## 1 Introduction  
Recently, phase change memory (PCM) has received much attention as an attractive next generation memory technology because of its benefits, such as fast its programming speed, non-volatility, low cost, promising scalability, good endurance, and capability of performing complicated non-binary arithmetic processing and computation [1; 2; 3; 4; 5; 6]. PCM cells store data by means of reversible transitions between conductive crystalline (SET) and highly resistive amorphous (RESET) states of a small active region within phase change materials (common Ge\({}_{2}\)Sb\({}_{2}\)Te\({}_{5}\) (GST) [7]), induced by appropriate heating via electrical pulses. RESET operation requires a short and intense electrical pulse to heat the active region above its melting temperature, and a subsequent rapid quenching solidifies the GST materials into the amorphous state allowing it insufficient time to crystalize. The reverse process, SET operation, involves recrystallization of the amorphous region formed during the RESEToperation, where a moderate amplitude longer duration pulse is used to switch the amorphous region back to a crystalline state through annealing above crystallization temperature or melting followed by slower cooling.  
Given the large temperature gradients and current densities during the switching operation, thermoelectric effects have a large impact on the performance of PCM cells [8]. The thermoelectric effects are the result of the energy exchange between the charge carriers and the lattice in the presence of an electric current [9]. When the junction of different materials is heated, electrons are enabled to pass from the material in which the electrons have the lower energy into that in which their energy is higher, giving rise to an electromotive force, namely the Seebeck effect. The Peltier effect appears as heating/cooling at the junction, because the energy transported by the electrons is altered when a current passes from one material to another. The Thomson effect consists of reversible heating or cooling as charge carriers absorb or release energy along a uniform material under an electrical current due to a temperature gradient. These thermoelectric effects influence the temperature profiles within the cell through heating or cooling depending on the direction of current, and then change the final phase distribution and the corresponding resistance of the cell.  
For future cell design, it is necessary to investigate these thermoelectric phenomena in detail. Owing to the short phase change timescales involved and the small length scales of actual PCM cells, quite a few numerical simulations have been executed for a systematic analysis of the PCM cell operations, however they have typically neglected the phase change process or not included the thermoelectric effects [8; 10; 11; 12]. In reality, the phase-change behavior is closely related to the temperature and its history. The final phase distribution cannot be accurately captured only using the temperature profile, especially in the SET operation, which requires enough temperature and time for crystallization. A model containing phase change kinetics is essential for a comprehensive study of the thermoelectric effects during the PCM cell operations.  
In this article, we employed a three-dimensional finite element simulation to study the temperature profiles within the PCM cells, which is available for arbitrarily complex cell structure. We carry out electrical, thermal, and phase change simulations for a complete description of switching operations in the PCM cells, considering the temperature dependence of material parameters. The thermoelectric effects are included by the modification of the current continuity equation and the heat conduction equations. The simulated temperature profiles are studied in detail for the analysis of thermoelectric effects in switch processes. The impact of isotropic scaling on thermoelectric effects is also addressed.