Carrier accumulation near electrodes in ferroelectric films due to polarization boundary conditions

Abstract

We study the effect of surface polarization on the distribution of free carriers in a wide bandgap semiconductor ferroelectric (FE) film using a thermodynamic approach. We show that free carriers, namely, holes and electrons from ionizable impurities or atomic vacancies can accumulate near the film-electrode interface, if FE polarization profile has a very steep change near the surface that is specified by the extrapolation length. Such an outcome is just the opposite of what happens in a Schottky junction in a partially or fully depleted film. This is also an entirely different effect than what has been often studied in similar structures, where the work function and screening length of the electrode metal determines the electronic character of the interface. Even for low-to-moderate densities of ionizable defects with states within the bandgap close to the band edges, high densities of carriers can localize close to the electrodes in a single domain state FE film when above a critical thickness. For very low densities of such ionizable defects, short extrapolation lengths cause electrical domain formation with minimal carrier accumulation because of the already weak depolarizing fields. This is also true for films below a critical thickness with low-to-moderate densities of ionizable impurities, i.e., electrical domains get stabilized regardless of defect density. The implications of our findings for polarization controlled Schottky to Ohmic-like transition of an interface and experimental results are discussed. It is also found that interfaces of an n-type FE heterostructure can behave like a p-type depending on the barrier heights and impurity density. We conclude that, for low-to-moderate ionizable impurity densities, it is the rate of change of polarization at the interface with position rather than solely its presence that leads to carrier accumulation and that both interfaces can become Ohmic-like with opposite signs of carriers.