Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation F. Zirkelbach, M. H#berlen, J. K. N. Lindner, and B. Stritzker Institute of Physics, University of Augsburg, Universit#tsstrasse 1, D* *-86135 Augsburg, Germany Abstract Ion irradiation of materials which undergo a drastic density change upon amo* *rphiza- tion have been shown to exhibit selforganized, nanometric structures of the amo* *rphous phase in the crystalline host lattice. In order to better understand the proces* *s a Monte- Carlo-Simulation code based on a simple model is developed. In the present work* * we focus on high-dose carbon implantations into silicon. The simulation is able to repro* *duce re- sults gained by cross-sectional TEM measurements of high-dose carbon implanted * *silicon. Necessary conditions can be specioed for the selforganization process and infor* *mation is gained about the compositional and structural state during the ordering process* * which is diOEcult to be obtained by experiment. 1 1 Introduction The formation of nanometric, selforganized, amorphous, lamellar precipitates as* * a result of high-dose implantation of impurity ions is observed at certain implantation * *conditions for various ion/target combinations [1-3]. This is surprising since high-dose * *impurity implantations usually result in the formation of unordered ensembles of precipi* *tates with a broad size distribution [4]. The present work focuses on high-dose carbon imp* *lantations into silicon, with doses of 1 - 10 x 1017cm-2, an ion energy of 180 keV and su* *bstrate temperatures below 400 OC [4,5]. An example of such a lamellar structure is giv* *en in the cross-sectional transmission electron microscopy (XTEM) image in Figure 5. A m* *odel describing the selforganization process is introduced in this article. This mo* *del is used to implement a Monte-Carlo simulation code which reproduces the amorphization a* *nd precipitation process. Simulation results will be compared with XTEM measureme* *nts. Necessary conditions for creating lamellar precipitates are identioed and some * *additional, diOEcult-to-gain measure information like the carbon distribution and the inAEu* *ence of stress on the amorphous/crystalline structure in the layers is obtained. 2 2 Model A model describing the formation of nanometric, selforganized, regularly arrang* *ed, amor- phous SiCx inclusions was introduced in [5]. The basic idea is schematically di* *splayed in Figure 5, giving the evolution into ordered lamellae with increasing dose. As a result of supersaturation of carbon atoms in silicon at high concentrat* *ions there is a nucleation of spherical SiCx precipitates. Carbon implantations at much highe* *r implan- tation temperatures usually lead to the precipitation of cubic SiC (3C-SiC, a =* * 0.436 nm) [4]. The lattice misot of almost 20% of 3C-SiC would cause a large interfacial * *energy with the crystalline Si matrix [6]. This energy could be reduced if one of the phase* *s exists in the amorphous state. Energy oltered XTEM studies in [7] have revealed that the * *amor- phous phase is more carbon-rich than the crystalline surrounding. In addition, * *annealing experiments have shown that the amorphous phase is stable against crystallizati* *on at temperatures far above the recrystallization temperature of amorphous Si. Prol* *onged annealing at 900 OC turns the lamellae into ordered chains of amrphous and crys* *talline 3C-SiC nanoprecipitates [8] demonstrating again the carbon-rich nature of amorp* *hous inclusions. Since at the implantation conditions chosen pure a - Si would recry* *stallize by ion beam induced crystallization [9], it is understandable that it is the carbo* *n-rich side of the two phases which occurs in the amorphous state in the present phase sepa* *ration process. Stoichiometric SiC has a smaller Si atomic density than c - Si [10,11]. A r* *educed density is also assumed for substoichiometric a - SiCx. Hence the amorphous SiC* *x tends to expand and as a result compressive stress is applied on the Si host lattice * *represented by arrows in Figure 5. As