Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

Подождите немного. Документ загружается.

138 Thin ﬁlm growth

land on the surface or stick to any particle on the surface if the two particles

are within the nearest-neighbor distance. It is easy to see that after deposition

the differences between the local surface heights around the newly added

particle should be zero or unity in magnitude. This characteristic feature is

dramatically different from the non-ballistic sticking model just discussed

above and is similar to the so-called ‘restricted solid-on-solid growth’ model

(Kim and Kosterlitz, 1989). With this non-trivial model, the aggregations of

particles on seed arrays form ballistic fan structures as shown in Fig. 6.10. We

denoted the simulation time F as the number of total particles sent into the

simulation system. The snapshots of the structures were taken at a constant

(a)

(c)

(b)

(d)

j = 66°

j 66°

F = 1.8 ¥ 10

F = 3.6 ¥ 10

6.10 Top-view and cross-sectional snapshots of fan structures in the

ballistic sticking model with normal incident ﬂux. (a) and (b) are

images of the fans on the small seeds taken at two simulation times.

parameter is set to K = 100.

ThinFilm-Zexian-06.indd 138 7/1/11 9:41:18 AM



139Silicon nanostructured ﬁlms grown on templated surfaces

frequency with simulation time F = 9 × 10

particles. The simulated fan

structures resemble the experimental results in that the fan-out angle j is

measured to be 66∞ in the simulations and the experiments. They all have a

dome-shaped top with rather straight outlines on the sides.

We studied the dynamic growth of the width R of the simulated ballistic

fans in terms of the power law behavior, R = kt

, of the expansion of the

fans in the lateral direction. The average width R of the fans was measured

from the top-view images as shown in Fig. 6.10(a) and (c) plotted in Fig.

6.11. The exponent p in the power law format denes the geometrical shape

of the ballistic fans. Specically, a cylindrical shape has an exponent p = 0;

a hyperbolic shape has an exponent p = ½; and a cone shape would have

p = 1. In obtaining the p value more quantitatively from the simulations, we

believe that the initial size of the cylindrical seeds has a non-trivial effect.

We suppose that the size of structure is identical to the size of the seeds at

the beginning of the growth. Therefore, the width R is a function of ‘adjusted

time’ t instead of the real time t¢, as R = kt

and t = t¢ + t

. Clearly, t

is an

imaginary time that satises the boundary condition: R

= kt

, where R

the initial size of the seeds. After the adjustment of the time, it provides

the possibility of comparing the simulated results with our experimental

observations and with previous analytical and simulation results obtained

using ballistic aggregation with a point seed. One can see from the plots

in Fig. 6.11 that the growth of the ballistic fans has a power law behavior

with the exponent p ≈ 1.0. The cone-shape geometry of the fans observed

Small seeds

Big seeds

p = 0.99

p = 1.01

5 ¥ 1 0

Adjusted simulation time t

Width of fans R

500

250

100

6.11 Growth of the ballistic fans on small and big seeds in Monte

Carlo simulations with normal incident ﬂux. The ﬁtting of the curves

demonstrates that the growth is linear with the exponent p ª 1.

ThinFilm-Zexian-06.indd 139 7/1/11 9:41:18 AM



140 Thin ﬁlm growth

in our experiment, as shown in Fig. 6.4, is consistent with this prediction in

simulations. This linear behavior is, within error, independent of the strength

of diffusion, and the size of seeds. Thus, we conclude that the linear growth

(p ≈ 1) of the width of the ballistic fans may be a universal characteristic of

ballistic aggregation, even when diffusion is allowed.

6.4 Fan-out growth on templated surfaces with

oblique angle incident ﬂux

We discussed the ballistic sticking model to describe the fan-out growth on

templated surface with normal incident ux in the previous section. Now we

move on to the oblique incident case in this section. Intuitively, the morphology

of structures deposited on templated surfaces should be different for the latter

case due to the global shadowing effect. Nonetheless, the ballistic sticking

and surface diffusion still remains as the main mechanisms that control the

growth dynamics of the nanostructured lms. The question we may ask is to

what extent global shadowing can affect the fan-out growth on the non-at

surface. Here, we will present our answer to this important question from

the experimental and modeling results.

6.4.1 Experimental demonstration of fan-out growth with

oblique angle incident ﬂux

In oblique angle deposition of Si lms, the substrates with W pillars were

placed at a position such that their normal vectors were turned 5∞ from

the horizontal plane. Thus, the incident angle of the ux q is equal to 85∞

with respect to this surface normal vector. The incident ux was aligned

to the axis of the square lattice and the shadowing effect only comes from

the nearest neighbors. The direction of the incident ux on the plane of

the substrate is assigned to be the x-axis and the perpendicular direction is

assigned to be the y-axis, as shown in Fig. 6.12. We observed experimentally

Seeds

Flux

85°

6.12 The alignment of the ﬂux with respect to the geometry of the

seed’s lattice.

