(Digital Presentation) Calculation of the Energy Band Diagram and Estimation of Electronic Transport Parameters of Metastable Amorphous Ge₂Sb₂Te₅

Phase change memory (PCM) is a high speed, high density non-volatile resistive memory technology that utilizes different phases (crystalline and amorphous) of phase change materials such as Ge2Sb2Te5 (GST) to store information [1]. Here, the material undergoes two types of reversible switching phenomena: (i) Ovonic Threshold Switching (OTS), which causes the amorphous phase of the material to switch from a highly resistive state to conductive state with application of high electric fields, resulting in current flow and (ii) Ovonic Memory Switching (OMS), which is due to the change of the phase of the material between amorphous and crystalline phases induced by heating [2]. Even though PCM entered high volume manufacturing, the electronic properties of the phase change materials are still not well understood [3,4]. In this work, we construct the energy band diagram of amorphous GST as a function of temperature using a temperature dependent model of effective activation energy of conduction in metastable amorphous GST [5], which we obtained from high-speed experiments on GST line-cells [6]. Assuming the bandgap energy to linearly decrease with temperature [7,8] and p-type conduction (based on positive Seebeck coefficients measured in a wide temperature range [9]) , we determine a temperature dependent Fermi energy level from 0K to melting temperature, Tmelt ~ 858 K. Liquid GST is expected to become metallic (bandgap collapsing to 0) at ~ 894K, based on the experimental results. We also estimate the carrier concentration at Tmelt utilizing the latent heat of fusion (126 kJ/kg) [10] to be pmelt = 1.47 x 1022 cm-3. Using the melt resistivity measured on GST thin film, we calculate the carrier mobility at melting point as µmelt ~0.187 cm2/V-s, close to the previously reported value of 0.15 cm2/V-s based on crystalline state mobility and a density of states calculation [2]. Assuming a weak temperature dependence of the mobility [5], we obtain the carrier concentration of ~3.37× 1017 cm-3 at room temperature which lies within the ~1017-1018 cm-3 range estimated in a former study [3]. Finally, we calculate conduction activation energy of as-deposited amorphous GST from temperature dependent Seebeck coefficient measured simultaneously with the resistance [9]. The activation energy varies as a parabolic function of temperature where it starts from 0 eV at 0 K, reaches a peak of ~0.257 eV near glass transition temperature (~400 K) with the room temperature value of ~0.24 eV and becomes 0 eV again at ~810 K. We also utilize the Seebeck coefficient measurements along with the band edges and Fermi energy level information from the energy band diagram to calculate the ratio of minority carrier concentration to the total carrier concentration as a function of temperature; this is useful to predict the temperature beyond which bipolar conduction becomes significant. Acknowledgment: Analysis is performed with the support of US National Science Foundation (NSF) award ECCS 1711626. The experimental data used for this analysis were collected with the support of US NSF DMR-1710468 on devices fabricated with the support of US Department of Energy Office of Basic Energy Sciences. References: [1] S. W. Fong et al., IEEE Trans. Electron Devices, vol. 64, no. 11, pp. 4374–4385, 2017. [2] A. Pirovano et al., IEEE Trans. Electron Devices, vol. 51, no. 3, pp. 452–459, 2004. [3] T. Kato et al., Japanese J. Appl. Physics, vol. 44, no. 10, pp. 7340–7344, 2005. [4] M. Schumacher et al., Sci. Rep., vol. 6, no. June, pp. 1–11, 2016. [5] S. Muneer et al., AIP Adv., vol. 8, no. 6, p. 65314, Jun. 2018. [6] F. Dirisaglik et al., Nanoscale, vol. 7, no. 40, pp. 16625–16630, 2015. [7] E. M. Vinod et al., J. Non. Cryst. Solids, vol. 356, no. 41–42, pp. 2172–2174, 2010. [8] Y. Kim et al., Appl. Phys. Lett., vol. 90, no. 17, pp. 1–4, 2007. [9] L. Adnane et al., J. Appl. Phys., vol. 122, no. 12, 2017. [10] Z. Fan et al., Japanese J. Appl. Physics, vol. 42, no. 2 B, pp. 800–803, 2003.