• What is Scaling?
• Proportional adjustment of the dimensions of
an electronic device while maintaining the
electrical properties of the device
10
Feature Size (m)
10
6
3
1.5
1
1
0.8
0.6
0.35
0.25
0.18
0.13
0.09
0.1
1965
1970
1975
1980
1985
Year
1990
1995
2000
2005
• Impact of scaling is characterized in terms of
several indicators:
Minimum feature size
Number of gates on one chip
Power dissipation
Maximum operational frequency
Die size
Production cost
1) Full Scaling (Constant Electrical Field)
• Ideal model – dimensions and voltage scale
together by the same scale factor
2) Fixed Voltage Scaling
• Most common model until recently – only the
dimensions scale, voltages remain constant
3) General Scaling
• Most realistic for today’s situation – voltages and
dimensions scale with different factors
• Device scaling modeled in terms of generic
scaling factors: 1/α and 1/β
1/ β : scaling factor for supply voltage VDD
and gate oxide thickness D
1/α: linear dimensions both horizontal and
vertical dimensions
• Gate area Ag
Where L: Channel length and W: Channel width
and both are scaled by 1/α
• Thus Ag is scaled up by 1/α2
• Gate capacitance per unit area Co or Cox
Where εox is permittivity of gate oxide(thin-ox)= εins εo
and D is the gate oxide thickness scaled by 1/ β
• Thus Cox is scaled up by
• Gate capacitance Cg
Thus Cg is scaled up by β * 1/α2 = β/α2
• Parasitic capacitance Cx
• Cx is proportional to Ax/d
where d is the depletion width around source or
drain and scaled by 1/ α
Ax is the area of the depletion region around
source or drain, scaled by (1/α2 ).
• Thus Cx is scaled up by
• Carrier density in channel Qon
• where Qon is the average charge per unit area
in the ‘on’ state.
• Co is scaled by β and Vgs is scaled by 1/β
• Thus Qon is scaled by 1
• Channel Resistance Ron
• Where μ = channel carrier mobility and
assumed constant
• Thus Ron is scaled by 1
• Gate delay Td
• Td is proportional to Ron*Cg
• Td is scaled by
• Maximum operating frequency fo
• fo is inversely proportional to delay Td and is
scaled by
• Saturation current Idss
• Both Vgs and Vt are scaled by (1/β). Therefore,
Idss is scaled by
• Current density, J= Idss/A
• where A is cross sectional area of the
• Channel in the “on” state which is scaled by
(1/ α 2)
• So, J is scaled by
• Switching energy per gate Eg
• So Eg is scaled by
• Power dissipation per gate Pg
• Pg comprises of two components: static component Pgs
and dynamic component Pgd:
Where, the static power component is given by:
And the dynamic component by:
Since VDD scales by (1/ β) and Ron scales by 1, Pgs scales
by (1/ β2).
Since Eg scales by (1/ α2β ) and fo by (α2 / β), Pgd also
scales by (1/ β2).
Therefore, Pg scales by (1/ β2).
• Power dissipation per unit area Pa
• Power – speed product PT