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Physica E 40 (2008) 2446–2453 Multilevel modeling of the influence of surface transport peculiarities on growth, shaping, and doping of Si nanowires A. Efremov a , A. Klimovskaya a,à , I. Prokopenko a , Yu. Moklyak a , D. Hourlier b a Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 45 Nauki Avenue, 03028 Kyiv, Ukraine b Institute d’Electronique, de Microe ´ lectronique et de Nanotechnologies, ISEN, UMR-CNRS 8520, F-59652 Villeneuve d’Ascq, France Available online 15 February 2008 Abstract The growth, shaping, and doping of silicon nanowires in a catalyst-mediated CVD process are analyzed within the framework of a multilevel modeling procedure. At an atomistic level, surface transport processes and adsorption are considered by MC simulations. At the macroscopic level, numerical solutions of chemical kinetics equations are used to describe nanowire elongation growth and doping. Both atomistic and kinetic considerations complementing each other reveal the importance of surface transport and the role of low- mobility impurities present on the catalyst surface in the nanowire growth process. In particular, a controllable shaping and selective doping of nanowires is possible by means of well-directed effects on the surface transport of both silicon and impurity adatoms. Some nonlinear effects in the growth and doping caused by percolation-related phenomena are demonstrated. r 2008 Elsevier B.V. All rights reserved. PACS: 62.23.Hj; 81.10.Aj; 82.20.Wt; 05.10.Ln; 68.35.Fx; 66.30.Pa Keywords: Nanowire growth; MC simulations; Kinetic modeling; Nanowire doping; Controllable shaping 1. Introduction The semiconductor industry nowadays decidedly ap- proaches the era of nanotechnologies. In view of prospects for further decreasing sizes of circuitries and their elements, a vital need arises in low-dimensional materials and objects with strictly controlled electronic properties determined by a nanostructure. Silicon nanowires (NWs), grown in a catalyst-mediated CVD process, are still considered to be the most promising type of nano-objects. This fact is associated with a significant amount of device applications in addition to those already realized. However, a selective synthesis of NWs possessing a desired structure and properties remains a rather difficult problem so far. To determine the best conditions for the growth of NWs and for a better understanding of the role played by different macro- and micro-parameters of the synthesis (temperature, pressure, catalyst surface properties, growth- limiting factors), it is necessary that numerical and statistical simulation techniques be us ed more extensively. This will enable us to predict the NW structure, shape and size evolution, distribution of impurities, and other relevant properties determined at the growth stage. In this work, we consider some essential mechanisms of a catalyst-mediated synthesis of NWs involving a surface transport across the catalyst particle surface. We use multilevel (combined) modeling as a tool. At an atomistic level, it includes an Monte- Carlo (MC)-simulation of selected key stages of the process. A macroscopic descrip- tion of the growth process is based on a numerical solution of a system of rate equations for chemical reactions and mass transfer. We will consider the influence of the mass transfer of adatoms with different local mobilities (silicon itself, conventional dopa nts, products of surface reactions, etc.) across the catalyst surface on the growth, shape, and doping of NWs. Using the MC technique, we have obtained the dependence of an effective coefficient of silicon adatom surface diffusion on the surface coverage and catalyst ARTICLE IN PRESS www.elsevier.com/locate/physe 1386-9477/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2008.01.015 à Corresponding author. Tel.: +38 044 5257091; fax: +38 044 5258342. E-mail address: kaignn@rambler.ru (A. Klimovskaya). particle size for a single- and two-component system. For the case where the second component is a low-mobility impurity, we have simulated the kinetics of adatom spreading across the catalyst surface and their approaching sidewalls of NWs. It has been shown that when the surfa ce coverage with a low-mobility impurity exceeds some critical value, the mass transfer of mobile adatoms is passed from diffusion to sub- diffusion [1]. When the coverage increases further, a full blocking of the surface trans port occurs. The results obtained allow us to explain a number of experiments where some unusual shape of an NW was observed [2–7] and to predict several nontrivial effects when NWs are doped from a gaseous phase during the growth process. 