Compositional and structural changes in TiB2 films induced by bias, in situ and post-deposition annealing, respectively

Article abstract of DOI:10.1016/j.physb.2005.12.260

Structural changes in TiB₂ films were induced at relatively low temperatures by the application of bias and in situ annealing or by post-deposition heat treatment of samples subjected to bias with simultaneous in situ annealing. In situ annealing by itself evoked only partial crystallization. Application of bias by itself only modified the composition of the as deposited film. A simple model is presented to explain the variation of the composition when RF bias is applied to a cold substrate. The crystallized films had a (0 0 0 1) texture. A model has been suggested to explain the observed preferred orientation, based on the contribution of surface and strain energies. Both, the surface energy and strain energy are direction dependent. These were evaluated for two film orientations reported in the literature, namely, the (0 0 0 1) and ( 1 0 over(1, -) 1 )orientations. The preferred orientation of the film is determined by the lowest overall free energy resulting from the competition between the surface energy and the strain energy on different lattice planes. The surface energy is not film thickness dependent while the strain energy is thickness dependent and increases with it. For small film thickness, as in this work, the surface energy term is significant and (0 0 0 1) orientation with a minimum surface energy is preferred. At large film thicknesses the strain energy becomes dominant and the ( 1 0 over(1, -) 1 ) preferred orientation is observed. Under certain experimental conditions strain energy effects may tip the preferred orientation to ( 1 0 over(1, -) 1 ). The elastic moduli in the (0 0 0 1) and ( 1 0 over(1, -) 1 ) directions were determined as 435 and 538 GPa, respectively.

Full text of DOI:10.1016/j.physb.2005.12.260

ARTICLE IN PRESS
Physica B 381 (2006) 118–127
www.elsevier.com/locate/physb
Compositional and structural changes in TiB2 films induced by bias,
in situ and post-deposition annealing, respectively
Ã
Joshua Pelleg , G. Sade, M. Sinder, D. Mogilyanski
Department of Materials Engineering, Ben Gurion University of the Negev, 84105, Beer Sheva, Israel
Received 23 November 2005; received in revised form 22 December 2005; accepted 22 December 2005
Abstract
Structural changes in TiB2 films were induced at relatively low temperatures by the application of bias and in situ annealing or by post-
deposition heat treatment of samples subjected to bias with simultaneous in situ annealing. In situ annealing by itself evoked only partial
crystallization. Application of bias by itself only modified the composition of the as deposited film. A simple model is presented to
explain the variation of the composition when RF bias is applied to a cold substrate. The crystallized films had a (0 0 0 1) texture. A
model has been suggested to explain the observed preferred orientation, based on the contribution of surface and strain energies. Both,
the surface energy and strain energy are direction dependent. These were evaluated for two film orientations reported in the literature,
¯
namely, the (0 0 0 1) and ð1 0 1 1Þorientations. The preferred orientation of the film is determined by the lowest overall free energy
resulting from the competition between the surface energy and the strain energy on different lattice planes. The surface energy is not film
thickness dependent while the strain energy is thickness dependent and increases with it. For small film thickness, as in this work, the
surface energy term is significant and (0 0 0 1) orientation with a minimum surface energy is preferred. At large film thicknesses the strain
¯
energy becomes dominant and the ð1 0 1 1Þ preferred orientation is observed. Under certain experimental conditions strain energy effects
¯
¯
may tip the preferred orientation to ð1 0 1 1Þ. The elastic moduli in the (0 0 0 1) and ð1 0 1 1Þ directions were determined as 435 and
538 GPa, respectively.
r 2006 Elsevier B.V. All rights reserved.
PACS: 68.55.ꢀa; 68.55.Jk; 81.15.Aa; 81.15.ꢀz
Keywords: Sputtering; TiB2 film; Bias; In situ annealing; Post-deposition annealing
1. Introduction
sublayer [1,5]. B diffusivity in TiSi2 is insignificant up to
1173 K [6,7]. The barrier properties of the bilayer, such as
its resisitivity, crystallinity, composition, diffusion barrier
effectiveness against Cu penetration, etc., depend on the
structure of the TiB2 overlayer. To avoid undesirable
changes in the bilayer-diffusion barrier during device
preparation and obtaining the most stable configuration,
it is desirable to understand the possible changes in TiB2
which may arise during the various steps of the fabrication
process. Application of bias, bias and insitu annealing and
TiB2 is a widely accepted material for applications
including microelectronics, diffusion barriers, wear and
erosion-resistant coatings and for cutting tools. Control of
the structure of TiB2 films is of importance for its
successful operation in the silicon technology as a diffusion
barrier [1,2]. TiB2 cannot be used in direct contact with Si
due to very extensive B outdiffusion [3,4], which might
affect the original doping of the Si and even change its
character from an n-type to a p-type. A remedy for B
outdiffusion into Si was realized in the form of a TiSi2
post-deposition annealing were observed to have
significant effect on the overall properties of TiB2 [1].
a
In this communication the changes induced by bias, bias
and in situ annealing and post-deposition annealing are
considered. Experimental results were obtained by X-ray
Ã
Corresponding author. Tel.: +972 8 646 1823; fax: +972 8 647 2946.
