L-C. Leu, M-H. Hon /Journal of Crystal Growth 236(2002)171-175 G G1 Fig. 3. The effect of droplet size on the liquid/solid equilibrium omposition(X, vs. Xo)[10]. (The size of droplet designated by r is smaller than the one designated by oo.) Droplet Sie(um) Fig. 2. The dependence of incubation time on the size of the liquid droplet during CVD of Sic whiskers. the shortest incubation period of about 3 min was found for the whiskers with a droplet size of about 2 um. The values of incubation periods will ncrease for whiskers with either larger or smaller droplet size. The tendency of incubation behavior can be explained as follows, where the balance 000648 between the solute supersaturation and the droplet volume size effect is believed to be the determining Fig 4. SEM micrograph shows the nucleation result of droplet are expected to take more time to accumulate ion different dimensions in an intermediate stage of incuba- factors. It is intuitive that droplets with larger size solute from the vapor supply to reach the desired degree of supersaturation. On the other hand, due Gibbs-Thomson effect can lead to different to the presence of the Gibbs-Tompson effect (or equilibrium compositions, Xr and Xo, at the curvature effect)the droplets with smaller dimen- liquid /solid interface for droplets with different sions are expected to have higher equilibrium sizes, i.e., X, is larger than Xo in the present case composition at the solid/liquid interface. The In brief, the smaller the dimensions of the droplets, relation is schematically illustrated in Fig 3 [10 the higher the equilibrium compositions at the for the free energy curve of droplets with different liquid/ solid interface are. Consequently, the higher sizes. In Fig 3, the dimension for droplet r is the required degree of supersaturation will be smaller than that for droplet oo, and their free needed in the liquid droplet to facilitate whisker energies are designated as Gr and Go, respectively nucleation. The shortest incubation period of (the superscript B in Fig 3 represents the phase of about 3 min for droplets with 2 um in diameter is nterest). As a result of the presence of the Gibbbs- believed to be the balanced effect of these two Thomson effect, the value of Gr is expected to be competing parameters, i. e, the curvature effect higher than Go. From the common tangent and the volume effect. Fig 4 is a typical SEM construction in Fig 3 [10], the presence of the micrograph showing the nucleationthe shortest incubation periodof about 3 min was foundfor the whiskers with a droplet size of about 2 mm. The values of incubation periods will increase for whiskers with either larger or smaller droplet size. The tendency of incubation behavior can be explainedas follows, where the balance between the solute supersaturation andthe droplet volume size effect is believedto be the determining factors. It is intuitive that droplets with larger size are expectedto take more time to accumulate solute from the vapor supply to reach the desired degree of supersaturation. On the other hand, due to the presence of the Gibbs–Tompson effect (or curvature effect) the droplets with smaller dimen￾sions are expectedto have higher equilibrium composition at the solid/liquid interface. The relation is schematically illustratedin Fig. 3 [10] for the free energy curve of droplets with different sizes. In Fig. 3, the dimension for droplet r is smaller than that for droplet N, andtheir free energies are designated as Gr and GN; respectively (the superscript b in Fig. 3 represents the phase of interest). As a result of the presence of the Gibbbs– Thomson effect, the value of Gr is expectedto be higher than GN: From the common tangent construction in Fig. 3 [10], the presence of the Gibbs–Thomson effect can leadto different equilibrium compositions, Xr and XN; at the liquid/solid interface for droplets with different sizes, i.e., Xr is larger than XN in the present case. In brief, the smaller the dimensions of the droplets, the higher the equilibrium compositions at the liquid/solid interface are. Consequently, the higher the requireddegree of supersaturation will be needed in the liquid droplet to facilitate whisker nucleation. The shortest incubation periodof about 3 min for droplets with 2 mm in diameter is believedto be the balancedeffect of these two competing parameters, i.e., the curvature effect andthe volume effect. Fig. 4 is a typical SEM micrograph showing the nucleation result of 0 1 2 3 4 Droplet Size (um ) 2 3 4 5 6 7 8 9 1 0 Incubation Period (min) Fig. 2. The dependence of incubation time on the size of the liquid droplet during CVD of SiC whiskers. Fig. 3. The effect of droplet size on the liquid/solid equilibrium composition (Xr vs. XN) [10]. (The size of droplet designated by r is smaller than the one designated by N:) Fig. 4. SEM micrograph shows the nucleation result of droplet with different dimensions in an intermediate stage of incuba￾tion. 174 I.-C. Leu, M.-H. Hon / Journal of Crystal Growth 236 (2002) 171–175