Considering its very simple stoichiometry, GeTe is a rather unconventional and complex compound from the fundamental point of view. In its amorphous phase (a-GeTe), it is covalently bond, mainly in 4-fold coordinated sp3 tetrahedra,[16] a configuration quite commonly found with amorphous semiconductors.[17] In fact, the electrical and optical properties of a-GeTe are what one could expect from any amorphous semiconductor. It is really the crystalline phase of GeTe (c-Gete) that displays extraordinary properties.
Ge Te
Figure 1.2:Schematic model of a cubicβ-GeTe crystal with its rock-salt structure.
To fully describe its structure, it is best to start with a simplified model where all Ge and Te atoms are sitting on their own sub-lattice, in a rock-salt structure. Incidentally, this cubic GeTe crystalline phase does exist at high temperature, and is called theβ-GeTe phase (Figure 1.2). While the rock-salt structures are usually found for crystals with a stronger ionic character, more compatible with the necessity to accommodate six direct neighbors, the octahedral configuration in GeTe is stabilized by another phenomena; it is owed to resonant bonding.
1.2.1 Resonant bonding
Both Ge and Te use electrons in their outerpshell to create bonds, and between them they possess three electrons in average per atom. This amount is clearly insufficient for the for-mation of saturated bonds with all six neighbors. Instead, a compromise is reached by adopting a resonant state, stemming from the superposition of equivalent virtual states where they would form saturated bonds with only half of the neighbors. Bonding is therefore achieved in each of the three dimensions by one unsaturated resonant orbital, binding each atom with the two neighbors at opposite sides.[2,18] Resonant bonding is illustrated in the case of pure Sb in Figure 1.3. This peculiar bonding mechanism, which can neither be defined as ionic, nor as hybridized,[19]is truly at the origin of the distinct optical properties of c-GeTe. In this configuration, the p electron density is highly de-localized and polarizable, which has a critical incidence on the dielectric function and reflectivity of the material.[2,20]
Virtual state C
1Virtual state C
2Resonant bonding
Figure 1.3:Schematic model of crystalline Sb, with its resonant bonds originating from the superposition of the two virtual statesΨ1andΨ2.[2]
1.2.2 Peierls distortion
The best proof of the compliance in this resonant structure resides in the second funda-mental phenomenon that defines its shape: Peierls distortions, also called Yahn-Teller effect when applied to covalent molecules. These terms describe the intrinsic desire for any metallic periodic chain of atoms to form dimers. Because from an electronic point of view, going from a mono-atomic chain to di-atomic means splitting the single metal-lic band into two separate bands and opening a bandgap at the Fermi level. This has for effect to stabilize the system by lowering slightly the energy of the occupied states, while raising the level of the empty conduction band. This is illustrated schematically in Figure 1.4. Of course the trade-off is that the elastic energy is upset, the atoms being displaced from their ideal positions.[21]
a
Mono‐atomic chain
a
Dimerization
0 k π/a
E(k)
E
F0 k π/a
E
PeierlsFigure 1.4:Schematic band diagrams showing the electronic stability gained by dimerization of a mono-atomic chain.
But in resonantly bonded structures, displacing atoms does not cost so much elastic en-ergy, because of their compliance and high electron delocalization discussed above. As long as the porbitals overlap each other, the structure maintains a good stability.[22] In GeTe, Peierls distortion has for effect the formation of alternated short strong bonds and longer weaker ones.[19,23]Incidentally, it has been shown to be favorable for these short and long bonds to be distributed in an orderly fashion, into layers in the ⟨111⟩ direc-tion.[24]As a result, the crystal is elongated in this direction, leading to a rhombohedral distortion of the cubic rocksalt unit cell. The structure of α-GeTe found at room
tem-perature (RT) is thus obtained, as illustrated in Figure 1.5. In this schematic model, the short strong bonds are represented by thicker connectors, while the long weak bonds are thinner.
Figure 1.5:Schematic model ofα-GeTe, with the primitive cell in rhombohedral coor-dinate system highlighted. The additional atoms of the distorted rocksalt unit cell are shown in transparent overlay.
The direct consequence of this ordered rhombohedral distortion is a shift of the Ge sub-lattice with respect to the Te atoms. The two subsub-lattices no longer share the same center of charge, a ferroelectric polarization is induced inα-GeTe.[25–28]At a longer range, This dipolar moment also exists spontaneously, already without prior polarization by an ex-ternal field. The favorable ordering of the Peierls distorted bonds acts like a driving force, guiding and aligning the polarization direction in neighboring crystalline unit cells.
Rashba spin-splitting has also been demonstrated in GeTe.[29] It is intriguing that such properties are present in GeTe, because they are usually expected from two-dimensional systems. It is again the alternation of the strong and weak bonds that give the GeTe sim-ilar properties than layered materials. The Rashba effect is of special interest in GeTe be-cause it synergies very well with its ferroelectric properties. Indeed, the dipolar moment in GeTe could be utilized to control and switch the electronic spin simply via an electric field.[30,31] The coupling between these properties opens up a whole new dimension of possible spintronic devices.
As stated above, GeTe adopts a cubic β-GeTe structure at high temperature (∼720K), which can initially lead to think that the Peierls effect is suppressed. This could even be understood from the schematic in Figure 1.4; as thermally activated electrons start filling the higher energy states in the conduction band, the splitting of the bands is not favorable anymore, and it would be better to merge the bands again and go back to a periodic mono-atomic chain. This view has however been challenged:[32] Using X-ray absorption fine structure (EXAFS) measurements, it has been shown that bond hierarchy by Peierls effect was still present in the cubicβ-GeTe phase, except that the long and short bonds would be randomly distributed, leading to a structure that appears to be cubic in average.
1.2.3 Intrinsic Ge vacancies
As shown very schematically in Figure 1.4, the Peierls distorted GeTe should be a semi-conductor with its Fermi level in the middle of the gap. But this is contradicted by exper-imental data, where p-type conduction with a carrier concentration of the order of 1020 cm−3is typically measured.[33–35]The reason for this discrepancy has been identified as the presence of defects in the form of Ge vacancies in a far from negligible concentration of∼8−10% on the Ge sublattice.[36]These defects have been shown to have the lowest formation energy among a collection of different possible candidates.[37]In fact, starting from a perfect crystal, with a Fermi level in the middle of the bandgap, the formation energy of Ge vacancies is even negative, meaning that they will form spontaneously and are intrinsic to the material.
In the same publication, it has been shown that the germanium vacancy is "self-healing", meaning that upon removal of one Ge atom, the neighboring Te atoms keep their three-fold resonantporbitals and simply bind more strongly to the other Ge atom still present on the other side. But these p states still need the electrons previously provided by the Ge atom. With each less Ge atom, only the associatedsstate is truly removed, with its concomitant need for two electrons. But four outer-shell electrons are taken out of the system. Therefore, each vacancy leads to a total of two missing electrons, or in other words, the formation of two holes. On the band diagram, the introduction of these in-trinsic holes will lead to a lowering of the Fermi level toward the valence band. And as the Fermi level is lowered, the formation energy of further vacancies gradually increases and becomes less likely. By the time an equilibrium concentration of Ge vacancies is reached, the Fermi level is already in the top part of the valence band, giving to GeTe it’s
characteristic but at first unexpected p-type conduction. Combined with the intrinsic fer-roelectric polarization, these two electric properties that are not often found in the same