N. Wang et al. /Materials Science and Engineering R 60 (2008)1-51 11 Gibbs-Thomson effect, i. e, the decrease of supersaturation as a [123] have calculated the minimum radii of Si wires formed unction of the whisker diameter [6] from Si-M systems based on appropriate phase diagrams and A△uo4as21 he interface energy asw. Smaller radii can be reached at lower 3.1.5) growth temperatures. As illustrated in Fig. 12, the radii of some small Si nanowires have approached some effective limit set by or the liquid composition 4032 Though the classical VLS reaction can still be extrapolated △=△0-d (.1.6) to explain the growth of most nanowires, ultra-thin nanowires where Au(also the driving force for whisker growth)is the (diameter 10 nm)of different materials show distinct growth behaviors. In the classical vls reaction it is believed that the effective difference between the chemical potentials of Si in the catalyst is in molten state which absorbs the source materials to vapor phase and in the whisker. Apo is the chemical potential form a supersaturated liquid droplet(Fig. 13(a)).The LS difference for the plane boundary case, i.e., the whisker dia- interface structure is very critical to nanowire growth. At the LS meterd-o0. S2 is the atomic volume of Si; a the specific free interface, there is a region consisting of several layers of atoms energy of the whisker surface. Due to the change of the driving in which atoms are in semi-molten state, i.e., atoms can move force(the chemical potential difference), Si whiskers with easily between the crystal lattice sites [124]. Atom precipitation small diameters(<. I um)grow very slowly. Obviously, there occurs at the LS interface. The growth rate of the nanowires is is a critical diameter at which Au =0 and the whisker growth determined by the supersaturation in the catalyst droplet(Au/ stops completely. Those whiskers with diameters smaller than kD). Givargizov et al. [6, 125] determined the whisker growth the critical diameter will stop growing. Thick whiskers grow rate as a function of the driving force(supersaturation Au/kT) state, the stability of a liquid droplet depends on the degree of stability can be described by dmin=(4a 32)(kT In S). Here, s V dL persaturation. For a liquid droplet in its own vapor. the kBT dbT (3.1.9) is the degree of supersaturation (the chemical potential △uL= kTln s) b and n(2)are empirical fitting Although Eq (3. 1.5)can well predict the VLS growth for relationship was later justified(numerically) by Givargizov most whiskers. however, it is not sufficient to describe the vls using a 2D island nucleation-growth model [6] reaction because(1)the droplet size may not be the same to that of the whisker and (2)the binary alloy nature(Metal-Si) of the V=VoexP( 3k Th Au (3.1.10) droplet should be considered [123]. For the VLs reaction (Fig. 10(a), four phases of materials are involved. They are Si and metal (M)vapor phases, the M-Si liquid droplet and the Si where n is the island edge energy density and h is the crystal. Because of the binary nature of the metal droplet, two thickness. Again, these results indicated that in minimum diameters are defined on the basis of thermody- deposition, thick whiskers grow faster than narrow ones.But namics by Tan et al. [123]: the minimum droplet diameter di (equal to the critical diameter of the Si-M liquid droplet constant nucleated by the two vapor phases Si and M)and minimum wire diameter ds A 401 4OLV S2L min KTIn(Psi/Psi) KT In(PM/PM (3.1.7) E Au-Cui et al.(2001) Here Psi and PM are partial pressures of Si and M. Psi and PM Fe-Gu et al. (2000) Fan et al. (2001) are unique values of the Si and M vapor phase pressures Fe-Morales& Lieber(1998) respectively allowing the two phases and the liquid phase with Fe-Fen et al.(2000 a flat surface to coexist under thermal equilibrium condition equal to the critical diameter of a cylindrical Si crystal grown 2 10 The minimum Si wire diameter d min has a similar form which is from the liquid Si-M droplet of diameter 5 KTIn(Psi/Psi) 1000 1200 Psi is the Si vapor phase pressure in the thermal equilibrium T(C) state. According to Eqs. (3.1.7)and (3. 1.8), thermodynamically there is no absolute limit on the diameters of the Si-M droplet Fig. 12. Calculated curve using Eq. (3.1.8)for the Si-M systems. The and Si wire. The diameters of Si wires can reach smaller sizes if radi of Si nanowires have approached the effective limits(from Ref. [1231 there is no limit from the kinetic process in the VLs. Tan et al. reproduced with permission from American Institute of Physics)
Gibbs–Thomson effect, i.e., the decrease of supersaturation as a function of the whisker diameter [6]: Dm kT ¼ Dm0 kT 4aV kT 1 d ; (3.1.5) or Dm ¼ Dm0 4aV d ; (3.1.6) where Dm (also the driving force for whisker growth) is the effective difference between the chemical potentials of Si in the vapor phase and in the whisker. Dm0 is the chemical potential difference for the plane boundary case, i.e., the whisker diameter d ! 