Online proceedings - EDA Publishing Association

however, a rotation for coincidence by self-alignment will
occur as shown in Fig. 1(a), and the rotation has the potential to
realize a uni-directional self-alignment if a special binding
pattern is employed as shown in Fig. 1(b). This implies that
two-dimensional asymmetric patterns are useful to aligning
micro-parts to a determined direction on substrate.
11-13
May 2011, Aix-en-Provence, France
surface-energy model for the self-alignment of flat silicon parts
[4] can thus be applied and the total interfacial energy E 1 before
self-alignment can be approximated by Equation (1):
E
= γ S + P
(1)
1 Lub , Water
γ
SAM , Water
Ⅲ. ANALYZING SELF-ALIGNMENT USING OVERLAP RATIO
To accomplish a high alignment yield, a suitable binding
pattern must be a global energy minimum (with maximum
overlap), while other (local) energy minima (low energy
barrier) corresponding to an unsuitable pattern design must be
avoided.
However, the overlap ratio, as defined in Fig. 2, which is the
ratio of the overlap area to the total area of the binding site, is
maximized in the fully aligned orientation, and gradually
declines toward the energy barrier. The overlap ratio is
therefore very useful to find out suitable patterns for
self-alignment. In this case, two important parameters, the
energy barrier and the angular span of the designed shape, must
be kept as small as possible to ensure a highly efficient
uni-directional alignment. Since direction-specific and high
precision self-alignment depends on adhesion force, overlap
ratio and correct pattern design predicted by the surface energy
model, the aforementioned parameters should be carefully
analyzed by simulation with the surface energy model.
where γ Lub,Water is the interfacial energy between lubricant
adhesive and water, γ SAM,Water is the interfacial energy between
SAMs and water, S is the binding area on substrate, and P is
the binding area on micro-part. Supposing S = P in present
case, the total interfacial energy E 2 after self-alignment can then
be described by the following Equation (2):
E2
= γ
γ
E
Lub,
Water
Lub,
Overlap
SAMLub
1
( AS ) γ ( − )
Overlap
+−
SAM , Water
AP
Overlap
×+
A
(2)
−−+=
γγγ
(
, SAM Lub , Water SAM , Water
) A Overlap
where γ Lub,SAM is the interfacial energy between lubricant
adhesive and SAMs, and A overlap is the overlap area as defined in
Fig. 2. If using Δ E to express the interfacial energy change as
the following Equation (3),
Δ
( γ Lub , SAM
− γ Lub , Water
− γ SAM Water
) A Overlap
E =
,
(3)
the total interfacial energy E 2 after self-alignment can be written
as
= 12
+ ΔEEE (4)
When an adhesive droplet sits on a substrate surface with a
contact angle α, Young’s equation gives the following
relationship:
Fig. 2. Schematic illustration of the overlap ratio, which is defined as the ratio
of the overlap area to the total area of the binding site.
A. Surface energy model
The interfacial energy minimization gives rise to the
attraction of the micro-parts to the binding sites. As shown in
Fig. 3, if the thickness of the adhesive droplet is thin enough
that two dimensional approximation is valid and the sidewall
interfacial energy of the adhesive is negligible, the
surface-energy model for the self-alignment of flat silicon
γ Lub,Water
α
γ SAM,Water
Lub
γ Lub,SAM
SAM
Au
Fig. 3. Schematic figure of the contact angle between the lubricant and the
surface modified by SAMs in water.
γ
,
γ cosα
+ γ
= (5)
SAM Water Lub,
Water
Lub,
SAM
The above Equation (5) can thus be rewritten as
γ
[ cos( α ) 1]
Lub , SAM
− γ
Lub,
Water
− γ
SAM , Water
−= γ
Lub,
Water
+
where ∀α
∈ ( 0 , 180 )°° . Equation (6) means that ΔE is less
than zero for any adhesive, micro-part surface and environment
medium.
B. Overlap ratio
From the above Equations (3) and (6), it can be noted that
the interfacial energy has a minimum value when the
micro-part is exactly aligned with the binding site (receptor
site). Since E 1 is a constant, theΔE thus appears to be linearly
proportional to the overlap area A overlap as:
[ cos( α ) ] A Overlap
Lub , Water
+
(6)
ΔE ∝ −γ 1
(7)
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