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Nano-Ferroelectric Materials and Devices

J. F. Scott, F. D. Morrison, M. Miyake and P. Zubko

Centre for Ferroics, Dept. of Earth Sciences, University of Cambridge

Downing Street, Cambridge CB2 3EQ, U.K.

A summary is presented of recent developments in ferroelectric nanotubes, nanowires and nanodots,

their electrical characterization and related theories of their structures, including the possibility of

toroidal ordering. Also summarized is recent work on ultra-thin single crystals and a status report on

thin films, particularly in [3D] configurations for DRAM or FRAM trenched capacitors.

NANO-FERROELECTRIC MATERIALS AND DEVICES

INTRODUCTION

In the past four years in several countries, including Russia, Germany, the UK, and the

USA, ferroelectric nano-structures have been produced and characterized. At present a

variety of techniques are employed for their deposition or construction, including sol-gel,

CVD, and FIB (focussed ion beam). A popular technique involves the use of porous

sacrificial substrates of either silicon or alumina. With this method one can obtain nanotubes

and nanowires from ca. 20 nm diameter to approximately 4 microns. An SEM micrograph of

SBT nanotubes from our lab is shown in Fig.1. A high degree of registration is obtainable

with porous Si, less so with Al2O3. Meso-porous GaAs and GaN are also available.

In the present manuscript we would like to show some examples of such ferroelectric

nano-technology, together with a summary of the relevant theories and models, and

suggestions for prototype devices.

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FERROELECTRIC NANOTUBES, NANOWIRES, AND NANODOTS

Theory

There are four theories of particular relevance to nanotubes, nanowires and nanodots:

First is that of Ebenezer and Ramesh [1] for the piezoelectric response in polarized

cylindrical structures. The second is the model of Gutkin, Ovid’ko et al. [2,3] for the

behavior of misfit dislocations in a nanotube or nanowire with a core of a different material.

The third is the theory of Ginzburg [4] for toroidal ordering. And the fourth is the recent

extension of that work by Naumov et al. [5,6].

Ebenezer and Ramesh calculated the piezoelectric response for cylindrical structures

(such as nanotubes) in which the polarization lay along the tube long axis z or radially

through the wall r. They did not calculate the response to a tube with polarization azimuthally

around the tube circumference θ; however, they appear to be doing so at present (D.

Ebenezer, private communication). Because the experimental measurements to date [7] are

limited to P(θ), this is necessary before one can extract quantitative dij values for nanotubes.

Conversely, it will permit us to determine via AFM piezo-mode measurements what

percentage of polarization in a ferroelectric nanotube is along z, r, and θ.

Gutkin, Ovid’ko et al. have done some very interesting studies of misfit dislocations in

nanotubes. Normally when one prepares an epitaxial ferroelectric on a planar substrate, there

is a lattice constant mismatch that results in misfit dislocations. These dislocations lower total

energy by relieving strain. However, if you fabricate a ferroelectric nanotube having a

coherent interface with the core material, the cylindrical boundary conditions result in a

clamping that necessitates a nanotube diameter expansion for each misfit. For small nanotube

diameters this is energetically costly, and misfit dislocations are therefore forbidden. For

larger diameters, misfit dislocations can occur but are isolated, random and sparse. Finally for

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the largest nanotubes misfit dislocations are abundant and periodic. This gives rise,

theoretically, to a rich phase diagram as a function of nanotube diameter and temperature. It

should prove interesting to study these phenomena in ferroelectric nanotubes.

Ginzburg et al. showed that toroidal ordering should be possible in ferroelectrics, and

not just rectilinear parallel or antiparallel alignment of polarizations. This was extended by

Gorbatsevich and Kopayev and more recently by Naumov et al. A hunt was made for such

ordering, initially but apparently mistakenly reported by Zheludev et al. [8]. As in the more

famous case of cold fusion, such spurious reports tended to discredit the field for awhile and

deter other investigators from looking more carefully. No unambiguous report of toroidal

polarization ordering experimentally has followed.

EXPERIMENTS

I personally do not know who made the first ferroelectric nanotubes. Several groups

wisely delayed publication until patents could be filed. But the first publications were in 2002

by Mishina et al. in Moscow [9] and Hernandez et al. in Colorado [10]. Mishina used 20-30

nm diameter porous alumina, and Hernandez employed a sol-gel solution in porous Si of

greater tube diameter.

The next important step was by Alexe’s group in Halle [7], who explored various

etchants to free the ferroelectric nanorods or tubes and also measured P(θ) for a fallen tube on

a metal substrate, and by Morrison et al. in Cambridge [11,12] who removed only part of the

Si sacrificial bloc to produce a structure resembling a nano-hairbrush, which could have

nanotubes open at each end to permit its use as a microfluid device for, e.g., ink-jet printers or

liquid drug delivery systems. Fig.1 illustrates SBT nanotubes from our group.