1. V is the atomic volume of Si; a the specific free energy of the whisker surface. Due to the change of the driving force (the chemical potential difference), Si whiskers with small diameters (<0.1 mm) grow very slowly. Obviously, there is a critical diameter at which Dm = 0 and the whisker growth stops completely. Those whiskers with diameters smaller than the critical diameter will stop growing. Thick whiskers grow faster than narrow ones [6]. At the thermodynamic equilibrium state, the stability of a liquid droplet depends on the degree of supersaturation. For a liquid droplet in its own vapor, the stability can be described by dmin = (4aV)/(kT ln S). Here, S is the degree of supersaturation (the chemical potential Dm = kT ln S). Although Eq. (3.1.5) can well predict the VLS growth for most whiskers, however, it is not sufficient to describe the VLS reaction because (1) the droplet size may not be the same to that of the whisker and (2) the binary alloy nature (Metal–Si) of the droplet should be considered [123]. For the VLS reaction (Fig. 10(a)), four phases of materials are involved. They are Si and metal (M) vapor phases, the M–Si liquid droplet and the Si crystal. Because of the binary nature of the metal droplet, two minimum diameters are defined on the basis of thermodynamics by Tan et al. [123]: the minimum droplet diameter dl min (equal to the critical diameter of the Si–M liquid droplet nucleated by the two vapor phases Si and M) and minimum wire diameter ds min: dl min ¼ 4aLVVL KT lnðPSi=P¯ SiÞ ¼ 4aLVVL KT lnðPM=P¯ MÞ (3.1.7) Here PSi and PM are partial pressures of Si and M. P¯ Si and P¯ M are unique values of the Si and M vapor phase pressures respectively allowing the two phases and the liquid phase with a flat surface to coexist under thermal equilibrium condition. The minimum Si wire diameter ds min has a similar form which is equal to the critical diameter of a cylindrical Si crystal grown from the liquid Si–M droplet of diameter dl min: dS min ¼ 2aSVVS KT lnðPSi=P¯ eq SiÞ (3.1.8) P¯ eq Si is the Si vapor phase pressure in the thermal equilibrium state. According to Eqs. (3.1.7) and (3.1.8), thermodynamically there is no absolute limit on the diameters of the Si–M droplet and Si wire. The diameters of Si wires can reach smaller sizes if there is no limit from the kinetic process in the VLS. Tan et al. [123] have calculated the minimum radii of Si wires formed from Si–M systems based on appropriate phase diagrams and the interface energy aSV. Smaller radii can be reached at lower growth temperatures. As illustrated in Fig. 12, the radii of some small Si nanowires have approached some effective limit set by the liquid composition. Though the classical VLS reaction can still be extrapolated to explain the growth of most nanowires, ultra-thin nanowires (diameter < 10 nm) of different materials show distinct growth behaviors. In the classical VLS reaction, it is believed that the catalyst is in molten state which absorbs the source materials to form a supersaturated liquid droplet (Fig. 13(a)). The LS interface structure is very critical to nanowire growth. At the LS interface, there is a region consisting of several layers of atoms in which atoms are in semi-molten state, i.e., atoms can move easily between the crystal lattice sites [124]. Atom precipitation occurs at the LS interface. The growth rate of the nanowires is determined by the supersaturation in the catalyst droplet (Dm/ kT). Givargizov et al. [6,125] determined the whisker growth rate as a function of the driving force (supersaturation Dm/kT) and first empirically described their results by the relationship: V ¼ dL dt ¼ b Dmo kBT 4Vs dkBT n ; (3.1.9) where b and n (2) are empirical fitting parameters. This relationship was later justified (numerically) by Givargizov using a 2D island nucleation-growth model [6]: V ¼ Vo exp pVh2 3k ThDm ; (3.1.10) where h is the island edge energy density and h is the layer thickness. Again, these results indicated that in the VLS deposition, thick whiskers grow faster than narrow ones. But if the nanowire is thick enough, the growth rate will tend to be a constant. Fig. 12. Calculated curve using Eq. (3.1.8) for the Si–M systems. The surface energy used for the calculation is aSV = 1610 erg/cm2 . Some available smallest radii of Si nanowires have approached the effective limits (from Ref. [123]; reproduced with permission from American Institute of Physics). N. Wang et al. / Materials Science and Engineering R 60 (2008) 1–51 11
N. Wang et al/Materials Science and Engineering R 60(2008)1-51 for thin ZnSe nanowires(diameters <100 nm) grown by Au- catalyzed MBE. It is very obvious that smaller nanowires have a higher growth rate compared to thicker ones [127, 128. The relationship between the growth rates and the diameters can be described by V=Cld(cis a constant). This relation agrees with the growth model controlled by surface diffusion [126] Diffe (b) deviation of the growth behavior of ultra-thin nanowires from the classical VLS [129, 130]. The main reason for the deviation Fig. 13. Different diffusion or the source atoms to incorporate into the of the growth rates is attributed to the change of the owth front of the classical VLS.(b) The metal droplet is in incorporation process and the diffusion paths of source atoms. partially molten state. Its su interface are liquid, he core of the For a thick nanowire. the surface diffusion contributes droplet is solid. (c) The metal catalyst is solid, but the interface is liquid. insignificantly to the growth rate because the ratio of cross- section area to the circumference is large. for an ultra-thin Wang et al. [52] have shown that in some cases the nanowire nanowire, however, the surface diffusion becomes significant growth may be controlled by surface diffusion. In their Especially when the growth temperature is low and the metal diffusion-induced VLS model, molecules in the vapor phase are catalyst becomes solid (or partially solid), the interface between considered to first fall on the liquid surface and then diffuse the catalyst and nanowire may still be in semi-melting state along the surface to the Ls interface