**2. Fundamentals of laser-matter interaction**

Fig. 1 illustrates schematically the laser-matter interaction at a wide range of power and/or energy density. The pulsed laser we used at the Nanostructure Laboratory, Princeton University, is a 308 nm XeCl excimer laser with pulse duration of 20 ns (FWHM), maximum output energy of 200 mJ per pulse, and power of 160 MW/cm2 for a beam size of (2.5 mm)2 if assuming a rectangular temporal pulse shape. With this laser, a power density of order of 10 MW/cm2 is needed to melt a 200 nm-thick thin metal or semiconductor film on an insulator, whereas order 100 MW/cm2 is necessary for substantial vaporization and/or plasma formation. In the following sections, three topics will be covered in some detail: light absorption by metals and semiconductors, transient heat transfer and temperature distribution, and vaporization, plasma formation and plasma propagation.

Fig. 1. Schematic laser-material interaction. (a) Absorption and heating. (b) Melting and flowing. (c) Vaporization. (d) Plasma formation in front of the target. Under certain conditions the plasma can detach from the target and propagate toward the laser beam.

#### **2.1 Absorption of laser light**

Laser light must first be absorbed in order to cause any lasting effect on a material. Electromagnetic radiation with a wavelength between UV and IR interacts exclusively with electrons, as atoms are too heavy to respond significantly to the high frequencies (>1013 Hz) involved. Therefore, the optical properties of matter are determined by the energy states of its valence electrons (bound or free). Generally, bound electrons can only weakly respond to the external electromagnetic wave and merely affect its phase velocity. Free electrons are able to be accelerated, i.e., to extract energy from the field. However, since the external field is periodically changing, the oscillating electrons re-radiate their kinetic energy, unless they undergo frequent collisions with the atoms – in this case energy is transmitted to the lattice (absorbed) and the external field is weakened. Re-radiation of the energy is the cause of reflection.

For absorbing media the refractive index is a complex number with the form n=n+ik. The reflectivity at normal incidence is (n=1 for air or vacuum)

$$R = \frac{\left(n - 1\right)^2 + k^2}{\left(n + 1\right)^2 + k^2} \tag{1}$$

The emissivity, or the fraction of incident radiation absorbed, is then

$$
\varepsilon \equiv \mathbf{1} - \mathbf{R} = \frac{4n}{\left(n+1\right)^2 + k^2} \tag{2}
$$

The absorption coefficient is defined as

114 Recent Advances in Nanofabrication Techniques and Applications

within ~100 ns. It can also anneal the patterned metallic nanostructures. More importantly, the current method is not limited to ductile metals, and hard metals like nickel can be

Various applications have been developed, and here we will present laser assisted direct imprint, wafer planarization, via-hole filling, transfer printing, and nano-tip formation. Other important applications using pulsed laser nanofabrication, such as self-perfection by liquefaction (SPEL) that removes nanostructure fabrication defects (notably line edge roughness) (Chou 2008, Xia 2010), and nano-channel fabrication using sealing by laser-

Fig. 1 illustrates schematically the laser-matter interaction at a wide range of power and/or energy density. The pulsed laser we used at the Nanostructure Laboratory, Princeton University, is a 308 nm XeCl excimer laser with pulse duration of 20 ns (FWHM), maximum output energy of 200 mJ per pulse, and power of 160 MW/cm2 for a beam size of (2.5 mm)2 if assuming a rectangular temporal pulse shape. With this laser, a power density of order of 10 MW/cm2 is needed to melt a 200 nm-thick thin metal or semiconductor film on an insulator, whereas order 100 MW/cm2 is necessary for substantial vaporization and/or plasma formation. In the following sections, three topics will be covered in some detail: light absorption by metals and semiconductors, transient heat transfer and temperature

distribution, and vaporization, plasma formation and plasma propagation.

Fig. 1. Schematic laser-material interaction. (a) Absorption and heating. (b) Melting and flowing. (c) Vaporization. (d) Plasma formation in front of the target. Under certain conditions the plasma can detach from the target and propagate toward the laser beam.

(a) (b) (c) (d)

Laser light must first be absorbed in order to cause any lasting effect on a material. Electromagnetic radiation with a wavelength between UV and IR interacts exclusively with electrons, as atoms are too heavy to respond significantly to the high frequencies (>1013 Hz) involved. Therefore, the optical properties of matter are determined by the energy states of its valence electrons (bound or free). Generally, bound electrons can only weakly respond to the external electromagnetic wave and merely affect its phase velocity. Free electrons are able to be accelerated, i.e., to extract energy from the field. However, since the external field is periodically

structured readily.

melting (Xia 2008), will not be presented.

**2.1 Absorption of laser light** 

**2. Fundamentals of laser-matter interaction** 

$$\alpha = -\frac{1}{\text{I}} \frac{dl}{dz} = \frac{4\pi k}{\lambda} \tag{3}$$

where I is the intensity of the incident light (also termed irradiance, in W/cm2). The inverse of is referred as the absorption length. For normal incidence the power density (in W/cm3) deposited at depth z is

$$\Phi(z) = I(1 - R)\alpha e^{-\alpha \cdot z} \tag{4}$$

#### **2.1.1 Low light intensity and temperature regime**

Both n and k (thus ) are generally functions of wavelength and temperature. For a semiconductor such as silicon (see Fig. 2 (a)), the absorption coefficient increases with decreasing wavelength gradually near its indirect band-gap at 1.1 eV (1.13 µm), but increases rather abruptly near its direct band-gap at 3.4 eV (0.36 µm) because no phonons are involved for direct transition. At photon energies significantly exceeding Eg, the optical response of semiconductors tends towards that of metals.

