MATERIALS SCIENCE AND CHEMISTRY

Introduction

Materials possessing piezoelectric characteristics generate an electric signal as a response to mechanical stress, and mechanical strain if an electric field is applied.

Such materials are indispensable for actuators, transducers and sensors. Piezoelectric devices can be found in the phone and digital cameras, microscope lenses, fuel injectors, micro-pumps, inkjet printers, medical instruments.

The most prominent piezoelectric materials are based on the perovskite crystal structure but may lose their properties in nano-scaled devices.

Recently, a ferroelectric phase was stabilized in HfO2 and ZrO2 based thin films which persisted down to a few nanometer thicknesses [Bö]. In contrast to all prominent piezoelectrics, this material is based on the fluorite crystal structure. The scope of the current study is to reveal the possible piezoelectric effects. All ferroelectric films are known to be piezoelectric, but very large piezoelectric constants are found in antiferroelectric materials where the electric field induces a phase transition from a paraelectric to a ferroelectric phase. The large mechanical strain derives then from the volume difference of the participating phases. The field-induced strain mechanism is known to be realized in recently developed lead-free ceramic materials such as barium titanate, BaTiO3 (BT), bismuth sodium titanate, Bi0.5Na0.5TiO3 (BNT), and potassium-sodium niobate, K0.5Na0.5NbO3 (KNN) [Jo].

Methods

To bring the material into the antiferroelectric state, extrinsic doping can be used [2]. To explore the potential of hafnia and zirconia as piezoelectric and to find the material with the largest strain, a dopant screening study was done. 58 possible dopants were chosen as a dopant in HfO2 and ZrO2 in a concentration of 3.125% and 6.25%. Because the dopant can be inserted in several positions, a large number of doped configurations was built to find the energetically most favourable.

Finally, because the favoured crystal phase is uncertain under these conditions, the structures were considered for all relevant, competing crystal phases, among them the paraelectric and ferroelectric phase in focus.
The calculation of the energy and crystal volume of thousands of structures was then done ab initio with density functional theory calculations. Such calculations require massive parallel computer modelling.

Results

The calculations revealed at first the most favourable dopant configuration and the energetic order of the possible crystal phases. The achieved configuration furthermore depends on the oxygen chemical potential, which is controlled with the production process. The achieved results, therefore, include the recommended production condition.

Then the energetic order of the crystal phases was analyzed. In the case of paraelectric and ferroelectric crystal energies with a certain difference, which is suitable to allow a field-induced phase transition, a potential material with the desired antiferroelectric properties was recognized.

Last, the volume difference between the paraelectric and ferroelectric phase was searched and the according effective piezoelectric coefficient calculated. The final result in Figure 3 gives calculated coefficients for differently doped materials, including a specification of the required chemical potential for the production process.