Modeling heterogeneous melting in phase change memory devices

Abstract

We present thermodynamic crystallization and melting models and calculate phase change velocities in Ge2Sb2Te5 based on kinetic and thermodynamic parameters. The calculated phase change velocities are strong functions of grain size, with smaller grains beginning to melt at lower temperatures. Phase change velocities are continuous functions of temperature which determine crystallization and melting rates. Hence, set and reset times as well as power and peak current requirements for switching are strong functions of grain size. Grain boundary amorphization can lead to a sufficient increase in cell resistance for small-grain phase change materials even if the whole active region does not completely amorphize. Isolated grains left in the amorphous regions, the quenched-in nuclei, facilitate templated crystal growth and significantly reduce set times for phase change memory cells. We demonstrate the significance of heterogeneous melting through 2-D electrothermal simulations coupled with a dynamic materials phase change model. Our results show reset and set times on the order of ~1 ns for 30 nm wide confined nanocrystalline (7.5 nm -25 nm radius crystals) phase change memory cells.Solids tend to melt heterogeneously: the liquid phase initially forms at high energy sites such as grain boundaries and material interfaces. While many materials heat ~20% above their melting temperature (Tmelt) before the liquid phase forms within the bulk solid, heterogeneous melting may occur below Tmelt 1 . In this manuscript, we consider the impacts of heterogeneous melting on phase change memory (PCM). PCM is a non-volatile memory technology which stores information as the low resistivity crystalline or high resistivity amorphous phase of a material (Fig. 1). PCM retention, endurance, and speed depend on the physics underlying crystallization and melting. We model temperature and grain size dependent phase change velocities in Ge2Sb2Te5 (GST), a common phase change material, based on kinetic and thermodynamic parameters. We incorporate heterogeneous melting into a finite element phase change model coupled with electrothermal physics 2-7 and show that it can account for the experimentally demonstrated PCM performance improvement with decreasing grain size 8,9 .Tmelt is the temperature at which the Gibbs free energy difference between bulk liquid and crystalline phases (Δglc) is zero. However, melting becomes thermodynamically favorable below Tmelt at crystal interfaces. The Gibbs free energy of a spherical crystal surrounded by liquid (ΔGcrys) is calculated by classical nucleation theory aswhere r is the crystal radius and γlc is the energy penalty at a liquid-crystal interface (Fig. 2a). (1) has extrema at r = 0 and r = rc, the critical radius:(2) Crystals with r < rc are subcritical and can reduce ΔGcrys by shrinking, i.e. melting. rc increases with T: Δglc decreases with increasing T, crossing 0 at Tmelt. γlc is difficult to measure in GST and often used as a fitting parameter; however, γlc increases with T in metals as well as in t...

Phase‐Change Logic via Thermal Cross‐Talk for Computation in Memory

“…This approach is significantly more efficient compared with discrete nucleation models using individual domains to define the material characteristic. [ 73,74 ] The models used for Figure 6 include grain boundary amorphization which initiates amorphization at the grain boundaries and material interfaces as we describe in the study by Scoggin et al [ 66 ] and accounts for latent heat of fusion as we describe in the study by Scoggin and co‐workers. [ 37,75 ]…”

“…While it is typically assumed that reset operation requires melting, it is possible to amorphize grain boundaries and interfaces at temperatures substantially below bulk melting temperature (T MELT ). [66] It is also possible to amorphize at lower temperatures by substantial hole injection at steep thermal gradients or junctions, through impact ionization by high-voltage short duration pulses. [38] PCM cells have been demonstrated with endurance >10 12 cycles, [42] while 10 15 -10 17 cycles of endurance are necessary to achieve logic operations at the CPU clock speed.…”

“…[72] This model uses grain boundary amorphization and treats a-GST as supercooled liquid. [36][37][38]51,66] The simulations use an out-of-plane depth of 20 nm and V supply ¼ 3.3 V. www.advancedsciencenews.com www.pss-rapid.com…”

“…This approach is significantly more efficient compared with discrete nucleation models using individual domains to define the material characteristic. [73,74] The models used for Figure 6 include grain boundary amorphization which initiates amorphization at the grain boundaries and material interfaces as we describe in the study by Scoggin et al [66] and accounts for latent heat of fusion as we describe in the study by Scoggin and co-workers. [37,75] We have demonstrated that the thermoelectric contribution is substantial, therefore there is a significant impact of the device polarity through our computational studies, as was also experimentally demonstrated by others.…”

Cellular automata dynamics of nonlinear optical processes in a phase-change material

“…Similar constraints apply to numerical, finite element and finite difference time domain, multiphysics simulations. Alternative approaches to describing phase transition processes, capable of encompassing disparate length/timescales are offered by rate equations 58,59 , phase field methods 60,61 , Monte Carlo models 62 and, as considered here, cellular automata (CA) [63][64][65][66][67][68] . Indeed, CA have been applied to modelling dynamics in a remarkably diversity of complex systems, from laser emission to the growth of snowflakes and from ionic diffusion in concrete to pattern recognition in networks [69][70][71][72] , as well as the melting and solidification (crystal nucleation/growth/dissociation) of materials [63][64][65][66][67][68] .…”