Fig. 2 (b) depicts the light-coupling parameters for Al and Au. Metals, due to their large density of free electrons close to the Fermi level, have large absorption coefficients (corresponding to absorption lengths -1 around only 10 nm) over the whole spectrum. Their reflectivity is more difficult to determine than that of semiconductors. Generally, their reflectivity is high above a certain critical wavelength that is related to its electron plasma frequency p given by (4Ne2/me)N, where N is electron density and me is electron mass. Below the critical wavelength, which is in the UV or visible part of the spectrum, R decreases sharply. For Au and Cu, the plasma frequency is reduced (which causes their yellow color) by transition from d-band states.

#### **2.1.2 High light intensity and/or temperature regime**

At higher light intensities and/or higher temperatures, the optical properties can be modified by three mechanisms: lattice heating, free carrier generation (for semiconductors only) and excitation. At elevated temperatures, more phonons are present, leading to an increase of lattice-carrier collision. As a result, the reflectivity of most metals decreases with increasing temperature, and this effect makes metals susceptible to thermal runaway.

Ultrafast Fabrication of Metal Nanostructures Using Pulsed Laser Melting 117

Fig. 3. Schematic energy diagram of the electrons in a semiconductor under intense irradiation. The electron temperature Te is higher than the lattice temperature. The shaded

Auger 10-9s

At sufficiently high light intensity, the rate of energy gain by carriers exceeds the rate of energy loss to the lattice. The result is a splitting up of carrier and lattice temperatures (see Fig. 3), and the carriers behave collectively, i.e., according to the equations governing a plasma (but this plasma behavior is not to be confused with the generation of actual plasma shown in Fig. 1(d); the plasma here is just a large number of electrons inside the conduction band of the semiconductor). The plasma may be regarded as an independent system which absorbs light and exchanges energy with the lattice. As far as coupling is concerned, the effect of the plasma is ultimately to limit the rate of local energy deposition by increasing R at high carrier density such that p > , and by diffusing away the hot carriers from the absorbing surface to the material underneath, which effectively increases

a: band-to-band absorption b, c: free carrier absorption

 e-ph collisions 10-12s

Finally, Si and Ge become metallic (silicon's electrical conductivity is 30 times higher) upon

Heating in an irradiated sample is a consequence of the balance between the deposited energy, governed by optical parameters of the sample and characteristics of the laser pulse, and the heat diffusion, determined by thermal parameters and the pulse duration. Strictly speaking, as discussed in the previous section, the primary product of absorbed laser light is not heat but the carriers' excess energy. But for simplicity, and because the our laser pulse has a relatively long duration of 20 ns, it can be assumed that the overall energy relaxation time E is negligible compared to the pulse duration (E~10-13s for metals, ~10-12 10-9s for semiconductors). With this assumption, a simple estimate of the temperature rise is possible for two limiting cases in which the optical absorption depth is small compared with the thermal diffusion length during the pulse (i.e. -1<<2Dt.), or vice versa. However, for many practical cases, complex analytical or numerical evaluations must be performed. In particular, if phase transitions occur during the irradiation, only numerical solutions are

melting due to bandgap collapsing, leading to a strong increase in both and R.

area depicts electron plasma. (adapted from Poate 1982)

the heated volume.

0

a

h

b

c

 e-e collisions 10-14s


kTe

E

available.

**2.2 Heating and melting by laser** 

For semiconductors like silicon, a large number of free carriers can be generated not only by thermal excitation at high temperature and further facilitated by the band-gap narrowing, but also by photons at a rate of I/h (I is light intensity, is the absorption cross section) when h > Eg. Fig. 3 depicts the energy diagram of the electrons (holes have similar diagram) under intense irradiation such that the carrier generation rate exceeds that of carrier relaxation rate. Due to free carrier generation, the carrier density and thus the absorption coefficient of semiconductors increase strongly as a function of light intensity. The effect of free carriers on the optical properties is to reduce the real part and to increase the imaginary part of **n**. As a result, free carrier generation tends to decrease the reflectance for p < (now pN is a variable depending on light intensity, while is fixed). Only for carrier density N large enough that p > does the reflectance begin to increase with the light intensity towards unity by further increasing p. Such a rich variation of reflectivity on light intensity and time has been observed for crystalline Si irradiated by red 90 fs pulses (Shank 1983).