E-mail address: pelleg@bgumail.bgu.ac.il (J. Pelleg).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.physb.2005.12.260

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119
75
diffraction (XRD), Auger electron spectroscopy (AES),
resistivity measurements, transmission electron microscopy
(TEM) and high-resolution electron microscopy (HREM).
Particular attention is given to the mathematical analysis of
substrate bias effect on the compositional variation in
sputter-deposited TiBx by applying an RF bias during
deposition [8]. A model is suggested to explain the observed
preferred orientation in TiB2 films.
70
65
60
55
50
45
40
2. Experiment
Film thickness-30 nm
Specimens used as substrates cut from 3-in n-type Si
wafers, having a resistivitiy of ꢁ10 O cm, were chemically
cleaned by dipping them into a 5% HF solution followed
by rinsing in deionized water, acetone and alcohol [9,10].
Magnetron cosputtering was performed onto rotating Si
(1 0 0) wafers from two targets of Ti and B to obtain thin
films of TiB2. Cosputtering from two independent magne-
tron sources was preferable since the ratio of the
components comprising the film can be varied, thus
providing maximum flexibility. Presputtering of the targets
was performed before film deposition. The base pressure in
the deposition chamber was o30 mPa. High purity Ar
(99,999%) at a pressure of ꢁ0.5 Pa was used during all
sputter depositions. Residual gas analysis monitored by
Inficon quadrupole mass-spectrometer (Quadrex 200)
showed pressures of the following residual gases: H2-
2.8 mPa, N2/CO2ꢀ5 mPa, H2O ꢀ15 mPa and O2 ꢀ0.03 mPa.
Mass flow controller (MKS) was used to regulate the Ar
flow and the total gas pressure in the chamber was
monitored by capacitive manometer (Baratron). Informa-
tion on deposition rate and thickness of films were
obtained from Sycon deposition rate controller. Typical
input RF power to the B target was 320 W, which was kept
constant, whereas the DC power to the Ti target varied in
the range of 50–75 W to provide variable B/Ti ratios. This
way sputtering conditions could be correlated with
composition and resistivity of the film. A deposition rate
of typically 0.15 nm/s of TiB2 was obtained when 320 and
60 W powers were applied on the B and Ti targets,
respectively. The structure and the properties of the
growing boride film were affected by applying an RF bias
on the substrate either heated or kept at room temperature.
The RF bias voltage varied from ꢁꢀ100 to ꢀ250 V. The
film thickness was in the range of 30–230 nm. The
composition of the as-deposited film was determined by
AES depth profiling, electrical resistivity of the films was
calculated from routine sheet resistance measurements.
Film thickness was verified by profilometer, Jeol scanning
electron microscopy (SEM) and measured from the cross-
sectional TEM images.
80
100
120
140
160
180
200
220
240
260
Bias voltage (V)
Fig. 1. Sheet resistance of TiB2 thin film as a function of RF bias voltage.
from the work of Shikama et al. [11] and from calculations
of the B sputtering yield by Seah [12] according to
Sigmund’s model [13]. The guidelines were successfully
applied for TiB2 thin film deposition on cold substrate
without RF bias [14]. Structural modifications can be
induced by applying bias on films deposited on cold
substrate. Fig. 1 shows the sheet resistance variation of
ꢁ30 nm thick film as a function of the application of a
negative RF bias. The powers applied were 320 and 70 W
on the B and the Ti targets, respectively. These deposition
conditions were maintained close to those used for
cosputtering onto grounded substrates (no bias applied).
At appropriate deposition times a thickness of ꢁ30 nm was
also obtained. No heating was applied, and XRD analysis
revealed that the film has remained amorphous. A
minimum in sheet resistance of ꢁ50 O/& was obtained at
a bias of ꢀ150 to ꢀ180 V. The increase in resistivity beyond
the minimum is probably related either to microstructural
changes or to variation in composition or to both; the
XRD amorphous nature of the film prevailed. Resistivity
changes induced by compositional variation in amorphous
TiB2 films were experimentally observed [14] and they were
associated with B enrichment of the film. A compositional
variation by applying bias is expected, when cosputtering
from elemental targets is performed, because the difference
in sputtering yields of B and Ti [12]. AES analysis confirms
the compositional variation in titanium boride films on
applying RF bias voltage to the substrate during deposi-
tion. The results are summarized in Fig. 2 showing the
chemical composition of titanium boride films as a function
of the applied RF bias voltage.
