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Growth, defect structure, and THz application of stoichiometric lithium niobate
K. Lengyel, Á. Péter, L. Kovács, G. Corradi, L. Pálfalvi, J. Hebling, M. Unferdorben, G. Dravecz, I. Hajdara, Zs.
Szaller, and K. Polgár
Citation: Applied Physics Reviews 2, 040601 (2015); doi: 10.1063/1.4929917
View online: http://dx.doi.org/10.1063/1.4929917
View Table of Contents: http://scitation.aip.org/content/aip/journal/apr2/2/4?ver=pdfcov
Published by the AIP Publishing
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APPLIED PHYSICS REVIEWS
Growth, defect structure, and THz application of stoichiometric lithium
niobate
K. Lengyel,
1
A. P
eter,
1
L. Kov
acs,
1
G. Corradi,
1
L. P
alfalvi,
2
J. Hebling,
2,3
M. Unferdorben,
2
G. Dravecz,
1
I. Hajdara,
1
Zs. Szaller,
1
and K. Polg
ar
1
1
Wigner Research Centre for Physics, Hungarian Academy of Sciences, 1121 Budapest,
Konkoly-Thege M.
ut 29-33, Hungary
2
Institute of Physics, University of P
ecs, 7624 P
ecs, Ifj
us
ag
utja 6, Hungary
3
MTA-PTE High Field Terahertz Research Group, 7624 P
ecs, Hungary
(Received 15 April 2015; accepted 17 June 2015; published online 20 October 2015)
Owing to the extraordinary richness of its physical properties, congruent lithium niobate has
attracted multidecade-long interest both for fundamental science and applications. The combination
of ferro-, pyro-, and piezoelectric properties with large electro-optic, acousto-optic, and photoelastic
coefficients as well as the strong photorefractive and photovoltaic effects offers a great potential
for applications in modern optics. To provide powerful optical components in high energy laser
applications, tailoring of key material parameters, especially stoichiometry, is required. This paper
reviews the state of the art of growing large stoichiometric LiNbO
3
(sLN) crystals, in particular,
the defect engineering of pure and doped sLN with emphasis on optical damage resistant (ODR)
dopants (e.g., Mg, Zn, In, Sc, Hf, Zr, Sn). The discussion is focused on crystals grown by the high
temperature top seeded solution growth (HTTSSG) technique using alkali oxide fluxing agents.
Based on high-temperature phase equilibria studies of the Li
2
O–Nb
2
O
5
–X
2
O ternary systems
(X ¼Na, K, Rb, Cs), the impact of alkali homologue additives on the stoichiometry of the lithium
niobate phase will be analyzed, together with a summary of the ultraviolet, infrared, and far-infrared
absorption spectroscopic methods developed to characterize the composition of the crystals. It will
be shown that using HTTSSG from K
2
O containing flux, crystals closest to the stoichiometric
composition can be grown characterized by a UV-edge position of at about 302 nm and a single
narrow hydroxyl band in the IR with a linewidth of less than 3 cm
1
at 300 K. The threshold
concentrations for ODR dopants depend on crystal stoichiometry and the valence of the dopants;
Raman spectra, hydroxyl vibration spectra, and Z-scan measurements prove to be useful to
distinguish crystals below and above the photorefractive threshold. Crystals just above the threshold
are preferred for most nonlinear optical applications apart holography and have the additional
advantage to minimize the absorption even in the far-infrared (THz) range. The review also provides
a discussion on the progress made in the characterization of non-stoichiometry related intrinsic and
extrinsic defect structures in doped LN crystals, with emphasis on ODR-ion-doped and/or closely
stoichiometric systems, based on both spectroscopic measurements and theoretical modelling,
including the results of first principles quantum mechanical calculations on hydroxyl defects. It will
also be shown that new perspective applications, e.g., the generation of high energy THz pulses with
energies on the tens-of-mJ scale, are feasible with ODR-doped sLN crystals if optimal conditions,
including the contact grating technique, are applied.
V
C
2015 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4929917]
TABLE OF CONT ENTS
I. INTRODUCTION ............................ 2
II. GROWTH OF STOICHIOMETRIC LiNbO
3
..... 2
A. Early works ............................ 2
B. Phase equilibria of Li
2
O–Nb
2
O
5
–X
2
O
(X ¼Na, K, Rb and Cs) ternary systems. . . . 3
C. HTTSS growth of sLN crystals from K
2
O-
fluxed melts ............................ 6
D. Growth of ODR-ion doped sLN crystals. . . . 7
III. COMPOSITION AND PROPERTIES OF PURE
AND ODR-ION DOPED LiNbO
3
CRYSTALS . . 8
A. Spectroscopic characterization of undoped
LN.................................... 8
1. Ultraviolet absorption edge . . . . . . . . . . . . 8
2. OH
absorption ...................... 9
B. Properties of Mg-doped sLN crystals. . . . . . . 10
1. OH
vibration, UV absorption edge and
Raman spectroscopy .................. 11
2. Z-scan measurements . . ............... 15
1931-9401/2015/2(4)/040601/28/$30.00
V
C
2015 AIP Publishing LLC2, 040601-1
APPLIED PHYSICS REVIEWS 2, 040601 (2015)
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3. Absorption, refractive index in the far-
IR (THz) range. . ..................... 16
C. Other divalent, trivalent, and tetravalent
ODR dopants ........................... 18
D. Transition metal and rare earth dopants . . . . 20
IV. THEORETICAL MODELS FOR INTRINSIC
AND EXTRINSIC DEFECTS . . .............. 21
A. Intrinsic defects ......................... 21
B. Dopant ions ............................ 22
C. OH
ions .............................. 22
V. THz GENERATION—A PROMISING
APPLICATION ............................. 23
VI. SUMMARY AND OUTLOOK . .............. 25
I. INTRODUCTION
Lithium niobate (LiNbO
3
, LN) has been recognized as
one of the most versatile materials for applications in modern
optics in a broad range extending from the near UV to the far
IR. The combination of ferro-, pyro-, and piezoelectric prop-
erties with large electro-optic, acousto-optic, and photoelas-
tic coefficients as well as strong photorefractive and
photovoltaic effects made LN to one of the most extensively
studied materials over the last 50 years. Extended device
applications required the growth of high-quality single crys-
tals with properties depending on a detailed control of their
intrinsic and extrinsic defect structures.
In the late 1960’s and early 70’s, detailed investiga-
tions of the binary phase diagram showed that LiNbO
3
was
a congruently melting material with a congruent composi-
tion noticeably differing from the stoichiometric one repre-
sented by the chemical formula:
1–5
in fact, non-
stoichiometry implies several percents of defect sites in the
lattice making the crystal sensitive to high energy laser
radiation.
By the end of the 1980’s, by using the Czochralski
growth method, the preparation of high quality congruent
single crystals had been solved and huge amounts of data on
physical properties were collected,
6–9
opening the way for
technical applications. At the same time, both characteriza-
tion methods for controlling the real state of LN and theoreti-
cal models for understanding the formation and role of
native defect structures were rapidly progressing.
Starting from the early 90’s, interest in the use of LN for
higher energy laser applications was intensified. As congru-
ent LiNbO
3
(cLN) was easily damaged, to provide more re-
sistant optical components for laser applications, tailoring of
key material parameters via stoichiometry control and/or
doping by additives promoting optical damage resistant
(ODR) behaviour in the visible–near infrared region, e.g.,
Mg, Zn, In, Sc, etc.,
10
has been introduced. For producing
stoichiometric samples, new techniques, including the prepa-
ration of stoichiometric wafers or fibers from cLN crystals
by the vapor transport equilibration (VTE) method
11,12
as
well as various solution growth techniques, have been
applied. As the demand for pure and doped bulk stoichiomet-
ric LiNbO
3
(sLN) crystals kept increasing, efforts became
concentrated on the development of crystal growth techni-
ques, such as the continuous filling double crucible growth
13
and the high temperature top seeded solution growth
(HTTSSG).
14
Technological advances in the growth of large stoichio-
metric crystals led to a breakthrough in defect engineering of
pure and ODR-ion doped sLN crystals promoting, e.g., the
development of quasi-phase-matched frequency conversion
applications using periodically poled LN (PPLN) crystals
15
and also the advent of new devices for the generation of high
energy THz pulses.
16
The present review starts with a history of solution
grown LN crystals describing recent progress in the under-
standing and control of their chemical and structural inho-
mogeneities. We focus on developments achieved in our
laboratories i n the preparation, charact erization, modelling,
and application of undoped and doped sLN crystals with
emphasis on ODR dopants. A detailed description will be
given on the high temperature phase equilibria of the
Li
2
O–Nb
2
O
5
–K
2
O ternary system and on the optimization
of the flux composition for the growth of sLN. Methods
worked out for the determination of the crystal composition
of congruent to stoichiometric LN (based on the UV
absorption edge or the OH
absorption and Raman band
shapes) will be discussed. Spectroscopic achievements are
also supported by recent results on theoretical modelling
based on quasi-potentials for intrinsic and extrinsic defects
and on first principles quantum mechanical calculations for
hydroxyl ions in sLN. Finally, a new promising application
for the generation of high energy THz pulses using ODR-
ion doped sLN crystals will be presented.
II. GROWTH OF STOICHIOMETRIC LiNbO
3
A. Early works
Investigation of the homogeneity of Czochralski grown
crystals in the early 1970’s led to the identification of
non-stoichiometric, congruently melting oxides wit h LiNbO
3
among the first examples. Peterson
1
and Carruthers et al.
2
found that stoichiometric crystals could be pulled only from
strongly off-stoichiometric melts with 58.0 mol. % Li
2
O
content and even those crystals were small and/or of inferior
quality.
Based on detailed investigations of the phase diagram of
the Li
2
O–Nb
2
O
5
binary system, Byer et al.
3
grew high qual-
ity LN crystals, thereby locating the congruently melting
composition of LiNbO
3
at 48.6 mol. % Li
2
O content. Lerner
et al.’s investigation
4
of the phase equilibrium showed that
LN has an asymmetric solid solution range, which narrows
towards the stoichiometric composition with decreasing tem-
perature (extending at 1000
C from 46.0 to 50.0 mol. %
Li
2
O and at room temperature only from 48.0 to 50.0 mol. %
Li
2
O). As reported by Svaasand et al.,
5
the binary solidus
path is limited by the temperature of the binary eutectic reac-
tion of LiNbO
3
–Li
3
NbO
4
at 1160
C. The upper temperature
limit of the solidus at stoichiometric composition is at about
1170
C, above this temperature, the solid phase composition
shifts towards the Li deficient side. This means that in order
to shift the thermodynamic equilibrium towards the stoichio-
metric composi tion, the crystallization temperature has to be
kept close to or below 1170
C.
040601-2 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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From the late 1970’s, several attempts have been made
to obtain sLN crystals by using flux methods for lowering
the crystallization temperature. To a large extent, the success
of the flux growth depends on the choice of the flux composi-
tion and the appropriate growth conditions. Voronkova
et al.
17
tested V
2
O
5
,WO
3
, and B
2
O
3
containing fluxes.
Kondo,
18
Hemmerling and Hergt,
19
and Hibiya
20
reported
the Li
2
O-V
2
O
5
mixture to be a suitable solvent both for liq-
uid phase epitaxy and bulk flux growth of sLN crystals.
Recently, Huang et al.
21
identified the crystallization region
of LN in the B
2
O
3
–Li
2
O–Nb
2
O
5
ternary system. Despite the
lower critical crystallization temperatures below 1170
C for
all these growth experiments, the results of the composition
measurements were not fully satisfactory as the solvent com-
ponents (V, B, W ions) were also incorporated into the crys-
tals (Voronkova reported built-in concentrations of
3–5 at. %).
The preparation of bulk stoichiometric crystals derives
from the report of Vartanyan
22
on the unusual properties of
“congruent” crystals doped with 6 wt. % K
2
O. As was shown
by Malovichko et al.,
23,24
these crystals are nearly potassium
free and their composition is close to stoichiometric. To
obtain pure stoichiometric crystals, Kitamura et al.
13
also
used an alkali additive, i.e., Li by applying the continuous
filling double crucible method, thereby again preparing bulk
crystals in the Li
2
O–Nb
2
O
5
binary system from extremely
Li-rich melt (58% Li
2
O) similarly to the early attempts of
Peterson
1
and Carruthers et al.
2
Later, by using starting melts
with K
2
O added in concentrations from 10 to 16 mol. %,
Polg
ar et al.
14
showed that the high temperature top-seeded
solution growth technique was an effective method for grow-
ing stoichiometric LiNbO
3
single crystals.
Following the early results, considerable development
has been achieved in the growth of large stoichiometric crys-
tals. In this section, the current state of sLN crystal growth
will be reviewed, and based on the results of Cochez et al.,
25
P
eter et al.,
26
and Dravecz et al.
27
on high-temperature phase
equilibria of Li
2
O–Nb
2
O
5
–X
2
O(X¼Na, K, Rb, Cs) ternary
systems, the impact of alkali homologue additives (Li/Na/K/
Rb/Cs) on the stoichiometry of the lithium niobate phase
will be discussed. In addition, the effect of ODR dopants on
the growth of sLN crystals will be summarized.
B. Phase equilibria of Li
2
O–Nb
2
O
5
–X
2
O(X5 Na, K, Rb
and Cs) ternary systems
The interest to establish more precisely the high-
temperature phase equilibria of the Li
2
O–Nb
2
O
5
–K
2
O ter-
nary system has arisen due to the increasing demand of the
preparation of sLN crystals. The first experiments on grow-
ing sLN with K
2
O additive used congruent Li/Nb ratios in
the starting melt.
23
Later, by testing various flux composi-
tions, Polg
ar et al.
28
found that the crystals grown from
fluxes with starting composition of Li/Nb ¼1 and K
2
O in the
range of 0.16–0.195 [K
2
O]/[LiNbO
3
] ratio resulted in
improved stoichiometry. It was also shown that the key pa-
rameter determining the composition of the growing crystal
was the crystallization temperature.
The optimization of the flux composition and the growth
conditions requires an extended knowledge of the crystalli-
zation range of hLiNbO
3
i in the Li
2
O–Nb
2
O
5
–K
2
O ternary
system. Previously, the phase relations of the
Li
2
O–Nb
2
O
5
–K
2
O system were examined by Scott et al.
29
and Ikeda and Kiyohashi
30
in the solid-solution field of tung-
sten bronze-type K
3
Li
2
Nb
5
O
15
(KLN) and K
3
LiNb
6
O
17
com-
pounds. The primary crystallization field and the phase
relations of hLiNbO
3
i have first been investigated by Cochez
et al.