and finally incorporate into This is similar to the case of a grain boundary whose melting the solid wire(see Fig. 13(b)). Then, the nanowire growth rate temperature is always lower than that of its bulk crystals. It is mainly depends on the surface concentration gradient Vs and known that grain boundaries are fast channels for atomic the surface diffusion coefficient As. The relative growth rate Vs diffusion. At a certain temperature the atoms at the interface is proportional to the inverse of the nanowire diameter, V:= between Si and metal may be in partially molten state [51] (AL/At)=(4A Vs/ d)[52, 126, 127]. The surface diffusion Therefore, at a low growth temperature, a solid metal catalyst model becomes important for the growth at a low temperature. can also lead to growth of ultra-thin nanowires through surface In addition to the direct impinging atoms, the source atoms may diffusion since the interface is still active, while in this case, the also arrive at the droplet by diffusion along the substrate surface growth of a thick nanowire(a large solid catalyst) through nd wire side surfaces(Fig. 13(c)). Nanowires formed by this interface diffusion should be difficult. The growth rates of ultra- model usually show tapering shape at their roots. At a relatively thin nanowires controlled by surface diffusion are proportional high growth temperature, however, this growth model should be to the inverse of the diameters. Recently, Kodambaka et al. [54] inhibited because no adatom can stay at solid surfaces have demonstrated by in situ TEM observation that solid The measured growth rates V [6] of the VLs grown Si catalysts can lead to Ge nanowire growth whiskers as a function of their diameters d is shown in At the same growth condition, the melting temperatures of Fig. 14(a). According to Eq. (3. 1.9), VIn and l/d should be metal catalysts are size-dependent. On the one hand, small linear dependence, and this dependence matches the experi- catalysts have lower melting temperatures due to the nanosize mental results fairly well. The data can fit to straight lines for effect. On the other hand, due to the gibbs-Thomson effect, n=2. The classical VLS model can predict the growth decreasing the diameter of the catalyst droplet results in a lower behaviors of whiskers well. However, the growth behaviors of solubility of the source atoms and thus shifts the melting ultra-thin nanowires may be totally different from that of temperature of the catalyst(see also the phase diagram in whiskers. As an example, Fig. 14(b)illustrates the growth rates Fig. 1(b)). Therefore, when the growth temperature falls below Fitting with =cd 30405060 d. 10-cm
Wang et al. [52] have shown that in some cases the nanowire growth may be controlled by surface diffusion. In their diffusion-induced VLS model, molecules in the vapor phase are considered to first fall on the liquid surface and then diffuse along the surface to the LS interface and finally incorporate into the solid wire (see Fig. 13(b)). Then, the nanowire growth rate mainly depends on the surface concentration gradient 5s and the surface diffusion coefficient As. The relative growth rate V0 s is proportional to the inverse of the nanowire diameter, V0 s ¼ ðDL0 s=DtÞ¼ð4A0 sr0 s=dÞ [52,126,127]. The surface diffusion model becomes important for the growth at a low temperature. In addition to the direct impinging atoms, the source atoms may also arrive at the droplet by diffusion along the substrate surface and wire side surfaces (Fig. 13(c)). Nanowires formed by this model usually show tapering shape at their roots. At a relatively high growth temperature, however, this growth model should be inhibited because no adatom can stay at solid surfaces. The measured growth rates V [6] of the VLS grown Si whiskers as a function of their diameters d is shown in Fig. 14(a). According to Eq. (3.1.9), V1/n and 1/d should be linear dependence, and this dependence matches the experimental results fairly well. The data can fit to straight lines for n = 2. The classical VLS model can predict the growth behaviors of whiskers well. However, the growth behaviors of ultra-thin nanowires may be totally different from that of whiskers. As an example, Fig. 14(b) illustrates the growth rates for thin ZnSe nanowires (diameters <100 nm) grown by Aucatalyzed MBE. It is very obvious that smaller nanowires have a higher growth rate compared to thicker ones [127,128]. The relationship between the growth rates and the diameters can be described by V = C/d (C is a constant). This relation agrees with the growth model controlled by surface diffusion [126]. Different theories have been developed to explain the deviation of the growth behavior of ultra-thin nanowires from the classical VLS [129,130]. The main reason for the deviation of the growth rates is attributed to the change of the incorporation process and the diffusion paths of source atoms. For a thick nanowire, the surface diffusion contributes insignificantly to the growth rate because the ratio of crosssection area to the circumference is large. For an ultra-thin nanowire, however, the surface diffusion becomes significant. Especially when the growth temperature is low and the metal catalyst becomes solid (or partially solid), the interface between the catalyst and nanowire may still be in semi-melting state. This is similar to the case of a grain boundary whose melting temperature is always lower than that of its bulk crystals. It is known that grain boundaries are fast channels for atomic diffusion. At a certain temperature the atoms