Microscopic mechanism of polarization-controlled electron tunneling into ferroelectric surfaces under a biased conductive tip

Maksymovych and co-workers (Science 2009) showed that electrons injected from a biased atomic-force-microscope tip into epitaxial Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ ferroelectric films tunnel in the high-field Fowler–Nordheim regime, with abrupt current jumps coinciding with local ferroelectric polarization switching and conductance contrasts up to 500:1. Quantitatively, their current–voltage data could be fitted equally well by two mutually incompatible microscopic pictures: field localization at a nanoscale tip asperity (a conducting-disk model requiring an emitting asperity of radius below roughly 5 nm, i.e. an effective tunneling area of about $4\ \mathrm{nm}^2$) and a thin, polarization-dependent Schottky/depletion barrier in a defect-doped, effectively semiconducting ferroelectric (with rechargeable gap-state densities up to about $10^{20}\ \mathrm{cm}^{-3}$ and an extracted barrier height of about $1.1\ \mathrm{eV}$). The open problem is to determine which microscopic mechanism actually governs this tip–ferroelectric junction — and, more broadly, to establish the origin and spatial extent of the effective tunneling area, the density distribution and screening role of gap states and defects, and the electrostatic and chemical structure of the tip–ferroelectric interface. Later work by the same group (2011) partially discriminated the mechanisms for this junction (low-bias trap-assisted interface tunneling — tunneling relayed through intermediate defect levels in the barrier — plus high-bias bulk hopping — thermally assisted jumps between localized defect sites —, with disorder dominated by interfacial barrier-height heterogeneity), and the parallel ferroelectric-tunnel-junction device literature settled the analogous question for metal/ultrathin-ferroelectric/metal junctions; the general tip-junction mechanism question remains open.

Background

A ferroelectric is an insulating crystal with a spontaneous, switchable electric polarization P. The bound polarization charge at a surface is screened by free carriers, adsorbates, or defects; how completely this screening occurs controls the local electrostatics. Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ (PZT) is the archetypal perovskite (a common cubic-oxide crystal structure shared by many functional ceramics) ferroelectric used in memories and actuators. Because ferroelectricity usually vanishes below a few nanometres of film thickness, while quantum tunneling across an insulating barrier requires an ultrathin barrier, the idea of a ferroelectric tunnel junction — a metal/ultrathin-ferroelectric/metal device whose resistance depends on the polarization direction, an effect called tunneling electroresistance (TER) — was for decades hindered by the absence of suitable junctions. In 2009, several groups demonstrated TER, either in capacitor-type junctions with ultrathin barriers or with local probes.

In this context, Maksymovych, Jesse, Yu, Ramesh, Baddorf, and Kalinin (Science 324, 1421, 2009) used a different route that avoids the ultrathin-film limit: they injected electrons from a Pt-coated atomic-force-microscopy (AFM) tip into a relatively thick ($30\ \mathrm{nm}$) epitaxial PZT film in ultrahigh vacuum. Piezoresponse force microscopy (PFM) — a scanning-probe technique that reads the local piezoelectric strain to map ferroelectric polarization — was operated simultaneously with current measurement, so that current–voltage (I–V) curves and local switching events were recorded at the same position. The current followed Fowler–Nordheim (FN) tunneling, i.e. field-assisted quantum tunneling through a triangular barrier that dominates when the electric field is so high (of order $10^{8}$–$10^{9}\ \mathrm{V/m}$) that the barrier becomes thin on the tunneling scale; FN tunneling is identified experimentally by a linear dependence of log(I/V$^2$) on 1/V. Abrupt jumps in the current coincided, within experimental resolution, with ferroelectric switching events, and switching produced conductance changes of up to 500:1, attributed to polarization-dependent narrowing of the tunneling barrier.

