Comparative Analysis of Timing Yield Improvement
under Process Variations of Flip-Flops Circuits
Hassan Mostafa, M. Anis, and M. Elmasry
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada N2L3G1
{hmostafa@uwaterloo.ca, manis@vlsi.uwaterloo.ca, elmasry@uwaterloo.ca }
Abstract—In synchronous systems, any violation of the timing
constraints of the flip-flops can cause the overall system to
malfunction. Moreover, the process variations create a large
variability in the flip-flop delay in scaled technologies impacting
the timing yield. Overtime, many gate sizing algorithms have been
introduced to improve the timing yield. This paper presents an
analysis of timing yield improvement of four commonly used flip-
flops under process variations. These flip-flops are designed using
STMicroelectronics 65-nm CMOS technology. The analyzed flip-
flops are compared for power and power-delay product (PDP)
overheads to achieve this timing yield improvement. The analysis
shows that the sense amplifier based flip flop (SA-FF) has a power
overhead and PDP overhead of 1.7X and 2.8X, respectively, much
higher than that of the transmission-gate master-slave flip flop
(TG-MSFF) . The TG-MSFF exhibits the lowest relative power
and PDP overheads of 30.87% and 9% ,respectively.
I. I NTRODUCTION
As CMOS technologies continue to scale towards the
nanometer regime, the device parameters, such as threshold
voltage, channel length, oxide thickness and mobility, will
have large statistical process variations [1-5]. Consequently,
these process variations will lead to delay uncertainty. There-
fore, the deterministic design methodology is replaced by the
statistical design methodology [6]. The process variations can
be classified as die-to-die (inter-die) variations or within-die
(intra-die) variations. In die-to-die variations, all devices on the
same die are assumed to have the same parameters. However,
devices on the same die are assumed to behave differently
for within-die variations [1]. Although die-to-die variations
were originally considered as the main source of process
variations, within-die variations have now become the major
design challenge as technology scales [3,4]. Moreover, the
demand for higher performance has moved the clock frequen-
cies up to multi-GHz in microprocessors and other advanced
applications. These increased clock frequencies lead to very
deep pipelining which means that hundreds of thousands of
flip-flops are required to control the data flow under strict
timing constraints. A violation of the timing constraints at a
flip-flop can result in latching incorrect data causing the overall
system to malfunction [7].
Deterministic gate sizing tools size the circuits to optimize
the power-delay-product (PDP). However, due to random
process variations, a large number of circuits might not meet
the target delay. Consider as an intuitive example, a flip-flop
that is designed for optimum PDP, which exhibits a specific
target delay. Due to random process variations, the delay
can be modeled by a normal distribution with the probability
density function (pdf) shown in Figure 1. Here, 50% of the
total number of flip-flops will not meet the desired target
delay constraint. Therefore, the flip-flops must be designed
by using statistical sizing tools to improve the timing yield
[8, 9]. In [10], a comparative analysis of the impact of the
process variations on flip-flops power and delay is introduced.
However, the analysis utilizes deterministic sizing tools to size
the flip-flops, resulting in a poor timing yield (less than 50%).
Therefore, the utilization of statistical sizing tools for timing
yield improvement is more appropriate for an efficient and fair
comparison, since the timing yield is the main concern in high
performance applications. This paper provides a comparative
analysis of timing yield improvement under process variations
of four different flip-flops topologies, especially for the delay
variability and the required power and PDP overheads for
timing yield improvement. These flip-flops represent different
trade-off choices between performance and power dissipation.
The paper is organized as follows: Section 2 introduces
the selected flip-flops designs and summarizes the flip-flops
timing characteristics. Sections 3 and 4 describe the simulation
setup and the simulation results, respectively. Finally, some
conclusions are drawn in Section 5.
Fig. 1. The delay pdf due to process variations under deterministic gate
sizing algorithms. It shows, intuitively, that up to 50% of flip flops will not
meet the target delay (50 ps in this example)
2009 IEEE Computer Society Annual Symposium on VLSI
978-0-7695-3684-2/09 $25.00 © 2009 IEEE
DOI 10.1109/ISVLSI.2009.23
133
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