at the interface between Si and metal may be in partially molten state [51]. Therefore, at a low growth temperature, a solid metal catalyst can also lead to growth of ultra-thin nanowires through surface diffusion since the interface is still active, while in this case, the growth of a thick nanowire (a large solid catalyst) through interface diffusion should be difficult. The growth rates of ultrathin nanowires controlled by surface diffusion are proportional to the inverse of the diameters. Recently, Kodambaka et al. [54] have demonstrated by in situ TEM observation that solid catalysts can lead to Ge nanowire growth. At the same growth condition, the melting temperatures of metal catalysts are size-dependent. On the one hand, small catalysts have lower melting temperatures due to the nanosize effect. On the other hand, due to the Gibbs–Thomson effect, decreasing the diameter of the catalyst droplet results in a lower solubility of the source atoms and thus shifts the melting temperature of the catalyst (see also the phase diagram in Fig. 1(b)). Therefore, when the growth temperature falls below Fig. 13. Different diffusion models for the source atoms to incorporate into the growth front of the nanowire. (a) The classical VLS. (b) The metal droplet is in partially molten state. Its surface and interface are liquid, while the core of the droplet is solid. (c) The metal catalyst is solid, but the interface is liquid. Fig. 14. The growth rates of (a) VLS Si whiskers (from Ref. [6]; reproduced with permission from Elsevier Science) and (b) VLS ZnSe nanowires plotted as a function of diameters. 12 N. Wang et al. / Materials Science and Engineering R 60 (2008) 1–51
N. Wang et al. /Materials Science and Engineering R 60 (2008)1-51 13 the eutectic point, the metal catalysts at the tips of nanowires only AuGa2 binary alloy formed by annealing, and arsenic did with relatively small diameters became solid first, while those not participate in the nanowire growth. The reaction of the catalysts with relatively large diameters remained in the liquid catalysts can be described as state. This interesting phenomenon has been observed by in TEM[54]. 2GaAs(solid )+ Au(solid)- AuGa2(solid)+ 2As(gas) For Si or Ge nanowire growth, Au catalysts are liquid or solid (3.1.11) solution. For compound semiconductors, such as GaAs, th In this reaction arsenic is extracted from the substrate structure and chemical composition of Au catalysts are during the formation of AuGa2 alloy Then, arsenic may diffuse complicated. Fig. 15(a)and(d)shows the Au particles formed out of the catalyst surface and evaporate [192, 193]. For large on a GaAs(1 1 1)surface after annealing at 530"C Fig 15(a)is catalysts, the Ga rich form(Au Ga2)of the Aul-Ga alloy remains an enlarged image showing the typical hexagonal shape of an Au at the tips of ZnSe nanowires(see Fig. 15(f)).However,the catalyst in which 2D moire patterns are clearly visible. The solubility of Ga in an ultra small catalyst is largely reduced,and selected-area electron diffraction(SAED) patten(Fig. I5(b) only Au solid solution(in FCC structure of Au) is formed taken from this particle illustrates clearly strong diffractions of (Fig. 15(g). The change of Ga solubility in the catalyst is due to GaAs(along the [lll] zone axis) surrounded by satellite spots the well-known Gibbs-Thomson effect. Due to the change of which come from the double diffraction effect that occurs when the solubility, the melting point of the catalyst shifted according to Au-Ga phase diagran relationship. The structure of the catalysts has been identified On the surfaces of zn Se. a similar reaction occurred when to be Au Gaz(face center cubic(FCC), space group Fm3m, lattice Au catalysts reacted with Zn Se to form Zn-Au alloy droplets parameter a=0.6073 nm) by electron diffraction and TEM and Se evaporated(see Fig. 16(a). According to the Zn-Au image simulation [131]. The moire fringes are due to the overlap phase diagram, a Au rich Au-Zn alloy should form.As between GaAs substrate and AuGaz particles. The AuGaz observed by TEM, the catalysts were single crystalline FCC catalysts are single crystalline if their sizes are small. Two grains structures, same to that of Au. The interaction between Au often form(marked by I and II in Fig. 15(a) in a large catalyst. nanoparticles and ZnSe or Zns buffer layer(grown on According to the SAED patterns in Fig. 15(b)(along the [l 11] GaAs(1 00)substrate)displayed interesting features.Thermal zone axis)and(c)(along the [1 12 zone axis), only one Au Ga2 annealing always induced the movement of the droplets along a grain epitaxially forms on the substrate with orientation relations certain pair of( 11 0) direction(see the inset in Fig. 16(b)and of [1 GaAs//100AuGa, and (0]GaAs//[0 1 OJAuGaz formed parallel trenches on their path [128]. Fig. 16(b) shows For Au-GaAs system, the catalysts reacted with the the SEM image of the trenches on a ZnSe substrate surface substrate during annealing and formed sharp interfaces between caused by the sliding of Au-catalysts. Separate atomic force the catalyst and GaAs substrate. Fig. 15(e)is the cross-sectional microscopy(AFM) imaging done on this sample revealed that view of an individual AuGa2 catalyst The orientation relations the nanotrenches are quite uniform in width and depth with between Au Ga2 grain II and the substrate agree well with the typical width of 20 nm and depth of a few nanometers SAED results. The chemical composition of the catalysts was Similar thermal annealing resulted six symmetric (11 0) characterized using electron energy-loss spectroscopy and X- oriented nanotrenches on the sample grown on a GaAs(111)B ray energy dispersive spectroscopy, and the results indicated substrate. These results together indicated that some specific that the catalysts consisted of Au and Ga, but no As was (110) directions ware the preferred orientation of the detected in the catalysts. The interface of the catalyst at the nanotrenches substrate (about 7.4%0 of mismatch) was (1 1 1)at which The formation of these nanotrenches is believed to be due to interfacial dislocations occurred. It was interesting to note that the special interaction between Au particles and the substrate. AuG Au-Ga lI Fig. 15.