Ferroelectric Switching Pathways and Energetics in (Hf,Zr)O2
Authors: Barabash Sergey V. , Pramanik Dipankar , Nishi Yoshio , Magyari-Kope Blanka , Zhai Yahong 
Published: February 2020

The recent discovery of ferroelectricity and antiferroelectricity in doped and pure (Hf,Zr)O2 films [1] have spurred intensive research. Compared to the more traditional ferroelectrics such as PZT, (Hf,Zr)O2 films have the advantage of a larger band gap, more uniform structure (lack of layering), and are expected to meet fewer integration problems, as evidenced by other phases of (Hf,Zr)O2 being successfully integrated into the mass-manufactured devices. Unlike the widely studied perovskite-based ferroelectrics, (Hf,Zr)O2has a distorted fluorite structure. Several recent theoretical studies considered the mechanism of ferroelectric switching in this structure and arrived at somewhat conflicting conclusions. The effect of the additional “dopants” on the ferroelectric behavior is of particular interest, however, the earlier theoretical predictions of this effect do not match the experimental data.
Here, we use density functional calculations (including the highly accurate hybrid HSE) to achieve a deeper understanding of the phase stability and of switching mechanisms that could help improving the ferroelectric characteristics critical for applications. Since the saturation polarization is only defined with respect to a particular switching pathway, changes to the pathway energetics could alter the observed polarization even in the absence of substantial changes to the equilibrium fully polarized state. For example, in HfO2, the calculations predict that the intrinsic spontaneous polarization of 0.51 C/m2 could be increased to 0.68 C/m2 if one could suppress switching via the normally lowest-energy pathway. The observed remanent polarization (which is a lower value due to polycrystallinity and the domain structure) would also increase.
To gain insight into this possibility, we start by developing a unified view of different fluorite-based phases. Noting that the ferroelectric Pca21
and the high-pressure antiferroelectric Pbca phases are particular orderings within the same fractionally-occupied “parent” orthorhombic Pbcm lattice, we consider other possible orderings within the same “parent” lattice. In all these structures, half of the oxygen atoms remain unpolarized, and the other half decorate the polarized sites of the Pbcm structure, thus forming two sublattices. We demonstrate that this lattice also gives rise to the monoclinic P21/cphase.
Next, we systematically study the energetics of possible ferroelectric switching pathways in different environments. We find that the energetically preferred transformation leading to the change in the net polarization does not connect simply the two oppositely-polarized ferroelectric decorations of the same “parent” Pbcm lattice. Instead, in the absence of defects and dopants, the lowest-energy pathway connects two ferroelectric configurations belonging to different“parent” lattices (see figure).
Contrary to a trivial energy barrier profile reported earlier [2] we find that the lowest-barrier pathway has a secondary energy minimum at the transformation midpoint (cf. figure inset). In this secondary minimum region, the unpolarized oxygen sublattice rapidly develops a strong distortion, and the structure approaches that of the tetragonal P42/nmc phase. A similar pathway was recently considered in Ref.[3]; however, contrary to findings of Ref.[3] we find that at T=0K the ferroelectric structure is clearly preferred to the tetragonal one in both HfO2 and ZrO2, and is stabilized at finite temperatures by vibrational entropy. The same low energy barrier is also found in alternative polarization switching pathways that change the roles of the two oxygen sublattices. Accounting for multiple switching pathways with identical activation energy may be important when evaluating the switching mechanisms in the presence of defects. Finally, we show that in the presence of a moderate strain (particularly with a shear component), switching may also proceed via rotating the polarization direction by ~90o, rather than reversing it. This analysis builds the framework for further studies of the effect of alloying and of defects on the switching barriers. In particular, we discuss the relative effects of the oxygen vacancies and of alloying HfO2 with ZrO2.

References

[1] T. S. Boscke et al, Appl. Phys. Lett., 99, 102903 (2011); J. Müller et al, Nano Letters, 12, 4318 (2012).
[2] Clima et al., Appl. Phys. Lett. 104, 092906 (2014).
[3] Reyes-Lillo et al. Phys. Rev. B 90, 140103(R) (2014).

Figure 1