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<reference>
Optical ridge waveguides in lithium niobate and
potassium titanyl phosphate

Von der Fakultät für Elektrotechnik
der Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg
zur Erlangung des akademischen Grades eines Doktor-Ingenieur
genehmigte

DISSERTATION
vorgelegt von

Martin Volk

aus Oberwesel
Hamburg 2018

Tag der mündlichen Prüfung: 08.02.2019
Gutachter: 1. Univ.-Prof. Dr. rer. nat. Detlef Kip
2. Univ.-Prof. Dr.-Ing. Christian Schäffer

Contents

1

Introduction and Motivation

1

2

Fundamental concepts and methods

7

2.1

Wave equation and finite element methods . . . . . . . . . . . . . .

7

2.2

Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.3

Losses in optical waveguides . . . . . . . . . . . . . . . . . . . . . .

10

2.4

Measurement of losses in optical waveguides . . . . . . . . . . . . .

14

2.5

Nonlinear frequency conversion . . . . . . . . . . . . . . . . . . . .

16

2.6

Properties of lithium niobate and potassium titanyl phosphate . . .

24

2.7

Electric field poling of lithium niobate . . . . . . . . . . . . . . . . .

28

2.8

The diamond blade dicing saw . . . . . . . . . . . . . . . . . . . . .

31

2.9

Wafer direct bonding and crystal ion slicing . . . . . . . . . . . . . .

34

3

4

5

Ridge waveguides in lithium niobate thin films

45

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.2

Ridge waveguides in LNOI from cooperation partner . . . . . . . .

46

3.3

Fabrication of LNOI . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.4

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

Electric field poling of lithium niobate

59

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.2

The setup for ferroelectric poling . . . . . . . . . . . . . . . . . . . .

60

4.3

Periodic poling of congruent lithium niobate with gel electrodes . .

61

4.4

Periodic poling of congruent lithium niobate with Cr electrodes . .

66

4.5

Periodic poling of Ti-diffused lithium niobate ridge waveguides . .

69

4.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Ridge waveguides in z-cut KTP

73

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

5.2

Fabrication of ridge waveguides in z-cut KTP . . . . . . . . . . . . .

75

III

IV

CONTENTS
5.3
5.4

Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . .

76
88

6

Side-exchanged ridge waveguides in KTP
89
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Fabrication of side-exchanged ridge waveguides . . . . . . . . . . . 91
6.3 Characterization of side-exchanged waveguides . . . . . . . . . . . 95
6.4 Thermal stability of side-exchanged waveguides . . . . . . . . . . . 97
6.5 Modeling and simulations . . . . . . . . . . . . . . . . . . . . . . . . 99
6.6 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 102

7

Summary and conclusion

105

Acknowledgment

107

List of publications

109

Bibliography

111

Chapter 1
Introduction and Motivation
This thesis treats the fabrication of optical ridge waveguides in lithium niobate
(LN, LiNbO3 ) and potassium titanyl phosphate (KTP, KTiOPO4 ) by use of a diamond blade dicing saw and their linear and nonlinear optical characterization.
The used materials, lithium niobate and KTP, are both ferroelectric crystals which
have found widespread application due to their favorable nonlinear optic, electrooptic and piezoelectric properties. Lithium niobate is widely used for fabrication
of surface acoustic wave devices, such as filters and transducers, that are needed
in all types of radio frequency devices, for instance cellular phones, Wi-Fi appliances and televisions [1, 2]. In the field of optics, lithium niobate is used for
fabrication of electro-optical modulators for long-haul communication or nonlinear optical frequency converters [3–5]. KTP crystals are also used as optical
frequency converters and are particularly widespread for frequency doubling of
neodymium lasers from 1064 nm wavelength to 532 nm [6, 7]. This technique of
obtaining green laser light is for example commonly used in green laser pointers
and in laser sources for medical therapy [8]. Further, it is a preferred material for
generation of entangled photons at telecommunication wavelength of ∼1550 nm
for quantum optics and quantum cryptography because it allows for an especially
large phasematching bandwidth [9, 10].
Waveguides can be used to guide an optical wave from one optical component to another and thereby integrate and miniaturize optical systems. In
waveguides optical waves can be kept tightly confined over longer distance with
low propagation loss. This is advantageous in optical frequency conversion because the conversion efficiency is proportional to intensity (and therefore inverseproportional to the mode area) and proportional to the squared interaction length.
It is for example also beneficial in optical modulators. Here, the electrodes that
surround a waveguide can be placed closer than those of a modulator for a freebeam. Hence, lower voltages are sufficient to achieve a needed field strength.
1

2

CHAPTER 1. INTRODUCTION AND MOTIVATION

The most widespread methods for waveguide fabrication in lithium niobate
and KTP are titanium diffusion or proton exchange [11, 12], and rubidium exchange [6, 13], respectively. In these methods, a photolithographically structured
Ti pattern is in-diffused, or ions are in-diffused through a photolithographically
defined mask. The diffused ions have higher polarizability, and hence their concentration profile goes along with an increase of the refractive index resulting in
light guiding. These diffused waveguides confine light in both horizontal and
vertical direction.
Also methods exist that result in a planar waveguide formation and need further processing to enable guiding in lateral direction. Among such planar waveguides are crystalline thin films, which are bonded onto a material of lower refractive index [14], epitaxially grown thin films [15, 16] or crystalline layers that
are separated from bulk by a layer of implanted ions with decreased refractive
index [17]. Lateral confinement can be achieved in these planar waveguides
by definition of ridges. Optical modes are then strongly confined in horizontal direction due to the refractive index step from material to air. Ridges can be
formed by laser ablation [18], wet etching [19], dry etching [20, 21] or mechanical grinding [22–24]. Laser ablation results in typical surface roughness of the
order of 500 nm (RMS) [18] and this goes along with relatively high attenuation.
Wet etching of crystalline material can result in quite smooth surfaces and low
waveguide losses [19], though sharp edges can occur in bends because different
faces of crystalline materials are commonly etched at different rates. Dry etching
includes methods for material removal by bombardment with charged ions or
neutral particles. The character of the etching process can be of physical nature,
i. e. sputtering of the surface through impact of swift ions. The process can have a
chemical nature, i. e. material removal through a chemical reaction with free radicals and formation of a volatile product. Or it can combine physical and chemical
etching. When the present work began in 2013 and until we presented our results
on cut ridge waveguides, dry etched waveguides in lithium niobate thin films of
thickness . 1 µm had rather high losses of 10 − 17 dB/cm which were commonly
attributed to surface roughness [20, 21]. By now optimized dry-etching processes
have enabled definition of ridge waveguides in lithium niobate thin films with
very low losses of 0.3 − 0.4 dB/cm [25, 26].
Commonly, wafer saws are used to singulate thousands of electronic semiconductor chips that are fabricated in parallel on a single wafer [27, 28]. In these
saws a blade with synthetic diamonds in a polymer or metal matrix cuts wafers
that are mounted on a translation stage. Various blades of different width can be

3
acquired that are appropriate for different materials. During dicing it is important to avoid chipping and microcracks because weakened dies might otherwise
break in a following mounting or packaging step. Further, wafer saws are required to precisely cut narrow kerfs along predefined streets. At the same time
cutting speed needs to be high and wear low to make the singulation process
economic. These requirements, which are fulfilled by modern automated wafer
saws, make them ideally suited for preparation of low-roughness, low-loss optical ridge waveguides in crystalline materials. It shall also be mentioned that
wafer saws are standard equipment in semiconductor fabrication plants and well
equipped research facilities; and they are hence easily accessible.
Wafer saws were first used around 2001 by Kawaguchi et al. from NGK I N SULATORS and M ATSUSHITA E LECTRIC I NDUSTRIAL C O . LTD (PANASONIC ) for
preparation of ridge waveguides [29, 30], and also by Nishida et al. from NTT
P HOTONICS L ABORATORIES [22,23]. They bonded a lithium niobate wafer to material of lower refractive index, lapped and polished it down to 3 − 10 µm thickness, and then defined ridges. Based on these ridge waveguides, frequency conversion modules are available from NTT Electronics1 . Kishimoto and Nakamura
from O KI E LECTRIC I NDUSTRY C O . LTD . [31] and Sun and Xu from M C M AS TER U NIVERSITY , Canada [32] prepared cut ridge waveguides in planar protonexchanged lithium niobate. Courjal et al. from F EMTO -ST I NSTITUTE in Besancon,
France prepared ridge waveguides in lithium niobate of especially large aspect
ratio, with 1 µm top width and height of 500 µm [24]. Further they presented
a technique to prepare tapers for ridge waveguides by use of a wafer saw to
improve in-coupling into narrow ridge waveguides [33]. At H ELMUT S CHMIDT
U NIVERSITY in Hamburg, Germany optical ridge waveguides have been formed
in ion implanted KTP by use of diamond blade dicing saw [34]. In Hamburg as
well optical ridge waveguides have been cut in Nd-doped yttrium aluminum garnet (Nd:YAG) and Nd-doped sapphire, materials that possess high Mohs hardness of 8.5 to 9 [35, 36].
The ridge geometry allows to strongly confine optical modes because of the
large step of refractive index between waveguide material and surrounding air.
Especially when ridge waveguides are formed in a thin-film material, that is
bonded to a lower-index substrate, strong confinement and good overlap between interacting modes of different wavelengths can be achieved. This allows
for high conversion efficiency in frequency conversion processes [23, 30, 37]. A
drawback of ridge definition by use of a diamond blade saw is that it only allows
1 Model: WH-0780-000-A-B-C, WH-0780-000-F-B-C, WS-0578-000-A-B-C

4

CHAPTER 1. INTRODUCTION AND MOTIVATION

for straight waveguides. It is not possible to cut bends or splitters, which are for
example necessary for modulators.
The present work discusses research results on ridge waveguides that are
formed in different materials by use of a wafer saw. In chapter 2 theory and
fundamentals are reviewed briefly, which are helpful for understanding the following chapters on experimental and simulation results (chapters 3-6). These
findings have already been presented on conferences and published in journals
[38–43]. It follows a summary and conclusion in chapter 7.
Chapter 3 reviews our results on fabrication of lithium niobate thin films via
crystal ion slicing, ridge waveguide definition and characterization. The crystal ion slicing process consists of H+ ion implantation to a depth of ∼1 µm in
a LN substrate, bonding this substrate to a material of lower refractive index,
and exfoliation of the thin film by heat treatment [14, 44, 45]. A 1 µm thick film of
monocrystalline lithium niobate on a material of lower refractive index is formed.
Into these thin films we cut ridge waveguides. For a 2.1 µm wide and 9 mm long
waveguide we measured propagation loss of 1.2 dB/cm (2.8 dB/cm) for TE (TM)
polarization at a wavelength of 1550 nm. These values are below losses that other
groups achieved at that time for comparable waveguides that they had prepared
by dry-etching [20, 21]. Research in the material platform of lithium niobate thin
films, which is also termed lithium-niobate-on-insulator (LNOI), is motivated by
the high refractive index step between the core material and the surrounding
cladding. This high index step allows for particularly strong mode confinement
and hence high efficiency in frequency conversion processes [14, 46]. Further, it
allows much narrower bending radii of waveguides of about 10 µm instead of
10 mm in conventional waveguides. This allows for a strong reduction of the
footprint of optical components and thus enables higher integration density.
A special type of optical ridge waveguide in lithium niobate has been presented by Suntsov et al. [47]. These waveguides are prepared by in-diffusion of
titanium (and erbium to provide amplification) through the three faces (top and
two sides) of a ridge waveguide and profit from a concentration profile that is
more homogeneous than those of the waveguides diffused from top only [47, 48].
Due to good overlap of modes of different wavelength, these waveguides could
also be advantageous for frequency conversion. To enable efficient frequency
conversion, lithium niobate needs to be periodically poled. This is achieved by
photolithographic patterning of electrodes on the crystal and application of high
voltage [49]. In chapter 4 we discuss results on periodic poling of virgin lithium
niobate substrates and further demonstrate that it is possible to periodically pole

5
Ti-diffused ridge waveguides. Periodic poling of samples with ridge waveguides
is challenging because care needs to be taken during several process steps to not
destroy the fragile ridges. Further, the electric field is influenced by the thickness
variation due to the ridges and grooves, as well as by the Ti diffusion profile. It is
not reasonable to periodically pole lithium niobate wafers first and subsequently
produce the Ti-diffused ridges because during Ti-diffusion a domain inverted
layer is formed [50, 51].
Potassium titanyl phosphate possesses favorable nonlinear and electro-optical
properties, wide transparency range, high damage threshold and good thermal
stability [6]. It is therefore a preferred material for frequency conversion applications and modulators. Further, it has attracted attention because it allows to
generate particularly indistinguishable entangled photons at telecommunication
wavelength for quantum optics and quantum cryptography [9, 10]. The most
common method for waveguide preparation in KTP is Rb-exchange through a
photolithographically patterned mask [13]. Since ridge geometry can provide
advantages over conventional channel waveguide geometry due to stronger confinement, we investigated whether it is possible to combine the methods of Rbexchange with ridge definition by use of a wafer saw. In the exchange process,
K+ ions are replaced for Rb+ ions and at the surface KTiOPO4 is thus converted
to K1− x Rbx TiOPO4 with x ≈ 1. This causes tensions in the surface-near material and makes the crystal more brittle. Still, we found parameters that allow
for definition of chipping- and fracture-free ridge waveguides with low surface
roughness of 1 − 2 nm and attenuation of 1.3 − 1.6 dB/cm. Results of this research
project, that we performed in collaboration with the I NTEGRATED Q UANTUM O P TICS workgroup of Prof. Silberhorn from U NIVERSITY OF PADERBORN , are given
in chapter 5. The obtained findings helped to prepare ridge waveguides in periodically poled KTP in a following work for second harmonic generation in the
ultraviolet [52].
In KTP Rb and Ba ions are only mobile along the crystallographic z axis [6]
and we used this characteristic for preparation of a novel type of ridge waveguide. For fabrication of these waveguides we defined ridges into KTP substrates
that have their z axis lying perpendicularly to the waveguide in the substrate’s
surface plane. When these samples are immersed into a melt of rubidium and
barium nitrate, Rb and Ba ions diffuse through the ridge flanks along the z axis
into the waveguide. After annealing homogeneous Rb and Ba concentrations are
obtained in the rectangular waveguide cross section, and the refractive index is
homogeneously increased in this region. This step-like refractive index profile re-

6

CHAPTER 1. INTRODUCTION AND MOTIVATION

sults in an improved overlap of modes of different wavelength and can hence enable higher conversion efficiency in frequency conversion processes. In contrast,
in conventional diffusion profiles, modes of lower wavelength are pulled closer
to the surface while modes of longer wavelength extend further into the depth.
Another advantage of the novel waveguides is that they are resistant against elevated temperature since the Rb and Ba ions cannot diffuse into depth like in
conventional waveguides. This allows to operate the waveguides at higher temperature and thereby avoid gray tracking [53]. Experimental results are discussed
in detail in chapter 6.

