N

PD

a

ARRAA

P8866

KSES

1

orfndSaMitprpsomIaaI

0h

Applied Surface Science 284 (2013) 569– 574

Contents lists available at ScienceDirect

Applied Surface Science

j ourna l ho me page: www.elsev ier .com/ locate /apsusc

on-monotonic roughening at early stages of isotropic silicon etching

rabhjeet Kaur Dhillon, Subhendu Sarkar ∗

epartment of Physics, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, Punjab 140001, India

r t i c l e i n f o

rticle history:eceived 1 March 2013eceived in revised form 17 June 2013ccepted 16 July 2013vailable online 1 August 2013

ACS:1.05.Cy1.65.Cf

a b s t r a c t

Isotropic etching using a mixture of HF, HNO3 and CH3COOH was carried out for single crystalline Si sur-faces for different times and the resulting morphologies were investigated using atomic force microscopy.The acquired data were analyzed using dynamic scaling theory. It was found that for each surface, thereexists two roughness exponents which correspond to two different length scales. Moreover, the localroughness properties undergo a reversal between these two length scales before and after an etchingtime of 120 s. The power spectra density (PSD) curves of the analyzed images also show a reversal in theoverall trend before and after 120 s. It is further noted that the PSD spectra of the surfaces resembles morethat of a superstructured surface which is a distinct departure from the self affine nature of the surfaces

8.37.Ps8.35.Ct

eywords:emiconductorstchingcaling analysis

investigated. The deviation is by far the largest for the 120 s etched surface. The morphology evolution inthe present scenario does not follow the dynamical model of progressive hardening of the solid surface.Hillock flooding analyses of the AFM images exhibit the percolation nature of the process.

Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved.

. Introduction

In the present day world of miniaturization of devices, devel-pment of electronic device technology toward nanometer scaleelies largely on the substrate properties upon which the device isabricated. Generally, such substrates fulfill two basic properties,amely, they should be of high crystallinity with low defectensity and should be appropriate for integrating processes withi based electronics [1]. It is due to the latter, that the structuralnd electronic properties of Si surfaces are extensively studied.oreover the production of clean and smooth surfaces plays an

ncreasingly important role in the microelectronic industry sincehe presence of defects and impurities degrade the electronicroperties of materials. Silicon surface texturing also plays a keyole in the solar cell fabrication industry [2,3]. Several etchingrocesses are thus widely used for structuring and modifyingilicon surfaces [4]. The orientation independent isotropic etchingr the orientation dependent anisotropic etching are the keyethodologies used for bulk micromanufacturing of silicon [5].

sotropic etching plays a key role in a number of applications such

s liquid handling devices, removing rough and sharp corners afternisotropic etching, delineation of electrical junctions, etc. [6,7].t has been found that an acidic etched surface can absorb 0.5–1%

∗ Corresponding author. Tel.: +91 1881 242178.E-mail addresses: sarkar@iitrpr.ac.in, subhendu.sarkar@gmail.com (S. Sarkar).

169-4332/$ – see front matter. Crown Copyright © 2013 Published by Elsevier B.V. All rittp://dx.doi.org/10.1016/j.apsusc.2013.07.135

more incident light than an alkaline etched surface thus proving tobe a better harvester of solar energy [2]. The texturing, however,is found to depend largely on the original surface morphology ofsilicon [3]. An anisotropically etched Si surface has been provento absorb more incident light when it is pre-etched in an acidicmixture owing to the increased number of pyramid density on thesurface. Hence, the morphology study of acidic etched Si surfaceswarrants a detailed attention in the light of the above.

