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Electronic, Optical and Thermal Properties of the Hexagonal And JOURNAL OF APPLIED PHYSICS 110, 063716 (2011) Electronic, optical and thermal properties of the hexagonal and rocksalt-like Ge2Sb2Te5 chalcogenide from first-principle calculations Thierry Tsafack,1 Enrico Piccinini,2,a) Bong-Sub Lee3,b) Eric Pop,4 and Massimo Rudan2,1 1DEIS – Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy 2E. De Castro Advanced Research Center on Electronic Systems ARCES, University of Bologna, Via Toffano 2/2, I-40125 Bologna, Italy 3Department of Materials Science and Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 4Department of Electrical and Computer Engineering, Micro and Nanotechnology Lab, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA (Received 4 March 2011; accepted 11 August 2011; published online 26 September 2011) We present a comprehensive computational study on the properties of rock salt-like and hexagonal chalcogenide Ge2Sb2Te5 supported by experimental data. We calculate the electronic structure using density functional theory (DFT); the obtained density of states (DOS) compares favorably with experiments, and is suitable for transport analysis. Optical constants including refractive index and absorption coefficient capture major experimental features, aside from an energy shift owed to an underestimate of the bandgap that is typical of DFT calculations. We also compute the phonon DOS for the hexagonal phase, obtaining a speed of sound and thermal conductivity in good agreement with the experimental lattice contribution. The calculated heat capacity reaches 1.4 Â 106 J/(m3 K) at high temperature, in agreement with experiments, and provides insight into the low-temperature range (<150 K), where data are unavailable. VC 2011 American Institute of Physics. [doi:10.1063/1.3639279] I. INTRODUCTION The origin of this high optical contrast has been sought in the last years, and it has been linked to resonant bonded p Over the past two decades phase-change materials have states of the crystalline phase that are lost in the amorphous generated much interest in the area of electronic devices for configuration. As a consequence, the remarkable difference memory applications thanks to the scaling properties, small in the optical matrix elements associated to the two phases energy consumption (<100 fJ/bit),1 and large number (109) causes the strong optical contrast.11–13 of writing cycles.2 The ability of such materials to switch In the last decade several models have been between the crystalline and the amorphous phase makes them proposed14–16 to describe the snap-back phenomenon in the suitable candidates for data storage. In fact, the two phases I(V) characteristic of amorphous GST glasses. In fact, such a are associated with large differences in the optical constants feature is fundamental for using the material in the fabrica- and resistivity.3 Since the late 1960s digital disk-random tion of solid-state memories. Even though the hexagonal access memories, phase-change dual disks, re-writable phase is the stable one, the metastable cubic crystals play a optical media with increasing storage capability and, later on, major role in device applications. As a matter of fact the solid-state non-volatile memories, have been designed and amorphous structure of GST stems from a strongly distorted released to the market. rock salt-like one,7 and the material can easily switch Chalcogenide materials like Ge Sb Te (GST) have 2 2 5 between the amorphous and the crystalline phase due to extensively been investigated either theoretically or experi- Joule heating. The models describing carrier conduction in mentally in order to better understand the nature of their semiconductors are usually based on the knowledge of the structural, electronic, optical, thermal and electrical proper- electron and phonon dispersion relations for the material at ties. X-ray diffraction experiments have provided cell param- hand. In a similar manner this type of data are useful for a eters for the hexagonal and the cubic GST (Refs. 4–6), and better understanding of the transport characteristics of the several hypotheses have also been made about the amor- GST material. phous phase.7–9 The GST material is a semiconductor in This paper describes the results of a comprehensive both the crystalline and the amorphous phase. Its optical computational study of the GST chalcogenide, including bandgap has been estimated around 0.5 eV for the former band structures and optical constants for both the hexagonal phase and around 0.7 eV for the latter.10 Moreover, the opti- and the rock salt-like phases. Two former studies devoted to cal dielectric constant of the crystalline phase is about twice the hexagonal phase were recently published;17,18 they are to three times greater than that of the amorphous phase.11 considered here for comparison purposes. Moreover, the vibrational properties of the hexagonal phase are investi- a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. gated as well, in order to get information on the speed of b)Present address: Tessera Inc., 2025 Orchard Parkway, San Jose`, CA, USA. sound in the material, on the thermal conductivity, and heat 0021-8979/2011/110(6)/063716/9/$30.00 110, 063716-1 VC 2011 American Institute of Physics Downloaded 26 Sep 2011 to 192.17.112.46. