First-principles study of metal-induced gap states in metal/oxide interfaces and their relation with the complex band structure

Abstract

We develop a simple model to compute the energy-dependent decay factors of metal-induced gap states in metal/insulator interfaces considering the collective behaviour of all the bulk complex bands in the gap of the insulator. The agreement between the penetration length obtained from the model (considering only bulk properties) and full first-principles simulations of the interface (including explicitly the interfaces) is good. The influence of the electrodes and the polarization of the insulator is analyzed. The method simplifies the process of screening materials to be used in Schootky barriers or in the design of giant tunneling electroresistance and magnetoresistance devices. PACS numbers: 73.40.Gk, 73.30.+y, 77.80.Fm,Interfaces between different oxide materials exhibit a fantastic variety of functional properties, some of them intrinsic to the boundary between the constituent compounds [1]. A ubiquitous type of interface is that formed between a metal and an insulator or semiconductor, since the presence of electrodes is required for the application of electric fields in solid state devices. At any metal/insulator interface, bulk Bloch states in the metal side of the junction with eigenvalues below the Fermi energy and within the energy gap of the insulator cannot propagate into the insulating side. These states do not vanish right at the interface either, but they decay exponentially as they penetrate into the insulator [2]. Indeed, the tails of the metal Bloch states might have a significant amplitude for a few layers from the interface, creating a continuum of gap states [the so-called metal-induced gap states (MIGS)] [2]. These MIGS are essential to determine many interfacial properties. The transfer of charge associated to them contribute to the interfacial dipole, which enter into most of the models describing the formation of Schottky barriers. For this reason, theory of MIGS were deeply studied in semiconductor heterostructures [3, 4]. More recently, the attention has turned to metal/oxide interfaces, mostly due to several works that have first predicted [5, 6] and later demonstrated giant tunnel electroresistance [7-10] and magnetoresistance [11][12][13] in ferroelectric/metal junctions, where the decay length of the MIGS plays a major role.The eigenstates of the Hamiltonian for the interface can be described as the matching at the junction of two wave functions: an ordinary bulk Bloch state on the metal side, and an exponentially decaying function on the insulator side. Assuming that the interface is periodic in the plane parallel to the boundary [referred to as the (x, y) plane], then the components of the wave vectors parallel to the interface, k , are real and have to be preserved when the electron crosses the junction [14]. Therefore, the previous matching is possible only if the two wave functions do have the same associated energy, symmetry, and k [15].The exponential tails within the insulator decay only in the direction perpendicular to the junction (referred to as the z-direction), and ca...

Predictive modelling of ferroelectric tunnel junctions

“…54,57,58 In the case of ferroelectrics, the CBS has been calculated for BTO 20,23,52,59 and PTO. [60][61][62][63] The results show that there are multiple decay rates in the barrier for propagating states with different symmetry. The largest contribution to the transmission is expected from the bands that have lowest decay rates.…”

Designing functional ferroelectric interfaces from first-principles: dipoles and band bending at oxide heterojunctions

“…At the interface with a ferroelectric the polar distortions are perturbed, the local strain, bonding across the interface and the built-in electric field promote charge transfers and space charge build-up. In turn, these effects impact on the electronic structure, inducing relative shifts of the energy levels, modifications of band gap values, metal-induced band gap states (MIGS) and interfacial band bending effects [7,[44][45][46][47][48]. The band alignment scheme results as an effect of entangled microscopic mechanisms and plays a major role in setting the operating conditions of practical junctions [49,50].…”

“…Here it is worth highlighting that an insightful analysis of the MIGS and their effect on the interface dipole and formation of SBHs in ferroelectric/metal junctions has also been presented in [47]. These authors demonstrate that although the most penetrating bands are located at high symmetry points, for the study of tunneling conductance across ultra-thin layers or integrated quantities (where many k parallel points contribute) it is important to consider complex bands in the whole two dimensional Brillouin Zone (BZ).…”

“…These authors demonstrate that although the most penetrating bands are located at high symmetry points, for the study of tunneling conductance across ultra-thin layers or integrated quantities (where many k parallel points contribute) it is important to consider complex bands in the whole two dimensional Brillouin Zone (BZ). Also, a general recipe is outlined to estimate from the complex band structure of the bulk insulator the effective decay factor (and its dependence with the energy within the gap) of the MIGS in realistic interfaces [47].…”

“…Actually, one has to make a trade-off between using elaborate and accurate models, e.g. [45,47,55] and a practical approach which encompasses as much as possible the characteristics of the real system. To our knowledge, a proper explanation of size effects and interface specific properties in ferroelectric capacitors with ultra-thin layers is still an open issue.…”