Piezoforce Imaging of Confined Oxide Nanowires

8/11/2019 Piezoforce Imaging of Confined Oxide Nanowires

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Piezoforce Iagig of Cofied Oxide NaowiresAkash Levy

Al lder dice High Schoo l, Pit tsbur gh , PA 15217

[email protected]

AbstractA technique called piezoresponse force microscopy (PFM) was used to non-destructively image

and dimension conductive nanostructures created at the interface between LaAlO3and SrTiO3.

Comparisons of PFM imaging with a previously established destructive method for quantifying ~10

nanometer nanowires indicate very good agreement.

Nanoscale regions at the interface of LaAlO3/SrTiO3can be reversibly switched betweenelectrically conducting and electrically insulating with an Atomic Force Microscope (AFM) tip. A software

program was developed to scan a voltage-biased AFM tip in a programmed pattern over the LaAlO3

sufae, alloig aosale lies ad othe ople pattes to e itte ad eased at the

LaAlO3/SrTiO3interface. A three-dimensional visualization tool was developed to monitor the progress

of the nanoscale writing. Simultaneous measurements of the conductivity of these nanostructures were

performed using a lock-in amplifier.

The PFM response of the LaAlO3/SrTiO3interface was measured by applying an alternating

voltage to the conductive nanostructures, and measuring the resulting deflection of an electrically-

isolated AFM tip that scanned the surface of the sample. The raster-scanned PFM images were analyzed

to determine the wire widths. The PFM-derived widths were compared to those obtained from erasureexperiments. PFM had a spatial resolution of approximately 25 nm, with the advantage of being non-

destructive.

PFM imaging may become a useful technique for researchers interested in developing new

families of nanoelectronics circuitry using the LaAlO3/SrTiO3interface. The technique provides a

relatively simple, high-resolution method for the non-destructive imaging of conductive nanostructures.

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mailto:[email protected]:[email protected]:[email protected]


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ContentsAbstract ......................................................................................................................................................... 1

Introduction .................................................................................................................................................. 3

Development of Software for AFM Lithography........................................................................................... 4

Visualization and Measurement of Nanostructures ..................................................................................... 5

Procedure ...................................................................................................................................................... 6

Results ........................................................................................................................................................... 8

Discussion.................................................................................................................................................... 10

Conclusions ................................................................................................................................................. 11

Acknowledgements..................................................................................................................................... 11

References .................................................................................................................................................. 11


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IntroductionIn 2004, Ohtomo and Hwang1reported the existence of a two-dimensional electron gas (2DEG) at the

interface between two oxide semiconductors, LaAlO3and SrTiO3. A 2DEG can be described as a layer of

electrons that are free to move in only two dimensions. Since 2DEGs were discovered in LaAlO3/SrTiO3,

their properties in these materials have been explored by many research groups. Many remarkable

phenomena have been discovered such as electrical conductivity3,magnetism2and superconductivity4.

For these phenomena to appear, the LaAlO3/SrTiO3samples must be grown under very precise

conditions5(see structure inFigure 1(a)). It is crucial that the SrTiO3is TiO2-terminated, otherwise many

of the ateials iteestigproperties cannot be observed. The conductivity at the interface between

the LaAlO3layer and the SrTiO3layer is dependent on the thickness of the LaAlO3layer2;at or below a

critical thickness of three unit cells of LaAlO3, the interface is insulating, while at or above four unit cells

thickness, the interface is conducting. Near the critical thickness, the conductivity of the sample can be

locally and reversibly controlled with a voltage-biased conductive atomic force microscope (c-AFM) tip.

Applying a positive voltage to a c-AFM tip in contact with the sample produces local conductivity at the

point of contact. Conversely, applying a negative voltage to a point on a sample restores the insulating

state at that point on the sample. By controlling the path and voltage of the c-AFM tip, it becomes

convenient to write nanowires onto the sample6.