ThinFilm-Zexian-06.indd 140 7/1/11 9:41:18 AM



141Silicon nanostructured ﬁlms grown on templated surfaces

that the fan-out growth occurs on seeds in oblique angle deposition without

substrate rotation (Ye et al., 2004; Lu et al., 2005). In the ‘fan-out’ growth,

the size of the nanostructures overgrows along the direction perpendicular

to the incident deposition ux which is along the y-axis (or y-direction) as

labeled in Fig. 6.12. The net result is that the size of the nanostructured lms

cannot be controlled as they grow. If the deposition time is long enough,

the nanostructured lms grown on the seeds will touch and merge with their

neighbors from the side along the direction of the y-axis. Thus individual

nanostructures cannot be distinguished along this side. Due to the shadowing

effect, the gap between the seeds along the x-direction is still maintained

even with the merging occurring in the y-direction.

Figure 6.13 elucidates this phenomenon by the top-view and the cross-

sectional SeM images of the Si deposition on the W-pillar seeds arranged

in a square lattice. Si was deposited on the templated substrate with an 85∞

incidence angle. The normal thickness of the growth was 2000 nm measured

by the QCM. The samples were tilted to 15∞ when taking the cross-sectional

images. The morphology of the lms grown on the small size and the large

size W pillars is similar to each other. The top surface of the structure is

rough and has a rectangular shape with irregular sides. The structures on

Flux

500nm

RPI SEI 5.0kV X30.000 100nm WD 15.3mm RPI SEI 5.0kV X30.000 100nm WD 14.7mm

(a)

(c)

(b)

(d)

6.13 Fan-out growth of Si on W pillars with 85° incident ﬂux. (a)

Top-view and (b) tilted cross-sectional SEM images of Si ﬁlm grown

on small W pillars; ﬁlm grown on large-sized W pillars are shown

in (c) and (d) for the top-view and tilted cross-sectional images,

respectively.

ThinFilm-Zexian-06.indd 141 7/1/11 9:41:19 AM



142 Thin ﬁlm growth

both of the lattices were inclined toward the source at an angle b of 53 ± 1∞

measured from the normal of the substrate. The size of the structures along

the x-direction remained roughly constant at 340.3 ± 6.0 nm for the lms

grown on the square lattice seeds. From the images shown in Fig. 6.13,

it is clear that the top-end surface of the structures is smoother than the

surface on the sides. The side surfaces in Fig. 6.13(a) and (c) contain small

bers growing toward the source and bumpy top surfaces can be seen in

Fig. 6.13(b) and (d). This suggests that the structure may be constructed by

the bundling of those small Si bers. The fan-out growth of Si lms before

merging is shown in Fig. 6.14(a) and (b) for the deposition on small size

seeds and large size seeds, respectively. The normal thickness of the lms

was 800 nm as measured by the QCM. The fan-out angles j on the seeds

are measured to be 63.6 ± 0.6∞ and are the same for the fans on both the

small and the big seeds.

6.4.2 MC simulations of fan-out growth with oblique

angle incident ﬂux

As we discussed above, a particle will likely be trapped by the already

deposited particles through inter-atomic interactions or direct bonding. The

particle will become part of the surface at rst contact with the surface. In

the oblique angle deposition with ballistic sticking mechanism, the global

shadowing effect exists and comes into effect at every deposition event.

The strength of diffusion is controlled by the pre-set number K. Figure 6.15

shows the top-view and the cross-sectional images of the structures deposited

on the same templates as depicted in Fig. 6.8. The large square pictures

are the top-view images while the small rectangular pictures are the cross-

sectional images. In the top-view images, we can see the fan structures start

Flux

RPI SEI 5.0kV X30.000 100nm WD 12.7mm RPI SEI 5.0kV X30.000 100nm WD 12.7mm

(a) (b)

6.14 Fan-out growth of Si on (a) small-sized W pillars and (b) large-

sized W pillars. (Adapted from Ye and Lu, 2007b, reprinted with

permission.)

ThinFilm-Zexian-06.indd 142 7/1/11 9:41:19 AM



143Silicon nanostructured ﬁlms grown on templated surfaces

to grow even in an early stage of the growth, when the number of deposited

particles reaches F = 4 × 10

. The size of the simulation lattice is 1024 ×

1024 × 1024. The incident angle of the particles is 85∞ in this simulation.