2. Modeling We will restrict our consideration to the processes at the catalyst surface (Fig. 1 ). As compared to other parts of a nano-object, here most intensive decomposition of an active gas takes place and the highest concentration of mobile silicon atoms or dopants is maintained. The control of further redistribution of these atoms, while they are moving towards the interface and sidewalls of a NW, seems to be just the key, which controls the nano-object shape and its doping quality. The NW growth process in general and some of its stages can be considered within the kinetic approach framework (the mean field model) by a numerical solution of the corresponding balance equations [2]; however, an adequate consideration of the surface transport of adatoms across the catalyst requires another approach to be applied. Here, the concentrations of different components can be high enough and their mobilities can differ from each other in an arbitrary way. In this specific case, the surface transport cannot be consider ed as a usual diffusion, but represents the so-called ‘‘strange process’’. A kinetic description of such processes is possible within the frame- work of the so-called fractional dynamics or strange kinetics [1]. In particular, the Einstein relation transforms into [1] R 2 ¼ 4D eff t m . (1) Here /R 2 S is the mean-square displacement of a randomly walking particle during the time t, and in a general case m6¼1. For a multicomponent nonlinear system and also when the mass transfer is accompanied by other processes (adsorption from a gaseous phase, chemical reactions, etc.), this formalism meets great difficulties. At the same time, the above peculiarities, including a detailed description of the space distribution evolution of adatoms across the catalyst surface, can be directly studied by applying the MC techniques without using the ‘‘strange kinetics’’ formalism. We will deliberately restrict the application of the MC- simulation to this part of a growing nano-object alone and only to the above-mentioned key stage of the process. We will not use an atomistic approach to simulate the whole growth process. Such a consideration will be used to show how these results can be included into a more comprehen- sive macroscopic model based on a numerical solution of chemical kinetics rate equations for an axial or radial growth, shaping, doping, and other related pr ocesses. A local application of the MC-simulation to the transport processes in only this area allows us: (i) to estimate correctly the values of some physical parameters (the dependence of the transport coefficient on the surface concentration) with their subsequent utilization in a chemical kinetics simulation by numerical solution of the rate equations, (ii) to reproduce some key stages of a real physical experiment. Besides, we will demonstrate a number of advantages of ‘‘the multilevel simulation’’. This approach includes both atomistic and macroscopic descrip- tion within a single model framework and allows us to avoid the above-mentioned difficulties of the approach based on strange kinetics. While simulat ing atomic transport across the catalyst surface and analyzing the accompanying chemical pro- cesses, the following elementary events were selected: (i) The adsorption from a gaseous phase onto a single, randomly selected empty surface site [8]. (ii) A diffusion jump of a randomly selected adatom in a random direction for some distance l (the distance between the nearest sites) during a time step t if there is a free site. In a general case, an irreversible diffusion of the selected adatom into the catalyst bulk may be considered. This will be done in the framework of a growth kinetic model in the following sections. The MC-simulation that included the above processes was carried out on a two-dimensional lattice of 100  100 atomic cells in size, which corresponded to a real NW diameter of the order of 20 nm. ARTICLE IN PRESS Fig. 1. Distribution of molecular and atomic fluxes assumed in the kinetic NW growth model: (1) a liquid eutectic drop/solid metal catalyst particle, (2) the