The most common acidic agent used for isotropic etching of Siis a combination of HF, HNO3 and CH3COOH, commonly known asHNA. The first comprehensive study of the mechanism of isotropicetching of Si by HNA was done by Robbins and Schwartz [8–10]. Thecombination of these acids in HNA exhibits three areas of generalinterest: the high HNO3 region, the high HF region and the region inthe vicinity of maximum etch rate [9]. In the high HNO3 region, HFplays a kinetically important role and vice versa. In the region nearthe maximum etch rate, however, both reagents play an importantkinetic role [9]. The etching of Si in HNA is regarded as a two-stepprocess, the first of which is the oxidation of Si to SiO2 by HNO3 (Eq.(1)). This is followed by the subsequent dissolution of the formedSiO2 by HF (Eq. (2)). The overall reaction is given by Eq. (3).

3Si + 4HNO3 → 3SiO2 + 4NO + 2H2O (1)

SiO2 + 6HF → H2SiF6 + 2H2O (2)

3Si + 4HNO3 + 18HF → 3H2SiF6 + 4NO + 8H2O (3)

ghts reserved.

5 Surfac

iataraaaEbwaer

isewapcdhmaa

wrt

pfumtiNepwaiewwmetwiIcitp

2

Si

70 P.K. Dhillon, S. Sarkar / Applied

The above equation can be diffusion or etch rate limited depend-ng upon the relative concentration of HNO3 and HF [7]. For high HFnd low HNO3 the reaction is etch rate limited and is controlled byhe rate of oxidation, so that it tends to be orientation dependentnd affected by dopant concentration, defects and catalysis. In thisegime the temperature influence is more pronounced. For low HFnd high HNO3, on the other hand, the reaction is diffusion limitednd the etch rate is controlled by the ability of HF to remove the SiO2s it is formed. Here the temperature changes are less important.tches in this regime are isotropic and truly polishing, producing aright surface with anisotropies of 1% or less when used on 〈10 0〉afers. Studies have also shown that under this regime, with glacial

cetic acid as dilutent, the etching solution is the major concern intching with the type of etched semiconductor playing only a minorole [11].

Sapoval and his group has proposed a model for chemical etch-ng of a solid where a complex dynamics plays a vital role at theolid–solution interface [12]. According to their study, the weak-st sites are eroded first, thereby rendering the solid to be harderith erosion time. Additionally, the surface tends to get rougher

nd rougher uncovering the critical spatial correlations typical ofercolation. The distribution of debris produced by the etching pro-ess can be regarded as a chemical fragmentation process. Theependence of surface roughness on the corrosion front velocityas been modeled in a study by Tu et al. (KLT model) [13]. In theirodel, the eroding system is characterized by fluctuations which

re quenched random variables. The fluid interface moving through random medium is given by the equation

∂h

∂t= F + �∇2h + �(x, t) (4)

here F is the pushing force, � is the surface tension and �(x, t)epresents the quenched noise. This model has been found to beypical for percolation scenarios [13].

An alternative method followed to study the surface mor-hology is to use the dynamic scaling approach (discused in theollowing section). Although scaling analyses have been extensivelysed for studying the morphology of surfaces eroded by physicaleans [16,17], one can only find a handful of such studies applied

o surfaces eroded by chemical etching processes [18]. Scaling stud-es were done by Dotto and Kleinke for Si(1 0 0) surfaces etched byaOH under different conditions [19]. Their results indicated thattched Si surfaces in saturated ambient can be described by KLTercolation model. Etching in their case was however performedith a small drop of NaOH for increasing concentration gradient

nd for generating interfacial turbulence near the surface. Similarlyn 2004, Wisz et al. had studied fractal evolution in case of Si(1 0 0)tched with HF:HNO3 in the ratio 10:1 [20]. Samples in their caseere prepared from p-type and n-type Si(1 0 0) and the morphologyas studied for an etching time of 15 s. The present work deals withorphological characterization of the erosion dynamics of HNA

tched Si(1 0 0) system under the framework of dynamic scalingheory. The etching was performed with a finite solution of HNAhich was supposed to increase the surface roughness monoton-

cally with time according to the model proposed by Sapoval [12].n the current study, diffusion limited regime of HNA etching washosen by taking a low HF and high HNO3 concentration. The etch-ng process was monitored with respect to time using the scalingheory approach. Our findings were also discussed in the light ofercolation concepts.

