Kinetic Monte Carlo simulation of {1 1 1}-oriented SiC film with chemical vapor deposition

Computational Materials Science 43 (2008) 1036–1041

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Kinetic Monte Carlo simulation of {1 1 1}-oriented SiC film with chemical vapor deposition Cui-xia Liu *, Yan-qing Yang, Rong-jun Zhang, Xiao-xia Ren School of Materials, Northwestern Polytechnical University, 710072 Xi’an, PR China

a r t i c l e

i n f o

Article history: Received 21 August 2007 Received in revised form 15 January 2008 Accepted 25 February 2008 Available online 8 April 2008 PACS: 05.10.Ln 31.15.P 51.20.+d Keywords: Kinetic Monte Carlo SiC film Chemical vapor deposition Surface roughness Relative density

a b s t r a c t A three-dimensional atomic-scale kinetic Monte Carlo (KMC) model of {1 1 1}-oriented SiC film deposited by chemical vapor deposition is established in this paper. The growth process of {1 1 1}-oriented atomicscale SiC film is simulated. The model includes two parts: the first is kinetic process of chemical reaction and the second is deposition and diffusion of substrate surface. In this model, the relationship between temperature and growth rate, surface roughness and relative density and the relationship between growth rate and surface roughness and relative density are studied. The result indicates that the growth of film has three stages including formation of little islets, mergence and expanding of islets and dynamic balance between islets. With increase of substrate temperature, deposition rate, surface roughness and height of film all increase. With increase of deposition rate, surface roughness increases while relative density decreases. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction SiC fabricated by chemical vapor deposition (CVD) method has many excellent physical and chemical properties, such as high relative density, highly purity, high tensile strength, high stiffness, corrosion resistance, oxidation resistance and high temperature stability [1]. Therefore, SiC is used extensively in the field of high temperature structural material and aerial material. For example, titanium-matrix composite reinforced with continuous SiC fiber is mainly applied to the structure of NASP; SiC composited with aluminum is applied to the structure of aerocraft, automobile, machine; excellent composite of SiC and epikote is applied to turbine blades of jet engine, airscrew; SiC reinforced ceramic matrix composite has high temperature and plasticizing ceramic characters [2]. In CVD method, CH3SiCl3 (MTS) is the reacting gas admixed with hydrogen (H2) and argon (Ar), which is carried by H2 through bubbling mode, and is diluted and protected by Ar. All the gases are heated in the reaction chamber, from which MTS is heat-decomposed to form SiC [3]. In this complex process of physics and chemistry, all kinds of chemical reactions may influence the formation and the breakage of chemical bond, which plays a very important * Corresponding author. Tel.: +86 29 88688485. E-mail address: [email protected] (C.-x. Liu). 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.02.022

role in depositing SiC. A series of experiments and researches on the deposition principle of SiC are carried [4–7]. Four kinds of principles are provided. First, the MTS is heat-decomposed in a gas phase, the outgrowth of which adsorbs the surface of substrate, and is dechlorinated and dehydrogenized and forms SiC in the end. Second, the MTS is heat-decomposed in a gas phase, the outgrowth of which is polymerized–dechlorinated and polymerized– dehydrogenized and forms a liquid phase of high temperature including Si, C, H and Cl. This liquid phase adsorbs the surface of the substrate with a liquid drop type and is dechlorinated and dehydrogenized again, and then SiC is formed in the end. Third, the MTS may form a crystal druse, which deposits on the surface of the substrate with a molecular druse. And then the crystal druse is blended into the crystal lattice of SiC. Fourth, the MTS is heatdecomposed in a gas phase, dechlorinated and dehydrogenized, and then it nucleates, grows up, and deposits on the surface of the substrate to form SiC in the end. In the real process of deposition, all the above four SiC principles exist. Each principle occupied a different proportion in different equipments and processes. In this paper, the fourth principle is paid more attention and the model is established based on the above-mentioned main problem. The growth process of SiC film is one of the random proceses. Monte Carlo (MC) simulation is a promising approach to study the depositing principle of SiC through which many properties of

