# Laser-Induced Backside Wet Etching of Transparent Materials with Organic and Metallic Absorbers

Authors: K. Zimmer; R. Böhme
Journal: Laser Chemistry
 (2008)

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## Abstract

Laser-induced backside wet etching (LIBWE) allows the high-quality etching of transparent materials for micro- and nanopatterning. Recent own results of LIBWE with hydrocarbon and metallic absorbers (H- and M-LIBWE) are summarized and compared with selected results of other groups regarding the etching process and the etched surface. Significant results on the impact of the liquid absorber, the material and the wavelength, and the pulse length of the laser to the etching are selected for this comparison. The etching of submicron-sized periodic structures in sapphire and fused silica with interference techniques and the selection of the preferred method in dependence on the material and the processing goal  discussed. The experimental results are discussed on a thermal model considering both interface and volume absorption of the laser beam. These results have the conclusion that the etching at M-LIBWE is mainly due to material melting and evaporation whereas at H-LIBWE, a modified near-surface region with a very high absorption is ablated.


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## Body

## 1. Introduction

The high-quality, precise, low-damage processing of transparent
dielectrics by lasers with respect to high-quality micro- and nanopatterning of
these materials is still a challenge [1–3]. Therefore,
the lateral and vertical resolution of the patterning process should be reduced
and the surface quality, that is roughness, waviness, and processing-induced
near-surface material modification, must be improved.In addition to traditionally used nanosecond lasers that allow ablation of such
materials, for example, fused silica, at high laser fluences [4, 5], nowadays
ultrashort pulse or VUV lasers are exploited increasingly [6–9]. These lasers
cause material ablation after multiphoton and single-photon excitation and
enable material processing at low laser fluences with lower ablation rates
which can result in improved surface qualities. In consequence, one key for
high-quality materials processing is a high absorption of the laser beam by the
material, in particular the surface. This results in near-surface energy
deposition, high energy densities, and fast phase transitions and prevents
excessive melting of the material already at low laser fluences.With the aim of absorption enhancement of transparent materials, two
beam laser ablation techniques have been developed. Principally, a first
low-fluence high-photon-energy laser is used for the generation of free
electrons and temporary defects whereas a second high-fluence (UV) laser is
employed for ablation after photon absorption by the laser-induced transient
absorption centres [10, 11]. Such temporary modifications for surface
absorption enhancement were applied also to backside ablation. Zhang
etal. introduced laser-induced plasma-assisted ablation (LIPAA) that
makes use of laser-induced plasma from metal plate placed behind the
transparent sample. The laser plasma modifies the backside of the transparent
sample and the enhanced laser absorption resulting in backside
ablation [12–16].Nowadays a number of indirect laser processing methods is in development
that aims also to a
near-surface absorption of the laser energy at the backside of transparent
samples. However, the enhanced surface/interface absorption is achieved at
these methods by additional materials. Depending on the additive to enhance the energy
deposition near the transparent solid surface, different techniques can be
distinguished.The laser etching by surface-adsorbed layer (LESAL) technique uses hydrocarbon
layers adsorbed at the backside of the sample to enhance the laser beam absorption [17–20]. Recently,
the so-called laser-induced backside dry etching (LIBDE) was demonstrated by
Hopp etal. using a thin metal film for laser energy deposition [21].
Laser-induced backside wet etching (LIBWE) developed by Niino’s group makes use
of the high absorption of organic liquids (H-LIBWE—hydrocarbon LIBWE) for
excimer laser wavelengths [22–24]. Previously
Shafeev performed material processing at the interface to liquids with a
similar set-up but uses much higher laser fluences of a high repetition rate
copper vapour laser [25, 26]. Zimmer et al. applied liquid metals (M-LIBWE—liquid
metal LIBWE) instead of the initially exploited organic solutions for backside
wet etching [27–29].To ensure a sufficiently high absorption of the organic liquids, UV
excimer lasers (XeF, XeCl, KrF, ArF) have to be used for H-LIBWE. Higher
harmonics of high repetition rate Nd:YAG lasers (530 nm, 266 nm) were
applied for etching, too [30, 31]. However, the utilization of visible
wavelengths requires special dyes for absorption and in addition higher laser
fluences [30]. For very high repetition rates, the bubble lifetime can
exceed the pulse interval whereby the etching process is influenced and lower
etch rates were found [30, 31]. A wide range of liquids were investigated
for H-LIBWE comprising mainly solutions of dyes in organic solvents [22, 32], solutions of inorganic and organic absorbers in water [25, 26, 33, 34], and liquid metals [27, 35]. Only some experiments on LIBWE with
ultrashort pulse lasers are known [36, 37].The most studies aim at the
effects of specific material processing conditions (liquid, wavelength, etc.)
on the etching process and the properties of the etched surface. The effect of
H-LIBWE to the properties
of the processed surface was investigated in  [38, 39] and gave evidence for a
strong surface modification and incubation. Some studies aim at the comparison
of experimental LIBWE results with (numerical) model calculations [32, 40]. In [32], it was found that the interface temperature at H-LIBWE is below
the melting temperature of the fused silica for the laser fluences at the etch
threshold; however, in this work interface modifications were neglected. In Table 1, the most important characteristics of patterning processes for transparent
materials are listed for H- and M-LIBWE in comparison to laser ablation.Table 1
Main characteristics of the
backside etching techniques with nanosecond laser pulses in comparison to laser
ablation.
CharacteristicTechniqueH-LIBWEM-LIBWEAblationThreshold fluenceLowHighHighLaser wavelengthUV/visUV-IRUV (IR)Etch rateAverageHighHighIncubation effectsDistinctNoNoticeableEtching qualityVery goodGoodAverageAll the mentioned backside etching techniques have been used for micro-
and nanopatterning of different transparent glass and crystals [22, 23, 41–43]. Examples are the etching of submicron and nanometer gratings in fused
silica [44–46] and
sapphire [47], the submicron patterning on-the-fly with one laser
pulse [48], the etching of micro-optical elements [18, 39, 42, 49–53], and the
fabrication of arrays for biomedical purposes [30, 54].


## 2. Experimental

The basic configuration of the experimental set-up for LIBWE is shown in
Figure1. The etching chamber holds the substrates and contains the liquid
absorber. The chamber assembly is often incorporated into a laser workstation
or a similar installation for precise processing and full parameter control as
has been described elsewhere [30, 55]. In summary, the laser beam goes trough
the transparent sample and is absorbed at its
backside by the liquid.Figure 1
Basic experimental set-up for LIBWE.Mainly the following laser parameters were varied with one set-up: the
spot size, the laser fluence, the pulse number. Depending on the laser source
and the beam quality, the laser beam is directly focussed or used for mask
projection. In consequence, the intensity distribution of the laser spot is
either Gaussian-like for solid state lasers (e.g., Nd:YAG) or uniform with an
average deviation in the range of±5%
for excimer lasers. The wavelength, the pulse length, and the temporal pulse
shape are also characteristics of the used laser source: nanosecond (UV: XeF,
KrF, ArF excimer lasers and IR: Nd:YAG laser; tp∼20,…,30 nanoseconds) as
well as picosecond laser pulses (4th Nd:YAG laser, tp=150 picoseconds) were applied. Usually low
repetition rates (<10 Hz) were used in the basic experiments. To
achieve high spatial resolution down to the submicron range, interference
techniques such as phase mask projection [44] and interferometer
set-ups [47] were applied.


### 2.1. Samples

For backside etching, double-side polished
high-quality substrates were used. The material of choice in most of the
experiments was optical-grade fused silica (FS). Further, crystalline
materials such as quartz, sapphire, and fluorides (CaF2, MgF2)
with a thickness of some mm were utilized. To allow high-resolution mask
projection, thin samples (<1 mm) were used. The surface roughness
was always in the range of 1nm  rms or even lower; the fused silica
samples regularly have a roughness of about 0.2 to 0.3 nm rms. The samples
were used as received without further cleaning.


### 2.2. Liquids

Two classes of liquids are used: (i)hydrocarbon liquids that are solutions of pyrene in toluene (py:toluene), acetone,
tetrachloroethylene, and so forth, at concentrations of usually 0.5 M (M =
mol/L) and (ii) liquid metals such as gallium (Ga) and
mercury (Hg).


