**5. Lower and upper limit of achievable feature size**

So far, only structures with feature size of about 100 nm were described. Laser-assisted processes for much smaller and larger feature sizes will be discussed in this section, with a focus on factors that limit the achievable feature sizes of the techniques.

#### **5.1 Resolution limit**

In LADI, planarization, and via-hole filling processes, squeezing liquid metals or semiconductors into small trenches or via holes will be ultimately limited by the pulling pressure due to surface tension. Fig. 15 shows schematic drawing illustrating how much pressure is needed to fill trenches or via holes. For all cases, the pulling pressure is proportional to the surface tension constant and inversely proportional to feature size. Therefore, there is no fundamental resolution limit provided the applied pressure is high enough. In practice, the liquid metal and silicon generally have surface tension on the order of 1 N/m (for water, it is 0.076 N/m), which leads to a pressure of 200 bar to fill in 100 nm-wide trenches, or 2000 bar for 10 nm-wide trenches. This pressure is considerably higher

solidification across the gap should be uniform (since the melting time is order 100 ns that is much longer than pulse duration). Nano-tips are formed at the broken bridge necks before or during solidification due to surface tension and volume shrinkage, or after the two wafers

Fig. 14. Schematic of the physical mechanism behind the nano-tip formation. (a) Build-up of

condensation. (c) Nano-bridge formation due to attractive electrostatic force. (d) Bridging of approaching peaks and charge neutralization. (e) Break of bridges upon solidification or

So far, only structures with feature size of about 100 nm were described. Laser-assisted processes for much smaller and larger feature sizes will be discussed in this section, with a

In LADI, planarization, and via-hole filling processes, squeezing liquid metals or semiconductors into small trenches or via holes will be ultimately limited by the pulling pressure due to surface tension. Fig. 15 shows schematic drawing illustrating how much pressure is needed to fill trenches or via holes. For all cases, the pulling pressure is proportional to the surface tension constant and inversely proportional to feature size. Therefore, there is no fundamental resolution limit provided the applied pressure is high enough. In practice, the liquid metal and silicon generally have surface tension on the order of 1 N/m (for water, it is 0.076 N/m), which leads to a pressure of 200 bar to fill in 100 nm-wide trenches, or 2000 bar for 10 nm-wide trenches. This pressure is considerably higher

free charges on the two wafers. (b) Metal transfer to lower wafer by evaporation-

**5. Lower and upper limit of achievable feature size** 

focus on factors that limit the achievable feature sizes of the techniques.

were separated.

after separation.

**5.1 Resolution limit** 

than that used for regular thermal nanoimprint lithography (order of 10 bar). However, considerably lower applied pressure would be sufficient for patterning metals and silicon if: (1) the molten metal partly wets the SiO2 substrate; and/or (2) the mold consists of sparse protruded patterns to create sparse recessed metal features (such as a periodic hole array having diameter ~100 nm and pitch 500–600 nm in Au for extraordinary optical transmission devices (Lesuffleur 2008)), because the effective local pressure at the protruded mold features is significantly higher than the applied pressure (applied force divided by wafer surface area).

Fig. 15. Schematic drawing showing the calculation of minimum pressure to squeeze a liquid into (a) a trench, (b) a trench with liquid partly squeezed against the bottom, and (c) a via hole. The pressures are calculated assuming 90o contact angle and no wetting/adhesion.

#### **5.2 Upper limit of achievable feature size**

The maximum feature size that can be patterned depends on how far the molten metal can flow before re-solidification. For a rough estimation, the dynamic flowing process is modeled as in Fig. 16. It is assumed that the grating structure has a period 2L and a trench depth h0; and the entire layer is melted at t=0 and re-solidification takes place simultaneously throughout the film thickness at time t=. The mold will travel a distance of h0/2 and the residual molten layer thickness will decrease to h0/2 when the trench is fully filled. Since L is large, the effect of surface tension can be ignored and thus the internal pressure at x=L/2 is zero. There are three forces acting on the liquid: the pressing force from the mold, the viscous force, and the inertial force.

We first consider only the effect of viscous force by assuming that a steady flow develops momentarily at t=0 (i.e. ignore inertial force). Then the maximum grating half pitch L1 that can be patterned (trench fully filled) before the liquid metal solidifies is given by (Heyderman 2000, Cui 2006):

$$L\_1 = h \sqrt{\frac{P\tau}{\mu}} \tag{11}$$

where *h* is the metal film thickness (200 nm), P is the applied pressure (order 100 bar), is the viscosity, and is the melting duration (~ 200 ns) that depends on laser fluence. The

Ultrafast Fabrication of Metal Nanostructures Using Pulsed Laser Melting 135

Thus even within a very short melting time of order 100 ns, the calculated L2 values are

The critical length can also be estimated by experiment. For example, Fig. 17a shows a backside-irradiated 200 nm-thick Ni film by a single laser pulse with fluence 0.60 J/cm2 that partly blew the film off the substrate. The surface tension was the force driving the flow, and the driving pressure can be estimated by 2/h (h is the film thickness, and the factor 2 accounts for the top and bottom surface/interface), which was 180 bar. The SEM image indicates that Ni flowed about 4 m before the film re-solidified. For LADI, we achieved 17 m isolated Cu mesas with 100 nm height (Fig. 17b), but it was found that a pattern of several tens of micrometer size required multiple pulses. Therefore, the maximum patternable feature size using one laser pulse lies on the lower tens of m, close to the

Fig. 17. (a) A 200 nm-thick Ni film irradiated from backside by a single laser pulse with a fluence of 0.60 J/cm2 that partly blew the film off the substrate. The liquid traveled about 4 m before it froze. (b) AFM image of isolated Cu mesas patterned by LADI at laser fluence of 0.45 J /cm2. The mesas have a length on each side of 17 μm and a height of 100 nm.