Fig. 2. Reflection and absorption coefficient as a function of wavelength for (a) silicon, and (b) Al and Au. The critical wavelength of Al is below 100 nm, so its reflectivity is close to 1 over the data range in the figure. (from Allmen, 1995)

For semiconductors like silicon, a large number of free carriers can be generated not only by thermal excitation at high temperature and further facilitated by the band-gap narrowing, but also by photons at a rate of I/h (I is light intensity, is the absorption cross section) when h > Eg. Fig. 3 depicts the energy diagram of the electrons (holes have similar diagram) under intense irradiation such that the carrier generation rate exceeds that of carrier relaxation rate. Due to free carrier generation, the carrier density and thus the absorption coefficient of semiconductors increase strongly as a function of light intensity. The effect of free carriers on the optical properties is to reduce the real part and to increase the imaginary part of **n**. As a result, free carrier generation tends to decrease the reflectance for p < (now pN is a variable depending on light intensity, while is fixed). Only for carrier density N large enough that p > does the reflectance begin to increase with the light intensity towards unity by further increasing p. Such a rich variation of reflectivity on light intensity and time has

Fig. 2. Reflection and absorption coefficient as a function of wavelength for (a) silicon, and (b) Al and Au. The critical wavelength of Al is below 100 nm, so its reflectivity is close to 1

Wavelength

Wavelength (m)

Absorption coefficient

Absor

ption coefficient

(cm-1)

(cm-1)

over the data range in the figure. (from Allmen, 1995)

(b)

(a)

been observed for crystalline Si irradiated by red 90 fs pulses (Shank 1983).

Reflectivity

Reflectivit

y

Fig. 3. Schematic energy diagram of the electrons in a semiconductor under intense irradiation. The electron temperature Te is higher than the lattice temperature. The shaded area depicts electron plasma. (adapted from Poate 1982)

At sufficiently high light intensity, the rate of energy gain by carriers exceeds the rate of energy loss to the lattice. The result is a splitting up of carrier and lattice temperatures (see Fig. 3), and the carriers behave collectively, i.e., according to the equations governing a plasma (but this plasma behavior is not to be confused with the generation of actual plasma shown in Fig. 1(d); the plasma here is just a large number of electrons inside the conduction band of the semiconductor). The plasma may be regarded as an independent system which absorbs light and exchanges energy with the lattice. As far as coupling is concerned, the effect of the plasma is ultimately to limit the rate of local energy deposition by increasing R at high carrier density such that p > , and by diffusing away the hot carriers from the absorbing surface to the material underneath, which effectively increases the heated volume.

Finally, Si and Ge become metallic (silicon's electrical conductivity is 30 times higher) upon melting due to bandgap collapsing, leading to a strong increase in both and R.

#### **2.2 Heating and melting by laser**

Heating in an irradiated sample is a consequence of the balance between the deposited energy, governed by optical parameters of the sample and characteristics of the laser pulse, and the heat diffusion, determined by thermal parameters and the pulse duration. Strictly speaking, as discussed in the previous section, the primary product of absorbed laser light is not heat but the carriers' excess energy. But for simplicity, and because the our laser pulse has a relatively long duration of 20 ns, it can be assumed that the overall energy relaxation time E is negligible compared to the pulse duration (E~10-13s for metals, ~10-12 10-9s for semiconductors). With this assumption, a simple estimate of the temperature rise is possible for two limiting cases in which the optical absorption depth is small compared with the thermal diffusion length during the pulse (i.e. -1<<2Dt.), or vice versa. However, for many practical cases, complex analytical or numerical evaluations must be performed. In particular, if phase transitions occur during the irradiation, only numerical solutions are available.

Ultrafast Fabrication of Metal Nanostructures Using Pulsed Laser Melting 119

Fig. 4. Normalized temperature as a function of normalized time t/tp at various depths z/ (=2Dtp, tp is pulse duration) for a pulse of rectangular temporal shape, according to Eq. 6. Temperature is normalized to the surface temperature at the end of the pulse. (adapted from

Normalized time t/tp

Next, consider the case when the film is melted. The melting starts from the sample surface and propagates inside the sample until a maximum molten thickness is reached some time after the end of the pulse. The time period of melting depends on the energy density of the pulse and thermal properties of the material, and can be much longer than the pulse duration tp. Fig. 5 sketches the temperature distribution and molten layer thickness variation with time. The latent heat Hsl (the subscript "sl" denotes solid-liquid) for melting Al, Au, Cu, Ni and W ranges from 1/3 to 1/2 that of the energy needed to heat the materials from 300K to its melting temperature (H300KTsl), but for crystalline silicon the latent heat is 40% higher than its H300KTsl. Therefore, the film temperature is "pinned" near Tsl to a larger degree for silicon than for those metals. During re-solidification, the velocity of the liquidsolid interface is determined by the rate of heat extraction from the interface into the bulk,

> *sl i T*

(9)

*H z* 

where (T/z)i is the temperature gradient just behind the interface, which is typically on the order of 1 K/nm. The resulting velocity is then on the order of several meters per second

Due to their very low absorption length, the process window of irradiance for melting metals or semiconductors without surface vaporization is actually very narrow. At slightly higher laser intensity, significant material vaporization is induced and a dense vapor plume is formed in front of the target, a phenomenon known as ablation. For the our laser with 20 ns pulse duration and for film thickness around 200 nm, vaporization occurs when

*v*

for silicon, and several tens of meters per second for metals.

**2.3.1 Evaporation and plasma formation** 

**2.3 Evaporation, plasma formation and plasma propagation** 

Allmen 1995)

Normalized temperature

tp

and is given by

In the current experiment with XeCl excimer laser irradiation of semiconductors or metals, the absorption depth is much smaller than the thermal diffusion length. However, great complexities come from the multi-layered substrate/mold system bearing on its surface subwavelength patterns. Moreover, melting or even boiling was always seen in these experiments. And the parameters such as reflectivity, absorption coefficient, thermal conductivity and specific heat, are all strong functions of temperature. As a consequence, even numerical calculation will be very difficult unless significant simplifying assumptions are made. Therefore, in this section, only a rough estimation of the temperature distribution will be derived.

