Modeling of the oscillation decay in PCM

Thanks to the transition from a highly-resistive to a conductive state exhibiting an N-shaped characteristic VS(I), a number of amorphous chalcogenide materials are used in the fabrication of nonvolatile phase-change memories (PCM) [1]. This is a relatively recent area of application for materials that have been used since the 70s for optical data storage [2]. For the case of memories the transition is forced by a suitable electrical pulse that produces heating; depending on the amplitude and duration of the pulse, a transition from the amorphous to the crystalline phase is induced, or viceversa [3]. Measuring the VS(I) curve or other electrical parameters of the PCM in the amorphous phase by means of a static-measurement setup is rather complicate, because the N-shaped curve imposes the use of a current generator and also because parasitics are present. A more effective approach is that of exploiting the intrinsic instability due to the negative differential-resistance branch of the PCM characteristic, and arranging a dynamic-measurement setup [5], [6]. In this setup the characteristic of the external load intersects that of the PCM in the negative-resistance branch, so that the circuit is forced to oscillate. Here the dynamic scheme for extracting the PCM parameters is examined. The experimentally-observed oscillation decay due to the successive heating and quenching of the material is modeled by means of a set of differential and algebraic equations. The method allows one to extract important design parameters of the PCM, along with their temperature dependence. The dynamic measurement brings about a problem, namely, the heating produced by it determines a partial crystallization of the material. The consequent increase in conductivity modifies, and possibly extinguishes, the oscillations. In fact, a typical pattern of the oscillatory regime is the following [6]: the first oscillation has a larger peak, followed by oscillations with a stable amplitude, followed by oscillations with a decaying amplitude. The strong decrease in amplitude from the first peak to the next ones is explained by the sudden crystallization of a finite portion due to the concentration of the current flow-lines. In fact, the heater is much narrower than the amorphous region, and the temperature is the highest because the whole device is still amorphous. The conspicuous crystallization occurring in the first oscillation leaves a smaller resistance for the next cycles. The behavior from the second peak on is ascribed to the decrease in the remaining volume of the amorphous phase due to rapid heating and quenching, that produces the formation of small crystalline nuclei (nucleation) [6],[7]. As a consequence, the description of the oscillations must include a time-dependent thermal analysis along with the modeling of nucleation [8].