### 2.3. Processing Procedure

After mounting the samples to the chamber, the
etching was performed. For large area processing, for example, writing of
arrays or micro-optical patterns, a circulating pump assembly might be used [30]. This
allows the continuous exhaust, the filtering, and the cooling down of the used
solution. After processing the samples were cleaned from the liquid absorber
either by washing in organic solvents (acetone, ethanol, etc.) or by etching in
suitable acids (e.g., nitric acid); ultrasonic can be applied, in
addition. Subsequently, the samples were washed in water and dried in a dry
nitrogen stream. For removing adherent carbon contaminations a soft oxygen-plasma
cleaning procedure was applied, too [37].


### 2.4. Analytic of Etched Surfaces

The topography over the full range of spatial
frequencies, laser-induced modifications, and the near-surface material
properties (composition, absorption structure, etc.) of the etched samples were
investigated by the following analytical techniques: Scanning electron
microscope (SEM, either a JEOL JSM 6600 or a Zeiss CARL ZEISS Ultra 55) was
employed for taking top-view or cross-section images of the etched samples.
White-light interference microscopy (e.g., Micromap 512) was frequently
performed to measure the etch depth, the topography, the waviness, and the
roughness (μm-range) of the etched surfaces with an accuracy down to
1 nm in depth. High-resolution investigations of the topography and the
roughness are performed by AFM measurements using a Nanoscop III
instrument. The transmission of irradiated sample regions was measured utilizing
a scanning UV/VIS spectrometer (Shimadzu UV-2101PC UV/VIS scanning
spectrophotometer, λ=200–800 nm). For determining structural
defects in solid material and near-surface contaminations channeling/RBS-
(Rutherford Back Scattering) measurements with a 2MeV-He2+ beam of about 1.5 mm diameter were performed.


## 2.1. Samples

For backside etching, double-side polished
high-quality substrates were used. The material of choice in most of the
experiments was optical-grade fused silica (FS). Further, crystalline
materials such as quartz, sapphire, and fluorides (CaF2, MgF2)
with a thickness of some mm were utilized. To allow high-resolution mask
projection, thin samples (<1 mm) were used. The surface roughness
was always in the range of 1nm  rms or even lower; the fused silica
samples regularly have a roughness of about 0.2 to 0.3 nm rms. The samples
were used as received without further cleaning.


## 2.2. Liquids

Two classes of liquids are used: (i)hydrocarbon liquids that are solutions of pyrene in toluene (py:toluene), acetone,
tetrachloroethylene, and so forth, at concentrations of usually 0.5 M (M =
mol/L) and (ii) liquid metals such as gallium (Ga) and
mercury (Hg).


## 2.3. Processing Procedure

After mounting the samples to the chamber, the
etching was performed. For large area processing, for example, writing of
arrays or micro-optical patterns, a circulating pump assembly might be used [30]. This
allows the continuous exhaust, the filtering, and the cooling down of the used
solution. After processing the samples were cleaned from the liquid absorber
either by washing in organic solvents (acetone, ethanol, etc.) or by etching in
suitable acids (e.g., nitric acid); ultrasonic can be applied, in
addition. Subsequently, the samples were washed in water and dried in a dry
nitrogen stream. For removing adherent carbon contaminations a soft oxygen-plasma
cleaning procedure was applied, too [37].


## 2.4. Analytic of Etched Surfaces

The topography over the full range of spatial
frequencies, laser-induced modifications, and the near-surface material
properties (composition, absorption structure, etc.) of the etched samples were
investigated by the following analytical techniques: Scanning electron
microscope (SEM, either a JEOL JSM 6600 or a Zeiss CARL ZEISS Ultra 55) was
employed for taking top-view or cross-section images of the etched samples.
White-light interference microscopy (e.g., Micromap 512) was frequently
performed to measure the etch depth, the topography, the waviness, and the
roughness (μm-range) of the etched surfaces with an accuracy down to
1 nm in depth. High-resolution investigations of the topography and the
roughness are performed by AFM measurements using a Nanoscop III
instrument. The transmission of irradiated sample regions was measured utilizing
a scanning UV/VIS spectrometer (Shimadzu UV-2101PC UV/VIS scanning
spectrophotometer, λ=200–800 nm). For determining structural
defects in solid material and near-surface contaminations channeling/RBS-
(Rutherford Back Scattering) measurements with a 2MeV-He2+ beam of about 1.5 mm diameter were performed.


## 3. Experimental Results for Laser Etching of Transparent Materials

As already mentioned the most principal task of the rear side liquid is
the absorption of the laser radiation near the solid backside surface. Therefore
can be expected a better the material etching for laser beam absorption closer
to the surface. Two basic classes of liquid absorbers must be considered:(i)
hydrocarbon liquids or
solutions (H-LIBWE),(ii)
liquid metals
(M-LIBWE).The classical H-LIBWE requires nanosecond-pulsed UV or VIS laser to match the absorption of the liquid. Nevertheless, typical laser
penetration depths of organic liquids are some microns. The liquid metal LIBWE
permits the utilization of IR laser pulses for etching since metal absorbs
efficiently over the whole range of the spectrum with a short penetration
depths (α−1≪100 nm).Typical images of the etched fused silica surfaces are shown in Figure2
for H-LIBWE with py:toluene in (a) and M-LIBWE with gallium in (b). The size
and the shape of the edges and the etched bottom show a very good quality in
both cases. Although the microroughness is low for both techniques, M-LIBWE
shows a higher waviness of the etched surface that looks like frozen waves.
These features together with the high etch rates let us suggest that the material etching for
M-LIBWE involves a molten phase that resolidifies after material ejection.SEM images of etched square patterns in fused silica with100×100 μm2 by 248 nm excimer laser: (a)
H-LIBWE with py:toluene (300 pulses at 1.4 J/cm2) and (b) M-LIBWE
with Ga (30 pulses at 3.4 J/cm2).
(a)(b)


### 3.1. Etch Rate of Fused Silica

The most accessible and informative experimental result is the etch rate
of the material depending
on the laser fluence and the pulse number. The etch rate of fused silica for
248 nm excimer laser pulses depending on the laser fluence and the pulses number is shown in
comparison for H-LIBWE with a 0.5 mol/L pyrene/toluene solution
(0.5 M py:toluene) and M-LIBWE with gallium in Figure3,
respectively.Etch rate of fused silica with 248 nm excimer laser
pulses and a spot with size of100×100 μm2. Comparison of H-LIBWE
with a 0.5 M py:toluene and M-LIBWE with gallium. (a) Etch rate depending
on the laser fluence. (b) Normalized etch rate depending on the pulse number.
(a)(b)At least three etching characteristics are different for both
approaches: (i) M-LIBWE offers much higher etch rates than H-LIBWE but (ii)
requires much higher laser threshold fluences for etching. In addition, (iii)
strong incubation effects were detected at H-LIBWE whereas M-LIBWE features
almost no incubation effects [27, 56]. The higher threshold fluences at
M-LIBWE can be explained in parts by the higher reflectivity of the interface
and the higher thermal conductivity of the liquid metal absorber,
respectively [28, 35]. Because all other experimental parameters are
similar, the incubation must be linked to the used liquid that should cause an
additional laser irradiation-induced change of the interface region in order to
enhance the laser absorption either in the liquid or in the near-solid region.
The negligible incubation effect at M-LIBWE can be explained by the high
absorption coefficient and the high stability of the liquid metals. On the
other hand, the organic liquids and solutions used at H-LIBWE suffer from
photothermal and/or photochemical decomposition under intense pulsed UV laser
irradiation [57].The analysis of hydrocarbon solutions showed among a lot of soot a
number of decomposition products at HPLC-MS due to laser exposure. However, the
composition of the liquid is not altered in this extent to explain a much
higher (local) absorption coefficient of the liquid  [58]. The decomposition of
hydrocarbon liquids under UV laser irradiation can result in conjunction with
high temperatures to the formation of excited atoms or radicals. This can be of
interest when halogenated hydrocarbons are used that might form chemical
radicals that are able to etch solid materials directly [59].