. Material and methods

Si samples of the size of 10 mm × 10 mm cut from undopedi(1 0 0) single crystal wafers were cleaned and rinsed using deion-zed water (� ∼ 18.2 M�) from a Milli-Q Gradient water purification

e Science 284 (2013) 569– 574

sysytem (Millipore). Before etching, all samples were cleaned bysonicating with isopropyl alcohol for 15 min each. Etching solutionof HF, HNO3 and glacial CH3COOH in the ratio 2:3.5:5.5 (by volume)(5M:5.3M:8.7M by molar conc.) was prepared and ultrasonicated inorder to ensure homogenity of the etching solution. Samples wereetched for 30 s, 60 s, 120 s, 240 s, 360 s, 480 s and 600 s respectivelyalong with ultrasonication. After etching, samples were thoroughlyrinsed with DI water and dried. The samples were thereby imagedin ambient by Atomic Force Microscopy (AFM) using a Multimode8 Scanning Probe Microscope (SPM) equipment operating in thetapping mode. A large number of AFM images each having a res-olution of 512 × 512 pixels were acquired over different regionsof each sample. This was done for better statistical averaging ofquantities obtained from the AFM data.

The AFM data were statistically analyzed using the dynamicscaling approach. In this formalism, the steady state morphologyand dynamics of a rough surface can be characterized by the fluc-tuations of surface height h(r, t), around its mean value <h>, throughthe root-mean-square (rms) roughness or interface width definedas w(r, t) =< (h(r, t)− < h >)2>1/2

r , where t is the erosion timeand < > r denotes average over all r in a system of size L and r ≤ L.A similar correlation function used in the scaling arguments isthe height–height correlation function defined as H(r, t) =< (h(x + r,t) − h(x, t))2 >, where h(x + r, t) and h(x, t) denotes the surface heightwith respect to the substrate at a position (x + r) and x respectivelyon a surface at time t [14]. In the absence of any characteristic lengthin the problem, growth processes are expected to obey power-law behavior of the correlation functions in space and time andthe Family-Vicsek dynamic scaling law w(L, t) = t˛/zf (L/�(t)) holds,where ̨ is the roughness exponent and � is the lateral correla-tion length. The dynamic exponent z is defined as ˛/ ̌ where ̌ isthe growth exponent describing the surface roughening process intime through the power law behviour of w∼tˇ. Beyond the shortrange lateral correlation of a surface, even though surface heightsare not significantly correlated, they may exhibit a periodic behav-ior on all length scales larger than the lateral correlation length. Inorder to determine this long-range behavior, the structure factor orpower spectral density function (PSD) of the interfacial fluctuationsis taken into consideration. This is defined as PSD(k, t) = 〈H(k, t)H(k,t)〉, where H(k, t) is the Fourier transform of the surface height in asystem size L, with k being the spatial frequency in reciprocal space[15].

3. Results and discussion

Fig. 1 shows the morphology evolution of HNA etched Si surfacesobtained by using AFM. Fig. 1a shows the pristine Si surface beforeetching. After etching for about 30 s, globular structures appear onthe Si surface (Fig. 1), almost similar to what was found in the studyby Wisz et al. [20]. However, in their case, the size of each globulewas approximately 10 �m while in our case it is about 50 nm. Thiscontrast is primarily due to the differences in choice of the pristineSi wafer and concentration of the etching solution accompaniedwith sonication. The size of the globules, however starts decreasingwith etching time until 120 s of etching. After this a macroscopicmorphology evolves on the Si surface which in turn influences theglobular morphology obtained earlier. This effect is further noticedin samples etched for 480 s and 600 s.