(a) (b)

In this chapter, five nanofabrication processes using pulsed excimer laser were described. These methods share the common advantage of being orders faster than most other fabrication techniques. They are also very suitable to patterning metals, which are more difficult to process than semiconductors by conventional lithographies and

The first was laser-assisted direct imprinting, which produced 200 nm-period Cu, Ni and Al gratings over about 1 mm2 area within ~100 ns. LADI of W failed due to its high thermal stress. The second was wafer planarization using a flat and smooth "mold". With this technique, Cu surface was planarized by laser melting under pressure, which also squeezed the molten film to fill completely voids under the film. Cu conducting lines embedded in a dielectric matrix were created by an additional etching step. Third, a similar process could also fill 100 nm-wide and 500 nm-deep via-holes with Si and Cu. Fourth, sub-100 nm diameter Cr dots were melt-transferred to the receiving substrate using a laser-induced

order 20 µm for applied pressure of 100 bar.

theoretical prediction.

4m

**6. Conclusion** 

etching.

viscosity of molten Au and Cu is around 4 cp (only 5 that of wafer (Yaws 1998)), leading to L1~ 5 m. To pattern isolated metal mesas, the liquid flows from four sides to fill a square-shaped hole in the mold, so the maximum patternable mesa size should be roughly doubled to ~10 m, which qualitatively agrees with the experiment (17 m). Moreover, it is interesting to see how far molten SiO2 can flow under similar conditions. For example, its viscosity at 2200 K is 8107 cp (a very tacky "liquid"), 7 orders higher than that of Au and Cu, leading to a calculated L1 of only ~1 nm if assuming a top 200 nm SiO2 layer is molten. This explains why the quartz mold can be used to pattern a metal at temperature slightly higher than its melting point, though the mold could not be used repeatedly for >>10 times.

Fig. 16. Dynamics of molten metal flowing into trenches during LADI. Assume that grating line-width and trench-width are both equal to L, and trench depth and molten layer thickness are both equal to h0.

Next, to estimate the inertial force which decides how fast the steady flow develops, it is assumed that the liquid metal is inviscid (μ = 0) for simplicity. The applied pressure is to accelerate the flow along the x-direction with acceleration given by (note that the effective pressure is doubled for a grating with equal line and trench width, and z is the direction perpendicular to the paper):

$$a = \frac{F}{m} = \frac{2P \times hz}{\rho \times hz \text{(L/2)}} = \frac{4P}{\rho L} \tag{12}$$

The velocity is then u=at at time t, and the flow-rate Q=uh=ath (ignoring the z-dimension). On the other hand, the volume of the liquid changes at a rate

$$Q = -\frac{L}{2}\frac{dh}{dt}\tag{13}$$

Therefore, solving the equation

$$\frac{4P}{\rho L}t\text{h} = -\frac{L}{2}\frac{dh}{dt}\tag{14}$$

gives (h=h0, h0/2 at t=0, )

$$L\_2 = 2\sqrt{\frac{P}{\rho \ln 2}} \tau \sim \sqrt{\frac{P}{\rho}} \tau \tag{15}$$

Thus even within a very short melting time of order 100 ns, the calculated L2 values are order 20 µm for applied pressure of 100 bar.

The critical length can also be estimated by experiment. For example, Fig. 17a shows a backside-irradiated 200 nm-thick Ni film by a single laser pulse with fluence 0.60 J/cm2 that partly blew the film off the substrate. The surface tension was the force driving the flow, and the driving pressure can be estimated by 2/h (h is the film thickness, and the factor 2 accounts for the top and bottom surface/interface), which was 180 bar. The SEM image indicates that Ni flowed about 4 m before the film re-solidified. For LADI, we achieved 17 m isolated Cu mesas with 100 nm height (Fig. 17b), but it was found that a pattern of several tens of micrometer size required multiple pulses. Therefore, the maximum patternable feature size using one laser pulse lies on the lower tens of m, close to the theoretical prediction.

Fig. 17. (a) A 200 nm-thick Ni film irradiated from backside by a single laser pulse with a fluence of 0.60 J/cm2 that partly blew the film off the substrate. The liquid traveled about 4 m before it froze. (b) AFM image of isolated Cu mesas patterned by LADI at laser fluence of 0.45 J /cm2. The mesas have a length on each side of 17 μm and a height of 100 nm.