### 3.2. Etch Characteristics for Different Materials and Absorbing Liquids

The etch characteristics,  for example etch rate
and surface morphology, depend on the used liquid for both classes of liquid
absorbers: hydrocarbon solutions and liquid metals. The etch rates of fused
silica are shown in Figure4 for two different absorbers in each case—gallium and
mercury and py:toluene and py:halogenated benzenes. In both cases, the
threshold fluence and the etch rate dependency are affected by the used liquid.
The comparison for M-LIBWE in Figure 4(b) shows that mercury has a less
etch threshold (Hg: 0.76 J/cm2; Ga:
1.3/2.1 J/cm2) and a slightly
lower etch rate than gallium. However, in both cases a linear rise of the etch
rate, no incubation effects, and similar etch pits with well-defined edges and
flat bottoms have been observed [27, 29]. The lower threshold of mercury
can be explained by the twofold lower thermal diffusion length (Hg:
0.66 μm; Ga: 1.24 μm at tp=25 nanoseconds).
The lower slope of the etch rate raise for mercury can be discussed also by the
different material properties of mercury.Etch rates of fused silica for different liquids at
248 nm laser pulse irradiation. (a) Etch rate of fused silica for toluene
with and without solved pyrene and for halogenated benzenes (fluorine and
chlorine benzene) at 300 pulses. (b) Etch rate for fused silica at 30 pulses
using gallium and mercury as liquid metals.
(a)
H-LIBWE(b)
M-LIBWEThe etch rate dependencies achieved for H-LIBWE
of fused silica using either pyrene-doped toluene or monohalogenated
benzenes   (0.5 M) are rather dissimilar; however, above a certain
laser fluence of about 0.7 J/cm2, similar etch
rates and a linear rise can be observed. Especially at low fluences, a much
lower rate and a higher slope of the rate were measured for the halogenated
solvent although the absorption coefficient was similar due to the high pyrene
concentration. It should be noted that the threshold fluence for the
pyrene-doped solutions is similar  (∼0.33 J/cm2) but
significantly less than the threshold for pure toluene  (0.45 J/cm2). The etch rate
with pure toluene also increases almost linearly but is only a bit less than that
achievable with pyrene. Though the threshold depends on the liquid absorption,
there is no linear correlation as the pyrene doping causes a sevenfold increase
of the absorption but the threshold is reduced only little.The laser-induced decomposition
of halogenated
hydrocarbons, however, can result in halogen radicals
[57, 58, 60, 61]
and can,
therefore, contribute to the etching [58, 62]. However, this does not
explain the lower etch rate if at halogenated organics the same processes
occur. Therefore, the halogen radicals may also affect the overall processes of
the etching, for example, in the liquid, vapour, bubble, and so forth, where
different chemical reactions and physical processes might occur.Similar to the liquid absorber, the properties of the material etched by
LIBWE affect the etch result. The SEM images in Figure5 depicting etch
pits in sapphire, calcium fluoride (CaF2), and fused silica show
this clearly. In contrast to the flat bottom and the well-defined edges of the
fused silica, the etched patterns of both sapphire and CaF2 feature
an uneven, grainy surface and an irregular edge.Surface morphology of H-LIBWE etched sapphire (a) and CaF2 (b) in comparison to the standard material fused silica (c).
(a)(b)(c)The main differences of the materials that can account for the
morphological changes are the thermal properties and the mechanical and
chemical resistance of the materials. For instance, the thermal conductivityk of the crystals (sapphire: 40 and CaF2: 9.7 W·(m·K)-1)
is much higher than that of fused silica (1.4 W·(m·K)-1).
Therefore, the higher heat diffusion length forces the heat dissipation and
does not allow as high heating rates and high temperatures as for fused silica.
With these arguments, the surface morphology of sapphire and CaF2 can be interpreted by melting, melt ejection, and resolidification of a
near-surface layer. The formation of microcracks in these brittle materials
must be taken into account in addition.


### 3.3. Modification of the Etched Surface at H-LIBWE

The surfaces of etched fused silica and quartz
samples were investigated with different analytical techniques such as XPS,
Raman spectroscopy, and RBS to study the process-induced near-surface chemical
and structural modifications [23, 39, 62, 63]. The kind and the amount of
the modification depend on the applied laser fluence and the pulse
number [58]. In general, with increasing laser fluence, the mainly found
carbon contaminations at low fluences reduce whereas the depth of structural
transformations increases.To study the impact of the near-surface material modifications on the
etching process, optical transmission measurements were performed. The inset of
Figure6 shows the transmission of an etched fused silica sample
(0.76 J/ccm2) depending on
the wavelength (200 nm to 800 nm). In general, a reduced transmission
in the UV is obvious and can also be observed for other fluences and pulse
numbers. According to  [58],
the spectrum can be
interpreted as a superposition of the spectra from carbon and defect-enriched
fused silica. Thus, the observed changes of the spectra taken at different etch
conditions also refer to alterations of the surface modification. The change of
the absorption at λ=248 nm with the applied laser fluence for
etched and wiped samples is shown in Figure 6, too. It should be noted
that surface modifications occur below the threshold and the modifications can
be divided in loosely adherent—that can be
whipped away—and incorporated
modifications. Together with the XPS and Raman spectroscopy results, the
loosely adherent modifications are mainly carbon or carbon products from the decomposition of the
organic absorber [58]. The near-surface fused  silica modifications can be removed completely by ion
beam sputtering of about 50 nm [58, 64]. This depth is similar to the
depth of structural defects found in quartz [63].Figure 6
Absorption of etched
fused silica surface depending on the laser fluence. The inset shows spectra of
an etched fused silica sample (F = 0.76 J/cm2) with a reduced
transmission in the UV.The remarkable high absorption of a thin (<50 nm) near-surface
region of about 30 to 40% is due to structural modifications of the fused
silica and a chemical modification of the surface or by a carbon-containing
film.


### 3.4. Etching of Submicron Patterns in Transparent Materials

From the basic results, it is clear that
micropatterning of fused silica can be easily achieved with different liquids
and laser sources. A lot of examples are known for different technical fields.
However, with the reduction of the feature size, the requirements for the
etching process are enhanced concerning the resolution of the etching process,
the homogeneity of the etching, and the smoothness of the surface.


#### 3.4.1. Submicron Grating Etching in Fused Silica

These requirements for etching of
submicron patterns are fulfilled for fused silica for both H- and M-LIBWE. The
first experiments on etching high-resolution 1 D gratings with a period of∼750 nm are presented in   [44]. Depending on the average fluence and
the pulse number, grating depths of up to 180 nm with a nearly sinusoidal
profile were achieved. This profile mainly results from the sine interference
pattern together with the linear etch rate rise. However, additional to the
gratings an overall etching, that is, etching in the fringes minima at F∼0, was observed especially
at higher laser fluences and pulse numbers. Further experiments on overetching
of already prepatterned substrates showed that the modulation depth of
submicron patterns reduces at overetching with a homogeneous laser
beam [65]. The effect was discussed by the better heating of topographic
peaks by heat transport from the liquid but the effect seems to be too strong
to be completely explained therewith.Results on high-resolution etching of surface
relief line gratings in fused silica down to 104 nm periods presented in
[45, 46] show a reduction of the grating depth with the reduction of the
period. This finding can be discussed by the reduction of the modulation of the
interface temperature because of the thermal diffusion length of the material
given by LT=2⋅DT⋅t  with DT=k/ρ⋅cp.
The thermal diffusion lengths LT for fused silica and organic solvents are in the order of 0.18 and 0.09 μm
for the used 8-nanosecond 266 nm laser pulses [45, 46] and about
0.3 μm and 0.15 μm for pulse lengths of 25 nanoseconds, respectively. For pattern periods p of
similar or smaller than thermal diffusion length (e.g., ∼100 nm), the heat
transport smears interference patterns and only shallow gratings are etched
whereas ∼0.5 μm gratings can be etched proper. This means that
high-resolution patterns with high modulation depths can be hardly obtained for
materials—either the solid
and the liquid or both—with high LT.In Figure7, 2 D gratings in FS with periods of about 550 nm
and 780 nm are shown for H- and M-LIBWE in comparison. The maximal
achieved grating depth of ∼160 to 180 nm is similar in both cases
and is achieved near the threshold of grating etching. However, with M-LIBWE
gratings with a depth of 60 nm can be etched with one laser pulse and can enable submicron
patterning “on-the-fly” [48]. The thermal diffusion length of ∼0.6 μm
can result in a strong overetching effect especially at rising laser fluence
that can occur than already with the first  laser pulse.Submicron 2 D gratings with
periodsp∼550 nm and 780 nm etched in fused silica,
respectively. (a) Grating obtained by H-LIBWE with a py:acetone solution and (b)
grating etched on a prepatterned substrate (line width ∼7.5 μm,
prepattern depth ∼3μm) using mercury as absorber.
(a)(b)