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FIGURE 1. SEM micrograph of strontium bismuth tantalate nanotubes from misted CSD

deposition. Porous Si template from Prof. Lorenzo Pavesi at Trento University. 2 µm bar.

Devices

At present three groups are working on prototype self-trenched capacitors for DRAMs

or FRAMs. The most advanced of these is a cooperative project involving IMEC in Belgium,

S T Microelectronics in France, and groups at the University of Toulon. They have produced

[13,14] a mushroom-shaped FRAM structure with the top electrode and an SBT capacitor

extending down the sidewall, as illustrated in Fig.2. This device gives a 50% increase in

capacitance for the same area on the chip and is nearly ready to manufacture. An early

problem was that the sidewalls did not always have the same Aurivillius phase as the top part

of the dielectric layer.

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FIGURE 2. SEM cross-section of IMEC [3D] SBT capacitor, showing how the top electrode

and SBT ferroelectric layer fold down over the edges to add sidewall capacitance.

Another successful step towards [3D] nano-ferroelectric devices is trenched

electroding. This one (Fig.3) is from a Samsung-Tokyo Institute of Technology collaboration

of Funakubo et al.[15] They achieve excellent step coverage using CVD ruthenium from an

organic ruthenium-DER compound (Tosoh Corp.).

FIGURE 3. Samsung-TIT [3D] ruthenium-coating trenches (Funakubo et al. [15]).

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Cambridge [3D] structures:

Our group has also fabricated [3D] structures with Ru electrodes from Ru-DER.

These are shown in Fig.4 (M. Miyake, unpublished). In our case we were able to modify our

misted deposition system to achieve the excellent results shown below, which have a 400 nm

Ru bottom electrode conformally coating a ca. 100 micron trench. This system is being used

to provide the outer electrode on SBT nanotubes.

FIGURE 4. SEM cross-section of trenched capacitor electrode of 80 µm deep trench

deposited in our Cambridge lab with Ru-DER at 275 oC to give 2.5 nm step coverage.

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ULTRA-THIN FILMS

PVDF

For Langmuir-Blodgett films of polyvinylidene fluoride there have been some recent

developments. First Dawber et al. [16,17] showed that the coercive field varied as a single

power law

Ec(d) = A d-n (1)

over more than four orders of magnitude in thickness d, with exponent n = 0.66±0.02

satisfying the prediction of Stadler’s early work [18] and an extension [17] of the Kay-Dunn

Model, which gives n = 2/3 exactly. They also showed that there was no evidence for an

“intrinsic” switching phenomenon at very thin thicknesses, as had been proposed by Fridkin

and Ducharme [19,20]. Instead, they observed that the deviations from Eq.(1) were

quantitatively compatible with the Fermi-Thomas screening in the metal, which yielded an

instability at a thickness of ca. 2.4 nm. Then more recently Kliem and Tadros-Morgane

remeasured [21] the PVDF samples from Fridkin. They found the same result as Dawber et

al.: (1) A simple power-law describes the coercive field dependence upon thickness d for d >

2.7 nm; (2) The exponent n = 0.64 agrees exactly with that of 0.66±0.02 of Dawber et al.; (3)

There is no evidence of a different kind of switching for the thinnest films (no “two-

dimensional ferroelectricity” and no domain-wall-free “intrinsic” switching, or as Fridkin

termed it, “Landau switching”). Despite this detailed agreement, Kliem and Tadros-Morgane

did not refer to the nearly identical results of Dawber et al. or Chandra et al. Their reasons for

this “rediscovery” without citation is unknown. They wrote to the present authors that “it was

not necessary to cite this work.”

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PVDF devices

Private communication to the authors from Intel Corp. reveals that they have had an active

program to make digital computer FRAM memories from PVDF films. However, these have

not yet been successful because of problems with imprint and retention. The imprint problem

may arise from electret-like behavior of mobile charged defects.