NW body, (3) adsorption of molecules from a gaseous phase, (4) surface transport of adatoms towards the NW sidewalls, (5) bulk transport of silicon (impurity) adatoms towards the catalyst/silicon interface. A. Efremov et al. / Physica E 40 (2008) 2446–2453 2447 We have carried out four types of numerical experi- ments, which complemented each other: (i) A migration of a test particle across the catalyst surface from the center of a round region until the first contact with its boundary is achieved. This was simulated for various coverages. Then its path time was averaged [9]. In this case, other atoms represented some kind of a background for the test particle movement. They jumped with a local mobility of D loc ¼ 1/4l 2 /t, which, in a general case, did not coincide with the local mobility of the test particle itself. The adsorption was ignored in the experiment. This MC-simulation experiment allows us to estimate an effective transport coefficient D eff as a function of the coverage and the exponent m, which describes the state of such a surface (Fig. 2a). (ii) A classical MC-simulation experiment was also carried out [9,10] where (at periodic boundary conditio ns) random trajectories of all the atoms were monitored. After that, the values of the mean-square displacement /R 2 S were calculated for a given process duration of t. These results are compared with the previous case. (iii) We simulated the behavior of a system consisting of two kinds of atoms with strongly differing mobilities. We observed a non-steady-state kinetics of mobile atoms, which left the catalyst surface and diffused towards the NW sidewalls at various initial concentra- tions of components (Fig. 3). (iv) We calculated a steady-state relation between the input flux of molecules adsorbed from a gaseous phase (J inp ) and the output flux of adatoms (J out ) leaving the catalyst surface due to the surface mass transfer (Fig. 1). In a similar man ner, we determined the relation between J inp /J out and the resul ting steady-state average concentration of adatoms /YS at the catalyst surface (Fig. 4a and b). The first two versions of simulations enable us to obtain transport coefficients and to use them in a numerical solution of rate equations describing the grow th of NWs. The second tw o MC experiments reproduce a fragment of a ARTICLE IN PRESS Fig. 2. Results of MC simulation of the mass transfer at the catalyst particle surface. (a) The dependence of a normalized effective diffusion coefficient on the surface coverage and its analytical approximation. It is obtained from the relationship between the mean path time of a test particle /tS and the corresponding mean-square displacement /R 2 S ¼ R 2 . Here D 0 corresponds to a surface diffusivity value at zero coverage. The MC experiment conditions: (1) migration of a test particle at the surface covered with the mobile atoms, which are identical to the test particle itself. Periodic boundary conditions are applied to the background adatoms. The test particle moves along a random trajectory from the center of the region with a given radius of R until the first contact with its boundary is achieved. (2) Migration of a mobile test particle across the surface previously covered with a low-mobility impurity. Here, the mobilities of the test and background particles differ by more than three orders of magnitude. (b) Space distribution of allowed trajectories of a test particle at the surface covered with a slow background impurity at Y slow ¼ 0.38, 0.41, 0.42, and 0.43, respectively. Fig. 3. The MC simulations of the kinetics for spreading of the mobile atoms across the surface in a two-component system. At t ¼ 0, both mobile and slow background impurity atoms are randomly and uniformly distributed over the surface. The curves, smoothed by a median filter, describe the time dependence of mean coverage with the mobile atoms /Y mob S corresponding to different initial coverages with slow impurity Y slow of 0, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, and 0.69 (1–8). The initial coverage with the mobile atoms for all the cases is identical and equals 0.3. A. Efremov et al. / Physica E 40 (2008) 2446–24532448 real physical process and allow us to compare the results of MC and kinetic simulations. 