25
using differential scanning calorimetry (DSC) experi-
ments and X-ray powder diffraction. The temperatures corre-
sponding to the lithium niobate liquidus surface and the solid
phases involved in the ternary invariant reactions were estab-
lished along the vertical sections cut along the 10, 20, and
25 mol. % K
2
O isopleths within the ranges from 25–55,
30–60, and 40–60 mol. % Nb
2
O
5
, respectively. Vertical sec-
tions of the LN phase field along g
1
¼(LiNbO
3
–K
2
O),
g
2
¼(LiNbO
3
–E
1
), and g
3
¼(LiNbO
3
–KNbO
3
(KN)) lines
(see Fig. 1(a)) were detailed later by Polg
ar et al.
31
The liqui-
dus surface beyond the LiNbO
3
–KNbO
3
join for Nb
2
O
5
con-
tent between 50 and 55 mol. % was only estimated.
The phase boundaries were established by DSC analyses
discussed in Ref. 25. The liquidus surface of hLNi is limited
by four monovariant lines with endpoints shown on Fig.
1(a): (i) Liq. þhLi
3
NbO
4
iþhLiNbO
3
i ranging from e
1
to
E
1
, (ii) Liq. þhKNbO
3
iþhLiNbO
3
i from P to E
1
, (iii)
Liq. þhKLNiþhLiNbO
3
i from X to P, and (iv)
Liq. þhLiNb
3
O
8
iþhLiNbO
3
i from e
2
to X. At 997
C, a ter-
nary eutectic reaction occurs between liquid, hLiNbO
3
i,
hLi
3
NbO
4
i, and hKNbO
3
i. The composition of the eutectic
liquid (E
1
) was located at about 45.0 mol. % Nb
2
O
5
,
26.0 mol. % K
2
O, and 29.0 mol. % Li
2
O. A quasi-peritectic
reaction has also been identified at a temperature of about
1050–1055
C. The quasi-peritectic liquid (P) has a composi-
tion roughly equal to 49 mol. % Nb
2
O
5
, 25.5 mol. % K
2
O,
and 25.5 mol. % Li
2
O.
During crystallization of the hLNi phase, the point rep-
resenting the liquid in equilibrium with the solid moves on
the liquidus surface towards one of the monovariant lines,
limiting the liquidus surface. Upon further decrease in the
temperature, the liquid composition reaches a point on one
of the monovariant lines, and the liquid composition pro-
ceeds along this line while the two solids separate.
Solidification is completed when the liquid composition
reaches the ternary eutectic point E
1
.
The assessment of the phase diagram by crystal growth
experiments was reported by P
eter et al.
26
The evolution of
the solid composition was determined by the HTTSSG
method, covering the whole single-phase area with pulling
out of the maximum amount of single crystal. Since K
2
Ois
insoluble in lithium niobate (K
þ
practically not entering the
lattice), the crystallization path may be traced with ease;
crystallization of hLNi starts when the temperature reaches
that corresponding to the liquidus and the liquid composition
evolves along the straight line joining the starting composi-
tion with that of LiNbO
3
and ends at a point on an intersect-
ing monovariant line (as shown by the “g” lines in Fig. 1(a)).
In Fig. 2, crystals grown from compositions located on
the LiNbO
3
–K
2
O(g
1
) and the LiNbO
3
–KNbO
3
(g
3
) lines are
040601-3 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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shown. These crystals were prepared by continuing the
growth process after having pulled out the maximum amount
of the single crystalline phase. On the bottom part of the
boule, polycrystalline phase separation can be seen. The con-
stituent phases determined by X-ray phase analysis were
hLiNbO
3
iþhLi
3
NbO
4
i and hLiNbO
3
iþhKLN solid sol-
utioni for g
1
and g
3
growth, respectively, in accordance with
the evolution of the composition of the remaining liquid
along the corresponding monovariant line (e
1
–E
1
, and P–E
1
),
respectively. Using the results of various growth experiments
covering the whole single-phase area, the yield of the hLNi
phase can be determined. Assuming stoichiometric composi-
tion and no K
2
O contamination for the solid phase, the coor-
dinates of the limits of the LiNbO
3
liquidus surface can be
calculated. These estimates for the limits, compared with
those given by the phase diagram, are in good agreement.
26
The establishment of isothermal tie lines, representing
solid-liquid concentration relationships across the solid-
solution range, relies on the same principle: as the actual
crystallization temperature is determined by the melt compo-
sition, the tie lines can be located by assessing the evolution
path of the solid composition and the corresponding K
2
O
content of the melt as functions of the crystallization
fraction. The determination of the Li/Nb ratio of the crystals
requires the use of a well established physical method of
sufficient precision, better than available by chemical analyt-
ical techniques. The measurement of the position of the fun-
damental absorption edge in the near UV region, as reported
by F
€
oldv
ari et al.
32
and Kov
acs et al.,
33
and described in
more detail in Section III A 1, has proved to be a convenient
and fast method to determine the solid composition. For
establishing the solid-liquid concentration relationships, the
solid composition along the growth axes can be determined
on crystal slices cut perpendicular to the growth axes,
providing also the actual liquid composition if the mass
balance of the pulled amount is taken into account. Hence,
the corresponding crystallization temperature can be deduced
from the vertical cut of the phase diagram.
Using K
2
O containing melts, the solidus paths can be
extended down to 1000
C(Fig.1(b)). For crystals grown
on the LiNbO
3
–K
2
Oline(g
1
), for K
2
O > 13.8 mol. %, below
1114
C, the solidus composition path clearly has a constant
segment with a composition very close to Li/Nb ¼1. Working
with a Li/Nb < 1 ratio in the flux (see, e.g., the growth along
the g
2
and g
3
lines), the stoichiometric composition can also
be approached; however, at the same crystallization tempera-
ture, less and less stoichiometric crystals with decreased
Li/Nb ratio are obtained. On the g
2
line, solid compositions in
FIG. 1. Phase relations in the growth of stoichiometric lithium niobate. (a)
The projection of the primary crystallization field of hLNi phase in the
Li
2
O–Nb
2
O
5
–K
2
O ternary system. E
1
: LiNbO
3
–Li
3
NbO
4
–KNbO
3
ternary
eutectic point, e
1
,e
2
binary eutectic points, P: peritectic point, g
1
,g
2
,g
3
:
traces of investigated vertical sections of the phase diagram. LN: LiNbO
3
,
L3N:Li
3
NbO
4
, KLN: tungsten bronze-type solid solution, gray area: crystal-
lization region of hsLNi. Reproduced with permission from K. Polg
ar et al.,
Phys. Status Solidi A 201, 284–288 (2004). Copyright 2004 Wiley. (b)
Evolution of the solidus in the Li
2
O–Nb
2
O
5
binary system in the region
close to the near-stoichiometric LN composition for the g
1
,g
2
,g
3
growth
experiments. Reproduced with permission from
A. P
eter et al., J. Alloys
Compd. 386, 246–252 (2005). Copyright 2005 Elsevier.
FIG. 2. Crystals grown by continuing the process beyond the single phase
stage along a monovariant line limiting the liquidus surface, the starting
compositions located (a) on the LiNbO
3
–K
2
Og
1
line at 10 mol. % K
2
O
content; Reproduced with permission from G. Dravecz et al., J. Cryst.
Growth 286, 334–337 (2006). Copyright 2006 Elsevier and (b) on the
LiNbO
3
–KNbO
3
g
3
line at 20 mol. % K
2
O content. The co-crystallized
phases on the bottom (see white polycrystalline and yellow parts) were
identified as hLiNbO
3
iþhLi
3
NbO
4
i and hLiNbO
3
iþhKLN solid solutioni
for g
1
and g
3
growth, respectively.
040601-4 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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On: Thu, 19 Nov 2015 14:18:02
the range from Li/Nb ¼0.979 to 0.992 can be achieved; along
the g
3
line, the composition limit to be reached is at about Li/
Nb ¼0.984. For Li/Nb > 1 ratios and similar K
2
O content in
the flux, the yield is rather low, the stoichiometric composi-
tion can be obtained only at the end of the crystallization
range, when the liquidus practically reaches the monovariant
line near 1100
C.
31
The above results on solid-liquid concen-
tration relationships obtained from the assessment of the
phase diagram by crystal growth experiments
26
compare well
with earlier data published in the literature, i.e., are consistent
with the solid compositions deduced from UV cut-off wave-
lengths (measured at a ¼20 cm
1
absorption; see the results
of Serrano et al.,
34
Niwa et al.,
35
and Polg
ar et al.
28
).
Solvents, based on other alkali metal oxides (Na
2
O,
Rb
2
O, and Cs
2
O), have also proved to be useful fluxes for
the growth of sLN crystals by lowering the crystallization
temperature.
27
While Na ions entered the crystal lattice with
a segregation coefficient of k
sol/liq
(Na
2
O) 0.2, the others
(Rb
2
O and Cs
2
O) were found practically insoluble in
LiNbO
3
, similarly to K
2
O. The phase boundary limit of the
LiNbO
3
liquid surface in the Li
2
O–Nb
2
O
5
–X
2
O(X¼Na, K,
Rb, Cs) ternary systems monotonously shifted with the
increase in the ion radius of alkali ion added: For the vertical
cut along the Li/Nb ¼1 ratio, the liquid phase boundaries for
K
2
O-, Rb
2
O- and Cs
2
O-containing fluxes were found to be at
alkali oxide contents of 17.2, 16.5, and 15.8 mol. %, respec-
tively. In the case of the Na
2
O-based flux, from the yield of
the pulled-out hLNi phase and the amount of incorporated
Na content, this limit was estimated to be 14.1 mol. % of
Na
2
O. The establishment of isothermal solid-liquid concen-
tration relationships for K
2
O, Rb
2
O, and Cs
2
O based fluxes
on the Li/Nb ¼1 vertical cut of the ternary phase diagram is
shown in Fig. 3. At the same alkali content, the crystalliza-
tion temperature was found to be lowest for K
2
O containing
flux, and slightly increased (by 25–50
C) for Cs
2
O, Rb
2
O,
and Na
2
O additives (Fig. 3(a)). These differences in the crys-
tallization temperatures are manifested in the results of the
UV measurements and also in the evolution of the solidus
composition paths as shown in Figs. 3(b) and 3(c). While for
crystals grown from K
2
O-, Rb
2
O-, or Cs
2
O-based fluxes, the
measured UV-edge position (i.e., the Li/Nb ratio) depends
on the crystallization temperature alone, for the crystal
grown from Na
2
O containing flux, it is also affected by the
incorporated Na ions. Thus from the point of view of the
HTTSS growth of stoichiometric LiNbO
3
crystals, the choice
of starting compositions along the Li/Nb ¼1 line (above
13 mol. % K
2
O content) is advisable. For doped crystals, to
ensure both sufficient incorporation and near stoichiometry
of the crystals, starting compositions with Li/Nb < 1 have to
be considered as well.
For LN crystals grown from Li-rich melts by the double
crucible growth method, Li/Nb ratios in the range
0.988–0.993 were reported by Furukawa et al.
36
In this case,
the seeding temperature had to be chosen close to the upper
temperature limit of the binary solidus (1165–1175
C for
stoichiometric composition) as the crystallization tempera-
ture was limited from below by the temperature of the binary
eutectic at 1160
C. With the use of other alkali fluxed melts
(K
2
O or even Rb
2
OorCs
2
O), the stoichiometry of the grown
crystals can be further improved, since for flux compositions
located on the LiNbO
3
–X
2
O join, the crystallization temper-
ature can be lowered down to 1000
C. The seeding tem-
peratures at 1165
C can already be ensured with only
10.6 mol. % of K
2
O or between 12 and 13 mol. % content
of Rb
2
OorCs
2
O.
FIG. 3. Establishment of solid-liquid concentration relationships for the
Li
2
O–Nb
2
O
5
–X
2
O(X¼Na, K, Rb and Cs) ternary system. (a) Vertical sec-
tions of the LiNbO
3
phase field in the Li
2
O–Nb
2
O
5
–X
2
O ternary system
along the LiNbO
3
–X
2
O line (LN: LiNbO
3
, L3N:Li
3
NbO
4
). (b) UV absorp-
tion edge positions of consecutive slices cut perpendicular to the growth axes
of crystals grown with starting compositions Li/Nb ¼1and10mol.%X
2
Oal-
kali additives. Reproduced with permission from G. Dravecz et al.,J.Cryst.
Growth 286, 334–337 (2006). Copyright 2006 Elsevier. (c) Evolution of the
solidus composition paths in the Li
2
O–Nb
2
O
5
binary system for liquidus paths
along the LiNbO
3
–X
2
O line of the X
2
O–Nb
2
O
5
–Li
2
O ternary system.
040601-5 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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Alkali additives have been reported to be beneficial in
the growth of other ferroelectric compounds of the
Li
2
O–Nb
2
O
5
–K
2
O ternary system as well. In the growth of
KN and the tungsten bronze-type KLN crystals by the
HTTSSG method, Beh et al.
37
used Rb
2
O, P
eter et al.
38
used
Cs
2
O additive in the melt to improve the stoichiometry of
the KN and KLN crystals, respectively. Again, the fluxing
agents practically did not enter either the KN or the KLN lat-
tices, similarly to the role of K
þ
ions in the growth of LN
crystals; they have affected the crystal properties only via
decreasing the crystallization temperature; thus, as K
2
Oin
the case of LN, these additives could also be considered as
appropriate fluxing agents in the respective systems. The
impact of alkali homologue ions (Na
þ
,K
þ
,Rb
þ
and Cs
þ
)on
the compositional variation of ferroelectric single crystals
seems to be correlated with their ionic radii: The incorpora-
tion of the smaller alkali ions into the crystal is promoted via
the mixed alkali effect (i.e., enforced, preferential occupancy
of low energy sites by the smaller cations, e.g., K
þ
!Li:LN,
Rb
þ
!K:LN, and Cs
þ
!K:KLN).
C. HTTSS growth o f sLN crystals from K
2
O-fluxed
melts
The information obtained from the investigation of the
high-temperature phase equilibria of the Li
2
O–Nb
2
O
5
–K
2
O
ternary system has greatly advanced the technology of grow-
ing sLN crystals with desired perfection and homogeneity.
According to the phase diagram, the stoichiometric composi-
tion of the crystals can be ensured by using starting composi-
tions situated along the LiNbO
3
–K
2
O line of the ternary
system, with the potassium content of the fluxes above
13.8 mol. %. In these cases, the liquidus-solidus tie lines
evolve along the quasi-binary join and the Li/Nb 1 ratio
stays constant both in the liquid and the growing crystal.
The use of K
2
O-fluxed melts necessitated an adaptation
of the technology to the requirements of solution growth
(i.e., increased viscosity of the fluxed melt, decreased growth
rates, and finer temperature control). For the bulk growth of
good quality crystals, the top-seeded arrangement with
steep thermal gradients above the melt has proved quite
adequate.
14
The proper choice of the operating parameters of
the HTTSSG method is related to the design of apparatus.