The part of the paper that this problem concerns is its quantitative interpretation. Two incompatible models fitted the smooth I–V curves equally well. In the first, the tip–surface junction is modeled as a conducting disk in contact with a dielectric, which concentrates the field at a nanoscale asperity: fitting required an emitting asperity radius smaller than about 5 nm, corresponding to an effective tunneling area of roughly $4\ \mathrm{nm}^2$, much smaller than the nominal tip diameter of tens of nanometres. In the second, the ferroelectric is treated as a defect-doped wide-band-gap semiconductor (PZT is a semiconductor with a band gap of about $3.5\ \mathrm{eV}$) containing a high density (up to about $10^{20}\ \mathrm{cm}^{-3}$) of rechargeable gap states (electronic defect levels inside the band gap that can trap and release charge), so that a thin Schottky barrier — the depleted interfacial region that forms at a metal–semiconductor contact, whose width is set by the ionized defect density — forms at the tip interface; inserting the bias-dependent maximum depletion field into the FN equation fitted the data with an average Schottky barrier height of about $1.1 \pm 0.1\ \mathrm{eV}$, and the depletion width, and hence the field, becomes polarization-dependent. The two pictures differ in where the current flows (a few-$\mathrm{nm}^2$ patch under a tip asperity versus the screened interface region of a doped semiconductor), in what sets the effective tunneling area, and in what the extracted parameters mean physically. The authors could not determine from these measurements which scenario governs the junction, and identified the spatial extent and microscopic origin of the effective tunneling area, the role and density distribution of gap states or defects in screening the polarization charge, and the detailed chemical/electrostatic structure of the tip–ferroelectric interface as open issues requiring further experiment and modeling.

Problem Statement

Determine the microscopic mechanism by which a biased conductive scanning-probe tip injects electrons into a ferroelectric surface, and the microscopic structure of that junction, in the regime where the current is polarization-controlled and Fowler–Nordheim-like. Specifically: (i) identify which physical picture governs the junction — field localization at a nanoscale tip asperity (the conducting-disk picture, with an effective emitting area of order a few $\mathrm{nm}^2$) or a thin, polarization-dependent Schottky/depletion barrier formed in a defect-doped, effectively semiconducting ferroelectric — and establish the bias, environment, tip-geometry, and sample-defect conditions under which each channel (including trap-assisted interface tunneling, i.e. tunneling relayed through intermediate defect levels in the barrier; bulk hopping, i.e. thermally assisted jumps between localized defect states; and electrochemical/ionic motion, i.e. field-driven redistribution of charged ions or vacancies) dominates; (ii) determine the origin and spatial extent of the effective tunneling area, i.e. whether the current-carrying patch is set by tip asperity geometry, by the field distribution of the tip–surface electrostatics, or by the polarization-dependent depletion region; (iii) determine the density and spatial distribution of gap states and charged defects near the ferroelectric surface and quantify their role in screening the bound polarization charge that produces the polarization-dependent barrier narrowing; and (iv) establish the chemical and electrostatic structure of the tip–ferroelectric interface (charge, band alignment, and any mobile ionic species) that underlies the extracted barrier parameters. The question is jointly posed across all of (i)–(iv), including the conditions map in (i), which together constitute the research target.