In all of our experiments, as deposited TiB2 films were
amorphous. Obtaining crystalline as deposited TiB2 film
requires substrate heating and/or simultaneous application
of bias. The degree of crystallinity at a certain bias level is
temperature dependent. For example, in situ heating at
ꢁ673 K at an RF bias level of 15 W providing a self-bias
voltage of ꢁꢀ180 V induced crystallization which is
illustrated in Fig. 3(a). The bias applied corresponds to
3. Results
Deposition of TiB2 by cosputtering from the elemental
targets is a rather complicated process, mainly because of
the very low yield of B. Some guidelines were extracted

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2.3
2.2
2.1
2.0
1.9
1.8
1.7
80
100 120 140 160 180 200 220 240 260 280
Negative bias voltage (V)
Fig. 4. TEM cross-sectional bright field image deposited with bias and in
situ annealing at 673 K followed by post-deposition annealing at 1273 K.
Fig. 2. Chemical composition (B/Ti ratio) of TiB2 thin film as a function
of RF bias voltage.
nealing in vacuum furnace at very high temperature
resulted in randomly oriented grains in the film. Bias
deposited film with in situ heating followed by annealing at
high temperature results in complete crystallization of TiB2
at a temperature level lower than when deposition occurs
without bias. In addition, bias applied deposition and
annealing at a sufficiently high temperature induces C54
TiSi2 formation as well. This is illustrated in Fig. 3(b) for a
TiB2 film deposited with an RF bias of 15 W with a voltage
of ꢁꢀ150 V and in situ annealed at 673 K, followed by
annealing at 1273 K. At this temperature Ti from TiB2 has
reacted with the Si substrate to form C54 TiSi2. A
significant drop, by about an order of magnitude, in
resistivity occurred, resulting in ꢁ13.6 mO cm as a con-
sequence of TiB2 grain growth and the contribution of C54
TiSi2 formation. Cross-sectional TEM of this specimen can
be seen in Fig. 4, which reveals its growth morphology. It
was obtained under bright field condition. The thickness of
this layer is ꢁ250 nm, its grain size is ꢁ35–70 nm, it is dense
and characterized by a strong (0 0 0 1) preferred orienta-
tion. Electron diffraction from a selected area, its schematic
diagram and a HREM image of a TiB2 grain are seen in
Figs. 5(a),(b), and (c), respectively. The measured inter-
planar distance, d is 0.323 nm which corresponds exactly to
the given in the literature [15,16]. In addition, the HREM
images show stacking faults and low-angle grain bound-
aries in regions of the film, as seen in Figs. 6(a) and (b),
respectively. A ꢁ145 nm thick C54 TiSi2 interlayer between
TiB2 and substrate is formed as the consequence of
reaction between excess Ti in the film and Si substrate as
seen in Fig. 7(a). Figs. 7(b) and (c) are an electron
diffraction pattern from a selected area and its schematic
diagram, respectively.
Fig. 3. XRD spectra of TiB2: (a) deposited with simultaneous application
of RF bias (15 W, ꢀ180 V) and in situ annealing at 673 K; (b) post-
deposition annealing of specimen (a) in vacuum at 1273 K for 1 h.
the minimum bias range shown in Fig. 1. Crystallites of
ꢁ10 nm were obtained. The induced crystallization by the
combined effect of bias and in situ heating resulted in a
(0 0 0 1) preferred orientation, whereas conventional an-
4. Discussion
The deposition technique affects the structural properties
of the TiB2 film and its structure that can vary from

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limitation for a particular purpose is useful. To apply
TiB2 as an effective diffusion barrier crystallization has to
be avoided. In the range of the RF bias applied during the
cosputtering on cold substrates, only compositional change
(see Fig. 2) and no crystallization were observed. Shikama
et al. [11,18] obtained as-deposited crystalline TiB2 by
cosputtering on Mo substrates and the application of a
negative bias accompanied by heating to 870 K. In this
work crystallization was induced also, already at 673 K by
the simultaneous application of bias and heating (see
Section 4.3). In the following, a model is presented to
understand the effect of bias on compositional change in
Section 4.1, the structural changes induced by in situ
annealing are presented in Section 4.2, the contribution of
in situ heating when applied in conjunction with bias is
considered in Section 4.3 and the influence of post-
deposition heat treatment on specimens prepared by bias
and in situ annealing are discussed in Section 4.4. A model
to understand preferred orientation in the film is suggested
in Section 4.5.
4.1. A simple model describing deposition with RF bias on
cold substrates
The variation of the composition with substrate bias is
shown in Fig. 2. As can be seen the B content in the
deposited films increases with increasing substrate bias
voltage. This phenomenon is explained by resputtering of
Ti atoms from the growing film by energetic Ar ions
generated in the RF discharge induced near the substrate
when bias is applied. On application of a negative bias to
the substrate, the number of ionized particles in the plasma
increases. The energetic electrons from the target strike the
substrate causing emission of secondary electrons, which
are accelerated into the plasma by the bias field. Since the
ionization probability due to electron impact has a
maximum at ꢁ100–150 eV for most gases, the electrons
accelerated by the bias field are effective in increasing the
ionization of the plasma. The total number of Ar ions on
the substrate increases. As the bias increases, the energy of
the species impinging the substrate also increases, as does
the resputtering [18,19].
