On the origin of in-gap states in amorphous Ge$_2$Sb$_2$Te$_5$

Abstract

The localized states in the band gap of amorphous phase change alloys like Ge$_2$Sb$_2$Te$_5$ control the electrical conduction via the Poole-Frenkel mechanism. Understanding the origin of in-gap states and their evolution in time during aging of the glass is therefore important for the control of the resistance drift in phase change memory devices. Here, we use a machine learning interatomic potential to generate several models of Ge$_2$Sb$_2$Te$_5$ whose electronic structure is then analyzed within density functional theory with a hybrid functional. A detailed statistical analysis of the structural motifs on which the in-gap states are localized, reveals that the vast majority of in-gap states involve wrong bonds (homopolar or Ge-Sb bonds) often accompanied by Ge in tetrahedral configurations or overcoordinated Ge and Sb atoms. Metadynamics simulations mimicking glass aging support the picture that structural relaxations lead to the depletion of in-gap states and then to an increase of resistance. The simulations thus provide important insights for the mitigation of the resistance drift in phase change memory devices.

Figures (8)

• Figure 1: Distribution of the coordination numbers resolved per chemical species in the 7992-atom a-GST model of Ref. omar2024. The distributions are computed by integrating the partial pair correlation functions up to the bonding cutoff given in Table \ref{['coord']} (see Ref.omar2024).
• Figure 2: a) Electronic density of states (DOS) and Inverse Participation Ratio (IPR) of the 999-atom model. The zero of energy is the highest occupied state (highest occupied molecular orbital, HOMO). b)-e) Isosurface of the most localized KS states, the HOMO (hole trap), the LUMO and LUMO+1 deep electron traps, and the LUMO+2 shallow electron trap. Ge, tetrahedral Ge (Ge$_{\rm T}$), Sb and Te atoms are depicted with gray, green, yellow and blue spheres (see color code in panel b). Isosurfaces with different signs are depicted with different (orange or azure) colors. The LUMO is localized on the axial Ge-Te bonds of an overcoordinated Ge atom. The LUMO+1 is localized on the axial bonds of a long chain Sb-Sb-Ge-Sb-Te-Sb-Sb with wrong bonds. The LUMO+2 is localized on a Sb-Ge-Ge-Ge chain with wrong bonds atoms, which involves overcoordinated Sb/Ge and tetrahedral Ge atoms..
• Figure 3: Electronic density of states (DOS) and Inverse Participation Ratio (IPR) of two 297-atom NN models a) with and b) without in-gap states. The zero of energy is the HOMO.
• Figure 4: a) Comparison of the electronic DOS averaged over NN models (red curve) and over DFT models (blue curve) close to the band gap. All the DOS are aligned to the bottom of the deep 5s band of Te. The zero of energy is the HOMO assigned by the integration of the average DOS. b) Electronic DOS averaged over all models. The DOS at the VB and CB edges is fitted with a band-like contribution (black continuous curves) $N_v\sqrt{E_v-E}$ and $N_c\sqrt{E_c-E}$ where $E_v$=-0.099 eV and $E_c$=0.571 eV are the band edges that yield a band gap of 0.67 eV. In turn $N_{v/c}=\frac{1}{2\pi^2} (\frac{2m_{v/c}^*}{\hbar^2})^{\frac{3}{2}}$ assign the effective masses $m_v^*$= 2.16 and $m_c^*$ = 1.8 (in electronic mass) from $N_{v}=$ 0.0219 and $N_{v}=$ 0.0168 states/eV$^\frac{3}{2}$/Å$^3$. The edge of the valence band above -0.099 eV is fitted by an Urbach tail $exp({-E}/{E_U})$ with $E_U$=85 meV. The presence of shallow acceptor (empty) states close to the CB prevents the fitting of the Urbach tail at the conduction edge. c) The same of panel b) in semilogarithmic scale to highlight the exponential Urbach tail at the VB edge.
• Figure 5: Example of localized in-gap states showing the typical features of the atomic environment discussed in the text. a) An overcoordinated Ge atom in a crystal-like environment. b) A long chain of wrong bonds including an overcoordinated Sb atom and a tetrahedral Ge atom. c) A four-coordinated Ge atom bonded to two tetrahedral Ge atoms with two wrong bonds. The central Ge atom forms two axial bonds with the two tetrahedral Ge atoms. d) A two-coordinated Te atom forming three long Te-Te contacts. The color code is the same used in Fig. \ref{['DOS-999']}. Ge, tetrahedral Ge (Ge$_{\rm T}$), Sb and Te atoms are depicted with gray, green, yellow and blue spheres.