Chapter 2
Fundamental concepts and methods
In the following chapter theoretical fundamentals are reviewed which are necessary to follow discussions in the subsequent chapters. These fundamentals include theory of guided waves, nonlinear optics and properties of the used crystalline materials. Further, experimental methods of waveguide fabrication and
characterization are discussed. Among the applied fabrication methods are diffusion processes, wafer direct bonding, use of a diamond blade dicing saw, and
electric field poling.

2.1

Wave equation and finite element methods

p
For a given refractive index profile n ( x, y) = ε r ( x, y) , that is constant along the
optical axis z, modes are fields that retain their transverse field distribution while
propagating in z direction, i. e. E = E0 ( x, y) exp [i ( βz − ωt)]. With k0 = 2π/λ0 ,
the propagation constant in vacuum, β = k0 neff defines the propagation constant
of a certain mode and neff the corresponding effective mode index. Frequency
and time are denoted by ω and t. In the following, the wave equation for the
transverse electric field will be derived.
Let us first deduce an equation that is used in a later transformation: We start
from Gauss’s law




1
∂ε r
∂Ez
0 = ∇ · D = ∇ · ( ε r E ) = ∇ t · ( ε r Et ) +
Ez + ε r
,
(2.1)
ε0
∂z
∂z
with displacement field D, vacuum permittivity ε 0 and relative permittivity ε r .
The transverse component of the electric field E is denoted by Et and ∇t stands
for the transverse component of the nabla operator. Since we assumed the per7

8

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

mittivity to be z-invariant, we find
∂Ez
1
= −ε−
r ∇ t · ( ε r Et ) .
∂z

(2.2)

From Maxwell’s curl equations with magnetic field B and magnetizing field H
∂B
∂H
= − µ0
,
∂t
∂t

(2.3)

∂D
∂E
= ε0εr ,
∂t
∂t

(2.4)

∇×E = −
∇×H =
we can derive

∇ × ∇ × E = ∇ (∇ · E) − ∇2 E = −µ0 ε 0 ε r

1 2
∂2
ω ε r E = k20 ε r E.
E
=
2
∂t2
c0

(2.5)

The transverse component of this equation can be transformed:

∇t (∇ · E) − ∇2 Et = k20 ε r Et ,


∇t

∂
∇t · Et + Ez
∂z



(2.6)

∂2
Et = k20 ε r Et .
∂z2

(2.7)

− ∇2t Et + β2 Et = k20 ε r Et ,

(2.8)

− ∇2t Et −

And by use of Eq. (2.2) we can write

∇t



1
∇ t · Et − ε −
r ∇ t · ( ε r Et )



and further simplify:


1
2
2
2
∇ t ∇ t · Et − ε −
·
ε
E
−
∇
·
E
(∇
)
t
r
t
t
t − ∇t Et + β Et = k 0 ε r Et ,
r

(2.9)


 

1
2
2
2
∇t ε −
·
ε
E
+
∇
+
k
ε
r) t
r (∇t
t
0 r Et = β Et .

(2.10)

Equation (2.10) is the wave equation for the transverse electric field for a z-invariant dielectric geometry. The equation is still valid for geometries in which
permittivity varies slowly in z direction and Eq. (2.2) becomes a good approximation. This wave equation can be solved analytically only for a few simple
problems, such as a planar dielectric waveguide. In general it needs to be solved
numerically. When the transverse electric field is found, Ez and H can be obtained
from Eq. (2.2) and Eq. (2.3).
To perform a numerical analysis, first a model needs to be generated of the real
world’s object. This model is discretized on a mesh grid. Further, Eq. (2.10) can

2.2. DIFFUSION

9

be discretized and formulated in a matrix form, whereupon derivatives are calculated as difference quotients. The discretized wave equation is an eigenvalue
problem and can be numerically solved for its eigenvalues β2n and corresponding
field distributions En,t (eigenvectors). In the course of this work mainly the commercial software L UMERICAL MODE SOLUTIONS was used [54] which is based on
a method described in more detail by Zhu and Brown [55]. Simulation results
can have two origins of inaccuracy. One source of inaccuracy is the limited reproduction of the real worlds object by the model, for example, when the model’s
material parameters deviate from actual ones or if the geometry cannot be reproduced with all details. The other source of inaccuracy is the simulation itself. In
general a finer mesh grid results in more precise results, though increasing the
computing time.

2.2

Diffusion

Common methods for waveguide fabrication in lithium niobate are titanium diffusion [11] and proton exchange [12]. For Ti diffusion, Ti is deposited onto a
lithium niobate substrate, photolithographically patterned and the metal is then
diffused at & 1000 ◦C. Titanium increases the refractive index by about 10−3 to
10−2 [11], and a waveguide is formed. To prepare proton exchanged waveguides,
the substrate is masked photolithographically with a metal mask and afterwards
immersed into hot benzoic acid near the boiling point of ∼250 ◦C. As proton exchange increases the extraordinary refractive index of lithium niobate and lowers
the ordinary one, it results only in waveguiding for the extraordinary polarization. In KTP, waveguides can be formed through exchange of potassium ions for
rubidium or other alkali metal ions, when a masked substrate is immersed into a
nitrate melt [6, 13].
The driving force of a diffusion flux j is a gradient in concentration c:
j = − D ∇c.

(2.11)

Here, D is termed diffusion coefficient and it typically increases with increasing
temperature. The formula is known as Fick’s first law. Mass conservation of the
diffusant can be expressed as
dc
+∇·j = 0
dt

(2.12)

10

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

and from equations (2.11, 2.12) Fick’s second law can be derived:
dc
= D ∇2 c.
dt

(2.13)

Two cases of one dimensional diffusion in a semi-infinite medium shall be discussed briefly now: (I) Diffusion of a certain amount of diffusive substance on
the surface and (II) diffusion from an infinite source at surface. Case (I) corresponds to in-diffusion of a titanium layer into lithium niobate, and time t and
depth z dependent concentration is given by a Gaussian distribution
M
c(z, t) = √
exp
2 πDt



− z2
4Dt


,

(2.14)

´∞
where constant M = 0 c dz [56]. Case (II) is realized for a substrate that is
exchanged in a melt, i. e. proton exchange of lithium niobate or ion exchange in
KTP. When the concentration at surface c0 is kept constant, the time and depth
dependent solution is described by a complementary error function [56]

c = c0


1 − erf

z
√
2 Dt


.

Analytical solutions for numerous geometries exist [56, 57], and in general it is
possible to find a solution numerically for given initial concentration and boundary conditions. For the two previously discussed solutions a constant diffusion
coefficient was assumed. However, that is not always the case. For example proton diffusion in lithium niobate is strongly concentration dependent and leads to
step-like diffusion profiles [12].

2.3

Losses in optical waveguides

Propagation losses in optical waveguides occur due to absorption, radiation and
scattering. As it is helpful to know about their origin and how to measure them,
they shall be discussed in the following.

Absorption
Absorption in optical materials occurs due to electronic transitions, lattice vibrations, and free-carrier effects [58]. Within the wavelength range of 0.5 − 5 µm absorption losses of lithium niobate are negligibly small [58], and the same applies
to Ti-diffused waveguides where attenuation of 0.03 dB/cm could be determined

2.3. LOSSES IN OPTICAL WAVEGUIDES

11

at 1.15 µm [59]. KTP is transparent from 0.35 µm to 4.5 µm [58] and losses in Rb
exchanged waveguides are < 0.4 dB/cm at 633 nm [13]. Towards the UV, photons
whose energy exceeds the band gap, can excite electrons from the valence to the
conduction band. The absorption edge is commonly not sharp, but described by
a temperature dependent exponential absorption edge - the Urbach tail. At the
infrared edge of insulators, absorption is caused by excitation of phonons (lattice
vibrations). Since higher harmonics of fundamental resonances can be excited,
this absorption edge is not sharp too, but characterized by an exponential law.
Free-carrier absorption occurs typically in metals or in semiconductors, but it can
also arise in crystals with larger band gap at elevated temperatures.
KTP, lithium niobate and other nonlinear crystals exhibit transmission loss
due to scattering and absorption when they are irradiated with light of shorter
wavelength at high intensity. This effect is referred to in lithium niobate as greeninduced infrared absorption (GRIIRA) and in KTP as gray tracking (see also
sec. 6.4). In KTP electron hole pairs can be generated through nonlinear mechanisms which are then trapped by vacancies or impurities [53, 60, 61]. In lithium
niobate the effect is assumed to be caused by polarons that form at NbLi anti-site
defects, where a Nb ion occupies a Li site. The effect of GRIIRA can be strongly
reduced in lithium niobate by doping with Mg, Zn, In, or Hf [62,63] or by heating
to & 160 ◦C [63]; and for KTP gray tracking can be avoided by heating the crystal
to temperatures above 170 ◦C [53].

Surface roughness
Tien derived a formula for propagation loss due to scattering on the top and bottom surface of a planar dielectric waveguide [64]:

α=

4π

q

2 + σ2
σ12
10

λ

2




cos3 θ1
2 sin θ1



1
W + (1/p10 ) + (1/p12 )


4.34 dB.

(2.15)

2 and σ2 are the variances
Here λ is the wavelength in the guiding layer, and σ12
10
of surface roughness of the guiding layer towards upper and lower layer, defined
as σi2 = z2 − z2 for their height profile. The angle under which the light rays
propagate in the guiding layer in a simple zigzag model is denoted by θ1 . It is
given by sin θ1 = n1 /n where n1 is the effective mode index and n is the refractive
index of the guiding layer. The layer thickness is denoted by W, and p10 and p12
are the extinction coefficients of the mode into the upper and lower layer.

12

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

This model shall be applied to two examples for demonstration and in both
cases we assume a vacuum wavelength of 1.55 µm and surface roughness σ10 =
σ12 = 2 nm, which can be achieved when preparing ridge waveguides with a
dicing saw. Tien’s simple model is not extended here to account for the additional
interfaces in a ridge waveguide, but the principles of the model will be reflected
and the orders of magnitude of the derived attenuation values are expected to be
correct.
First we assume the case of a Rb-diffused waveguide in KTP or a Ti-diffused
waveguide in lithium niobate. We treat it as a W = 10 µm thick slab whose
refractive index is slightly increased by 0.01, as this is a typical value for the index
increase through metal diffusion or ion exchange. The fields that leak out of the
guiding layer shall be neglected, i. e. (1/p10 ) = (1/p12 ) = 0. Next, we assume
that a certain mode’s effective index is increased over the substrate index by 0.005
and obtain θ1 = arcsin (1.8/ (1.8 + 0.005)) = 85.7◦ . The attenuation is then given
by 0.0016 dB/cm and can be neglected for samples of few cm length.
Next we investigate the case of a LNOI waveguide. That is, we assume a
thin film of W = 1 µm height and refractive index 2.2 bonded to silica, whose
refractive index is 1.5. Again we consider surface roughness of σ = 2 nm and
a wavelength of 1.55 µm. For a fundamental mode in a wide ridge waveguide,
the mode index can be close to the refractive index of the guiding layer, and let us
assume θ1 = 74°.2 As the mode extends into the air above and the SiO2 below, we
use (1/p10 ) + (1/p12 ) ≈ 0.3 µm. Then we find considerable loss of 0.62 dB/cm.
We note that scattering loss from surface roughness scales as (σ/λ)2 . Higher
order modes propagate at lower angle θ1 and experience higher loss, as we see
from the second factor in Eq. (2.15). In the ray-optic zigzag model they undergo
more reflections along a waveguide of certain length and further they experience
higher loss per reflection [64]. Also, scattering losses increase for narrower waveguides, as light is reflected more often in the simple zigzag model. Further, it
might be astonishing at first that scattering losses from surface roughness scale
as α ∼ λ−2 and not like α ∼ λ−4 , as known from Rayleigh scattering. The reason
is that the scattering assumed here is caused by surface roughness with long coherence length, i. e. smooth hills and valleys whose distance is large compared to
the wavelength.