#### 3.4.2. Submicron Grating Etching by
Ultrashort Laser Pulses

To overcome the problem and enable high-quality etching of highly
conductive materials by LIBWE, shorter laser pulses must be applied. For 150-picosecond
pulse duration, for example, of the fourth harmonic (266 nm) of an EKSPLA
Nd:YAG-laser system, the thermal diffusion length is reduced by a factor
greater than 10 and results in thermal diffusion lengths of less than
200 nm for application-relevant highly conductive materials. For sapphire
with a rather high thermal diffusivityD of 1.63×10−5 m2/s, a length of
70 nm can be calculated.Surface relief gratings were inscribed in sapphire and in fused silica
as well as in different fluorides using H-LIBWE with 266 nm, 150-picosecond
laser pulses by applying different interference techniques, for example, phase
mask placed in contact to the front surface of the sample. As shown in Figure8,
the quality of surface relief gratings with an average depth of
∼50 nm etched in sapphire is similar to that achieved for fused
silica. However, the threshold laser fluence for etching of gratings is in
parts higher for sapphire due to the higher melting and evaporation temperature
and due to the, of course, higher thermal conductivity. Details for sapphire
grating etching are
given in  [47].H-LIBWE etched line gratings with a period of∼530 nm in fused silica (a) and sapphire (b). The SEM images show a
similar quality of the inscribed gratings.
(a)(b)Therefore, H-LIBWE with ultrashort laser pulses is favourable for
etching patterns in several dielectrics with periods shorter than 500 nm
due to the combination of the advantages of ultrashort processing and backside
etching [37]. The etching of well-developed 100 nm patterns with ultrashort
laser pulse H-LIBWE in fused silica was shown recently [66].


## 3.1. Etch Rate of Fused Silica

The most accessible and informative experimental result is the etch rate
of the material depending
on the laser fluence and the pulse number. The etch rate of fused silica for
248 nm excimer laser pulses depending on the laser fluence and the pulses number is shown in
comparison for H-LIBWE with a 0.5 mol/L pyrene/toluene solution
(0.5 M py:toluene) and M-LIBWE with gallium in Figure3,
respectively.Etch rate of fused silica with 248 nm excimer laser
pulses and a spot with size of100×100 μm2. Comparison of H-LIBWE
with a 0.5 M py:toluene and M-LIBWE with gallium. (a) Etch rate depending
on the laser fluence. (b) Normalized etch rate depending on the pulse number.
(a)(b)At least three etching characteristics are different for both
approaches: (i) M-LIBWE offers much higher etch rates than H-LIBWE but (ii)
requires much higher laser threshold fluences for etching. In addition, (iii)
strong incubation effects were detected at H-LIBWE whereas M-LIBWE features
almost no incubation effects [27, 56]. The higher threshold fluences at
M-LIBWE can be explained in parts by the higher reflectivity of the interface
and the higher thermal conductivity of the liquid metal absorber,
respectively [28, 35]. Because all other experimental parameters are
similar, the incubation must be linked to the used liquid that should cause an
additional laser irradiation-induced change of the interface region in order to
enhance the laser absorption either in the liquid or in the near-solid region.
The negligible incubation effect at M-LIBWE can be explained by the high
absorption coefficient and the high stability of the liquid metals. On the
other hand, the organic liquids and solutions used at H-LIBWE suffer from
photothermal and/or photochemical decomposition under intense pulsed UV laser
irradiation [57].The analysis of hydrocarbon solutions showed among a lot of soot a
number of decomposition products at HPLC-MS due to laser exposure. However, the
composition of the liquid is not altered in this extent to explain a much
higher (local) absorption coefficient of the liquid  [58]. The decomposition of
hydrocarbon liquids under UV laser irradiation can result in conjunction with
high temperatures to the formation of excited atoms or radicals. This can be of
interest when halogenated hydrocarbons are used that might form chemical
radicals that are able to etch solid materials directly [59].


## 3.2. Etch Characteristics for Different Materials and Absorbing Liquids

The etch characteristics,  for example etch rate
and surface morphology, depend on the used liquid for both classes of liquid
absorbers: hydrocarbon solutions and liquid metals. The etch rates of fused
silica are shown in Figure4 for two different absorbers in each case—gallium and
mercury and py:toluene and py:halogenated benzenes. In both cases, the
threshold fluence and the etch rate dependency are affected by the used liquid.
The comparison for M-LIBWE in Figure 4(b) shows that mercury has a less
etch threshold (Hg: 0.76 J/cm2; Ga:
1.3/2.1 J/cm2) and a slightly
lower etch rate than gallium. However, in both cases a linear rise of the etch
rate, no incubation effects, and similar etch pits with well-defined edges and
flat bottoms have been observed [27, 29]. The lower threshold of mercury
can be explained by the twofold lower thermal diffusion length (Hg:
0.66 μm; Ga: 1.24 μm at tp=25 nanoseconds).
The lower slope of the etch rate raise for mercury can be discussed also by the
different material properties of mercury.Etch rates of fused silica for different liquids at
248 nm laser pulse irradiation. (a) Etch rate of fused silica for toluene
with and without solved pyrene and for halogenated benzenes (fluorine and
chlorine benzene) at 300 pulses. (b) Etch rate for fused silica at 30 pulses
using gallium and mercury as liquid metals.
(a)
H-LIBWE(b)
M-LIBWEThe etch rate dependencies achieved for H-LIBWE
of fused silica using either pyrene-doped toluene or monohalogenated
benzenes   (0.5 M) are rather dissimilar; however, above a certain
laser fluence of about 0.7 J/cm2, similar etch
rates and a linear rise can be observed. Especially at low fluences, a much
lower rate and a higher slope of the rate were measured for the halogenated
solvent although the absorption coefficient was similar due to the high pyrene
concentration. It should be noted that the threshold fluence for the
pyrene-doped solutions is similar  (∼0.33 J/cm2) but
significantly less than the threshold for pure toluene  (0.45 J/cm2). The etch rate
with pure toluene also increases almost linearly but is only a bit less than that
achievable with pyrene. Though the threshold depends on the liquid absorption,
there is no linear correlation as the pyrene doping causes a sevenfold increase
of the absorption but the threshold is reduced only little.The laser-induced decomposition
of halogenated
hydrocarbons, however, can result in halogen radicals
[57, 58, 60, 61]
and can,
therefore, contribute to the etching [58, 62]. However, this does not
explain the lower etch rate if at halogenated organics the same processes
occur. Therefore, the halogen radicals may also affect the overall processes of
the etching, for example, in the liquid, vapour, bubble, and so forth, where
different chemical reactions and physical processes might occur.Similar to the liquid absorber, the properties of the material etched by
LIBWE affect the etch result. The SEM images in Figure5 depicting etch
pits in sapphire, calcium fluoride (CaF2), and fused silica show
this clearly. In contrast to the flat bottom and the well-defined edges of the
fused silica, the etched patterns of both sapphire and CaF2 feature
an uneven, grainy surface and an irregular edge.Surface morphology of H-LIBWE etched sapphire (a) and CaF2 (b) in comparison to the standard material fused silica (c).
(a)(b)(c)The main differences of the materials that can account for the
morphological changes are the thermal properties and the mechanical and
chemical resistance of the materials. For instance, the thermal conductivityk of the crystals (sapphire: 40 and CaF2: 9.7 W·(m·K)-1)
is much higher than that of fused silica (1.4 W·(m·K)-1).
Therefore, the higher heat diffusion length forces the heat dissipation and
does not allow as high heating rates and high temperatures as for fused silica.
With these arguments, the surface morphology of sapphire and CaF2 can be interpreted by melting, melt ejection, and resolidification of a
near-surface layer. The formation of microcracks in these brittle materials
must be taken into account in addition.