References

1. Peter Maksymovych, Stephen Jesse, Pu Yu, Ramamoorthy Ramesh, Arthur P. Baddorf, Sergei V. Kalinin (2009). Polarization Control of Electron Tunneling into Ferroelectric Surfaces. Science 324, 1421-1425. DOI: 10.1126/science.1171200, https://doi.org/10.1126/science.1171200
2. Peter Maksymovych, Minghu Pan, Pu Yu, Ramamoorthy Ramesh, Arthur P. Baddorf, Sergei V. Kalinin (2011). Scaling and disorder analysis of local I-V curves from ferroelectric thin films of lead zirconate titanate. Nanotechnology 22, 254031. DOI: 10.1088/0957-4484/22/25/254031, https://doi.org/10.1088/0957-4484/22/25/254031
3. A. N. Morozovska, E. A. Eliseev, S. V. Svechnikov, A. D. Krutov, V. Y. Shur, A. Y. Borisevich, P. Maksymovych, S. V. Kalinin (2010). Finite size and intrinsic field effect on the polar-active properties of ferroelectric-semiconductor heterostructures. Physical Review B 81, 205308. DOI: 10.1103/PhysRevB.81.205308, https://doi.org/10.1103/PhysRevB.81.205308
4. Sergei V. Kalinin, Stephen Jesse, Alexander Tselev, Arthur P. Baddorf, Nina Balke (2011). The Role of Electrochemical Phenomena in Scanning Probe Microscopy of Ferroelectric Thin Films. ACS Nano 5, 5683-5691. DOI: 10.1021/nn2013518, https://doi.org/10.1021/nn2013518
5. Peter Maksymovych, Anna N. Morozovska, Pu Yu, Eugene A. Eliseev, Ying-Hao Chu, Ramamoorthy Ramesh, Arthur P. Baddorf, Sergei V. Kalinin (2012). Tunable Metallic Conductance in Ferroelectric Nanodomains. Nano Letters 12, 209-213 (online 2011). DOI: 10.1021/nl203349b, https://doi.org/10.1021/nl203349b
6. A. Gruverman, D. Wu, H. Lu, Y. Wang, H. W. Jang, C. M. Folkman, M. Ye. Zhuravlev, D. Felker, M. Rzchowski, C.-B. Eom, E. Y. Tsymbal (2009). Tunneling electroresistance effect in ferroelectric tunnel junctions at the nanoscale. Nano Letters 9, 3539-3543. DOI: 10.1021/nl901754t, https://doi.org/10.1021/nl901754t
7. Daniel Pantel, Haidong Lu, Silvana Götze, Peter Werner, Dong Jik Kim, Alexei Gruverman, Dietrich Hesse, Marin Alexe (2012). Tunnel electroresistance in junctions with ultrathin ferroelectric Pb(Zr0.2Ti0.8)O3 barriers. Applied Physics Letters 100, issue 23, article 232902. DOI: 10.1063/1.4726120, https://doi.org/10.1063/1.4726120
8. Z. Wen, C. Li, D. Wu, A. Li, N. Ming (2013). Ferroelectric-field-effect-enhanced electroresistance in metal/ferroelectric/semiconductor tunnel junctions. Nature Materials 12, 617-621. DOI: 10.1038/nmat3649, https://doi.org/10.1038/nmat3649
9. Vincent Garcia, Manuel Bibes (2014). Ferroelectric tunnel junctions for information storage and processing. Nature Communications 5, 4289. DOI: 10.1038/ncomms5289, https://doi.org/10.1038/ncomms5289
10. A. V. Ievlev, C. C. Brown, J. C. Agar, G. A. Velarde, L. W. Martin, A. Belianinov, P. Maksymovych, S. V. Kalinin, O. S. Ovchinnikova (2018). Nanoscale Electrochemical Phenomena of Polarization Switching in Ferroelectrics. ACS Applied Materials & Interfaces 10, 38217-38222. DOI: 10.1021/acsami.8b13034, https://doi.org/10.1021/acsami.8b13034
11. F. Zhang, H. Fan, B. Han, Y. Zhu, X. Deng, D. Edwards, A. Kumar, D. Chen, X. Gao, Z. Fan, B. J. Rodriguez (2021). Boosting Polarization Switching-Induced Current Injection by Mechanical Force in Ferroelectric Thin Films. ACS Applied Materials & Interfaces 13, 26180-26186. DOI: 10.1021/acsami.1c04912, https://doi.org/10.1021/acsami.1c04912
12. Seongmun Eom, Pravin Kavle, Deokyoung Kang, Yeongyu Kim, Lane W. Martin, Seungbum Hong (2025; online 2024). Unveiling the Nanoscale Dielectric Gap and Its Influence on Ferroelectric Polarization Switching in Scanning Probe Microscopy. Advanced Functional Materials 35, issue 11, article 2406944. DOI: 10.1002/adfm.202406944, https://doi.org/10.1002/adfm.202406944