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SiC film are predicted. Atomistic MC model of film growth is first raised by Abraham and White [8]. Based on the model, Bruschi et al. [9] studied the effect of deposition rate and substrate’s temperature on the film in detail, but they only focused on the deposition and the diffusion of gas-phase atom on the surface of the film. Battaile et al. [10], Grujicic and Lai [11], Zhang [12] simulated the growth of atomic-scale diamond film, but they only focused on all the possible chemical reactions in the reaction zone. On the basis of the above research, we give the math model of CVD SiC film {1 1 1}-oriented with a three-dimensional atomic lattice, synthetically consider not only many chemical reactions in the reaction chamber but also the deposition and diffusion of gas-phase atoms, establish the kinetic Monte Carlo model, respectively, and achieve all the work of simulation with MATLAB programming language. 2. Modeling and method In the process of CVD SiC, MTS is heated in the reaction chamber. It is supposed to be heat-decomposed to form Si, C, H and Cl atoms, in which Si and C atoms deposit on the substrate on the principle of the corresponding energy and crystal lattice. If the atom still has energy, it may continue to diffuse until the stable position is found. SiC film is formed in the end. According to such a process, the following two kinds of KMC models are established. First, the KMC model of chemical reaction in the reaction chamber is established. The deposited gas-phase atom Si or C is selected according to all the possible chemical reactions in the reaction chamber. Second, the KMC model of deposition and diffusion is established. In the model, the atom, selected from the first model, is deposited on the surface of the substrate to become the absorption atom, which will diffuse and become nucleus finally. 2.1. KMC model of chemical reaction in the reaction chamber There are supposed to be 25 kinds of chemical reactions listed in Table 1 according to Reference [13]. The kinetics rate of chemical reactions is represented using the general Arrhenius [16] formula   E n ð1Þ kf ¼ AT exp  RT

where A is the pre-exponential factor, n is the temperature exponent, E is the activation energy for all the surface reactions, R is the universal gas constant and T is the absolute temperature of the substrate. In the model, SiC crystal lattice is supposed to appropriate stiffness, and atom vibration and interface reaction on the substrate surface are ignored. One chemical reaction is allowed to occur at one site during each time step, which is defined as one event. At each time step, a list of all possible events is constructed and the probability for each event is set proportional to the rates of the associated surface reaction relative to the rates of the surface reactions associated with all the other possible events. In other words, at one time step, a random number n that uniformly distributes in the range (0,1) is selected, through which the event m is selected from M possible events. The relation is denoted by , , m1 M m M X X X X rj : rj < n 6 rj : rj ð2Þ j¼0

j¼0

j¼0

j¼0

where rj is the surface reaction rate of the event j, which is calculated in terms of formula (1) with the corresponding data in Table 1. r0 = 0. After one event has occurred, the total number of possible events M and the occurrence sequence should be updated and repeated. During the simulation, all the time steps are variable. That is KMC method. The selection to the time step is denoted by , M X ri ð3Þ Dt ¼  lnðhÞ : i¼1

where h is a random number which uniformly distributes in the range (0,1) and the denominator represents the total rate of all possible events in setting simulation-time step. The event with higher rate can be easily selected in one time step in terms of formula (3). 2.2. KMC model of deposition and diffusion When Ning and Pirouz [14] studied SCS-6 fiber with TEM, they found that b-SiC crystal grain preferentially grew in {1 1 1}-oriented direction. So they drew a conclusion that such direction is

Table 1 Chemical reaction model of CVD SiC film No.

Reaction

A (mol cm3 s1)

b

Ea (kJ mol1)

k1200

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

MTS + H2?CH3 + SiCl3 + H2 MTS + MTS?CH3 + SiCl3 + MTS CH3 + SiCl3?MTS CH3 + SiCl3?CH3Cl + SiCl2 CH3Cl + SiCl2?CH2 + SiCl3 CH3 + H2?CH4 + H CH4 + HC?CH2 + H2 CH3 + H?CH2 + H2 CH3 + H + X?CH4 + X CH3 + CH2?C2H4 + H CH2 + CH2 + X?C2H6 + X C2H6 + X?2CH3 + X C2H6 + H?C2H5 + H2 C2H5 + X?C2H4 + H + X C2H4 + X?C2H2 + H2 + X SiCl3 + H2?HSiCl3 + H HSiCl3 + H?SiCl3 + H2 SiCl4 H?SiCl3 + HCl SiCl3 + HCl?SiCl4 + H SiCl3 + H?SiCl2 + HCl HSiCl3?SiCl2 + HCl SiCl2 + HCl?HSiCl3 2SiCl2?SiCl4 + SiCl2 SiCl3?SiCl2 + C CH4 + Cl?CH3 + HCl

– – – – – 660 22,000 1.8  1014 8.0  1026 4.0  1012 3.2  1041 2.5  1037 5.4  102 2.4  1036 1.5  1018 – – – – – – – – – 3.0  1013

– – – – – 3.0 3.0 0 3.0 0 7.03 4.6 3.5 5.36 0 – – – – – – – – – 0

330,000 330,000 – – – 32,400 32,600 62,761.5 0 0 11,556.5 412,133.9 21,757.3 174,895.4 233,472.8 – – – – – – – – – 14,900

