## 2 Material Properties
### Electrical Properties  
One of the fundamental properties of phase change materials is the large resistivity contrast between amorphous (high resistivity) and crystalline (low resistivity) phases. The as-deposited GST thin films are in the amorphous state. The resistivity of GST at different phases is generally characterized by a 4-point probe which is an electrical impedance measuring technique that can measure the sheet resistance of the thin films. The resistivity as a function of annealed temperature is usually used to characterize the phase transitions during the annealing process. In Figure 3, we show the resistivity of GST as a function of annealing temperature. This GST film is created by using magnetron sputtering. The sample is placed on a hot plate at discrete temperatures between 25 \({}^{\circ}\)C to 350 \({}^{\circ}\)C for 2 min, then the sample is cooled down to room temperature before 4-point measurement. There are two distinct transitions in the resistivity plot. The first transition near 150 \({}^{\circ}\)C corresponds to the amorphous to face-centered-cubic (fcc) phase transition, while the second transition near 230 \({}^{\circ}\)C is due to the fcc to hexagonal close-packed (hcp) phase [28]. The temperature dependence of resistivity has a slope between the first and second phase transition, which comes from the mixture states. Namely the mixed states between amorphous state and fcc state near the first transition, and the that of fcc and hcp states near the second transition. The resistivity of the phase change material plays an important role since it determines the power efficiency and stability. There are several factors that can affect the phase change material's resistivity characteristics, such as film thickness, heating rate, and fabrication methods and parameters. Figure 4a shows the effect of film thinness on the resistivity characteristic. In the very thin (less than 100 nm) regime, with a smaller GST film thickness, the phase transition temperature and the resistivity at both amorphous and crystalline states increase. This phenomenon may be due to the segregation or loss of tellurium from the alloy, or it may be due to the limited amount of material available for nuclei formation as the films become very thin [29]. The problem of deg  
Figure 3: Resistivity of GST as a function of annealed temperature. Figure 2: The ‘SET’, ‘RESET’ and ‘READ’ pulses for a PCM device. films in PCMs was solved by [PERSON] et al. [30], where they were able to achieve broadly the same crystallization temperatures in a 2 nm GST thin film as the bulk material. In Section 3.1, we will introduce several types of modified cell structures that have been explored to circumvent this issue. Figure 4b shows the effect of heating rate on the crystallization behavior of amorphous GST thin films. The crystallization temperature from the amorphous to fcc state increases logarithmically with the heating rate. The overall effective activation energy for the crystallization is 2.34 eV at a low heating rate (less than 40 \({}^{\circ}\)C/minute) and 0.49 eV at a higher heating rate [31]. The difference in the effective activation energy for crystallization affects the nucleation and the growth of fcc crystalline structures. Deposition methods and parameters can also lead to resistivity discrepancy. In fact, even the same deposition method can yield different phase transition characteristic due to the variation in experimental parameters, such as pressure and power. Therefore, the phase-change resistivity characteristics of GST thin films have been found varies between different research groups, as summarized in Figure 5.  
Figure 4: Crystallization behavior of amorphous GST thin films by in situ electrical sheet resistance measurement at a wide range of annealing temperatures with (**a**) different film thickness, Adapted with permission from Reference [29]. ©2010 American Institute of Physics. and (**b**) different heating rates. Adapted with permission from Reference [31]. ©The Electrochemical Society.