The diffusion parameter for this set of simulations is set to K = 100, which

means that there are 100 attempts at diffusion within a cycle of deposition.

When the deposition time is sufciently long, the structures connect to each

other from the side perpendicular to the direction of ux. From the cross-

sectional image, the top end surface declined to an angle of about 8∞ from

horizontal. This result is similar to what we observed in experiments. A

series of simulations were run with different K values.

The growth of the width R of the ballistic fans was plotted as a function

of the adjusted simulation time t following the method described above, as

shown in Fig. 6.16. The tting of the plots in the format of power law growth

yields the growth exponent p ª 1 before the fans start merging with their

(a) F = 4 ¥ 10

(b) F = 2.4 ¥ 10

(d) F = 6.4 ¥ 10

6.15 Top-view and cross-sectional images of fan structures in MC

simulation with ballistic sticking model. The incident angle of ﬂux is

85°. The diffusion parameter is set to K = 100.

ThinFilm-Zexian-06.indd 143 7/1/11 9:41:19 AM



144 Thin ﬁlm growth

neighbors. Combined with the observations we found in the case of normal

deposition, we can conclude that the fan-like structure is a result of ballistic

sticking of particles. The ballistic sticking, or ‘self-shadowing effect’, has a

characteristic growth exponent p ª 1. We also found from the simulations

that the fan-out angles decrease when diffusion increases. In the oblique

angle deposition, the tilt angle of the structures increases as K increases.

We measured the fan-out angle j and the tilted angle b of the simulated

structures. Compared to our experimental results, we can deduce that K =

100 ts the Si ballistic fan’s fan-out angle j and tilted angle b, which are

65.0 ± 4.0∞ and 51.7 ± 0.3∞ respectively, in the simulated structures.

6.5 Control of fan-out growth with substrate

rotations

As previous studies revealed, it is possible to create complicated nanostructured

thin lms by oblique angle deposition with delicate control of substrate

rotation (Robbie et al., 1995a, 1996, 1998; Lakhtakia and Weiglhofer, 1995;

Robbie and Brett, 1997; Kennedy et al., 2002; Zhao et al., 2002b). There

are two types of nanostructures whose optical, mechanical, and electrical

properties we are interested in: nanosprings and slanted nanorods. Isolated

nanostructured thin lms such as slanted nanorods and nanosprings could

provide an ideal platform to study mechanical, electrical, thermal, and

optical properties of materials on a nanometer scale. Therefore, the ability

to uniformly deposit individual nanostructured thin lms is of great practical

value. These two structures are relatively difcult to fabricate by traditional

300

250

200

150

100

Width R (a.u.)

p = 1.0 p = 0.99

p = 0.98

K = 50

K = 100

K = 150

2¥10

4¥10

6¥10

8¥10

Adjusted simulation time t

6.16 The linear growth of ballistic fans in oblique incident ﬂux.

(Source: Ye and Lu, 2007b, reprinted with permission.)

ThinFilm-Zexian-06.indd 144 7/1/11 9:41:19 AM



145Silicon nanostructured ﬁlms grown on templated surfaces

lithographic methods, but using oblique angle deposition, we may achieve

the required structures relatively more easily.

The growth of uniform slanted nanorod lms on an existing array of seeds

is challenging but achievable. As shown in the previous sections, the fan-out

growth is intrinsic to the nature of thin lm growth with strong self-shadowing

effect. Therefore, fundamental research in controlling the fan-out growth has

been the rst priority in the development of this technique. One strategy to

fabricate uniform nanostructured thin lms is based on diminishing the fan-

out growth by substrate rotation. During substrate rotation, some part of the

growth front will be interrupted. The growth on that spot will start again at

a later time or be terminated entirely, depending on the relative local height.

Overall, each part of the growing surface will receive ux for a short period,

effectively smoothing the growth front and resulting in uniform growth with

no fan-out features even for a very long deposition time.

The geometric parameters of the structure, such as the tilt angle b with

respective to the substrate normal, diameter R and separation D of the

structures, can be tailored by changing the vapor incident angle q, thus,

changing their physical properties. In general, the column tilt angle b is less

than the vapor incident angle q, and follows the empirical tangent rule or

cosine rule discussed above. However, the variation of the incident angle q

simultaneously changes the three geometric parameters (namely, b, R, and

D), which causes some difculty in controlling the geometry and the physical

properties of the nanostructured lms by simply changing the incident angle

q in oblique angle deposition. Therefore, it is desirable to have other methods

to tailor the structures other than the variation of q. Fortunately, there are

some substrate rotation methods that can deposit nanostructured thin lms

with variable geometric parameters at a xed incident ux angle q in this

research area.