Crystals can be prepared using either RF or resistance heat-
ing furnaces. Vertical temperature gradients just above the
melt surface were reported within the range of 0.5–7
C/mm,
the pulling rates adjusted to 0.1–0.2 mm/h, and seed rotation
rates between 4 and 45 rotations per minute (rpm).
14,35
The
increased viscosity of the solution limits mixing and mass
transport, and makes it difficult to obtain uniform supersatu-
ration and effective convection to the growth interfaces.
Szaller et al.
39
have investigated the optimal conditions for
facet-free growth of crystals pulled along the Z axis. To
eliminate the flow instabilities and to achieve an interface
shape conform to the very low convexity requirement a grad-
ually adjusted rotation rate pr ogram was used realising ther-
mal conditions characterized by the relation Gr/Re
2
> 1 for
the mixed convection interaction parameter (where Gr is the
dimensionless Grashof number and Re the rotational
Reynolds number, characteristic for the buoyancy and the
forced convection, respectively).
The crystallization temperature of stoichiometric crys-
tals pulled from K
2
O-fluxed melts is below the Curie temper-
ature all along the growth process, thus the resulting domain
structure of the crystals is no more related to the ferroelectric
phase transition but only to the self-generated poling effects
during growth or cooling down. The temperature gradients,
and in some cases the impurity/dopant concentration gradi-
ent via the induced non-uniform electric field can supply
potential differences sufficient for poling. By all means, the
poling field required for domain reversal is much less in
stoichiometric crystals than in the congruent ones, as shown
by Grisard et al.
40
and Gopalan et al.
41
The HTTSS grown sLN crystals show pronounced
tendency towards faceting. The presence of the facets can be
delineated by the associated strain pattern, chemical etching,
or by the observation of incorporated micro-inclusions at
edges of the facets. Facets cause regions of strain in crystals
which are usually accommodated elastically, but sometimes,
the stress developed may exceed the yield point of mechani-
cal twinning (Fig. 4(a)). Close connection has been observed
between faceted growth and the appearance of domain rever-
sal as well. The low coercive fo rce typical for sLN promotes
ferroelectric domain reversal in the faceted region (Figs. 4(b)
and 4(c) central regions) and also the formation of
micro domains manifested as small light scattering centres in
Fig. 4(c).
Faceting, related to both the shape of the growth inter-
face and the pulling direction, generally occurs in those areas
of the crystal-melt interface, where the growth front is paral-
lel to the morphologically important (heaviest packed)
crystal planes. In these cases, both the impurity segregation
at facets and the developing stress may promote the reversal
of domain patterns of the crystal. Polg
ar et al.
28
carried out
comparative studies with growth axes parallel to the
Z ¼h0001i,Y¼h01
10i,X¼h2
1
10i axes as well as in the
h01
11i and h0
222i directions and showed that development
FIG. 4. (00.1) slices of faceted as-
grown sLN crystals pulled along
Z ¼h0001i direction. (a) Mechanical
twins observed through crossed polar-
izers. (b) Pyramidal facets on the bottom
and (c) domain patterns of an adjacent
bottom slice observed through crossed
polarizers.
040601-6 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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of facets occurred primarily along the {01
12} pyramidal
planes. For LN crystals, the pyramidal facets may form
when the angle between the growth direction and the direc-
tion normal to the {01.2} planes is obtuse. Thus to reduce or
eliminate the facets for pulling along the Z, X, and Y direc-
tions near planar for the h01
11i or h0
221i growth directions,
slightly convex growth interface shapes are required. Pulling
along the Z axis, the steep axial thermal gradient by itself
was sufficient for the growth of single domain crystals with-
out additional poling. The crystals grown with nearly planar
interface were always single domain, virtually all along the
boule; for the other growth directions, the resulting domain
structure depended on the ratio of the axial and radial tem-
perature gradients at the growth interface. For crystals grown
along the directions perpendicular to the spontaneous polar-
ization vector (e.g., along the X or Y direction), the boule
usually consisted of two domain regions, with a vertical
boundary parallel to the growth axis.
The degree of structural perfection is highly affected by
the necking process. Growth ridges on the shoulder surface
and facets on the growth front are the major source of struc-
tural defects. After seeding, the crystal grows with conically
increasing diameter on a strongly convex growth front until
the desired diameter is reached. The rate of the increase in
the crystal diameter is influenced by the cone angle. Ridge
formation also depends on the cone angle (i.e., direction of
growth at the conical part): On crystals grown along the
Z-axis with acute cone angle, at the shoulder part, both
(10.
2) and (01.
2) type pyramidal planes assist in ridge for-
mation, while at the cylindrical part where the growth condi-
tions are stable, only type (10.
2) is acting. Stress associated
with large ridges promotes both cracking and mechanical
twinning during the cooling down process. Therefore, to
avoid faceting is a must for the growth of good quality
crystals, together with a near planar growth interface during
the preparation of the cylindrical part.
D. Growth of ODR-ion doped sLN crystals
For the photonic application of nonlinear optical materi-
als at high light intensities, the optical damage is a major
scientific and technological issue. Light induced refractive
index change due to the combined action of photoconductiv-
ity and electro-optic activity may result in chaotic beam
distortion, ruling out any control of the propagating light
wave front. The unwanted appearance of the photorefractive
effect is a serious obstacle for the application of nominally
undoped LiNbO
3
as well. Understanding this problem
requires detailed knowledge of the defect structure and the
charge transport properties of the material.
Controlling optical damage in LN crystals essentially
involves the removal of rechargeable defects, both extrinsic
and intrinsic, playing central roles in photorefraction (PR).
The main defects in question are the impurities Fe, Cu, Mn,
and Rh (contaminants from raw materials and crucible), and
antisite Nb. Elimination of the latter can be achieved, beside
improving the stoichiometry, by doping with optical damage
resistant elements above a given threshold concentration.
The family of ODR ions includes divalent (Mg, Zn), trivalent
(In, Sc), and tetravalent (Hf, Zr, Sn) ions as well.
The defect chemistry of LN crystals based on the pre-
ferred Li vacancy model
42
will be detailed in Section III,
where the impact of ODR ions in suppressing the antisite
Nb
Li
defects will also be discussed. As follows from the
analysis, the critical threshold concentrations of the ODR
dopants depend both on the actual Li/Nb ratio and the
valence of the built-in dopant. A stoichiometric LiNbO
3
crystal having fewer intrinsic defects requires lower dopant
concentrations for tailoring its properties. While for cLN, the
threshold concentration for di-, tri-, and tetravalent ODR
ions is roughly 5, 4, and 2 mol. %, respectively, it is below
1 mol. % for sLN crystals. Understanding of the respective
models and advances in the technology of growing stoichio-
metric crystals strongly promoted the preparation of large
optical-damage-resistant single crystals with desired perfec-
tion and homogeneity (Fig. 5). Most widely used in applica-
tions from the visible to the THz range are MgO doped LN
crystals. Periodically poled sLN:Mg (PPLN), in particular,
received special attention in quasi-phase-matched frequency
conversion devices.
15
Investigations on the critical threshold concentration of
ODR ions in HTTSS grown near stoichiometric crystals
have been reported for Mg, Zn, In, and Zr ions using alkali
fluxed systems,
43–46
and for Sc using a Li-rich solution;
47
further references and discussion on this topic will be given
in Section III C.
Thermal analyses have shown that in the Li
2
O–Nb
2
O
5
–
K
2
O ternary system, the MgO additive of concentrations
below 2 mol. % has minimal influence on the solidus-
liquidus phase relations of the fluxed system. Similar results
may be expected for the other ODR additives as well.
Therefore, it seems reasonable to explain the crystallization
of ODR-ion doped crystals on the basis of the knowledge
gained on the phase equilibria of undoped Li
2
O–Nb
2
O
5
–K
2
O
ternary and Li
2
O–Nb
2
O
5
binary systems, including their par-
titioning behaviour between Li and Nb sites during the
growth. The Li/Nb ratio of the solidus can be ensured to be
nearly constant and close to the stoichiometric composition
by the appropriate choice of the flux composition both in
the framework of HTTSS growth and the double-crucible
automated powder supply technique. As was shown for the
Li
2
O–Nb
2
O
5
–K
2
O ternary system, growth along the g
1
line
FIG. 5. High quality stoichiometric LiNbO
3
crystal grown by the HTTSSG
method.
040601-7 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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results in a constant composition segment of the solidus
(detailed in Fig. 1(b)). In the Li
2
O–Nb
2
O
5
binary system, the
use of an automated powder supply technique maintaining
fixed molar [Li
2
O]/[Nb
2
O
5
] 58/42 ratio
36
allows to keep
constant both the liquid and solid compositions. To interpret
the incorporation of ODR ions into flux grown LN crystals,
both the segregation between solvent and solute and the
distribution of dopants between Li and Nb sites have to be
considered at the same time.
As examined for MgO doping in the Li
2
O–Nb
2
O
5
–K
2
O
ternary system,
43
the decrease in the growth yield (i.e., the
maximal amount of available LiNbO
3
phase) is already
considerable at 0.1 mol. % doping and decreases further at
higher dopant concentrations. Chemical analysis of the built-
in concentration of Mg indicates a slightly higher value for
the segregation coefficient in the case of below-threshold
crystals compared to above-threshold ones (for both cases
k
eff
1, independently of the Li/Nb ratio). The optimal con-
centration of MgO required for the growth of damage resist-
ant (above threshold) crystals was found to depend on the
crystallization temperature; thus by choosing an optimal
combination of the crystallization temperature (i.e., Li/Nb
ratio) and the amount of dopant, the crystal properties can be
tailored. It is interesting to note that conditions may slightly
change along the boule, i.e., in crystals doped with MgO
near to the critical threshold concentration, an extended
transition region may be produced separating the clearly
below- and above-threshol d parts, with the transition region
manifesting defect characteristics of both type (e.g., OH
absorption bands at both 3465 and 3534 cm
1
) indicating
that Mg ions may simultaneously be incorporated at both Li
and Nb sites (see Fig. 9 in Sectio n III).
In the Li
2
O–Nb
2
O
5
–K
2
O ternary system, the lowest
in-melt concentration of the MgO dopant resulting in above-
threshold crystals is 0.2 mol. %. For Zn-doped near sLN
grown from K
2
O fluxed melt, the reported threshold concen-
tration was between 2 and 3 mol. %,
44
for In doping at about
1.1 mol. %,
45
and for Zr doping at about 0.1 mol. %.
46
In the Li
2
O–Nb
2
O
5
binary system using Li
2
O rich solu-
tion, to suppress the photorefractive damage with Mg dop-
ing, a minimum of 1 mol. %,
48
with Sc 0.4 mol. % (Ref. 47)
was required. The scatter of these values is related both to
the unknown real Li/Nb ratio in the allegedly “near stoi-
chiometric” LiNbO
3
crystals and to the differing valences of
the dopants as it will be discussed in detail in Section III C.
It should be not ed that in crystals prepared for device appli-
cations, ODR dopant concentrations slightly above the criti-
cal threshold are preferred in order to suppress the formation
of unwanted microdomains (see Fig. 4(c)).
III. COMPOSITION AND PROPERTIES OF PURE AND
ODR-ION DOPED LiNbO
3
CRYSTALS
The stoichiometric composition of LiNbO
3
, compared
to congru ent, not only requires different growth conditions
but also results in markedly different, mostly advantageous
physical properties due to the far more perfect lattice, as,
e.g., increased resistance to optical damage. The change of
physical properties, on the other hand, can be used for the
determination of the crystal composition. Several straightfor-
ward methods, such as measurements of lattice constants,
density, ferroelectric Curie-temperature, etc., have originally
been used to characterize crystals with compositions from
congruent to stoichiometric. Later, a number of optical
properties, including refractive indices, birefringence, optical
frequency doubling (phase matching tuned by temperature or
angle), holographic scattering, etc., have been used to
develop calibrations for the determination of the crystal com-
position. All these methods, including also various spectro-
scopic techniques were summarized by W
€
ohlecke et al.
49
The spectroscopic techniques, in particular, two easily appli-
cable methods most sensitive for near-stoichiometric and
ODR-ion doped LiNbO
3
, will be discussed in detail in
Section III A.
ODR dopants making LiNbO
3
optical damage resistant
(see also Section II D) also change the properties of the
crystal in a manner often similar to improved stoichiometry.
Best results for application can in fact be achieved by com-
bining both crystal tailoring strategies, thereby avoiding
structural instabilities of highly stoichiometric crystal growth
and reducing the required threshold concentrations of ODR
dopants. The effect of ODR dopants on the properties of
LiNbO
3
will be discussed in Sections III B and III C.An
overview about the incorporation of transition metal and rare
earth ions in LN with various compositions and/or ODR
co-dopings will be given in Section III D. Special attention
will be paid to Mg and its effects on nonlinear optical prop-
erties in the far-IR spectral range playing an essential role in
recent THz applications (see Section V).
A. Spectroscopic characterization of undoped LN
Out of the numerous spectroscopic methods considered
for the characterization of the composition and properties of
LN,
49
here only two techniq ues, those involving the mea-
surement of the fundamental UV absorption edge and the
IR absorption of the hydroxyl ion (OH
) stretch mode,
respectively, will be summarized. Both methods are simple,
fast, and accurate for the determination of the crystal compo-
sition especially near to the stoichiometric composition.
1. Ultraviolet absorption edge
Though the difference in the position of the optical
absorption edge for a congruent and a more stoichiometric
LiNbO
3
crystal has already been measured by Redfield and
Burke,
50
the concept of using the spectral position of the fun-
damental UV absorption edge as an indicator for the compo-
sition of LiNbO
3
crystals was introduced by F
€
oldv
ari et al.
32
in 1984. At that time, however, no samples with well defined
near stoichiometric compositions were available. Later,
based on the results of successful HTTSS growth and vapour
transport equilibration treatments, LiNbO
3
crystals with a
wide range of crystal compositions from Li/Nb 0.9 to
Li/Nb 1 could be investigated.
33
The real crystal composi-
tion of the samples was determined using accurate birefrin-
gence and second harmonic generation (SHG) measurements
based on careful comparisons with Curie temperature cali-
brations.
51
The next step was to produce a calibration curve
040601-8 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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connecting crystal compositions to results of simple absorp-
tion measurements in the near UV spectral range. The posi-
tion of the band edge was defined as the wavelength where
the absorption coefficient a equalled 20 cm
1
, but the param-
eters of the calibration curve have also been determined for
a ¼15 cm
1
. This relatively weak absorption in the band tail
is related less to the perfect lattice but essentially to intrinsic
defects like antisite niobiums Nb
Li
(Ref. 32) and possibly
lithium vacancies V
Li
.
52
Both types of defects are present
in nonstoichiometric crystals charge compensating each
other and disappear simultaneously at the stoichiometric
composition.
