Ferroelectrics at the nanoscale:a first principle approach.

NUÑEZ, MATIAS

Advances in Ferroelectrics

InTech

Año: 2012; p. 401 - 427

Understanding the finite size effects in ferroelectric thin film is now days a hot andchallenging topic of research. Being a collective effect, it was thought for a long timethat ferroelectricity was suppressed in small particles and thin films below a critical size ofabout 100 Angstrom. This would prevent the use of ferroelectric materials in devices smaller than this threshold. However, new advances in the synthesis and characterization of ferroelectric oxide thin films with a control at the atomic scale, have allowed the observation of ferroelectricitywell below the previously accepted critical thickness of 10 nm. This has broughta great amount of research activity within the field in order to understand ferroelectricityin ultrathin films.Investigation in the field is also driven by the possible use of ferroelectric materialsin various micro-electronic devices that take advantage of their multifunctional properties.The existence of a switchable spontaneous polarization is at the basis of the design ofnon volatile ferroelectric random access memories (FERAMs), where one bit of informationcan be stored by assigning one value of the Boolean algebra (?1? or ?0?) to each of the polarizationstates. Also, the high dielectric permitivity of ferroelectrics makes them possiblecandidates to replace silica as the gate dielectric in metal-oxide-semiconductor field effecttransistors (MOSFETs). Their piezoelectric behavior enables them to convert mechanicalenergy in electrical energy and vice versa. Their pyroelectric properties are the basis forhighly sensitive infrared room temperature detectors.The current miniaturization of microelectronic technology, imposed by the semiconductorindustry, raises the question of possible size effects on th properties of the components.Except for the case of the gate dielectric problem in MOSFET?s, the thickness ofthe films used in contemporary applications is still far away from the thickness range wheresize effects become a concern; therefore the question at the moment is merely academic.Nevertheless, it is very possible that the fundamental limits of materials might be reachedin the future.Despite the efforts and advancement in the field, both theoretically and experimentally, many questions still remain open. The main reason for the poor understanding of some of the size effects on ferroelectricity is the vast amount of different effects that compete and might modify the delicate balance between long range dipole-dipole electrostatic interactions and the short range forces, whose subtle equilibrium is known to be at the origin of the ferroelectric instability.This drive towards the miniaturization of electronic devices has offered newchallenges for the description of polarization at the nanoscale, as size effects and interfacestructure strongly affect the polarization. First principles calculations are in a uniqueposition to shed light on these problems since they can be used to analyze detailed physicalfeatures athe nanoscale and can describe the details of the electronic and structural behaviorof these systems that other phenomenological theories cannot address. The success of theseapproaches is well documented in the literature: since the seminal paper of Junquera etal 1, where the problem of polarization of nanoscale thin films was addressed for the firsttime using ab initio simulations, the number of these studies has burgeoned.In this respect, Density Functional Theory (DFT) has played and still plays a pivotal role in the field of computational Physics of materials. Within the DFT framework, the ground state of an interacting system of electrons in an external potential can be expressed as a functional of the ground state electronic density.Compared with other methods that use the complex wavefunctions of the system, itsapproach is interesting as it relies only on the density and not on the complete knowledgeof the N-electron wavefunction. Although the theory is exact, there is an unknown part inthe energy functional called the exchange correlation energy that needs to be approximatedfor practical applications. Despite its limitations, DFT?s applications continuously increasedue to their better scaling with the number of atoms. Moreover, the above limitations areassociated with the particular choice of approximation scheme for the exchange and correlationfunctional that however can be improved with the introduction of more sophisticatedapproaches.The chapter will give an overview of the main concepts involved in the moderntheory of polarization2. A definition of a local polarization will be given in terms of thecenters of the wannier functions3 associated with the band structure of the system. Next,some basic electrostatic notions related with ferroelectric films will be given, in particularthe concept of depolarization field and screening by metal contacts.