## 3.3. Modification of the Etched Surface at H-LIBWE

The surfaces of etched fused silica and quartz
samples were investigated with different analytical techniques such as XPS,
Raman spectroscopy, and RBS to study the process-induced near-surface chemical
and structural modifications [23, 39, 62, 63]. The kind and the amount of
the modification depend on the applied laser fluence and the pulse
number [58]. In general, with increasing laser fluence, the mainly found
carbon contaminations at low fluences reduce whereas the depth of structural
transformations increases.To study the impact of the near-surface material modifications on the
etching process, optical transmission measurements were performed. The inset of
Figure6 shows the transmission of an etched fused silica sample
(0.76 J/ccm2) depending on
the wavelength (200 nm to 800 nm). In general, a reduced transmission
in the UV is obvious and can also be observed for other fluences and pulse
numbers. According to  [58],
the spectrum can be
interpreted as a superposition of the spectra from carbon and defect-enriched
fused silica. Thus, the observed changes of the spectra taken at different etch
conditions also refer to alterations of the surface modification. The change of
the absorption at λ=248 nm with the applied laser fluence for
etched and wiped samples is shown in Figure 6, too. It should be noted
that surface modifications occur below the threshold and the modifications can
be divided in loosely adherent—that can be
whipped away—and incorporated
modifications. Together with the XPS and Raman spectroscopy results, the
loosely adherent modifications are mainly carbon or carbon products from the decomposition of the
organic absorber [58]. The near-surface fused  silica modifications can be removed completely by ion
beam sputtering of about 50 nm [58, 64]. This depth is similar to the
depth of structural defects found in quartz [63].Figure 6
Absorption of etched
fused silica surface depending on the laser fluence. The inset shows spectra of
an etched fused silica sample (F = 0.76 J/cm2) with a reduced
transmission in the UV.The remarkable high absorption of a thin (<50 nm) near-surface
region of about 30 to 40% is due to structural modifications of the fused
silica and a chemical modification of the surface or by a carbon-containing
film.


## 3.4. Etching of Submicron Patterns in Transparent Materials

From the basic results, it is clear that
micropatterning of fused silica can be easily achieved with different liquids
and laser sources. A lot of examples are known for different technical fields.
However, with the reduction of the feature size, the requirements for the
etching process are enhanced concerning the resolution of the etching process,
the homogeneity of the etching, and the smoothness of the surface.


### 3.4.1. Submicron Grating Etching in Fused Silica

These requirements for etching of
submicron patterns are fulfilled for fused silica for both H- and M-LIBWE. The
first experiments on etching high-resolution 1 D gratings with a period of∼750 nm are presented in   [44]. Depending on the average fluence and
the pulse number, grating depths of up to 180 nm with a nearly sinusoidal
profile were achieved. This profile mainly results from the sine interference
pattern together with the linear etch rate rise. However, additional to the
gratings an overall etching, that is, etching in the fringes minima at F∼0, was observed especially
at higher laser fluences and pulse numbers. Further experiments on overetching
of already prepatterned substrates showed that the modulation depth of
submicron patterns reduces at overetching with a homogeneous laser
beam [65]. The effect was discussed by the better heating of topographic
peaks by heat transport from the liquid but the effect seems to be too strong
to be completely explained therewith.Results on high-resolution etching of surface
relief line gratings in fused silica down to 104 nm periods presented in
[45, 46] show a reduction of the grating depth with the reduction of the
period. This finding can be discussed by the reduction of the modulation of the
interface temperature because of the thermal diffusion length of the material
given by LT=2⋅DT⋅t  with DT=k/ρ⋅cp.
The thermal diffusion lengths LT for fused silica and organic solvents are in the order of 0.18 and 0.09 μm
for the used 8-nanosecond 266 nm laser pulses [45, 46] and about
0.3 μm and 0.15 μm for pulse lengths of 25 nanoseconds, respectively. For pattern periods p of
similar or smaller than thermal diffusion length (e.g., ∼100 nm), the heat
transport smears interference patterns and only shallow gratings are etched
whereas ∼0.5 μm gratings can be etched proper. This means that
high-resolution patterns with high modulation depths can be hardly obtained for
materials—either the solid
and the liquid or both—with high LT.In Figure7, 2 D gratings in FS with periods of about 550 nm
and 780 nm are shown for H- and M-LIBWE in comparison. The maximal
achieved grating depth of ∼160 to 180 nm is similar in both cases
and is achieved near the threshold of grating etching. However, with M-LIBWE
gratings with a depth of 60 nm can be etched with one laser pulse and can enable submicron
patterning “on-the-fly” [48]. The thermal diffusion length of ∼0.6 μm
can result in a strong overetching effect especially at rising laser fluence
that can occur than already with the first  laser pulse.Submicron 2 D gratings with
periodsp∼550 nm and 780 nm etched in fused silica,
respectively. (a) Grating obtained by H-LIBWE with a py:acetone solution and (b)
grating etched on a prepatterned substrate (line width ∼7.5 μm,
prepattern depth ∼3μm) using mercury as absorber.
(a)(b)


### 3.4.2. Submicron Grating Etching by
Ultrashort Laser Pulses

To overcome the problem and enable high-quality etching of highly
conductive materials by LIBWE, shorter laser pulses must be applied. For 150-picosecond
pulse duration, for example, of the fourth harmonic (266 nm) of an EKSPLA
Nd:YAG-laser system, the thermal diffusion length is reduced by a factor
greater than 10 and results in thermal diffusion lengths of less than
200 nm for application-relevant highly conductive materials. For sapphire
with a rather high thermal diffusivityD of 1.63×10−5 m2/s, a length of
70 nm can be calculated.Surface relief gratings were inscribed in sapphire and in fused silica
as well as in different fluorides using H-LIBWE with 266 nm, 150-picosecond
laser pulses by applying different interference techniques, for example, phase
mask placed in contact to the front surface of the sample. As shown in Figure8,
the quality of surface relief gratings with an average depth of
∼50 nm etched in sapphire is similar to that achieved for fused
silica. However, the threshold laser fluence for etching of gratings is in
parts higher for sapphire due to the higher melting and evaporation temperature
and due to the, of course, higher thermal conductivity. Details for sapphire
grating etching are
given in  [47].H-LIBWE etched line gratings with a period of∼530 nm in fused silica (a) and sapphire (b). The SEM images show a
similar quality of the inscribed gratings.
(a)(b)Therefore, H-LIBWE with ultrashort laser pulses is favourable for
etching patterns in several dielectrics with periods shorter than 500 nm
due to the combination of the advantages of ultrashort processing and backside
etching [37]. The etching of well-developed 100 nm patterns with ultrashort
laser pulse H-LIBWE in fused silica was shown recently [66].


## 3.4.1. Submicron Grating Etching in Fused Silica

These requirements for etching of
submicron patterns are fulfilled for fused silica for both H- and M-LIBWE. The
first experiments on etching high-resolution 1 D gratings with a period of∼750 nm are presented in   [44]. Depending on the average fluence and
the pulse number, grating depths of up to 180 nm with a nearly sinusoidal
profile were achieved. This profile mainly results from the sine interference
pattern together with the linear etch rate rise. However, additional to the
gratings an overall etching, that is, etching in the fringes minima at F∼0, was observed especially
at higher laser fluences and pulse numbers. Further experiments on overetching
of already prepatterned substrates showed that the modulation depth of
submicron patterns reduces at overetching with a homogeneous laser
beam [65]. The effect was discussed by the better heating of topographic
peaks by heat transport from the liquid but the effect seems to be too strong
to be completely explained therewith.Results on high-resolution etching of surface
relief line gratings in fused silica down to 104 nm periods presented in
[45, 46] show a reduction of the grating depth with the reduction of the
period. This finding can be discussed by the reduction of the modulation of the
interface temperature because of the thermal diffusion length of the material
given by LT=2⋅DT⋅t  with DT=k/ρ⋅cp.
The thermal diffusion lengths LT for fused silica and organic solvents are in the order of 0.18 and 0.09 μm
for the used 8-nanosecond 266 nm laser pulses [45, 46] and about
0.3 μm and 0.15 μm for pulse lengths of 25 nanoseconds, respectively. For pattern periods p of
similar or smaller than thermal diffusion length (e.g., ∼100 nm), the heat
transport smears interference patterns and only shallow gratings are etched
whereas ∼0.5 μm gratings can be etched proper. This means that
high-resolution patterns with high modulation depths can be hardly obtained for
materials—either the solid
and the liquid or both—with high LT.In Figure7, 2 D gratings in FS with periods of about 550 nm
and 780 nm are shown for H- and M-LIBWE in comparison. The maximal
achieved grating depth of ∼160 to 180 nm is similar in both cases
and is achieved near the threshold of grating etching. However, with M-LIBWE
gratings with a depth of 60 nm can be etched with one laser pulse and can enable submicron
patterning “on-the-fly” [48]. The thermal diffusion length of ∼0.6 μm
can result in a strong overetching effect especially at rising laser fluence
that can occur than already with the first  laser pulse.Submicron 2 D gratings with
periodsp∼550 nm and 780 nm etched in fused silica,
respectively. (a) Grating obtained by H-LIBWE with a py:acetone solution and (b)
grating etched on a prepatterned substrate (line width ∼7.5 μm,
prepattern depth ∼3μm) using mercury as absorber.
(a)(b)


