IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 9, NO. 2, MARCH 2010 229

Fabrication of Fractal Surfaces byElectron Beam Lithography

Pablo Stoliar, Annalisa Calo, Francesco Valle, and Fabio Biscarini

Abstract—We describe a method based on electron beam lithog-raphy to fabricate patterns of fractal islands on a surface. Theisland morphology resembles that of a random deposition of parti-cles in a diffusion-limited aggregation regime in 2-D, which is oftenencountered in the growth of atoms and molecules upon ultrahighvacuum sublimation. With our fabrication protocol, the morpho-logical parameters of the fractal islands (correlation length, fractaldimension, coverage, and roughness) can be controlled. The fab-ricated structures can be used as templates for investigating theinterplay of self-affinity on thin film nucleation and growth, theadsorption of functional molecules, and the anchoring of livingcells. Also they can be exploited as masters for nanoimprintinglithography and replica molding.

Index Terms—Electron beam lithography (EBL), geometricmodeling, thin-film devices, semiconductor materials.

I. INTRODUCTION

ORGANIC semiconductors thin films [1] grown by ultra-high vacuum sublimation or molecular beam deposition

(OMBD) exhibit a self-affine morphology, which means a sta-tistical invariance of morphological properties upon anisotropicrescaling [2]. This characteristic arises because they form innonequilibrium conditions, where thermodynamic equilibriumdoes not apply and the dominant kinetic mechanism of growthdetermines their morphology.

Organic FETs (OFETs) [3] based on these films are of tech-nological interest for organic electronics. A typical OFET con-figuration requires the deposition of an organic semiconductoron the gate dielectric between the source and drain electrodes toform the transistor channel. The charge carriers flow within thefirst few (1–5) monolayers in contact with the gate dielectric.

OFETs are emerging as ultrasensitive environmental sen-sors, not only for gases [4] but also for large biomolecules [5].The sensing scheme is a change of OFET parameters as thebiomolecule approaches the Debye–Helmholtz layer, a fewnanometers away from the accumulation layer [6]–[9]. OFETresponse will not be exclusively related to a local interaction,as the adsorbate will sample the different length scales accord-ing to its size, shape (e.g., tertiary structure), and diffusivity

Manuscript received April 1, 2009. First published July 14, 2009; currentversion published March 10, 2010. The work of A. Calo was supported by theProject EU-STRP 033355 STAG. The work of P. Stoliar was supported by theProject EURYIDYMOT. The review of this paper was arranged by AssociateEditor J. Li.

The authors are with the Consiglio Nazionale delle Ricerche (CNR) Isti-tuto per lo Studio dei Materiali Nanostrutturati (ISMN), 40129 Bologna, Italy(e-mail: pstoliar@bo.ismn.cnr.it; a.calo@bo.ismn.cnr.it; f.valle@bo.ismn.cnr.it;f.biscarini@bo.ismn.cnr.it).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TNANO.2009.2027232

Fig. 1. Image taken with the AFM of a typical pentacene film.

on the organic semiconductor surface [10]. It is important tounderstand the interaction of the biomolecules on the semicon-ductor, and relate the device response to the possible interac-tion regimes. This becomes particularly interesting when thetarget species consists of large objects, as for instance viablecells [11]. A cell can sample multiple length scales of the sub-strates [12] through the different mechanism of interactions,from secretion of binding proteins [13], focal contacts [14], upto meso- and microscopic mechanical forces [15], [16]. In orderto understand the influence of the morphological parameters oncell absorption, it is important to control them in a systematicway.

Our idea is to generate a model substrate where this control isachieved in a deterministic manner, providing at the same timea large enough number of discrete elements to build a robuststatistical set.

This work is inspired by the morphology of pentacene thinfilms grown in OMBD [17]. Pentacene is the most exten-sively studied organic semiconductors. The typical pentacenesubmonolayer film consists of separated islands (see Fig. 1)with a dendritic morphology resembling the one produced bya diffusion-limited aggregation (DLA) mechanism [1]. The is-lands have a thickness h = 1.5 nm, corresponding to the heightof a pentacene molecule standing up normal to the surface [18].The description of the morphology can be coarse-grained intoa few parameters: the characteristic distance ξ [19]–[21] rep-resenting the mean distance between the nucleation points ofthe islands (coincident with the center of mass of each island),the coverage θ that is the fraction of the surface area coveredby the islands, the fractal dimension df , which is the effec-tive dimension of the space occupied by the laterally growingisland, and that describes its dendritic shape. The film meanheight is 〈h〉 = h · θ, and the rms surface roughness, which is aself-affine scaling property, is σ = h · (θ · (1 − θ))0.5 (as longas nucleation is 2-D [19]).