Figure 1. Images of LaAlO3/SrTiO3. (a) A visualization of the molecular structure of LaAlO 3/SrTiO3. (b) Nanowires being written on

a sample by a c-AFM tip.

The c-AFM lithography process is analogous to the sketching of a picture. The c-AFM tip acts as a pe,

the sample behaves as a sheet of pape ad thevoltage applied acts as ik. The pituesthat are

sketched onto the sample are usually circuits and their components. It is possible to write nanodevices

such as field-effect transistors6(FETs), photodetectors7,terahertz sources and detectors8and single

electron transistors9(SETs) as depicted inFigure 2.All of these devices have potential applications in a

variety of disciplines. Field-effect transistors serve as the building block for nanoscale computational

systems. Terahertz microscopy has the potential to characterize single molecules placed between a

(LaO)+

(AlO2)

(LaO)+

(AlO2)

(LaO)+

(TiO2)0

(SrO)0

(TiO2)0

(SrO)0

(TiO2)0

(SrO)0

(a) (b)


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source and a detector. Although they have not yet been commercialized, room-temperature single

electron transistors could one day serve as low-power alternatives to the classical transistors that

opeate i the ajoit of todas eletoi deies.

Figure 2. Examples of nanodevices produced by c-AFM lithography of LaAlO3/SrTiO3.

Development of Software for AFM LithographyPefoig AFM lithogaph euies peise otol oe the AFM tips positio ad applied oltage.

Using LabVIEW in conjunction with Inkscape, this process becomes very manageable13.The software

used previously to perform lithography was very limited in functionality. It lacked important features

such as the ability to draw curved paths and fill in shapes. Thus, the software was redesigned from

scratch to enhance its capabilities (seeFigure 3). The new program was modular, allowing it to operate

with several varieties of AFMs, and was also much more stable. Additionally, a simulation tool was

itte i VPtho that opeated as itual hadae, offeig the ailit to test aoitig

procedures before conducting experiments. In addition, the tool provided a way to track the

nanowriting process during the experiments.

PhotodetectorField effect transistor (FET) Single electron transistor (SET)

(a) (b) (c)


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Figure 3. Front panel of the LabVIEW AFM lithography software. (RED) Mode, AFM Type, and Simulator controls. (ORANGE)

Controls to specify background image and circuit design files. (YELLOW) Properties of shapes to draw on sample surface.(GREEN) A control that allows you to specify the order you want each of the shapes to be written. (BLUE) An estimated time

required for lithography based on the path lengths and speeds for the paths.

Visualization and Measurement of NanostructuresOne challenge of working with LaAlO3/SrTiO3has been measuring the dimensions of nanowires

produced by c-AFM lithography. The written nanostructures cannot be imaged by an atomic force

microscope, because there is no measureable difference in the topography of a conducting versus an

insulating one. This essentially means that an AFM image of a sample withnanowires present appears

the same as an image of a sample withoutnanowires. One research group approached this problemusing electric force microscopy10(EFM). EFM imaging involves scanning the charge present at the

surface of a sample. Although this method was somewhat effective in visualizing nanostructures, it does

not directly measure the variations in carrier density that account for conductivity.

In the past, precise width measurement of nanowires has been performed by making cuts and

measuring the conductance drop as a function of time11.From the conductance drop, it is possible to

infer the width of that particular nanowire. However, this erasure method is not generally useful for


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imaging nanostructures because it destroys the circuit. In this paper, a novel technique for imaging

samples of LaAlO3/SrTiO3is reported. The discovery that a sample exhibits different piezoelectric

responses in conducting regions of the sample versus insulating regions allows for the use of piezoforce

microscopy (PFM) to do imaging. LaAlO3/SrTiO3displays the inverse piezoelectric effect, meaning that

the material exerts an upward force on the tip in the presence of an electric field. The strength of this

upward force is measurably different for areas where the sample is conducting versus areas where it isinsulating, thus enabling a useful system for imaging nanostructures.

