Diffusion Limited Growth of Ultra-thin Organic Films

I. Melnichuk, A. Choukourov, D. Slavínská, and H. Biederman Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.

Abstract. After a metal and inorganic coatings era, more and more attention is given to the growth of organic thin films as they find great number of applications in various fields including organic semiconductor displays, microelectronics, medicine etc. For well-controlled fabrication it is important to understand the basic growth principles that govern adsorption, surface diffusion, chemical binding and other atomic processes at surfaces, from the very beginning. Several organic precursors (for example, pentacene and para-sexiphenyl) have been successively processed by Physical Vapor Deposition (PVD) to fabricate thin films. Often, their morphological development can be described sufficiently well with a diffusion limited aggregation model, a universal concept widely applied to inorganic systems before. Our work reviews the progress achieved in the field of organic film growth with the emphasis set on the early stages of the film formation. Furthermore, the first results are presented on the island-type PVD growth of ultra-thin poly(ethylene) films. Applicability of the already existing theories to description of dynamic phenomena is discussed.

Introduction Organic thin films are regarded to be promising subject of research nowadays. This interest is

partially motivated by the number of organic substances which is overwhelmingly larger than that of inorganic materials, and also because of new and useful properties of organic thin films can be expected. The applications of vacuum-deposited materials are broad including, for example, displays, light-emitting diodes, transistors, solar cells, sensors, etc., with undoubtedly big potential for future devices. The successful development of above-described applications strongly depends on our ability to control composition and structure of the resulting thin films.This can only be achieved once a fundamental understanding of the underlying growth mechanisms is established, in particular with respect to the initial stages of first layer growth.

Organic molecular beam deposition (OMBD) is a typical ultrahigh-vacuum method of thin film preparation for organic semiconductors and it has an advantage of providing both precise thickness control and an atomically clean environment. In inorganic thin-film growth by molecular beam epitaxy (MBE), a diffusion-limited aggregation (DLA) model [1–3] has led to predictions of the fractal character of individual aggregates and it has also been employed to formulate scaling theories (for example, a Dynamic Scaling Theory) to describe the island size distribution and its evolution with coverage. However, little analogous quantitative information exists about the applicability of diffusion models to organic films prepared by OMBD.

The Dynamic Scaling Theory (DST) is a material independent concept that sets a strong correlation between the critical island size and the island size distribution, a fundamental quantity in the kinetic description of island growth. In this context, the critical island size i is defined as a largest nucleus which still has a significant probability to decay at the given growth temperature and deposition rate [14]. Or conversely, i + 1 is the smallest number of atoms or molecules that will form a stable nucleus. The critical size depends on the interatomic (intermolecular) forces between the monomers of the film material and the substrate atoms. This value is critical for the further film growth, the final film structure and morphology. Recently, the first reports appeared on application of the DST to characterization of the critical nucleus size for different small organic molecules. Typically sizes between 2 and 4 are found for rod-like molecules. For para-hexaphenyl (C36H26), the values between 2 and 3 are reported [6, 8], similar to i = 3–4 reported for pentacene (C22H14) growth on SiO2 [4, 5, 9, 10] or cyclohexane terminated Si(001) [11]. Nevertheless, a question arises of whether the dynamic scaling can also be applied to the nucleation and growth of films consisting of large organic molecules. The simplest system that can be explored in this context is linear aliphatic macromolecules such as poly(ethylene) (PE). Previously, the group of Li reported that PVD could be used for patterning of poly(ethylene) oligomers on carbon nanotubes (CNTs) [12, 13]. PE single-crystal rods

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were deposited uniformly over CNTs with their axes being perpendicular to the CNT axes. The rods spanned relatively periodically along the entire surface covered by CNTs. Numerous small PE islands with an average height of 10 nm were also formed on the substrate regions unoccupied by the CNTs. The authors, however, did not pay significant attention to them while focusing on interaction of PE macromolecules with the CNTs themselves.

In this work, we focus on the nucleation and growth of PE islands fabricated by the PVD method onto smooth silicon substrate. We first describe the nucleation model of the DST, which can be seen as a model system for organic film growth. In the next section, we give an overview of the deposition technique and details of the AFM analysis used for the estimation of the scaling behavior of the islands. Finally, the first results are presented.

Model Growth of organic thin films is an enormously rich subject with many different theoretical

approaches. The chain of elementary processes following the impact of an oligomer molecule on the surface is schematized in Figure 1. A thorough treatment of its theoretical aspects can be found in [14–17]. Here we want to briefly touch upon the aspects of the adatom diffusion and formation of stable islands as well as on dynamic scaling of islands.