Taking into account a correction for reflection losses as
well, for increasing Li
2
O content, a monotonously decreas-
ing wav elength was obtained (Fig. 6). A square root fit for
the energy shift of the absorption edge versus the deviation
from stoichiometric composition was found to be accurate in
the whole composition range (see the inset of Fig. 6)
E ¼ k ð50 – c
Li
Þ
1=2
þ E
0
; (3.1)
where E is the photon energy corresponding to the absorption
edge at the chosen value of a,c
Li
is the Li
2
O concentration in
the sample in mol. %, k and E
0
are the parameters of the fit.
For T ¼22
C and ordinary polarization, k representing the
slope of the straight line is equal to 0.189 6 0.003 eV/
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mol: %
p
and E
0
¼4.112 6 0.002 eV (for a ¼20 cm
1
) corre-
sponding to the absorption edge of the stoichiometric crystal
with c
Li
¼50 mol. %. The absolute accuracy thus provided is
better than 0.1 mol. %, while for near stoichiometric composi-
tions, the relative accuracy reached an exceptional value of
about 0.01 mol. %. As proved later by IR absorption measure-
ments of hydroxyl stretching vibrations described in Section
III A 2, the latter value can also be considered as the absolute
accuracy in the near stoichiometric limit.
This simple and efficient technique was used for charac-
terizing the composition of LN crystals during the investiga-
tions of phase equilibria and HTTSS growth from various
alkali oxide solvents as reviewed in Section II. Though the
calibration curve shown in Fig. 6 is valid only for undoped
LN crystals, the method could be extended and successfully
used also for Mg doped crystals since the effect of Mg pre-
vails through changing the number of antisite niobiums and
their compensating lithium vacancies (see Section III B).
The technique was widely applied by research groups work-
ing on stoichiometric LiNbO
3
crystals for determining the
crystal composition of their samples, see, e.g., Refs. 34 and
53–57, etc.
2. OH
2
absorption
LiNbO
3
crystals grown in air always contain hydroxyl
ions (OH
) incorporated during the growth process. The
OH
ions occupy regular oxygen sites in the lattice with pos-
sible charge compensators in their surroundings. The stretch-
ing vibration of the OH
ion in cLN can be detected in the
IR spectral range at about 3484 cm
1
(2.87 lm). It was found
that the shape of the absorption band depends on the compo-
sition of LN crystals.
58
In cLN crystals, the band is broad
with a full width at hal f maximum (FWHM) of at about
30 cm
1
containing at least three overlapping components.
The closer the composition to stoichiometric the narrower
the band components, and the amplitudes of the high fre-
quency components are approaching zero (see Fig. 7). This
tendency culminates in the OH
band of the stoichiometric
crystal characterized by a single narrow line at about
3465 cm
1
with an FWHM equal to at about 3 cm
1
at
300 K.
14
The complex absorpt ion band of cLN crystals is related
to the presence of defects in the vicinity of the hydroxyl
ions. The various surroundings of the OH
ions result in dif-
ferent stretching frequencies. In sLN crystals with practically
no intrinsic defects, only a single line appears.
Consequently, the OH
spectra can be used as a probe of the
defect structure of lithium niobate. In Section IV, we discuss
various defect models and their relation to the O–H vibra-
tional frequencies.
The possibility of considering the OH
band shape as a
characteristic of the crystal composi tion has arisen in the
early works of Kov
acs et al.
58,59
At that time, however, no
FIG. 6. The fundamental absorption edge of LiNbO
3
at a ¼20 cm
1
for
ordinary polarization as a function of crystal composition. The lines are
calculated using Eq. (3.1) with the parameter values given in the text.
Reproduced with permission from L. Kov
acs et al., Appl. Phys. Lett. 70,
2801–2803 (1997). Copyright 1997 American Institute of Physics.
FIG. 7. The change of the OH
vibration band as a function of crystal com-
position. Reproduced with permission from K. Polg
ar et al., J. Cryst.
Growth 177, 211–216 (1997). Copyright 1997 Elsevier.
040601-9 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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stoichiometric LN crystals were available, and the decompo-
sition of the OH
band shape of congruent and near-
congruent crystals was ambiguous. Another difficulty imped-
ing this ambition was the change of the band shape with
time.
60
Finally, both problems were solved, and a simple
technique for the determination of the crystal composition
based on the intensity ratio (R) of two components at 3465
and 3480 cm
1
was introduced and successfully used close
to the stoichiometric composition.
61,62
A series of LN crystals were grown by the HTTSSG
method from fluxes containing additional alkali metal oxide
(K
2
O, Rb
2
O, or Cs
2
O) as described in Section II. The Li
2
O
contents of the samp les between 49.7 and 50.0 mol. % were
determined by UV absorption edge measurements with a rel-
ative accuracy of 0.01 mol. %. The OH
absorption spectra
measured by a Bruker IFS 66v/S FTIR spectrometer showed
the presence of three bands at 3465, 3480, and 3490 cm
1
,
the latest being very weak (see Fig. 8). Thus, the intensity ra-
tio R ¼I
3480
/I
3465
can be easily determined. The spectra in
Fig. 8 were normalized to the 3480 cm
1
band. The higher
the Li
2
O content of the crystal, the higher the intensity of the
3465 cm
1
line, i.e., the intensity ratio R decreases almost
linearly with increasing Li
2
O content
RðtÞ¼SðtÞðC –½Li
2
OÞ; (3.2)
where [Li
2
O] is the lithium oxide content of the crystal in
mol. % and S(t) is the slope of the straight lines changing
with sample storage time. Using least square fits, the parame-
ter C was always found to be equal to 50 with a very high
accuracy (<0.005 mol. %). This result is highly expected, since
at the stoichiometric composition (at [Li
2
O] ¼50 mol. %), the
OH
defects appearing at 3480 cm
1
due to non-stoichiometry
should disappear providing R ¼0 (see the lowest (red) curve in
Fig. 7). The fact that R reaches 0 exactly at 50 mol. % in all
cases proves that the absolute accuracy is also in the range of
0.01 mol. %. Aposteriorithis also demonstrates that the UV
absorption edge method on its turn, used for the composition
determination of the samples, has an absolute accuracy of at
least 0.01 mol. % in this region. Earlier, this was assumed to be
only at about 0.1 mol. % and the composition calibration, in the
absence of a “zero-parameter” like R, was only based on less
precise Curie-temperature measurements.
51
Fig. 8(b) shows, however, that the slope of the curves
changes with time passed after crystal growth. This indicates
that the thermal equilibrium of the protons moving from one
oxygen site to another is reached after a long time. The
obtained slope values for given storage times fit well to a
first order exponential curve
SðtÞ¼S
1
– A expð– t =sÞ; (3.3)
where S
1
represents the slope of the calibration line at t ¼1
(i.e., in thermal equilibrium at RT) and s is the time constant
of the thermally induced change of the OH
bands
(S
1
¼2.01 6 0.02 1/mol. %, A ¼1.27 6 0.02 1/mol. %,
s ¼5.9 6 0.3 months). This value of s is in good agreement
with the lifetime of holographic gratings in photorefractive
LN crystals, proving the role of hydroxyl ions in the holo-
gram erasure/fixation process.
63,64
Equations (3.2) and (3.3)
allow one to determine the Li
2
O content of the crystal kept
at RT for any time after the growth. Thus, beside UV absorp-
tion edge measurements, another simple independent
non-destructive method is available for the determination of
the composition of LN crystals near to the stoichiometric
composition.
Although only undoped crystals were used to prepare
the calibration described above, our experience showed that
dopants and impurities below at about 0.1 mol. % do not
affect the OH
spectra. The ODR dopants like Mg, Zn, In,
Sc, etc., influence the OH
bands only if added at the level
of at least 0.1–0.2 mol. % even in near-stoichiometric
LiNbO
3
, where a new OH
band appears as described in
detail in Sections III B and C.
B. Properties of Mg-doped sLN crystals
By doping with MgO above the threshold concentration,
the optical damage resistance of a congruent LiNbO
3
crystal
can be improved by several orders of magnitude.
65
Moreover, quite a number of physical properties like Curie
temperature,
66
Raman spectrum,
67
UV-edge,
68
etc., depend
on MgO addition, showing, in particular, an abrupt change at
the threshold. The latter was found at about 5 mol. % MgO
FIG. 8. Absorption spectra of LN crystals with 49.72 (black), 49.80 (red),
and 49.94 mol. % (blue) Li
2
O content, normalized to the peak at 3480 cm
1
(a). The intensity ratio (R ¼I
3480
/I
3465
) of the OH
band components as a
function of crystal composition was measured at 0 (䊏), 7.5 (䉱), 16 (䉲), and
18 (䊉) months after crystal growth (b). Reproduced with permission from
G. Dravecz and L. Kov
acs, Appl. Phys. B 88, 305–307 (2007). Copyright
2007 Springer ScienceþBusiness Media.
040601-10 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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for congruent LiNbO
3
,
65,69
strongly depending on the stoi-
chiometry of the crystal.
60
In this section, the IR, UV,
Raman, and Z-scan spectroscopic data measured in Mg
doped LN crystals of a wide range of Mg concentrations and
Li/Nb ratios are summarized.
To analyse the spectroscopic results, some assumptions
about the Mg incorporation mechanism have to be made.
Models describing the incorporation of Mg ions
42,70–72
usu-
ally assume that Mg ions compete for Li sites with antisite
Nb
Li
ions up to the threshold concentration where all anti-
sites are eliminated, while above the threshold, Mg ions
replace both Li and Nb ions in the lattice. The main differen-
ces in the models are the specific reaction formulas describ-
ing the incorporation mechanism in the successive stages.
The composition of an undoped LiNbO
3
crystals can be
characterized using a parameter x defined by the (Li
2
O)
50x
(Nb
2
O
5
)
50þx
formula. Owing to the lack of a direct method
to characterize the Li/Nb ratio in the Mg-doped samples, the
definition of the x-value was extended to the Mg-doped crys-
tals by assigning the same x-value to all cry stals grown from
melts with the same Li/Nb ratio and the same growth condi-
tions.
73
This definition is independent of the Mg incorpora-
tion model, which is required for calculating the Li/Nb ratio
and the antisite niobium concentration on the basis of x and
the Mg concentration c
Mg
in the bulk. Following the model
of Liu et al.,
42
the threshold, where the Nb
Li
antisites vanish,
can be determined as
c
th
Mg
¼
1000x
3 100 þ 2x
ðÞ
; (3.4)
where c
th
Mg
is the threshold concentration of Mg in units of
mol. %.
1. OH
2
vibration, UV absorption edge and Raman
spectroscopy
Infrared absorption measurements.
In below-threshold
Mg doped sLN crystals, the complex OH
band appears near
3465 cm
1
, similarly to undoped samples. In this case, Mg
doping onl y affects the linewidth of the OH
band decreas-
ing with growing Mg content.
68
Upon increasing the MgO
concentration above the threshold, this band is replaced by
another OH
band at a higher freq uency of at about
3534 cm
1
.
65
This behaviour was observed at different Mg
concentrations in LiNbO
3
crystals with various Li/Nb
ratios.
60
As discussed in Section II, the concentration of Mg,
Li, and Nb in the solution or melt usually undergoes changes
during the growth process. Accordingly, for suitable near-
threshold starting mixtures, a transition along the boule from
below- to above-threshold states can be achieved. The OH
infrared absorption spectra of sLN:Mg samples resulting
from such a growth can be seen in Fig. 9.
In Fig. 10, symbols corresponding to a series of Mg
doped LiNbO
3
samples are shown in the c
Mg
–x plane.
Triangle, square, and circle symbols represent the congruent
(x 1.4), intermediate (x 0.75), and stoichiometric
(x < 0.2) compositions, respectively. A symbol is full
(empty) if, according to the IR spectra, the Mg concentration
of the sample is above (below) the threshold. The theoretical
solid line corresponding to Eq. (3.4) displays the threshold
concentrations in agreement with experiment by separating
the below- and above-threshold samples.
Additional information can be derived for Mg concen-
trations exceeding the threshold concentration: the OH
stretching vibrational band positions monotonically shift to
higher wavenumbers with increasing Mg content above the
threshold
74
(see Fig. 11). The band frequency does not
depend on the composition of the samples but only on the
Mg concentration. Samples with different compositions
(plotted with various symbols) but with the same Mg content
have equal frequencies of the OH
absorption band. An
approximate square root relationship
FIG. 10. Undoped and Mg-doped LiNbO
3
samples represented in the c
Mg
–x
plane (open and full symbols denote below- and above-threshold samples,
respectively; for the definition of x characterizing the crystal composition,
see text). The theoretical solid line corresponds to Eq. (3.4). Reproduced
with permission from K. Lengyel et al., Phys. Status Solidi C 2, 171–174
(2005). Copyright 2005 John Wiley and Sons.
FIG. 9. IR spectra of samples from various parts of a threshold doped nearly
stoichiometric, LN:Mg crystal boule: below threshold at the top (a) and
above threshold at the bottom part (c), with a transition region in between
where OH
absorption bands at both frequencies can be seen (b).
Reproduced with permission from
A. P
eter et al., J. Cryst. Growth 284,
149–155 (2005). Copyright 2005 Elsevier.
040601-11 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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¼ a
ffiffiffiffiffiffiffi
c
Mg
p
þ b (3.5)
was determined from the data points, the calculated fitting
parameters are a ¼1.05 6 0.05 cm
1
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðmol: %Þ
p
and
b ¼3533.1 6 0.2 cm
1
, the latter corresponding to the fre-
quency of the OH
absorption band of an ideal stoichiomet-
ric LiNbO
3
:Mg crystal just above the threshold.
These results suggest a simple method for determining
the Mg content of over-threshold samples using IR absorp-
tion measurements. As shown in Ref. 70, the lattice constants
of LiNbO
3
:Mg crystals increase with growing Mg concentra-
tion, resulting in an increase in the O–O distances. This in
turn leads to increased OH
vibration frequencies as the
adjacent O
2
ion moves away.
75
Thus, the correlated
increase in OH
frequency and Mg concentration above the
threshold can be interpreted via the increasing lattice
constant.
In addition to data on band position and shape, both
characterizing the immediate neighbourhood of the proton,
basic information concerning its migration in the lattice can
also be derived from IR spectroscopy. To investigate the sta-
bility of OH
defects, the IR spectra of over-threshold LN:Mg
crystals with different Li/Nb ratios and Mg contents were
measured in the 20–500
C temperature range.
76
Upon heating,
the 3465 cm
1
band, well-known from crystals slightly below
the threshold, appeared and kept growing at the expense of the
over-threshold band. The process, shown in Fig. 12(a) for a
cLN:Mg crystal, was rev ersible for all samples. For crystals
with fixed Li/Nb ratio, the temperature of the appearance of
the 3465 cm
1
band shifted with growing excess Mg concen-
tration above the threshold towards higher temperatures, as
indicated for sLN:Mg crystals in Fig. 12(b).
