Enabling Universal Memory by Overcoming the Contradictory Speed and Stability Nature of Phase-Change Materials

Transcription

1 Supplementary Information for Enabling Universal Memory by Overcoming the Contradictory Speed and Stability Nature of Phase-Change Materials Weijie Wang 1, Desmond Loke 1,2,, Luping Shi 1,*, Rong Zhao 1, Hongxin Yang 1, Leong-Tat Law 1, Lung-Tat Ng 1, Kian-Guan Lim 1, Yeo-Chia Yeo 3, Tow-Chong Chong 4 and Andrea L. Lacaita. 1 1 Data Storage Institute, DSI Building, A*STAR, Engineering Drive 1, Singapore NUS Graduate School for Integrative Sciences and Engineering, 28 Medical Drive, Centre for Life Sciences #0-01, Singapore Department of Electrical and Computer Engineering, National University of Singapore, 1 Engineering Drive 3, Singapore Singapore University of Technology & Design, 287 Ghim Moh Road, Singapore Dipartimento di Elettronica e Informazione and the IFN-CNR Sez. Milano, Politecnico di Milano, Milano I Italy. * To whom correspondence should be addressed. shi_luping@dsi.a-star.edu.sg

2 Finite Element Simulation Thermal simulation was carried out to study the temperature distribution of the PCRAM cells with varying cell and grain sizes during reset. The properties of the cell materials are assumed to be independent of the temperature. Heat is mainly generated in the phasechange layer. The thermal transfer follows the standard heat conduction equation: " k"t + Q = #c $T $t (1) where is the gradient operator, k, the thermal conductivity, c, the specific heat, ρ, the density, t, the time, T, the temperature and Q, the Joule heat per unit volume and per unit time, which is known as the heat density. Figure S1 shows the simulated temperature distribution of the PCRAM cells after constant voltage pulse activation. The temperature distribution is calculated through a thermal finite element simulation using the ANSYS program. In the simulation, the grains of the phase-change material are assumed to be 1 identical and closely packed. The grains of nm and 9 nm are represented by nm and 9 9 nm squares, respectively. The cell size of 30 nm and nm were employed. The thermal conductivity of the grain boundary was assumed to be 2 times lower than that of the grain, considering the relative thermal conductivity of nitride compounds at the grain boundary compared to that of the bulk phase-change material. 1-3 The pulse duration 20 employed was 30 ns. From the calculations, the peak temperature is observed to increase as the cell size decreases. Further increase in the peak temperature is achieved as the grain size decreases. Such observations indicate sharp changes in the thermal property the of the PCRAM cells, which can be related to the change in the phase-change mechanism. 2

3 PBC Theory The Periodic Bond Chain (PBC) theory is often used to predict the morphology of crystals. According to this theory, the crystal morphology is controlled by a set of uninterrupted chains of strong bonds formed in the crystal lattice. 4 Because the formation of a crystal is dominated by the relative growth rate of the various faces, also the relative growth rate is proportional to the attachment energy, the morphology can thus be derived by calculating the attachment energy. The attachment energy is defined as the energy released per mole when a new layer is deposited on a crystal face. In this work, we consider the relationship between the statistic number of strong bonds and the curvature radius of the boundary between the amorphous and crystalline phases. From figure S2, we can see that the statistical number of strong bonds increases as the curvature radius becomes smaller. Because the relative growth rate is proportional to the number of the strong bonds, we can conclude that the growth rate will increase. This conclusion is also applicable to the polycrystalline state because the relationship 1 between the statistical number of strong bonds and the curvature radius of the boundary between amorphous and crystalline phases is similar. 3

4 Figure S1. Simulated temperature distributions of PCRAM cells after constant voltage pulse activation. Higher peak temperature is observed in the (a) 30 nm cell with nm grain compared to the (b) 30 nm cell with nm grain, (c) nm cell with nm grain and (d) nm cell with nm grain. The thermal conductivity of the grain boundary was assumed to be two times lower than that of the grain of the phase-change material. 4

5 (a) Larger curvature radius (b) Smaller curvature radius Figure S2. Illustration showing the effect of PBC on the curvature radius based on a single crystal. Dependence of the number of strong bonds on the interface curvature of (a) larger curvature radius, and (b) smaller curvature radius.

6 Figure S3. TEM image of a PCRAM cell with grain size of nm that had been switched for 000 cycles. The grain size of the NGST in the cell is observed to around nm, showing that the grain size is practically unchanged after cycling. 6

7 References 1. Jung, M. C. et al. Ge nitride formation in N-doped amorphous Ge 2 Sb 2 Te. Appl. Phys. Lett. 91, (2007). 2. Ryu, S. W. et al. Phase transformation behaviors of SiO 2 doped Ge 2 Sb 2 Te films for application in phase change random access memory. Appl. Phys. Lett. 92, (2008). 3. Huang, Y. J., Chen, Y. C., Hsieh, T. E. Phase transition behaviors of Mo- and nitrogen-doped Ge 2 Sb 2 Te thin films investigated by in situ electrical measurements. J. Appl. Phys. 6, (2009). 4. Hartman, P., Perdok, W. G. On the relations between structure and morphology of crystals. I Acta Cryst. 8, 49-2, 21 (19). 7