3. Results and discussion 3.1. Effective transport coefficients and their use in an NW- growth kinetic model The experiments with a test particle migration on a lattice covered with the mobile atoms of the same kind have shown that the Einstein relation remains valid within a wide range of surface concentrations. An effective transport coefficient D eff is a monotonically decreasing function of Y shown in Fig. 2a. Here, in our case, the mean residence time of an adatom at the surface /tS depends on the system size R and the diffusion coefficient D eff exactly like the quasi-steady-state diffusion time (QSSDT) does [11] in an ordinary diffusion process. Let us remember that QSSDT is the time in which about two-thirds of all the atoms leave a given region. Using this analogy and applying some analytical approximation of the obtained dependence for an effective diffusion coeffi- cient (e.g. D eff ¼ D 0 (1–Y) n , where n is some app ropriate exponent and D 0 is the surface diffusivity on a free surface), we can obtain a simple balance equation for the mean concentration of adatoms at the catalyst particle surface (shown in Fig. 1 in the form of a hemisphere of radius R). We note that the NW axial growth (elongation) rate is also expressed as a function of mean concentration of adatoms at the surface. Therefore, without considering the fine details of the adatom space distribution (that we even cannot find within the framework of an ordinary kinetics), we will write the following system of NW-growth rate equations in the form s dY dt ¼ J inp ð1 À YÞÀsYðb þ 1=htiÞ, dh dt ¼ 2 bsYO, (2) where s is the surface density of sites available both to diffusion and to adsorption, b is the rate constant for bulk transport of adatoms while they are passing through the catalyst particle bulk, Y is the mean coverage. For b, the following estimate can be taken: b % k D b Rl b , where D b is the bulk diffusion coefficient in the catalyst material, l b is the lattice spacing in the catalyst bulk, and k is the factor of the order 0.5. The input flux J inp is determined by the number of molecules, which impinged and would be really adsorbed on the surface (if the surface was free), per unit area and unit of time J inp ¼ nJ mol expðÀE a =k B TÞ, (3) where n is the number of silicon (or impurity) atoms in a molecule, E a is an activation energy for chemisorption, k B is the Boltzmann constant, and T is the temperature of the surface. The surface transport intensity is given by a reciprocal characteristic particle residence time /tS at the hemisphere surface. In our case /tS À1 ¼ a D 0 (1–y) n /R 2 , where a ¼ m 0 2 / (p/2) 2 E4.615 is a coefficient of shape in a QSSDT approximation for a hemispheric region [11],andm 0 is the first root of the zero-order Bessel function. The second equation of the system describes the NW axial growth due to bulk diffusion of silicon atoms from the surface to the catalyst/NW interface. Here, h is the height of the NW and O is the atomic volume of a silicon atom in a silicon lattice, the factor 2 is the ratio of the catalyst external surface area to that of the interface for a hemispheric catalyst particle. ARTICLE IN PRESS Fig. 4. The MC simulations of the surface steady-state characteristics under the adsorption of silicon-containing molecules together with the surface transport of silicon adatoms towards the sidewalls. (a) The dependencies of a normalized steady-state output flux J out /J inp (1) and an averaged steady-state surface coverage /YS (2) on the input flux of molecules to the surface J inp . (b) The normalized steady-state output flux as a function of the averaged steady-state surface coverage. A. Efremov et al. / Physica E 40 (2008) 2446–2453 2449 A steady-state (dY/dt ¼ 0) equation corresponding to a constant axial growth rate is nonlinear. The input flux J inp is a parameter in it. The equation in a dimensionless form can be written as follows: J inp J 0 ¼ð1 À E r sb Þ Y ð1 À YÞ þ E r sb Yð1 À yÞ nÀ1 . (4) E r sb ¼ t b =ðt b þ t s Þ corresponds to a fraction of the surface channel within the total mass transfer, t b ¼ Rl b /kD b is the characteristic time of bulk diffusion towards the catalyst particle interface, and t s ¼ R 2 /aD 0 is the corresponding characteristic time of the surface mass transfer towards the boundary line between the catalyst particle and the NW sidewall. A relative role of the surface transport can be character- ized by the ratio of times t b =t s ¼ða=kÞðl b =RÞðD 0 =D b Þ% 0:1ðD 0 =D b Þ.HereJ 0 ¼ s/t eff is the characteristic