NANO LETTERS
Homogeneous Nucleation of Epitaxial CoSi2 and NiSi in Si Nanowires
2009 Vol. 9, No. 6 2337-2342
Yi-Chia Chou,*,† Wen-Wei Wu,*,‡ Lih-Juann Chen,§ and King-Ning Tu† Department of Materials Science and Engineering, UniVersity of California, Los Angeles, Los Angeles, California 90095-1595, Department of Materials Science and Engineering, National Chiao Tung UniVersity, Hsinchu 300, Taiwan, Republic of China, and Department of Materials Science and Engineering, National Tsing Hua UniVersity, Hsinchu 300, Taiwan, Republic of China Received March 11, 2009; Revised Manuscript Received April 28, 2009
ABSTRACT Homogeneous nucleation is rare except in theory. We observed repeating events of homogeneous nucleation in epitaxial growth of CoSi2 and NiSi silicides in nanowires of silicon by using high resolution TEM. The growth of every single atomic layer requires nucleation. Heterogeneous nucleation is prevented because of non-microreversibility between the oxide/Si and oxide/silicide interfaces. We determined the incubation time of homogeneous nucleation. The calculated and the measured nucleation rates are in good agreement. We used Zeldovich factor to estimate the number of molecules in the critical nucleus; it is about 10 and reasonable. A very high supersaturation is found for the homogeneous nucleation.
Nucleation is basic in all physical and biological phenomena of phase change. In essence, it is a fluctuation of composition and structure in the matrix of a metastable phase.1-6 It has to overcome an energy barrier to become stable because an interface has to be formed between the nucleus and the metastable phase. In the fluctuation process, a spectrum of nuclei or embryos exists in the metastable phase; they grow and shrink at the same time because of microreversibility. Microreversibility is the principle for elementary reaction in any equilibrium system; the favored reaction path in one direction must have the reverse path in the opposite direction, and the rate constants are the equilibrium constant. A stable nucleus is defined as the one that has reached beyond a critical size and will grow continuously. While the steady state kinetic theory of fluctuation in size space is rather advanced,3 it is for homogeneous nucleation only. However, in real events of nucleation, heterogeneous nucleation is encountered inevitably7,8 because of the large difference in activation energy between the two. Thus there is a gap in our understanding of the basic of nucleation between theory and experiment. To reduce the effect of heterogeneity, nucleation in small droplets was studied, for instance.9,10 The crystallization of small liquid droplets has been found to require a much larger under-cooling than that in a bulk liquid phase. It shows that homogeneous nucleation is indeed much * To whom correspondence should be addressed. E-mail: (Y.C.C.)
[email protected]; (W.W.W.)
[email protected]. † University of California, Los Angeles. ‡ National Chiao Tung University. § National Tsing Hua University. 10.1021/nl900779j CCC: $40.75 Published on Web 05/19/2009
2009 American Chemical Society
more difficult than heterogeneous nucleation in real thermodynamic systems. We report here the finding of repeating events of homogeneous nucleation in epitaxial growth of CoSi2 and NiSi silicides in the axial direction of nanowire of Si. Using high resolution TEM, we observed that the growth of every single atomic layer of the silicides requires nucleation. It is homogeneous nucleation because heterogeneous nucleation has been suppressed due to the surface oxide of the Si nanowire. Owing to the repeating events, we can measure the distribution of incubation time of nucleation. Knowing the incubation time, we can calculate the steady state rate of homogeneous nucleation, that is, the number of stable critical nucleus per unit area per unit time, when the activation energy of nucleation is measured. Since it is homogeneous nucleation, we are able to apply Zeldovich factor to obtain the number of molecules in forming the critical nucleus in the steady state process. In this report, we have correlated the theory and experiment of homogeneous nucleation. One-dimensional nanostructures, such as nanowires of Si, have been attractive for nanotechnology since their morphology, size, and electronic properties make them suitable to serve as the basic components in electronic and optoelectronics devices, especially biosensors.11-13 Well-defined nanoscale building blocks such as ohmic contacts and gates on Si nanowires must be developed in order to be assembled into functional device structures. It requires a systematic study of chemical reactions in the nanoscale to form these
Figure 1. Low magnification TEM images of Si nanowires and the CoSi2/Si and NiSi/Si heterostructures. (a) Contact of Si and Co nanowires before annealing. (b) Heterostructure of CoSi2/Si/ CoSi2. (c) Heterostructure of NiSi/Si/NiSi.
