Finite-Element Modeling of Hopping Transport and Percolation in Reset Phase Change Memory Cells

Phase change memory (PCM) is an emerging high-speed non-volatile electronic memory technology that has been scaled down to sub-10 nm regime. Typical PCM cells are composed of a small volume of a phase change material, such as Ge₂Sb₂Te₅ (GST), and two electrical contacts The phase change materials in the active areas of PCM cells are electrothermally switched between highly-conductive crystalline phase and the highly-resistive amorphous phase using short (~1-1000 ns) voltage pulses. In our experiments on GST line-cells with width x length x thickness of ~ 100 nm x ~ 500 nm x ~ 20 nm, performed in the 80 K – 250 K temperature range, we observe (i) linear current-voltage (I-V) characteristics when the cells are in their low-resistance (crystalline) state, (ii) I-V characteristics with a hyperbolic sine behavior in the low-field regime (&lt; 20 MV/m) and (iii) I-V characteristics with a stronger exponential response in the high-field (&gt; 20 MV/m) regime, in their high-resistance (amorphous) state^[1-3]. We are able to accelerate and stop resistance drift by stressing the devices with high-field for a few minutes. Hence, the characteristics obtained after the high-field stress are stable. Hyperbolic sine behavior is expected for thermionic emission over an energy barrier modulated by an external field and possibly hopping transport as a result. We have constructed a 2D hopping transport model using our experimental results that allows us to extract the hopping distances, hopping angles and activation energies related to the rate-limiting processes as a function of temperature.<br/><br/>In this study, we use a finite-element multi-physics platform (COMSOL) to study the impact of random variations in activation energy within GST to capture the naturally occurring random distributions inside the amorphous material. The exponential nature of the thermionic emission process leads to filaments (percolation paths) that carry significant portion of the current and are prone to threshold switching and local thermal runaway that initiates the set process. The fluctuations in the activation energy give rise to read noise in the high-resistance state, which hampers the multi-bit-per-cell implementations for PCM. Details of the model, the finite element results and the consequences of local variations will be presented.<br/><br/>References<br/><br/>1. R. S. Khan, F. Dirisaglik, A. Gokirmak, & H. Silva, Resistance drift in Ge2Sb2Te5 phase change memory line cells at low temperatures and its response to photoexcitation. <i>Appl Phys Lett</i> <b>116</b>, 253501 (2020).<br/>2. R.S. Khan, A.H. Talukder, F. Dirisaglik, H. Silva, and A. Gokirmak, “Accelerating and Stopping Resistance Drift in Phase Change Memory Cells via High Electric Field Stress,” ArXiv:2002.12487, (2020).<br/>3. A. Talukder, M. Kashem, M. Hafiz, R. Khan, F. Dirisaglik, H. Silva, and A. Gokirmak, “Electronic transport in amorphous Ge2Sb2Te5 phase-change memory line cells and its response to photoexcitation,” Appl Phys Lett <b>124</b>(26), (2024).