5.0  106 2.0  106 3.0  1014 3.0  1014 1.0  109 4.4  1010 1.0  1012 3.3  1011 4.6  1017 4.0  1013 2.3  1010 2.0  105 3.7  1012 1.8  1012 1.0  105 5.0  1010 1.0  1013 3.6  1011 1.4  1010 1.0  1013 5.0 1.0  105 1.0  1014 3.0  102 6.7  1012

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the preferred growth one, which is why we use {1 1 1}-oriented SiC as the study direction. When the film growth is simulated at atom-scale, the position and nearby relation of C and Si atoms in SiC crystal lattice and boundary condition should be characterized in mathematics. The math model of {1 1 1}-oriented SiC is established [11,12]. The ori y ¼ ½1 1  0 and entation of the lattice is defined as x ¼ ½1 1 2; z = [1 1 1]. The film is allowed to grow along the Z direction. The surface of the substrate is supposed to be tetragonal lattice and every lattice site represents one atom. According to the principle of minimum energy, the deposited atom only states the coordinate position of the lattice site. The position of the deposited atom is selected randomly, and every atom only diffuses the length of the lattice constant every time. If the lattice site is empty, the atom will deposit. If not, the atom will go on to diffuse on the surface of the film until it reaches an empty point. In order to avoid the film edge effects, the following periodic boundary condition is given. In the vertical direction of film growth, when energy and diffusion direction are calculated, the top row is regarded as the neighbor of the bottom row, and the leftmost column is regarded as the neighbor of the rightmost column [15], which is shown in Fig. 1. More energy is needed to overcome when the atom diffuses to near nearby neighbor. So such a kind of diffusion is ignored. In other words, the deposited atom only diffuses to the empty point of 12 nearest neighbor lattice sites of the same and lower layers. The blue circle is the deposited atom depicted in Fig. 2. Numbers from 1 to 6 are the nearest neighbor lattice sites and numbers from 7 to 18 are near nearby neighbors. If all the points around the deposited atom are not empty, the atom cannot diffuse. The diffusion and desorption rate of the atom is represented as (4) [16].   Ek ð4Þ vk ¼ v0 exp kB T where v0 is the vibration rate of the crystal lattice (v0 = 2kBT/h, h is Plank constant), kB is Boltzmann factor, T is temperature of the

Fig. 1. Periodic boundary condition.

Fig. 2. The surface morphology of the substrate.

substrate, and Ek is the energy needed by the adsorption atom when it diffuses. Ek = DEijkl + esk, where DEijkl means the barrier energy needed by one atom when it jumps from the position of (i,j) to (k,l), denoted by formula (5); esk is the diffusion energy of the atom on the substrate surface (=0.751 [17,18]). DEijkl ¼ Ekl  Eij

ð5Þ

where Eij and Ekl is the sum of barrier energy of all the nearest atoms when the atom locates at (i,j) and (k,l) positions, respectively. P Pm Eij ¼ m s¼1 ðuij Þs ; Ekl ¼ s¼1 ðuij Þs , where (uij)s and (ukl)s are the interaction potentials between the adsorption atom locating at (i,j) and (k,l) positions, respectively, and their numbers is the nearest atom. The interaction potential among the atoms is described with Morse energy denoted by formula (6) [16] in the model. Compared with other energy functions, Morse energy has the following advantages. We do not need to consider the difference of interaction energy among atoms derived from different materials. All the influence of the nearby atoms can be considered only through selecting one reasonable parameter        r r —1  2 exp a —1 ð6Þ u ¼ u0 exp 2a r0 r0 where u is the interaction among the nearby neighbors, u0 is the energy between two atoms at equilibrium position (=esk/2), r is the distance between near atoms at equilibrium position, r0 is the distance between two atoms at equilibrium position, and a is the range of actions (=2) [16]. 2.3. Method By combining the above two models, the detailed arithmetic is given as the following steps: Step 1: Calculate the reaction rate ri of all the possible chemical reactions according to formula (1). Step 2: Select the number m chemical reaction according to formula (2), select the deposited atom and calculate the deposition time Dt according to formula (3). Step 3: Generate random number h and locate the deposited position of the atom. Step 4: Find all the active atoms which can diffuse according to the number of nearby atoms around the adsorption atom. Step 5: Calculate the diffusion rate vj of all the active atoms, total P rate Rh(Rh = vj)and the needed time to diffuse to one step s(s = 1/Rh). Step 6: Generate random number n1 2 ð0; 1Þ. The diffusion atom Ph P is decided according to h1 j¼1 vj < n1 Rh 6 j¼1 vj . If the random number meets this formula, the number h atom is selected. Generate another random number n2 2 ð0; 1Þ. The diffusion direction of atom is decided according to Pp i Pp1 i i¼1 vh < n2 vh 6 i¼1 vh . If the random number meets this formula, the atom jumps to the number p empty point. vih is the diffusion rate of atom h jumping to direction i and P i vh is the total diffusion rate of atom h0. vh ¼ Step 7: Finish the diffusion process. Update the diffusion rate vj and total rate Rh, which are influenced by atoms around the diffusion atom. Step 8: Compare the diffusion time s and deposition time Dt. If Dt P s, go to Step 6 and the selected atom will continue to diffuse. If Dt 6 s, go to Step 1. The above process will be carried circularly until all the simulation process is finished. All the simulation work is carried on Person Computer with Pentium IV CPU, Windows XP professional operate system and 1 GB RAM with MATLAB programming language.