Let us designate the flows of B and Ti from the targets
which land on the substrate by J+B and JT+i, respectively.
Application of RF bias creates a flow of energetic Ar ions
which are accelerated towards the substrate, resulting in
resputtering of the growing layer. Let us designate the flow
of incident Ar ions by JAr. Flow means the number of
atoms condensed per unit time per unit surface. The film
growth rate of TiB2 is indicated by V, and the number of B
and Ti atoms in the unit volume of TiB2 is designated by rB
and rTi, respectively. The flow of the resputtered B and Ti
atoms by the energetic Ar ions from the growing TiB2 film
are JꢀB and JTꢀi, respectively. Then from the atom flow
balance of the growing layer we obtain
Fig. 5. TEM images: (a) electron diffraction from a selected area; (b)
schematic diagram of the diffraction pattern; (c) HRTEM of a TiB2 grain
of the specimen shown in Fig. 4.
amorphous/nanocrystalline to crystalline. Each deposition
technique has its advantages and disadvantages and the
desired results for a particular application should dictate
the production method to be used. For diffusion barrier
applications an amorphous film is preferential. Diffusivity
in amorphous structures is expected to be lower than in
crystalline structure at equivalent temperatures. It is
therefore believed that amorphous structures will act as
more effective diffusion barriers. The effectiveness of TiB2
depends whether it is a low-resistive amorphous or
crystalline film. Since deposition with bias improves film
quality and purity [17] and increases its density, application
of bias during deposition might be beneficial for barrier
properties as long as crystallization is not induced.
Application of bias has other effects also, it changes the
composition of a film, and it might create nucleation sites
and modify the phase formation tendency. Therefore,
applying a bias is important and knowledge of its
rBV ¼ JþB ꢀ JꢀB ,
(1)

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122
Fig. 6. HRTEM of the specimen of Fig. 4: (a) stacking fault; (b) low-angle grain boundary.
resputtering rate (in our case the flows JꢀB and JTꢀi) is
proportional to the flow of the incident Ar ions and the
number of B and Ti atoms on the sputtered surface. Thus
we have
JꢀB ¼ SBrBJAr
and
(4)
JꢀTi ¼ STirTiJAr
,
(5)
where SB and STi are the sputtering yields of B and Ti,
respectively. Eqs. (1)–(5) are the model equations. From
these equations and knowing the values of J+B , JT+i, OB, OTi,
SB and STi the growth rate, V and the composition of the
deposited TiB2 can be determined as a function of the flow
of the incident ions (JAr).
Multiplying Eqs. (1) and (2) by OB and OTi, respectively,
adding them and using Eqs. (3)–(5), we have
JþTiOTi
JþOB
V þBJArSB V þ JArSTi
þ
¼ 1.
(6)
A plot of V vs. JAr according to Eq. (6) is shown in
Fig. 8. This schematic graph shows a monotonic decrease of
the film growth rate with increasing incident ions JAr. We
can make the following conclusions on the basis of Eq. (6):
Fig. 7. XTEM image of C 54 TiSi2 interlayer: (a) dark field; (b) electron
diffraction pattern from a selected area; (c) schematic diagram of the
electron diffraction pattern.
(a) In the absence of flow of Ar incident ions, JAr ¼ 0, i.e.,
no bias is applied to the substrate, growth rate is
maximal and V0 ¼ JþB OB þ JTþiOTi.
(b) The flow of the energetic Ar ions when no deposition
occurred, i.e., the deposition rate equals to the
resputtering rate (V ¼ 0 in our case):
rTiV ¼ JþTi ꢀ JꢀTi,
(2)
with the assumption that the atoms in TiB2 are densely
packed we can write
JþB OB JþTiXTi
max
Ar
J
¼
þ
(7)
SB
STi
rBOB þ rTiOTi ¼ 1,
(3)
where OB and OTi are volumes per atom of the respective
atoms in TiB2. From the sputtering theory [13,20], the
From Eqs. (1) and (2), and using Eqs. (4) and (5) the
composition of the deposited TiB2 as a function of the flow

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J. Pelleg et al. / Physica B 381 (2006) 118–127
123
by the element with the smaller sputtering yield, B in
our case.
As can be seen from Eq. (6) increasing JAr reduces
the deposition rate of TiB2 film (V) and consequently from
Eq. (8) rB/rTi, (the ratio of B to Ti atoms in the unit
volume of TiB2) is going to its maximum value as shown
in Fig. 9.
ꢀ
ꢁ
ꢀ
ꢁ
qB
JþB STi
qB
STi
SB
¼
¼
.
