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Effect of Variation of threshold voltage on power consumption, delay and area of a 32x32 bit array Multiplier

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### Effect of Variation of threshold voltage on power consumption, delay and area of a 32x32 bit array Multiplier

ELEC 6970: Low Power Design

Class Project

By: Sachin Dhingra

Outline

- Introduction
- Design of the multiplier
- Background
- Leakage Power
- Threshold Voltage
- Results
- Conclusion
- Future Work

ELEC 6970: Low Power Design

Introduction

- Design and Verification of an array multiplier using VHDL
- Reduction of leakage current of the circuit by variation of the threshold voltage (Vt)
- Sub-threshold conduction current decreases as the Vt increases
- Increase in Vt also leads to higher switching delays
- Aim: To reduce the leakage current by varying the threshold voltage of the transistors and observe its effect on the overall power consumption, delay and area

ELEC 6970: Low Power Design

VDD

IG

Ground

R

n+

n+

Isub

IPT

ID

IGIDL

Leakage Power- Leakage Power components
- Sub-threshold Leakage current
- Reverse bias p-n junction conduction
- Gate induced drain leakage
- Drain source punch through (Short channel effects)
- Gate tunneling
- Sub-threshold Leakage current
- Carrier diffusion between the source and the drain region of the transistor
- Grows exponentially as Vt decreases

Where,

Vt – Threshold voltage

I0 – Ids @ cutoff i.e. Vgs = Vt

n – experimentally derived constant

ELEC 6970: Low Power Design

Threshold Voltage

- Threshold Voltage is given by the expression:

Vt = Vt0 + γ[(Φs+Vsb)½- Φs½]

Where,

- Vt0 - Threshold voltage when source is at body potential
- γ – Body effect parameter
- Function of doping level, permittivity and oxide thickness
- Φs – Surface potential
- function of thermal voltage and doping level
- Vsb – Source to Body voltage
- Hence, Threshold Voltage is a function of:
- Doping concentration
- Thickness of oxide
- Source to Body Voltage

ELEC 6970: Low Power Design

Threshold Voltage

- Increase in Threshold Voltage
- Reduction of Leakage power due to decrease in Sub-threshold conduction
- Increase in gate delay
- α ~ 1 for short channel devices
- Vt variation
- Body bias control
- Vt is a function of Vsb
- Vt increases as Vsb increases
- Change in process parameters
- Doping concentration
- Oxide thickness

ELEC 6970: Low Power Design

B3

B2

B1

B0

0

0

0

0

A0

0

A1

0

A2

0

A3

0

Y6

Y5

Y3

Y4

Array

Multiplier Design and Analysis- The multiplier was designed in VHDL using nested conditional generate statements and port mapping
- Synthesis and Critical path analysis was done using Leonardo
- TSMC 0.25µm library
- Timing and Power analysis was done using ELDO
- TSMC 0.25µm library
- TSMC 0.18µm library

Critical Path

(using Leonardo)

ELEC 6970: Low Power Design

B3

B2

B1

B0

0

0

0

0

A0

0

A1

0

A2

0

A3

0

Y7

Y6

Y5

Y3

Multiplier- 4x4
- Area: 82 gates
- Critical paths
- A0 → Y7
- B2 → Y7
- A1 → Y7
- 32x32
- Area: 6995 gates
- Critical paths
- A0 → Y63
- B2 → Y63
- A1 → Y63

ELEC 6970: Low Power Design

Vt variation: Cell

ELEC 6970: Low Power Design

Optimum Value ~ +0.2

The optimal threshold voltage for the cell design which gives the best tradeoff between Leakage Power and Delay is approximately:

+0.7V for NMOS & -0.7V for PMOS

ELEC 6970: Low Power Design

Conclusion

- The Leakage Power reduced as the threshold voltage was increased
- The Delay of the cell also increased as we incremented Vt
- Area of the circuit remained unaffected
- Power – Delay product was evaluated to find the optimum value of Vt for the given cell design
- ∆Vt ~ 0.2 V
- Leakage Power reduction = 75%
- Delay increase = 17%
- Total Power reduction = 8%

ELEC 6970: Low Power Design

Future Work

- Variation of threshold using Body bias Voltage
- New Library design required
- Results for Multipliers of different sizes
- Extrapolation of results for larger multipliers
- Dual threshold design
- Threshold assignment algorithm
- Analysis of Delay and Power
- Analysis of Power and Delay for different design libraries
- TSMC 0.18 µm
- TSMC 0.13 µm
- Detailed study of power estimation and timing analysis tools

ELEC 6970: Low Power Design

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