## 3.4.2. Submicron Grating Etching by
Ultrashort Laser Pulses

To overcome the problem and enable high-quality etching of highly
conductive materials by LIBWE, shorter laser pulses must be applied. For 150-picosecond
pulse duration, for example, of the fourth harmonic (266 nm) of an EKSPLA
Nd:YAG-laser system, the thermal diffusion length is reduced by a factor
greater than 10 and results in thermal diffusion lengths of less than
200 nm for application-relevant highly conductive materials. For sapphire
with a rather high thermal diffusivityD of 1.63×10−5 m2/s, a length of
70 nm can be calculated.Surface relief gratings were inscribed in sapphire and in fused silica
as well as in different fluorides using H-LIBWE with 266 nm, 150-picosecond
laser pulses by applying different interference techniques, for example, phase
mask placed in contact to the front surface of the sample. As shown in Figure8,
the quality of surface relief gratings with an average depth of
∼50 nm etched in sapphire is similar to that achieved for fused
silica. However, the threshold laser fluence for etching of gratings is in
parts higher for sapphire due to the higher melting and evaporation temperature
and due to the, of course, higher thermal conductivity. Details for sapphire
grating etching are
given in  [47].H-LIBWE etched line gratings with a period of∼530 nm in fused silica (a) and sapphire (b). The SEM images show a
similar quality of the inscribed gratings.
(a)(b)Therefore, H-LIBWE with ultrashort laser pulses is favourable for
etching patterns in several dielectrics with periods shorter than 500 nm
due to the combination of the advantages of ultrashort processing and backside
etching [37]. The etching of well-developed 100 nm patterns with ultrashort
laser pulse H-LIBWE in fused silica was shown recently [66].


## 4. Mechanism of Laser Etching

### 4.1. Processes at Laser Backside Etching

The irradiation of the solid-liquid interface by pulsed laser results in
a number of processes in both materials, for instance fast heating, transient
pressure, shock waves, melting and boiling, bubble formation and collapse, and
modification or decomposition of the materials. These processes are linked
together in a complex manner and finally cause materials erosion. However, it is generally
accepted that laser absorption and heating of the near-interface regions of
both materials is the main process for backside etching. Figure9 shows a
sketch of the processes in discussion that are involved in the etching
mechanism.Figure 9
Sketch of the main processes at LIBWE. These processes,
however, contribute to etching for both LIBWE versions in a different manner.In consequence of the laser heating during LIBWE, the softening and the
material [23] or phase transitions [32, 40, 50, 64] are discussed with regards
to materials erosion. The softened, destabilized, weakened, or even melted
material region near the surface might be expelled by mechanical forces
resulting from the fast heating, shockwaves, or bubble formation [23]. The
complete modeling of all processes is extremely complex as thermal, mechanical,
chemical, and transport processes interacting   each other within a very short time have to
be considered.


### 4.2. Modeling of Thermal Processes at Laser Backside Etching

Thermal processes are very important for backside etching processes with
nanosecond lasers but cannot be neglected for even shorter pulses. A correct
solution for the temperature field is very complex because a number of
processes are simultaneously coupled to the diffusive heat transfer. Therefore,
usually the simple models considering only heat diffusion are used.In Figure10, the laser absorption and the temperature profiles are
sketched together with the characteristic lengths (LT,LO=α−1) for H- and M-LIBWE. In addition, the laser
intensity IL and the laser pulse energy accounting for
interface heating EP(I) are shown. From
Figure 	10, it is clear that the absorbed laser
radiation is utilized in a different manner for heating at both LIBWE
approaches. Whereas at M-LIBWE (LOL≪LTL), the high thermal flux determines the
temperature evolution at H-LIBWE (LOL≫LTL), the laser energy absorption in the liquid
mainly affects the temperature distribution and only minor heat energy
dissipates from the interface region to the liquid. Therefore, the highest
temperature occurs at H- and M-LIBWE in the liquid and at the interface,
respectively. It is also seen, that the temperature profiles at different times
(t1<tp and tp) reflect the
different processes.Sketches of the temperature profiles, the laser
intensity, and the absorbed laser energy together with the characteristic
lengths are shown for H- and M-LIBWE.Ep is the laser pulse energy causing the heating of the interface.
(a)(b)Although the primary laser-matter interaction upon ultrashort laser
irradiation is often different due to the additional processes induced by the
short pulses, for example, multiphoton absorption and other nonlinear
phenomena, the absorbed energy finally is transformed into heat and can induce
similar processes as with nanosecond
lasers.


### 4.3. Thermal Calculations for LIBWE

For the rough estimation of the influence of experimental parameters on
the etching process, simple thermal models have been developed. As only thermal
processes are considered—this does not
include the processes of material etching itself—they are only
suitable to estimate specific values, for example, the threshold fluenceFth or a critical interface temperature.
In such models, regularly constant material parameters and no phase transitions
are presumed.Analytical solutions of the heat equation for surfaces are known for the
approximations of fixed coefficients, a constant laser power, and neglecting
phase transitions [2, 67]. Further, Carslow/Jaeger gives a solution for heating of an internal
interface for interface absorption that can be well applied for M-LIBWE
considering the reflectivity and the absorption of the interface [67].This solution is not valid for H-LIBWE because the absorption
coefficient at H-LIBWE is much less, a remarkable interface absorption was
measured, and(αL)−1≫LTL.
However, an approximation for calculating the interface temperature TI  at H-LIBWE is given in
[64]. This approximation combines the analytical solution for the interface
absorption with a caloric approach accounting for the absorption in the liquid.An analytical solution forT1   for LIBWE for the heating by the laser pulse with a duration τp (0≤t≤τp) considering both volume and interface
absorption is given in  [68] to be(1)TI=DLkFS⋅DL+kL⋅DFS⋅{IVL⋅αL4⋅LTL⋅LTFS+IIFS⋅LTFSπ}, whereas  D,  k,
and  LT denote the thermal diffusivity, the thermal
conductivity, and the heat diffusion length, respectively. II and IV represent the absorbed laser power at the interface and into the liquid volume
and α  stands
for the absorption coefficient. The superscripts FS and L indicate the
fused silica and the liquid that can be either a metal or a hydrocarbon solution,
respectively.The most important outcomes from the models are that higher absorption
coefficients of the liquid and/or an elevated absorption of the interface
result in higher interface temperatures. A low thermal conductivity and short
pulses are additional opportunities to get higher temperatures. Calculated
laser-induced temperatures across a solid-liquid interface at H-LIBWE are shown
in Figure11. In the left side (a) shows analytically and numerically
calculated temperatures of the fused silica/py:toluene interface with and
without interface absorption in comparison and demonstrates the large effect of
an additional interface absorption. For example, due to 10% interface
absorption, the temperature rises more then twice and exceeds the boiling temperature
of fused silica. Although the temperature gets higher—resulting from
the additional interface absorption raise—also for sapphire
samples (dashed lines in Figure 11), the effect is much less for sapphire than for fused silica due
to the significant higher thermal conductivity (kFS∼1.4 and kSp∼40 W/m·K) and does not result in
temperatures exceeding the critical temperature for etching, for example, the
boiling temperature. Therefore, the low surface quality observed for
dielectrics with a high thermal conductivity can be explained by the
temperatures field. However, with shorter pulses and a sufficient interface
absorption, the melting and boiling of the sapphire surface can be easily
achieved as shown in Figure 11(b) in addition.Calculated temperature profiles across the solid/liquid
interface for H-LIBWE (248 nm, py:toluene: (a) analytically and
numerically calculated temperatures for fused silica samples of different
interface absorption values of 0, 10, and 50% and (b) sapphire sample for two
laser pulse lengths of 15 nanoseconds and 150 picoseconds and
different interface absorptions.
(a)(b)Combining the experimental found interface absorption values with the
experimental applied laser exposure parameters, the interface temperature for
H-LIBWE at the multipulse threshold fluence for laser etching of fused silica
with a 0.5 M py:toluene absorber was calculated using the mentioned
models. Temperatures of more than 4000 K were calculated at Fth = 0.32 J/cm2 mainly due to
the interface absorption of ∼35% [62]. These extremely high
temperatures already at the threshold cause highly dynamic processes of phase
transitions and material etching. Furthermore, as the peak power of the
(excimer) laser pulse is at the beginning of the pulse and much higher than the
average pulse (F/tp) used for the calculations, it is expected that the etching
(material removing) occurs within the pulse length. The high temperatures and
the expected fast (explosive) processes resemble laser ablation of polymers.
However, in the case of H-LIBWE, the ablation-like processes are limited to the
near-surface volume that is modified having a very high absorbance. Therefore,
the etch rate at H-LIBWE is not predetermined by the thermal diffusion into the
fused silica but is
given by the amount and the depth of the surface modification.The comparison of the experimental found etch thresholds at M-LIBWE (Ga,
FS,λ=248 nm) provides a basically different result [ 27, 28, 29]. Here the
first threshold fluence correlates with the melting temperature of fused silica
whereas at the second threshold the boiling temperature is exceeded. Some other
characteristics of Ga-LIBWE, such as the high etch rates and the smooth,
wavelike etched surface with rim-like borders indication melting and
resolidification, point at a different etch mechanism. A more evaporation-like
mechanism can be suggested from the comparison of the etching efficiency with
the only three times larger volumetric energy density for fused silica
evaporation.