flux and t eff ¼ t s t b /(t s +t b ) is the effective time of adatom residence at the catalyst surface. It is seen that the surface-transport relative role increases with the decreasing in catalyst particle size. It is possible to show that the surface transport will surely dominate over that of the bulk (e.g. at t b /t s E100) for an NW with the dimensions of Rp100l b (Rp20 nm) in the case when the surface diffusion coefficient (for zero cover- age) exceeds that of the bulk by about three orders of magnitude. The last condition is met in excess for many materials and diffusants, although there are also exclusions. A steady-state coverage Y, as a function of the dimensionless input flux J inp /J 0 , was numerically calculated in agreement with Eq. (4) for n ¼ 1.5 (Fig. 2a). The dependences obtained are shown in Fig. 5. It is seen that some narrow interval of critical values of the input flux exists for the system. Just here a sharp step is observed on the dependence. In this case, the system is located in the vicinity of the percolation threshold Y ¼ 1/2. Within this critical interval, the steady-state equation has three solutions x 1 , x 2 , and x 3 , corresponding to a given input flux (Fig. 5a). And even small input flux fluctuations in the critical region will cause great oscillations in the value of Y and all parameters associated with this value including axial and radial growth rates. As the input flux increases, the concentration of adatoms at the outset increases gradually. However, when passing the percolation threshold, the system sharply switches to the state with a high surface concentration of adatoms and high axial growth rate. Any reverse changes in the input flux against the background of an intensive bulk transport will cause reactivation of the surface mass transfer, a gain in shell growth, a sharp decrease in the surface concentra- tion, and the corresponding slowdown of the axial growth. As a result of such fluctuations in the input flux and the surface coverage during the growth process , variations in the shape become possible (including the appearance of periodic oscillations [3,4]). Besides, it should be emphasized that in the critical region of the fluxes, depending on the initial conditions on the catalyst particle surface (which generally are weakly controllable), the surface may come to any of the three above-mentioned steady states, which correspond to Eq. (4) roots. Thus , at given conditions of temperature and pressure in the growth chamber, three different axial growth rates may be observed for the NWs. As a result, this can cause an unexpected scattering in NW lengths for a given ensemble. The dependences between the input and output fluxes obtained using the MC technique (Fig. 3) have shown that in a system of a finite size at a high-input flux, the surface transport is suppressed only in the central part of the nano- object surface. Here, the local surface concentration a easily overcomes the percolation threshold, and the situation is ARTICLE IN PRESS Fig. 5. The solutions of a steady-state Equation (4). (a) A graphic illustration of the solution at different E r sb . Curves 1–5 correspond to the right-hand part of Eq. (4) denoted by Y(Y) and Curve 6 is the straight line corresponding to the given value of the normalized flux in the left-hand part of this equation. The points of intersection of the two curves give the steady-state solutions (coverages) for a given input flux. Curves 1–5 are obtained at E r sb ¼ 0.95, 0.983, 0.99, 0.995, and 1.00, respectively. (b) The steady-state coverage as a function of the input flux at different values of E r sb obtained as the first (least) root of Eq. (4). This solution is realized for a zero initial condition at the surface. Curves 1–5 correspond to E r sb ¼ 0.90, 0.95, 0.983, 0.99, and 0.995, respectively. Corresponding values of the ratio of times t b /t s are 9, 19, 57.8, 99, and 199. A. Efremov et al. / Physica E 40 (2008) 2446–24532450 similar to that predicted by a kinetic model Eq. (4). At the same time, due to the presence of a near-boundary sink for atoms towards the NW sidewall, a narrow strip containing sufficient number of vacant sites always exists at the catalyst particle periphery. Not only a rapid surface transport is possible through these sites, but also local adsorption from a gaseous phase goes on. The main contribution to the output surface