Thin Ferroelectric Film between Double Schottky Barriers
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Thin Ferroelectric Film between Double Schottky Barriers Lyuba A. Delimova 1, Igor V. Grekhov 1, Dmitri V. Mashovets 1 Sangmin Shin2, June-Mo Koo3, Suk-Pil Kim3, Youngsoo Park3 1 Solid State Electronics Division, Ioffe Physicotechnical Institute RAS, Politekhnicheskaya 26, St.Petersburg 194021, Russian Federation. 2 Materials & Devices Laboratory, Samsung Advanced Institute of Technology, Suwon 440-600, Korea. 3 Process Engineering Laboratory, Samsung Advanced Institute of Technology, Suwon 440-600, Korea. ABSTRACT Thin-film uniform metal-ferroelectric-metal (M/F/M) structure between back-to-back Schottky barriers (SBs) is considered. The ferroelectric is assumed to be a p-type semiconductor, and the film thickness is far less than the depletion layer induced by the SB. Numerical integration of the Poisson equation is used to analyze the influence of double Shottky barriers on the distributions of the electric field, potential, and polarization across the film thickness as functions of external bias and the film electrical history. The range of structure parameters is determined, where the Poisson equation for M/F/M structure can be solved analytically providing an obvious and easy-to-interpret representation of the M/F/M behavior. Electric fields induced by back-to-back SBs under zero external bias compensate each other to a great extent. As a result, the potential across the ferroelectric film remains virtually unchanged providing the flat-band condition in the energy diagram of zero-biased M/F/M structure; in fact, the external bias applied to M/F/M structure exerts influence only on the reverse-biased barrier. INTRODUCTION A metal/ferroelectric/metal (M/F/M) thin-film structure is one of the key elements of modern ultra-large-scale-integration memory; it can be used both as a high dielectric constant capacitor for stored charge of dynamic random access memory (DRAM) [1], and a polarization-switching capacitor of nonvolatile random access memory (NVRAM) [2]. The basic operations of a memory element are information writing, storage, and reading. These functions are executed by applying an external bias of different value and polarity to an M/F/M structure. The most widely researched ferroelectric films (FFs), such as PbZrxTi1-xO3, (BaSr)TiO3, SrBi2Ta2O9 perovskite oxides, can be considered as wide-bandgap semiconductors. Therefore, a barrier at the metal ferroelectric interface can be regarded as the Schottky barrier (SB), which arises due to the difference between the metal work function and electron affinity of a semiconductor [3]. The SB induces a space charge region in the ferroelectric where an internal electric film E(x), potential ψ(x) and polarization P(x) depend on the distance x following the Gauss’ law ∂E ρ = ∂x ε + ∂P o ∂E ∂ψ = − E (x ) ∂x
(1)
(2)
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∂P ∂P ε −1 = ρ( ) , where ε = 1 + ε o−1 ∂x ε ∂E
,
(3)
Here ρ and ε are the density of free space charge and dielectric constant of a ferroelectric, εo = 8.85*10-14 F/cm. A standard way to find E(x), Ψ(x), and P(x) distributions in an
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