First, consider the case when phase change is absent. The excimer laser has a 2.5 mm beam size, which is many orders larger than the film thickness, so the heating and cooling can be approximated as a one-dimensional problem governed by the following equation:

$$\frac{\partial \Gamma}{\partial t} = \frac{\Phi(z, t)}{\rho \mathbb{C}\_p} + \frac{1}{\rho \mathbb{C}\_p} \frac{\partial}{\partial z} (\kappa \frac{\partial \Gamma}{\partial z}) \tag{5}$$

where (z,t) is given by Eq. 4 that represents the source term, and , Cp and are the density, specific heat and thermal conductivity, respectively. This equation can be solved analytically under the following assumptions: no temperature dependence of all optical and thermal parameters, rectangular temporal pulse shape of duration tp and intensity I0 (the actual pulse shape is close to Gaussian), very small absorption length (-1), and infinite sample thickness. The temperature distribution during and after the pulse is described by (Allmen 1995)

$$T(z,t) = \frac{2I\_0(1-R)}{\kappa} \sqrt{\text{Diter}} [z \mid 2\sqrt{\text{D}t}] - [t > t\_p] \sqrt{\text{D}(t-t\_p)} i\text{erfc}[z \mid 2\sqrt{\text{D}(t-t\_p)}] \tag{6}$$

$$
\text{erfc}(\mathbf{x}) = \bigcap\_{\mathbf{x}} \text{erfc}(\mathbf{x}')d\mathbf{x}' \text{ and } \text{erfc}(\mathbf{x}) = \frac{2}{\sqrt{\pi}} \int\_{\mathbf{x}}^{\mathbf{x}} e^{-t^2}dt\tag{6'}
$$

where thermal diffusivity D/Cp and the symbol [t>tp] equals one if t>tp and zero otherwise. The characteristic thermal diffusion length within time t is defined as 2Dt. Eq. 6 is visualized in Fig. 4, which suggests the maximum temperature at z==2Dtp is about 1/5 that of peak surface temperature and it is reached at about t=2tp. The surface temperature at the end of the pulse is

$$T(0, t\_p) = \frac{2I\_0(1 - R)}{\kappa} \sqrt{\mathcal{D}t\_p / \pi} \propto \sqrt{t\_p} \tag{7}$$

On the other hand, for metal or semiconductor film sandwiched between the thermal insulating mold and substrate, if the film thickness h is far less than , a more uniform temperature distribution is expected at the end of the pulse, and can be approximated by

$$T(z, t\_p) = \frac{I\_0 (1 - R) t\_p}{C\_p \rho h} \propto t\_p \tag{8}$$

In the current experiment with XeCl excimer laser irradiation of semiconductors or metals, the absorption depth is much smaller than the thermal diffusion length. However, great complexities come from the multi-layered substrate/mold system bearing on its surface subwavelength patterns. Moreover, melting or even boiling was always seen in these experiments. And the parameters such as reflectivity, absorption coefficient, thermal conductivity and specific heat, are all strong functions of temperature. As a consequence, even numerical calculation will be very difficult unless significant simplifying assumptions are made. Therefore, in this section, only a rough estimation of the temperature distribution

First, consider the case when phase change is absent. The excimer laser has a 2.5 mm beam size, which is many orders larger than the film thickness, so the heating and cooling can be approximated as a one-dimensional problem governed by the following

> *p p T zt T t C Cz z*

where (z,t) is given by Eq. 4 that represents the source term, and , Cp and are the density, specific heat and thermal conductivity, respectively. This equation can be solved analytically under the following assumptions: no temperature dependence of all optical and thermal parameters, rectangular temporal pulse shape of duration tp and intensity I0 (the actual pulse shape is close to Gaussian), very small absorption length (-1), and infinite sample thickness. The temperature distribution during and after the pulse is described by

 

> 

 <sup>0</sup> 2 (1 ) (,) [ /2 ] [ ] ( ) [ /2 ( )] *p p <sup>p</sup> I R Tzt Dtierfc z Dt t t D t t ierfc z D t t*

> ( ) ( ') ' *x ierfc x erfc x dx*

<sup>0</sup> 2 (1 ) (0, ) *<sup>p</sup> p p* / *I R T t Dt t*

0(1 ) (, ) *<sup>p</sup>*

(6)

( ) *<sup>t</sup> x erfc x e dt* 

(7)

(8)

(6')

and <sup>2</sup> <sup>2</sup>

where thermal diffusivity D/Cp and the symbol [t>tp] equals one if t>tp and zero otherwise. The characteristic thermal diffusion length within time t is defined as 2Dt. Eq. 6 is visualized in Fig. 4, which suggests the maximum temperature at z==2Dtp is about 1/5 that of peak surface temperature and it is reached at about t=2tp. The surface

On the other hand, for metal or semiconductor film sandwiched between the thermal insulating mold and substrate, if the film thickness h is far less than , a more uniform temperature distribution is expected at the end of the pulse, and can be approximated by

> *p p p I Rt Tzt t C h*

(5)

(,) 1 ( )

temperature at the end of the pulse is

will be derived.

equation:

(Allmen 1995)