2 The value of θ = 74° was calculated for a planar waveguide with the above stated properties.

2.3. LOSSES IN OPTICAL WAVEGUIDES

13

Radiation loss
In straight waveguides, modes with an effective mode index below the substrate
index are not bound, but radiate into the substrate. Also bound modes can experience radiation loss, when they are converted to higher order radiation modes due
to perturbations [65]. However, for well prepared straight waveguides that guide
well above cut-off, radiative loss is commonly negligible, compared to scattering
loss and absorption. When waveguides are bend radiation loss occurs due to the
following mechanism [65]: The field of the mode decreases exponentially into the
surrounding, but remains finite. To keep a straight phase front, the phase velocity at larger radius needs to increase and from a certain radius on, it is greater
than speed of light in the surrounding environment. This fraction of the field
is assumed to be not bound anymore and to experience radiative loss. Losses
of dielectric waveguides were quantified by Marcatili and Miller for a w wide
waveguide that is bend with a radius R [65]:








 

kx w
z −ks )
· exp − 2(kξk
R · exp wξ
2
s
αr = h
 · 2 · 4.34 dB.
 i2 

· w2 + 2k1x sin (kx w) + ξ cos2 k x2w
w + 2ξ cos kx2w

λS · 2ξ · cos2

(2.16)
Here λS is the wavelength in the substrate, ξ is the decay length of the mode into
the substrate, kx and kz are the propagation constants along the waveguide and
perpendicular to it and kS is the propagation vector in the substrate3 . The formula
 
1
can be summarized to αr = C1 · exp (−C2 R) and changed to R = C2 ln Cαr1 to
find the minimum radius that allows for a certain propagation loss. Below this
radius, losses increase exponentially and will decrease exponentially above it.
For demonstration, the bending radius at which losses of αr = 0.1 dB/cm occur shall be calculated for a Ti-diffused waveguide and a LNOI waveguide for
a vacuum wavelength of λ0 = 1.55 µm. For simplicity we treat the Ti-diffused
waveguide as if the refractive index was increased homogeneously over a rectangular cross section. Assumed parameters and results are listed in Table 2.1. We
see that Ti-diffused waveguides need bending radii of the order of a centimeter, and the same applies to other metal-diffused or ion-exchanged waveguides.
Since most integrated optic elements need bend waveguide structures, this radius
restricts the minimum size of such a component. In contrast, LNOI waveguides
allow for sharp bending radii of the order of 10 µm, and hence enable considerable size reduction.
3 A factor of 2 · 4.34 dB was added to the original formula to convert it to dB units.

14

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS
Case
Ti:LN
LNOI

nWG
2.2166
2.21

w [µm]
8
1.5

nS
2.2112
1.44

neff
2.2139
1.83

R for αr = 0.1 dB/cm
7.9 mm
7.1 µm

Table 2.1: Calculation of the bending radius R that causes losses of αr =
0.1 dB/cm in a LNOI waveguide and in a Ti-diffused waveguide with refractive index of the guiding layer nWG , waveguide width w, substrate index nS and
mode index neff .

Experimentally micro-rings with radii of 100 µm [20] or 50 µm [66] have been
realized for example in lithium niobate thin films. In silicon-on-insulator, applications with micro-rings of radii down to 1.5 µm for an operation wavelength of
1.55 µm [67] have been presented.

2.4

Measurement of losses in optical waveguides

In the following, methods for determination of propagation loss in waveguides
are described. All these methods were used in the course of the presented work,
and with slight variations they are widely applied.

Cut-back method / transmission
A very straightforward approach is to endfire couple light into a waveguide
and detect the transmitted power. The ratio of transmitted Pout to impinging
power Pin determines the insertion loss and is commonly given in dB units: αI =
10 dB · log10 ( Pout /Pin ). As the insertion loss consists of coupling and propagation loss, the propagation loss cannot be deduced from a single measurement
without further assumptions. Coupling losses can be estimated by taking into account Fresnel reflection and calculating the overlap κ of experimentally obtained
or simulated modes, e. g. the modes of an optical fiber and the mode of the waveguide [68]:
´
2
| E1∗ E2 dA|
κ=´
.
(2.17)
´
| E1 |2 dA · | E2 |2 dA
Here E1 and E2 are the complex electric field amplitudes. When experimental
mode images are to be evaluated, the field amplitude can be obtained from the
√
intensity I since E ∼ I, and it is further necessary to manually change the sign
of the lobes of higher order modes.
A more accurate technique is to successively measure the insertion loss and
shorten the waveguide. When the insertion loss is plotted over the sample length,

2.4. MEASUREMENT OF LOSSES IN OPTICAL WAVEGUIDES

15

the propagation loss is given by the slope and coupling loss is given by the vertical intercept. One drawback of this cut-back method is that it is time-consuming to
cut and polish a waveguide several times. Another drawback is that this method
is destructive. A general problem about endfire coupling and measuring the
transmittance of multimode waveguides is that endfire coupling does not allow
for selective excitation of a certain mode. Selective excitation of a certain waveguide mode is possible by prism coupling and the excited mode can be detected
by out-coupling it through a second movable prism [64]. Such measurements can
be evaluated like in the cut-back method.

Resonator method
A more sophisticated method to determine waveguide attenuation was described
by Sohler and Regener [59], and by Walker [69, 70]. Coherent laser light is endfire coupled to a waveguide and the transmitted power is recorded while either
the laser wavelength is tuned or while the optical path length of the waveguide
is continuously changed (e. g. by heating the waveguide). Due to interference
of beams that are reflected from the waveguides endfaces multiple times, the
spectrum of a Fabry-Perot interferometer is observed. From its minimum and
maximum intensity Imin / Imax the contrast
K=

Imax − Imin
Imax + Imin

(2.18)

can be calculated. The loss per resonator round-trip can be determined from the
contrast, and it includes loss for twice propagation through the waveguide length
and twice the loss from an endface reflection. By subtracting the reflection loss
the propagation loss α can be obtained by
"
4.34 dB
α=
ln R − ln
l

1−

√

1 − K2
K

!#
.

(2.19)

In the stated formula l is the waveguide length. The endface reflectance R can
commonly be calculated from the Fresnel equations for normal incidence as R =
(nWG − nair )2 /(nWG + nair )2 , where nair and nWG are the refractive indices of the
surrounding air and the waveguide material, respectively. For very narrow LNOI
waveguides, the reflectance can no longer be calculated using the Fresnel formula
because the modes are not described well by plane waves and reflection coefficients need to be determined in other ways, e. g. by simulations. This resonator

16

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

technique is independent of the coupling efficiency and non-destructive. It is also
worth mentioning that the uncertainty ∆α decreases for lower attenuation (and
hence higher contrast):
4.34 dB
∆α =
l



∆K ∆R
+
K
R


.

(2.20)

Here, the approximation of a low contrast K  1 was done, which is justified e. g.
for Ti-diffused waveguides in lithium niobate. Imperfections in endface preparation can reduce the reflectance and hence can result in overestimating propagating loss. Attenuation values measured by this method therefore give an upper
bound, when imperfections are present or cannot be excluded. When the resonator method is applied, care should be taken to avoid building up a second
resonator between the coupling optic and the waveguide because this resonator
can change the reflectance in Eq. (2.19). It is also important that this technique
only works for singlemode waveguides or when the fundamental mode is selectively excited by good alignment because higher order modes would add a
background to the measured spectrum.

Measurement of scattered light
Our workgroup owns a commercial M ETRICON prism coupler, which allows to
excite fundamental as well as higher order modes in a planar waveguide [71].
Light that is scattered along the excited light streak can be collected by an optical
fiber on a translation stage and transmitted to a detector. When the scattering
centers are homogeneously distributed along the waveguide, the detected signal is proportional to the power in the waveguide. In this way the attenuation
can be determined for different modes by fitting an exponential function to the
measured power over length.

2.5

Nonlinear frequency conversion

Within the regime of linear optics, light propagation appears well behaved. That
is, the optical properties are independent of light intensity, light rays propagate
through each other without interaction and the wavelength remains unchanged
when light passes through a medium. In contrast, in the field of nonlinear optics the refractive index can depend on the light intensity, light rays can interact
and light of a certain wavelength can be converted to another. Nonlinear interac-

2.5. NONLINEAR FREQUENCY CONVERSION

17

tion can only occur in a medium, not in vacuum. It originates from the material
polarization [72]
P = ε 0 χE + 2dE2 + 4χ(3) E3 + ... ,
(2.21)
where ε 0 is the vacuum permittivity, E the electric field, χ linear susceptibility, d
the second-order nonlinear coefficient and χ(i) are higher-order susceptibilities.
As the oscillating polarization represents accelerated charge, it is a source of radiation. The linear term results in generated radiation of the same frequency as
the impinging wave, but with an angular phase shift. The superposition of these
waves can be reflected by the materials refractive index.
In practice, terms of higher order in Eq. (2.21) only play a role for high light
intensity and strong electric fields. They were therefore first observed after invention of the laser [73]. Further, coefficients of even order (like d) are non-zero
only in media without inversion symmetry, which is easy to understand from
geometric reasons.
Let us consider as an example second-order nonlinearity for two waves of


different frequencies ωi with electric fields Ei = 12 ci exp (iωi t) + ci? exp (−iωi t) ,
where we find a nonlinear polarization
1
PNL = 2dE1 E2 = d {c1 c2 exp [i (ω1 + ω2 ) t] + c1 c2? exp [i (ω1 − ω2 ) t]} + c.c. .
2
(2.22)
Obviously radiation of the sum frequency can be generated, as well as radiation
of the difference frequency. When only light of a single frequency impinges, then
the second-harmonic frequency can be generated or a (quasi-) DC polarization.
The processes described here are parametric interactions, meaning that no energy is exchanged with the medium. This leads to an energy conservation condition between three waves of frequency ωi :
ω1 + ω2 = ω3 .

(2.23)

Further, interacting waves need to fulfill a phasematching condition so that they
can interact constructively over longer distance:
k1 + k2 = k3 ,

(2.24)

where k i are the propagation vectors of the interacting waves. Starting from the
wave equation with a source term, that arises from the polarization, and applying a slowly varying envelope approximation (i. e. weak coupling in the sense
that the envelope changes only slightly over the length of one wavelength) a set

18

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

of coupled equations can be derived which describe three-wave mixing of copropagating plane waves along the z axis [72]:
da1
= − iga3 a2? exp (−i ∆k z) ,
dz
da2
= − iga3 a1? exp (−i ∆k z) ,
dz
da3
= − iga1 a2 exp (i ∆k z) .
dz

(2.25)
(2.26)
(2.27)

Here, ai (z) are normalized complex envelopes of the electric field Ei , which are
√
defined by Ei (z, t) =
2Zh̄ωi · ai exp (iωi t − ik i z) with the impedance of the
medium Z and the reduced Planck constant h̄. A phase-mismatch
∆k = k3 − k2 − k1

(2.28)

and a coupling strength g2 = 2h̄ω1 ω2 ω3 Z3 d2 are introduced.
Let us first solve the above stated coupled equations for second harmonic generation (SHG), with the simplification that we assume no pump-depletion (NPD)
and no phase-mismatch (∆k = 0). As we are regarding SHG and NPD, it follows
that a1 = a2 = const, and further
1
da3
= −i ga1 a1 .
dz
2

(2.29)

Integration over a propagation length L leads us to
1
a3 ( L) = −i ga1 a1 L.
2

(2.30)

The amplitude increases linearly with the propagation length and the pump power,
and hence the second harmonic (SH) power scales as the square of propagation
length and pump power. For the conversion efficiency within the no pumpdepletion regime we obtain [72]

ηSHG =

P3 ( L)
L2
d2
= C2 P1 , with C2 = 2ω 2 Z03 3 ,
P1 (0)
A
n

where Z0 is the impedance of free space. The SHG conversion efficiency is proportional to the intensity of the fundamental harmonic (FH) wave’s intensity
P1 /A and to the squared interaction length. When we now assume phase mis-

2.5. NONLINEAR FREQUENCY CONVERSION

19

match ∆k for SHG in the NPD regime, Eq. (2.27) leads us to
da3
1
= −i ga21 (0) exp (i ∆k z) .
dz
2

(2.31)

Integration over a propagation length L delivers
1
a3 ( L) = −i ga21 (0)
2

ˆL
0



1 2
exp (i ∆k z) L
exp (i ∆k z) dz = −i ga1 (0)
2
i ∆k
z =0

1
1
= − ga21 (0)
[exp (i ∆k L) − 1] .
2
∆k

(2.32)
(2.33)

The generated SH power is proportional to the square of the amplitude:
2

| a3 ( L)| =

 g 2
∆k

4

| a1 (0)| sin

2



∆k L
2


.

(2.34)

Thus we find that the conversion efficiency as a function of phase-mismatch [72]
L2
P3 ( L)
= C2 P1 (0) sinc2
ηSHG =
P1 (0)
A



∆k L
2π


(2.35)

has a (squared) sinc shape. When the pump wavelength is tuned or a nonlinear
crystal is heated, ∆k changes and commonly a sinc-shaped SH signal is observed.
Absolute conversion efficiency can of course not exceed 100 % due to energy conservation. For high pump powers or long propagation length the NPD approximation is no longer valid and the generated SH power saturates or is transformed
back to the fundamental harmonic.
Equations (2.25-2.27) can also be used to describe three-wave mixing outside
the NPD regime. Waveguide losses can easily be included. Also other processes, such as optic parametric amplification (OPA) or optic parametric oscillation (OPO) can be modeled.

Phasematching
Considerable conversion efficiency can only be achieved when the interacting
waves are phasematched (i. e. ∆k = 0). Within the course of this work birefringent and quasi-phasematching were used and therefore they shall be discussed
here. These two methods are also the most widespread ones [74], though others
exist.

20

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

Birefringent phasematching
The phasematching condition Eq. (2.24) can be expressed in terms of refractive
indices of the interacting waves ni :
n 3 ω3 = n 1 ω1 + n 2 ω2 .

