Resistor Network Approach to Electrical Conduction and. Breakdown Phenomena in Disordered Materials. C. Pennetta, E. Alfinito and L. Reggiani Dip. di Ingegneria dell’Innovazione,Universita’ di Lecce , Italy INFM – National Nanotechnology Laboratory, Lecce, Italy. Motivations:.
Breakdown Phenomena in Disordered Materials
C. Pennetta, E.Alfinito and L. Reggiani
Dip. di Ingegneria dell’Innovazione,Universita’ di Lecce, Italy
INFM – National Nanotechnology Laboratory, Lecce, Italy
To study the electrical conduction of disordered materials over the full range of the applied stress, by focusing on the role of the disorder.
To investigate the stability of the electrical properties and electrical breakdown phenomena inconductor - insulator composites,ingranular metals and in nanostructured materials.
To establish the conditions under which we expect failure precursors and to identify these precursors.
To study the properties of the resistance fluctuations,including their non-Gaussianity and to understand their link with other basic features ofthe system.
2D SQUARE LATTICE
R = network resistance
rn = resistance of the n-th resistor
I = stress current (d.c.), kept constant
T0 = thermal bath temperature
rreg (Tn) = r0[1 + (Tn -Tref) ]
rOP = 109 rreg (broken resistor)
Tn = local temperature
= temperature coeff. of the resistance
Resistor Network (BSRN) Model:
Pennetta et al, UPON, Ed. D. Abbott & L. B. Kish, 1999
Pennetta et al. PRE, 2002 and Pennetta, FNL, 2002
rregrOP defect generation probabilityWD=exp[-ED/kBTn]
rOPrreg defect recovery probabilityWR =exp[-ER/kBTn]
Tn =T0 + A[ rn in2 +(B/Nneig)m(rm,nim,n2-rnin2)]
Gingl et al, Semic. Sc. & Tech. 1996; Pennetta et al, PRL, 1999
<p> , <R>
p fraction of broken resistor, pC percolation threshold
sets the level of intrinsic disorder (<p>0)
t = t +1
Granular structure of the material
Atomic transport through grain boundaries dominates
Transport within the grain bulk
Film: network of interconnected
SEM image of electromigration
damage in Al-Cu interconnects
Tests under accelerated conditions
Qualitative and quantitative agreement
Resistance evolutionat increasing bias
Average resistance <R>:
Distribution of resistance
fluctuations, R = R-<R>
at increasing bias
probability density function (PDF)
Effect of the initial film resistance:
In the pre-breakdown region: I=3.7 0.3
of the bias conditions (constant
voltage or constant current) and of the temperature coefficient of the
independent on the initial resistance of the film
independent on the bias conditions
dependent on the temperature coef. of the
dependent on the recovery activation energy
= 1.85 ± 0.08
All these features are in good agreements with electrical
measurements up to breakdown in carbon high-density polyethylene composites
(K.K. Bardhan, PRL, 1999 and 2003)
of the bias conditions and of
the temperature coefficient of
Bramwell, Holdsworth and Pinton
(Nature, 396, 552, 1998):
in systems near criticality
a=/2, b=0.936, s=0.374, K=2.15
BHP distribution: generalization of Gumbel
a, b, s, K :
Bramwell et al. PRL, 84, 3744, 2000
networks NxN with: N=50, 75, 100, 125
Gaussian in the linear regime
NG at the electrical breakdown:
vanishes in the large size limit
At increasing levels of disorder
(decreasing values) the PDF
at the breakdown threshold
approaches the BHP
Pennetta et al., Physica A, in print
the corner frequency
moves to lower values at increasing
levels of disorder
We have studied the distribution of the resistance fluctuations of conducting
thin films with different levels of internal disorder.
The study has been performed by describing the film as a resistor network
in a steady statedetermined by the competition of two biased stochastic
processes, accordingto the BSRN model.
We have considered systems ofdifferent sizes and under different stress
conditions, from the linear response regime up to the threshold for electrical
A remarkablenon-Gaussianity of the fluctuation distribution is found near
breakdown. This non-Gaussianity becomes more evident at increasing levels
As a general trend, these deviations from Gaussianity are related to the
finite size of the system and they vanish in the large size limit.
Near the critical point of the conductor-insulator transition, the non-Gaussianity is found to persist in the large size limit and the PDF is well
described by the universal Bramwell-Holdsworth-Pinton distribution.
Laszlo Kish (A&T Texas), Zoltan Gingl (Szeged), Gyorgy Trefan
Fausto Fantini (Modena), Andrea Scorzoni (Perugia), Ilaria De Munari (Parma)
Stefano Ruffo (Firenze)
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