Theoretical Model of Crystal Nucleation in PCM Nano-Glasses
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1072-G01-07
Theoretical Model of Crystal Nucleation in PCM Nano-Glasses V. G. Karpov1, Y. A. Kryukov1, M. Mitra1,2, and I. V. Karpov2 1 Physics and Astronomy, University of Toledo, Toledo, OH, 43606 2 Intel Corporation, Santa Clara, CA, 95054 ABSTRACT We propose a theoretical analysis of crystal nucleation in disordered nano-glass structure of chalcogenide phase change memory. Statistical fluctuations of microscopic structure parameters translate into statistical distribution of nucleation times determining the transition from the highly resistive (glassy) to the low resistive (crystalline) state. This distribution is shown to be log-normal with the peak time exponentially dependent on field strength, temperature, cell area and material parameters. INTRODUCTION The recent applications of chalcogenide materials in phase change memory (PCM) [1] sparked an interest in seeking a better understanding of crystal nucleation in glasses. We recall that PCM devices utilize electrically initiated, reversible amorphous-to-crystalline phase change in multi-component chalcogenides, such as Ge 2 Sb 2 Te 5 (GST). The markedly different crystalline and amorphous state resistances are used as the two logic states. Crystal nucleation underlies the switching PCM transition from the high resistive (glassy) to low resistive (crystalline) state. In addition, spontaneous crystallization can limit PCM operations at very hight temperatures. The existing understanding of crystal nucleation in PCM is based on the classical nucleation theory neglecting statistical fluctuations in the disordered structure of a glass. Fluctuations of structure parameters (bond length, angles, coordination numbers, etc.) can have a significant impact on crystal nucleation [2]. In particular, they lead to fluctuations in nucleation barriers W between different locations in a glass. As a result, the nucleation will start at softest glass regions extending over time to harder (higher W ) locations. Here we propose a theory describing the probabilistic distribution of crystal nucleation (induction) times in a finite volume of a nano-glass between two conductive electrodes under external bias. This implies a certain degree of the field induced nucleation noticed earlier [3] for glassy materials in moderate fields, much below the typical switching field in PCM. In addition to the field effect, we take into account a unique nature of PCM crystal nucleation in which only the first nucleation switching event counts, because it turns the structure into the low resistive state. CRYSTAL NUCLEATION IN DISORDERED GLASS STRUCTURE According to the classical nucleation theory, [4] the free energy of a uniform spherical embryo is given by F0 = 4πR 2σ − 4πR 3 µ/3 (1)
where σ is the surface energy and µ is the difference between the chemical potentials of the two phases. Minimizing F gives the critical embryo radius and nucleation barrier, R0 = 2σ/µ , W0 = max[ F0 ( R )] = 16πσ 3 /3µ 2 . (2) The corresponding nucleation (induction) time is given by τ = τ 0 exp(W0 /kT ). (3) For th
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