(2.36)

This equation is typically not fulfilled since in the regime of normal dispersion,
n(ωi ) < n(ω j ) for ωi < ω j . One solution to overcome this issue is the use of a
birefringent crystal. In these optically anisotropic materials the refractive index
depends on polarization and propagation direction.
The linear optical properties of a material are described in general by three
principle refractive indices. When two of these principle refractive indices are
equal, such as in lithium niobate, the crystal is called uniaxial. It has one optical
axis and if light propagates along it, the refractive index is independent of polarization. For all other directions of propagation, one polarization experiences the
ordinary, direction-independent refractive index and the other polarization experiences the extraordinary, direction-dependent refractive index. Crystals with
three different principle refractive indices, such as KTP, are called biaxial because
they posses two optical axes.
To enable phasematching in a three-wave mixing process, the polarization of
the wave with shortest wavelength is always chosen to have the low refractive
index. The polarizations of the two waves of longer wavelength can be chosen to
both have high index, and this process is termed type-I phasematching. When the
two waves of longer wavelength have different polarizations, the process is called
type-II phasematching. The difference between the principle refractive indices ∆n
is called birefringence, and generally larger birefringence allows to compensate
larger phase-mismatch.
In Eq. (2.21) the polarization is given as a scalar function of electric field. The
vectorial form of the second-order term is given by







Px
d11 d12 d13 d14 d15

 
 Py  =  d21 d22 d23 d24 d25
Pz
d31 d32 d33 d34 d35

Ex2
Ey2






 


d16
 E2 
 

z
d26  · 
.
 2Ey Ez 


d36
 2E E 
x z 

2Ex Ey

(2.37)

The number of matrix elements d is reduced in general due to symmetry condi-

2.5. NONLINEAR FREQUENCY CONVERSION
orthorhombic mm2 (e. g. KTP)



0
0
0
0 d15 0
 0
0
0 d24 0 0 
d31 d32 d33 0
0 0

21

trigonal 3m (e. g. LN).

0
0
0
0 d15 −d22
 −d22 d22 0 d15 0
0 
d31 d31 d33 0
0
0


Table 2.2: Second-order nonlinear coefficients of KTP and lithium niobate [76].
tions from 18 to 10 [75]. Symmetries further reduce the number of independent
elements for different crystallographic groups and examples for KTP and lithium
niobate are given in Table 2.2.
When phasematching is achieved for a certain orientation toward the crystal
axes, an effective coefficient of second-order nonlinearity can be calculated. Often
the direction of light propagation is noted by its polar angle θ toward the optical
z axis and an azimuthal angle φ between its projection onto the xy plane and the
x axis. To calculate the effective nonlinear coefficient deff the projection of the
impinging wave’s electric field onto the crystal axes is calculated and then the
fraction of the polarization that points normal to the direction of propagation is
computed. For type-II SHG of KTP with propagation in the xy plane (θ = 90°) it
can be found for example [75]:
deff = d15 sin2 φ + d24 cos2 φ.

(2.38)

Quasi-phasematching
The other common method to achieve phasematching between optical waves of
different wavelength in the context of three-wave mixing is quasi-phasematching
(QPM). In the presence of a phase-mismatch ∆k the interacting waves start to interfere destructively after having propagated the coherence length lc = π/∆k, as
can be seen from Eq. (2.32). If the crystal orientation is inverted after every coherence length, a phase shift of π is introduced and the waves continue to interact
constructively. It is also possible to invert the crystal orientation after an uneven
multiple of lc . This so-called higher order phasematching is helpful when smaller
inversion lengths cannot be realized experimentally, but results in reduced efficiency.
If QPM is applied, conversion efficiency is reduced compared to a homogeneous phasematched material because the interacting waves are not exactly in
phase (see Eq. 2.32). This can be reflected by a nonlinear coefficient dQPM , which
is reduced compared to the nonlinear coefficient of the homogeneous medium

22

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

deff . For QPM of first order

2
d
(2.39)
π eff
can be found [77]. Though the nonlinear coefficient is reduced by about one third,
QPM has strong advantages: First of all, it enables phasematching between arbitrary wavelengths, while birefringent phasematching is restricted by the crystal’s
limited birefringence. Further, for lithium niobate and KTP QPM allows to make
use of the d33 coefficient which is six times (four times) larger than any other coefficient of LN (KTP). Also QPM can be applied to materials that possess high nonlinearity but lack birefringence, such as gallium arsenide. Another advantage is
that QPM always allows to achieve phasematching along a crystallographic axis.
Such a phasematching scheme is called uncritical (in contrast to critical phasematching) because it is less sensitive to angular misalignment.
dQPM =

QPM was first described by Armstrong et al. in 1962 [78] and first realized
by stacking up to tens of plates, whose thickness was an uneven multiple of the
coherence length, with alternating orientation [79–81]. Bonding the individual
plates was introduced to reduce the reflection losses at the numerous interfaces
between crystal plates and intermediate air gaps [82, 83]. However, it seems impractical to stack a 1 cm long artificial crystal from plates of 3 µm,4 especially
when remembering that the long term periodicity is crucial. In 1993 it was found
that the ferroelectric domains in lithium niobate crystals can be permanently periodically oriented by applying a strong electric field with a comb-structured metal
electrode [49]. This method emerged to be the most widespread technique for
fabrication of periodically poled lithium niobate (PPLN). Other earlier invented
methods for fabrication of periodically poled lithium niobate include the growth
of PPLN by application of a modulated current during crystal growth [84] or
inverting ferroelectric domains by electron bombardment [85, 86]. Further, indiffusion of periodically patterned metal or ion exchange through a comb-shaped
mask are known methods for periodic poling of ferroelectric crystals - though
only the surface is inverted to a shallow depth of ∼10 µm [50].

Phasematching bandwidth


L
According to Eq. (2.35) SHG efficiency is proportional to sinc2 ∆k
2π . As the
phase-mismatch ∆k is a function of pump wavelength and temperature, a phasematching bandwidth can be specified. The phase mismatch can be expanded in a
4 The coherence length for SHG of 1064 nm in lithium niobate, using the largest nonlinear co-

efficient d33 is ∼3 µm.

2.5. NONLINEAR FREQUENCY CONVERSION

23

Taylor series around the phasematching wavelength λPM in terms of fundamental wavelength
∆k (λPM + ∆λ) =

1 ∂2 ∆k
∂ ∆k
· (∆λ)2 + ...
· ∆λ +
2
∂λ λ=λPM
2 ∂λ λ=λPM

(2.40)

and often the quadratic and higher order terms can be neglected. Let us as an
example calculate the bandwidth of type-II SHG in KTP for a pump wavelength
of λFH,PM = 1064 nm and propagation along the y axis. The phase mismatch
(Eq. 2.28) is given by
∆k(λFH ) =

2 · 2π · nx (λFH /2) 2π · nz (λFH ) 2π · nx (λFH )
−
−
,
λFH
λFH
λFH

(2.41)

where λFH is the FH wavelength
 the refractive indices are those for x/z po and
L
is 0.5 for ∆k L = 0.443 · 2π and hence the full
larization. The function sinc2 ∆k
2π
width at half maximum (FWHM) of the bandwidth length product is

|∆λ · L| = 2 · 0.443 · λ ·

dnx
dnz
dnx
−
−
dλ λ=λSH,PM
dλ λ=λFH,PM
dλ λ=λFH,PM

= 0.66 nm · cm.

! −1

(2.42)

Here, dispersion values from Kato and Takaoka were used [87].
For certain materials, at a specific fundamental harmonic wavelength the linear term in Eq. (2.40) can vanish. This results in a particularly wide phasematching bandwidth and is called extended phasematching. KTP is of special interest, as
it allows for extended phasematching of SHG from 1550 nm to 775 nm. Experimentally, a bandwidth of 67 nm · cm could be realized [10]. Also generation of
entangled photons of identical frequency at telecommunication wavelength via
parametric down-conversion over a wide spectral range is enabled [9, 10]. Another example for extended phasematching is the generation of mid infrared radiation at about 3.5 µm from a pump source of ca. 1064 nm with a signal at ca.
1.55 µm [88].
When periodic poling is used to obtain QPM, a method to achieve a wider
phasematching range (or non-sinc2 phasematching curves) is the use of special
poling patterns or imperfect poling patterns [89]. The bandwidth is then increased on the cost of a lower conversion efficiency. On the other hand, when
the theoretically predicted phasematching bandwidth is obtained, this indicates
a high quality of the domain structure. For a waveguide QPM device, a narrow

24

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

bandwidth (i. e. low deviation from theoretically predicted value) can also indicate homogeneity of the waveguide profile.
Influence of attenuation on waveguide SHG
If in a waveguide SHG process attenuation is present for the fundamental harmonic α1 and for the second harmonic α3 , conversion efficiency is reduced. The
influence of the attenuation can be reflected by an effective length of the waveguide [90]
exp(−4.34 dB−1 α1 l ) − exp(−4.34 dB−1 α23 l )
,
leff =

−4.34 dB−1 α1 − α23

(2.43)

where attenuation needs to be inserted in dB/cm. The reduced effective length
also results in a wider phasematching bandwidth.

2.6

Properties of lithium niobate and potassium titanyl phosphate

Lithium niobate
Lithium niobate is a human-made crystal that does not exist in nature [4]. It is
transparent from the ultraviolet to the infrared (0.5 − 5 µm [58] based on 1 cm−1
absorption coefficient criterium). Due to its favorable optical, piezoelectric, electrooptic, elastic, photoelastic and photorefractive properties as well as easy and inexpensive growth methods, it has found widespread application and is one of
the most used crystalline dielectric materials [4, 5]. It is used for surface acoustic wave (SAW) devices, such as filters and transducers, in radio-frequency devices like cellular phones, television sets or bluetooth and WiFi devices [1, 2]. In
a SAW filter a radio frequency (RF) electromagnetic wave is transduced into a
surface acoustic wave through piezoelectric effect and transformed back into an
electromagnetic wave. Widespread optical waveguide devices in lithium niobate
include modulators for long-haul fiber-optic telecommunication. In these devices
the optical wave is guided in a Ti-diffused or (seldom) proton exchanged optical
waveguide and modulated by a co-propagating RF wave through the electrooptic effect [3]. It is also a common material for nonlinear optical frequency conversion (e. g. second harmonic generation, optical parametric generation/amplification). The ferroelectricity of lithium niobate was first discovered and reported

2.6. PROPERTIES OF LN AND KTP

2.31 Å

25

0.71 Å
−z

+z

0.26 Å

−z
paraelectric

+z
ferroelectric

ferroelectric
O2− Nb5+ Li+

Figure 2.1: Para- and ferroelectric phase of lithium niobate (following diagrams
of Weis et al. and Houe et al. [4, 92]); the arrows indicate the polarization.

in 1949 [91]. Larger homogeneous crystals of higher purity were grown at the
B ELL L ABORATORIES , and the structure and a range of physical properties were
reported comprehensively in 1966 [4].Lithium niobate’s crystal structure consists
of a deformed hexagonal close-packed lattice of oxygen ions [4]. The octahedral
interstices in-between the oxygen ions are filled one third by niobium ions, one
third by lithium ions and one third is vacant. This is shown in Fig. 2.1, middle and right. As the positively charged Li+ and Nb5+ ions are shifted relative
to the negative O2− octahedra (indicated by the dashed lines), a spontaneous polarization is present and the crystal is ferroelectric. The spontaneous polarization
can be inverted by application of an electric field above coercive field strength of
21 kV/mm [76]. In this high electric field the lithium and niobium ions change
their position within the crystal structure (compare Fig. 2.1, middle and right)
and this lets the direction of the spontaneous polarization change.
By doping with MgO, lithium niobate’s coercive field strength can be lowered
to 2.5 − 6 kV/mm [76]. This enables electric field poling of thicker crystals and the
doping also increases the crystal’s resistance against photorefractive damage [5].
When lithium niobate is heated above its Curie temperature of 1150 ◦C, the lithium
and niobium atoms can interchange between their positions (Fig. 2.1, middle and
right) and their average position is depicted in Fig. 2.1, left. The crystal becomes
non-polar in this paraelectric phase.
Ferroelectricity always goes along with pyroelectricity and piezoelectricity,
meaning that LN will charge up when heated/cooled or when mechanical stress
is applied. This makes it possible to determine the direction of the polar z axis.
The +z face charges up negatively when pressure is applied [4]. Further its +z
face charges up positively upon cooling [4].

26

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

Lithium niobate can be grown from a congruent melt (meaning that the melt
composition does not change as is solidifies) and the ratio of Li:Nb is then 48.5 :
51.5 [91]. Further it can be grown in its stoichiometric composition near Li:Nb=
50:50 [91].