Because island growth is an out-of-equilibrium process, thefluctuations of the deposition rate r, the deposition temperatureT, and the surface tension/roughness of the substrate can greatlyaffect the morphology. It is difficult to control the experimental

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230 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 9, NO. 2, MARCH 2010

conditions in order to obtain reproducible values for ξ [22] anddf .

In this paper, we address the problem of how to generate ar-tificial surfaces with a pentacene-like morphology, but with afine control via numerical design of the morphological parame-ters [17]. The technique used here is electron beam lithography(EBL), which is a maskless technique that allows one to draw anarbitrary pattern on a resist film. The DLA pattern is then trans-ferred on a technologically relevant substrate either by etchingor liftoff.

The paper is organized as follows. In Section II-A–D, we ex-plain how to numerically generate a DLA design with controlledmorphological parameters. In Section II-E, we briefly introduceEBL; in Section II-F and II-G, we describe the procedure to op-timize the electron beam path; in Section II-H, we describe thefabrication procedure of the sample1; in Section III, we showand discuss the results.

II. EXPERIMENTAL

A. DLA Pattern Generation

To generate the pattern, we start with a grid, viz., a squarematrix with a number of elements equal to a power of 2, whosepoints indicate a position available for a particle. Initially, wedeposit on the grid a number of particles called seeds. Then,we simulate the molecular deposition: a random position ischosen on the grid as the landing point of a particle arriving onthe surface. The particle then performs a Brownian-like motionuntil it finds another particle on its side and sticks to it. Thevery first arriving particles will stick to the seeds. This motion,once performed, gives rise to the formation islands with DLAgeometry [1].

In the following, we describe in sequence the operations per-formed by the program to generate the islands.

B. Data Structures

The program (written in ANSI C) stores the grid informationin an integer matrix of 512 × 512 points and the islandsinformation in an array of structures. The information on eachisland is stored into an abstract data type that contains the x andy coordinates for each particle belonging to an island, togetherwith a particle counter (see Fig. 2) [23].

C. Seeds Generation

In Fig. 3(a), the content of the array of structures after theprocess of seeds generation is shown. Each seed is the firstparticle of an island and is identified in the grid by a progressivenumber starting from 1, 0 being an empty position. The seedscoordinates are stored into the elements of the island array.

1The DLA geometry is one of the most typical fractal geometries with statis-tical self-similarity. In this case, a rescaling changes the size of the objects butit does not change their morphological statistical properties. On the other hand,geometries whose shape remains invariant after the rescaling are termed self-similar; typical examples include the Mandelbrot set and the Koch snowflake(see P. S. Addison, Fractals and Chaos—An Illustrated Course. Bristol, U.K.:IOP Publishing, 1997).

Fig. 2. Data-type declaration.

The seeds are distributed into a hexagonal configuration re-sembling an fcc crystal to have a well-defined statistical distancebetween the islands. The a parameter of the fcc structure repre-sents the characteristic length ξ.

D. Particle Deposition

In Fig. 3(b), the result of the deposition process for the firstparticle is shown. This particle has landed in a random position,and has moved through the matrix following a Brownian-likemotion till it finds the seed of island 4. Consequently, this par-ticle belongs to island 4 and its coordinates are added in thecorresponding element of the island array.

This process is repeated until the desired number of particleson the surface (coverage) is reached. Fig. 3(c) and (d) show thegrid after 11 and 21 iteration cycles, respectively.

Fig. 4 is the corresponding portion of the source code. In thecalculation of the indexes for the grid, we perform an AND op-eration to ensure a proper folding over the edges; this operationrequires that the dimension of the matrix is a power 2.