(a) Plan-view TEM image of Au catalysts formed on GaAs substrate surface by the annealing treatment. (b)and(c)SAED patterns taken along the [1 11]and [112] zone axes of the catalyst, respectively. (d)Morphology of Au catalyst (e)Cross-sectional HRTEM image(along the[11 0] direction)of the catalyst formed or the substrate. (f) Au Ga2 phase in a large catalyst. (g) Au-Ga solid solution in a small catalyst in FCC structure
the eutectic point, the metal catalysts at the tips of nanowires with relatively small diameters became solid first, while those catalysts with relatively large diameters remained in the liquid state. This interesting phenomenon has been observed by in situ TEM [54]. For Si or Ge nanowire growth, Au catalysts are liquid or solid solution. For compound semiconductors, such as GaAs, the structure and chemical composition of Au catalysts are complicated. Fig. 15(a) and (d) shows the Au particles formed on a GaAs (1 1 1) surface after annealing at 530 8C. Fig. 15(a) is an enlarged image showing the typical hexagonal shape of an Au catalyst in which 2D moire´ patterns are clearly visible. The selected-area electron diffraction (SAED) pattern (Fig. 15(b)) taken from this particle illustrates clearly strong diffractions of GaAs (along the [111] zone axis) surrounded by satellite spots which come from the double diffraction effect that occurs when the particle and the substrate have a certain orientation relationship. The structure of the catalysts has been identified to be AuGa2 (face center cubic (FCC), space group Fm3m, lattice parameter a = 0.6073 nm) by electron diffraction and TEM image simulation [131]. The moire´ fringes are due to the overlap between GaAs substrate and AuGa2 particles. The AuGa2 catalysts are single crystalline if their sizes are small. Two grains often form (marked by I and II in Fig. 15(a)) in a large catalyst. According to the SAED patterns in Fig. 15(b) (along the [1 1 1] zone axis) and (c) (along the ½1 1 2¯ zone axis), only one AuGa2 grain epitaxially forms on the substrate with orientation relations of ½100 GaAs==½100 AuGa2 and ½010 GaAs==½010 AuGa2 . For Au–GaAs system, the catalysts reacted with the substrate during annealing and formed sharp interfaces between the catalyst and GaAs substrate. Fig. 15(e) is the cross-sectional view of an individual AuGa2 catalyst. The orientation relations between AuGa2 grain II and the substrate agree well with the SAED results. The chemical composition of the catalysts was characterized using electron energy-loss spectroscopy and Xray energy dispersive spectroscopy, and the results indicated that the catalysts consisted of Au and Ga, but no As was detected in the catalysts. The interface of the catalyst at the substrate (about 7.4% of mismatch) was (1 1 1) at which interfacial dislocations occurred. It was interesting to note that only AuGa2 binary alloy formed by annealing, and arsenic did not participate in the nanowire growth. The reaction of the catalysts can be described as 2GaAsðsolidÞ þ AuðsolidÞ ! AuGa2ðsolidÞ þ 2AsðgasÞ (3.1.11) In this reaction, arsenic is extracted from the substrate during the formation of AuGa2 alloy. Then, arsenic may diffuse out of the catalyst surface and evaporate [192,193]. For large catalysts, the Ga rich form (AuGa2) of the Au–Ga alloy remains at the tips of ZnSe nanowires (see Fig. 15(f)). However, the solubility of Ga in an ultra small catalyst is largely reduced, and only Au solid solution (in FCC structure of Au) is formed (Fig. 15(g)). The change of Ga solubility in the catalyst is due to the well-known Gibbs–Thomson effect. Due to the change of the solubility, the melting point of the catalyst shifted according to Au–Ga phase diagram. On the surfaces of ZnSe, a similar reaction occurred when Au catalysts reacted with ZnSe to form Zn–Au alloy droplets and Se evaporated (see Fig. 16(a)). According to the Zn–Au phase diagram, a Au rich Au–Zn alloy should form. As observed by TEM, the catalysts were single crystalline FCC structures, same to that of Au. The interaction between Au nanoparticles and ZnSe or ZnS buffer layer (grown on GaAs(1 0 0) substrate) displayed interesting features. Thermal annealing always induced the movement of the droplets along a certain pair of h110i direction (see the inset in Fig. 16(b)) and formed parallel trenches on their path [128]. Fig. 16(b) shows the SEM image of the trenches on a ZnSe substrate surface caused by the sliding of Au-catalysts. Separate atomic force microscopy (AFM) imaging done on this sample revealed that the nanotrenches are quite uniform in width and depth with typical width of 20 nm and depth of a few nanometers. Similar thermal annealing resulted six symmetric h110i oriented nanotrenches on the sample grown on a GaAs(1 1 1)B substrate. These results together indicated that some specific h110i directions ware the preferred orientation of the nanotrenches. The formation of these nanotrenches is believed to be due to the special interaction between Au particles and the substrate. Fig. 15. (a) Plan-view TEM image of Au catalysts formed on GaAs substrate surface by the annealing treatment. (b) and (c) SAED patterns taken along the [1 1 1] and ½112¯ zone axes of the catalyst, respectively. (d) Morphology of Au catalyst. (e) Cross-sectional HRTEM image (along the [1 1 0] direction) of the catalyst formed on the substrate. (f) AuGa2 phase in a large catalyst. (g) Au–Ga solid solution in a small catalyst in FCC structure. N. Wang et al. / Materials Science and Engineering R 60 (2008) 1–51 13