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3. Results and discussion On the basis of the above-mentioned three-dimensional model, the atom’s spatial arrangement figure of {1 1 1}-oriented SiC crystal lattice can be gotten, a small segment of which is shown in Fig. 3 (The blue and big circle represents atom Si. The red and small circle represents atom C hereafter. There is a covalent bond which is marked by a black line between the two atoms). Such a structure of SiC crystal lattice is consistent with the one of the diamonds studied by Grujicic and Lai [11]. Put the substrate into the reaction chamber heated by radio-frequency power, in which the pressure is about 0.1 MPa. The temperature of the substrate changes from 1000 K to 1400 K. u([MTS]) = 30%, u([H2]) = 50%, u([Ar]) = 20%, where u represents volume fraction. The crystal lattice of SiC is 10  10. There is supposed to be a layer of atom C, which is connected to atom Si by a covalent bond, on the surface of the substrate at the beginning of deposition. 3.1. Qualitative analysis to different stages of deposition According to such deposition condition (u([MTS]) = 30%, u([H2]) = 50%, u([Ar]) = 20%), when the temperature of the substrate is 1200 K, it results in a three-dimensional morphology which is shown in Fig. 4. It can be seen that some isolated islets are formed on the even atomic substrate at the first stage of deposition (Fig. 4a). And then, the film continues to grow at the middle stage. There are two features at this stage. First, the growth direction of islets is the same as that of the film. Second, the islets grow in cross direction towards the lateral face. Because of the abovementioned features, the islets begin to merge, from which the empty of (1 1 1) layer can be filled and expanded (Fig. 4b–d). The structure of the atom will enter the stage of a dynamic balance after a period of deposition. The empty of (1 1 1) layer continues to be filled by atoms Si and C, from which the final complete morphology is got (Fig. 4e). The growth characteristic is also in accordance with the corresponding theory [18]. Moreover, it provides evidence for the experiment of Zheng and Zhang [3]. Fig. 4. Surface morphologies of CVD SiC (1 1 1) layer at different stages of deposition. (a) Some isolated islets are formed on the SiC surface at the first stage of deposition. (b–d) The islets begin to merge and expand at the middle stage. (e) The structure of the atom enters the stage of a dynamic balance after a period of deposition.

3.2. Processing parameter’s influences to the quality of SiC film The deposition rate of {1 1 1}-oriented SiC film is calculated as v ¼ N 1 D=N 2 t

Fig. 3. A section of the b-SiC substrate for CVD of a SiC film. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

ð7Þ

where N1 is the number of deposited atoms in timing interval t, D is the average gauge of (1 1 1) layer (D = 0.126 nm), and N2 is the number of atoms Si and C on the layer which is fully filled. The influence of different temperatures of substrate to growth rate of (1 1 1) layer of SiC film is shown in Fig. 5. The other condition is maintained constant, and the temperature of the substrate is 1000 K, 1200 K and 1400 K, respectively. From Fig. 5, it can be seen that when the temperature is constant, the deposited atoms Si and C can find a stable position quickly at the first stage of deposition. The deposition rate of the film is large because of (1 1 1) layer surface morphology of SiC. After a period of deposition, the deposition rate begins to decrease, the reason of which is that the step surfaces of different heights are formed by a part of the deposited atom, which makes the next atom to deposit difficultly. The deposition rate becomes stable when the growth

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Fig. 5. The influence of different temperatures of substrate to growth rate of (1 1 1) layer of SiC film.