Fig. 5 shows as a bitmap image the content of the grid afterthe seeds generation [see Fig. 5(a)], and after the deposition of16 250 [see Fig. 5(b)] and 64343 [see Fig. 5(c)] particles. Thecoverage is 0.2%, 6.4%, and 25%, respectively.

E. Electron Beam Lithography

To translate drawings like those shown in Fig. 5 into a pat-tern on a surface, we use EBL. We deposit a thin film ofpoly(methylmethacrylate) (PMMA) 200 nm thick on a siliconsubstrate with 200 nm thick thermally grown silicon oxide layer.The PMMA used has an average MW equal to 950 kDa [24].When an electron beam irradiates the PMMA film, the polymerchains are broken so that the average molecular weight dimin-ishes. As the molecular weight is smaller, the solubility rate ina suitable solvent increases [25].

Our EBL system is an SEM field emission gun (FEG)HITACHI 4000 fitted with a pattern generator [26], whichallows us to raster the beam according to a preset patterndrawing.

F. Optimization of the Beam Path

The particles deposition into the islands occurs in a randomway. As the EBL performs the writing process sequentially onthe surface, it is therefore necessary to order: 1) the islands one

STOLIAR et al.: FABRICATION OF FRACTAL SURFACES BY ELECTRON BEAM LITHOGRAPHY 231

Fig. 3. Grid and corresponding array of structures in different steps during the program execution. (a) Seeds generation. Seed number = index + 1. (b) Depositionof 1 particle. (c) Deposition of 11 particles. (d) Deposition of 21 particles.

232 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 9, NO. 2, MARCH 2010

Fig. 4. Part of the source code that simulates the DLA motion.

with respect to another and 2) the points forming an island.If the identification numbers for the seeds are assigned in anordered way, the order between the islands follows the orderin the seeds generation. In this case, the beam will draw theislands sequentially, following the ascending order, but it willscan chaotically inside each island [see Fig. 6(a)]. For this, wesort the information about the particle coordinates inside theisland structures using a bubble sort algorithm [27]. In this way,the coordinates for the particles in Fig. 3(d) are reordered asfollows:

island [0]x [ ] = {0, 1, 1, 1}island [0] y [ ] = {2, 1, 2, 3}island [0]n = 4

island [1]x [ ] = {5, 5, 5, 5, 5, 6, 6}island [1] y [ ] = {0, 1, 2, 3, 4, 1, 3}island [1]n = 7

island [2]x [ ] = {3, 4, 4}island [2] y [ ] = {5, 4, 5}island [2]n = 3

island [3]x [ ] = {6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10}island [3] y [ ] = {5, 6, 4, 5, 6, 7, 4, 5, 6, 6, 6}island [3]n = 11.

The resulting beam path is shown in Fig. 6(b).

G. Saving in a .dxf File

One of the operation modes for EBL consists of providinga list of lines to be written on the sample. This list is input tothe pattern generator using a .dxf format [28] and the lines arewritten in the same sequence as they appear in the .dxf file.

Consequently, a filled area arises from a sequential list of par-allel lines. The distance between the lines needs to be consistentwith the line width, which, in turn, depends on the electron dose(expressed in linear dose units, in nanocoulombs per centime-ter), the beam diameter, and the developing process [25].

The process to write the islands implies that the beam hasto fill each squared grid position, and it is represented in the

Fig. 5. Bitmap images of the content of the grid (in black are indicated thefilled elements). From the top: seeds generation, deposition of 16 250 particles,deposition of 64 343 particles.

Fig. 6. Beam path (a) before and (b) after the optimization process.

STOLIAR et al.: FABRICATION OF FRACTAL SURFACES BY ELECTRON BEAM LITHOGRAPHY 233

Fig. 7. Drawing of the whole beam path necessary to generate the 1.024 mm× 1.024 mm pattern. Inset: result of the concatenation of segments betweenadjacent squares.

inset of Fig. 7. The software should generate a set of linesfor each grid position starting from the first square of the firstisland, write sequentially all the squares of the first island, andthen, complete sequentially all the remaining islands. When thecoverage approaches to 1, the number of squares tends to 262144and each one requires a certain number of parallel lines. Toreduce efficiently the number of lines, we concatenate the linesbelonging to adjacent squares, as shown in the inset of Fig. 7.