The Arrhenius plots of the ratios of below- and above-
threshold band areas (see Fig. 13) gave the same energy
parameter DE ¼0.25 6 0.02 eV for all samples, independent
of the Li/Nb ratios and c
Mg
values. Assuming that the mov-
ing species are protons migrating from oxygen to oxygen,
this activation energy can be interpreted as the difference
of the bonding energies of protons in below- and above-
threshold environments. This is supported by the identical
result of Arizmendi et al.
77
obtained for thermal treatments
and holographic fixing in Mg and Mg þFe doped cLN.
UV absorption edge measurements. The position of the
UV absorption edge of undoped LiNbO
3
crystals, as
FIG. 11. Wavenumber of the OH
vibrational band vs. the Mg concentra-
tion in over-threshold LiNbO
3
crystals. Reproduced with permission from
K. Lengyel et al., Phys. Status Solidi C 2, 171–174 (2005). Copyright 2005
John Wiley and Sons.
FIG. 12. IR absorption spectra measured at 100–500
C in a cLN crystal
containing 6.1 mol. % Mg (a) and at 400
C in sLN crystals containing 0.6,
1.3, 2.5, and 4.3 mol. % Mg (b). Reproduced with permission from K.
Lengyel et al., Appl. Phys. Lett. 96, 191907 (2010). Copyright 2010
American Institute of Physics.
FIG. 13. Determination of the bonding energy difference of OH
ions in below-
and above-threshold environments in LN:Mg samples with different Li/Nb ratios
and Mg contents. Reproduced with permission from K. Lengyel et al., Appl.
Phys. Lett. 96, 191907 (2010). Copyright 2010 American Institute of Physics.
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discussed in Section III A, is determined by intrinsic def ects,
antisite Nb
Li
ions in the first place. As found earlier for con-
gruent crystals, upon Mg doping with increasing concentra-
tion up to the threshold, the UV-edge gradually shifts
to shorter wavelength, while this tendency is reversed for
further increase above the threshold.
68
The behaviour of
below-threshold samples was again attributed, though quali-
tatively, to the decreasing Nb
Li
concentration.
More recently, for understanding the role of the Mg dop-
ant in the whole composition region, detailed UV absorption
studies have been performed. The same series of crystals
with various Mg concentrations and Li/Nb ratios as used pre-
viously for IR studies has systematically been investigated in
the near UV region.
73
The UV-edge positions are plotted in
Fig. 14(a) as a function of MgO concentration using the sym-
bol types introduced in Fig. 10. For over-threshold samples,
a linear dependence of the UV-edge position on the Mg
concentration was found independent of the x value of the
LiNbO
3
:Mg samples. A linear calibration function
k ðat a ¼ 20 cm
1
Þ¼a c
Mg
þ b (3.6)
was fitted to these data points with parameters
a ¼0.95 6 0.03 nm/mol. % and b ¼303.6 6 0.1 nm, the value
of b approximating the UV-edge position of an ideally stoi-
chiometric LiNbO
3
:Mg crystal just above the threshold.
Since above the threshold, no Nb
Li
antisites are present, the
shift of the UV-edge to longer wavelengths had to be attrib-
uted to an increasing number of Mg-associated defects.
The UV-edge position of below-threshold samples
within all three composition groups (congruent, intermediate
and stoichiometric) was found to shift to shorter wavelengths
with increasing Mg concentration (see open symbols in Fig.
14(a)) in agreement with previous experimental results.
68,78,79
The conclusion was that the edge position of below-threshold
LiNbO
3
:Mg crystals is determined by both Nb
Li
and Mg-
associated defects. The contribution of Nb
Li
to the UV-edge
shift of undoped crystals can be derived using charge
compensation models and Eq. (3.1).
Hence, assuming simple additivity of the contributions,
the effect of Mg defects could be separately estimated below
the threshold. For this calculation, the antisite niobium
concentration (c
Nb
Li
) was determined as a function of x and
c
Mg
using the model of Liu et al.
42
The UV-edge shift due to
this c
Nb
Li
was calculated using Eq. (3.1) and subtracted from
the experimental UV-edge position. The results plotted in
Fig. 14(b) fit excellently to the over-threshold data re-plotted
in the figure. This coincidence suggests that Mg ions have a
uniform effect on the UV-edge in the whole concentration
region,
73
apparently independent of their incor poration site.
This experimental result also indirectly supports Liu’s model
for the description of Mg incorporation into the LiNbO
3
crystal lattice below and above the threshold.
Raman spectroscopic measurements. As described in the
review of Fontana and Bourson (see this issue of APR),
80
the
Raman spectrum of LiNbO
3
crystals sensitively depends on
the composition changes and the amounts of doping materi-
als, so it can also be used to investigate the incorporation of
Mg into the crystal lattice. Although the Raman spectra of
undoped as-grown LiNbO
3
crystals were investigated soon
after the first successful Czochralski growth,
81
the exact
assignment of all bands to vibrational modes was established
only three decades later.
82
In previous Raman experiments,
the Mg incorporation was investigated only in congruent
crystals.
67,83
However, our series of undoped and Mg-doped
LiNbO
3
crystals with different Li/Nb ratios successfully
used in other experiments for clarifying the incorporation
mechanism of Mg ions led us to extend the investigations
also to Raman spectroscopy.
74,84
The E(TO
3
)–E(TO
9
) and A
1
(TO
1
)–A
1
(TO
4
) phonon
modes were investigated in y(zx)y and y(zz)y geometries,
respectively. The normalized E(TO) spectra of undoped and
heavily Mg-doped (7.8 mol. %) cLN samples and the A(TO)
modes of a similar pair (0 and 4.9 mol. % Mg) of sLN crys-
tals can be seen in Figs. 15(a) and 15(b), respectively.
For a detailed analysis of the spectra, a careful fitting
process to der ive the band parameters was performed. The
E(TO) band positions, except for the E(TO
7
) mode,
74,84
are
practically independent of the Mg doping and Li/Nb ratio as
well (the frequency data are scattered in a range of about
FIG. 14. UV-edge of the LN:Mg samples as a function of Mg concentration
(a), the same after subtracting the contribution of Nb
Li
ions (b). Open/full
symbols represent samples below/above the threshold, triangles, squares,
and circles indicating congruent (x 1.4), intermediate (x 0.75), and stoi-
chiometric (x < 0.2) composition, respectively. Reproduced with permission
from K. Lengyel et al., Phys. Status Solidi C 2, 171–174 (2005). Copyright
2005 John Wiley and Sons.
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1.5 cm
1
). However, the halfwidth of the E(TO) bands of
undoped samples changes with composition, while for a
given x-value, the halfwidths of the below-threshold samples
only slightly increase with Mg content (see, e.g., E(TO
6
)in
Fig. 16(a)). In contrary, for over-threshold samples, the
damping varies linearly with the Mg concentration independ-
ent of the Li/Nb ratio.
The A
1
(TO) modes can be divided into two groups. In
the first group, the positions of the A
1
(TO
1
)andA
1
(TO
4
)
bands essentially do not change, while in the second group,
the frequencies of the A
1
(TO
2
) and A
1
(TO
3
) bands slightly
decrease with increasing Mg content for all Li/Nb ratios.
83
The halfwidths of all A
1
(TO) modes (see, e.g., A
1
(TO
4
)in
Fig. 16(b)) show the same composition-dependent threshold
effect as the E(TO) bands. It is important to notice that the
threshold concentrations inferred from Raman halfwidths
coincide with those derived from IR and UV spectroscopy.
The Mg concentration of the above-threshold LiNbO
3
crystals
can be determined by measuring the halfwidth of, e.g., the
E(TO
6
)orA
1
(TO
4
) Raman bands (see Figs. 16(a) and 16(b))
c
Mg
¼ 0:453C
EðTO
6
Þ
8:1; (3.7)
c
Mg
¼ 0:644C
A
1
ðTO
4
Þ
12:3; (3.8)
where the units to be used are mol. % and cm
1
, and the
error of the calculated Mg content is estimated to be
about 6 0.2 mol. %.
The A
1
(LO) bands together with the E(TO) modes can
be measured in z(xx)z backscattering geometry (see Fig.
17(a)). The A
1
(LO
4
) phonon mode at 873 cm
1
, a band well
separated from all other bands, could be decomposed into a
main band with a satellite. The halfwidth of the main
A
1
(LO
4
) band as a function of c
Mg
can be seen in Fig. 17(b).
The damping of the above- and below-threshold samples
with a given x-value increases linearly with growing Mg
concentration. Almost parallel lines were obtained for the
stoichiometric, intermediate, and congruent series. For the
above-threshold samples, this behaviour differs from that
obtained for the E(TO) and A(TO) Raman bands. This prop-
erty can be used to determine both the composition and the
Mg content of LiNbO
3
crystals above the photorefractive
threshold by measuring, e.g., the halfwidth of the A
1
(TO
4
)
band to calculate c
Mg
and that of the A
1
(LO
4
) band to esti-
mate the x-value of the sample using Figs. 16(b) and 17(b),
respectively. The different behaviour of the transverse and
FIG. 15. Raman spectra of undoped and heavily Mg-doped (7.8 mol. %)
cLN crystals in y(zx)y (a) and undoped and strongly Mg-doped (4.9 mol. %)
sLN crystals in y(zz)y (b) backscattering geometries. Reproduced with per-
mission from K. Lengyel et al., Appl. Phys. B: Lasers Opt. 87, 317–322
(2007). Copyright 2007 Springer ScienceþBusiness Media.
FIG. 16. The Mg dependence of the half-width of E(TO
6
) (a) and A
1
(TO
4
)
(b) modes. The triangle, square, and circle symbols represent the congruent
(x 1.4), intermediate (x 0.75), and stoichiometric (x < 0.2) compositions,
respectively. Empty/full symbols indicate samples with Mg content below/
above the photorefractive threshold. Reproduced with permission from K.
Lengyel et al., Appl. Phys. B: Lasers Opt. 87, 317–322 (2007). Copyright
2007 Springer ScienceþBusiness Media.
040601-14 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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longitudinal modes may be related to the large anisotropy of
the crystal.
2. Z-scan measurements
Z-scan is the most popular and powerful technique for
the study of nonlinear absorption and refraction because of
its simplicity, accuracy, and sensitivity.
85
The method was
elaborated for the determination of the parameters usually
required for nonlinear optical applications, the nonlinear
index of refraction n
2
, and the nonlinear absorption coeffi-
cient b. In the measurement, the nonlinear sample is scanned
along the propagation direction z of a focused Gaussian
beam in the vicinity of its focal plane, and the transmittance
is monitored in the far field as shown in Fig. 18.
If one is interested in n
2
, the aperture size has to be cho-
sen significantly smaller than the far field beam radius
(closed-aperture Z-scan), thus the transmitted power is pro-
portional to the on-axis intensity. In order to determine b, the
aperture has to be opened to let the whole beam enter the de-
tector (open-aperture Z-scan). In each case, the transmittance
curves should be normalized by the transmittance value
measured for the sample position far from the focus. Typical
Z-scan curves are shown in Fig. 19. The nonlinear parame-
ters can be obtaine d by fitting the Z-scan curves by appropri-
ate theoretical formulae.
85,86
Evaluation of the measured
curves with these theories is valid if the variation of the re-
fractive index and the absorbance can be given as Dn ¼ n
2
I
and dI ¼bIdz, respectively.
If Mg doped sLN samples are exposed to cw light with
intensity levels in the kW/cm
2
-MW/cm
2
region, basically
two effects are responsible for the laser induced change of
the refractive ind ex: PR and the thermo-optical effect.
87
(The Kerr-effect due to cubic nonlinearity is negligible in
this intensity range.) The characteristic features of PR are (i)
negative nonlinearity (prefocal peak, postfocal valley in the
Z-scan curve) which cannot be given in the simple form of
Dn ¼ n
2
I, (ii) elliptically shaped beam distortion, (iii) char-
acteristic build-up time on the second scale that depends on
the stoichiometry and the concentration of the incorporated
Mg.
87–89
Due to these facts onl y an estimated value of n
2
can
be given to characterize PR. In contrary, the thermo-optical
effect shows (i) positive nonlinear refraction (Z-scan struc-
ture with pr efocal valley and postfocal peak) which can be
given in the form of Dn ¼ n
2
I, (ii) beam distortion with cy-
lindrical symmetry, (iii) practically composition independent
build-up time in the sub-ms scale. These characteristics are
verified also theoretically.
87,89,90
In order to clarify the contribution of the PR and the
thermo-optical effect to the light induced change of refrac-
tion in sLN:Mg, Z-scan measuremen ts were performed on
various samples differing in Mg content.
88,89
Measurements
complementary to the Z-scan were also performed, such as
FIG. 17. Raman spectra of undoped and 4.9 mol. % Mg-doped stoichiomet-
ric (x < 0.2) LN:Mg crystals in z(xx)z backscattering geometry (a) and the
Mg concentration dependence of the halfwidth of the A
1
(LO
4
) band (b). For
symbol types, see Fig. 16. Reproduced with permission from K. Lengyel
et al., Appl. Phys. B: Lasers Opt. 87, 317 (2007). Copyright 2007 Springer
ScienceþBusiness Media.
FIG. 18. The Z-scan measurement setup.
FIG. 19. Z-scan traces of sLN: 0.7 mol. % Mg measured at different incident
light powers (P ¼0.6, 1, 1.85 W). The continuous lines are theoretical fitting
curves. The inset shows the linear power dependence of n
2
. Reproduced
with permission from L. P
alfalvi et al., J. Appl. Phys. 95, 902–908 (2004).
Copyright 2004 American Institute of Physics.
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the detailed diagnostics of the beam transmitted through the
sample during scanning and the measurement of the build-up
time of the nonlinear effect at fixed sample positions. For the
measurements, the focused beam of an all-line visible cw
Ar-ion laser was used with MW/cm
2
maximal intensity level
at the focus. The thickness of the crystals was 2 mm.
From the results of these measurements, it was recog-
nized that the effect of PR can be reduced by increasing the
Mg content. For sLN samples with Mg concentrations
exceeding the threshold value, none of the features (i, ii, iii)
characteristic for PR were observed. The positive sign of n
2
determined from the Z-scan fittings, the isotropic distortions,
and the sub-ms value of the build-up time, all unambigu-
ously verified the exclusively thermo-optical origin of the
observed nonlinear effect.