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions 063716-2 Tsafack et al. J. Appl. Phys. 110, 063716 (2011) capacity. The starting point of the analyses is the calculation stacking where all Sb and Ge atoms exchange their positions,5 of the band structure by means of the density-functional while Matsunaga and coworkers suggested that Sb and Te can (DFT) theory using plane waves as basis set. randomly occupy the same layer, thus resulting in a mixed con- After calculating the band structure, the imaginary part figuration.6 Among these configurations, we have adopted that i(x) of the dielectric tensor ab(x) (including Drude-type proposed by Kooi and de Hosson, whose total energy is contributions) is derived using the Drude-Lorentz expres- claimed to be the lowest in the computational studies available 17,18,24 sion. The real part r(x) is then calculated through the in the recent literature. As for the rock salt-like structure, Kramers-Kronig transformation. The Maxwell model allows the fact that the phase transition occurs easily from the hexago- one to link r(x) and i(x) to the refractive index n(x) and nal phase suggests that the transformation does not imply a the extinction coefficient k(x), as well as the absorption large atomic rearrangement, and the two stackings must share coefficient a(x). Two measurable quantities like the optical a common background. reflection R(x) and transmission T(x) are derived from n(x) The unit cell for the hexagonal phase here considered is and k(x) using exact equations considering multiple reflec- then made up of nine atoms and arranged in the stacking tions in a thin film. They are compared to the corresponding sequence Te – Ge – Te – Sb – Te – Te – Sb – Te – Ge, while experimental data. the rock salt-like structure comes out from shifting the hex- Finally, the phonon density of states (DOS) is calculated agonal Te – Sb – Te – Ge sub-unit along the [210] direction through the density-functional perturbation theory (DFPT) to the next crystallographic plane, thus creating a vacancy for the hexagonal crystalline phase. From this, it is possible site (v) in between. That leads to a unit cell of 27 atoms and to evaluate the sound velocity and the thermal conductivity, three vacancies arranged in the stacking sequence Te – Ge – which compare well with experimental data on the phonon Te–Sb–Te–v–Te–Sb–Te–Gerepeated three times contribution in hexagonal GST. Moreover, the heat capacity (Fig. 1). This sequence corresponds to a rock salt-like config- for this phase is obtained over a wide temperature range uration where Te atoms occupy the Cl sites, while Na posi- (5–870 K) by integrating the DOS. tions are filled either by Ge atoms, Sb atoms, or vacancies. The experimental values for the cell parameters are: a ¼ 4.22 A˚ , c ¼ 17.18 A˚ for the hexagonal phase,25 and a ¼ 6.02 A˚ , II. METHOD AND CALCULATIONS 0 corresponding to a ¼ 4.26 A˚ , c ¼ 52.13 A˚ in the equivalent The electronic structure has been computed using the hexagonal system, for the rock salt-like structure.26 The ge- DFT equations that are implemented in the Quantum ometry relaxation resulted in a difference from the experi- Espresso 4.1 code.19 This software uses plane waves as a ba- mental data of Da ¼ 0.08%, Dc ¼3.02% for the hexagonal sis set for the expansion of atomic orbitals, and implements phase, and of Da ¼2.05%, Dc ¼1.8% for the cubic periodic boundary conditions. The local density approxima- phase. Moreover, a slight shift in the position of internal tion (LDA) by Perdew and Zunger20 has been considered for planes is also found. The calculated shrinkage of the c the exchange-correlation energy. The electron-ion interac- parameter is consistent with the adopted LDA approximation, tions have been described by means of norm-conserving and can also be found in the works of Sun et al.24 and of Lee ionic Bachelet-Hamann-Schluter pseudopotentials without and Jhi,17 but contrasts with the results of Sosso et al.18 non-linear corrections.21 The valence configurations are A12Â 12 Â 4 k-point grid for the hexagonal GST and a 4s24p2,5s25p3, and 5s25p4 for Ge, Sb, and Te, respectively. 12 Â 12 Â 1 grid for the rock salt-like phase have respec- Recent papers17,22 included explicitly the role of Te 4d elec- tively been used for the self-consistent calculation in order to trons in the valence configuration (and not as a core contribu- tion).
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