(10)
þ
qTi
SB
qTi
JTi
max
JAr¼0
The model explains to a first approximation the
experimentally observed compositional variation in the
TiB2 film as a consequence of applying a negative RF bias
on the substrate. In order to maintain a desired B/Ti ratio,
the applied bias has to be chosen as indicated in Fig. 9. The
model also predicts that in order to produce high-quality
TiB2 films at the desired B/Ti ratio a moderated bias
voltage should be applied to reduce its influence on the
compositional variations, recalling that high bias voltage
results in a reduction of the deposition rate. Fig. 2 shows
the experimentally observed change in B/Ti with applied
bias. Above ꢀ150 V bias the curve resembles the line of the
proposed model shown in Fig. 9. Under the experimental
conditions saturation in the B/Ti ratio occurs at ꢁ2.2 as
seen in Fig. 2. It could be noted that the model presented
here can be useful in other cases as well when cosputtering
with bias application is used for film deposition.
Fig. 8. Schematic graph of TiB2 deposition rate as a function of flow of Ar
incident ions.
4.2. In situ annealing
In general amorphous TiB2 is obtained in sputter
deposited films, and only in exceptional cases a crystalline
structure can be the result. Similar results were reported
when TiB2 was deposited by reactive sputtering [21] and
low-pressure CVD [22]. Low-resistive amorphous TiB2
films are useful for application as a diffusion barrier
against Cu (or Al) penetration in Si technology. Sometimes
it might be a matter of technological or scientific interest to
obtain low-resistive crystalline boride films, or alternatively
to know the conditions to avoid its formation during the
various steps of device fabrication. As deposited and
annealed TiB2 films are resistant to crystallization up to
very high temperatures as indicated by XRD in Fig. 10(a),
whereas crystallization at relatively low temperatures can
be induced if in situ annealing is applied to the substrate.
This can be seen in Fig. 10(b). The high temperature
required for crystallization should not be surprising since it
is related to the melting point of a material, 3498 K for B.
However, in the in situ annealed specimen, the heating
during deposition causes the surface atoms just landed not
to be frozen in at their landing sites, but rather execute
diffusion jumps by the available thermal energy. Surface
adatom mobility occurs in each monatomic layer during
the deposition and it is dictated by the prevailing
temperature during the process of deposition. As a
consequence of the adatom mobility there is in each layer
Fig. 9. Schematic graph of TiB2 composition as a function of flow of Ar
incident ions.
of incident Ar ions can be found by the relation
ꢀ
ꢁ
rB
rTi
JþB V þ STiJAr
¼
,
(8)
JþTi V þ SBJAr
where V as a function JAr is determined from Eq. (6)
The composition of the deposited TiB2 film with bias vs.
JAr is a monotonically increasing curve as seen in Fig. 9.
The compositional variation of TiB2 as a function of Ar
incident ion flow, when the deposition rate is large enough,
i.e., the influence of the flow of Ar ions is not significant on
the film deposition rate, can be determined approximately
from Eqs. (6) and (8):
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
qB
qB
qB
ðSTi ꢀ SBÞ
V0
ꢀ
¼
JAr.
(9)
qTi
qTi
qTi
JAr¼0
JAr¼0
Thus, if STi4SB, namely, if the sputtering yield of Ti
exceeds that of B, the deposited TiB2 layer will be enriched

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124
at 1173 K is completely amorphous. We do not have at
present an explanation for this observation beyond some
speculation as follows. Since the codeposition of Ti and B
was performed on hot Si substrate it is possible that Ti and
B diffused into the silicon during the deposition. Boron
diffusivity into Si is much smaller than that of Ti [23],
therefore the film is expected to be enriched in B with
increasing temperature. B is known to promote amorphi-
zation and thus the amorphous structure is obtained.
1100 °C
950 °C
900 °C
800 °C
700 °C
4.3. In situ annealing with bias
as-deposited
A negative bias voltage applied to substrates enhances
crystallization of TiB2 with the magnetron sputtering
technique. In Fig. 3(a) the combined effect of bias and a
relatively low-temperature annealing is shown. Bias influ-
ences the nature of the film in several ways, but for the
subject considered here, its effect on creating nucleation
sites is of interest. Already at 673 K crystallization sets in
when in situ annealing and the application of a 15 W RF
bias providing a self-bias voltage of ꢁꢀ180 V (which
corresponds to the minimal sheet resistance of the film as
seen in Fig. 1), are applied. Fig. 3(a) indicates that the film
has a preferred orientation. Only the (0 0 0 l) film peak is
observed indicating that the c-axis is perpendicular to the
film surface.
15
20
25
30
35
40
45
50
55
60
2θ
(a)
Si kβ
Si (200)
SiB6 (333), (442), (540)
TiB(102)
950 °C
900 °C
800 °C
TiB2 (100)
TiB2 (101)
TiB2 (101)
700 °C
600 °C
500 °C
400 °C
Ti2B5 (103)
TiB2 (100)
TiB2 (101)
TiB2 (101)
Most of the reports indicate a (0 0 0 1) preferred orienta-
tion of deposited and annealed TiB2 films irrespective to the
substrate or the deposition technique used. See for example
Refs. [24–27]. However, there are some reports indicating a
TiB2 (100)
25
30
35
40
45
50
55
60
¯
2θ
ð1 0 1 1Þ texture also [28,29]. The strong c-axis alignment of
(b)
TiB2 in the majority of experiments might indicate that the
deposition parameters are not the only critical factor which
determines the evolution of a strong (0 0 0 1) texture, since
such orientation was obtained irrespective of the substrate
or deposition techniques and the use of bias. In general one
could state that the plane with the lowest free energy is
expected to be the preferred plane where the film will grow.