N. Wang et al/Materials Science and Engineering R 60(2008)1-51 Au-Zn GaAs substrate Catalyst 200nm Fig. 16.(a) Au-Zn nanocatalyst formed on ZnSe substrate (b)Sliding of the catalysts by annealing results in trenches along the [11 0] direction n the substrate By annealing at a high temperature, Au droplets first react with There are three ways to generate atomic steps on a flat droplets while the other by-products are vaporized. In this difficult because the nucleation barrier is high, and there s the ZnSe thin film to form AuZn,(with x less than 14%)alloy surface: (I)nucleation of new two-dimensional islands which buffer by a fraction of their size until the composition of the eventually(see Fig. 17(a));(2)screw dislocations which alloy is saturated. Further annealing will lead to migration of generate atomic steps to help atoms to deposit continuously the alloy droplets along a most preferred direction accompany-(Fig. 17(b); and (3)twining structures which contain ditches at ing the decomposition of ZnSe along the path. The observed the cross of two grain surfaces. Atoms deposit at the ditches specific [1 1 0] direction of the trenches can be explained by the resulting in atomic steps along twining surfaces. The resulting fact that the bonding between(1 10 planes are the weakest for growth can be continuous along the direction of the twining most of the zinc blende structures. During the migration, the plane(Fig. 17(c). Followings are important factors for the AuZn alloy droplets will act as a catalyst for decomposing the nanocrystal growth in the VS process ZnSe along the path. Both Zn and Se decomposed from this reaction most likely are vaporized, so nanotrenches are 3.2.1. Internal anisotropic surfaces developed along the path. The perfect alignment of these Because of anisotropic properties of different surfaces in a template for fabricating ID structures of other material non crystal, such as the preferential reactivity and binding of gas nanotrenches make them potentially useful as a cor reactants on specific surfaces and all crystals tend to minimize their total surface energy, rod- or wire-like shapes are properties of crystals is not significant large, highly anisotropic without the aid of metal catalysts, the vapor-solid(VS) growth(i.e, the length-to-diameter ratio >100)of nanocrystals growth has been mainly used to synthesize metal oxide and at or near the thermal equilibrium state is not expected some semiconductor nanomaterials. It is often called self- catalytic growth since the nanostructures grow directly from 3. 2.2. Crystal defects vapor phases. Plausible growth mechanisms such as the Screw dislocations( the well known Burton-Cabrera-Frank anisotropic growth, defect-induced growth(e.g, through a theory)are known to significantly enhance the crystal growth of screw dislocation), and self-catalytic growth have been metals and some molecular materials [132]. This classical suggested based on electron microscopy studies, According mechanism is based on the fact that the growth of a crystal to the classical theories of crystal growth from liquid or vapor proceeds by adding atoms at the kink sites of a surface step phases, the growth fronts play a crucial role for the deposition Kink sites always exist on the steps even at the thermal f atoms. There are two kinds of microscopic surfaces: (1) equilibrium state. Due to the advance of the kink along the rough surfaces on which atoms of about several layers are not surface by the addition of atoms, the crystal grows well arranged. Deposition of atoms is relatively easy compared perpendicularly to the surface. In thermal equilibrium state, to a flat surface and crystal growth can continue if enough a perfect crystal should eventually contain no surface ster source atoms are continuously provided;(2) atomically flat Then, the growth of a perfect crystal depends on the nucleation surfaces on which atoms are well arranged. Atoms from the of surface steps For the growth of a real crystal, however, the source have a weak bonding with flat surfaces and can easily growth rate is much faster than that predicted for a perfect return to the liquid/vapor phase. Atoms deposition occurs only crystal because real crystals contain defects, e.g., dislocations on the atomic steps. twins. A dislocation cannot terminate inside a perfect