the process occurs near the target surface, stress is* * relaxing in the vertical direction and there is mainly lateral stress remaining ("R" in Fig* *ure 5). Thus volumes between amorphous inclusions will more likely turn into an amorphous ph* *ase as the stress hampers the rearrangement of atoms on regular lattice sites. In cont* *rast, a - Si volumes located in a crystalline neighbourhood will recrystallize in all probab* *ility at the present implantation conditions. Carbon is assumed to dioeuse from the crystalline to the amorphous volumes i* *n order to reduce the supersaturation of carbon in the crystalline interstices. As a co* *nsequence the amorphous volumes accumulate carbon. 3 3 Simulation Before discussing the simulation algorithm some assumptions and approximations * *have to be made. Figure 5 shows the stopping powers and carbon concentration prooles ca* *lculated by TRIM [12]. The depth region we are interested in is between 0 - 300 nm (furt* *heron called simulation window), the region between the target surface and the beginn* *ing of the continuous amorphous SiCx layer at the implantation conditions of Figure 5. The* * nuclear stopping power and the implantation proole can be approximated by a linear func* *tion of depth within the simulation window. The target is devided into 64 x 64 x 100 cells with a side length of 3 nm. E* *ach of it has a crystalline or amorphous state and keeps the local carbon concentration. * *The cell is addressed by a position vector "r= (k, l, m), where k, l, m are integers. The probability of amorphization is assumed to be proportional to the nuclea* *r stop- ping power. A local probability of amorphization at any point in the target is * *composed of three contributions, the ballistic amorphization, a carbon-induced and a str* *ess-induced amorphization. The ballistic amorphization probability pb is proportional to th* *e nuclear stopping power as mentioned before. The carbon-induced contribution is a linear* * func- tion of the local carbon concentration. The stress-induced portion is proportio* *nal to the compressive stress originating from the amorphous volumes in the vicinity, the * *stress am- plitude decreasing with the square of distance d = |"r- "r0|. Thus the probabi* *lity of a crystalline volume getting amorphous can be calculated as X psccarbon("r0) pc!a("r) = pb+ pcccarbon("r) + ___________2, (1) amorphousneighbours d with pb, pcand ps being simulation parameters to weight the three dioeerent mec* *hanisms of amorphization. The probability pa!c of an amorphous volume to turn crystalline * *should behave contrary to pc!a and is thus assumed as: pa!c = 1 - pc!a . (2) The simulation algorithm consists of three parts, the amorphization/recrysta* *llization process, the carbon incorporation and onally the carbon dioeusion. For the amorphization/recrystallization process random values are computed t* *o specify the volume which is hit by an impinging carbon ion. Two random numbers x, y 2 [* *0, 1] are generated and mapped to the coordinates k, l using a uniform probability distri* *bution, p(x)dx = dx,p(y)dy = dy. A random number z corresponding to the m coordinate is distributed according to the linear approximated nuclear stopping power, p(z* *)dz = (sz + s0)dz, where s and s0 are simulation parameters describing the nuclear en* *ergy 4 loss. After calculating the local probability of amorphization pc!a(k, l, m) of* * the selected volume another random number determines - depending on the current status - whe* *ther the volume turns amorphous, recrystallizes or remains unchanged. This step is l* *ooped for the average hits per ion in the simulation window as extracted from TRIM [12] c* *ollision data. In the same manner random coordinates are determined to select the cell wher* *e the carbon ion gets incorporated. In this step the probability distribution describ* *ing the stop- ping power proole is replaced by a distribution for the linearly approximated c* *oncentration proole. The local carbon concentration in the selected cell is increased. Following carbon incorporation