Thus, since the unit cell of TiB2 has two B and one Ti atoms,
respectively, the (0 0 0 1) plane having the smallest area will
have the denser bonds and therefore the lowest energy.
However, this by itself cannot explain the observation
Fig. 10. XRD of TiB2 films on Si (1 0 0) substrate: (a) of as deposited and
annealed films. The film is mainly amorphous up to a very high
temperature. (b) films deposited at the indicated temperatures. Already
at 673 K TiB2 peaks are observed.
an atomic environment which is sufficiently close to the
crystalline TiB2 phase. Therefore, moderate deposition
temperatures are sufficient for partial crystallization. Unlike
in the case of deposition on cold substrate, atoms arrive and
settle at their ‘‘landing’’ locations with limited mobility for
rearrangement for crystal formation and only short-range
ordering might exist. This situation prevails in each layer
and when the process of deposition is stopped at some
desired thickness of the film the structure remains frozen in.
Therefore, higher temperatures will be required to rearrange
the atoms to the required ratio for crystalline boride
formation. Even at a high temperature of 1373K only
minor crystallization has taken place as seen in Fig. 10(a).
Fig. 10(b) does not indicate full crystallization of the in
situ annealed films, and a large fraction remains amor-
phous. Furthermore, it is puzzling that with increasing
deposition temperature to the range of 973–1173 K the
amorphous fraction seems to increase, rather than decrease
as would be expected. As a matter of fact the film deposited
¯
ð1 0 1 1Þ orientation. In Section 4.5 the subject of preferred
orientation is considered.
4.4. In situ annealing with bias and post-deposition
annealing
Post-deposition heat treatment of specimens which were
in situ annealed with the application of bias was motivated
basically by two reasons. First to induce complete crystal-
lization in the film and test whether by additional annealing
the orientation relation remains the same and second to
explore the possibility of inducing TiSi2 sublayer forma-
tion. Fig. 3(b) seems to confirm both of them. Thus, the
orientation did not change and remained the same
following post-deposition annealing, but the intensity of

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125
¯
the first- and second-order peaks increased considerably.
Further C54 TiSi2 formation was induced. This result
motivated a set of experiments [30] to explore the
possibility of forming TiB2/TiSi2 bilayers from the reaction
of the Ti-rich component of a (Ti+B) film with the Si
substrate. The HREM image (Fig. 7(a)) confirms the XRD
results, regarding the C54 TiSi2 formation. A point of
practical interest is the location of the C54 TiSi2 formed in
the process of annealing. Fig. 7(a) shows that the TiSi2
layer is interposed between the TiB2 layer and the Si
substrate. It is clear that such a location of the TiSi2 is in
line with our idea to form a TiB2/TiSi2 barrier structure
[30] in a single step operation. Its thickness is ꢁ150 nm and
no other silicides were formed.
In addition to the morphology of the crystalline TiB2
film (Fig. 4), the presence of defects such as stacking faults
and low-angle grain boundaries were also revealed by
HREM (Fig. 6). A crystalline film with the microstructure
shown, hardly can be considered as an effective diffusion
barrier not only because the presence of grain boundaries,
but also since the mentioned defects are channels for very
fast diffusion. Fortunately, annealed amorphous TiB2
which is stable up to ꢁ1223 K as revealed by XRD [14]
provides an excellent diffusion barrier against Cu penetra-
tion with very low resistivity, which is essential in the
semiconductor technology [1].
considered that in the ð1 0 1 1Þ plane 2 B–B bonds at a
distance of 0.175 nm, 2 Ti–Ti bonds at a distance of
0.303 nm, 3 Ti–B bonds at a distance of 0.238 nm and 4
Ti–Ti bonds at a distance of 0.238 nm are broken. All
together the number of broken bonds, n1 0 1 1 ¼ 11 or
¯
8.72 ꢂ 1015 bonds/cm2. Using again Eq. (12), S1 0 1 1
¼
¯
2:19 ꢂ 10ꢀ3ðJ atomꢀ3Þ. Based on the surface energy calcu-
lation alone the (0 0 0 1) plane with the lowest surface
energy can explain our and other observations of the
(0 0 0 1) preferred orientation. However, it cannot by itself
¯
explain the ð1 0 1 1Þ preferred orientation observed in some
experiments reported in the literature [28,29]. Calculation
of the strain energy in the mentioned directions is based on
the strain and elastic stiffness data. The strain obtained
from XRD measurements in direction perpendicular to
sample surface (in our case the (0 0 0 1) plane) is equal to
e33 ¼ 3:473 ꢂ 10ꢀ3. In biaxial mode, the strain components
in directions parallel to surface are equal and can be
calculated as
e11 ¼ e22 ¼ ꢀ½ð1 ꢀ nÞ=2nꢃe33,
(13)
where the Poisson ratio, n is given as 0.151 [35]. So the
strain tensor in the principal coordinate system is
2
3
ꢀ9:764 ꢂ 10ꢀ3
0
0
6
4
7
5
.