Once this process is applied, the whole beam path will followthe sequence indicated in Fig. 7. The islands at this zoom factorappear as black features, but they are composed by a set of par-allel lines. The total area covered by the pattern is 1.024 mm ×1.024 mm, a single square being 2 µm × 2 µm.

H. Sample Fabrication and Characterization

Fig. 8 shows the different steps of the fabrication process.The substrate is a fragment of silicon wafer with a 200 nmthick layer of thermally grown SiOx [see Fig. 8(a)]. Afterthe cleaning procedure (2-propanol, acetone), a 250-nm-thickfilm of PMMA is deposited by spin coating [29] (5000 r/min,5 min) from a solution in ethyl lactate (3% solid content) [seeFig. 8(b)]. The film after preparation is baked in oven at 160 ◦Cfor 2 h.

The EBL exposition [see Fig. 8(c)] is performed with a linedose of 5 nC/cm, using an electron beam of 5 keV, 1 nA. Withthese parameters, the typical exposition time for medium cov-erage is on the order of a few minutes.

The developing process is performed first with a mixture of 2-propanol:4-methyl-2-pentanone 3:1 (70 s without shaking), andthen, with pure 2-propanol (20 s). The sample is, finally, gentlyrinsed in ultra high quality water and dried with dry N2 [seeFig. 8(d)]. We perform a postbaking step keeping the sample at160◦ for 5 min in oven.

Ti thin film, 13 nm thick, is deposited on the patterned sam-ple at room temperature (RT) using an electron beam evapora-tor (Triple EFM, Omicron GmbH, Germany) [30]. We apply apower of 16 W on a 2-mm-diameter Ti rod. The base pressure

Fig. 8. Various steps of the fabrication process.

is 1 × 10−7 mbar and the deposition rate is 0.4 nm/min [seeFig. 8(e)].

The liftoff process is performed by sonicating the sample inpure acetone for 5 min [see Fig. 8(f)].

The final step consists of a second PMMA deposition by spincoating (10 000 r/min, 5 min). It generates a film that followsthe pattern relief of thickness approximately equal to 150 nm[see Fig. 8(g)].

234 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 9, NO. 2, MARCH 2010

Fig. 9. Optical image in bright field of the whole pattern.

Fig. 10. (Top) AFM image of an island with (bottom) the corresponding heighthistogram.

Optical images were taken using Nikon Eclipse i80 Micro-scope equipped with a DS-Fi1 Nikon camera [31].

The atomic force microscope (AFM) images were acquiredwith a Smena AFM (NT-MDT, Moscow, Russia) [32] operatingin tapping mode in air. Commercial Au coated silicon tips wereused with a typical curvature radius of 10 nm (NSG 10/50) [32].All the images are analyzed using Gwyddion 2.9 software [33].

III. RESULTS

Fig. 9 shows the optical image of the sample in bright field,where the whole pattern is visible. As the starting substrate

Fig. 11. Series of AFM images (area: 40 × 40 µm2 ) containing single islandscorresponding to samples with a different coverage (θ). (a) and (b): θ = 6%.(c) and (d): θ = 10%. (e) and (f): θ = 16%. The nominal height of each islandis 9 nm. (g) Fractal dimension extracted from the scaling of the contour lengthversus area of each island.

for the islands deposition is thermal SiOx , 200 nm thick on Siwafer, it produces interference at visible wavelengths [34]. TheTi islands emerge from SiOx producing an important changein the interference properties of the substrate. For this reason,they are visible by optical microscopy even if their effectivethickness is only 10 nm.

The sample in Fig. 9 contains 505 seeds plus 64 343 particles;the coverage is 25%. The Fourier transform in the inset confirmsthat the islands are statistically distributed in a structure withhexagonal symmetry with a cell parameter a = 43 ± 3 µm.

STOLIAR et al.: FABRICATION OF FRACTAL SURFACES BY ELECTRON BEAM LITHOGRAPHY 235

Fig. 10 is the AFM image of an island with the contour of thedigitally generated island superimposed. The difference in thecontour length can be ascribed to the dissolution process andlocal fluctuations in the e-beam dose. From the height histogram,we measure a 9 nm island thickness. As the widths of the twoheight distributions in the histogram are the same (1.76 nmfor the ground and 1.79 nm for the island), we infer that theisland and the ground levels have the same roughness. This isan expected result, as they are both made of PMMA.