Figure 4. Methods of discovering nanostructure dimensions. (a) EFM images at various phases of nanowriting. (b) Erasure

experiment being conducted to measure wire width.

ProcedureThe sample used was 35 m by 35 m in size. All experiments are carried out under ambient conditions

at room temperature. In the first part of the experiment, itual eletodes ae eated writing

rectangular-shaped areas at each of the gold electrodes with a tip voltage of +8 V. The use of virtual

electrodes maximizes electrical contact with the Au electrodes present on the sample. Next, a nanowire

is drawn between these electrodes with a tip voltage of +8 V at 600 nm/s. Then, the nanowire is cut

using a tip voltage of -10 V at 10 nm/s while the conductance drop is monitored. The conductance is

then fit to the curve = tanh/ and the spatial derivative is used to determine

the width of the wire. The wire width is calculated by finding the full-width at half-maximum (FWHM)

of(seeFigure 5 below).

(a) (b)


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Figure 5. FWHM being calculated on a curve. The peak value of the curve, fmaxis found then halved to find the half-maximum.

This value of f is used to obtain the two x values where the curve is at this half-maximum value. The distance between these

curves yields the full-width at half-maximum of the wire.

The next part is the PFM experiment. To begin, the resonant frequency of the AFM probe needs to be

found. This is important because at the resonant frequency, deflection of the AFM cantilever is

amplified, yielding a better signal-to-noise ratio. To find the resonant frequency, a sweep of a wide

range of frequencies is performed in search of a distinct peak. Once the resonant frequency is obtained,

PFM imaging can be conducted. With the AFM tip electrically isolated, the sample is scanned (as shown

inFigure 6)and the induced piezoresponse is measured through the vertical deflection of the AFM tip.

These piezoresponse data values can be used to create an intensity graph, which serves as a useful

qualitative image of the nanostructures present on the sample. Calculating the FWHM along each line of

the PFM image yields a set of values for the wire width. Averaging the FWHM values produces a value

for the wire thickness as measured by PFM.

Figure 6. PFM imaging involves raster scanning the region of sample where the nanowire is located while measuring the

piezoresponse as a function of position.


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ResultsOver several experiments, it was found that the resonant frequency of the AFM cantilever used is

between 275 kHz and 300 kHz as shown inFigure 7(a). The wire width measured in the erasure

experiment was 8 nm in width (Figure 8). The average FWHM measured in the PFM experiment yielded

a width of 33 3 nm (Figure 9(b) and (c)). After several experiments at varying writing speeds and tip

voltages, a linear regression was used (Figure 9(d)) to correlate the calculated width from the erasure

experiment (Wfit) and the width measured in the PFM experiment (WPFM). The line of best fit correlating

Wfitand WPFMyielded = . . . The R2value was 0.9175 and the p-value was

less than 0.01. This procedure can be used to characterize the properties of arbitrary nanostructures,

e.g.,Figure 10.

Figure 7. Tuning the resonant frequency of the AFM cantilever and performing a PFM scan of a nanostructure. (a) Sweeping the

frequencies produces a maximum signal at approximately 283 kHz. This is the resonant frequency of the AFM cantilever. (b) A

PFM image of a nanostructure present at the interface.

Figure 8. Conductance curves as the nanowire is written and erased. (a) This graph plots the conductance G against time. The

first peak represents the conductance jump associated with the nanowire being written between the two electrodes. The drop

that occurs afterwards represents the conductance drop as the nanowire is being cut. (b) This graph plots the magnitude of the

(a) (b)

(a) (b)


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change in conductance versus time. The FWHM measurement yields a precise value for the wire width that will later be

compared to the wire width obtained by PFM.

