Modeling active dimension for phase change memory cell

The functionality of phase change memory (PCM) as a promising non-volatile memory (NVM) is realized by changing the material properties of phase change (PC) material in a near-bottom-electrode region called `active region´. The shape of the active region is usually assumed to be hemispheric as demonstrated by [1][2], based on which some work have been done to calculate the radius for further design optimization [3][4]. However the hemispheric assumption is only valid when the phase change element (PCE) layer, has large enough dimension to satisfy the requirement of semiinfinite thermal conductive medium used to calculate the heat generation [3]. And the dimension of the PCE layer might be small in actual design, in order to reduce the total phase change volume, which will invalidate the hemisphere assumption due to the finite geometry boundary of PCE layer [5]. So far very few work has been reported to include this situation for the calculation although the necessity is evident to develop a more general model to improve the universality of preceding work in 3-D resistance calculation, where active dimension is an indispensable element [6]. For this purpose an analytical model is proposed for active dimension calculation by solving 3-D heat conduction equation in this work, which is applicable to varying cell geometries including the situation without semi-infinite assumption.