circuit components. The point contact reaction between Si nanowires and metal nanowires of Ni and Co has been studied by in situ high-resolution transmission electron microscopy (HRTEM).14,15 Both the metal nanowires of Ni and Co and the Si nanowires have diameters ranged from 20 to 70 nm and lengths of a few micrometers. In situ annealing for point contact reactions and high-resolution lattice imaging were performed in a JEOL 2000 V ultrahigh vacuum TEM. The annealing temperature of Co and Si samples was at 800 °C and that of Ni and Si samples was from 450 to 750 °C. The vacuum in the sample stage was about 3 × 10-10 Torr. Figure 1 shows low magnification TEM images of Si nanowires, CoSi2/Si/CoSi2, and NiSi/Si/NiSi heterostructures. The epitaxial growth mode of NiSi and CoSi2 in Si nanowires was found to be the same. The growth in the axial direction occurs atomic layer by atomic layer with the moving of steps or kinks across the epitaxial interface. The growth rate of the silicide, at 450 to 750 °C for NiSi and at 800 °C for CoSi2, was measured from in situ HRTEM video. Figure 2a,b shows two consecutive HRTEM images of the motion of one NiSi atomic layer across the NiSi/Si interface, and the stepwise growth direction is the step motion in the radial direction of the wire. Similarly, Figure 2d,e shows two images of step motion of CoSi2. Surprisingly, we observed that there is a long period of stagnation between the growths of two successive atomic layers. This is true for both CoSi2 and NiSi. When we plotted the stagnation periods as well as the stepwise growth periods from the video recording, we obtained the stair-type curves as shown in Figure 2c and f. The stepwise growth rate of each of the silicide atomic layer is about the same, which is ∼0.17 s per layer for CoSi2 and ∼0.06 s per layer for NiSi, and we note that it is just the width of the vertical line in the stair-type curves. In between the vertical lines (the horizontal part of the steps in Figure 2c,f) is the stagnation period, which we define as the incubation time of nucleation of a new layer. In addition, Figure 2c,f, the nucleation and growth curves of silicide atomic layers, were obtained by in situ HRTEM videos. Since nucleation is a fluctuation phenomenon, the different incubation periods might be caused by fluctuation and impurities inside the Si nanowires so that the incubation time of 2338
Figure 2. High resolution TEM images of motion of a step on epitaxial silicide/Si interfaces and their growth curves. (a,b) Epitaxial NiSi/Si interfaces. (d,e) Epitaxial CoSi2/Si interfaces. The direction of the atomic layer motion is upward from the center of the nanowire to the edge in NiSi and downward in CoSi2. The first two numbers are in units of seconds and the following two smaller numbers are in units of 1/100 s. (c and f) The stair-type growth curves for NiSi and CoSi2, respectively. The insets are the distribution curves of incubation periods of nucleation.