By annealing at a high temperature, Au droplets first react with the ZnSe thin film to form AuZnx (with x less than 14%) alloy droplets while the other by-products are vaporized. In this reaction, the resulting AuZnx alloy droplets fall into the ZnSe buffer by a fraction of their size until the composition of the alloy is saturated. Further annealing will lead to migration of the alloy droplets along a most preferred direction accompanying the decomposition of ZnSe along the path. The observed specific [1 1 0] direction of the trenches can be explained by the fact that the bonding between {1 1 0} planes are the weakest for most of the zinc blende structures. During the migration, the AuZnx alloy droplets will act as a catalyst for decomposing the ZnSe along the path. Both Zn and Se decomposed from this reaction most likely are vaporized, so nanotrenches are developed along the path. The perfect alignment of these nanotrenches make them potentially useful as a common template for fabricating 1D structures of other materials. 3.2. Vapor–solid growth Without the aid of metal catalysts, the vapor–solid (VS) growth has been mainly used to synthesize metal oxide and some semiconductor nanomaterials. It is often called selfcatalytic growth since the nanostructures grow directly from vapor phases. Plausible growth mechanisms such as the anisotropic growth, defect-induced growth (e.g., through a screw dislocation), and self-catalytic growth have been suggested based on electron microscopy studies, According to the classical theories of crystal growth from liquid or vapor phases, the growth fronts play a crucial role for the deposition of atoms. There are two kinds of microscopic surfaces: (1) rough surfaces on which atoms of about several layers are not well arranged. Deposition of atoms is relatively easy compared to a flat surface and crystal growth can continue if enough source atoms are continuously provided; (2) atomically flat surfaces on which atoms are well arranged. Atoms from the source have a weak bonding with flat surfaces and can easily return to the liquid/vapor phase. Atoms deposition occurs only on the atomic steps. There are three ways to generate atomic steps on a flat surface: (1) nucleation of new two-dimensional islands which is difficult because the nucleation barrier is high, and there is almost no super-cooling. The islands will be exhausted eventually (see Fig. 17(a)); (2) screw dislocations which generate atomic steps to help atoms to deposit continuously (Fig. 17(b)); and (3) twining structures which contain ditches at the cross of two grain surfaces. Atoms deposit at the ditches resulting in atomic steps along twining surfaces. The resulting growth can be continuous along the direction of the twining plane (Fig. 17(c)). Followings are important factors for the nanocrystal growth in the VS process. 3.2.1. Internal anisotropic surfaces Because of anisotropic properties of different surfaces in a crystal, such as the preferential reactivity and binding of gas reactants on specific surfaces and all crystals tend to minimize their total surface energy, rod- or wire-like shapes are frequently resulted. However, the degree of the anisotropic properties of crystals is not significant large, highly anisotropic growth (i.e., the length-to-diameter ratio >100) of nanocrystals at or near the thermal equilibrium state is not expected. 3.2.2. Crystal defects Screw dislocations (the well known Burton–Cabrera–Frank theory) are known to significantly enhance the crystal growth of metals and some molecular materials [132]. This classical mechanism is based on the fact that the growth of a crystal proceeds by adding atoms at the kink sites of a surface step. Kink sites always exist on the steps even at the thermal equilibrium state. Due to the advance of the kink along the surface by the addition of atoms, the crystal grows perpendicularly to the surface. In thermal equilibrium state, a perfect crystal should eventually contain no surface steps. Then, the growth of a perfect crystal depends on the nucleation of surface steps. For the growth of a real crystal, however, the growth rate is much faster than that predicted for a perfect crystal because real crystals contain defects, e.g., dislocations and twins. A dislocation cannot terminate inside a perfect Fig. 16. (a) Au–Zn nanocatalyst formed on ZnSe substrate. (b) Sliding of the catalysts by annealing results in trenches along the [1 1 0] direction n the substrate surface. 14 N. Wang et al. / Materials Science and Engineering R 60 (2008) 1–51
N. Wang et al. /Materials Science and Engineering R 60 (2008)1-51 15 (b) Growth direction(c) Growth direction(d) Zno zn rich’o:6mn 5μm Fig 17.(a) Nanorods formed due to anisotropic growth of Zno crystals( b) Unidirectional growth of ZnO single crystals due to screw dislocation(c) Growth nduced by twining.(d) Self-catalytic growth of ZnO nanowires by Zn droplets (e) Zno crystals contain no catalysts and defects). (f) Zno whiskers growth due to dislocations. (g) Zno bi-crystal growth due to twining.(h) Zn or Zn-rich phase observed on the tips of ZnO nanowires (image(h) from Ref [62] reproduced with permission from American Physical Society crystal. They can terminate on a defect inside the crystal or on a thus no nanowires can be generated by heating Zno power at a surface. If a dislocation ends on a surface and its Burgers vector high temperature has a component normal to the surface(the screw component), a step forms starting from the emerging point of the dislocation. 