Potassium titanyl phosphate (KTP)
Potassium titanyl phosphate (KTP, KTiOPO4 ) is a ferroelectric crystalline material that possesses high nonlinear-optical and electro-optical coefficients [6]. Its
optical damage threshold is an order of magnitude larger than that of lithium niobate [6, 93], and its transparency range5 of 0.35−4.5 µm extends further to shorter
wavelengths [58]. It has therefore found widespread application in optical frequency converters, especially for Nd-based solid state lasers as it is capable of
birefringent phasematching for type-II SHG of ∼1064 nm pump light [7]. KTP
provides thermally stable phasematching and shows no “acoustic ringing”, and
is therefore a preferred material for optical modulators [93]. Its crystal structure
allows for periodic poling of fine, sub-micrometer periods through substrates
of 1 mm thickness [94, 95]. When lithium niobate is poled with such fine periods, periodic poling is achieved only to a depth of ∼10 µm from the combshaped electrodes while the domains are merged below [96]. These narrow periods are for instance necessary to compensate the large phase-mismatch in mirrorless OPOs, a concept where signal and idler waves counter-propagate and
provide a distributed feedback without mirrors [76, 95]. KTP’s birefringence and
dispersion further allow for “extended phasematching” in the telecom optical
wavelength bands. This means that phasematching of type-II between ∼775 nm
and the telecommunication wavelength of ∼1550 nm is achieved over a particularly spectrally-wide range because the phase mismatch as well as its derivative
are zero [9, 10]. It enables generation of especially narrow band and hence indistinguishable photon pairs for quantum optics and quantum cryptography [97,98].
KTP was first synthesized (purposefully) in 1971 at L ABORATOIRE D ’E LEC TROSTATIQUE ET DE P HYSIQUE DU M ETAL in Grenoble6 [99]. Its crystal lattice
is orthorhombic and belongs to the acentric mm point group [6] and has several isomorphs with chemical formula MTiOXO4 , where M is K, Rb, Cs, Tl or
NH4 and X is P or As [100]. The structure consist of a network of distorted
TiO6 octahedrals and PO4 tetrahedrals, with K ions that are weakly bonded to
the Ti octahedrals and P tetrahedrals [6, 99]. Along the crystallographic z axis
5 based on 1 cm−1 absorption coefficient
6 According to Shur et al. it was already grown in 1890 [96].

2.6. PROPERTIES OF LN AND KTP

27

channels exist, in which the K ions and other dopants (such as Rb) are mobile.
Diffusion in z direction is several orders of magnitude larger than within the xy
plane [6]. KTP is therefore sometimes termed a quasi 1D crystal and this property
also allows ferroelectric poling of fine patterns through a thick crystal, as stated
above, without merging of the domains. The coercive field strength of KTP is relatively low (∼2 kV/mm [76]) and therefore facilitates periodic poling of thicker
substrates. KTP starts to decompose upon melting at 1150 ◦C and thus can not
be grown from a melt. Instead it can be grown from a flux of various potassium
phosphates, tungstates and halides. Or it can be grown hydrothermally from an
aqueous solution at high pressure. A general problem about KTP is its spatially
varying vacancy concentration and hence ionic conductivity [16, 101]. It results
in difficulty to reproducibly fabricate waveguides.
Waveguides are fabricated in KTP typically by patterning of an adequate metal
mask on the substrate and subsequent immersion into a melt of Rb, Cs or Tl nitrate [13]. The Rb+ ions (or other monovalent ions) replace K+ and diffuse into
the crystal through a hopping mechanism. As they exhibit higher polarizability, the refractive index is locally increased and a waveguide is formed. When
barium nitrate is added to the melt, one Ba2+ ion replaces two K+ ions [102]. Additional hopping sites are created and the process of Rb diffusion is accelerated.
It is further assumed that addition of barium makes the diffusion spatially more
homogeneous [103].

Crystal cut
For piezoelectric or optical applications, crystals are usually cut into plates and
the crystal’s orthogonal Cartesian axes (x, y, z) can be oriented in an arbitrary
way to the plate’s axes. For rectangular plates of thickness t, width w and length
l with t < w < l a nomenclature exists to describe this orientation [104]. If the
plate’s cut is indicated by only one letter, e. g. “z-cut”, this indicates that the z
axis points out normal to the largest face, into the thickness direction. When two
letters are noted, e. g. “zx-cut”, this means that the plate is z-cut and further the
x axis is oriented along the length. The general case of crystal axes that are not
oriented along the plates axes is given e. g. as “(XYwt) 10°/20°”. This means that
one starts with a hypothetical plate, which is oriented as an xy-cut toward the
crystal axes. The hypothetical plate is rotated around its width axis by 10° and
then around its thickness axis by 20° while the crystal axes remain stationary. The
result is the plate’s orientation to the crystal axes.

28

2.7

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

Electric field poling of lithium niobate

The common method to achieve quasi-phasematching in lithium niobate is electric
field poling. Usually a comb-shaped electrode is patterned photolithographically
on one face (+z or −z) of a zx-cut substrate and on the other face a planar electrode is contacted. The comb-shaped electrode can be formed from metal stripes
and for insulation it is commonly covered with photoresist, spin-on-glass or the
whole substrate is immersed into oil during poling [49, 105, 106]. Alternatively
the substrate can be patterned with a photoresist grating and then a metal electrode can be deposited or a liquid electrode can be applied. As planar electrode
on the other side also a metal, liquid or gel electrode can be used [106–108]. By
applying an electric field above coercive field strength (EC,LN ≈ 21 kV/mm [76])
ferroelectric domains are inverted. The process of domain inversion can be divided into nucleation, domain wall motion and domain stabilization [105, 109]. It
was studied and described already in the 1950s for barium titanate (BaTiO3 ) and
is discussed in the following [109].
Small inverted micro- and nanodomains can already be present in nominally
single domain wafers [91]. Such micro- or nanodomains consist of a pyramid
with hexagonal base in the surface (xy plane) whose tip points into the substrate
(z direction). Their size is up to few micrometers and they can occur on the +z,
as well as on the -z face. In the surface plane the hexagon’s sides are parallel
to the crystal’s y axis (and equivalent directions). Inverted microdomains can
form when a lithium niobate substrate is rapidly cooled, e. g. when taken out of
an oven in the course of photolithography [110]. Further, when a strong electric
field is applied, nucleation will occur at the electrodes’ corners and edges, where
the electric field is strongest. Also the choice of electrode material is important.
Application of a liquid electrode of LiCl water solution does not result in additional nucleation. In contrast Ni or Cr deposition results in a high density of
nucleation sites [105].
A high number of nucleation sites within the electrode region is important to
homogeneously initiate the poling process. When the density of nuclei is too low,
inhomogeneous patterns are poled and domains in some regions grow together
while domain inversion has not started in others. Therefore, chromium electrodes
are preferred on the one hand, on the other hand chromium can diffuse into the
substrates and lead to photorefractive optical damage, especially in surface near
waveguides. Another technique to achieve more nucleation sites is insertion of
additional gaps into the electrode structure because the supplemental corners act
as additional nucleation sites [108]. Also acid treatment with HF:HNO3 has been

2.7. ELECTRIC FIELD POLING OF LITHIUM NIOBATE

29

found to make the poling process more homogeneous and increase the poling
quality [107]. Potentially, the acid removes a thin amorphous “Beilby layer” that
is built up during chemical mechanical polishing from wafer manufacturing.
When an electric field above coercive field strength is applied, the microdomains start to grow into depth until they reach the opposite surface. While they
grow needle-like into depth, also their width grows slightly. Typical ratios of
tip depth to width are 1:100 to 1:1000 [105]. On their way the tips can merge
with other tips that have started from the same surface or from the opposing
one. When the tip has reached the opposite surface, the domain walls quickly
straighten and then the domain wall propagation starts. Domain walls move
faster along the y direction than in x direction and while propagating they keep
their hexagonal shape. Due to this characteristic growth, zx-cut substrates are
preferentially used for periodic poling (i. e. the grating vector is in x direction).
The velocity of domain movement is determined by the electric field averaged
along the z axis (or within the zy plane). It was found to grow exponentially
(∼ exp (−δ/E), with constant δ) with the electric field E [111].
As explained earlier, domain inversion can start along the edges of electrodes,
where the electric field is enhanced. This lets the inverted domains’ width exceed
the electrode width. The domains from the two boundaries of an electrode stripe
merge quickly and after that the domain walls start to move into the field between
the electrodes. Here, the electric field is lower and the domain wall motion slows
down and potentially stops.
During poling typically the current as well as its integral over time are monitored. When a certain charge has flown, that corresponds to a poled domain
duty-cycle of 50:50, the voltage can be reduced. Another technique is to chose
a certain electrode width and applied voltage, which result in a self-determined
end of domain wall propagation at 50:50 domain duty-cycle. Further it is possible
to reduce the applied voltage, when the current starts to decrease because of the
reduced domain wall velocity. To completely invert a certain area A, it is necessary to let flow twice the spontaneous polarization PS,LN = 0.71 µC/mm2 [76]. To
obtain a 50:50 domain cycle, in other words to invert half of the area, charge of
Q = 2 · PS,LN · 1/2 A needs to flow.
It was found that domains of lithium niobate need about 30 ms to stabilize
[112]. If the voltage is rapidly decreased earlier, domains can switch back fully
or partially. To prevent this phenomenon, the poling voltage is commonly not
directly reduced to zero, but to a value slightly below coercive field strength and
held constant for > 100 ms.

30

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

Inverted domain patterns are not directly visible. However, at the boundary between domains stress appears which results in a refractive index change.
This makes domains visible in an optical microscope and visibility is especially
pronounced in “differential interference contrast” (DIC) mode or when crossed
polarizers are used. The domain walls appear diffuse and cannot be focused. For
better visibility, the poled substrate can be etched for 5 − 10 min in concentrated
hydrofluoric acid (HF) or a mixture of HF:HNO3 . The -z faces are etched faster
than +z faces [92], and after above stated time a differential etch depth of few tens
of nanometers is obtained. The poling pattern can also be made visible in the xz
plane because +y and -y faces are also etched at different rates. So, the poling
quality into the depth can be inspected when the poled substrate is cut vertically.
It shall be mentioned here that domain inversion can also be induced via diffusion processes [50]. This is important to know because the domain structures
can be affected by waveguide diffusion or annealing steps. Heat treatment of
lithium niobate at 800 − 1100 ◦C can lead to lithium out-diffusion and result in
a 1 − 15 µm thick inverted layer on the +z face [50, 113]. This configuration is
termed head-to-head, referring to the polarization vectors of the domains in the
bulk and in the formed layer. Metal in-diffusion can also result in a head-to-head
configuration. Therefore it is for example necessary to polish away the inverted
layer on the +z face after diffusion of titanium waveguides before poling [51]. By
ion-diffusion or proton exchange the coercive field strength can be increased or
lowered. This can be utilized in combination with electric field poling to achieve
especially fine patterns [114].
It is also worth to notice here that wafers from different suppliers were found
to possess different poling characteristics and result in different poling quality
[107]. This might be caused by impurities and by surface treatment during the
polishing process.

Tolerances
The influences of imperfections in periodic poling on SHG were discussed by
Fejer et al. [115]. Occasionally, after the periodic poling process a certain number
of domains remain unpoled. The decrease in conversion efficiency relative to the
ideal value η0 is given then by ηmiss rev /η0 = (1 − 2 f )2 , where f is the fraction
of domains with sign opposite to that of the ideal structure. Further the domain
width usually varies with a certain standard deviation σ. This results in a relative

2.8. THE DIAMOND BLADE DICING SAW

31

decrease of the optimum conversion efficiency given by


ηstat /η0 = exp −2π 2 σ2 /Λ2 ≈ 1 − 2π 2 σ2 /Λ2 ,

(2.44)

where Λ is the poling period and the approximation is done under assumption
of σ  Λ. This means that if 14.6 % of the domains that were supposed to be
inverted remain unpoled, the SHG efficiency is decreased to 50 %. Or if the width
of the inverted domains varies with a standard deviation σ = 0.19 · Λ, then SHG
efficiency is decreased by 50 %. These two examples indicate allowable tolerances
that should be met.

2.8

The diamond blade dicing saw

All ridge waveguides presented in this work were fabricated by use of a diamond
blade dicing saw7 . Therefore, this micromachining device shall be described here,
and its conventional use for singulation will be compared to its use for definition
of optical ridge waveguides.
In microelectronics industry numerous chips are fabricated simultaneously
on a single wafer. When the wafer is finished, the single dies are separated for
further packaging and assembly. Historically, the first technique used for die
singulation in the 1950s was “scribe and break”, where the wafer is scratched with
a diamond tip and then broken [27]. Later, laser scribing tools were introduced.
In the 1960s and 1970s IBM used gang saws, that comprised of stacked toothless
stainless-steel blades, which rotated in silicon carbide slurry to dice silicon wafers
[28]. These were the predecessors of the today commonly used diamond blade
dicing saws, which employ a high-speed rotating abrasive-edged blade and a
wafer mount on a translation stage.
The challenges of the singulation process include the aim to reduce the processing time needed to dice a wafer to reduce costs. At the same time the chipping beside the cut kerf shall be kept at low level, as it leads to microcracks that
reduce the die strength. Weakened dies might crack then in a following picking
or mounting step. Delamination of thin films (e. g. low-k dielectric films) has to
be prevented as it might proceed from the street to active areas of dies. In the
wafer design, streets are the areas between the active regions, in which the kerf is
cut. One challenge in the field of dicing is to reduce the width of theses streets
to allow for more dies on a wafer and higher yield. This is especially important
7 DAD322 from D ISCO C ORP.