In order to study the roughening process quantitatively, adynamical scaling approach was used. Roughness was calculatedfor all possible length scales for all scanned AFM images using a

Fortran program. These values were then averaged over identicallength scales. A large number of images from different regions of aparticular etched surface were used to find the average behavior ofeach scaling parameter for all etching times. Fig. 2 depicts a typical

P.K. Dhillon, S. Sarkar / Applied Surface Science 284 (2013) 569– 574 571

s, (b)

gsaprTiaef(astcv

d

Fose

(∼50–150 nm) and ˛2 s corresponded to a length scale higher thanthe former. It was found that (˛1 s) are higher compared to (˛2 s)before 120 s and lower thereafter (Fig. 3(a)). For a self-affine surface,a smaller value of ̨ implies a rougher local surface, where ̨ lies

(a)

Fig. 1. Tapping mode 5 × 5 �m2 AFM images of HNA etched Si surface for (a) 0

raph in which the interface width (roughness) versus lengthcale curves for six different images are plotted along with theirverage. A similar methodology was followed to extract all otherarameters from the AFM data. Fig. 2 shows variation of averagedms roughness for all etching times with respect to length scale.he plot indicates that for a given etching time there is an initialncrease in roughness with the length scale. This is followed by

saturation phase. The saturation roughness increases with thetching time except for the case of 120 s of etching. It is foundrom line profile analyses of the AFM images that the aspect ratioaverage height:average width) of the surface structures decreasest 120 s. The rate of increase of roughness with length scale islow before 120 s and becomes rapid thereafter. This indicates aransition in morphology evolution before and after 120 s. All the

urves, show two different slopes before the individual roughnessalues reach saturation.

Roughness exponents (˛) were calculated from the data. Twoistinct roughness exponents (˛1 s and ˛2 s) were obtained for

1Reg ion 1 Region2 Region3 Region4 Region5 Region6 Average of all regions

0.1

w (n

m)

10

0s 30s 60s 120s 240s

1

360s 480s 600s

10 100 1000

0.1

L(nm)

ig. 2. Top: Average curve for interface width (roughness) versus length scalebtained from images of different regions (scans) of the Si surface etched for 30; Bottom: Plot of the interface width w vs length scale L, corresponding to differenttching times.

30 s, (c) 60 s, (d) 120 s, (e) 240 s, (f) 360 s, (g) 480 s, and (h) 600 s etching time.

each of the curves. ˛1 s corresponded to a lower length scale

(b)

Fig. 3. (a) Variation of roughness exponent ̨ with respect to etching time. (b) Plotshowing variation of saturation interface width with respect to etching time.

572 P.K. Dhillon, S. Sarkar / Applied Surface Science 284 (2013) 569– 574

FI

biasitswgaeiwclFraaobc

csbteAg(tlitwettt6tf

105

107

0s30s60s120s

101

103

10-1

108120s240s360s480s

PSD

102

104

106 600s

1E-3 0.01 0.1100

10

k(nm-1)

data with the above mentioned model. It is interesting to note that

ig. 4. Plot showing the variation of lateral correlation length � with etching time.nset: HHCF curves obtained for different etching times.

etween 0 and 1 and vice versa [14]. This indicates that the surfaces locally smoother for lower length scales (below ∼50–150 nm)nd rougher for higher length scales below 120 s of etching i.e. localurface roughness increases with length scale before 120 s of etch-ng. After 120 s, ˛1 values are lower compared to those of ˛2, i.e.he surface becomes locally rougher for lower length scales andmoother for higher length scales. This phenomenon corroboratesith the AFM topography images of etched surfaces (Fig. 1). The

lobule sizes are seen to decrease till 120 s of etching and there-fter is accompanied by undulations in overall morphology of thetched surface. Fig. 3(a) plots the variation of ˛-values with etch-ng time. It is noticed that there is an exponential increase in ˛2

ith respect to time till 240 s after which it saturates thereby indi-ating that the surfaces become smoother exponentially at largerength scales with respect to time till 240 s and saturates thereafter.or smaller length scales, on the other hand, the surfaces becomeougher with respect to time, since ˛1 is seen to decrease, exceptt 240 s which shows smoother morphology at lower length scaless compared to other etching times. For ̨ < 1, the surface morphol-gy is a self-affine fractal with an “anisotropic” scaling relationshipetween vertical and lateral directions. Since overall ̨ < 1 in thisase, therefore the resultant etched surfaces are self affine [21].

