Microscopic origin of resistance drift in the amorphous state of the phase-change compound GeTe

Aging is a common feature of the glassy state. In the case of phase-change chalcogenide alloys the aging of the amorphous state is responsible for an increase of the electrical resistance with time. This phenomenon called drift is detrimental in the application of these materials in phase-change nonvolatile memories, which are emerging as promising candidates for storage class memories. By means of combined molecular dynamics and electronic structure calculations based on density functional theory, we have unraveled the atomistic origin of the resistance drift in the prototypical phase-change compound GeTe. The drift results from a widening of the band gap and a reduction of Urbach tails due to structural relaxations leading to the removal of chains of Ge-Ge homopolar bonds. The same structural features are actually responsible for the high mobility above the glass transition which boosts the crystallization speed exploited in the device.

Figure 1

Snapshot of Ge atoms in (a) defective octahedra, (b) pyramids, and (c) tetrahedra with a wrong Ge-Ge bond.

Figure 2

Partial pair correlation functions of a-GeTe before and after annealing simulations computed for model 1 and model 2 optimized at the DFT-PBE level with harmonic phonons (see text). Vertical lines are the cutoff used to define the bonds. The shoulder at about 3.2 $\AA$ in the annealed models are due to partial crystallization (cf. Ref. [26]).

Figure 3

(a) Distribution of the number of Ge-Ge chains as a function of the number of atoms in the chain for the model 2 before, after annealing, and after metadynamics simulations. The Ge atoms are considered bonded when their distance is shorter than 3.0 $\AA$ as assigned from the Ge-Ge pair correlation function of the amorphous phase (cf. Fig. 2). Only chains containing at least four Ge atoms are shown including branches and loops. A chain of homopolar bonds is shown in the inset. (b) Distribution of the length (dimension) of chains of homopolar Ge-Ge bonds in ten 216-atom models of a-GeTe generated by quenching from the melt either within NN-MD or DFT-MD as described in Ref. [26]. A long chain in the DFT model is indicated by an arrow. The number of chains is per model, i.e., it is normalized to the number (10) of models.

Figure 4

Distribution of the local order parameter $q$ for tetrahedricity (see text) for Ge atoms with different coordination (${\mathrm{N}}_c$) in model 2 of a-GeTe. Vertical lines indicate the values of $q$ for selected ideal geometries. The distribution is further resolved for fourfold coordinated Ge atoms with or without homopolar bonds in the lower panel.

Figure 5

(a) Projection of the electronic DOS on Ge atoms belonging to Ge chains of different lengths normalized to the total DOS (model 1 and model 2 in the left and right panels). (b) The total DOS and the inverse participation ratio (IPR; see text) for the two models of a-GeTe before annealing. Panels (c) and (d) are the equivalent of panels (b) and (a) after annealing at 500 K (see text). The Engel-Vosko functional was used, the corresponding plots for the PBE functional are given in Fig. S1 in the Supplemental Material (SM) [24]. The DOS before and after annealing are aligned at the lowest energy states at about $-14$ eV as shown in Fig. 6. The vertical dashed line indicates the highest occupied KS state, which coincides with the zero of energy before annealing.

Figure 6

Electronic density of states (DOS) of (a) model 1 and (b) model 2 before (continuous line) and after (dashed line) annealing in the full energy range. For model 2 the DOS is shown also after metadynamics simulations (dot-dashed line). The Engel-Vosko functional was used; the corresponding plots for the PBE functionals are given in Fig. S2 in the SM [24]. The DOS before and after annealing/metadynamics are aligned at the lowest energy states at about $-14$ eV, which also leads to an alignment of the lower edges of the $p$-like bands at about $-4.5$ eV. The vertical dashed line indicates the highest occupied Kohn-Sham (KS) state which coincides with the zero of energy before annealing. The DOS was computed from KS orbitals at the supercell $\mathrm{\Gamma }$-point broadened with a Gaussian function with variance of 27 meV.

Figure 7

(a) Electronic DOS close to the band gap of model 2 of a-GeTe before (continuous line) and after (dashed line) metadynamics simulations (cf. Fig. 5). (b) Inverse participation ratio (IPR) superimposed to the DOS before and (c) after metadynamics simulations. (d) Projection of the DOS on Ge atoms belonging to Ge chains of different lengths normalized to the total DOS for the model after metadynamics simulations; the corresponding plot before metadynamics is shown in the right panel of Fig. 5. The Engel-Vosko functional was used; the corresponding plots for the PBE functional are given in Fig. S5 in SM [24]. The DOS are aligned as in Fig. 5.

Figure 8

Tauc plot of the a-GeTe model before (top panel) and after (central panel) metadynamics simulations. The shaded area indicate the range of energies used for the linear extrapolation that gives the Tauc optical gap. The bottom panel shows a zoom of the linear plot close to the Tauc gap. The Engel-Vosko functional was used to compute the imaginary part of the dielectric function ${\varepsilon }_2\left(E\right)$.

Figure 9

Distribution of the length of chains of wrong bonds in four 459-atom models of amorphous ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ generated by quenching from the melt in DFT simulations as described in Ref. [48]. We considered chains formed by Ge-Ge bonds only, Sb-Sb bonds only, or chains containing Ge-Ge, Sb-Sb, and Ge-Sb wrong bonds. Two large chains are indicated by arrows. The atoms in the chains include branches and loops.