of the surface reaches the state of dynamic balance. Moreover, the deposition rate increases with the rising of temperature. Lee et al. [19] also drew a conclusion that the growth rate of SiC film varies with temperature through experimental condition. In order to describe the surface morphology of SiC film, two indexes of surface roughness and relative density are added. There are many kinds of surface roughnesses [15], of which the root mean square average r is used in this paper to describe the morphology of the film. It is denoted by r2 ¼

1 X  2 ðhði:jÞ  hÞ N i;j

ð8Þ

 is the average height of where h(i, j) is the height of point (i, j), h the film and N is the lattice number of substrate surface.Relative density is the ratio between population lattice number and completely compact lattice number of the crystal, which is denoted by d ¼ m1 =m2

ð9Þ

where m1 is population lattice number and m2 is total lattice number. In this paper, the following method is used to calculate relative density. In every deposition stage, the height of deposition is calculated. Select the middle-height layers to calculate the population ratio as the relative density of the film. For example, at one stage of deposition, the height of deposition has nine layers (form No. 1 to No. 9). The relative density is calculated based on middleheight layer (from No. 4 to No. 6). Under different temperatures, the surface roughness of SiC film (1 1 1) surface changes with simulation time which is shown in Fig. 6. It can be seen that at the first stage of growth, surface roughness increases rapidly with simulation time, the reason of which is that six series of adjacent surfaces are arranged as one periodicity on the (1 1 1) surface. Before the bottom layer is fully filled, some new islets are formed. Therefore, surface roughness increases at the first stage of deposition. And then, the film continues to grow to the middle stage. In this stage, surface roughness decreases because the lower (1 1 1) layer is fully filled gradually. When the growth process of the film begins to reach the balance state, the surface roughness is almost unchanged. So the curve of roughness appears in parallel to X-axis. Moreover, surface roughness increases when the temperature of the substrate increases, the reason of which is that when the temperature is lower, the film grows slowly and the atom has enough time to find a

Fig. 6. The surface roughness of SiC film (1 1 1) surface changes with simulation time under different temperatures.

stable position to deposit. Therefore, the surface roughness is little. When the temperature is higher, surface roughness increases with the increase of deposition rate. When the temperature is too high, the deposited atom has no time to find a position to deposit, which leads to the surface roughness increase. Such changing law is in agreement with those of Grujicic and Lai [11] and Zhang [12]. The relationship between the height of SiC film and the temperature is shown in Fig. 7. In the process of deposition, the height of SiC film presents near-linear with deposited time. The height of film increases with the increase of the temperature. Under different temperatures, surface roughness changes with growth rate under different temperatures shown in Fig. 8, which is supported by Kodigala et al. [20]. Surface roughness increases with the increase of growth rate, the reason of which is that when the growth rate is too large, the previous atom on film surface, having no time to deposit, is enclosed and covered by the following deposited atoms. Therefore, the atom cannot diffuse properly, from which the hole on the surface is formed. The relative density changes with growth rate, which is shown in Fig. 9. The relative density decreases with increase of the growth rate, which also strongly proves the previous result. That is, the film surface morphology is influenced by the growth rate.

Fig. 7. The height of the SiC film (1 1 1) changes with different temperatures.

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growth rate and surface roughness and relative density are simulated. Surface morphology of SiC film is represented as following: at the first stage of deposition, some isolated islets are formed on the even atomic substrate of (1 1 1) layer. And then, the film continues to grow into the middle stage, whose feature is that the islets begin to merge and expand. The structure of atom will enter the stage of dynamic balance after a period of deposition. With increase of the substrate temperature, the deposition rate, surface roughness and height of film increase. At the first stage of deposition, the deposition rate of film is large, and then decrease. It becomes stable when the growth of surface reaches the state of dynamic balance. The surface roughness increases sharply at the first stage and becomes stable after a period of deposition. The height of film increases with the deposition time. With increase of deposition rate, the surface roughness increases and the relative density decreases. Fig. 8. The surface roughness of CVD SiC (1 1 1) layer changes with growth rate under different temperatures.

Acknowledgements This work was supported by the Natural Science Foundation of China (Grant No. 50371069), the Chinese Education Ministry Foundation for Doctors (Grant No. 20030699013) and the Aviation Science Foundation of China (Grant No. 04G53044). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

Fig. 9. The relative density of CVD SiC (1 1 1) layer changes with growth rate under different temperatures.

4. Conclusion With KMC method, the three-dimensional atomic-scale growth model of (1 1 1)-oriented SiC film is established in this paper. The model has two parts: KMC model of chemical reaction in the reaction chamber and KMC model of atom’s deposition and diffusion. The relationship between temperature and growth rate, surface roughness and relative density and the relationship between

[13] [14] [15] [16] [17] [18] [19] [20]

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