In order to clarify the origin of the thermo-optical effect,
Z-scan measurements at different beam powers were per-
formed on a sLN: 0.7 mol. % Mg sample. The results are
shown in Fig. 19. The n
2
values determined from the fitting
of the curves show a linear dependence on the beam power
P. This behaviour verifies the dominant role of the nonlinear
absorption in the thermo-optical effect, since in this case, the
nonlinear refraction can be expressed as
89
n
2
¼ 0:06Pbðdn=dTÞ=pj; (3.9)
where j is the thermal conductivity and dn=dT the derivative
of the linear refraction with respect to the temperature. For
lack of knowledge of j and dn=dT values for the investigated
composition, the corresponding values of undoped congruent
LN were used in Eq. (3.9), resulting in values of the order of
magnitude 10
3
cm/GW for b. Z-scans with polarized beams
at fixed (2 W) power were also performed on sLN:
0.7 mol. % Mg samples;
89
for ordinary polarization of the
beam, the n
2
value was found to be approximately
three times larger than for extraordinary polarization (see
Fig. 20(a) and Table I).
The ratio of the b values obtained from the closed aper-
ture fittings (Fig. 20(a)) corresponding to different polariza-
tions was found to be identical with the ratio of n
2
values. In
order to obtain independent information on the non-linear
absorption, open-aperture measurements with both polariza-
tions were also performed. As shown in Fig. 20 and Table I,
the maximally absorbed power is about three times larger in
the case of ordinary compared to extraordinary polarization.
These measurements strongly proved the interdependence of
nonlinear absorption and nonlinear refraction, as well as their
anisotropy for sLN: Mg.
3. Absorption, refractive index in the far-IR (THz) range
The nonlinear optical properties of sLN advantageous
also in the THz frequency range can be utilized in experi-
ments, such as high-energy THz pulse generation, nonlinear
THz spectroscopy, and THz nonlinear optics. For designing
experiments and for preliminary model calculations, the
knowledge of the absorption coefficient and the refractive
index of the material in the THz range are of key importance.
Mg doping has an effect on various spectroscopic features of
sLN, such as the UV absorption edge,
68,79
the IR absorption
band,
68,91
and the PR effect (the latter is disadvantageous in
the case of nonlinear applications).
48
In order to obtain infor-
mation about the effect of Mg doping on THz absorption and
refraction, the following measurements were performed.
The extraordinary index of refraction and absorption
coefficient of a series of Mg-doped (0.7, 1.5, 4.2 mol. %
incorporated Mg content) and undoped sLN crystals were
determined in a wide spectral range (0.9–4.6 THz) with far-
infrared Fourier transform (FIR FT) spectroscopy. The trans-
mission of the samples was recorded by a Bruker 113 V FIR
FT spectrometer. The measurements were performed at tem-
peratures of 300, 200, 100, and 10 K. The sample thicknesses
were 0.2 and 0.5 mm.
92
Based on an analysis of the interferometrically resolved
transmitted spectra, the group indices were directly
FIG. 20. Closed- (a) and open-aperture (b) Z-scan traces of sLN: 0.7 mol. %
Mg. In both figures, open circles and squares denote extraordinary and ordi-
nary polarization, respectively. The continuous lines are theoretical fitting
curves. Reproduced with permission from L. P
alfalvi et al., J. Appl. Phys.
95, 902–908 (2004). Copyright 2004 American Institute of Physics.
TABLE I. Nonlinear characteristics for the sLN:0.7 mol. % Mg sample for
ordinary (O) and extraordinary (E) polarization.
89
Polarization n
2
[10
11
cm
2
/W] b [10
3
cm/GW] Maximal absorption
O 13.4 1.7 39.7%
E 4.3 0.55 11.9%
Ratio (O/E) 3.11 3.09 3.3
040601-16 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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determined and used for the calculation of the phase index of
refraction. The absorption coefficient as a function of fre-
quency was determined from the smoothed transmission
curve, taking into account Fresnel-losses.
For all samples, the extraordinary refractive index shows
a monotonous increase with frequency in the 0.9–4.6 THz
frequency range with a typical value of n 5 and an increase
in at about 20% in this frequency range.
The effect of the unwanted curvature of crystal surfa-
ces
92
caused difficulties in the evaluation of the measure-
ments. The correction was done in the absorption coefficient
values using an additive constant, which was chosen to result
in zero absorption at the lowest temperature (10 K) and
frequency (0.9 THz). For other frequencies and temperatures,
the same additive constant was used for a given sample.
Figure 21 shows the absorption coefficients of the
stoichiometric crystals at 10 K. The absorption coefficient
function increases with frequency approaching towards the
TO phonon resonance frequency, however, it has a fine
structure with local maxima, which can be explained by the
defect structure of the crystal. In the 0.9–3.3 THz frequency
range, the absorption coefficient is lowest when the Mg con-
tent is closest to the photorefractive threshold value, which is
near 0.7 mol. %.
92
In fact for this near threshold composition,
practically all antisite Nb ions are replaced by Mg which
results in an optimal defect structure decreasing absorption.
Above the photorefractive threshold (1.5 and 4.2 mol. %),
absorption monotonously increases with Mg content , since
in this region, Mg replaces Nb ions at Nb sites.
Control measurements were performed in order to
clarify the previously mentioned uncertainty in the absorp-
tion coefficient values due to the curved crys tal surfaces.
Undoped and Mg-doped (0.7, 1.5, 4.2 mol. % incorporated
Mg content) sLN samples originating from the same crystals
used for FIR FT spectroscopy with precisely polished plan-
parallel surfaces were investigated with a TERA K8 time-
domain THz spectrometer (Menlo Systems) in the 0.25–2.5
THz frequency range at 300 K temperature. The sample
thicknesses were 0.5 and 0.6 mm.
In time domain THz spectroscopy (TDTS) measu re-
ments, the electric field of a THz beam with and without
sample is monitored as a function of time. From the temporal
shape, the spectral amplitude and spectral phase can be
determined by Fourier transformation. From the spectral am-
plitude, the absorption coefficient, while from the spectral
phase, the refractive index was obtained.
Fig. 22 shows the frequency dependence of absorption
coefficient of Mg-doped sLN crystal with Mg dopant level
closest to the photorefractive threshold (0.7 mol. % Mg con-
tent) determined from FIR FT spectroscopy (black solid line)
and TDTS (red solid line) measurements. The absorption
coefficient curves differ from each other in an additive con-
stant. The deficiency of the results shown by the black solid
curve is the pr eviously mentioned uncertainty of the absorp-
tion coefficient explained by the nonparallel crystal surfaces
of the samples used for FIR FT spectroscopy measurements.
The deficiency of the results shown by the red solid curve is
the reduced confidential interval (about 0.3–2.5 THz).
Absorption data which are considered most reliable for a
wide frequency range are represented by the black dashed
line, which was constructed by shifting the black curve by a
constant value to fit the red one at low frequencies.
Figs. 23(a) and 23(b) show the frequency dependence of
ordinary and extraordinary refractive indices, respectively,
for undoped and Mg-doped sLN crystals measured by
TDTS. Both the extraordinary and the ordinary refractive
indices increase with frequency in the confidential interval
for all samples.
Beside the well known strong birefringence of sLN in
the THz range, it can be observed that for all compositions,
the dispersion is larger for the ordinary than for the extraor-
dinary refractive index. Furthermore, it can be seen that for
ordinary polarization, there is no significant difference
between the refractive index values belonging to different
compositions. For extraordinary polarization, the small dif-
ference between the curves belonging to three samples
(undoped, 0.7 and 1.5 mol. % Mg doped) is comparable to
the measurement error, but the curve of the sample with
FIG. 21. Frequency dependence of the absorption coefficient of undoped
and Mg-doped sLN crystals at 10 K temperature. Reproduced with permis-
sion from L. P
alfalvi et al., J. Appl. Phys. 97, 123505 (2005). Copyright
2005 American Institute of Physics.
FIG. 22. Frequency dependence of the absorption coefficient of a Mg-doped
sLN crystal near the photorefractive threshold (0.7 mol. % Mg concentra-
tion) at 300 K. The black solid line is obtained from FIR FT spectroscopy,
92
the red line from TDTS, the dashed black line indicating values considered
more reliable.
040601-17 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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4.2 mol. % Mg content is unambiguously separated from
them.
Figs. 24(a) and 24(b) show the frequency dependence of
absorption coefficients at 300 K for ordinary and extraordi-
nary polarization, respectively, in the case of undoped and
Mg-doped sLN crystals. Apart from noises, absorption coef-
ficients increase with frequency inside the confidential inter-
val for both polarizations. It is obviou s that the absorption
coefficient values are significantly higher for ordinary than
for extraordinary polarization and are practically independ-
ent of the Mg content especially in the ordinary case. For
extraordinary polarization, as seen in Fig. 24(b) for samples
with Mg content above the photorefractive thresho ld, the
absorption coefficient monotonously increases with Mg
content similarly to the 10 K case (see Fig. 21).
From the above results concerning THz absorption of
Mg-doped sLN samples together with the well-known photo-
refraction behaviour, one can conclude that most suitable
for THz applications is the near-threshold (0.7 mol. % Mg)
composition.
C. Other divalent, trivalent, and tetravalent ODR
dopants
Beside Mg, several other divalent, trivalent, or tetrava-
lent cations (e.g., Zn
2þ
,In
3þ
,Sc
3þ
,Hf
4þ
,Zr
4þ
,Sn
4þ
) above
a critical concentration are able to suppress the optical
damage related to photorefraction in LN crystals.
93–98
The
properties of LN doped with optical damage resistant ions
were first summarized in a review paper
10
and later in a book
by Volk et al.
99
Recently, Kong et al.
100
reviewed advances
in the photorefraction of doped LN, focusing on tetra-,
penta-, and hexavalent ions, includ ing doubly- and even
triply-doped crystals. They concluded that LN triply doped
by Zr, Fe, and Mn shows excellent non-volatile holographic
storage properties, and V and Mo single-doped LN have fast
response and multi-wavelength storage characteristics. In
this section, only recent results on ODR-ion single-doped
sLN crystals are summarized.
The critical concentration, above which the photorefrac-
tion is strongly suppressed—usually called “threshold”—
depends on the valence of the dopant and the stoichiometry
(Li
2
O content or Li/Nb ratio) of the crystal. As it was shown
above for Mg, the higher the Li
2
O content in the crystal, the
lower the threshold concentration in crystals doped with
other ODR ions.
44,45,47
In addition, the increase in the
valence of the dopant decreases the threshold.
94–98
In gen-
eral, the incorporation of ODR ions reduces the amount of
antisite Nb
Li
in the lattice. In nearly stoichiometric LN
crystals where the Nb
Li
concentration is almost zero, the
threshold value of the dopant concentration can be lower
than 0.2 mol. % as it was observed for Mg-doped sLN.
43
Similarly, a remarkable decrease in the threshold
FIG. 23. Frequency dependence of ordinary (a) and extraordinary (b) refrac-
tive indices of undoped and Mg-doped (0.7, 1.5, and 4.2 mol. % Mg content)
sLN crystals at 300 K.
FIG. 24. Frequency dependence of the absorption coefficients for ordinary
(a) and extraordinary (b) polarization in undoped and Mg-doped (0.7, 1.5,
and 4.2 mol. % Mg contents) sLN crystals at 300 K.
040601-18 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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concentration was observed for Sc
3þ
(Ref. 47) and In
3þ
doped
45
sLN crystals as compared to the congruent
counterparts.
The basic advantage of choosing higher valence ODR
dopants comes from their lower damage threshold concentra-
tions; lower built-in dopant content facilitates the growth of
more homogeneous crystals resulting in high quality samples
for device applications. Therefore, sLN crystals with various
concentrations of tetravalent Zr in the 0–0.45 mol. % range
have been grown by the HTTSSG technique.
46
All methods
(Z-scan, UV, IR, and Raman) used to characterize the
sLN:Zr crystals indicated that the photorefractive damage
threshold is at about 0.1 mol. % Zr in the crystal. Figure 25
shows the appearance of the OH
band at 3475 cm
1
already
at 0.085 mol. % Zr content, characteristic for the Zr
4þ
Nb
–OH
complex above the threshold. The spectra were normalized
to the OH
band characteristic for the pure sLN crystal at
3466 cm
1
. The intensity ratio of the two bands increased
with increasing Zr concentration .
Although the Z-scan measurement showed that the crys-
tal containing 0.09 mol. % Zr is below the photorefractive
threshold, the results obtained from other methods indicated
that the threshold must be close to this concentration. It has
been concluded that the transition between the below- and
above-threshold behaviour may not be sharply defined. A
similar observation was presented by Nava et al.
101
for con-
gruent Zr-doped LiNbO
3
crystals, showing that the photore-
fractivity is reduced at somewhat higher Zr concentration
than the threshold determined from refractive index
measurements.
The appearance of the new OH
vibrational band
proved to be as one of the most sensitive methods to detect
ODR ions on Nb site, thereby indicating the above-threshold
state of the crystal. In congruent LN crystals, however, the
new OH
band cannot be clearly detected for tetraval ent
dopants, since they overlap with the broad OH
vibrational
band already present in the undoped case (see Fig. 7). In a
recent systematic study on sLN crystals doped with all
known ODR ions, however, the OH
bands related to the
M
nþ
Nb
–OH
type complexes, where M
nþ
is the ODR ion with
valences n ¼2, 3, or 4, have been clearly identified.
102
Figure 26(a) shows the absorption spectra of hydroxyl ions
in ODR-ion doped sLN crystals. The new absorption band
appeared at higher frequency for all dopants than the
3466 cm
1
band seen in undoped sLN. In a few cases like
Zn
2þ
,Hf
4þ
, and Zr
4þ
doped crystals, the 3466 cm
1
band is
still present; presumably, the concentration of the incorpo-
rated dopants is close to the threshold value. The higher the
dopant concentration in the crystal, the higher the intensity
ratio between the new and the 3466 cm
1
band, as it was
observed, e.g., for sLN:Zr.
46
It is clearly seen that the spectra belonging to dopants of
different valences form different groups in sLN crystals. The
vibrational frequency for hydroxyl ions in the M
2þ
Nb
–OH
complex (i.e., for Mg
2þ
and Zn
2þ
dopants) is at about
3530–3535 cm
1
, in agreement with that in the congruent
crystal.
65,68
Similarly, for M
3þ
dopants (Sc
3þ
and In
3þ
), the
OH
bands appear at about 3505 cm
1
, in good agreement
with those observed for congruent,
94,103
and near-
stoichiometric LN.
45,47
For all M
4þ
tetravalent dopants (i.e.,
Hf
4þ
,Zr
4þ
,Sn
4þ
), the OH
vibrational frequency is found
at about 3475 cm
1
as previously shown only for Zr
4þ
.
46,104
Consequently, the OH
vibrational frequencies of doped
crystals show a monotonous decrease as a function of the
valence of the dopant which can be qualitatively understood
taking into account the stronger attractive force for the pro-
ton in a M
2þ
Nb
–OH
complex compared to that in M
4þ
Nb
–OH
.