To study the time dependent dynamics of the roughening pro-ess, the growth exponent ̌ was calculated, from the variation ofaturation roughnesses with respect to time (Fig. 3(b)). A power lawehavior was observed for saturated interface widths with etchingime. It is observed that the saturation roughness increases withrosion time for 30 s and 60 s. At about 120 s, this suffers a minima.fter 120 s the saturation roughness increases monotonically. Therowth exponent ˇ, evaluated from the curve is found to be 1.11>1) thereby indicating an unstable growth [22]. This tallies withhe roughness measurements which shows a vertical shift for thisength scale with erosion time. In this instability period, growths favored in the out-of-plane rather than in-plane direction. Fur-hermore, in this regime the upward shift of w(r, t) is quite abrupthich signifies steep increments in the local surface slopes of the

volved morphology. The dynamic exponent z was evaluated fromhe correlation lengths obtained from the height–height correla-ion curves (Fig. 4). It is interesting to find that in conformity withhe behavior of growth exponent ˇ, � increases with time up to

0 s, suffers a minima at 120 s and then increases monotonically upo the etching time observed in this study. In this final phase, z isound to have a value of 0.87.

Fig. 5. Logarithmic plot of the PSD functions versus wave number k, correspondingto different etching times. Top: From pristine surface to 120 s of etching, Bottom:From 120 s to 600 s of etching.

The long range behavior of the surface heights was obtainedfrom the PSD data (Fig. 5). In order to describe the surface rough-ness over a large range of spatial frequencies, the general PSDmodel includes contributions from the substrate, overlayer andtheir superstructures [23,24]. It is noticed that the nature of allthe curves is different from that of a typical self-affine surfacein the sense that all the obtained curves exhibit a slight dip atlower frequencies. Some earlier studies done on rough surfaceshave exhibited similar trends in the PSD spectra [23,24]. The resultswere explained by the existence of superstructures on the result-ing surface. Generally, an optically finished surface can be modeledusing the relation (referred to as substrate function in the graph)

PSDsubs(f ; K, n) = K

f n+1(5)

where f is the frequency, K gives the spectral strength and n thespectral indices. When the substrate is covered with a film like mor-phology, the resulting surface can be described using the relation(referred to as overlayer function in the graph)

PSDABC (f ; A, B, C) = A

(1 + B2f 2)(C+1)/2(6)

where C is a constant greater than 2. The correlation lengths andrms roughnesses are both functions of A, B and C. Strong fractal com-ponents have been found to be present at high spatial frequencies[24]. At small frequencies, well below the knee or crossover region,the PSD is determined by A and at high frequencies, beyond theknee, the surface is fractal and is determined by C. However, all theabove models are decreasing functions of spatial frequencies andcannot account for any local increase of PSD at lower frequenciesinduced by the formation of surface superstructures. A convenientPSD for the modeling of this local maximum is a Gaussian functionwith its maxima shifted to a non zero spatial frequency given by(referred to as superstructure function in the graph)

PSDsh(f ; �sh, sh, fsh) = �2sh2

sh exp(−22sh(f − fsh)2), (7)

In the above expression, sh and �sh corresponds to the size andheight of the superstructures respectively.

Fig. 6 shows a typical fit obtained by fitting the experimental

although the overall morphology is a self-affine one, yet the surfacehas a behavior which pertains to the superstructure PSD model. Theaverage sizes and heights of the structures obtained from the fits

P.K. Dhillon, S. Sarkar / Applied Surface Science 284 (2013) 569– 574 573

Table 1Average heights (�sh) and sizes (sh) of superstructures as obtained from the fits.

