Variability-Aware Reliability Simulation of
Mixed-Signal ICs with Quasi-Linear Complexity
Elie Maricau and Georges Gielen
ESAT-MICAS, KULeuven, Belgium
elie.maricau@esat.kuleuven.be
Abstract—This paper demonstrates a deterministic, variability-
aware reliability modeling and simulation method. The purpose
of the method is to efficiently simulate failure-time dispersion
in circuits subjected to die-level stress effects. A Design of
Experiments (DoE) with a quasi-linear complexity is used to
build a Response Surface Model (RSM) of the time-dependent
circuit behavior. This reduces simulation time, when compared
to random-sampling techniques, and guarantees good coverage
of the circuit factor space. The DoE consists of a linear screening
design, to filter out important circuit factors, followed by a
resolution 5 fractional factorial regression design to model the
circuit behavior. The method is validated over a broad range
of both analog and digital circuits and compared to traditional
random-sampling reliability simulation techniques. It is shown to
outperform existing simulators with a simulation speed improve-
ment of up to several orders of magnitude. Also, it is proven to
have a good simulation accuracy, with an average model error
varying from 1.5 to 5 % over all test circuits.
I. I NTRODUCTION
Scaling towards smaller transistor sizes in order to achieve
smaller, faster, lower power and less expensive chips, creates
evermore design problems. Die level reliability issues (e.g.
Negative Bias Temperature Instability (NBTI) and Hot Carrier
degradation (HC)) and increasing process variability are at the
forefront of problems to be dealt with in modern and future
CMOS technologies [1]. The effect of transistor ageing (i.e.
NBTI and HC) on circuit behavior, especially when combined
with process variability, is very complicated and not always
well understood. The lack of adequate knowledge about circuit
ageing can cause unreliable products or unnecessary design
margins.
Existing solutions (e.g. post-production accelerated stress
testing) become too expensive due to an increasing demand
for very low failure rates augmented with evermore reliability
and variability problems. A designer needs a statistical circuit
analysis tool that includes circuit ageing. Such a tool must
be fast (i.e. no more than a few hours of simulation time,
even for large circuits) but must also have a good simulation
accuracy. Moreover, a designer must be able to extract infor-
mation (i.e. weak-spot detection) to improve his design or to
implement countermeasures (i.e. circuit tuning). In literature,
most reliability simulation methods have been developed a few
years ago and are therefore intended for CMOS technologies
where variability was not yet an issue [2], [3]. To make a
reliable design in a sub 90nm technology, however, this is no
longer satisfactory. Bestory et al. [4] did include the effect
of variability, using a Monte-Carlo (MC) simulation wrapped
around a nominal reliability simulator based on high-level
behavioral transistor models. This approach is fast, but it lacks
accuracy, especially for analog circuits where the effects of
time-varying stress voltages are important. In previous work
[5], the authors presented a more accurate reliability simulator
able to cope with time-varying stress. In this work, the authors
also used a MC-approach in order to include variability effects.
But, although an MC-based reliability simulation is accurate,
it also has a large number of disadvantages: i) It is very cpu
intensive. ii) There are no weak-spot detection capabilities.
And iii) the simulation has to be rerun every time new or
extra process data is included.
In this paper, a reliability modeling and simulation method
to tackle the before-mentioned problems is presented:
1) The method is systematic and applicable to analog,
digital and mixed-signal circuits.
2) A set of experimental designs ensures the generation of
valid, defensible and accurate engineering conclusions.
3) A screening design identifies circuit weak spots and
reduces circuit simulation time guaranteeing a quasi-
linear complexity.
4) A regression design enables the generation of a circuit
Response Surface Model (RSM) of the circuit behavior
as a function of time.
The method, presented in this work, is built around a nominal
reliability simulator, the authors presented earlier [5]. A brief
review of this work is given in section II. The variability-aware
simulation framework is introduced in section III. Section
IV presents experimental simulation results and compares
the results with random-sampling based techniques. Finally
conclusions are drawn in section V.
II. NOMINAL RELIABILITY SIMULATION
The core of a reliability simulator is a method to calculate
the ageing of a circuit with fixed design parameters (i.e.
without process variability). Following subsections give a brief
overview of both the simulation method and the degradation
models used in this work and described in more detail in work
presented elsewhere [5], [6].
A. Simulation Methodology
Most degradation effects have an exponential dependence on
the transistor gate voltage. Therefore, time-varying stress volt-
ages have to be included when calculating circuit degradation.
To obtain accurate information about the time-varying stress
978-3-9810801-6-2/DATE10 © 2010 EDAA