flux is made not by impeded diffusion delivery from the central part to the periphery, but by the direct adsorption of molecules to the vacant sites located in the very peripheral region of a catalyst particle. The width of the region gradually decreases with the increase in the input flux. This feature is demonstrated in Fig. 4 where the depen- dences of J out /J inp ¼ f(/YS)andJ out /J inp ¼ j(J inp )onthe mean coverage /YS and on the input flux are presented, respectively. The input flux J inp is determined similarly to Eq. (3), but here it is measured as the number of adatoms incoming on a free surface (due to chemisorption and dissociation of impinging molecules) per one site, per one MC time step. In a like manner, the output flux is the number of adatoms leaving the given region of the surface (due to the surface transport), per one MC time step and per unit of the boundary length. The surface transport ceases coping with the flux that comes to the surface already beginning from /YSE0.25, which corresponds to reaching Y max E0.5 in the catalyst central part. B eginning from this moment, the initially homogeneous system is split into the central part, over- saturated with adatoms and a periphery, relatively free of adatoms. A rough-and-ready kinetic model, being incapable of describing these fine details in the surface distribution of atoms, nevertheless correctly predicts the dependence of the concentration on the flux in the catalyst’s central part, where the adatoms are distributed almost homogeneously. Thus, a kinetic simulation used in combination with the MC simulation of test particle random walks may be rather promising while studying a real growth. 3.2. Peculiarities of NW doping according to the kinetic model Let us add a seco nd (doping) component to the gaseous phase. We will consider that the parameters characterizing this doping impurity with regard to the molecular adsorption, bulk diffusion, and surface transport at the catalyst do not strongly differ from the corresponding parameters of sil icon. Using Eq. (4), we would rewrite the rate equations for coverages with atoms of silicon Y and impurity F in the followi ng form: s dY dt ¼ J 1 ð1 À Y À FÞÀsYðb 1 þ 1 = t 1 hiÞ , s dF dt ¼ J 2 ð1 À Y À FÞÀsFðb 2 þ 1 = t 2 hiÞ , V h ¼ dh dt ¼ 2sðYO 1 b 1 þ FO 2 b 2 Þ, Yð0Þ¼Y i and Fð0Þ¼F i ; x ¼ J 2 =J 1 . (5) Here, the subscripts ‘‘1’’ and ‘‘2’’ refer to the matrix and impurity atoms, respectively. The initial coverages are denoted by Y i and F i . The kinetics of NW bulk doping is determined by a relative impurity concentration near the interface during NW growth: C I ¼ C I ðtÞ¼b 2 F=ðb 1 Y þ b 2 FÞ%ðb 2 =b 1 ÞÁFðtÞ=YðtÞ. (6) Here from, C I ¼ C I (z),z ¼ h(t) will be the impurity distribution along the NW length after the growth process accomplishment. In the case when local mobilities of matrix and impurity atoms are close to each other and F/Y51, then a factor that retards diffusion will just be a summary coverage of the surface. The MC simulation results allow us to write the characteristic surface mass transfer times as t 1 hi À1 ¼ aD 01 ð1 À Y À FÞ n =R 2 ; t 2 hi À1 ¼ aD 02 ð1 À Y À FÞ n =R 2 : (7) We have studied system (5) numerically and calculated the impurity distribution along the NW length at different initial conditions and ratio of times t b /t s . The results obtained can be summarized as follows: (i) After a long enough period of time, the ratio of concentrations at the interface approaches that of fluxes in a gaseous phase, C I (t) t-N -x. However, the duration of this transient process strongly depends on the initial coverage Y i and on the relation between bulk and surface transport t b /t s p1/R. This effect is thus size dependent. (ii) In the case when the initial concentrations of both the components at the catalyst surface are equal to zero, the transient process is absent and C I (t) ¼ x already at the very beginning of the growth. As a result, a homogeneous bulk doping of an NW is achieved. (iii) If F i ¼ 0, Y i X0.5, and D 0 /D b X10 3 , the transient process duration becomes comparable with the total growth period. As a result, C I (t) slowly increases from 0tox. The base and middle parts of an NW turn out to be low-doped and only the upper part will be doped according to the relation x ¼ J 2 /J 1 . This effect can be used to form a heterostruct ure in the NW bulk. (iv) Any manipulations with the