32
a)

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS
b)

c)

0

100 µm

Figure 2.2: (a) Dicing saw in operation; (b) electroplated nickel-based blade
(left) and three different resin-based blades of different bond composition; (c)
microscope image of a nickel-based blade with synthetic diamond particles of
#2000 grit.

for small dies, such as light emitting diodes (LED), that posses a size of typically
250 µm×250 µm. Here a street width reduction from 50 µm to 20 µm adds 14 %
dies on a 2”-wafer [116]. On the other hand thinner blades tend to wear off or fail
faster. Also initial and running costs play a role in industrial application.
To allow for precise cuts, dicing saws are designed very rigid to prevent flexing under load and transmission of vibrations, further the stepper motors and
hydraulics need to enable precise alignment [28]. Dicing blades typically consist
of a ring of 2" diameter of a synthetic-diamond grit embedded in a binder. The
diamond particles have typical diameters between 2 − 45 µm and each diamond
acts as cutting tool. A coarser particle grit results in lower wear [28], but can
also result in higher roughness and chipping. Several industry standards exist
that define grit sizes by average particle size and allowable variation. Roughly
speaking, the grit size is given as the number of lines per inch of a sieve, through
which the grit would pass. Nickel, phenolic resin or sintered-metal are common
binders [117]. They keep the abrasive particles in place and sets free new ones
as the old diamonds are worn and loosened. For cutting a soft material, nickelbonded blades are recommended as the hard bond results in low wear. To cut
hard wafers resin-based blades are used since their softer bond enables faster replacement of worn diamonds. This prevents high load from a blunt blade that
can result in chipping. The bond hardness of sintered-metal is in-between that of
nickel and resin. Dicing blades are available in thickness ranges from ultra-thin
10 µm [118] over common sizes of 25 µm [28] to 200 µm [119] for special blades
for difficult-to-cut materials of high Mohs hardness or applications such as wafer
edge-trimming. Before cutting, blades have to be dressed: excess binder is machined off, new diamonds are freed, and the blades outer diameter and edges are

2.8. THE DIAMOND BLADE DICING SAW

33

trued [117]. Dressing can be performed by cutting into material of same composition as the blade itself or by cutting into special dresser-boards. Figure 2.2 (a)
shows a dicing saw in operation: Cooling water is sprayed onto the rotating blade
that cuts into a transparent crystalline material. In Fig. 2.2 (b,c) blades of different
bond composition and a microscope image of a nickel-based blade with synthetic
diamonds of grit #2000 are displayed.
In 2001 Kawaguchi et al. from NGK I NSULATORS and M ATSUSHITA E LEC TRIC I NDUSTRIAL C O . LTD (PANASONIC ) were the first ones to use a dicing saw
to define ridge waveguides in lithium niobate thin films [29, 30], and from 2003
on also Nishida et al. from NTT P HOTONICS L ABORATORIES presented results on
fabrication of such waveguides [22, 23]. They bonded lithium niobate wafers to
material of lower refractive index, lapped and polished them down to 3 − 10 µm,
and then cut ridges. High conversion SHG efficiency of e. g. 2400 %/W [120] or
370 %/(W cm2 ) [121] have been demonstrated in such waveguides. Currently,
based on this waveguide type, fiber-pigtailed converter modules are commercially available from NTT E LECTRONICS8 . Another manufacturer of telecommunication equipment that has presented research results on such waveguides
is O KI E LECTRIC I NDUSTRY C O . LTD . [31, 122]. Use of a wafer saw was also
made by Courjal et al. from the F EMTO -ST Institute in Besancon/France to prepare ridge waveguides in lithium niobate and thin-film lithium niobate (LNOI)
[24, 33, 37]. Further work on cut ridge waveguides in lithium niobate, thin-film
lithium niobate, YAG, sapphire and KTP was carried out at H ELMUT S CHMIDT
U NIVERSITY Hamburg [34–36, 38, 41, 123]. Sun et al. from M C M ASTER U NIVER SITY in Ontario/Canada fabricated proton exchanged optical ridge waveguides
in lithium niobate and compared them to cut ridge waveguides of lithium niobate
bonded on lithium tantalate [32]. Mittal, Carpenter and co-workers from U NI VERSITY OF S OUTHAMPTON in the UK used a dicing saw for end-facet preparation on optical waveguides in germanium telluride and lithium niobate [124,125].
They concluded that it can deliver in a single process step end-facets with low
roughness of 0.5 nm (RMS), which is comparable to results from endface preparation by lapping and polishing.
Compared to the field of die singulation, the focus shifts when a dicing saw is
used for optical waveguide fabrication. In die singulation chipping and roughness are reduced to minimize the street width and because roughness is an origin
of microcracks that reduce the die strength. Typical process parameters result in
shell-shaped chipping of several µm. To achieve acceptable attenuation in opti8 Model: WH-0780-000-A-B-C, WH-0780-000-F-B-C, WS-0578-000-A-B-C

34

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

cal waveguides the surface needs to exhibit roughness in the low nm-range and
be free of chipping. Such low roughness was achieved by the Besancon and the
Hamburg group by feed rates of 0.1 − 0.2 mm/s [24, 34], which are quite low
when compared to typical feed rates of 2 − 10 mm/s for singulation of SAW devices in lithium niobate [126]. The low feed rate at high rotation speed of typically 10 000 − 20 000 min−1 for blades of 2” diameter let the blade simultaneously
polish the waveguide sidewalls [24]. While hard nickel blades with diamond particle size of 3 − 8 µm or resinoid blades with particle size of 15 − 30 µm are recommended for lithium niobate singulation [126], resin-based blades with finest
available grit of 2 µm are used for optical waveguide preparation. In dicing processes blades with low wear are preferred to reduce maintenance work. Blade
wear during definition of ridge waveguides can lead to inhomogeneity of the
waveguide’s cross section along its length. This can result in inhomogeneity of
mode indices along the waveguide and hence to lower performance in e. g. frequency conversion processes.
When metals, oxides or nitride layers are found in a street on the top side
of a wafer, a common technique to reduce top and backside chipping and enhance throughput is dual-spindle dicing [28]. Here, first a wider blade is used
with optimum parameters to cut the surface, followed by a narrower second one
with optimized parameters to cut the substrate. In the process of optical ridge
waveguide fabrication we also make use of different blades. Typically the ridge
waveguides are defined with 10-30 µm deep cuts using a 200 µm wide, fine resinbased blade. The waveguides’ endfaces are prepared then by a 50 − 100 µm deep
cut of the same blade. To fully separate the waveguide sample from the rest of
the substrate a thinner nickel blade with coarser grit is used.

2.9

Wafer direct bonding and crystal ion slicing

Two sufficiently flat and smooth surfaces can stick together when brought into
contact. This is caused by van der Waals forces and hydrogen bonds, and is
typically reversible. By annealing, the bond strength can be improved through
formation of chemical bonds. The term direct bonding points out that no adhesive
is involved. Also the term fusion bonding is used, but it should not be confused
with anodic bonding, where borosilicate glasses are bonded through alkali ion diffusion. In the 19th century already it was found that polished glass plates can
strongly stick together [45]. This effect was used for example to mount mirrors to
the gas tubes of He-Ne gas lasers and to vacuum seal them thereby. Today silicon

2.9. WAFER DIRECT BONDING AND CRYSTAL ION SLICING

35

wafers are bonded together to form micromechanical devices, such as pressure or
acceleration sensors [45]. Different methods exist to fabricate silicon-on-insulator
and among them is the smart cut method, which involves oxidizing a first silicon wafer’s surface and implanting ions into it. The first wafer is then bonded
to a second handle wafer, and by a heat treatment the first wafer is sliced in the
implanted layer to obtain a silicon thin film on an insulating SiO2 layer.
To enable wafer bonding the involved surfaces need to be sufficiently clean,
flat and smooth [45]. When roughness is elevated or when wafers are not sufficiently flat, they do not bond to each other. The elastic energy, necessary to bring
the surfaces into contact, then exceeds the surface energy. Silicon wafers will typically bond spontaneously, when brought into contact, if their RMS roughness is
below 0.5 nm [127]. When silicon or lithium niobate wafers undergo chemicalmechanical polishing, their surface roughness is usually below this value. Commercial silicon or lithium niobate wafers of prime/optical grade have sufficiently
low roughness and flatness that allow for bonding.
A particle of 1 µm diameter between two standard silicon wafers can result
in an unbonded area with 1 cm diameter already [45]. To prevent particle contamination and achieve high cleanliness, wafer bonding is typically performed
in a class 10 or class 1 cleanroom. Wafers can be bonded manually or by use of
a commercial bonder, which allows to align the wafers. In the field of volume
manufacturing fully automated bonding machines are used. For research or low
budget production micro-cleanrooms were introduced that allow wafer bonding
in non-cleanroom environment [128, 129]. Here, the two wafers are separated by
spacers in an enclosed container. Particle free water is sprayed between them to
flush away contamination and after spin-drying the spacers are removed to bond
the wafers. Organic contamination typically does not lead to unbonded areas at
room temperature, but it can weaken bonds and initiate bubble formation in the
interface during annealing. Prior to bonding the wafers are typically wet cleaned.
Plasma treatment can not only clean, but also activate surfaces and enable higher
bond strength at room temperature [45, 130, 131].
The process of silicon bonding is very well understood and described in literature [45, 127, 132]; and it shall therefore be described here. Silicon’s surface
is covered by a 1 − 2 nm thick native oxide layer. The surface is terminated by
silanol groups (Si-OH) that make it hydrophilic and let it be covered by monolayers of water molecules. When two hydrophilic wafers are brought into contact,
their adhesion is mediated through hydrogen bonds of the chemisorbed water
molecules. During heat treatment above 110 ◦C, the chemisorbed water starts to

36

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

desorb. It can either diffuse along the interface to leave it or it can diffuse through
the thin native oxide layer to react with the silicon below:
Si + 2H2 O → SiO2 + 2H2 .

(2.45)

Opposing silanol groups that are close enough can then form covalent siloxan
bonds (Si − O − Si):

−Si − OH + OH − Si− → Si − O − Si + H2 O.

(2.46)

Hydrogen, as well as excessive water can diffuse along the interface. By heating
up to 200 ◦C surface energy of ∼1.2 Jm−2 can be reached. When the wafers are
annealed above 800 ◦C the native oxide can soften, close microgaps and hence
increase the surface energy to ∼2 Jm−2 [132]. This surface energy corresponds
to bulk fracture energy, and if pull tests are performed, the bonded wafer pair
will fracture in the bulk. By annealing at 1000 ◦C the few nm thick insulating
interface can be dissolved [45]. It was mentioned before that wafers will only
bond, if their surface roughness is below 0.5 nm. The order of magnitude of this
allowable roughness can be derived, when a monolayer of water is assumed on
two OH-determined silicon surfaces. OH-groups have a length of about 1.0 Å
and the distance between two oxygen atoms in ice is 2.76 Å [132]. So the distance
that can be bridged between the two surfaces is up to ∼10 Å, and accordingly the
surface roughness of each surface can be up to ∼5 Å [132].
When the native oxide layer of two silicon wafers is etched away in diluted
hydrofluoric acid, the surfaces become determined by Si − H groups and are hydrophobic. Adhesion between bonded wafers is promoted due to van der Waals
forces which are weaker than hydrogen bonds. At temperatures above 400 ◦C hydrogen desorbs from the surfaces and Si − Si bonds form, and from 700 ◦C on the
interface’s strength is that of bulk silicon [45].
As described before, high bond strength is achieved during high temperature
annealing. This can be incompatible with temperature-sensitive structures that
need to be defined on the wafers prior to bonding or can be problematic, when
materials with different thermal expansion coefficients need to be bonded. Extensive research has delivered several approaches to achieve strong bonding at lower
temperatures. It was found for example that silicon wafers, which are bonded in
vacuum, can obtain surface energy of 3 J/m2 when annealed at 150 ◦C [133]. It is
assumed that when wafers are bonded in ambient atmosphere, nitrogen prevents
silanol groups from joining. Also, surface activation by use of oxygen or argon

2.9. WAFER DIRECT BONDING AND CRYSTAL ION SLICING

37

allows for higher bonding strength at lower annealing temperature [134]. The
plasma treatment seems to attack the crystal surface and to increase the density
of bond sites. Surface activation can also be achieved by chemical treatment with
nitric acid or other acids [45]. The final bond strength can also be increased by applying certain pressure during room temperature bonding [134]. Also it is a common fact that long term storage increases the bond strength. Other methods that
allow for low temperature bonding include monolayers of special molecules [45].
During heat treatment bubbles can form at the interface that are caused by
outgassing of the bonding material, entrapped gas, thermal decomposition of
surface contamination or by chemical reactions at the bond interface [45]. Contamination should of course be prevented by appropriate cleaning. In silicon
wafer bonding it was found favorable to bond one wafer with thick thermal oxide layer to another wafer with thin native oxide [135]. Then water can diffuse
through the native oxide to react with silicon to form SiO2 , and hydrogen can
be absorbed into the open thermal oxide. Babic et al. used grooves as outlets for
volatile products when bonding InP to GaAs [136].
Several methods exist to quantify adhesion strength. The surface energy of
a bond can be determined by controlled cleavage, when a razor blade is stuck
between two bonded wafers [45]. As an equilibrium between surface energy and
elastic energy of the bend wafers sets in, the work of adhesion can be determined.
The work of adhesion between to thin plates of thickness di with Young’s moduli
Ei can be calculated as
3h2 E1 d31 E2 d32
,
(2.47)
WAB = 4
8c E1 d31 + E2 d32
when a razor blade of thickness h is inserted and a crack of length c opens [45].
Bond strength can also be quantified by tensile testing and this delivers a certain
stress at which the bonding interface delaminates, the wafers fracture in bulk, or
at which the mounting adhesive fails. Further, it is common to just note that a
bonded surface could withstand certain treatment, like lapping and polishing.
Direct bonding allows to bond a variety of materials to each other, such as
metals, carbides, fluorides, nitrides, oxides or chalcogenides [45]. Also different
materials can be bonded to each other (hetero bonding). Here, a challenge occurs
when the material’s thermal expansion coefficients strongly deviate. In contrast
to epitaxial methods the two materials do not need to have similar lattice constants. In general it seems, any material which can form H − F, H − O or H − N
terminated surface can be bonded at room temperature via hydrogen bonds to
the same or another material that possess O, N or F atoms on its surface [127].