carbon dioeusion is considered in order to al* *low a re- duction of the supersaturation of carbon in the crystalline volumes. This is d* *one by a simple dioeusion algorithm in which the concentration dioeerence for each two n* *eighbouring cells is considered and partially balanced according to a given dioeusion rate * *dr (simulation parameter). This time consuming dioeusion process is repeated after each dv (si* *mulation parameter) impinging ions. A switch is implemented to exclude dioeusion in z-di* *rection. As in experimental studies dioeusional broadening of carbon concentration prool* *es has not been observed even at signiocantly higher implantation temperatures where n* *o amor- phous phase is formed [13], dioeusion among crystalline volumes is assumed to b* *e zero in the following simulations. 5 4 Results Figure 5 shows a comparison of a simulation result and a XTEM bright-oeld image* * of silicon implanted at 150 OC with 180 keV C+ ions at a dose of 4.3 x 1017cm-2. S* *igniocant lamellar structure formation is observed in the depth interval between 200 and * *300 nm (Figure 4(b)). This is nicely reproduced by the simulation result shown in Figu* *re 4(a). Even the average length of the precipitates complies to the experimental data. * * The lamellae are arranged in uniform intervals. Obviously the simulation is able to* * reproduce lamellar, selforganized structures. Simulations with dioeerent model parameters allow to specify conditions for * *observing lamellar structures. First runs with a simplioed version of the program have sh* *own that it is essential to assume low amorphization probabilities to avoid early comple* *te amor- phization of the whole cell ensemble. Instead small amorphization parameters pb* *, pc, ps and a large number of simulation steps are required to observe lamellar structu* *res. This onding is in agreement to the fact that due to the low nuclear energy depositio* *n of the light carbon ions in silicon, amorphization would not be expected at all at the* *se elevated target temperatures [4] and thus carbon mediated amorphization has to be taken * *into account to explain the amorphization process. Figure 5 shows the results of two identical simulation runs with dioeusion i* *n z-direction switched ooe and on. The lamellar structures only appear if dioeusion in z-dir* *ection is enabled. Amorphous volumes denude the neighbouring crystalline layers of carbo* *n. In consequence the stability of such cells against recrystallization is enhanced, * *the probability to amorphize crystalline cells in the same depth is increased due to the stress* * term and the amorphization in the carbon denuded cells and their lateral vicinity is dec* *reased. This fortioes the formation of lamellar precipitates. The result highlights the imp* *ortance of the dioeusion in z-direction for the selforganization process. In Figure 5 two simulation results with dioeerent dioeusion rates are compar* *ed. Higher dioeusion rates cause a larger depth domain of lamellar structure. This can be * *understood since higher dioeusion rates result in amorphous volumes holding more carbon wh* *ich con- sequently stabilizes the amorphous state. In case of slower dioeusion rates (Fi* *gure 6(b)) the redistribution of carbon is too slow to allow for an eoeective agglomeratio* *n of car- bon atoms in amorphous cells to stabilize the amorphous state against recrystal* *lization. This results in a smaller total amount of amorphous material in Figure 6(a) com* *pared to Figure 6(b). The stabilization occurs only at a depth larger than approximately* * 240 nm where the total concentration of carbon is high enough. The suOEcient stabiliz* *ation of amorphous volumes in this deeper depth zone enables also the more eoeective con* *tribution 6 of the stress mediated amorphization. The inAEuence of the stress term ps is considered in Figure 5. For otherwise* * the same conditions as in Figure 6(b) calculations with decreased ps in Figure 7(c),(b),* *(a) show a systematically reduced extension of the lamellae zone. The mean diameter of amo* *rphous lamellae decreases with decreasing ps. Both observations support the assumption* * of stress mediated amorphization as a mechanism contributing to lamella formation. Figure 5 shows the extension of amorphous lamellae in plane view for two con* *secutive slices m and m + 1 of the ensemble. It is obvious that amorphous and crystallin* *e lamellae have a complementary arrangement in neighbouring slices (Figure 8(a),(b)) which* * again is a result of the carbon accumulation in the amorphous lamellae. This can be * *clearly seen by comparison with the corresponding carbon maps in Figure 8(c),(d). 