For systems where desorption can be neglected the kinetics of the surface diffusion process is determined by the ratio of the diffusion constant D to the incoming flux F (R=D/F). The mobility of the molecules on the surface is confined, and their movement can be described as a two-dimensional random walk with the surface diffusion coefficient D 𝐷 = 1/4𝑎2𝑣, (1) where a is the effective hopping distance between sites, and the factor 1/4 is a convention reflecting the two-dimensional nature of surface diffusion.

𝑣 = 𝑣0 ∙ 𝑒𝑥𝑝−𝐸𝐷𝑘𝑇 (2)

is the particle jump rate on the surface. Here ED is the potential energy barrier the particle has to overcome, T the temperature and kB the Boltzmann constant. The pre-exponential factor is often referred to as the attempt frequency. In the initial stage of growth on a flat surface, if the deposition rate F is fixed, the value of D determines the average distance an adatom will have to travel before (i) finding and joining an existing island or (ii) meeting another adatom to create the possibility of nucleating a new island.

Diffusion mediated growth involves four qualitatively different steps [18, 19]. Initially, monomers diffuse on a bare substrate and, as soon as a critical number of them meet, form a stable nucleus. In the second and intermediate regime new adsorbates still nucleate new islands or start aggregating into existing ones. Then, in the aggregation regime, the island density and size have become sufficiently large that every incoming molecule lands either near or on top of an existing island. Finally, the growing islands join and start coalescing and eventually second-layer growth occurs.

Figure 1. Schematic of processes relevant in thin-film growth, such as absorption, desorption, intra-layer diffusion (on a terrace), interlayer diffusion (across steps), nucleation and growth of islands [20].

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The DST assumes that molecules arriving on top of an island may diffuse towards its edges and move one step down without any inter-island step barrier. As long as a molecule steps down, it attaches to the rim and becomes a part of an island (no diffusion along the edge is allowed). Alternatively, several molecules on top of an island may meet to start the formation of the second layer. However, in view of the high D/F ratio this scenario is regarded unlikely in the DST. In the aggregation regime, the adatoms aggregate into existing islands only, thus inducing a lateral enlargement of the grains, but resulting in a nearly constant nucleation density. This 2D aggregation regime is well described by the DST.

The aggregation regime, with theoretical coverage 𝜃 between 0.1 and 0.5 of the monolayer (ML), is of particular interest because it shows a scaling behavior of the island size distribution and presents only one characteristic length scale [18]. According to the dynamic scaling assumption [18], the distribution of islands of size s per unit area, 𝑁𝑠(𝜃), scales with the mean island size 𝑆(𝜃) as 𝑁𝑠(𝜃) = 𝜃S(𝜃)−2𝑓(𝑢). (3) Here, 𝑢 = 𝑠/𝑆(𝜃) and 𝑓(𝑢) is a dimensionless 𝜃-independent scaling function that contains all system-specific information. The particular distribution of the scaling function is determined by the critical island size i. Amar and Family [7] proposed an analytical expression for the scaling function in the form: 𝑓(𝑢) = 𝐶𝑖𝑢𝑖exp (−𝑏𝑖𝑖𝑢1/𝑏𝑖), (4) where 𝐶𝑖 and 𝑏𝑖 are fixed by implicit geometrical equations, which assure normalization and proper asymptotic behavior of 𝑓(𝑢). Thus, one may check the applicability of the DST to a certain deposition by plotting the dependence of NsS2/θ vs u for different coverages. The resultant data should fall in this case into a single scaled distribution. The critical nucleus size i can be determined by fitting the experimental data with the above scaling function.

Experimental The experiments were performed in a cylindrical vacuum chamber of 0.04 m3 volume pumped

with rotary and diffusion pumps to a base pressure of 1×10−3 Pa. After reaching the base pressure, argon was let into the chamber at a 5 sccm flow rate and the working pressure was set at 1 Pa. Solid polyethylene (Sigma-Aldrich, M ≈ 180950 g·mol–1) was used as starting material for deposition process. PE granules were loaded into a copper crucible, which rested on two molybdenum stripes heated by electric current. Vacuum thermal degradation of polymers leads to emission of low molar mass fragments which can condense on adjacent surfaces. Polished silicon wafers were used as the substrates. The substrates as well as a quartz crystal microbalance (QCM) head used for the measurements of the deposition rate were placed 10 cm above the crucible. Prior to each deposition the experimental parameters (Ar pressure and flow rate, PE evaporation rate) were tuned. During this pre-adjustment stage, the substrates were residing in a load-lock chamber and after stabilization of the deposition conditions they were introduced to their working position above the crucible. Consequently, after the deposition the samples were removed from the evaporation zone to the load-lock chamber.