Figure 9. Results from the PFM experiment. (a) A PFM image of a single nanowire. The dashed line represents the y-value usedfor the data points plotted in (b). (b) The data points represent the amplitude of the piezoresponse at given x-values along the

dashed line in (a). The best fit curve for the data is used to determine the FWHM. (c) Moving the dashed l ine in (a) along the y-

axis and recalculating the values plotted in (b) yields a set of FWHM values which are used to make a scatterplot. The average

width calculated from this scatterplot was approximately 33 nm with a 99% confidence interval from about 30 nm to 36 nm. (d)

This plot displays data from several experiments using different lithography parameters. A line of best fit is constructed to

correlate the widths found by PFM imaging with the widths found in erasure experiments.

30

25

20

15

10

5

0

Wfit

(nm)

55504540353025

WPFM(nm)

10V 200nm10V 400nm10V 600nm10V 800nm10V 1000nm10V 1200nm8V 200nm8V 400nm8V 600nm8V 800nmfit

(a) (b)

(c) (d)


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Figure 10. Nanowriting and subsequent PFM imaging of a conductive nanostructure. (a) Screenshot showing AFM topography

with overlaid Inkscape pattern used to define the c-AFM path. (b) Three-dimensional visualization of nanowriting procedure. (c)

PFM image of the written nanostructure.

DiscussionThe line of best fit yielded from the experiments that were conducted shows an approximately one-to-

one relationship between the measured line width and the precise line width as calculated from the

erasure experiments. The offset of 25.6 nm represents the size of the smallest feature that PFM imaging

can resolve. From the data obtained, it is also clear that writing speed and tip voltage play a role in

determining the width of a nanowire.

Although there was random error observed in repeated experiments, this error did not affect the

validity of the data significantly. The error may have been due to fluctuations in environmental factors

such as temperature and humidity or caused by failure to fully erase conducting regions between

experiments. However it was necessary to use the same sample for every experiment as each sample of

LaAlO3/SrTiO3has slightly different characteristics.

14

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10

8

6

4

m

14121086420

m

-1.0

-0.5

0.0

0.5

V

(a) (b)

(c)


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It was reasonable to hypothesize that the variation of the piezoelectric signal as a function of

conductivity at the interface would allow for an imaging technique. The point of interest was whether or

not this method of imaging was destructive and what maximum resolution is attainable. Piezoforce

imaging has been done on many other materials in the past but this is the first time it is being performed

to image nanostructures at the interface of LaAlO3and SrTiO3. The resolution of the PFM images

produced is much higher than that of any other non-destructive imaging technique reported in the past.

The origin of the PFM signal is still not understood precisely. A previous study12showed that the writing

of nanowires causes structural reconstructions at the interface but it is not yet clear how these

reconstructions affect the piezoelectric properties of the sample. Further studies of these oxide

heterostructures could lead to an improved understanding of how structural reconfigurations change

the interfacial properties.

ConclusionsThe results indicate that piezoforce microscopy delivers a high-resolution, non-destructive way to image

electrical nanostructures present at the interface of LaAlO3and SrTiO3. PFM imaging can serve as a

technique for researchers studying nanostructures in LaAlO3/SrTiO3to acquire the dimensions of

nanowires and the devices they form as well as provide qualitative data about the appearance and

function of a nanocircuit.

AcknowledgementsThis work was carried out with Dr. Patrick Irvin and research group at the University of Pittsburgh.Figure

1(a) is adapted from Reference2.Figure 2(a) is adapted from Reference6,Figure 2(b) is adapted from

Reference7,andFigure 2(c) is adapted from Reference9.Figure 4(a) is adapted from Reference10 and

Figure 4(b) is adapted from Reference11.Figure 5 was illustrated by Arne Nordmann and published

under the Creative Commons Attribution-Share Alike 3.0 license. The resources used were supported by

grants from the U.S. National Science Foundation (NSF).

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Nature 427(6973), 423 (2004).

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C. Cen, S. Thiel, J. Mannhart, and J. Levy, Oxide Nanoelectronics on Demand, Science 323(5917),

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nanoscale oxide photodetector, Nat. Photon. 4(12), 849 (2010).

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Piezoforce Imaging of Confined Oxide Nanowires