JOURNAL OF APPLIED PHYSICS
VOLUME 90, NUMBER 6
15 SEPTEMBER 2001
Epitaxial NaCl structure ␦ -TaNx „001…: Electronic transport properties,
elastic modulus, and hardness versus NÕTa ratio
C.-S. Shin, D. Gall, Y.-W. Kim, P. Desjardins, I. Petrov, and J. E. Greene
Materials Science Department and Frederick Seitz Materials Research Laboratory, University of Illinois,
104 South Goodwin Avenue, Urbana, Illinois 61801
M. Odén
Department of Mechanical Engineering, Linköping University, S-581 83 Linköping, Sweden
L. Hultman
Department of Physics, Linköping University, S-581 83 Linköping, Sweden
共Received 9 March 2001; accepted for publication 13 June 2001兲
While metastable B1-NaCl-structure ␦ -TaNx is presently used in a variety of hard coating,
wear-resistant, and diffusion barrier applications, it is a complex material exhibiting a wide
single-phase field, x⯝0.94– 1.37, and little is known about its fundamental properties. Here, we
report physical properties of epitaxial ␦ -TaNx layers grown as a function of x on MgO共001兲 by
ultrahigh vacuum reactive magnetron sputter deposition. The room-temperature resistivity ( ␳
⫽225 ␮ ⍀ cm), hardness (H⫽30.9 GPa), and elastic modulus (E⫽455 GPa) of ␦ -TaNx (001) are
independent of x over the range 0.94 –1.22. However, changes in the electronic structure associated
with increasing x⬎1.22 lead to an increase in ␳ with a decrease in H and E. All ␦ -TaNx (001) layers
exhibit negative temperature coefficients of resistivity between 20 and 400 K due to weak carrier
localization. ␦ -TaNx is superconducting with the highest critical temperature, 8.45 K, obtained for
layers with the lowest N/Ta ratio, x⫽0.94. Based upon the above results, combined with the fact that
the relaxed lattice constant a 0 shows only a very weak dependence on x, we propose that the wide
phase field in ␦ -TaNx is due primarily to antisite substitutions of Ta on N 共and N on Ta兲 sites, rather
than to cation and anion vacancies. To first order, antisite substitutions in TaNx are isoelectronic and
hence have little effect on charge carrier density. At sufficiently high N/Ta ratios, however, simple
electron-counting arguments are no longer valid since large deviations from stoichiometry alter the
character of the band structure itself. © 2001 American Institute of Physics.
关DOI: 10.1063/1.1391214兴
I. INTRODUCTION
Polycrystalline TaNx is presently used in applications including hard and wear-resistant coatings on tools, thin-film
resistors, diffusion barriers in integrated circuits, and mask
layers for x-ray lithography. Unlike the more common
IVB–VA hard-coating material TiN, cubic TaN, a VB–VA
compound, is metastable. While the Ti–N equilibrium phase
diagram is relatively simple with the only compounds being
tetragonal Ti2N and NaCl-structure TiN, the Ta–N system is
extremely rich.1,2 In addition to the equilibrium phases of
body-centered-cubic 共bcc兲 ␣-Ta, solid-solution ␣-Ta共N兲,
hexagonal-close-packed 共hcp兲 ␥ -Ta2N, and hexagonal
⑀-TaN, a variety of metastable phases have been documented. The latter include tetragonal ␤-Ta, bcc ␤-Ta共N兲,
hexagonal Ta2N, the hexagonal WC structure ␪-TaN,
B1-NaCl-structure ␦-TaN, hexagonal Ta5N6, tetragonal
Ta4N5, and tetragonal Ta3N5. 1,2
Cubic transition-metal 共TM兲 nitrides have wide single
phase fields with that of TiNx , for example, extending from
x⫽0.6 to ⯝1.2.3 The cubic phase field of the VB–VA compound ␦ -NbNx is reported to range from x⫽0.86 to 1.06.4
We have previously shown that single-crystal B1-NaClstructure ␦ -TaNx layers can be grown on MgO共001兲 by ultrahigh vacuum 共UHV兲 reactive magnetron sputter deposi0021-8979/2001/90(6)/2879/7/$18.00
2879
tion at T s ⫽600 °C in mixed N2 /Ar discharges.5 Based upon
results for the low-temperature (T s /T m ⭐0.35) 共Ref. 6兲 epitaxial growth of TiN,7 Ti0.5Al0.5N, 8 and ScN,9 we used high
flux 共ion-to-Ta flux ratio⫽11兲, low-energy 共8.5 eV兲, ion irradiation during film growth. Epitaxial ␦ -TaNx layers exhibit
a cube-on-cube orientational relationship with MgO共001兲.