### 4.4. Mechanism of Backside Etching

The discussion of the experimental results with respect to thermal
models shows that basically at least two mechanisms of LIBWE have to be
distinguished. The first model bases on the heating by a highly absorbing
material without significant modification of the solid due to primary or
secondary processes at etching, that is, M-LIBWE, and the second mechanism is
heavily affected by surface modifications due to secondary processes in
combination with fast thermal processes at the solid-liquid interface, that is,
H-LIBWE. Additionally, other process characteristics, for example, the
confinement of the secondary processes by the absorber, may strongly influence
the mechanism at all as the comparison of backside ablation in water/air
confinement has been shown [69]. Therefore, the interaction strength of
secondary processes, for example, shock waves, liquid decomposition and
material deposition, laser-induced plasma and rapid melting and
resolidification, with the solid surface depends also on material
characteristics
of the absorber (liquid), the possible and most likely
paths of excitation and relaxation,  and the interaction time; all effects are
influenced by the confinement.The sketch shown in Figure12 gives an overview on the mechanism
and the near-surface processes essential for hydrocarbon laser-induced backside
wet etching. Here the main focus is on the surface whereas the other processes
already mentioned and shown in the figure are also going on.Figure 12
Schematic sketch of the processes at H-LIBWE. In
particular, the changes of the surface modification at prolonged laser irradiation
are shown and probably explain the observed incubation effects at H-LIBWE. The gray level is a measure of the strength.At the first laser pulse with a fluence above the etching threshold Fth(∞), the laser radiation is absorbed
by the organic liquid and heats it up to temperatures below the melting
temperature of the solid. However, the organic solution vaporizes and decomposes due to
photothermal and photochemical processes so that the formation of bubbles is
forced. Due to heating, decomposition, and bubble formation, the surface is
modified increasingly with the pulse number by liquid decomposition products, for
example, carbon, resulting in a thin highly absorbing film on top of the solid.
Due to this, the solid surface temperature increases with the pulse number and
exceeds a critical temperature Tc  at Ninc. At this state,
the transparent solid material is etched [58]. However, as has been shown,
the temperatures that can be achieved at etching are very high so that
ablation-like processes occur at the solid surface that is confined by the
liquid. This confinement may enhance the interaction of secondary processes
with the solid and results in a modified near-surface region of the solid with
a high absorption as shown in the figure. This modified near-surface solid
region highly absorbs the UV laser radiation and results in an efficient
interface heating. At this point the process of surface modification is
self-maintaining but needs the absorbing liquid. This general view is more or
less changed by the experimental conditions used.With this extended model considering process-induced surface
modifications, some experimental findings can be explained. So the threshold
fluence correlates at different UV wavelengths not with the absorption
coefficients of the liquid but with the measured absorption in the modified
layer according to the extended mechanism. Probably in the same manner the
neglectable change of the etching threshold with the absorption coefficient of
the liquid absorber (due to dye, e.g., pyrene, admixture) can be explained
because the threshold is mainly given by the enhancement of the absorption by
carbon-film surface modification from decomposition processes that also appear
without dyes. The concrete processes of solid modifications depend, of course,
on the composition of the organic liquid absorber whereby the different
thresholds can be explained, for instance.


## 4.1. Processes at Laser Backside Etching

The irradiation of the solid-liquid interface by pulsed laser results in
a number of processes in both materials, for instance fast heating, transient
pressure, shock waves, melting and boiling, bubble formation and collapse, and
modification or decomposition of the materials. These processes are linked
together in a complex manner and finally cause materials erosion. However, it is generally
accepted that laser absorption and heating of the near-interface regions of
both materials is the main process for backside etching. Figure9 shows a
sketch of the processes in discussion that are involved in the etching
mechanism.Figure 9
Sketch of the main processes at LIBWE. These processes,
however, contribute to etching for both LIBWE versions in a different manner.In consequence of the laser heating during LIBWE, the softening and the
material [23] or phase transitions [32, 40, 50, 64] are discussed with regards
to materials erosion. The softened, destabilized, weakened, or even melted
material region near the surface might be expelled by mechanical forces
resulting from the fast heating, shockwaves, or bubble formation [23]. The
complete modeling of all processes is extremely complex as thermal, mechanical,
chemical, and transport processes interacting   each other within a very short time have to
be considered.


## 4.2. Modeling of Thermal Processes at Laser Backside Etching

Thermal processes are very important for backside etching processes with
nanosecond lasers but cannot be neglected for even shorter pulses. A correct
solution for the temperature field is very complex because a number of
processes are simultaneously coupled to the diffusive heat transfer. Therefore,
usually the simple models considering only heat diffusion are used.In Figure10, the laser absorption and the temperature profiles are
sketched together with the characteristic lengths (LT,LO=α−1) for H- and M-LIBWE. In addition, the laser
intensity IL and the laser pulse energy accounting for
interface heating EP(I) are shown. From
Figure 	10, it is clear that the absorbed laser
radiation is utilized in a different manner for heating at both LIBWE
approaches. Whereas at M-LIBWE (LOL≪LTL), the high thermal flux determines the
temperature evolution at H-LIBWE (LOL≫LTL), the laser energy absorption in the liquid
mainly affects the temperature distribution and only minor heat energy
dissipates from the interface region to the liquid. Therefore, the highest
temperature occurs at H- and M-LIBWE in the liquid and at the interface,
respectively. It is also seen, that the temperature profiles at different times
(t1<tp and tp) reflect the
different processes.Sketches of the temperature profiles, the laser
intensity, and the absorbed laser energy together with the characteristic
lengths are shown for H- and M-LIBWE.Ep is the laser pulse energy causing the heating of the interface.
(a)(b)Although the primary laser-matter interaction upon ultrashort laser
irradiation is often different due to the additional processes induced by the
short pulses, for example, multiphoton absorption and other nonlinear
phenomena, the absorbed energy finally is transformed into heat and can induce
similar processes as with nanosecond
lasers.