It was concluded from polarization dependence measure-
ments that the higher the valence of the dopant, the closer
the O–H bond direction to the oxygen plane perpendicular to
the crystallographic c axis of the crystal. The model of the
defect complex deduced from the experiments is shown in
Fig. 26(b).
102
The presence of the OH
band in ODR-ion doped
stoichiometric LN can be used to determine the threshold
concentration of the dopants, even for tetravalent ions, which
was not possible for congruent crystals. The low damage
threshold concentration of the tetravalent ions especially in
FIG. 25. Stretching vibrational bands of hydroxyl ions in Zr-doped sLN
crystals. The spectra were normalized to the OH
band characteristic for the
pure sLN crystal at 3466 cm
1
. Reproduced with permission from L.
Kov
acs et al., Opt. Lett. 38, 2861–2864 (2013). Copyright 2013 Optical
Society of America.
FIG. 26. Infrared absorption spectra of stoichiometric LiNbO
3
crystals
doped with photorefractive damage resistant ions above their threshold con-
centrations (a). Schematic drawing of the proton location in the M
nþ
Nb
doped
sLN crystal lattice (b). Reproduced with permission from L. Kov
acs et al.,
Opt. Mater. 37, 55–58 (2014). Copyright 2014 Elsevier.
040601-19 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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stoichiometric LiNbO
3
facilitates the growth of more homo-
geneous crystals, resulting in high quality samples for device
applications.
D. Transition metal and rare earth dopants
Similarly to the case of ODR dopants, the incorporation
of other cations with charges 2–4 also involves strong inter-
action with intrinsic defects providing charge compensation.
Due to the similar octahedral surroundings of the Li and Nb
sites in LN, earlier studies on cation dopants came to con-
flicting conclusions concerning the incorporation site. In
fact, local lattice relaxation may lead to substantial changes
of the potential felt by the incorporated ion, further modified
by the possible presence of nearby charge compensating
defects, as shown by the failure of models (e.g., superposi-
tion model calculations of crystal field constants of the spin-
Hamiltonian) neglecting these effects. Decisive evidence
about the substitution site could be obtained, however, from
detailed angular dependent electron nuclear double reso-
nance (ENDOR) studies identifying and characterizing the
cation neighbours of the dopant, as performed for Mn
2þ
(Ref. 105) and Fe
3þ
(Ref. 106 ) in cLN, and for Cr
3þ
in near-
threshold LN:Mg,
107
sLN (Ref. 108) and LN with various
Li/Nb < 1 ratios.
109
Nearest ligands were also identified for
Yb
3þ
and Nd
3þ
in sLN.
110,111
In addition to data on the
ligand positions and/or the distribution of dopant spin den-
sity, these studies provided also information on local fields
and disorder, and in the case of sLN:Cr (Ref. 108) also about
the presence of a nearby proton. The ligand ENDOR results
showed that in cLN, all investigated transient element
dopants in their paramagnetic state were substituted at Li
sites, while for Cr
3þ
in sLN or over-threshold LN:Mg substi-
tution at the Nb site was found to be dominant. For the triva-
lent rare earth ion centers, however, up to now, no dominant
transfer of the substitution site was observed by ENDOR; at
least, the main axial species of Yb
3þ
and Nd
3þ
in sLN were
still found to substitute at the Li site.
110,111
Comparative studies of EPR of a given dopant carried
out in cLN and sLN on Fe
3þ
(Ref. 112)orCr
3þ
(Ref. 109),
or in cLN and near-threshold LN:Mg on Cr
3þ
(Ref. 107)or
Ti
3þ
(Refs. 113 and 114) or Er,
115
showed drastic changes of
the spectra; this could again be attributed to a change of the
incorporation site of these trivalent dopants upon approach-
ing the composition threshold. While for cLN and even for
crystals with Li
2
O content equal to 49.85 mol. % , the pres-
ence of a main axial Cr
3þ
Li
or Fe
3þ
Li
species and a large variety
of axially or non-axially charge-compensated minority
centers (all on Li sites) could be discerned,
116,117
in sLN,
only one nearly axial Cr
3þ
Nb
and two axial Fe
3þ
Nb
centers could
be observed, which differed, however, from those reported in
overthreshold cLN:Mg. This could be attributed to protons
or Mg
2þ
Li
playing the role of charge compensators instead of
or in addition to scarcely available cation vacancies. For an
earlier summary on defects in LN and related oxides, see
Ref. 118.
The observations of IR absorption bands of M
nþ
Nb
OH
–Mg
2þ
Li
type complexes in overthreshold LN:Mg:M crystals
with M ¼Cr, Nd, In, Sc, etc.,
119–121
are also clear indications
for these trivalent dopants to be at least partially incorpo-
rated at Nb sites. Proton induced X-ray emission (PIXE)/
channeling measurements on LN:Cr and overthreshold
LN:Mg:Cr confirmed the shift from Li to Nb substitution
upon Mg-codoping, but found already in LN:Cr a puzzling,
huge “minority” of 40% of Cr atoms on Nb sites despite the
low concentration of 0.1 mol. % Cr used.
122
Though the
exact Li/Nb ratio in these crystals remained uncharacterized,
these data might be an indication for the presence of diamag-
netic Cr
Li
-Cr
Nb
pairs on adjacent Li and Nb sites.
Paramagnetic exchange coupled Cr
Li
-Cr
Li
pairs at nearby Li
sites with slightly larger interatomic distances have been
reported in Refs. 117 and 109 but only for concentrations
exceeding 1 mol. %.
Nuclear methods like Rutherford backscattering/ion
beam channeling and perturbed angular correlatio ns also
contributed important information: e.g., for the nonparamag-
netic Hf
4þ
, clear indications for a change from Li to Nb
substitution upon approaching stoichiometry were
obtained.
123,124
EXAFS studies on a series of transition ele-
ment or rare earth doped polycrystalline or powdered single
crystal samples also provided information on the identity and
distance of ligand shells though without selectivity for the
charge and possible non-uniform surroundings of the dopant.
This was sufficient in cLN to locate the dominant Li substitu-
tion site for dopant cations with charges up to 4þ, but was
inconclusive or contradictory in near stoichiometric and
overthreshold LN. For references see, e.g., Refs. 125–128.
For some dopant ions with lower valence, however,
comparative EPR studies in cLN and sLN, carried out on
Mn
2þ
(Ref. 129)orCo
2þ
,
130
only showed narrowing but no
change of the EPR line positions, which was a proof for
unchanged incorporation at Li sites, as seen also for the
isoelectric dopants Ni
þ
and Cu
2þ
.
131,132
The case of the Ti dopant is of special interest since the
Ti
4þ
state occurring in as-grown crystals has a closed-shell
electron configuration similar to that of Nb
5þ
. Both ions,
occupying either Li or Nb site, can attract electron-polarons
forming similar 3d
1
and 4d
1
type states, respectively, offer-
ing useful comparisons for understanding and controlling
polaronic properties of LN, a topic dealt with in a separate
review of Imlau and co-workers in this volume. The EPR
and optical absorption parameters of these centres also char-
acterizing their Jahn-Teller effects have been compared in
Ref. 113.
The results of simultaneous EPR and optical absorption
measurements in Mg-Ti co-doped near-threshold LN (Ref.
114) are shown in Fig. 27. To obtain the paramagnetic Ti
3þ
charge state, high temperature reduction in vacuum had to be
performed. Along with trace amounts of Ti
3þ
Li
centres well
known from similarly reduced cLN:Ti crystals, Ti
3þ
Nb
centres
with a nearly isotropic EPR line (Ref. 113) were formed (see
Fig. 27(a)) corresponding to optical absorption bands (Fig.
27(d)) slightly redshifted with respect to similar bands of
Ti
3þ
Li
(Fig. 27(c)). After subsequent thermal oxidization, part
of the Ti
3þ
Nb
centres was returned to the 4þ state, however, an
opposite change for minority Ti
3þ
Li
centres occurred (Fig.
27(b)). A similar counter-mainstream increase in the Ti
3þ
Li
EPR signal was observed upon low temperature optical
040601-20 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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bleaching of the reduced sample as well. These effects can
be explained by assuming the existence of Ti
3þ
Li
–Nb
4þ
Nb
bipo-
larons formed during reduction and partially ionized in the
second step, leaving Ti
3þ
Li
polarons with a normal Nb
5þ
Nb
neighbour. Alternatively the effects can be explained by the
existence of Ti
4þ
pairs on neighbouring Li and Nb sites:
upon reduction, the pairs are transformed into Ti
3þ
Li
–Ti
3þ
Nb
“extrinsic” bipolarons with subsequent partial oxidization to
obtain Ti
3þ
Li
with a Ti
4þ
Nb
neighbour.
114,133
IV. THEORETICAL MODELS FOR INTRINSIC
AND EXTRINSIC DEFECTS
As discussed earlier, defects due to non-stoichiometry or
doping strongly influence the properties of LiNbO
3
crystals;
therefore, a clear understanding of their structure is essential.
Computer modelling can make an important contribution to
the understanding of material properties at the atomic level.
For this kind of calculations, some assumptions concerning
the formation of defect structures have to be made. At the
beginning of each Subsections IV A-IV C, the main assump-
tions and characteristics of the theoretical models used will
be outlined.
The first interatomic potentials capable to reproduce
basic features of the real defect structure of LiNbO
3
have
been elaborated by Donnerberg et al., Tomlinson et al.,
Catlow and co-workers.
134–138
Major improvements could
be achieved recently by another set of interatomic poten-
tials
139
reproducing the properties of both the ferroelectric
and paraelectric phases of LiNbO
3
and yielding a generally
better level of agreement with experi ment. The new set of
pseudopotentials was based on the GULP code
140
and could
be used to determine the formation energies of various intrin-
sic and extrinsic defects. These results are summarized in
Sections IV A and IV B.
Defect structures in LiNbO
3
crystals have also been
investigated by first-principles methods, however, the correct
treatment of boundary conditions and problems in the model-
ling of point defects within the density functional theory
(DFT) made the calculations rather difficult. The results,
similarly to the case of pseudopotential methods, supported
the Li vacancy incorporation model by preferring clusters
consisting of a niobium antisite compensated by lithium
vacancies as the most stable under Nb
2
O
5
-rich conditions,
while for Li
2
O-rich conditions, Li-Frenkel defects turned out
to have the lowest formation energy.
141,142
Recently, it was
shown by Li et al.
143,144
mainly using hybrid functional DFT
calculations that the formation energies of V
Li
and V
Nb
depended on the position of the Fermi level in the band gap
and the actual occurrence of these defects was strongly deter-
mined by their tendency to form clusters among each other
and with Nb
Li
antisite defects. A realistic charge distribution
around defects was obtained by relaxing the lattice (for
polarons in LiNbO
3
crystals see the review of Imlau
145
).
It has been shown in Section III that hydroxyl ions are
probes of the defect structure in both undoped and doped
LiNbO
3
crystals. Therefore, computer modelling of defects
related to OH
ions is of fundamental importance. To ana-
lyse and understand the properties of OH
ions in the
LiNbO
3
crystal lattice, first principles theoretical calcula-
tions had to be performed. A good choice for making the
required electronic structure calculations was the SIESTA
computational code.
146,147
The results of a calculation of
proton incorporation in sLN, using density functional theory
along with the supercell method implemented in
SIESTA,
148–150
are summarized in Subsection IV C.
A. Intrinsic defects
After decades of experimental and theoretical efforts,
the controversies concerning the intrinsic defect structure of
LiNbO
3
are only partly resolved.
6,9,151,152
Density measure-
ments showed that neither oxygen vacancies nor oxygen
interstitials are present in the lattice.
4,153
It can be assumed
that excess Nb is mainly incorporated on Li sites forming
Nb
Li
antisites though Nb ions occupying structural intersti-
tial sites also remain a debated option. Another important
question is the mechanism of charge compensation for the
surplus charges of the antisites described until recently by
two competing assumptions in the literature. Initially, Nb
vacancies V
Nb
(Refs. 154 and 155) were assumed to play the
role of charge compensators, as indirectly suggested by early
nuclear magnetic resonance (NMR) measurements
154
and
also by high resolution electron microscopy results.
156
However, charge compensation can be realised also by Li
vacancies, V
Li
as deduced from X-ray diffraction results,
157
FIG. 27. Spectra of LN:Ti and LN:Mg:Ti crystals doped by 6 mol. % Mg
and/or 0.5 mol. % Ti and annealed in vacuum and thin air at 850
C. EPR
spectra taken in the double-doped sample at T ¼14 K after vacuum reduc-
tion for 150 min (a) and after a subsequent oxidizing treatment in air for
90 min (b), asterisks denoting background signals. Optical absorption differ-
ence bands of the reduced crystals taken at RT (with respect to similarly
treated crystals without Ti doping) assigned to the Ti
3þ
Li
(c) and Ti
3þ
Nb
(d)
centres, respectively, and their decomposition into Gaussians. Reproduced
with permission from G. Corradi et al., Appl. Phys. B 78, 607–614 (2004).
Copyright 2004 Springer ScienceþBusiness Media.
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time of flight neutron diffraction measurements,
158
and later
NMR results.
159
To describe recent Raman spectroscopic
results, a mixed model containing both lithium and niobium
vacancies was also introduced.
160
Our spectroscopic results
shown in Section III favour the Li vacancy model which is
commonly accepted as also em phasized in Ref. 99.
Computer simulations were started to clarify the feasibil-
ity of the various defect models. The studies of Donnerberg
et al.
135
stressed the role of (Nb
Li
-V
Nb
) and isolated Nb
Li
antisite defects. Their results had to be interpreted by assum-
ing the existence of ilmenite-like stacking sequences in
LiNbO
3
as suggested by Smyth.
161
To clarify the controver-
sial situation, new potentials were simultaneously determined
for the structures of LiNbO
3
(ferroelectric phase), Li
2
O, and
Nb
2
O
5
using the free energy minimization option of the
GULP code.
139
Based on the new potentials, formation ener-
gies of intrinsic defects in LiNbO
3
, such as vacancies, cation
interstitials at structural vacancies (i.e., in empty oxygen
octahedra), Frenkel and Schottky defects, were deter-
mined.
162,163
Subsequently, three reactions were separately
investigated, where the antisite niobium was compensated by
lithium or niobium vacancies and the interstitial niobium by
lithium vacancies
5Li
Li
þ
1
2
Nb
2
O
5
! 4V
0
Li
þ Nb
••••
Li
þ
5
2
Li
2
O; (4.1)
5Li
Li
þ 4Nb
Nb
þ
1
2
Nb
2
O
5
! 4V
00000
Nb
þ 5Nb
••••
Li
þ
5
2
Li
2
O;
(4.2)
5Li
Li
þ
1
2
Nb
2
O
5
! 5V
0
Li
þ Nb
•••••
int
þ
5
2
Li
2
O: (4.3)
It was concluded that only the formation of an antisite
niobium charge compensated by four lithium vacancies
(Eq. (4.1)) was energetically feasible in accordance with the
spectroscopic results presented in Section III.