Fig. 4. Normalized temperature as a function of normalized time t/tp at various depths z/ (=2Dtp, tp is pulse duration) for a pulse of rectangular temporal shape, according to Eq. 6. Temperature is normalized to the surface temperature at the end of the pulse. (adapted from Allmen 1995)

Next, consider the case when the film is melted. The melting starts from the sample surface and propagates inside the sample until a maximum molten thickness is reached some time after the end of the pulse. The time period of melting depends on the energy density of the pulse and thermal properties of the material, and can be much longer than the pulse duration tp. Fig. 5 sketches the temperature distribution and molten layer thickness variation with time. The latent heat Hsl (the subscript "sl" denotes solid-liquid) for melting Al, Au, Cu, Ni and W ranges from 1/3 to 1/2 that of the energy needed to heat the materials from 300K to its melting temperature (H300KTsl), but for crystalline silicon the latent heat is 40% higher than its H300KTsl. Therefore, the film temperature is "pinned" near Tsl to a larger degree for silicon than for those metals. During re-solidification, the velocity of the liquidsolid interface is determined by the rate of heat extraction from the interface into the bulk, and is given by

$$
\sigma v = \frac{\kappa}{\Delta H\_{sl} \rho} \left(\frac{\partial T}{\partial z}\right)\_i \tag{9}
$$

where (T/z)i is the temperature gradient just behind the interface, which is typically on the order of 1 K/nm. The resulting velocity is then on the order of several meters per second for silicon, and several tens of meters per second for metals.

#### **2.3 Evaporation, plasma formation and plasma propagation 2.3.1 Evaporation and plasma formation**

Due to their very low absorption length, the process window of irradiance for melting metals or semiconductors without surface vaporization is actually very narrow. At slightly higher laser intensity, significant material vaporization is induced and a dense vapor plume is formed in front of the target, a phenomenon known as ablation. For the our laser with 20 ns pulse duration and for film thickness around 200 nm, vaporization occurs when

Ultrafast Fabrication of Metal Nanostructures Using Pulsed Laser Melting 121

vapor pressure of the plasma is order of tens of atm. Above the cut-off electron density (1.21022 cm-3 for 308 nm XeCl excimer laser) where p>, the plasma behaves essentially like a metal with large absorption coefficient and high reflectivity. Below the cut-off density, the absorption coefficient of the plasma p decreases strongly with increasing temperature. The second breakdown mechanism of the vapor or ambient gas is optical breakdown when the electrical field E of the light, given by 2I/0nc, reaches a critical point for avalanche ionization. The threshold irradiance Ith is 109−1011W/cm2 in *clean* air (no dust) at atmospheric pressure. In this case, initial ionization is achieved via multi-photon excitation since h<EI. However, for optical breakdown in front of a target, it was found that Ith is about two to three orders of magnitude lower than if without a target. This is mainly due to the availability of primary electrons emitted from impurities absorbed on the target, which are evaporated and ionized far below the melting point of the target material, plus the temperature increase near a target. In laser processing, optical breakdown is the chief

When ambient gas is present, three different laser intensity thresholds for plasma initiation should be distinguished: surface vaporization threshold Ivap, metal vapor plasma threshold Ii,m, and ambient gas plasma threshold Ii,g. Generally Ii,g> Ii,m because metal atoms are easier to ionize than gas atoms. But gas breakdown usually occurs first for pulsed IR lasers because Ivap is very high (so no metal vapor is produced for plasma formation) owing to metals' high reflectivity in the IR and rapid heat loss to the substrate. On the other hand, when a pulsed UV laser is used, metal vapor breakdown may happen first (Boulmer-

With the formation of plasma, the plume strongly absorbs the laser light and shields the substrate from further irradiation. However, in addition to the shielding effect, there is an important energy transfer from the radiation emitted by the plasma to the surface and via heat conduction. Actually, plasma-enhanced coupling between laser and substrate often results, owing to the fact that the radiation emitted by the plasma is generally in the UV

At still higher irradiances depending on the wavelength, very thick (up to 10 cm) plasma can form that absorbs a significant fraction of the laser light, so laser-induced material vaporization at the target surface ceases. Then the plasma can decouple from the substrate and propagate toward the incident beam. Such plasma is often termed as laser-supported absorption wave, and its dynamic behavior is determined by the laser energy absorption within the plasma plume and the energy loss via heat conduction and plasma radiation. As the plasma leaves the target, it may fade out due to energy loss and become transparent again, which allows the substrate to be re-heated and re-vaporized that leads to a new cycle of plasma formation and propagation. If the plasma propagates with subsonic velocity, it is termed as laser-supported combustion wave (LSCW). The velocity of this wave increases with laser intensity. Plasma propagating at supersonic velocity is termed as laser-supported detonation wave (LSDW). In contrast to LSCW, LSDW is not confined to the vapor. Instead, through target surface-mediated optical breakdown, it can form in cold ambient gas even before the target has started to evaporate. Once ionized, the initial plasma tends to be strongly absorbing and can readily be sustained and propagated as an LSDW for laser irradiances of order 108 W/cm2. The temperature and pressure in an LSDW can reach 105 K and 104 atm, and due to its explosive nature, a shock wave (mechanical force) is driven into

mechanism for plasma formation.

where most metals have low reflectivity.