nucleating each atomic layer varied. Accordingly, we plotted the distribution of incubation time as shown in the inset in Figure 2c,f. The average value of the incubation time of NiSi is about 3 s and that of CoSi2 is about 6 s. Our HRTEM videos show that the overall axial growth rate of the silicide layers is linear. Actually the linear curve can be decomposed into many stair-steps with the step height equal to an atomic layer thickness and the step width equal to the incubation time of nucleating a new step. After a step is nucleated, it propagates very rapidly across the Si/silicide interface. The overall reaction rate is limited by the incubation time of nucleation, so it is a nucleation-limited reaction, neither diffusion-limited nor interfacial-reaction-limited. Where is the nucleation site of the new step? The fast radial growth of CoSi2 and NiSi atomic layers starts from the center rather than from the edge of the nanowire. This is because we always observe that the step moves toward the edge, rather than away from the edge. We have five cases of video recording to substantiate the observation that NiSi and CoSi2 atomic layers grow toward both ends of the oxide of Si nanowires and some are observed as growing from the middle. (The videos are presented as Supporting Information). Because of the surface oxide of the Si nanowires, we assume that the energy of the oxide/silicide interface is higher than that of the oxide/ Si interface. This is a reasonable assumption since we found that when a step approaches the edge of the Si nanowire, it Nano Lett., Vol. 9, No. 6, 2009
per unit area of the circumference of the disk, and a is atomic height. Knowing the activation energy of formation of the critical disk, we can calculate the probability of nucleation of the metastable critical nucleus, that is, the number of critical nuclei per unit area per unit time. For a critical nucleus to become stable, at least one more atom or molecule has to join it. Experimentally what we have measured in Figure 2c,f is one stable critical nucleus on the cross section of the Si/silicide nanowire in the period of one incubation time. Thus we have the nucleation rate of Figure 3. High resolution TEM images and schematic diagrams of the triple points of oxide, Si, and CoSi2. (a) The delayed CoSi2 layer growth near the oxide edge at right side has caused a curved interface. (b) The image shows the curved interface at the left side oxide. (c) A cross-sectional schematic diagram of the curved interface at the triple points of oxide, Si, and CoSi2. (d) An enlarged schematic diagram of the curved interface at the triple point.
will slow down before it transforms the edge from the oxide/ Si interface to the oxide/silicide interface because of a high energy barrier. This is shown in Figure 3a,b where we can see a curvature of the untransformed Si near the oxide/Si edge because several of the silicide layers have greatly slowed down their growth within atomic distance in approaching the edge. The insets in Figure 3a,b are sketches of the observed curvature of the silicide layers. The schematic diagrams of the triple points are shown in Figure 3c,d. Furthermore, we kept the electron beam at the edge region and waited for heterogeneous nucleation to take place, but we were unable to observe one. Figure 4a,b shows that one NiSi atomic layer nucleates and grows from the middle region of the interface and spreads toward both ends of the oxide of the Si nanowire. This behavior is repeated for every atomic layer growth, which is a direct evidence of homogeneous nucleation of silicide in the epitaxial interface in Si nanowires. The heterogeneous nucleation of a step at the edge is depicted in Figure 5a. It must replace the low energy oxide/ Si interface by the high energy oxide/silicide interface. There is no microreversibility, so the heterogeneous nucleation is suppressed. In Figure 5b, a schematic diagram of a heterogeneous nucleus is assumed with a wetting angle larger than 90°. At the triple point, we consider γsilicide/oxide g γSi/oxide + γSi/silicide cos(180 - θ), where γ represents the surface energy per unit area of the interfaces. We note that the epitaxial interface between Si and silicide is a low energy interface. When the inequality is satisfied and θ ) 180°, heterogeneous nucleation will not occur and homogeneous nucleation of a circular disk in the center of the nanowire becomes possible, and the cross section is depicted in Figure 5c. In homogeneous nucleation of a circular disk as depicted in Figure 5d, the net change in energy is ∆G ) 2πraγ πr2a∆Gs. The critical nucleus has a size rcrit ) γ/∆Gs and the activation energy in nucleating the critical disk is ∆G* ) πrcritaγ, where ∆Gs is the gain in free energy of formation of the silicide per unit volume, γ is the interfacial energy Nano Lett., Vol. 9, No. 6, 2009