In experiments, it is possible to control the rotation of the substrate at

different rotation speeds, or change the direction or the rotation in every

revolution of the substrate movement. Thus the substrate can be rotated in

a non-uniform manner. By this means, the surface grows faster in some

directions than others. Thus, the structure of the lm will incline toward this

direction. On the other hand, since the substrate is rotated, the growth front

can still be interrupted and re-installed during growth which can potentially

limit the fan-out growth. The shadowing direction is changed from time to

time as well. We expect that the fan-out growth would be reduced by the

rotation of substrate.

In this section, three substrate rotation methods are reviewed and discussed:

‘two-phase’ rotation (Ye et al., 2004), ‘swing’ rotation (Ye et al., 2005), and

‘PhiSweep’ technique (Jensen and Brett, 2005). In the ‘two-phase’ rotation

method, one continuously rotates the substrate during deposition with two

different speeds to nish one complete revolution. First, the substrate is

ThinFilm-Zexian-06.indd 145 7/1/11 9:41:19 AM



146 Thin ﬁlm growth

rotated at a slower speed w

to an angle of f

(< 2p) in the surface plane of

the substrate, and then the speed will be switched immediately to a faster

in the rest of the angle f

= 2p – f

of a complete revolution (Ye et al.,

2004). The direction of rotation in these two parts is the same in the two-

phase rotation technique. In swing rotation, the substrate is rotated to an

angle f(< 2p) in the plane of the substrate. The substrate is then rotated back

to the initial position to cover one cycle of the motion (Ye et al., 2005). A

similar approach of non-uniform substrate swinging was published recently

by Jensen and Brett (2005). In their method, the substrate is rotated quickly

to an angle and stays at that position for a period of time, then the substrate

is rotated back to the original position and stays for an equal period; i.e. the

substrate is rotated to the other side with the same angle and stays for the

same period before it returns. This method is given the name ‘PhiSweep’

in their paper (Jensen and Brett, 2005).

The fan-out growth on seeds is greatly reduced by the aforementioned

substrate rotation techniques as shown in Fig. 6.17. For example, the Si

nanorods can be grown to several micrometers without touching the neighbors

RPI SEI 5.0kV X30.000 100nm WD 15.8mm

RPI SEI 5.0kV X15.000 1µm WD 15.3mm

Two-phase rotation

PhiSweep rotation

(a)

(c)

(b)

(d)

1 µm 500 nm

6.17 Top-view and cross-sectional SEM images of uniform Si

nanostructured ﬁlms grown on templated surfaces by ‘two-phase’

and ‘PhiSweep’ substrate rotation techniques. (Adapted from Gish et

al., 2006, reprinted with permission.)

ThinFilm-Zexian-06.indd 146 7/1/11 9:41:20 AM



147Silicon nanostructured ﬁlms grown on templated surfaces

from the side by the two-phase technique, as shown in Fig. 6.17(a) and (b).

Uniform nanorods without fan-out growth were also demonstrated using

the ‘PhiSweep’ substrate rotation method (Jensen and Brett, 2005). A set

of selected SeM top-view and cross-sectional images of Si nanostructured

lm grown by the ‘PhiSweep’ technique are reproduced in Fig. 6.17(c) and

(d) from the paper by Gish et al. (2006). Uniform nanostructured Si lms

on small and big seeds grown by ‘swing’ rotation are shown in Fig. 6.18.

The swing angle was set at 90∞ and the incident angle of ux was 85∞ in

this experiment.

We set up the Monte Carlo simulations to study the mechanism of reducing

the fan-out growth based on the swing rotation in oblique angle deposition.

Figure 6.19 shows the top-view and cross-sectional images of the Monte

Carlo simulation at two different stages with swing rotation. The size of the

simulation system is 1024 × 1024 × 1024. The swing angle in this simulation

was xed at f = 90∞. The rotation speed in this simulation was dened by the

number of particles deposited in one step of substrate rotation. In our code,

RPI SEI 20.0kV X30.000 100nm WD 15.5mm

RPI SEI 5.0kV X30.000 100nm WD 14.7mm

RPI SEI 20.0kV X30.000 100nm WD 15.5mm

Small seeds

Big seeds

(a)

(c)

(b)

(d)

6.18 Top-view and cross-sectional SEM images of uniform Si

nanostructured ﬁlms grown on small and big seeds by ‘swing’

substrate rotation.

ThinFilm-Zexian-06.indd 147 7/1/11 9:41:20 AM