**2.3.2 Plasma propagation** 

Leborgne 1995).

irradiance exceeds several tens of MW/cm2. There are two distinct modes of vaporization from a liquid, namely volume vaporization or boiling, and surface vaporization. For strongly absorbing media, surface vaporization is always the case. Yet boiling would take place first for backside irradiation, where the film is deposited on a transparent support and the irradiation comes from the support side. Owing to the inverse Mott's metal-insulator transition, the neutral (not ionized) metal vapor is insulating and transparent to the laser light.

Fig. 5. Schematic time evolution of the temperature distribution (left) and the molten layer thickness (right) of a laser-irradiated sample. (sketch is partly based on the numerical simulation in Poate 1982 and Baeri 1979)

However, the regime of normal vaporization is relevant only for pulse durations longer than ~1 s. For nanosecond pulses, unless the target is very thin and thus can be vaporized at low irradiance, the irradiance needed to substantially vaporize the target is often high enough to cause ionization and breakdown of vapor or gas (when ambient gas is present). The first breakdown mechanism is thermal ionization. The ratio of ions to neutrals for a gas in a local thermodynamic equilibrium is given by the Saha equation (Chrisey 1994):

$$\frac{n\_i}{n\_n} = 2.4 \times 10^{15} \frac{T^{3/2}}{n\_i} e^{-E\_l/kT} \tag{10}$$

where ni and nn are the ion and neutral densities and EI is the first ionization energy. Partially ionized gas absorbs light by thermally excited atoms as well as by electrons and ions (inverse-Bremsstrahlung absorption) (Hughes 1975). Light absorption further heats the vapor, which leads to even more ionization and absorption. The positive feedback favors the creation of plasma (substantially ionized vapor) in front of a vaporizing target. Thermal ionization turns on at lower irradiance for longer wavelength lasers because the optical absorption (I) of the plasma increases strongly with increasing wavelength. The typical plasma temperature is ~10000 K, well above the boiling point of metals; and the associated vapor pressure of the plasma is order of tens of atm. Above the cut-off electron density (1.21022 cm-3 for 308 nm XeCl excimer laser) where p>, the plasma behaves essentially like a metal with large absorption coefficient and high reflectivity. Below the cut-off density, the absorption coefficient of the plasma p decreases strongly with increasing temperature.

The second breakdown mechanism of the vapor or ambient gas is optical breakdown when the electrical field E of the light, given by 2I/0nc, reaches a critical point for avalanche ionization. The threshold irradiance Ith is 109−1011W/cm2 in *clean* air (no dust) at atmospheric pressure. In this case, initial ionization is achieved via multi-photon excitation since h<EI. However, for optical breakdown in front of a target, it was found that Ith is about two to three orders of magnitude lower than if without a target. This is mainly due to the availability of primary electrons emitted from impurities absorbed on the target, which are evaporated and ionized far below the melting point of the target material, plus the temperature increase near a target. In laser processing, optical breakdown is the chief mechanism for plasma formation.

When ambient gas is present, three different laser intensity thresholds for plasma initiation should be distinguished: surface vaporization threshold Ivap, metal vapor plasma threshold Ii,m, and ambient gas plasma threshold Ii,g. Generally Ii,g> Ii,m because metal atoms are easier to ionize than gas atoms. But gas breakdown usually occurs first for pulsed IR lasers because Ivap is very high (so no metal vapor is produced for plasma formation) owing to metals' high reflectivity in the IR and rapid heat loss to the substrate. On the other hand, when a pulsed UV laser is used, metal vapor breakdown may happen first (Boulmer-Leborgne 1995).

With the formation of plasma, the plume strongly absorbs the laser light and shields the substrate from further irradiation. However, in addition to the shielding effect, there is an important energy transfer from the radiation emitted by the plasma to the surface and via heat conduction. Actually, plasma-enhanced coupling between laser and substrate often results, owing to the fact that the radiation emitted by the plasma is generally in the UV where most metals have low reflectivity.

#### **2.3.2 Plasma propagation**

120 Recent Advances in Nanofabrication Techniques and Applications

irradiance exceeds several tens of MW/cm2. There are two distinct modes of vaporization from a liquid, namely volume vaporization or boiling, and surface vaporization. For strongly absorbing media, surface vaporization is always the case. Yet boiling would take place first for backside irradiation, where the film is deposited on a transparent support and the irradiation comes from the support side. Owing to the inverse Mott's metal-insulator transition, the neutral (not ionized) metal vapor is insulating and transparent to the laser

Fig. 5. Schematic time evolution of the temperature distribution (left) and the molten layer thickness (right) of a laser-irradiated sample. (sketch is partly based on the numerical

However, the regime of normal vaporization is relevant only for pulse durations longer than ~1 s. For nanosecond pulses, unless the target is very thin and thus can be vaporized at low irradiance, the irradiance needed to substantially vaporize the target is often high enough to cause ionization and breakdown of vapor or gas (when ambient gas is present). The first breakdown mechanism is thermal ionization. The ratio of ions to neutrals for a gas in a local

> 3/2 <sup>15</sup> / 2.4 10 *E kT <sup>I</sup> <sup>i</sup>*

*e*

(10)

thermodynamic equilibrium is given by the Saha equation (Chrisey 1994):

*n i n T*

where ni and nn are the ion and neutral densities and EI is the first ionization energy. Partially ionized gas absorbs light by thermally excited atoms as well as by electrons and ions (inverse-Bremsstrahlung absorption) (Hughes 1975). Light absorption further heats the vapor, which leads to even more ionization and absorption. The positive feedback favors the creation of plasma (substantially ionized vapor) in front of a vaporizing target. Thermal ionization turns on at lower irradiance for longer wavelength lasers because the optical absorption (I) of the plasma increases strongly with increasing wavelength. The typical plasma temperature is ~10000 K, well above the boiling point of metals; and the associated

*n n*

simulation in Poate 1982 and Baeri 1979)

light.