Istable-crit )
1 πR2τi
(1)
where R is the radius of the Si nanowire, and τi is the incubation time. Taking the diameter of Si nanowire to be 30 nm and the incubation time to be 3 s, we have Istable-crit ) 4.7 × 1010 stable nuclei/cm2 sec for the case of NiSi. In the steady state reaction, it indicates that during one period of incubation, it must have dissolved from the point contact nearly the same amount of Ni atoms to supply the growth of one atomic layer of the silicide. For simplicity, we assume there are 1015 atoms per atomic layer per cm2, and the flux of Ni needed to grow an atomic layer is JNi )
1015 ) 1.67 × 1014 atoms/cm2 sec 2×3
where in the denominator the factor of 2 is because of concentration of Ni in NiSi is half and the factor 3 is from the incubation time. While we can regard this to be a flux of Ni atoms being deposited onto the silicide/Si interface, we note that not all these Ni atoms will involve directly in the nucleation process. This is because, similar to thin film deposition on a substrate, we should consider the adatoms on the interface, and we assume that only the adatoms are taking part in the nucleation process. However, the adatoms have a residence time, τdes, on the interface because of desorption. τdes )
∆Gdes 1 exp νs kT
(2)
where νs is the vibrational frequency of an adatom, ∆Gdes is the activation energy of desorption of an adatom, and kT is thermal energy. Thus JNiτdes is the effective number of adatoms per unit area involved in the nucleation process. Then, the equilibrium concentration of critical nucleus can be given as
(
Ccrit ) JNiτdes exp -
∆G* kT
)
(3) 2339
Figure 4. High resolution TEM images of motion of steps on epitaxial NiSi/Si interface at 450 °C. (a) One NiSi atomic layer grows from the middle region of the interface and two steps are formed. (b) The motion of the two steps is toward both ends of oxide. After two steps reaches to the oxide ends, the layer growth ends and the interface becomes flat without steps.
Table 1. The Required Molecules to Form a Stable Silicide Nucleusa CoSi2 at 800 °C
NiSi at 700 °C
Z factor 1 0.1 0.05 1 0.1 0.05 n* 1.6 16 31 1.1 11 22 a n* is the number of molecules required to form a stable nucleus.
By assuming a circular disk shape of nucleus of atomic height, the Zeldovich factor can be rewritten as Z) Figure 5. Schematic diagrams of the cross-section of the epitaxial interface between silicide and Si. (a) It depicts a heterogeneous nucleation of a step at the right-hand side corner. To form the step, the oxide/Si interface will be replaced by the oxide/silicide interface, which is energetically unfavorable. (b) Triple point configuration of a heterogeneous nucleus. (c) Cross-section of homogeneous nucleation of a disk in the center of the silicide/Si interface. (d) Schematic diagram of the nucleation of a circular disk on the interface.
where Ccrit has the unit of number of nuclei per unit area. On the basis of assumption of thermally activated process of fluctuation of subcritical nucleus, the steady state homogeneous nucleation rate has been given as
[ ( )]
s In* ) βn*CcritZ ) βn*C0e-∆G*n /kT -
2 1 ∂ ∆Gn 2πkT ∂n2
1/2
n*
(4)
where βn* is the frequency of atomic jump toward an critical nucleus that converts it into a stable nucleus, and Ccrit ) C0 exp(-∆Gn*/kT) is the equilibrium concentration of critical size nucleus, which we note is the same as eq 3. The Zeldovich factor has been included in the nucleation rate equation as a kinetic factor that stands for the percentage of critical size nuclei that become stable. This is because the nucleus which has overcome the nucleation barrier may not definitely become a stable nucleus until at the least one more atom has joined it, otherwise most of them may shrink back to subcritical size. The Zeldovich factor is less than 1 in all real cases. 2340
