Where, m>1 is a constant. This form of the relationship between % and %v was originally proposed by Nieuwenhuizen and Haanstra (1966) with m=2. Since that time, however, it has been necessary to modify the value of m to more accurately describe CTFs made of various materials under differing conditions
(Hodgkinson and Wu 1998, Hodgkinson et al. 2001). In any case, the relationship is not accurate at extremely low angles, as experiments show (Messier et al. 1997) that, contrary to Eq. 15.1, % approaches a value near 20o as %v approaches 0o. An alternative description of the %-%v relation, derived by geometrical arguments, has been proposed by Tait et al. (1993), but that too is not universal.
With proper conditions for column formation established, the substrate may be rotated about various axes during deposition to change the direction of growth, producing curved columns or nanowires. Nanowires of virtually any curvilinear form desired can be shaped by programming the rotation of the substrate as a function of the amount of film deposited, and hence the name scul tured thin film (Lakhtakia et al. 1996). The substrate may be rotated gradually and continuously, producing smoothly curving nanowires; or it may be changed abruptly, producing a kink in an otherwise smoothly curved or straight section of nanowire. The change in % resulting from an abrupt change in substrate orientation has been shown to occur over a film thickness as small as ~3 nm (Niewenhuizen and Haanstra 1966). Since 3 nm is much less than optical wavelengths, the change in % may be considered instantaneous for optical applications.
STFs can be classified by nanowire shape into two canonical classes: sculptured nematic thin film (SNTF), and thin film helicoidal bianisotropic medium (TFHBM) (Lakhtakia 1997). When the axis of rotation of the substrate lies in the plane of the substrate, the nanowires form two dimensional shapes and a SNTF results.
When the axis of rotation is perpendicular to the substrate, helicoidal structures are formed resulting in a TFHBM or chiral STF. Of course, the two types of rotation may be combined to produce even more complex shapes. Various shapes have been produced to date. Examples of SNTF shapes that have been produced are: zigzag, "C" shaped, and "S" shaped. STFs of the TFHBM type which have been made are: helical, square helical, slanted helical, and superhelical. Fig. 15.3 shows electron micrographs of a few STFs with various shapes. Fig. 15.3(a-c) are examples of SNTFs; Fig. 3.3(d) is a chiral STF; while Fig. 15.3(e) is an example of a STF composed of two different sections, with the bottom one chiral and the top one a chevron shaped SNTF. Growth rates and film thicknesses vary from one experimental set up to another. In some recent experiments Horn et al. (2004), using a rastered electron beam evaporation technique, have achieved growth rates as high as 0.4 pm/min and uniform column diameters for large thickness (> 3 |im) films. Furthermore, they were able to produce highly uniform STFs over a large area (75 mm diameter). Previous to this work, areas were more typically on the order of 1 cm2. In addition to the basic STF growth technique just described, various refinements and modifications have been developed. Producing well-defined columns oriented normal to the surface is difficult with the basic growth method. Deposition at normal incidence to the substrate yields columns, which tend to expand in diameter, as they grow taller except under narrowly controlled conditions (Messier and Lakhtakia 1999). Furthermore, the columns are rather densely packed. Two solutions have been developed, both employing deposition at oblique angles.