At still higher irradiances depending on the wavelength, very thick (up to 10 cm) plasma can form that absorbs a significant fraction of the laser light, so laser-induced material vaporization at the target surface ceases. Then the plasma can decouple from the substrate and propagate toward the incident beam. Such plasma is often termed as laser-supported absorption wave, and its dynamic behavior is determined by the laser energy absorption within the plasma plume and the energy loss via heat conduction and plasma radiation. As the plasma leaves the target, it may fade out due to energy loss and become transparent again, which allows the substrate to be re-heated and re-vaporized that leads to a new cycle of plasma formation and propagation. If the plasma propagates with subsonic velocity, it is termed as laser-supported combustion wave (LSCW). The velocity of this wave increases with laser intensity. Plasma propagating at supersonic velocity is termed as laser-supported detonation wave (LSDW). In contrast to LSCW, LSDW is not confined to the vapor. Instead, through target surface-mediated optical breakdown, it can form in cold ambient gas even before the target has started to evaporate. Once ionized, the initial plasma tends to be strongly absorbing and can readily be sustained and propagated as an LSDW for laser irradiances of order 108 W/cm2. The temperature and pressure in an LSDW can reach 105 K and 104 atm, and due to its explosive nature, a shock wave (mechanical force) is driven into

Ultrafast Fabrication of Metal Nanostructures Using Pulsed Laser Melting 123

All laser fluences given in this chapter are values *before* passing through the quartz window and cover. The actual laser fluences received by the films should be about 15% less due to the reflection at four quartz/air interfaces. In addition, most experiments used only one

Fig. 6. Schematic setup of the excimer laser, optical components and sample stage. The laser can be used as light sources with different wavelengths by filling different rare-gas-halides

In this section we will present laser assisted direct imprint, wafer planarization, via-hole

The most straightforward application of laser assisted nanofabrication is LADI (Cui 2010, Chou 2002). In the LADI process, a single laser pulse passed through a transparent quartz mold and melted a thin layer of the substrate material, or the film material if it was different from the substrate. The characteristic time constant for electron-phonon collision to reach thermal equilibrium between excited electron gas and the lattice in metals is on the order of picoseconds, which is negligible compared to the laser pulse duration. The molten layer was then embossed by the quartz mold. Once the liquid layer re-solidified, the mold was separated from the substrate. As can be seen, the most prominent feature of LADI is that it is a one-step patterning process – it replaces the steps of resist patterning in photolithography or nanoimprint lithography, subsequent pattern transfer by etching or liftoff, and resist removal all into one single step. Besides LADI of metal or silicon, one can also imprint a polymer resist that absorbs UV light thus gets heated by the laser pulse (Xia 2003, Xia 2010). Fig. 7 shows SEM images of 200 nm period Al, Au, Cu and Ni gratings with ~100 nm linewidth imprinted by LADI. Only one pulse was used to melt and imprint those metals at a fluence of 0.22, 0.53, 0.24 and 0.41 J/cm2 for Al, Au, Cu and Ni, respectively. We found that multiple pulses up to 50 pulses had insignificant effects to the imprint results. As shown in the figure, although 100 nm features in metal were imprinted, the resolution was not near

**4. Applications of pulsed laser assisted nanofabrication** 

filling, transfer printing, and nano-tip formation.

**4.1 Laser-assisted direct imprint (LADI)** 

laser pulse.

into the laser gas chamber.

both the ambient gas and the substrate material. For a more detailed discussion, refer to (Bäuerle 2000 and Allmen 1995).

### **3. Experimental setup**

Fig. 6 shows the diagram of the setup. XeCl excimer laser with FWHM pulse duration of 20 ns was used to irradiate the samples. For 20 ns pulse duration, the characteristic thermal diffusion length (=2Dtp) is calculated to be ~0.2 µm for SiO2 and ~2 µm for metals and silicon. The maximum per pulse laser output energy is 200 mJ, yet 160 mJ was always set as maximum for more reproducible output fluence (energy divided by area, J/cm2). The attenuator allows a transmission range of 10−90%. The incident laser beam has a square shape and its size, determined by the separation between the imaging doublet and the substrate, is chosen to be between 2 to 3 mm. With a 160 mJ pulse energy within 20 ns over the (2.5 mm)2 beam area, the light intensity is calculated to be 130 MW/cm2, high enough to cause vaporization and plasma formation in front of many metal targets. The sample stage is put either in air or in a vacuum chamber with vacuum better than 200 mTorr. The pressure between the mold and the substrate was applied by sandwiching them between two large press plates held by springs.