Fig. 11 shows AFM images of islands generated with 16 250,26 375, and 41 562 particles. The corresponding coverage is6.2%, 10%, 16%, respectively. The fractal dimension is calcu-lated from the relation between the area (A) and the perimeter(P), viz., P ∝ Adf /2 . The data obtained by the analysis on thewhole array is shown in Fig. 11(g). The trend is consistent withthe one reported in [17], where the DLA fractal dimension isapproached at coverages above the threshold value of 20%.

IV. CONCLUSION

We presented a fabrication method based on EBL to generatepatterns of fractal objects on surfaces. We show that characteris-tics distance, fractal dimension, and coverage can be preset andtransferred to the pattern by means of an optimized matrix for-malism and rastering, together with a fabrication process. Themetrological assessment shows a good agreement between thedesigned and the transferred motif.

These structured surfaces can be used for studying molecu-lar adsorption or cell adhesion upon a systematic variation ofmorphological features.

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1981.

Pablo Stoliar was born in Buenos Aires, Argentina,on December 15, 1972. He received the Master’s de-gree in electronic engineering from the UniversidadNacional de la Matanza, Buenos Aires, in 1999, andthe Ph.D. degree in science and technology, mentionphysics, from the Universidad Nacional de GeneralSan Martin—Instituto de Tecnologıa Jorge A. Sabato,Buenos Aires, in 2004.

He was a Postdoctoral Training and Research inItalian Laboratories (TRIL) Fellow at Abdus SalamCentre for Theoretical Physics, Trieste, Italy, in the

Istituto per lo Studio dei Materiali Nanostrutturati (ISMN), Bologna, Italy. Since2007, he has been a Research Scientist at ISMN, Bologna. His current researchinterests include organic and molecular electronics, biosensors, software devel-oping, numerical calculus, and development of instrumentation.

236 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 9, NO. 2, MARCH 2010

Annalisa Calo was born in Castellammare di Stabia,Italy, on March 12, 1976. She received the Master’sdegree in chemistry of materials from the Univer-sita degli Studi di Bologna Alma Mater Studiorum,Bologna, Italy, in 2006. She is currently workingtoward the Ph.D. degree in chemistry at ConsiglioNazionale delle Ricerche (CNR) ISMN. Her currentresearch interests include surface chemistry, nanofab-rication, scanning probe microscopy, scanning elec-tron microscopy, and images analysis.

Francesco Valle was born in Savona, Italy, onOctober 24, 1973. He received the Master’s degree inphysics from the University of Roma “La Sapienza,”Rome, Italy, in 1999, and the Ph.D. degree in sci-ence from the University of Lausanne, Lausanne,Switzerland.

He was a Postodoctoral Fellow in the Ecole Poly-technique Federale de Lausanne (EPFL). He was aPostodoctoral Fellow at the University of Bologna“Alma Mater Studiorum.” Since 2008, he has beena Research Scientist at CNR-ISMN, Bologna, Italy.

His current research interests include polymer physics, single-molecule tech-niques, protein folding, and cell adhesion.

Fabio Biscarini was born in Perugia, Italy, on April15, 1962. He received the Laurea degree in industrialchemistry from the Universita di Bologna, Bologna,Italy, in 1986, and the Ph.D. degree in chemistry fromthe University of Oregon, Eugene, in 1993.

He was a Postdoctoral Fellow at CNR Istitutoper la Microelettronica e i Microsistemi (IMM) andISMN, Bologna, where he was also a CNR ResearchScientist in 1996, and is currently a Senior Scientistand the Head of the Nanotechnology of Multifunc-tional Materials Research Division. He has authored

or coauthored more than 140 publications and holds 16 patents. He has beenthe Principal Investigator and the a Coordinator of several European (EU) andNational Projects. He is a Co-Founder of Scriba Nanotecnologie Srl, one of thefirst spin-off companies of CNR Bologna.

Dr. Biscarini is a Fellow of the Royal Society of Chemistry. He received theEU Descartes Prize 2007.