Fig. 15.3. Electron micrographs of STFs: (a) Chevron SNTF (b) "S" SNTF (c) Slant "S" SNTF (d) Chiral STF (e) Mixed chiral and chevron STF. Micrographs courtesy of Russell Messier, and Mark Thorn, Pennsylvania State University if e)
Fig. 15.3. Electron micrographs of STFs: (a) Chevron SNTF (b) "S" SNTF (c) Slant "S" SNTF (d) Chiral STF (e) Mixed chiral and chevron STF. Micrographs courtesy of Russell Messier, and Mark Thorn, Pennsylvania State University
In one case (Robbie et al. 1999), the substrate is rotated about the z-axis, as in the production of a chiral STF, but at a much faster rate. At high rotation rate, a chiral STF is not produced; rather, the coils of the helix merge to produce a vertical column with constant diameter. In the other method, serial bideposition (Robbie et al. 1998), deposition at a fixed %v is used, but the film is grown as a series of short depositions with a rotation of 180o about the z -axis between each deposition. The tilt, which would normally result from oblique deposition, is averaged out by deposition from both sides of the normal. The spacing of nanowires is related to %. Thus, in addition to creating well-defined, constant diameter columns normal to the substrate, these methods also offer a degree of control over the density of the film. Serial bideposition also offers additional control over the nanowire morphology. Nanowire cross-sections become more flattened as %v is decreased, with the long axis of the cross-section perpendicular to the plane of incidence of the vapor flux. With bideposition, the cross-section of the nanowire can be flattened by depositing at low %v, yet a vertical column can still be produced. The anisotropy of the film in the x-y plane is thus controllable. This can be particularly important for optical applications, especially when high optical activity (Hodgkinson et al. 2000) is desired. Serial bideposition, however, is not limited to producing columns normal to the surface. The method can be altered to produce chiral STFs, slanted CTFs, and virtually any other shape by varying the series of rotations about the z-axis with angles other than 180o. Simultaneous bideposition, using two vapor sources, has been discussed extensively by Kranenburg and Lodder (1994). Their work is comprised of both experimental studies as well as computer simulations. They discuss using two sources with identical material to control morphology, as well as two sources with different materials to control local chemical composition. It may be advantageous in some instances to cover the STF with a final capping layer of material. This has been studied by Robbie and Brett (1997), with emphasis on avoiding stress fractures and preventing the void region of the film from being filled with material. They describe a method in which the angle of incidence relative to the film normal is decreased exponentially with time in order accomplish both objectives. The crystal structure of the material composing the columns is another property which can be important in some applications, catalysis for instance. Suzuki et al. (2001) have shown that it is possible, in at least one case (TiO2), to anneal STFs after deposition and still maintain the original STF structure. X-ray diffraction revealed that the material within the STF, originally showing no diffraction peaks, was converted by the annealing process to the single anatase phase of TiO2.
The modeling of STF growth is currently in its infancy with much of the work on CTFs. As yet, the ability to enhance the design of STFs by simulation has been limited (Lakhtakia and Messier 2004; Kaminska et al. 2004). Once a solid framework for handling CTFs in detail is developed, the application of the models to obtain a thorough understanding of STF growth should proceed swiftly. Several different approaches have been taken to understand the growth of CTFs; most seem to fall into two broad classes. The first type uses a simplified model to calculate the growth of the CTF (Meakin et al. 1986; Tait et al. 1993; Vick et al. 1999; Smy et al. 2000; Suzuki and Taga 2001; Kaminska et al. 2004). Typically, the model assumes: a nanoscale sized particle, often represented as squares, discs, or cubes restricted to discrete grid positions; a distribution of angles describing the trajectory of particles in the beam; some sort of sticking coefficient between the particle and film; and parameters characterizing limited diffusion or hopping on the film. Various calculational schemes are used to simulate the CTF, among them are: Monte Carlo, molecular dynamics, or a combination of methods. The advantages of such models are that: they are able to simulate the growth of a thin film in a reasonable amount of computation time, and they actually produce CTF and even STF structure. Some simulations are restricted to 2-D while others simulate a 3-D film. However, the models are a crude representation of physical reality and do not give specific information which would be helpful in engineering particular nanowire morphologies for particular materials. The models have been used to calculate % as a function of %v with moderate success (Meakin et al. 1986; Tait et al. 1993). The porosity of the film has also been characterised using these methods. The other type of model works at the opposite extreme by simulating the growth of the thin film on the atomistic scale with atom by atom addition to the film (Kranenburg and Lodder 1994; Dong et al. 1996). Several simulations have been done using a Leonard-Jones potential and molecular dynamics calculation to simulate the growth. This type of calculation is extremely, computationally intensive. To make the calculations tractable, the simulations are often done in only two dimensions. Furthermore, due to long calculation times, the thickness of the film which can be grown in this type of calculation is very limited.
Although crude channels and column like structures begin to appear in these simulations, the size of the film simulated is too small to show the development of a true CTF. The calculations have been used to estimate % for various situations as well as the porosity of the film. Though this type of calculation may be more physically realistic, the models simulate a generic film with no real insight into engineering particular characteristics in a real film. Furthermore, the physical realities of fabricating a film are often not accounted for, such as degree of beam collimation, and residual gas pressure. Given the impractical requirements of performing an atomistic type simulation of a real CTF over the vast range of length and time scales involved in growing a STF, it is almost certain that an understanding of STF growth will be obtained using a model which is a hybrid of atomistic and macroscopic models. This approach has been used with some success in other areas (Huang et al. 1998; Rahman et al. 2004; Shenoy 2004).
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