Transcript Basic Interconnects

VLSI
Design
Basic Interconnects
VLSI Design EE213
These slides contain some notes on interconnections
in VLSI circuits. Full details are in Pucknell and
Eshraghian pages 94 - 107
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Introduction
• Wiring-Up of chip devices takes place through various
conductors produced during processing
• Today, interconnects constitute the main source of delay in
MOS circuits
• We will examine:
–
–
–
–
–
Sheet Resistance – Resistance / Unit Area
Area Capacitance
Delay Units
CMOS Inverter Delay
Rise and Fall Time Estimation
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Sheet Resistance
•
•
•
•
•
Resistance of a square slab of material
RAB = ρL/A
t
=> R = ρL/t*W
Let L = W (square slab)
=> RAB = ρ/t = Rs ohm / square
A
w
L
B
RAB = ZRsh
Z = L/W
EE213 VLSI Design
Stephen Daniels 2003
Typical sheet resistance values for materials
are very well characterised
Layer
Rs (Ohm / Sq
Aluminium
0.03
N Diffusion
10 – 50
Silicide
2–4
Polysilicon
15 - 100
N-transistor Channel
104
P-transistor Channel
2.5 x 104
Typical Sheet Resistances for 5µm Technology
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
VLSI
N-type Minimum Feature Device
Polysilicon
L
N - diffusion
2λ
W
2λ
R = 1sq x Rs = Rs = 104 Ώ
EE213 VLSI Design
Stephen Daniels 2003
Design
VLSI
Design
Polysilicon
W = 8λ
L = 2λ
N - diffusion
R = Z Rs
R = (L/W) * Rs
R = 4 104 Ώ
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Exercise
Calculate the ON resistance for a depletion pull – up
Nmos inverter with Zpu : Zpd ratio 4:1
Use sheet resistance values given in earlier slide
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Area Capacitance of Layers
• Conducting layers are separated from each
other by insulators (typically SiO2)
• This may constitute a parallel plate
capacitor, C = є0єox A / D (farads)
• D = thickness of oxide, A = area,
• єox = 4 F/µm2
• Area capacitance given in pF/µm2
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Capacitance
• Standard unit for a technology node is the
gate - channel capacitance of the minimum
sized transistor (2λ x 2λ), given as •
Cg
• This is a ‘technology specific’ value
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
References
• Pucknell and Eshraghian pages 94 - 102
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
Delay Unit
• For a feature size square gate, τ = Rs x •
Cg
• i.e for 5µm technology, τ = 104 ohm/sq x 0.01pF = 0.1ns
• Because of effects of parasitics which we have not
considered in our model, delay is typically of the order of
0.2 - 0.3 ns
• Note that τ is very similar to channel transit time τsd
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
CMOS Inverter Delay
• Pull-down delay = Rpd x 2 •
Cg
• Pull-up delay = Rpu x 2•
Cg
• Asymmetry in rise and fall due to resistance difference
between pull-up and pull-down (factor of 2.5) (due to
mobilities of carriers)
• Delay through a pair of inverters is 2 τ (fall time) + 5 τ
(rise time)
• Delay through a pair of CMOS inverters is therefore 7 τ
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
CMOS Inverter Delay
• Asymmetry can be improved by reducing resistance of pull
- up
• Reduce resistance of pull - up by increasing channel width
( typically by a factor of 2.5)
• Note that increasing channel width also increases the
capacitance
• The overall delay (after increasing channel width by 2.5)
will be the same 7 τ
EE213 VLSI Design
Stephen Daniels 2003
VLSI
Design
CMOS Inverter Rise and Fall Time Estimation
• Tf ~ 3CL / βVDD
• Τr ~ 3CL / βVDD
• (Derivations for the above are in Pucknell and Eshraghian
Pages 105 - 107)
• So, τ r/ τf = βn/βp
• Given that (due to mobilities) βn = 2.5 βp, rise time is
slower by a factor of 2.5 when using minimum dimensions
of n and p transistors
EE213 VLSI Design
Stephen Daniels 2003