The evolution and growth of PE islands were investigated at a constant QCM frequency shift (20 Hz/min). Thin films with different nominal layer thickness values, starting from very low coverages all the way through the coalescence and percolation regimes, were fabricated. A comparison of the nucleation density for the films with 0.09 ML ≤ θ ≤ 0.29 ML reveals that the nucleation density is already saturated assuring that the aggregation regime is fulfilled. AFM in tapping mode has been used under ambient conditions to characterize the resulting film morphology; for each sample, 5×5 μm height images were statistically analysed. The parameters observed included the number of grains per analysed area, the grain size and density, the first monolayer coverage, the grain heights and in general the grain morphology.

Results and discussion In order to learn quantitatively more about the growth dynamics of polyethylene on silicon we

have analyzed the scaling law of the polyethylene island size distribution in the aggregation regime

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Figure 2. (a), (b) The AFM height images of polyethylene islands at 0.12 and 0.29 ML, respectively. (c) Island size distribution Ns(θ) of polyethylene islands at various coverages in the range 0.09 ML ≤ θ ≤ 0.29 ML grown on silicon at room temperature. (d) Scaled island size distribution for polyethylene grown on silicon at room temperature. The scaling function f(s/S) for critical cluster size of i = 2.3 is indicated by the solid curve.

(corresponding to coverages in the range 0.09 ML ≤ θ ≤ 0.29 ML) at room temperature. An example of two different submonolayer coverages is shown in Figures 2a,b. Visual inspection shows that island size and separation are quite regular. The island size distribution density Ns(θ) can be extracted from a frequency count analysis of the AFM micrographs and are plotted for different coverages in Figure 2c, where s is expressed in μm2 and Ns(θ) in μm–4 as a distribution density such that ∫𝑁𝑠(𝜃)𝑑𝑠 = 𝑁. In detail, five 5×5 μm2 AFM images of the same sample have been used for better statistics to build the histogram of areas, where the area occupied by each island was calculated previously and the entire range of areas was divided into bins with constant interval. The number of islands was per the bin interval. For each coverage the distribution density exhibits a well-defined maximum at S(θ). The average island size S increases with increasing θ and the distribution broadens. After applying the scaling law according to 𝑁𝑠(𝜃) = 𝜃𝑆(𝜃)−2𝑓(𝑢), all data collapse into a single scaling function f(s/S), as shown in Figure 2d. It is possible to model the distribution of the universal scaling curve according to the critical size i with the empirical expression [9]. The least square fit, with the best agreement between experimental data and model, gives i = 2.3 (solid line in Figure 2d), i.e., once 3 or 4 polyethylene oligomers join, this nucleus will grow rather than decay. The quantitative agreement of the scaling function with the island size data indicates that polyethylene on silicon exhibits DST growth behaviour.

Conclusion Submonolayers of polyethylene grown by physical vapor deposition at stable deposition rate on

silicon consist of compact islands. It was experimentally shown that the aggregation regime, that is,

θ=0.29

a) b)

θ=0.12

0,00 0,05 0,10 0,150

30

60

900

50

100

1500

50

100

1500

50

100

150

Island area, s, µm2

θ =0.29

θ =0.21

Isla

nd d

istrib

utio

n de

nsity

, Ns(θ

), µm

-4

θ =0.18

θ =0.12

0 1 2 3 4 50,0

0,2

0,4

0,6

0,8

1,0

θ = 0.09

N sS2 /θ

s/S

θ = 0.12 θ = 0.18 θ = 0.21 θ = 0.24 θ = 0.29

i = 2.3 (free fit)

c) d)

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where the number of islands remains essentially constant, lies between 0.09 and 0.29 monolayers. The dynamic scaling confirmed that the formation of the first layer is a diffusion-mediated process and that dynamic scaling model well known in inorganic thin-film growth can be applied to the first monolayer of polyethylene on silicon. A critical island size of 2.3 was deduced, indicating that trimers or tetramers of PE form stable islands. The further research will be focused on deposition of PE-like plasma polymer films by plasma enhanced physical vapor deposition and their comparison with the results of the PVD deposition.

Acknowledgments. The present work was supported by the grant SVV 267305/2013.

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