Aging Phenomena
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
Bias Temperature Instability (BTI)
Bias Temperature Instability (BTI) is recognized as the most
relevant aging mechanism for current integrated circuits (ICs)
BTI increases the absolute value of pMOS/nMOS conduction
threshold voltage Vth (e.g., more than 50mV ↑ for pMOS, over
ten years)
Vth ↑ ↓ of transistors’ current ↓ of transistors’ speed
↑ IC’s delay over time
If IC’s delay above a certain limit the IC may fail to meet
its timing constraints reliability issues
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
1
Impact of BTI on Time-Critical Data-Paths
Time-critical data-path consisting of:
A combinational block Ci with propagation delay tpd
Qi Si Qi+1
Di
FFi
Ci
FFi+1
Flip-flops FFi & FFi+1:
CK
TCK
CK both sampling on the CK
rising edge
CK
Qi
tset : setup time of both FFs
Si tpcq : for each FF, time interval
tpcq tpd from the CK edge to the
tset
instant at which the FF output
reaches its final state value
Si should reach its final state before the FFi+1 tset
Due to BTI Ci may become slower possible late
transitions of Si occurring during the FFi+1 tset incorrect
sampled datum
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
BTI Degradation: Reaction-Diffusion Model
Stress phase (pMOS ON):
high electric fields and temperatures
Silicon-Hydrogen bonds at the Si-
SiO2 interface dissociate H
atoms/molecules diffuse towards the
gate & broken Si bonds acting as
interface traps (IT) for holes in the
channel ↑ Vth
∆Vth
𝒒
Vth increase given by: ∆𝑽𝒕𝒉 = 𝒕 , 𝑵
𝑪𝒐𝒙 𝑰𝑻
where NIT (t) is the # of ITs (changing in time) Stress time
(ON) t0
𝑵𝑰𝑻 (𝒕) ∝ 𝑵𝟎 𝑫𝑯 𝒕 𝒏 N0: initial number of unbroken Si-H bonds;
n: fitting parameter (n=1/6);
D : diffusion coefficient for H Cecilia Metra
Reliable Data Processing and Storage for Intelligent HSystems M
2
BTI Degradation: Reaction-Diffusion Model
(cnt’d)
Recovery phase (pMOS OFF):
Some of the H atoms/molecules
diffuse back towards the Si-SiO2
interface and anneal some of the Si
bonds ↓ NIT ↓Vth
However, the previous Vth value
(during the previous stress phase) is ∆Vth
not fully recovered, since only some
of the previously generated NIT are
annealed NIT (t1) > NIT (t=0) Stress Recovery Stress time
(ON) t0 (OFF) t (ON)
1
𝜹(𝒕 − 𝒕𝟎 ) NIT(t0): number of interface traps at
𝑵𝑰𝑻 (𝒕) ∝ 𝑵𝑰𝑻 (𝒕𝟎 ) the end of the stress phase
𝒕
δ= H diffusion parameter
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
BTI Degradation: Frequency Independence
With operating time,
BTI degradation becomes independent of the transistor
ON/OFF frequency, and becomes dependent only on the
total ON time, with respect to the total OFF time
Duty-Cycle = 50%
∆𝑽𝒕𝒉_𝒇𝟏 = ∆𝑽𝒕𝒉_𝒇𝟐
Duty-Cycle = 50%
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
3
BTI Degradation Modelling
The trend of Vth variation over time (Vth) induced by BTI can
be modeled as [2, 3]: ∆V th
∆𝑽𝒕𝒉 (𝒕) = 𝜸 𝒃 𝜶𝒏 ∆𝒕𝒏
where: Stress
(ON)
Recovery
(OFF)
Stress
(ON)
time
= ton/t, where t is the IC operating time; ton is the time
during which the pMOS (nMOS) is under stress (ON)
n (process dependent parameter) = 1/6 and b (process,
temperature, and Vdd dependent parameter) = 3.910-3
[V/(s1/6)], both for 65nm CMOS technology
γ (fitting parameter) = 1 for pMOS and γ = 0.5 for nMOS
[2] S. Hamdioui, et al., “BTI Impact on Logical Gates in Nano-scale CMOS Technology”, in Proc. of IEEE International Symp. On Design and
Diagnostics of Electronic Circuits & Systems (DDECS), 2012, pp. 348 – 353.
[3] W. Wang, et al., “An Efficient Model to Identify Critical Gates under Circuit Aging”, in Proc. of IEEE/ACM Int. Conf. on Computer-Aided
Design, 2007, pp. 735-740.
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
BTI Degradation:
Increasing with Technology Scaling
As highlighted in [2], with technology scaling:
Increase in the ICs’ power consumption increase of ICs’
operating temperature
Lower scaling of Vdd than of oxide thickness increase of
electric field across the gate oxide during stress phase
(transistor ON)
BTI degradation is expected to increase with technology scaling
[2] M. Alam, et al., “A Comprehensive model of PMOS NBTI Degradation”, Microelectronics Rel. (Elsevier), 2005 (45), pp. 71 - 81.
Reliable Data Processing and Storage for Intelligent Systems M Cecilia Metra