For laser assisted direct imprint (LADI), we used 200 nm period quartz (fused silica) grating mold that was duplicated by nanoimprint lithography, liftoff and reactive ion etching from a master mold, which was fabricated by interference lithography with uniform grating pattern over an entire 4" wafer. The high purity quartz mold absorbs negligible laser energy at 308 nm wavelength. The substrate to be patterned was prepared by electron beam evaporation of 200 nm thick of the desired metal (Al, Ni, Au, Cu) with 5 nm thick Cr adhesion layer (the melting point of Cr is higher than the four metals studied here). The quartz mold was cut into a number of 1 mm2 quartz pieces, which is smaller than the 2.5 2.5 mm2 excimer laser spot size in order to ensure that the entire substrate area below the mold gets melted during the LADI process.

Excimer lasers are almost ideal sources for laser micro- or nano-patterning, some types of surface modifications, and thin film deposition. This is because they have high photon energies (short wavelengths), short pulse lengths (typically 10 to 40 ns), and relatively poor coherence (since an excimer laser's output is highly multimode and contains as many as 105 transverse modes (Bäuerle 2000)). The high photon energy of an excimer laser allows for strong optical absorption in many metals and virtually all semiconductors. The short pulse length is a prerequisite for spatially well-defined surface heating (as tp) with negligible heating or damage of the bulk substrate (see next paragraph). In addition, the short pulse produces chemically stoichiometric ablation, which is one of the key advantages for pulsed laser deposition. Finally, the poor spatial coherence of excimerlaser light diminishes interference effects. Their disadvantages include low efficiency, poor pulse-to-pulse stability (when set at 160 mJ, the output energy ranged from 140 to 180 mJ), and high operating cost.

It should be pointed out that the optimal pulse length depends on the specific application. When substrate heating is not a concern, a longer pulse is desirable for more uniform heating through the film thickness and less damage of the film surface; a longer melting time also allows larger features to be patterned. If only the surface layer needs to be melted or ablated, then a shorter pulse is favored to reduce threshold fluence and substrate heating.

both the ambient gas and the substrate material. For a more detailed discussion, refer to

Fig. 6 shows the diagram of the setup. XeCl excimer laser with FWHM pulse duration of 20 ns was used to irradiate the samples. For 20 ns pulse duration, the characteristic thermal diffusion length (=2Dtp) is calculated to be ~0.2 µm for SiO2 and ~2 µm for metals and silicon. The maximum per pulse laser output energy is 200 mJ, yet 160 mJ was always set as maximum for more reproducible output fluence (energy divided by area, J/cm2). The attenuator allows a transmission range of 10−90%. The incident laser beam has a square shape and its size, determined by the separation between the imaging doublet and the substrate, is chosen to be between 2 to 3 mm. With a 160 mJ pulse energy within 20 ns over the (2.5 mm)2 beam area, the light intensity is calculated to be 130 MW/cm2, high enough to cause vaporization and plasma formation in front of many metal targets. The sample stage is put either in air or in a vacuum chamber with vacuum better than 200 mTorr. The pressure between the mold and the substrate was applied by sandwiching them between two large

For laser assisted direct imprint (LADI), we used 200 nm period quartz (fused silica) grating mold that was duplicated by nanoimprint lithography, liftoff and reactive ion etching from a master mold, which was fabricated by interference lithography with uniform grating pattern over an entire 4" wafer. The high purity quartz mold absorbs negligible laser energy at 308 nm wavelength. The substrate to be patterned was prepared by electron beam evaporation of 200 nm thick of the desired metal (Al, Ni, Au, Cu) with 5 nm thick Cr adhesion layer (the melting point of Cr is higher than the four metals studied here). The quartz mold was cut into a number of 1 mm2 quartz pieces, which is smaller than the 2.5 2.5 mm2 excimer laser spot size in order to ensure that the entire substrate area below the

Excimer lasers are almost ideal sources for laser micro- or nano-patterning, some types of surface modifications, and thin film deposition. This is because they have high photon energies (short wavelengths), short pulse lengths (typically 10 to 40 ns), and relatively poor coherence (since an excimer laser's output is highly multimode and contains as many as 105 transverse modes (Bäuerle 2000)). The high photon energy of an excimer laser allows for strong optical absorption in many metals and virtually all semiconductors. The short pulse length is a prerequisite for spatially well-defined surface heating (as tp) with negligible heating or damage of the bulk substrate (see next paragraph). In addition, the short pulse produces chemically stoichiometric ablation, which is one of the key advantages for pulsed laser deposition. Finally, the poor spatial coherence of excimerlaser light diminishes interference effects. Their disadvantages include low efficiency, poor pulse-to-pulse stability (when set at 160 mJ, the output energy ranged from 140 to

It should be pointed out that the optimal pulse length depends on the specific application. When substrate heating is not a concern, a longer pulse is desirable for more uniform heating through the film thickness and less damage of the film surface; a longer melting time also allows larger features to be patterned. If only the surface layer needs to be melted or ablated, then a shorter pulse is favored to reduce threshold fluence and

(Bäuerle 2000 and Allmen 1995).

**3. Experimental setup** 

press plates held by springs.

mold gets melted during the LADI process.

180 mJ), and high operating cost.

substrate heating.

All laser fluences given in this chapter are values *before* passing through the quartz window and cover. The actual laser fluences received by the films should be about 15% less due to the reflection at four quartz/air interfaces. In addition, most experiments used only one laser pulse.

Fig. 6. Schematic setup of the excimer laser, optical components and sample stage. The laser can be used as light sources with different wavelengths by filling different rare-gas-halides into the laser gas chamber.