38

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

The formation of a bonding interface via oxygen covalent bonds, described in
Eq. (2.46), is assumed to take place also for other metal oxides [132]. For nitrides
a comparable process can occur, where instead of OH-groups NH-groups are involved and polymerization between the surfaces is performed through a covalent
−N− bond.
Eda et al. bonded lithium niobate to lithium tantalate after surface activation
with a mixture of hydrogen peroxide, ammonia solution and water [137]. After heat treatment above 300 ◦C, the bonding interface had achieved the strength
of the bulk material. They assumed a mechanism of initial bonding via hydroxyl groups followed by formation of a chemical bond from oxygen and constituent atoms of the crystal during annealing. Takei et al. applied argon and
oxygen plasma activation to silicon-on-insulator, Ce:YIG, InP, and LiNbO3 for
direct bonding [130]. They found the argon plasma to increase the surface roughness of Ce:YIG, InP and LiNbO3 , and hence degrade bonding quality. In contrast
short exposure to oxygen plasma lowered the surface roughness and is therefore assumed to improve the bond strength. Further, oxygen plasma is known
to increase the density of hydroxyl groups and lead to higher bonding strength
for low-temperature bonding [45]. Namba et al. bonded lithium niobate and its
isomorph lithium tantalate to silicon [131]. By use of transmission electron microscopy they found a 2 nm thick amorphous intermediate layer between lithium
niobate and silicon. This proofs bonding at an atomic order. As silicon and fused
silica have the same surface chemistry [45], also fused silica and lithium niobate
can be assumed to build chemical bonds .

Crystal ion slicing and other techniques for preparation of crystalline thin films
One important field of application for wafer direct bonding is the fabrication of
thin crystalline films on a handle wafer [45, 138]. Here, fabrication of mono crystalline silicon on an insulating layer is of special interest because the isolating
layer can diminish parasitic effects in electronics. Parasitic capacity is reduced
and faster microprocessors are enabled, or alternatively the power consumption
can be reduced. A driving force for development of silicon-on-insulator (SOI)
was also the demand for electronics with enhanced radiation hardness for military and aerospace application [138]. The insulating layer prevents free charges,
which are generated from ionizing radiation, from reaching the silicon thin film
with the active components. Different methods exist, but only the smart cut tech-

2.9. WAFER DIRECT BONDING AND CRYSTAL ION SLICING

39

nique shall be discussed in detail because it is closely related to the method used
in this work for the fabrication of lithium-niobate-on-insulator (LNOI).
The first SOI wafers were produced by implanting an oxygen layer to a certain depth in a silicon wafer and oxidizing it to separate the top crystalline layer
through a SiO2 layer from the rest of the silicon wafer. This method is termed
SIMOX, as an acronym for separation by implantation of oxygen. Another, quite
straightforward method for the fabrication of SOI is to bond two oxidized wafers,
and lap and polish one wafer down. This method allows to obtain SOI of 10 −
100 µm thickness [138]. To achieve thinner uniform films one wafer can be implanted with boron at a certain depth prior to bonding to form an etch-stop. After
mechanically grinding away most of the implanted wafer, it can be etched to the
etch-stop layer. This method is named bond-and-etchback (BESOI). Disadvantages
about this technique include contamination of the silicon thin film with boron.
The smart cut technique was developed and patented 1994 by Michael Bruel
from C OMMISSARIAT E NERGIE ATOMIQUE (CEA), France [139]. A “seed” silicon
wafer is oxidized and hydrogen implanted at a certain depth. After bonding it to
a second “handle” silicon wafer, the seed wafer is sliced in the implanted depth
through a heating step. Elevated temperature at the same time strengthens the
wafer bonding. The technique is also referred to as crystal ion slicing (CIS) or ion
exfoliation. It should be noticed that although the term smart cut is often used,
also when thin films of other crystalline materials are prepared, it is actually a
proprietary name.
It was found that hydrogen doses > 2 · 1016 cm−2 result in microcavity formation, and hydrogen is partially bond to dangling bonds and partially filling the
voids [138]. The passivation of the dangling bonds by hydrogen prevents the microcracks from healing. When heated to 400 − 500 ◦C hydrogen segregates from
the dangling bonds and forms molecular hydrogen. Pressure rises and blisters
form. By Oswald ripening larger voids grow on the cost of smaller ones. A weakened plane builds up, in which the silicon crystal is cleaved by mechanical stress
or pressure. The separated surfaces have roughness on the order of few nm and
are touch-polished to obtain sub-nm roughness [138]. After polishing, the high
quality seed wafer can be reused to form a thin film for another SOI wafer. As
handle wafer, a wafer of lower quality can be used since it provides only the mechanical support. By use of crystal ion slicing, silicon thin films of 5 nm to 1.5 µm
can be fabricated on oxide layers of 5 nm to 5 µm [138].
When hydrogen doses above 1017 cm−2 are implanted, blistering occurs already without heat treatment. For too low doses < 2 · 1016 cm−2 the void for-

40

a)

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

He+

SiO2

b)

c)
LN substrate A

LN substrate A

LN substrate B

LN substrate B

d) LN subs
trate

A

LN substrate B

Figure 2.3: Fabrication process of LNOI: (a) He implantation into a first lithium
niobate substrate A (seed wafer); (b) SiO2 deposition onto a second LN wafer B
(handle wafer); (c) pre-bonding; (d) crystal ion slicing and bond-strengthening
by heat treatment.

mation is insufficient [138]. The hydrogen diffuses and dissolves during annealing. It was also found that combinations of hydrogen and helium implantation
provide advantages in terms of lowered necessary dose [140]. While doses of
2 · 1017 cm−2 of H+ alone or 6 · 1016 cm−2 of He+ alone are necessary to achieve
splitting, a combination of 7.5 · 1015 cm−2 H+ and 1016 cm−2 He+ allows for splitting already. It is important to implant hydrogen first to form voids, and helium
aids then by building up pressure.
Lithium niobate thin films
The smart cut process has also been applied to lithium niobate to obtain lithium niobate thin films on a second material with lower refractive index, like
silica or an adhesive [14]. Referring to SOI, here the name lithium-niobate-onoptical-insulator (LNOI) is used. The term “optical insulator” is used to indicate the lower-index material below which “optically insulates” the lithium niobate thin film and enables waveguiding. The fabrication process is depicted in
Fig. 2.3. First, a seed wafer is ion implanted to form the weakened plane and silica is deposited onto a second handle wafer by evaporation or chemical phase
epitaxy. After pre-bonding the wafers at room temperature, the wafer pair is
heated to initiate crystal ion slicing. By further tempering the bond strength can
be improved and implantation damage can be annealed. Alternatively to SiO2
deposition and direct bonding [141, 142], the wafers can be bonded with an adhesive [20], such as benzocyclobutene (BCB). By now, LNOI wafers are commercially available [143, 144]. The LNOI thin film can be further structured to obtain
waveguides with cross-sections of ∼1×1 µm2 that enable enhanced efficiency of
nonlinear optical components and small bending radii [14].
To obtain crystal ion slicing in z-cut lithium niobate Levy et al. implanted a
dose of 5 · 1016 cm−2 He ions at 3.8 MeV normal to the surface [145]. Instead

2.9. WAFER DIRECT BONDING AND CRYSTAL ION SLICING

41

of heat treatment they etched the implanted layer away. This is possible since
the implanted layer is removed at a more than 1000 times higher rate than the
unimplanted crystal. In a study Szafraniak et al. investigated crystal ion slicing
of several ferroelectrics with hydrogen alone, helium alone or a combination of
both at energies of 105 − 160 keV [146]. Different doses were implanted at different temperatures and optimum ion slicing was found for lithium niobate for He
implantation of 5 · 1016 cm−2 at room temperature and 105 keV. Other parameters
can result in exfoliation during implantation or did not show blistering and ion
slicing during annealing at all. While Levy et al. implanted the lithium niobate
normal to the surface, Szafraniak et al. performed implantation at an angle of 7°
to the normal to prevent channeling. Channeling effects can occur when swift
ions propagate along a crystals axis through channels in the crystal lattice and
thereby reach large penetration depth. Other workgroups also used He implantation with doses between 3.5 · 1016 cm−2 and 4 · 1016 cm−2 that result in proper
crystal ion slicing [141, 142]. While many others only employed He implantation
or found implantation of He alone more suitable, Diest et al. combined implantation of 6 · 1016 cm−2 hydrogen with 5 · 1016 cm−2 of helium to obtain lithium
niobate thin films [147]. It shall be noted here that higher ion energy results in a
larger implantation depth and hence a thicker ion sliced layer.
To initiate crystal ion slicing Szafraniak et al. and Diest et al. heated the prebonded samples to 500 ◦C [146, 147]. Hu et al. tempered the pre-bonded samples
at 165 ◦C for 16 h and further at 190 ◦C for 6 h to improve bond strength and then
heated the sample for 2 h at 228 ◦C [142]. Rabiei et al. used a temperature of 220 ◦C
to induce exfoliation [141] and in their review Poberaj et al. explain that crystal
ion slicing occurs at around 220 ◦C [14].
Ions in matter are stopped due to interaction with electrons and the nucleus.
For swift ions the electronic stopping power is far greater than the nuclear stopping power, and it is described by the Bethe formula [148]
4πnZ2
dE
=−
·
dx
me v2



e2
4πe0

2



· ln

2me v2
I


,

(2.48)

with energy loss per propagation length dE/dx, electron density of the target
material n, atomic number of the ion Z, electron mass me , electron charge e, ion
velocity v, and average excitation potential per electron I. The stopping power is
maximum at a certain value, which is about 500 keV for silicon and 700 keV for
lithium niobate when penetrated by He ions, and decreases towards higher and
lower energies. To predict implantation profiles use can be made of the SRIM soft-

42

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

ware package [149]. It is based on a quantum mechanical treatment of ion-atom
collisions [150, 151]. Models and corrections are adopted to reproduce experimental results . The overall accuracy of the SRIM code is stated as 4 %, meaning
that only 4 % of experimentally obtained stopping powers deviate more than 5 %
from calculated values [149].
Other methods for preparation of lithium niobate thin films include chemical
vapor deposition [152], sol-gel processing [153], epitaxy from melt [154], molecular beam epitaxy [155], RF sputtering [156], and pulsed laser deposition [157].
However, it is not possible to epitaxially grow a single crystalline film on an amorphous layer, such as silica. Instead epitaxy is restricted to crystalline substrates
with appropriate lattice, like lithium tantalate. If MgO is used as a buffer layer,
its thickness should be restricted to a maximum of ∼100 nm to allow for epitaxy [153], which is not sufficient to prevent leakage of a waveguide mode into
the substrate. Further, many of the mentioned methods result in polycrystalline
lithium niobate [156] or their crystal quality or nonlinearity is degraded.
Waveguide formation in LNOI
The common methods for waveguide formation in bulk lithium niobate are titanium diffusion and proton exchange, i. e. exchange of lithium atoms for hydrogen. Titanium needs to be diffused at ∼1000 ◦C for several hours to produce an
optical waveguide [11]. But since LNOI wafers cannot withstand temperatures
above ∼500 ◦C [46], this method is incompatible with LNOI. Proton exchange can
be performed at about ∼250 ◦C and it has already been used to fabricate waveguides in LNOI [158, 159]. However, only the extraordinary refractive index increases whereas the ordinary index is decreased. Thus only one polarization is
guided. Further, proton exchange only allows for an index increase of maximum
0.12 [12] and typically annealing is used to lower waveguide losses which at the
same time lowers the maximum index increase. Therefore, bending radii in proton exchanged LNOI are limited to the millimeter range.
Beside proton exchange, several methods exist for waveguide preparation in
LNOI. One field of methods comprises techniques to remove the lithium niobate
beside the waveguide, either fully or only to a certain depth. The other field of
methods includes techniques to prepare a strip of high index material on top of
the lithium niobate thin film to obtain a strip-loaded waveguide.
Most widespread for ridge definition in LNOI are dry etching methods, and
these methods are assumed to be promising for commercial application [14, 46].
A metal mask is photolithographically patterned and afterwards the LNOI is ex-

2.9. WAFER DIRECT BONDING AND CRYSTAL ION SLICING

43

posed to a plasma. Different gases and parameters were used and it was found
that gases with fluor are partially not suitable, because lithium fluoride is redeposited hindering further etching and causing surface roughness [25, 160]. It
seems more suitable to use purely physical dry etching with argon gas, or a combination of chemical and physical etching [25, 26]. While in earlier works attenuation of 10 − 17 dB/cm was found in dry etched ridge waveguides [20, 21], optimized process parameters allow for LNOI waveguides with losses of 0.3 dB/cm
in recent publications [25, 26].
Other methods that were used to prepare ridge waveguides in LNOI are wet
etching [19] and focused ion beam milling (FIB) [161]. A general problem about
wet etching is that different crystal faces of lithium niobate are etched at different
rates, and this results in abrupt edges in bends. By use of FIB for example fine
photonic crystal structures have been created [14]. However, serial writing of
structures with an ion beam is time and cost intensive, and rather considered to
be a method for proof of concept [46].
For preparation of strip-loaded waveguides different materials such as chalcogenide glass [162], silicon nitride [163], tantalum oxide [164] or titanium oxide
[165] have been used. These methods can result in low loss waveguides (e. g.
0.3 dB/cm [163]) and can be applied in industrial fabrication. An advantage of
strip-loaded waveguides is that the attenuation can be lower due to the absence of
scattering from the sidewalls. A drawback is the lower index step, which results
in reduced mode confinement and makes larger bending radii necessary. Still,
low loss micro-ring modulators with 200 µm radius have been presented [162].
There is not as much research on LNOI as on SOI integrated optics, and in
SOI far more elements have been demonstrated, such as wavelength-divisionmultiplexing (WDM) filters and multiplexers, polarization splitters and polarization rotators, or spatial multiplexers [166]. Still, the principles of functional
elements are the same and many silicon-based applications could be transferred
to LNOI.