B. Dopant ions
Since the most frequently used ODR ion is magnesium,
most experiments and models are concerned with the incor-
poration of this dopant. The main assumption of these mod-
els is that Mg ions first substitute at Li sites thereby
preventing the formation of Nb
Li
antisites. This process is
completed at the threshold concentration where no antisites
are left. For larger Mg concentrations, magnesium enters
both Li and Nb sites.
42,70,72,135
This scenario was refined by
crystal density measurements in LiNbO
3
crystals doped with
Mg in a wide concentration range.
164
Although no direct ex-
perimental evidence for the existence of additional charge
compensation was found, in principle both niobium and lith-
ium vacancies and even antisites should be admitted to
describe the incorporation mechanism in detail.
Bearing this in mind, the incorporation of a number of
divalent and trivalent cations into the LiNbO
3
crystal lattice
has been recently investigated also by potential calcula-
tions,
162,163
taking into account substitution at both the Li
þ
and the Nb
5þ
sites. In all cases, considerable defect binding
was found, in the sense that dopant and charge compensating
defects are likely to occupy adjacent sites. In the case of
divalent dopant ions, both for 0 K and room temperature cal-
culations, it was found that the charge compensation mecha-
nism with the lowest energy involves dopants entering both
Li and Nb sites without intrinsic defect generation
4MO þ 3Li
Li
þ Nb
Nb
! 3M
•
Li
þ M
000
Nb
þ Li
2
O þ LiNbO
3
;
(4.4)
where
•
and
0
denote positive and negative charge with
respect to a normally filled lattice site. There are only two
exceptions viz., the Fe
2þ
and Cd
2þ
ions, but only at room
temperature, where antisite niobiums should come into exis-
tence during incorporation
RT : 4MO þ 3Li
Li
þ 2Nb
Nb
! 3M
•
Li
þ 2M
000
Nb
þ Nb
••••
Li
þ Li
2
O þ LiNbO
3
: (4.5)
In the case of trivalent dopants, depending on the tempera-
ture, two different schemes were found to be energetically
favourable:
0K: M
2
O
3
þLi
Li
þNb
Nb
! M
••
Li
þM
00
Nb
þLiNbO
3
; (4.6)
RT : M
2
O
3
þ Li
Li
þ 2Nb
Nb
! 2M
00
Nb
þ Nb
••••
Li
þ LiNbO
3
:
(4.7)
Again two exceptions were found: at room temperature, Ce
and Eu dopants prefer the first scheme.
Most recently, double-doped LiNbO
3
has also been
studied, and the energetics of solid-state reactions leading to
dopant incorporation was calculated.
165
Predictions of
computer modelling of this kind may be helpful for tailoring
material properties without expensive and time consuming
experiments.
C. OH
2
ions
As seen in the infrared absorption experiments, the
incorporation of hydrogen into LiNbO
3
during the growth
process occurs in the form of an OH
ion. The experimental
data have usually been analyzed by employing simplified,
phenomenological models
58,166–168
with only rare
attempts
169
to analyse and supplement them by first princi-
ples theoretical calculations. Some information on dynamics
and kinetics, i.e., activation barrier height and rate constants,
has been deduced from analysing the temperature dependent
of ionic conductivity
170
and IR spectra
64
as well as holo-
graphic scattering,
171
while
1
H NMR measurements have
been employed to find the location of protons within the
crystal lattice.
172–174
To model a stoichiometric LiNbO
3
crystal, a supercell
composed of 2 2 2 hexagonal unit cells (240 atoms)
along with periodic boundary conditions has been
employed.
148,150
For starting the calculation, a Li ion was
removed from the cell to compensate the charge of the pro-
ton added in a nearby position. Subsequently, the structure
of the supercell has been fully optimized and relaxed by
letting all nuclei move. But for the proton, all other ions
essentially remained in their initial positions. The results
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show that in the most stable configuration, the proton is nei-
ther on nor in the vicinity of a line connecting nearest neigh-
bour oxygens, but is located near a bisector of an oxygen
triangle, tilted by 4.3
out of the oxygen plane towards a lith-
ium vacancy. The geometry of the most stable configuration
in the lattice is shown in Fig. 28. The distance of the hydro-
gen from the nearest oxygen, the equilibrium OH
bond
length, is r
eq
¼0.988 A
˚
.
Proton dynamics was modelled using a potential energy
surface (PES) derived via the Born-Oppenheimer approxima-
tion. The PES was determined on a grid of 2251 points by
placing the hydrogen atom into various positions within the al-
ready relaxed supercell and calculating the total energy. Then,
employing these sample points, an analytical approximation
for PES has been constructed;
150
the 2D projections of this
PES are shown in Fig. 29. Using this analytical approximation
and a new method for quantum chemical calculations, the
transition frequencies and dipole moments of several vibra-
tional normal modes of the incorporated OH
and OD
ions
were determined. The obtained frequencies were compared to
results of IR absorption measurements. For the stretching,
bending, and higher energy combination bands, the deviation
between the theoretical and experimental frequencies was less
than 1%. This result was confirmed experimentally on a thick
LiNbO
3
sample where the otherwise missing lower wavenum-
ber stretching–bending combination band could also be
detected.
149
V. THz GENERATION—A PROMISING APPLICATION
In the last decade, due to the rapid development of far
infrared (THz) sources, a 10
7
-fold increase was reached in
THz pulse energy opening the way towards several applica-
tions.
175
THz pulses with typical energies in the fJ region
with corresponding peak electric field strengths of hundreds
of V/cm are suitable for linear THz spectroscopy. Reaching
the lJ energy level with hundreds of kV/cm electric field
strength opened the way for nonlinear THz spectroscopy.
175
For tens of mJ pulse energy with tens/hundreds of MV/cm
peak electric field strength, several interesting potential
applications are in sight like acceleration, longitudinal com-
pression, and undulation of relativistic electron bunches—
which can lead to attosecond pulse generation—
176,177
post-
acceleration and monochromatization of laser-generated
proton bunches with potential applications for Hadron
therapy.
178
Optical rectification of near infrared ultrashort laser
pulses in nonlinear crystals is an effective way for generation
of (near) single cycle THz pulses. LN is very suitable for that
because of its extremely high second order nonlinear optical
coefficient value (168 pm/V) which is 2.5 times larger than
that of ZnTe. For efficient THz generation, velocity matching
is necessary, i.e., the group velocity of the pump has to be
equal to the phase velocity of the generated THz wave. The
extreme large refractive index difference between THz and
optical wavelengths makes collinear phase matching in LN by
conventional techniques impossible. Non-collinear
FIG. 28. The optimal proton position in the LiNbO
3
crystal lattice as
deduced from quantum chemical calculations. Reproduced with permission
from K. Lengyel et al., IOP Conf. Ser. Mater. Sci. Eng. 15, 012015 (2010).
Copyright 2010 IOP Publishing.
FIG. 29. The potential energy surface (PES) of the incorporated proton around the optimal location. The q
1
,q
2
, and q
3
vectors represent the two bending and
the stretching vibrational modes, respectively. Reproduced with permission from V. Szalay et al., J. Chem. Phys. 135, 1–9 (2011). Copyright 2011 American
Institute of Physics.
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techniques, such as Cherenkov-type excitation
179,180
and fo-
cusing to a line
181
were not very effective, and the geometry
of the THz radiation was not practical for applications. The
most important innovative step in the history of high energy
THz science was the introduction of the so called tilted pulse
front (TPF) excitation technique
182
as a velocity matched THz
generation process with lots of advantages. In such a scheme,
the intensity front of the pump pulse is tilted relative to its
wave front by an angle of c. Thus, instead of the pump veloc-
ity, only its projection perpendicular to the propagation direc-
tion of the generated THz radiation has to be equal to the THz
velocity
v
p;gr
cosðcÞ¼v
THz;ph
: (5.1)
Fig. 30 shows the TPF excitation scheme. The pulse
front tilt is related to the angular dispersion created by the
grating and is modified by an imaging system which is either
a single lens (as shown in Fig. 30) or a telescopic system.
The necessary in-crystal pulse front tilt is adjusted by the
adequate (de)magnification.
The efficiency that can be reached by TPF excitation is
lower than it would be in the case of collinear phase match-
ing, however, even in spite of the relatively large (c ¼63.5
)
pulse front tilt angle needed in LN, it is higher than for other
nonlinear materi als. The most important advantages of the
TPF excitation are tunability of the THz frequency by
varying the pulse front tilt angle, and the energy scalability.
Initially amplified Ti:sapphire sources delivering pulses
with about 100 fs pulse length were used for THz generation.
The first reported result of THz generation in 2 mol. % Mg
doped sLN was 30 pJ pulse energy at room temperature and
98 pJ at 77 K, with corresponding THz conversion efficien-
cies of 1.3 10
5
and 4.3 10
5
, respectively.
183
The
reason of the better results at lower temperature is the signifi-
cantly lower THz absorption, which is a key point in THz
generation efficiency.
It was theoretically justified that taking into account all
relevant material parameters (including THz absorption as
well), LN is the most promising material for THz genera-
tion.
184
The strong Mg dopant concentration dependence of
THz absorption suggested the use of sLN crystals with the
optimal 0.7 mol. % Mg content
181
instead of ones with
2 mol. %. This essential change in the measurement setup of
Ref. 183 alone resulted in a four-fold increase in the meas-
ured THz pulse energy and efficiency (400 pJ and
1.7 10
4
).
184
By increas ing the pump pulse energy to 500 lJ and 20
mJ in 0.7 mol. % Mg doped sLN, THz pulse energies of 240
nJ (Ref. 185) and 10 lJ, (Ref. 186), were reached with corre-
sponding conversion efficiencies of 5 10
4
and 6 10
4
,
respectively.
It was shown that imaging conditions have to be set in a
way that the TPF and the image of the grating become tan-
gential to each other inside the crystal in order to obtain the
optimal transform limited pump pulse length values along
the TPF.
187
In order to optimize the THz output either for
pulse energy
187
or for peak electric field strength,
188
model
calculations were performed taking into account THz and
pump absorption, multi-photon-absorption, noncollinear
propagation of the pump and the THz beam, variation of
pulse length due to material and angular dispersion.
187,188
Varied parameters were temperature, crystal length, and
pump pulse duration. It was found that in the case of LN
with optimal thickness, the optimal pump pulse duration is
between 350 and 600 fs depending on temperature. It was
theoretically predicted that instead of pump pulses with
100 fs pulse length (used initially), longer transform lim-
ited pump pulses are needed. The reason is that for the short-
est pulses, the pulse duration changes very fast during the
propagation in the crystal, and for a finite crystal length, the
spatially averaged pulse duration is shortest not for the short-
est pulses, but for pulses having optimal Fourier transform
pulse duration.
188
Furthermore, the temperature has to be as
low as possible.
188
It was also declared that although at higher THz
frequencies, semiconductors are competitive with sLN, this
is not the case for lower frequencies, where for the genera-
tion of THz pulses with large bandwidth sLN is the most
advantageous.
187
As a result of experiments with quasi-optimized setups
at 1030 nm pump wavelength at room temperature, THz
pulse energies of 125 lJ (Ref. 189) and 430 lJ (Ref. 190)
with corresponding conversion efficiencies of 0.25 (Ref.
189) and 0.77% (Ref. 190) were obtained in sLN:0.7 mol. %
Mg with nearly transform limited pump pulse durations
of 1.3 ps (Ref. 189) and 785 fs,
190
respectively. Theoretical
predictions of Ref. 187 were verified with the enhanced THz
pulse energy and efficiency values. At cryogenic tempera-
tures using pump pulses with closer to optimal lengths, THz
pulse energies exceeding 1 mJ are in sight.
Fig. 31 demonstrates the powerful development due to
the TPF technique. The rapid increase in THz pulse energy
and THz generation efficiency achieved in sLN in the last
decade is shown.
The TPF THz generation setups used in experi-
ments
183–186,189–192
suffer from imaging errors, leading to
local broadening of pump pulses along the tilted pulse front
resulting in a limitation for the pump spot size and for the
THz pulse energy.
187
In order to exclude this limiting factor,
a so called contact-grating setup was proposed, which means
that a relief dielectric periodic structure is etched on the crys-
tal surface making the imaging optics superfluous.
193
For
this setup, THz generation efficiencies exceeding 10% with
tens of mJ pulse energy are predicted.
FIG. 30. The TPF excitation scheme. The propagation of the THz radiation
is perpendicular to the TPF (green stretches).
040601-24 Lengyel et al. Appl. Phys. Rev. 2, 040601 (2015)
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VI. SUMMARY AND OUTLOOK
Development of over half a century in the field of
LiNbO
3
sets a good example on the co-operation and com-
munication between fundamental scientists, device design-
ers, and engineers. By now, defect formation mechanisms
are essentially clarified and satisfactory, or at least better
understanding of the impact of stoichiometry and doping on
the physical properties is achieved. Crystals with extremely
low intrinsic defect contents offer extraordinary opportuni-
ties for producing controlled defect systems as examples of
crystal engineering. Established and recent applications,
including real-time holography based on polaronic states,
THz generation, waveguides, and nanostructured devices as
discussed in the present and following papers of this volume,
open further perspectives for the use of LN. Future research
targets may be the extension of transparency and damage re-
sistance towards the UV region by the combination of a par-
tial Ta-Nb exchange and the use of Zr as an ODR
additive.
194
As the demand for crystals has increased, cost reduction
by scaling-up (i.e., growing crystals with >75 mm diameter)
has become the main driving force also for sLN growth.
Enlarged crystal diameter poses additional problems for con-
trolling heat and mass transfer and also for the homogeniza-
tion of the melt composition, meaning new technological
challenges for the refinement and renewal of growth equip-
ment, including furnace design and control systems.
To overcome these problems, alternative technologies
are still competing, exampl es are the “low melt-level
Czochralski” technique
195
(a variant of the double crucible
method ensuring the stability of the crystal-melt system by
using extremely small melt heights of 1–3 mm in the cruci-
bles), or the “heat field rotation” method proposed by Kokh
and co-workers
196
allowing to govern the heat and mass
transfer even in a very viscous liquid phase. The dynamic
development of bulk growth technology promises further
progress in the next decades.
ACKNOWLEDGMENTS
Support of the Hungarian Scientific Research Fund
(OTKA) Grant Nos. K 83390, K 101846 and funding
under the Contract No. SROP-4.2.2.A-11/1/KONV-2012-
0065 are kindly acknowledged. A supercomputer operated
by the National Information Infrastructure Development
Institute (Hungary) has been used for quantum chemical
calculations.
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