(14)
0
ꢀ9:764 ꢂ 10ꢀ3
0
0
0
3:473 ꢂ 10ꢀ3
4.5. Preferred orientation
Pelleg et al. [31] have proposed a model to explain
preferred orientation in TiN films. In this model, they
assumed that the total free energy of the system is described
by the sum of surface energy, S, and strain energy, U, of
the TiN film. This model will be applied to explain the
tendency of a specific texture evolution in the TiB2 film
also. The overall free energy Wh k l of a film is assumed to
be the sum of the surface, Sh k l and strain Uh k l energies.
Suppose that Wh k l is
¯
To estimate the strain perpendicular to the ð1 0 1 1Þ plane
the tensor transformation due to coordinate rotation was
applied. In the new x0,y0,z0 coordinate system z0 is the
normal direction of the plane ð1 0 1 1Þ and the strain tensor
¯
is expressed as
2
3
ꢀ9:764 ꢂ 10ꢀ3
0
0
6
4
7
5
0
ꢀ4:502 ꢂ 10ꢀ3
6:5 ꢂ 10ꢀ3
.
0
6:5 ꢂ 10ꢀ3
ꢀ1:789 ꢂ 10ꢀ3
Wh k l ¼ Sh k l þ Uh k l
.
(11)
(15)
Sh k l for different orientations can be evaluated on the
basis of the sublimation energy, Ls. For TiB2, Ls is given
[16] as 435 kcalmolꢀ1 (3.02 ꢂ 1018 Jatomꢀ1). Sh k l can be
expressed as
Here ꢀ1.789 ꢂ 10ꢀ3 is the strain e33 in the ½1 0 1 1ꢃ
direction (in the new coordinate system).
The elastic stiffnesses were evaluated by the general
gradient approach approximation by Milman and Warren
[33] (they are designated in their Table 3 as CGAa). For the
hexagonal TiB2 the stiffness matrix from their Table 3 [33]
is given by
Sh k l ¼ Lsnh k l=zðJ cmꢀ2
Þ
(12)
since the sublimation energy is proportional to the broken
bonds, nh k l per unit area and the coordination number, z.
In TiB2 z ¼ 12 and nh k l has been calculated using images
based on the hard sphere model [32] as follows: The area of
the (0 0 0 1) plane is 0.795 nm, n0001 ¼ 6, thus the number of
broken bonds/cm2 is 7.55 ꢂ 1015. Therefore, by Eq. (12)
2
3
656 66
98
0
0
0
0
0
0
6
6
6
6
6
6
7
7
7
7
7
7
66 656 98
S0 0 0 1 ¼ 1.9 ꢂ 10ꢀ3(J atomꢀ2). The area of the ð1 0 1 1Þ
98
0
98 461
0
0
0
¯
plane is 1.261 nm2. This face is more complex since it
contains not only one Ti atom but also two B atoms almost
at the same level which are puckered slightly below and
above the Ti plane only by 0.034 nm. Thus, it can be
c :¼
.
(16)
0
0
0
0
0
0
259
0
0
0
6
6
4
7
7
5
0
259
0
0
0
0
295

ARTICLE IN PRESS
J. Pelleg et al. / Physica B 381 (2006) 118–127
126
Following Nye [34] the compliance is given as c ¼ sꢀ1
,
energy which does not vary with thickness and the thickness-
dependent strain energy. For all thicknesses the strain energy
thus in matrix notation it can be written as
2
3
0:00158
ꢀ1:12525 ꢂ 10ꢀ4 ꢀ3:12466 ꢂ 10ꢀ4
0
0
0
6
6
7
7
ꢀ4
ꢀ1:12525 ꢂ 10
0:00158
ꢀ3:12466 ꢂ 10ꢀ4
0
0
0
6
6
6
7
7
7
ꢀ3:12466 ꢂ 10ꢀ4 ꢀ3:12466 ꢂ 10ꢀ4
0:0023
0
0
0
s ¼
.