7 5 Summary and conclusion A simple model explaining the selforganization process of lamellar, amorphous p* *recipi- tates during high-dose ion implantation is introduced. The implementation of th* *e model in a simulation code is described. The simulation is able to reproduce the expe* *rimentally observed formation of lamellae. The evolution of these lamellar structures gets* * traceable by the simulation. The weight of dioeerent mechanisms which contribute to the s* *elforgani- zation process is explored by variation of simulation parameters. It is found t* *hat dioeusion in z-direction and stress mediated amorphization are necessary to create ordere* *d arrays of amorphous, lamellar precipitates. Thus by simulation, information is gained * *about the selforganization process which is not easily accessible by experimental techniq* *ues. 8 References [1] L.L. Snead, S.J. Zinkle, J.C. Hay, M.C. Osborne, Nucl. Instr. and Meth. B * *141 (1998) 123. [2] A.H. van Ommen, Nucl. Instr. and Meth. B 39 (1989) 194. [3] M. Ishimaru, R.M. Dickerson, K.E. Sickafus, Nucl. Instr. and Meth. B 166-1* *67 (2000) 390. [4] J.K.N. Lindner, Appl. Phys. A 77 (2003) 27-38. [5] J.K.N. Lindner, M. H#berlen, M. Schmidt, W. Attenberger, B. Stritzker, Nuc* *l. Instr. and Meth. B 186 (2000) 206-211. [6] W.J. Taylor, T.Y. Tan, U.G#sele, Appl. Phys. Lett. 62 (1993) 3336. [7] M. H#berlen, J.K.N. Lindner, B. Stritzker, to be published. [8] M. H#berlen, J.K.N. Lindner, B. Stritzker, Nucl. Instr. and Meth. B 206 (2* *003) 916-921. [9] J. Linnross, R.G. Elliman, W.L. Brown, J. Mater, Res. 3 (1988) 1208. [10] L. L. Horton, J. Bentley, L. Romana, A. Perez, C.J. McHargue, J.C. McCallu* *m, Nucl. Intr. and Meth. B 65 (1992) 345. [11] W. Skorupa, V. Heera, Y. Pacaud, H. Weishart, in: F. Priolo, J.K.N. Lindne* *r, A. Nylandsted Larsen, J.M. Poate (Eds.), New Trends in Ion Beam Processing of* * Ma- terials, Europ. Mater. Res. Soc. Symp. Proc. 65, Part 1, Elsevier, Amsterd* *am, 1997, p. 114. [12] SRIM2000 Version of the TRIM program described by J.F. Ziegler, J.P. Biers* *ack, U. Littmark in: The Stopping and Range of Ions in Matter, vol. 1, Pergamon* * Press, New York, 1985. [13] J.K.N. Lindner, W. Reiber, B. Stritzker, Mater. Sci. Forum Vols. 264-268 (* *1998) 215-218. 9 Figure Captions 1. XTEM image of a Si sample implanted with 180 keV C+ ions at a dose of 4.3* * x 1017cm-2 and a substrate temperature of 150 OC. Lamellar and spherical am* *orphous inclusions are marked by L and S. 2. Schematic explaining the selforganization of amorphous SiCx precipitates * *and the evolution into ordered lamellae with increasing dose (see text). 3. Nuclear and electronic stopping powers and concentration proole of 180 ke* *V C+ ions implanted in Si calculated by TRIM. 4. Comparison of a simulation result and a XTEM image (180 keV C+ implantati* *on into silicon at 150 OC and a dose of 4.3 x 1017cm-2). Amorphous cells are* * white. 5. Two identical simulation runs with dioeusion switched ooe (left) and on (* *right). 6. Two identical simulation runs with dioeerent dioeusion rates dr. All othe* *r parameters are as in Figure 5(b). 7. Four simulation runs with dioeerent simulation parameter ps. All other pa* *rameters are as in Figure 5(b). 8. Plane view display of amorphous (white) and crystalline (black) cells in * *two consec- utive slices m and m + 1 (a,b) and corresponding carbon map (c,d). Higher* * carbon concentrations are given by higher brightness in (c,d). 10 1 2 11 3 4 12 5 6 7 13 8 14