMOS ring
oscillator 101 stage
• 10% decrease in
performance  30%40% reduction in active
power
Gate oxide
• Gate oxide thickness ↓ α L ↓
• tox ~ 1/25-1/50 L
– tox ~ 3nm: a few layers of atoms
• Gate leakage : Quantum Mech.
Tunneling
– Exponentially proportional to tox
– Direct tunneling: gate voltage do not
play an important role
– Only for turned on NMOS (gate is on)
– PMOS is better
• For 0.1cm2 gate area on a chip,
tolarable gate leakage 1-10 A/cm2
• Minimum tox is 1.5-2nm
Gate oxide
• Two other phenomena:
– Inversion layer quantization:
• Density of inversion electrons 1nm below the Si
surface  effectively 0.3-0.4 nm thicker tox (SiO2)
– Polysilicon gate depletion effect:
• Thin space charge layer within the poly  reduces
the effectiveness of the gate
• At tox = 2nm; 20% loss in inversion charge

Gate
• Poly:
– Resistive (silicide)
– Depletion effect
• Why poly and not metal?
– Metal : mid-gap bands
– Compensating doping  poor short channel
effect
Channel profile design
• Both tox and Wdm must
be scaled
– Wdm ↓  Na ↑  higher
depletion charge @ surface
 higher electric field 
higher threshold voltage
this to happen
Channel profile design
• Comparison between the
uniform and (extreme)
• For the same Wdm
depletion charge and
hence the electrical field is
half of that of the uniform
Other channel doping effects
• Body-effect coeff.
m=1+3tox/Wdm
• Inverse subthreshold
slope, (ln 10) mkT/q
• Substrate sensistivity ↑,
subthreshold slope↑
• We need to keep m
close to 1; m<1.5 or
3tox/Wdm<0.5
Halo Doping
• Non-uniform lateral profile
• Ion-implantation, self aligned
to gate + diffusion (a little)
• Counter acts short-channel
effects
– Off current robust against L
variations
– Shortest channel length possible
Halo Doping
• Flat Vt dependence on
channel length
– Lower Vt is posssible
• Performance
Suffered from SCE
 i.e., Vds influences Vt
Interconnect scaling
• Everything is scaled,
including the oxide
between the stacked wires
• Wire length Lw is also
scaled as a result of tech
scaling
• Fringing cap, wire-to wire
caps/length remains
constant
tw
Ww
Interconnect scaling
• Cw= K (gap between the wires) x 1/K (width)
• τ (Tau) =1/K (C for a scaled length) x K (R for a
scaled length)
• Current density increases; Electromigration
Interconnect scaling
• Some typical values:
– @0.25um ; Cw = 2pF/cm
– For aluminum
• Tau = 3 x 10-18 (sec) x L2/(Ww x tw)
• For a 0.25u x 0.25u size wire x 100um long; delay
= 0.5pSec; comparable to a cmos inverter in 0.1u
tech (20pSec).
• Conclusion: local wires is not a big issue
Global wire issues
• Global block to block cross-chip wires
• The chip size usually do not scale; it may
even increase
– When remains the same; Tau increases by
K2(see last page L cte)
– The cross-chip wires can create up to 1ns
delay
Global interconnects
• Solutions:
– Use of copper: 40% faster
– Minimizing the number of corss-chip
– Repeaters
• Fundamental solution
– Thicker wires (lower resistance, higher cap)
– wider dielectric spacing (lower cap)
Global interconnects
• Strategy:
– Scale down the size and spacing of
local interconnects
– Un-scaled, scaled up
wires/distance for higher layers
(reduction in delay for a given length)
• Limit: Transmission Line delay
(when inductance becomes
dominant)
– Rise time is shorter than the flight
time over the length
• Speed of electromagnetic wave,
Global interconnects
• For oxide, time of flight
is:
– 70pSec/cm
• A longer global wire 
larger wire cross
section
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