A PERCOLATIVE SIMULATION OF DIELECTRIC-LIKE BREAKDOWN C. PENNETTA Dipartimento di Fisica, UniversitaÁ di Lecce, Via Arnesano, 73100 Lecce, Italy Z. GINGL JATE University, Department of Experimental Physics, Dom ter 9, Szeged H-6720, Hungary L. B. KISS Uppsala University, Material Science Department, Angstrom Laboratory, Box 534, S-75121 Uppsala, Sweden L. REGGIANI and M. DE VITTORIO Istituto Nazionale di Fisica della Materia (INFM), Dipartimento Scienza Materiali, UniversitaÁ di Lecce, Via Arnesano, 73100 Lecce, Italy A. COLA and M. MAZZER Istituto Nuovi Materiali per l'Elettronica (IME) CNR, Via Arnesano, 73100 Lecce, Italy (Received 5 December 1996; in revised form 5 May 1997) AbstractÐDielectric-like degradation of thin-®lm conductors is simulated up to ®nal breakdown within a biased percolation model. As relevant indicators we take the damage pattern, current distribution, re- sistance variation, failure lifetime and relative resistance ¯uctuations. The results show that biased per- colation predicts well several known features taking place close to the abrupt failure of thin ®lms in close agreement with available experimental results. # 1998 Elsevier Science Ltd. INTRODUCTION Degradation of thin-®lm devices due to high current densities or to high ®elds is a critical issue in ultra- large scale integration (ULSI) and very large scale integration (VLSI) technology [1±14]. A large amount of work has been done on silicon dioxide [1±8], yet a wide interest also exists in investigating degradation of semi-insulating materials and met- allic interconnections [9±14]. Indeed, the latter can play a crucial role in determining the lifetime of a large variety of electronic devices. Of particular im- portance is the development of sensitive and non- destructive experimental techniques and of theoreti- cal models able to investigate device reliability and predict its anticipated failure [9±16]. The aim of this paper is to present a model of biased percolation to simulate dielectric-like degradation up to the ®nal breakdown of a thin ®lm. As a speci®c system of interest we have in mind a semi-insulating ®lm or a metallic interconnection. We assume that the ®lm degradation is starting because of the spontaneous creation of short-circuit-like defects, while the prob- ability of generation of further defects is determined by the local Joule heating [17, 18]. The paper is organized as follows. In the ®rst section the model we use for the biased percolation is described. Then, the details of the numerical simulation and some experimental evidence are given. The main conclusions are drawn in the last section. MODEL We consider a spatially homogeneous thin ®lm modelled as a two-dimensional network of identical resistor elements deposited on an insulating sub- strate at temperature T 0 . The initial network is a perfect square lattice contacted at the opposite sides to an external applied voltage which is kept con- stant (constant-voltage operation mode). The alternative case corresponding to a constant total current ¯owing through the ®lm can also be con- sidered. By means of an elementary circuit analysis we determine the current distribution, the (total) re- sistance and its ¯uctuations [18±20]. In our model a defect corresponds to an element whose resistance is equal to zero (short-circuit model) [19, 21]. The complete degradation of the network occurs when at least one continuous path of defects between the two opposite contacts of the square lattice is Microelectron. Reliab., Vol. 38, No. 2, pp. 249±253, 1998 # 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0026-2714/98 $19.00 + 0.00 PII: S0026-2714(97)00046-2 249