[
1 ∆G* · 4πkT (n*)2
]
1/2
(5)
where ∆G* and n* are respectively the activation energy in forming the critical nucleus and the number of molecules in it. Knowing the activation energy of NiSi to be 1.25 eV/ atom,14 we can calculate n* at a given value of Z. Table 1 shows the n* of NiSi at 700 °C and CoSi2 at 800 °C with different Zeldovich factors. For CoSi2, we took the activation energy from thin film study at 800 °C.16 Typical experimental value of Z factor is about 0.05.3 Table 1 lists the value of n* to be about 10 for both silicides. The n* value of CoSi2 is higher than that of NiSi, and it may be one of the reasons that the temperature of reaction of CoSi2 is higher than that of NiSi. Since we know the experimentally measured steady state nucleation rate as given by eq 1, we can check it by using eqs 3 and 4. We have ∆G* 1 Z ) βn* JNi × kT νs ∆G* - ∆Gdes 1 Z ) ν0JNi × exp kT νs ∆G* - ∆Gdes + ∆Gβ Z exp kT
(
Istable-crit ) βn* JNiτdes exp -
(
)
)
(
)
where we assume that βn* ) ν0 exp(-∆Gβ/kT), and ν0 is Debye frequency of vibration and ∆Gβ is the activation energy of adding an atom to the critical nucleus. It is worthwhile mentioning that the basic nature of the parameter of βn* is microreversibility. In order to maintain the equilibrium distribution of subcritical size embryos in nucleation, Nano Lett., Vol. 9, No. 6, 2009
the frequency of adding and subtracting atoms among the embryos is high. Hence we can assume ∆G* . ∆Gβ, so we can ignore ∆Gβ. To evaluate the products on the right-hand side of the above equation, we cancel ν0 against νs owing to the fact that both are Debye frequency of atomic vibration. For ∆Gdes, it is known from epitaxial growth of Si on Si, where ∆Gdes ) 1.1 eV/atom. For the desorption of Ni, the activation energy should be lower and we assume ∆Gdes ) 0.7 eV/ atom. Then we take the measured ∆G* ) 1.25 eV/atom and Z ) 0.1. Since JNi ) 1.67 × 1014 atoms/cm2 sec, the products on the right-hand side at T ) 700 °C is 3 × 1010 nuclei/cm2 sec, which is in good agreement with the measured nucleation rate of 4.7 × 1010 nuclei/cm2 sec. We caution that there is some uncertainty about ∆Gdes. While we have no measured data, we note that even if we give it a high uncertainty by taking ∆Gdes ) 0.7 ( 0.2 eV/ atom, it will only change the outcome by a factor about 10. Since this is the first attempt to correlate theory and experiment on homogeneous nucleation, it is expected to have a large uncertainty. Nucleation requires supersaturation. We can calculate the supersaturation in the nucleation of NiSi. The solubility of Ni in Si at 700 °C is about 1015-1016 Ni-atoms/cm3.17 Since there are 2.5 × 1022 Si atoms/cm3, the equilibrium concentration of Ni in Si is about 10-7-10-8. When we have dissolved half of a monolayer of Ni (which has a layer thickness of 0.3 nm) into a Si nanowire of 3 µm long before homogeneous nucleation occurs, the concentration of Ni is 0.5 × 10-4, so the supersaturation is ∼103, which seems very large. Since Ni atoms are dissolved into nanowire of Si, the solubility can be increased due to Gibbs-Thomson effect by a factor of exp(γΩ/rkT). To calculate this factor, we take Ω ) a3 and a ) 0.3 nm as atomic diameter, r ) 15 nm, and kT ) 0.084 eV at 973 K. When we let γa2 ) 1-2 eV, we obtain the factor to be 1.25 to 1.58, respectively, which is small as compared to the estimated supersaturation of 1000. Below we show that the high supersaturation is reasonable for homogeneous nucleation. Considering the equilibrium solubility of Ni over the critical disk, we have from the Gibbs-Thomson equation that ncrit/n0 ) exp(γΩ/rcrit kT), where ncrit and n0 are the equilibrium solubility of Ni above a flat silicide/Si interface and that above a critical nucleus, respectively. Thus,
silicide/Si interface. For reference, we know that on (111) surface of Si, each surface atom has a broken bond, so the surface energy is about 1 eV/atomic area. Here we shall take γ ) 0.5 eV/a2 (which is about 800 erg/cm2) and kT ) 0.084 eV at 973 K, we have ncrit/n0 = 1800 from the equation below. For γ ) 0.4 eV/a2, we have ncrit/n0 = 120. ∆G* )
π(γa2)2 3.14 × 0.25 ) ncrit ncrit kT ln 0.084 ln n0 n0
( )
( )