(17)
6
6
7
7
0
0
0
0
0
0
0
0
0
0:00386
0
0:00386
0
0
0
6
6
4
7
7
5
0
0
0:00339
¯
¯
The angle between the planes (0 0 0 1) and ð1 0 1 1Þ is
is smaller on the ð1 0 1 1Þ plane and its contribution to W
increases with thickness. At some thickness value the strain
energy can tip the overall energy value making it smaller on
50.911. After rotation the coordinate to the system where z-
axis is perpendicular to ð1 0 1 1Þ plane the new compliances
¯
¯
matrix is
the ð1 0 1 1Þ plane. As long as this value is small compared to
2
3
0:00171 ꢀ0:00019 ꢀ0:00015
ꢀ0:00019 0:00158 ꢀ0:00023
ꢀ0:00015 ꢀ0:00023 0:00186
0
0:00014
ꢀ0:0001
0:00021
0
0
6
7
0
0
6
7
6
6
6
6
7
7
7
7
0
0
0
s ¼
.
(18)
0
0
0
0:00067
0
0:00036
0
6
7
6
4
7
5
0:00014 ꢀ0:00009 0:00021
0:00012
0
0
0
0
0:00036
0:00051
Thus, the calculated elastic moduli are E0 0 0 1 ¼ ð1=0:0023Þ
the surface energy, the latter dominates the overall free energy
and an (0001) preferred orientation is sustained. At a certain
thickness value, however, the strain energy of whatever origin
will be the dominant factor dictating the outcome of the film
orientation. The approximation given above explains our and
some reported results [28,29] as long as other cardinal
parameters of film deposition do not interfere with the
outcome of the orientation along the proposed model.
and E1 0 1 1 ¼ ð1=0:00186Þor 435 and 538 GPa, respectively.
¯
The strain energy for the two-dimensional case with equal
principal stresses can be expressed as
Uh k l ¼ e2h k lEh k lð1 ꢀ nÞ.
(19)
It provides for U0001 ¼ 4:455 ꢂ 10ꢀ3 GPa cmꢀ3 and for
U1 0 1 1 ¼ 1:462 ꢂ 10ꢀ3 GPa cmꢀ3; respectively. The value of
¯
Uh k l per unit area depends on film thickness. Table 1
summarizes the results of all energy terms of films of various
thicknesses and among them that of our experiments. (0001)
orientation is expected in the thickness range up to about
250–1000 nm. The thickness of the film is an important factor
in determining the film orientation as seen. It can be thus
conjectured that the evolution of a certain preferred
orientation is a result of competition between the surface
5. Conclusion
As deposited TiB2 film is amorphous and in order to
induce structural changes high-temperature annealing is
essential. Application of bias during deposition without
substrate heating changes the composition of the film. A
model was suggested to explain the changes invoked by the
Table 1
Surface, strain and overall energy terms for several TiB2 film thicknesses
Thickness (nm)
Orientation
0 0 0 1
Remarks
¯
1 0 1 1
S (J cmꢀ2
)
U (J cmꢀ2
)
W (J cmꢀ2
)
S (J cmꢀ2
)
U (J cmꢀ2
)
W (J cmꢀ2
)
100
250
1.9 ꢂ 10ꢀ3
1.9 ꢂ 10ꢀ3
1.9 ꢂ 10ꢀ3
1.9 ꢂ 10ꢀ3
1.9 ꢂ 10ꢀ3
1.9 ꢂ 10ꢀ3
4.46 ꢂ 10ꢀ5
1.11 ꢂ 10ꢀ4
2.22 ꢂ 10ꢀ4
4.45 ꢂ 10ꢀ4
6.68 ꢂ 10ꢀ4
1.78 ꢂ 10ꢀ3
1.94 ꢂ 10ꢀ3
2.01 ꢂ 10ꢀ3
2.12 ꢂ 10ꢀ3
2.35 ꢂ 10ꢀ3
2.57 ꢂ 10ꢀ3
3.68 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
2.19 ꢂ 10ꢀ3
1.46 ꢂ 10ꢀ5
3.65 ꢂ 10ꢀ5
7.31 ꢂ 10ꢀ5
1.45 ꢂ 10ꢀ4
2.19 ꢂ 10ꢀ4
5.85 ꢂ 10ꢀ4
2.20 ꢂ 10ꢀ3
2.23 ꢂ 10ꢀ3
2.25 ꢂ 10ꢀ3
2.34 ꢂ 10ꢀ3
2.41 ꢂ 10ꢀ3
2.77 ꢂ 10ꢀ3
Our experimental results
500
1000
1500
4000
In Ref. [30] the thickness is 1500 nm
In Ref. [29] the thickness is 4000 nm

ARTICLE IN PRESS
J. Pelleg et al. / Physica B 381 (2006) 118–127
127
application of bias on cold substrates. In situ annealing at
moderate deposition temperature is sufficient to induce
partial crystallization in the film. Low-temperature in situ
annealing at 673 K combined with bias application induces
crystallization by creating nucleation sites. Post-deposition
heat treatment of in situ annealed biased specimens induces
complete crystallization without changing the observed
(0 0 0 1) orientation. A model has been suggested to explain
the observed preferred orientation. The preferred orienta-
tion of the film is determined by the lowest overall free
energy resulting from the competition between the surface
energy and the strain energy on different lattice planes.
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Acknowledgement
The authors acknowledge the valuable help of Ada
Pelleg.
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