BST

Barium strontium titanate films are good candidates for high-dielectric replacements of

capacitors in DRAMs. Their properties, including phase transitions and broadening

mechanisms were reviewed in detail by the authors very recently.[22] The results show that

the phase transition temperatures do not shift as a function of thickness and that the

broadening of dielectric peaks near transition temperatures is extrinsic, probably due to

oxygen vacancy gradients.[23]

PZT

Lead zirconate titanate is one of two ferroelectrics used for FRAMs and is favored by

Samsung, Toshiba, Fujitsu, and others (with IMEC, ST Microelectronics, and

Matsushita/Panasonic favoring SBT). Several device issues remain. Recently Liu et al. have

shown [24] that the Dawber-Scott model [25] of oxygen-vacancy-driven fatigue satisfies their

data, and Jung et al. [26] have shown that whereas the Landauer model of coercive field is

satisfied in PZT cells greater than 1 µm on a side, the smaller 0.32 µm2 and 0.19 µm2 cells for

4 Mbit and 32 Mbit FRAMs require the Pulvari model, which includes nucleation as a rate-

limiting step in switching (neglected by Landauer). The 0.19 µm2 cells meet the industry

requirements for 2007 on the FRAM roadmap.

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KNO3

Although recently neglected for device purposes because of its extreme water solubility,

potassium nitrate retains great fundamental interest as an easily-fabricated thin-film

ferroelectric. In bulk its ferroelectric phase is stable over a very narrow temperature range

and is reentrant, accessible only upon cooling, but in thin-film form the ferroelectric phase

temperature width varies as reciprocal thickness 1/d and can exceed 200K, including the full

military and commercial operating range (-50 to +130 F). What is particularly interesting is

that the phase diagram of T versus 1/d for thin films [27] strongly resembles the T versus

pressure P diagram for bulk, strongly suggesting that the 1/d dependence comes from uniaxial

stress, as in the “Pertsev” T vs. stress diagrams. Because of this and the fact that KNO3

exhibits eight phases in the P/T diagram, it is very attractive for ab initio modelling, and that

is underway by Vanderbilt. It is also notable that the maximum temperature achieved Tc(d)

achieved for thin films fits exactly the value calculated by neglecting electrostriction in the

Landau-Devonshire free energy. This shift of Tc is 69K from bulk and suggests that in thin

films the striction is clamped out, i.e. neutralized by the substrate misfit stress. Memory

devices could probably be made from this material, provided a sealed-atmosphere FAB line

was used with dry nitrogen ambient.

ULTRA-THIN SINGLE CRYSTALS

Two systems have been fabricated via focussed ion beam (FIB) techniques down to ca.

70 nm thickness by Gregg et al. In Belfast. The first is BaTiO3 – for which the SEM results

of nanodomain structures are amazing (Fig.5). There are no theories for details of domain

wall structures in [3D] nano-systems. High-field electrical transport measurements on sub-

100 nm lamella have been detailed. These show space charge limited current at high fields

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and electrical breakdown at E > 1.4 GV/m, which presents remarkable device

possibilities.[28]

FIGURE 5. Nanodomains in BaTiO3 single crystals (J. M. Gregg, Queen’s Univ., Belfast,

private communication). Scale bars: left (2 microns), right (200 nm).

The second FIB single crystal system is SrTiO3 – on which electrical transport

measurements have also been detailed. These show ionic space charge limited current

transients similar to those reported by Zafar et al. in BST,[29] and which appear to satisfy the

predictions of Many and Rakavy [30] that peak current occurs at

t = 0.78 d2/(Vµ). (2)

Thus far we have verified the V-dependence of Eq.2 but not the d-dependence. Fig.6 shows

that the peak moves out to longer times with repetitive voltage pulses. This was known from

Ref.[31] and is due to accumulation of unrelaxed space charge with repeated voltage

applications.

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FIGURE 6. Ionic space charge limited transient currents (in Amps) versus time in seconds

for single-crystal SrTiO3. The runs, top to bottom, are each a few minutes apart. At 100V

applied the peaks shift by x10 to faster times ca. 10-20 s.

CONCLUSIONS

Nano-ferroelectrics are of considerable interest for commercial devices where lateral

area must now be < 0.2 µm2 and thicknesses ca. 120 nm for FRAMs and thinner for DRAMs.

We are rapidly acquiring an understanding of what physical effects occur at these dimensions,

and which are extrinsic and which intrinsic. Oxygen vacancies play a key role among the

former. True finite size effects do not occur for thicknesses > 2 or 3 nm. [3D] devices are of

maximal interest at present, including self-trenching capacitors and nanotubes, nanorods

(nanowires), and nanodots. Theories and experiments are converging to be operative finally

in the same size range, as ab initio models come up to ca. a hundred nm and experiments

come down to that value. In the next few years it should prove interesting on the fundamental

physics side to study misfit dislocations in epitaxial nanotubes to examine regions of stability,

to look for toroidal ordering, and to model [3D] nano-domain structures. On the device side,

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[3D] self-trenching structures may prove useful for random access memories (DRAMs and

FRAMs) and for MEMs applications involving micro-fluid transport.

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