## 4.3. Thermal Calculations for LIBWE

For the rough estimation of the influence of experimental parameters on
the etching process, simple thermal models have been developed. As only thermal
processes are considered—this does not
include the processes of material etching itself—they are only
suitable to estimate specific values, for example, the threshold fluenceFth or a critical interface temperature.
In such models, regularly constant material parameters and no phase transitions
are presumed.Analytical solutions of the heat equation for surfaces are known for the
approximations of fixed coefficients, a constant laser power, and neglecting
phase transitions [2, 67]. Further, Carslow/Jaeger gives a solution for heating of an internal
interface for interface absorption that can be well applied for M-LIBWE
considering the reflectivity and the absorption of the interface [67].This solution is not valid for H-LIBWE because the absorption
coefficient at H-LIBWE is much less, a remarkable interface absorption was
measured, and(αL)−1≫LTL.
However, an approximation for calculating the interface temperature TI  at H-LIBWE is given in
[64]. This approximation combines the analytical solution for the interface
absorption with a caloric approach accounting for the absorption in the liquid.An analytical solution forT1   for LIBWE for the heating by the laser pulse with a duration τp (0≤t≤τp) considering both volume and interface
absorption is given in  [68] to be(1)TI=DLkFS⋅DL+kL⋅DFS⋅{IVL⋅αL4⋅LTL⋅LTFS+IIFS⋅LTFSπ}, whereas  D,  k,
and  LT denote the thermal diffusivity, the thermal
conductivity, and the heat diffusion length, respectively. II and IV represent the absorbed laser power at the interface and into the liquid volume
and α  stands
for the absorption coefficient. The superscripts FS and L indicate the
fused silica and the liquid that can be either a metal or a hydrocarbon solution,
respectively.The most important outcomes from the models are that higher absorption
coefficients of the liquid and/or an elevated absorption of the interface
result in higher interface temperatures. A low thermal conductivity and short
pulses are additional opportunities to get higher temperatures. Calculated
laser-induced temperatures across a solid-liquid interface at H-LIBWE are shown
in Figure11. In the left side (a) shows analytically and numerically
calculated temperatures of the fused silica/py:toluene interface with and
without interface absorption in comparison and demonstrates the large effect of
an additional interface absorption. For example, due to 10% interface
absorption, the temperature rises more then twice and exceeds the boiling temperature
of fused silica. Although the temperature gets higher—resulting from
the additional interface absorption raise—also for sapphire
samples (dashed lines in Figure 11), the effect is much less for sapphire than for fused silica due
to the significant higher thermal conductivity (kFS∼1.4 and kSp∼40 W/m·K) and does not result in
temperatures exceeding the critical temperature for etching, for example, the
boiling temperature. Therefore, the low surface quality observed for
dielectrics with a high thermal conductivity can be explained by the
temperatures field. However, with shorter pulses and a sufficient interface
absorption, the melting and boiling of the sapphire surface can be easily
achieved as shown in Figure 11(b) in addition.Calculated temperature profiles across the solid/liquid
interface for H-LIBWE (248 nm, py:toluene: (a) analytically and
numerically calculated temperatures for fused silica samples of different
interface absorption values of 0, 10, and 50% and (b) sapphire sample for two
laser pulse lengths of 15 nanoseconds and 150 picoseconds and
different interface absorptions.
(a)(b)Combining the experimental found interface absorption values with the
experimental applied laser exposure parameters, the interface temperature for
H-LIBWE at the multipulse threshold fluence for laser etching of fused silica
with a 0.5 M py:toluene absorber was calculated using the mentioned
models. Temperatures of more than 4000 K were calculated at Fth = 0.32 J/cm2 mainly due to
the interface absorption of ∼35% [62]. These extremely high
temperatures already at the threshold cause highly dynamic processes of phase
transitions and material etching. Furthermore, as the peak power of the
(excimer) laser pulse is at the beginning of the pulse and much higher than the
average pulse (F/tp) used for the calculations, it is expected that the etching
(material removing) occurs within the pulse length. The high temperatures and
the expected fast (explosive) processes resemble laser ablation of polymers.
However, in the case of H-LIBWE, the ablation-like processes are limited to the
near-surface volume that is modified having a very high absorbance. Therefore,
the etch rate at H-LIBWE is not predetermined by the thermal diffusion into the
fused silica but is
given by the amount and the depth of the surface modification.The comparison of the experimental found etch thresholds at M-LIBWE (Ga,
FS,λ=248 nm) provides a basically different result [ 27, 28, 29]. Here the
first threshold fluence correlates with the melting temperature of fused silica
whereas at the second threshold the boiling temperature is exceeded. Some other
characteristics of Ga-LIBWE, such as the high etch rates and the smooth,
wavelike etched surface with rim-like borders indication melting and
resolidification, point at a different etch mechanism. A more evaporation-like
mechanism can be suggested from the comparison of the etching efficiency with
the only three times larger volumetric energy density for fused silica
evaporation.


## 4.4. Mechanism of Backside Etching

The discussion of the experimental results with respect to thermal
models shows that basically at least two mechanisms of LIBWE have to be
distinguished. The first model bases on the heating by a highly absorbing
material without significant modification of the solid due to primary or
secondary processes at etching, that is, M-LIBWE, and the second mechanism is
heavily affected by surface modifications due to secondary processes in
combination with fast thermal processes at the solid-liquid interface, that is,
H-LIBWE. Additionally, other process characteristics, for example, the
confinement of the secondary processes by the absorber, may strongly influence
the mechanism at all as the comparison of backside ablation in water/air
confinement has been shown [69]. Therefore, the interaction strength of
secondary processes, for example, shock waves, liquid decomposition and
material deposition, laser-induced plasma and rapid melting and
resolidification, with the solid surface depends also on material
characteristics
of the absorber (liquid), the possible and most likely
paths of excitation and relaxation,  and the interaction time; all effects are
influenced by the confinement.The sketch shown in Figure12 gives an overview on the mechanism
and the near-surface processes essential for hydrocarbon laser-induced backside
wet etching. Here the main focus is on the surface whereas the other processes
already mentioned and shown in the figure are also going on.Figure 12
Schematic sketch of the processes at H-LIBWE. In
particular, the changes of the surface modification at prolonged laser irradiation
are shown and probably explain the observed incubation effects at H-LIBWE. The gray level is a measure of the strength.At the first laser pulse with a fluence above the etching threshold Fth(∞), the laser radiation is absorbed
by the organic liquid and heats it up to temperatures below the melting
temperature of the solid. However, the organic solution vaporizes and decomposes due to
photothermal and photochemical processes so that the formation of bubbles is
forced. Due to heating, decomposition, and bubble formation, the surface is
modified increasingly with the pulse number by liquid decomposition products, for
example, carbon, resulting in a thin highly absorbing film on top of the solid.
Due to this, the solid surface temperature increases with the pulse number and
exceeds a critical temperature Tc  at Ninc. At this state,
the transparent solid material is etched [58]. However, as has been shown,
the temperatures that can be achieved at etching are very high so that
ablation-like processes occur at the solid surface that is confined by the
liquid. This confinement may enhance the interaction of secondary processes
with the solid and results in a modified near-surface region of the solid with
a high absorption as shown in the figure. This modified near-surface solid
region highly absorbs the UV laser radiation and results in an efficient
interface heating. At this point the process of surface modification is
self-maintaining but needs the absorbing liquid. This general view is more or
less changed by the experimental conditions used.With this extended model considering process-induced surface
modifications, some experimental findings can be explained. So the threshold
fluence correlates at different UV wavelengths not with the absorption
coefficients of the liquid but with the measured absorption in the modified
layer according to the extended mechanism. Probably in the same manner the
neglectable change of the etching threshold with the absorption coefficient of
the liquid absorber (due to dye, e.g., pyrene, admixture) can be explained
because the threshold is mainly given by the enhancement of the absorption by
carbon-film surface modification from decomposition processes that also appear
without dyes. The concrete processes of solid modifications depend, of course,
on the composition of the organic liquid absorber whereby the different
thresholds can be explained, for instance.


## 5. Summary

High quality etching of transparent materials with pulsed laser
radiation can be achieved by two different LIBWE approaches using hydrocarbon
or metallic liquid absorbers. The processing parameters, the achievable
patterns, and the surface morphology depend on the used absorber. Hence, the
processing parameters such as wavelength, liquid absorber, laser fluence, and
so forth must be well chosen with respect to the solid material and the
processing goal. The thermal modeling of H-LIBWE shows that the highly
absorbing surface modification will cause extreme high temperatures of the modified solid
surface that probably results in ablation-like material erosion processes.
Submicron gratings can be etched by LIBWE not only in thermal low conducting
materials such as fused silica using organic or metallic absorbers but also in
crystalline materials, for example, sapphire, applying well-chosen parameters
to meet the preconditions for surface modification and high-modulation surface
heating of the transparent sample.



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*Source: 170632-2008-11-16.xml*