Time (s) 30 60 120

Height �sh (nm) 2.14 2.95 1.2

Size sh (nm) 200.66 295.34 228.12

1E-3 0.01 0. 110 1

10 2

10 3

10 4

10 5

10 6

10 7

PSD

k(nm )-1

Exptl.dataFit for substrate functionFit for superstructure functionFit for overlayer function

F

ae

pprHsbact

Fg

ig. 6. A typical PSD data fitted using the functional forms as discussed in the text.

re provided in Table 1. For an etching time of 120 s, these valuesxhibit a clear deviation from the general trend.

Etching studies similar to the present one have been com-ared with percolation processes by many researchers [25,26]. Theresent problem can be described by the KLT model [13] whichepresents an eroding system with quenched noise. In our case ofNA etching of Si(1 0 0), the reaction products predominantly con-

ists of an intermediate SiO2 (Eq. (1)). This gets further dissolved

y HF (Eq. (2)). The relative concentration of HNO3 and HF playsn important role in deciding the type of reaction. A higher HNO3oncentration means more oxidation of Si and hence further forma-ion of SiO2. Correspondingly, a low HF means relatively less of HF

ig. 7. Flooding analyses for the acquired AFM images done with reference to the maxirayscale images) indicates hills. (For interpretation of the references to color in this figu

240 360 480 6009.24 10.25 13.82 –

393.85 317.48 530.36 1873.14

to dissolve SiO2 to form soluble H2SiF6. In our case, HF:HNO3=2:3.5i.e. the solution is richer in HNO3. Therefore, we will have an excessof SiO2 and less of H2SiF6. Hence, the reaction will be limited by dif-fusion of products away from the surface and reactants to the site[9]. This etching process can be compared to a percolating system,where during the Si surface etching the solution plays the role ofa fluid; the SiO2 products block the “fluid invasion” similar to thequenched noise, and the resulting surface acts as a fluid invasionfront. In accordance to the KLT model (Eq. (4)), the driving force Fis associated with the etching rate and the quenched noise � is rep-resented by the silicate mask, which is SiO2 in our case. Accordingto this model, the value of ̨ evaluated for the fluid invasion frontvelocities varies from 0.55 (high velocities) to 0.93 (low velocities).In our study, ˛2 values lie in this range after 120 s of etching, i.e., forlarger length scales. The percolation process was corroborated bystudying the relative percentage of hills above a certain plane fromthe AFM images. Fig. 7 shows our results for this analysis. Here redregions (dark in grayscale images) indicate hills for all the images.For this analysis, the maximum height of the 30 s image was takenas the sea plane. Any height above this value is considered to bea hill. It is clear that the percentage of hills increases rapidly withetching time except for 120 s. This implies that the etching solutionis gradually invading the surface through the valleys as it happensin a percolation scenario.

4. Conclusion

An unusual self-affine behavior has been observed for Si surfacesisotropically etched with HNA. Dynamical scaling analyses done onthe etched surfaces exhibit two different roughness exponents cor-responding to two different length scales for all the surfaces. There

exists a reversal in the local roughness characteristic for these twolength scales in all the surfaces before and after 120 s of etching.The PSD spectra for the surfaces exhibit a trend which is atyp-ical for a standard self-affine surface and can only be explained

mum height for the 30 s etched surface as the threshold. Here, red color (dark inre legend, the reader is referred to the web version of the article.)

5 Surfac

utpiAesasaam

A

c1

R

[[

[[[[

[[[[[

[

[

[

74 P.K. Dhillon, S. Sarkar / Applied

sing the superstructure model. Again, the largest deviation fromhe standard picture is noticed for the surface etching for 120 s. Theresent etching process belongs to the universality class of a fluid

nterface moving thourgh a random medium with quenched noise.nalyses done on the acquired AFM images also show the nature oftching solution invasion through the valleys of the ongoing etchingurface, thus depicting a phenomenon similar to percolation. Fromll of the above analyses, it is observed that the surface morphologyuffers a crossover at an etching time of 120 s. It is therefore envis-ged that the early stages of etching are quite unstable. It is onlyfter one crosses this unstable regime that the roughness increasesonotonically as per the model predicted by Sapoval et al. [12].

cknowledgments

The authors are indebted to Dr. S. Dasgupta for valuable dis-ussions. S.S. acknowledges financial support from ISIRD grant No.6-1/2009/IITRPR/92.

eferences

[1] P. Capper, EMIS Data Review Series, Vol. 10, Inspec, London, UK, 1988.[2] N. Johan, M. Mohamad Shahimin, S. Shaari, Proc. 2010 IEEE Student Conf.