Since ∆G* is inversely proportional to ln(ncrit/n0), if we take ncrit/n0 ) 1000, we obtain ∆G* ) 1.35 eV/atom; ncrit/n0 ) 100 implies ∆G* ) 2 eV/atom; and ncrit/n0 ) 10 implies ∆G* ) 4.1 eV/atom. It shows that for a low supersaturation just over unity, the activation energy will be very high. This is the reason why in most real events of nucleation at a low supersaturation, it is heterogeneous rather than homogeneous nucleation. In conclusion, the formation of NiSi and CoSi2 in Si nanowires by point contact reactions has been investigated in situ by ultrahigh vacuum high-resolution transmission electron microscopy. We observed in video recording the stepwise growth of each atomic layer. It leads to axial growth of epitaxial silicide with a stair-type of growth mode. The growth of every new atomic layer of silicide requires an independent event of nucleation accompanied by a long incubation time. The nucleation stage and the growth stage of each layer of NiSi and CoSi2 can be separated. The distribution of incubation time of nucleation has been measured and it enables us to determine the steady state nucleation rate per unit area per unit time. The nucleation is homogeneous rather than heterogeneous. This is because the nanowire of Si has native oxide and the oxide has prevented heterogeneous nucleation to occur because the energy of the oxide/Si interface is lower than that of the oxide/silicide interface. The number of molecules required to form a stable NiSi or CoSi2 nucleus for homogeneous nucleation has been calculated to be about ten on the basis of Zeldovich factor approach and the measured activation energy of nucleation. The calculated and the measured homogeneous nucleation rates are in good agreement. The supersaturation needed for the homogeneous nucleation is about 1000.
( )
Acknowledgment. The authors Y.C.C. and K.N.T. acknowledge the support from NSF/NIRT contract CMS0506841 and the authors L.J.C. and W.W.W. acknowledge the support from NSC Grants 97-2120-M-007-003, 96-2628E-007-018-MY3 and 97-2218-E-009-027-MY3, 97-2120-M009-006. A review of the manuscript by Professor A. M. Gusak at Cherkasy National University, Ukraine and Professor F. G. Shi at University of California at Irvine is acknowledged.
In the last step of the above equation, we have taken Ω ) a3. Since we know ∆G* ) 1.25 eV/atom, we can calculate the ratio of ncrit/n0, provided that we know γa2, the interfacial energy per cross-sectional area of an atom of the epitaxial
Supporting Information Available: TEM videos of silicide epitaxial growth within Si nanowires at different temperatures. Supplementary Movie 1. High resolution in situ TEM video of CoSi2 growth within a Si nanowire at
rcrit )
γΩ and ncrit kT ln n0
( )
∆G* ) πrcritaγ )
Nano Lett., Vol. 9, No. 6, 2009
πγ2aΩ πγ2a4 ) ncrit ncrit kT ln kT ln n0 n0
( )
2341
800 °C. The CoSi2 atomic layers grow toward the left side oxide and the delayed CoSi2 layer growth near the oxide edge at the right side has caused a curved interface. The time of the image captured is given at the upper right corner. The first two numbers are in units of minutes and the following two numbers are in units of seconds. Scale bar is included in every image. Supplementary Movie S2. High resolution in situ TEM video of NiSi growth within a Si nanowire at 450 °C. The NiSi atomic layers grow from the middle and then spread out toward both ends of oxide of the Si nanowire. Supplementary Movie S3. High resolution in situ TEM video of NiSi growth within a Si nanowire at 650 °C. The NiSi atomic layers grow toward the lower right side oxide repeatedly and waiting periods of a few seconds exist between each NiSi atomic layer growth. Supplementary Movie S4. High resolution in situ TEM video of NiSi growth within a Si nanowire at 700 °C. The NiSi atomic layers grow toward the upper left side oxide repeatedly and waiting periods of a few seconds exist between each NiSi atomic layer growth. Supplementary Movie S5. High resolution in situ TEM video of NiSi growth within a Si nanowire at 750 °C. The NiSi atomic layers grow toward the upper left side oxide repeatedly and waiting periods of a few seconds exist between each NiSi atomic layer growth. This material is available free of charge via the Internet at http://pubs.acs.org.
2342
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NL900779J
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