input flux of molecules containing a doping impurity will be inefficient until YX0.5. For example, changes of J 2 in time do not allow us to achieve the corresponding impurity distribution along the NW length due to the existing time-lag between changes in the gaseous phase and those at the nano-object surface. (v) The retardation of the doping level from a given law for changes of the input fluxes x ¼ x(t) practically disappears if D 0 /D b p10 or/and Y 0 E0.1–0.2. There- fore, to achieve more or less homogeneous or controlled inhomogeneous doping of an NW along its length, one should use the mode of small input fluxes (J 1 and J 2 ). ARTICLE IN PRESS A. Efremov et al. / Physica E 40 (2008) 2446–2453 2451 (vi) The above-mentioned narrow peripheral region at the catalyst particle surface, which is saturated with the vacant sites, is just that place where small coverages are maintained during the whole growth process. This makes it possible (at great input fluxes of the silicon- containing molecules) to realize a selective and homogeneous coaxial doping of the NW external shell. 3.3. The influence of a slowly diffusing impurity at the catalyst surface on the NW growth processes In the pro cess of the deco mposition of silico n-containing molecules at the catalyst surface, together with mobile at oms, reaction by-products are also fo rmed. Some o f them, e.g. hydrides or chlorides, can possess a small mobility and for a long enough time occupy surfac e sites [2]. Below we consider this case of a two-component system, which is rather important as affecting the gr owth an d shaping of NWs. The MC exp eriments with surface random walks of a mobile test particl e in the prese nce of a low-mobility component show (Fig. 2) that w hen t he covera ge with a low-mobility impurity Y slow achieves a va lue of 0.42pY slow p0.43, practically comp lete blocking occurs in the most available ways used to deliver adatoms from the catalyst surface central part to the NW sidewalls (Fig. 2b). The co rrespond- ing dependence for D eff /D 0 ¼ F(Y slow )isshowninFig. 2a. As long as the fraction of the low-mobility at oms Y slow is smaller than 0.35, a quasilinear rel ation between a mean- square displacement /R 2 S and the duration of the random walks for a mobile test particle holds. However, beginning from Y slow E0.38, a nonlinear relation for /R 2 S ¼ 4D eff t m is realized. The so-called sub-diffusion (mo1) [1] is observed, and m continues to decrease while the coverage with slow atoms approaches 0.43 . In this critical interval of coverages, slowly diffusing atoms start forming individual coherent aggregations. In the range of 0.38pY slow p0.43, most of the diffusion ways gradually become temporarily blocked. As a result, the surface flux towards the periphery of the catalyst particle becomes increasingly more anisotropic. This effect of anisotropy can be responsible for the appearance of some unusual forms in the world of nano-objects, such as springs. Thus, the MC experiments on random walks of a mobile test particle have shown that the growth of the slow component concentration retards and then completely blocks the surface transport. The kinetics of the mobile adatom spreading from the catalyst surface that we observed in another MC-experiment (Fig. 3 ) is in full agreement with this statement. The kinetics allows us to estimate a characteristic time of adatom residence at the surface, for a fixed initial concentra- tion of the mobile particles, in d ependence on the coverage with slowly diffusing atoms. It is seen that at Y slow p0.2, slow particles weakly influence o n the situation at the surface. However, when their concentration approaches some thresh- old value of Y slow E0.4, the time of the particle residence at the surface sharply increases. T his is in agreement with the results of the above-mentioned series of MC experiments. At even greater coverages with a slow component ( up to 0.6), most mobile atoms (excluding those adsorbed directly at the catalyst periphery) h ave no access to a N W sidewall a nd cannot freely mo ve across t he surface. A single available transport channel for them remains in diffusion through the catalyst bulk i n t he direction of the ca ta lyst /silicon growth region. The latter feature seems to be rather u seful for the creation of NWs in the form of ideal cylinders although growth rate in this case is about twice as low. In particular, introduction of chlorine-containing com- plexes into a gaseous medium, used in Ref. [12], made it possible to suppress the formation of conical NWs and to grow practically ideal silicon cylinders by employing titanium silicide as a catalyst. A mechanism of the action of this additive on the NW shape may just be the surface transport suppression described above. 