Research and Development, 2010.[3] H. Park, S. Kwon, J.S. Lee, H.J. Lim, S. Yoon, D. Kim, Solar Energy Materials and

Solar Cells 93 (2009) 1773, ISSN 0927-0248.

[[

[

e Science 284 (2013) 569– 574

[4] M.S.J. Acker, K. Wetzig, Journal of Physical Chemistry C 112 (2008) 14139.[5] T.-R. Hsu, MEMS & Microsystems Design and Manufacture, Tata McGraw-Hill,

New Delhi, 2002.[6] V.B. Svetovoy, J.W. Berenschot, M.C. Elwenspoek, Journal of Micromechanics

and Microengineering 17 (2007) 2344.[7] M. Madou, Fundamentals of Microfabrication, CRC Press, Boca Raton, FL, 1997.[8] H. Robbins, B. Schwartz, Journal of the Electrochemical Society 106 (1959) 505.[9] H. Robbins, B. Schwartz, Journal of the Electrochemical Society 107 (1960) 108.10] B. Schwartz, H. Robbins, Journal of the Electrochemical Society 108 (1961) 365.11] A.F. Bögenschutz, W. Krusemark, K.-H. Locherer, W. Mussinger, Journal of the

Electrochemical Society: Solid State Science 114 (1967) 970.12] A. Gabrielli, A. Baldassarri, B. Sapoval, Physical Review E 62 (2000) 3103.13] H.L. David, A. Kessler, Y. Tu, Physical Review A 43 (1991) 4551.14] M. Pelliccione, T. Lu, Evolution of Thin Film Morphology, Springer, Berlin, 2007.15] P.K. Dhillon, S. Sarkar, A. Franquet, A. Moussa, W. Vandervorst, Applied Surface

Science 258 (2012) 9579, ISSN 0169-4332.16] J. Buijnsters, M. Camero, L. Vazquez, Physical Review B 74 (2006) 155417.17] M. Pelliccione, T. Karabacak, T.-M. Lu, Physical Review Letters 96 (2006) 146105.18] R. Cafiero, V. Loreto, P. Prosini, Europhysics Letters 42 (4) (1998) 389.19] M.E.R. Dotto, M.U. Kleinke, Physical Review B 65 (2002) 245323.20] G. Wisz, T.Y. Gorbach, P. Smertenko, A. Blahut, K. Zembrowska, M. Kuzma,

Superlattices and Microstructures 36 (2004) 353.21] H.-N. Yang, Y.-P. Zhao, A. Chan, T.-M. Lu, G.-C. Wang, Physical Review B 56

(1997) 4224.22] M.A. Auger, L. Vázquez, S.O.M. Jergel, R. Cuerno, M. Castro, Journal of Applied

Physics 97 (2005) 123528.23] J. Ferre-Borrull, A. Duparre, E. Quesnel, Applied Optics 40 (2001) 2190.

24] N.K. Sahoo, S. Thakur, R.B. Tokas, Thin Solid Films 503 (2006) 85.25] R. Buzio, E. Gnecco, C. Boragno, U. Valbusa, P. Piseri, E. Barborini, P. Milani,

Surface Science 444 (2000) L1, ISSN 0039-6028.26] S.V. Buldyrev, A.-L. Barabáasi, F. Caserta, S. Havlin, H.E. Stanley, T. Vicsek, Phys-

ical Review A 45 (1992) R8313.