2Zno- 2Zn+ o (3.2.1) Leading by the dislocation, steps can winds into a spiral, and the growth of the crystal is largely enhanced without the need of Another way to generate Zn or Zn oxide vapor phases is to add nucleation for fresh surface steps. There are many reasons for for carbon powders into Zno solid source, mass production of Zno the formation of a dislocation in a crystal. For Si nanowires, oxygen atoms may cause the nucleation of a dislocation [133] ure range of 500-800C In this case, Zn or Zn suboxide play a It has been frequently observed that screw dislocations are is because that at a high temperature condition(T>1100"C), geometries In ultra-thin nanowires, so far no screw dislocations carbon reduced Zno into Zn or Zn suboxides by the following have been evidenced. However, in thick wires, for example reactions: ZnO nanowires(diameters 200 nm), unidirectional growth 2Zn0 C-Zn + co (3.2.2) induced by dislocations in VS growth mode has been observed (Fig. 17(f)). The spiral feature at each whisker tip is obvious. ZnO+Co→Zn+CO2 (3.2.3) due to the steps generated by a screw dislocation. In thin Zno nanowires grown by the Vs growth, however, no screw Zno+(1-x)C0-ZnO+(1-x)COz (3.2.4) dislocations existing at the core of the nanowires have been found The carbon powder might directly react with Zno(for the ase of the sealed quartz tube)or first react with oxygen to form 3.2.3. Self-catalytic grow Co(for the case of the open-end quartz tube). Zn and Zn Self-catalytic growth has been proposed based on the fact suboxides have low melting temperatures(approximately that metal vapor, for example Zn, can be extracted from Zno 419C for both Zn and ZnOx, where x 1)compared to that vapor phase by heating ZnO powder in vacuum. When ZnO is of Zno(1975C)and should be in vapor phases at 1100C. At aled in an evacuated quartz tube(10- to 10)and heated at a the low temperature site, Zn vapor generated by reactions temperature above 1100C, ZnO may decompose into Zn and (3.2.2)and (3.2.3)will condense on the inner wall of the quartz oxygen as described in Eg (3.2.1)[62]. Zn droplets are easily tube forming liquid droplets, which are ideal catalysts for ZnO observed on the inner walls of the tube where the temperature is nanowire growth through the VLs mechanism. Carrying gases about 500-600C. Under a normal atmosphere condition, are not necessary for the formation of Zno nanostructures. however, no obvious decomposition of ZnO is observed, and Temperature is the critical experimental parameter for the
crystal. They can terminate on a defect inside the crystal or on a surface. If a dislocation ends on a surface and its Burgers vector has a component normal to the surface (the screw component), a step forms starting from the emerging point of the dislocation. Leading by the dislocation, steps can winds into a spiral, and the growth of the crystal is largely enhanced without the need of nucleation for fresh surface steps. There are many reasons for the formation of a dislocation in a crystal. For Si nanowires, oxygen atoms may cause the nucleation of a dislocation [133]. It has been frequently observed that screw dislocations are associated with growth of crystal in the dendrite or whisker geometries. In ultra-thin nanowires, so far no screw dislocations have been evidenced. However, in thick wires, for example ZnO nanowires (diameters > 200 nm), unidirectional growth induced by dislocations in VS growth mode has been observed (Fig. 17(f)). The spiral feature at each whisker tip is obviously due to the steps generated by a screw dislocation. In thin ZnO nanowires grown by the VS growth, however, no screw dislocations existing at the core of the nanowires have been found. 3.2.3. Self-catalytic growth Self-catalytic growth has been proposed based on the fact that metal vapor, for example Zn, can be extracted from ZnO vapor phase by heating ZnO powder in vacuum. When ZnO is sealed in an evacuated quartz tube (101 to 103 ) and heated at a temperature above 1100 8C, ZnO may decompose into Zn and oxygen as described in Eq. (3.2.1) [62]. Zn droplets are easily observed on the inner walls of the tube where the temperature is about 500–600 8C. Under a normal atmosphere condition, however, no obvious decomposition of ZnO is observed, and thus no nanowires can be generated by heating ZnO power at a high temperature. 2ZnO ! 2Zn þ O2 (3.2.1) Another way to generate Zn or Zn oxide vapor phases is to add carbon powders into ZnO solid source, mass production of ZnO nanowires and nanoribbons can easily realized in the temperature range of 500–800 8C. In this case, Zn or Zn suboxide play a crucial role for the nucleation of ZnO nanostructures [67]. This is because that at a high temperature condition (T > 1100 8C), carbon reduced ZnO into Zn or Zn suboxides by the following reactions: 2ZnO þ C ! Zn þ CO2; (3.2.2) ZnO þ CO ! Zn þ CO2; (3.2.3) ZnO þ ð1 xÞCO ! ZnOx þ ð1 xÞCO2; (3.2.4) The carbon powder might directly react with ZnO (for the case of the sealed quartz tube) or first react with oxygen to form CO (for the case of the open-end quartz tube). Zn and Zn suboxides have low melting temperatures (approximately 419 8C for both Zn and ZnOx, where x < 1) compared to that of ZnO (1975 8C) and should be in vapor phases at 1100 8C. At the low temperature site, Zn vapor generated by reactions (3.2.2) and (3.2.3) will condense on the inner wall of the quartz tube forming liquid droplets, which are ideal catalysts for ZnO nanowire growth through the VLS mechanism. Carrying gases are not necessary for the formation of ZnO nanostructures. Temperature is the critical experimental parameter for the Fig. 17. (a) Nanorods formed due to anisotropic growth of ZnO crystals. (b) Unidirectional growth of ZnO single crystals due to screw dislocation. (c) Growth induced by twining. (d) Self-catalytic growth of ZnO nanowires by Zn droplets. (e) ZnO crystals contain no catalysts and defects). (f) ZnO whiskers growth due to dislocations. (g) ZnO bi-crystal growth due to twining. (h) Zn or Zn-rich phase observed on the tips of ZnO nanowires (image (h) from Ref. [62]; reproduced with permission from American Physical Society). N. Wang et al. / Materials Science and Engineering R 60 (2008) 1–51 15