44

CHAPTER 2. FUNDAMENTAL CONCEPTS AND METHODS

Chapter 3
Ridge waveguides in lithium niobate thin
films
3.1

Introduction

It was discussed in chapter 2.3 that LNOI waveguides can allow for narrow bending radii of the order of ∼10 µm instead of centimeters in Ti-diffused or proton
exchanged waveguides in bulk LN. Experimentally ring resonators with diameters of 50 µm have been realized [66]. Further, thin-film waveguides can constrict modes to a cross section of A = 0.4 µm2 at 1550 nm while waveguides in
bulk have typical mode cross sections of the order of A = 16 µm2 [14]. As efficiency of frequency conversion processes scales with 1/A, much higher efficiency
can be expected in LNOI compared to bulk components. Higher conversion efficiency allows to shorten converters or to operate them efficiently at lower power.
Thin-film waveguides also allow for much narrower distance between electrodes
above and below [167], or left and right of a waveguide [164] in a modulator.
The voltage that is needed to obtain a certain field strength (and phase shift) can
be reduced by more than an order of magnitude and hence also the energy consumption is lowered. This motivates the general interest in research on LNOI.
In 2013 when the present work was started, reported propagation loss of ridge
waveguides in lithium niobate thin films were rather high. For example Guarino et al. and Hu et al. reported 17 dB/cm and 6.3 − 7.5 dB/cm, respectively, at
a wavelength of 1.55 µm in dry etched waveguides [20, 21]. These losses were
attributed to surface roughness and implantation damage. As discussed in section 2.3, surface roughness plays an especially pronounced role for such narrow
and thin waveguides. Takaoka et al. determined 10 dB/cm at 1.55 µm in wet
etched ridge waveguides in LNOI [168]. He also named surface roughness as
one origin of attenuation. But also leakage of the mode to the sides was men45

46

CHAPTER 3. RIDGE WAVEGUIDES IN LITHIUM NIOBATE THIN FILMS

tioned since the ridges were not etched down to the insulating adhesive layer.
Further, ridge waveguide preparation by use of a diamond blade dicing saw was
reported and the obtained losses were of the order of 1 dB/cm, though the presented waveguides were prepared in rather thick LN films of 3 − 4 µm and the
ridges were also several µm or even a mm wide [30, 120, 121, 169]. These rather
thick LN films of few µm were also not prepared by crystal ion slicing, but by mechanical lapping and polishing down an adhered wafer. Courjal et al. fabricated
ridge waveguides in crystal-ion-sliced lithium niobate of 1 µm, though they did
not state the attenuation or whether they were guiding at all [24].
The high losses in µm or submicrometer thick ridges originated from the surface roughness from dry etching. We therefore wanted to find out, whether it is
possible to cut low roughness waveguides in crystal-ion-sliced lithium niobate
by use of a diamond blade dicing saw. Whether this is possible or not depends
critically on the bond strength between the three layers: lithium niobate / silica
/ lithium niobate handle wafer. Our investigation on ridge preparation in LNOI,
that we were provided with from a cooperation partner, and LNOI, which we
prepared ourselves, is described in the following.

3.2

Ridge waveguides in LNOI from cooperation partner

We were provided from Prof. Hui Hu who is with S HANDONG U NIVERSITY and
J INAN J INGZHENG E LECTRONICS C O . LTD9 in Jinan/China with several lithium niobate thin-film samples. Hu had started research on LNOI as a postdoc in
the research group of Prof. Wolfgang Sohler in Paderborn/Germany, and there
had been a research cooperation between their group, the group of Prof. Volkmar
Dierolf from Lehigh University (Bethlehem, USA) and us. This research resulted
in cut ridge waveguides in LNOI with low losses of ∼1.4 dB/cm at a wavelength
of 1.5 µm [170]. The LNOI samples consisted of a LN thin film that was separated
from a LN handle substrate by a SiO2 layer. Compared to its BCB bonded counterpart, LNOI with a SiO2 intermediate layer allows for annealing at higher temperature to heal implantation damage. However, later on, the results appeared
difficult to reproduce. The LNOI that we were provided with appeared to delaminate upon cutting. A reason might have been that fabrication processes in Hu’s
new facilities had not been optimized at that time.
9 www.nanoln.com

3.2. RIDGE WAVEGUIDES IN LNOI FROM COOPERATION PARTNER
a)

47

1 mm

SiO2

LN thin film

LN h.w.

Figure 3.1: Delaminated lithium niobate thin film: During ridge definition the
LN thin film has partially delaminated, making visible the LN handle wafer
(h.w.) and the SiO2 buffer layer.

An example of a LN thin film that delaminated during processing with the
wafer saw is shown in Fig. 3.1. Over larger areas the LN thin film is removed
along with the silica layer. Between the ridges the silica is still present, showing
that it was tried to cut only into the silica layer but not into the handle wafer
below. It seems, if the blade reaches the interface between the handle wafer and
silica, the SiO2 layer exfoliates. This demonstrates weak adhesion of the SiO2 film
that was deposited on the handle wafer.
For one especially long sample from Hu propagation losses were investigated
with a commercial Metricon prism coupler, in which light is coupled via a prism
to the thin film and scattered light is detected along the light streak. The examined sample is 76 mm long and consists of a 598 nm thick planar xz-cut LN layer,
separated by a 2010 nm thick SiO2 film from the LN substrate. An exemplary
result from a measurement for TE polarization at 1550 nm is shown in Fig. 3.2.
The scattered intensity is displayed as the black curve. It looks inhomogeneous
and determined by point defects, e. g. by the pronounced one at 1.35 cm. This
indicates that the roughness and hence attenuation vary over the samples surface
and arise particularly at defects (scratches, fractures). The sample ends at 3.1 cm,
and light is scattered here strongly. By fitting the red exponential curve through
the marked minima (red circles) of the measurement, we estimate attenuation of
0.2 dB/cm. We assume the accuracy of this method to be rather low, but it seems

48

CHAPTER 3. RIDGE WAVEGUIDES IN LITHIUM NIOBATE THIN FILMS

intensity [a.u.]

500

measurement
fit

400

300

200
0

0.5

2
2.5
3
1
1.5
propagation distance [cm]

3.5

Figure 3.2: Measurement of propagation loss from scattered light in an LNOI
sample at 1550 nm for TE polarization.

clear that the attenuation within this planar waveguides is below 1 dB/cm. Comparable results were obtained at wavelengths of 532 nm, 1064 nm and 1550 nm
for TE and TM polarization. The LNOI samples, that we fabricated ourselves and
which are described later, were too small for this measurement method.

3.3

Fabrication of LNOI

To overcome the problems of the weakly bonded thin films, we started to investigate LNOI fabrication in Hamburg on our own. As discussed in section 2.9,
the LNOI fabrication process consists of the following steps: ion implantation,
SiO2 evaporation, room temperature bonding (pre-bonding) and tempering (slicing/annealing). Further, ridges are defined and end-facets need to be polished
by use of a diamond blade dicing saw.
Lithium niobate ridge waveguides on silica guide only the fundamental mode
for each polarization at telecommunication wavelength according to simulations
when their cross section is about 0.5 × 0.5 µm2 to 1 × 1 µm2 . The relation between
implantation energy of He ions and their projected range is given in Fig. 3.3 (a).
It was calculated with the SRIM software package [149] based on the chemical
composition of the target material and its density. For ion energy of 350 keV a
mean implantation depth of 1.01 µm is obtained. The depth distribution of He
ions that impinge on the LN target with 350 keV is depicted in Fig. 3.3 (b). It
was simulated for a number of 35 000 ions. We note that the distribution has a

4000 b)

a)

1.5
1
0.5
0

49

number of He ions

projected range [µm]

3.3. FABRICATION OF LNOI

0

200
600
400
ion energy [keV]

3000
2000
1000
0

0

0.5
1
depth [µm]

1.5

Figure 3.3: Results of SRIM simulation: (a) average projected range of He+ ions
in LiNbO3 ; (b) distribution of He+ with energy of 350 keV in LiNbO3 .

width of ∼0.2 µm and further the highest He density can be expected slightly
below the mean projected range. Finally, we had 3” LN wafers implanted into
their -z face with a dose of 4 · 1016 ions/cm2 He ions at 350 keV at H ELMHOLTZ Z ENTRUM D RESDEN -R OSSENDORF. The dose is within the range that resulted in
successful crystal ion slicing according to other works [141,142,146], as discussed
in section 2.9. To prevent charging of the insulating wafer during implantation a
thin gold film was deposited that we later etched off with potassium iodide.
As mentioned above, the weak point about the LNOI, that we were provided
with by Hu, was the adhesion of the SiO2 to the handle wafer, and we also found
it difficult to evaporate silica on lithium niobate. A general problem about joining
the two materials is that SiO2 evaporation as well as the subsequent exfoliation
process require higher temperature, while their thermal expansion coefficients
are quite different: αLN,a = 14.8 · 10−6 K−1 [58], αSiO2 = 0.51 · 10−6 K−1 [58]. Many
recipes to coat SiO2 were tested on our refurbished V EECO 7700 electron beam
evaporator. We evaporated silica without any adhesion promoter, with Cr, with
Ti and with Cr and Ti, and we also heated the LN substrate to different temperatures during deposition. Before coating, the LN substrates were cleaned with
B ALZERS substrate cleaner no. 1, ethanol, acetone, isopropanol and were further
plasma cleaned in an oxygen plasma for 5 min. The procedure that resulted in
best adhesion was to evaporate 5 nm of Ti, 1.5 nm of Cr and to deposit SiO2 at
200 ◦C. After deposition the wafer was annealed at 450 ◦C for 6 h. For samples,
which are discussed in the following, we deposited a 1.6 µm thick silica layer
onto the +z face of a 3” LN wafer. The SiO2 layer was shortly polished with a
colloidal-silica slurry (U LTRASOL 500 S) on a polyurethane pad to reduce rough-

50

CHAPTER 3. RIDGE WAVEGUIDES IN LITHIUM NIOBATE THIN FILMS

Figure 3.4: Self-constructed wafer chuck of micro-cleanroom for pre-bonding
of wafers.

ness. By use of a white light interferometer we determined roughness of 0.4 nm
(RMS) and the final layer thickness was 1.4 µm.
The seed wafer was implanted into its -z face and the handle wafer was SiO2
coated on its +z face. So, upon bonding the wafers face each other “head-totail” and electrostatic forces act attractively when the wafer pair’s temperature is
changed. To enable direct bonding both surfaces need to be sufficiently smooth
and clean. The silica’s roughness is below 0.5 nm (RMS) after polishing and the
implanted surface possess roughnesses of about 0.2 nm (RMS). Sufficient cleanliness is commonly only provided in a cleanroom because already a particle of 1 µm
diameter can result in an unbonded area of 1 cm in diameter [45]. A particle-free
environment is especially important for bonding of ferroelectrics, such as lithium niobate, because they can charge up and attract contamination. Our workgroup operates its own cleanroom with equipment for photolithography and a
gray-room with a sputter system, an electron beam evaporator and a dicing saw.
Within the cleanroom the concentration of particles with diameter > 0.3 µm is
commonly < 1 ft−3 and there are rarely any particles > 1 µm in a volume of 1 ft3 .
In the gray-room we found typically less than 50 ft−3 particles > 0.3 µm and less
than 5 ft−3 particles of size > 1 µm. The measurements were done with an “AeroTrak APC 9303” particle counter from TSI G MB H lying on a bench and volumes
of 2 ft3 were inspected in intervals.
To be able to try different bond recipes, we cut the implanted wafer to pieces
of 11 × 10 mm2 along the crystallographic x and y axes, and the SiO2 coated one
to plates of 13 × 12 mm2 . The rectangular form was chosen to indicate the crystallographic axes. Further, one piece has slightly larger dimensions so that it can be
placed with tweezers onto the smaller one without touching or getting too close

3.3. FABRICATION OF LNOI

51

Figure 3.5: Lithium niobate bonded to silicon; both pieces are separated by
aluminum foil and Newton’s rings are visible in the unbonded area.

to the bond area. Various methods were applied before pre-bonding of pieces
was achieved, that is snapping together of the two surfaces and strong adhesion. The method that repeatably delivered room temperature pre-bonding is as
follows: We cleaned both wafer pieces with acetone, isopropanol and deionized
water. Further, we cleaned and activated the surfaces in oxygen plasma for 300 s
at a pressure of 90 mTorr with parameters that we commonly use to remove photoresist at a rate of ∼1 nm/s. Directly after venting the plasma system the wafer
pieces were manually bonded using tweezers. Before this process was found to
work, we had brought the plasma cleaned plates from gray to cleanroom which
possesses a lower particle concentration and numerous wet cleaning techniques
had been tested there. Also bonding in deionized water was tested, but the wafer
pieces did not snap together and did not remain in contact. We had also started
building up a micro-cleanroom [128, 129], which is a device that allows to clean,
spin-dry and bond wafers in a sealed container without the need for a cleanroom. Its principal component is shown in Fig. 3.4. In contrast to Stengl et al.
and Lehmann et al. we constructed a chuck that allows to hold the wafers by vacuum suction at an adjustable distance. When the shown element is placed into a
closed container, solvents and purified water can be sprayed in for cleaning, and
after spin-drying, vacuum can be switched off to bring the wafers into contact
and pre-bond the

[The evaluation harness truncated this reference: showing the first 120000 of 267453 characters.]
</reference>

<statements>
1. As-Etched (Standard Ar+ Milling, Unannealed, Air Clad) has an optical propagation loss of 10 - 15 dB/cm (1000 - 1500 dB/m) at telecom.
2. Low-Damage ICP-RIE (Ar+ Low-Bias + HSQ Mask) has an optical propagation loss of 0.2 - 0.4 dB/cm (20 - 40 dB/m) at telecom.
</statements>

Begin the assessment now. Output only the JSON list, without any conversational text or explanations.