4. Conclusion An atomic transport at the catalyst particle surface has been studied using the MC technique. To estimate an effective transport coefficient and reproduce some aspects of a real situation, we have used four different scenarios for the MC experiment. In addition, we have carried out a kinetic simulation of the NW growth and doping by a numerical solution of the corresponding rate equations of chemical kinetics using the dependences obtained in the MC experiment. This enabled us to compare atomistic and macroscopic approaches. Such a multilevel simulation proved to be rather fruitful in view of improving our understanding of the general features of the process. The results obtained within the framework of a kinetic approach have been confirmed and amended by the MC simulation. These results have revealed an important role of surface transport in NW growth and doping. It has been shown that the presence of low-mobility impurities at the surface allows us to block the surface transport, efficiently suppress the flux from the catalyst surface towards the NW sidewalls, and control the NW shape. Similarly, by changing the relationship between the surface and bulk fluxes, we can obtain various versions of the doping impurity distribution along the NW length and radius. We have also observed several nonlinear effects: (1) total or partial blocking of the surface transport in the presence of slowly diffu sing additives at the surface; (2) appearance of the surface flux anisotropy and transfer to the mode of sub-diffusion, when the coverage with slowly diffusing atoms reaches the value of Y slow E0.4; (3) essential suppression of the surface transport at great input fluxes for a single-component system; (4) the presence in some cases of a significant time lag between a change in the concentration of impurity-containing molecules in the gaseous phase and the corres ponding changes in the concentration of impurity at the nanocatalyst surface. ARTICLE IN PRESS A. Efremov et al. / Physica E 40 (2008) 2446–24532452 The results of the simulation allow us to predict some approaches to control shape and impurity distribution during the NW growth. In particular, it becomes possible to realize controllable cylindrical or conical shapes, homogeneous or coaxial doping. References [1] L.M. Zelenyy, A.V. Milovanov, Usp. Fiz. Nauk. 174 (2004) 809. [2] A. Efremov, A. Klimovskaya, T. Kamins, B. Shanina, K. Grygoryev, S. Lukyanets, Semiconductor Phys. Quantum Electron. Optoelec- tron. 8 (2005) 1. [3] E.I. Givargizov, Growth of Filament-Like and Platelet Crystals from Vapor, Nauka Press, Moscow, 1977 (in Russian); D.N. McIlroy, D. Zhang, Y. Kranov, M. Grant Morton, Appl. Phys. Lett. 79 (2001) 1540. [4] D.N. McIlroy, A. Alkhateeb, D. Zang, J. Phys.: Condens. Matter 16 (2004) R415. [5] A.I. Klimovskaya, E.G. Gule, I.V. Prokopenko, in: Proceedings of the 17th Quantum Electronics Conference, Nis, Yugoslavia, MIEL 2000. [6] A.I. Klimovskaya, I.V. Prokopenko, I.P. Ostrovskii, J. Phys.: Condens. Matter 13 (2001) 5923. [7] A.I. Klimovskaya, I.V. Prokopenko, S.V. Svechnikov, J. Phys.: Condens. Matter. 14 (2002) 1735. [8] L.K. Orlov, T.N. Smyslova, Semiconductors 40 (2006) 43. [9] H. Hould, J. Tobochnik, An Introduction to Computer Simulation Methods. Application to Physical Systems. Part 2, Addison-Wesley Publishing Company, New York, 1988. [10] D.W. Heerman, Computer Simulations Methods in Theoretical Physics, Springer, Berlin, 1986. [11] A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Nauka Press, Moscow, 1987 (in Russian). [12] S. Sharma, T.I. Kamins, R. Stanley Williams, J. Cryst. Growth 267 (2004) 613. ARTICLE IN PRESS A. Efremov et al. / Physica E 40 (2008) 2446–2453 2453 . Physica E 40 (2008) 2446–2453 Multilevel modeling of the influence of surface transport peculiarities on growth, shaping, and doping of Si nanowires A mobilities (silicon itself, conventional dopa nts, products of surface reactions, etc.) across the catalyst surface on the growth, shape, and doping of NWs. Using