In this article, we present the results of an investigation
of the fundamental physical properties of ␦ -TaNx (001) as a
function of the N/Ta ratio x. All epitaxial ␦ -TaNx layers were
grown on MgO共001兲 following the procedure described in
Ref. 5. The layers are nearly fully relaxed and of high crystalline quality with relatively large x-ray coherence lengths
and low mosaicity. Analyses of high-resolution reciprocal
lattice maps show that the relaxed bulk lattice parameter of
␦ -TaNx decreases only slightly from 0.4355 nm with x
⫽0.94 to 0.4324 nm with x⫽1.37. However, the roomtemperature resistivity ( ␳ ⫽225⫾11 ␮ ⍀ cm), hardness (H
⫽30.9⫾1.9 GPa), and elastic modulus (E⫽455⫾27 GPa)
remain essentially constant with N/Ta over the range x
⫽0.94– 1.22. We attribute this to the compound having an
electronic structure which, for this composition range, is not
strongly perturbed by the formation of isoelectronic substitutional antisite defects. Higher N/Ta ratios (x⬎1.22) result
in significant changes in the electronic structure leading to an
© 2001 American Institute of Physics
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Shin et al.
J. Appl. Phys., Vol. 90, No. 6, 15 September 2001
increase in ␳ and a decrease in H and E. All ␦ -TaNx (001)
layers exhibit negative temperature coefficients of resistivity
between 20 and 400 K and are superconducting with the
highest critical temperature, 8.45 K, obtained for layers with
x⫽0.94.
II. EXPERIMENTAL PROCEDURE
␦ -TaNx (001) layers, 0.5 ␮m thick, were grown in a
load-locked multichamber UHV stainless-steel dc magnetron
sputter deposition system described in detail in Ref. 10. The
pressure in the sample introduction chamber was reduced to
less than 5⫻10⫺8 Torr (7⫻10⫺6 Pa), using a 50 l s⫺1 turbomolecular pump 共TMP兲, prior to initiating substrate exchange into the deposition chamber which has a base pressure of 5⫻10⫺10 Torr (7⫻10⫺8 Pa), achieved using a 500
l s⫺1 TMP. A water-cooled 6.35 cm diam Ta target with a
purity of 99.97% was mounted 10 cm from the substrate
holder. Sputter deposition was carried out at a constant
power of 150 W and a total pressure of 20 mTorr 共2.67 Pa兲 in
mixed atmospheres consisting of Ar 共99.9999% pure兲 and N2
共99.999%兲 mixtures. Film composition is determined by controlling the N2 fraction f N2. The gases are introduced through
high precision solenoid valves while the pressure is measured by a capacitance manometer and maintained constant
with an automatic mass flow controller.
A pair of external Helmholtz coils with Fe pole pieces
were utilized to create a uniform axial magnetic field B ext
⫽180 G in the region between the target and the substrate.
B ext has a strong effect on the ion flux incident at the
substrate, with only minor effects on the target atom flux,8
and provides, as determined by electrostatic probe
measurements,8 a high ion-to-metal flux J i /J Ta . The present
film growth experiments were carried out using J i /J Ta⫽11
with an incident ion energy of 8.5 eV.
The substrates were polished 10⫻10⫻0.5 mm3
MgO共001兲 wafers cleaned with successive rinses in ultrasonic baths of trichloroethane, acetone, ethanol, and deionized water and blown dry with dry N2. The wafers were
then mounted on resistively heated Ta platens using Mo clips
and inserted into the sample introduction chamber for transport to the growth chamber where they were thermally degassed at 800 °C for 1 h, a procedure shown to result in sharp
MgO共001兲1⫻1 reflection high-energy electron diffraction
patterns.11 Just prior to initiating deposition, the target was
sputter etched for 5 min with a shutter shielding the substrate. All ␦ -TaNx (001) layers were grown at T s ⫽600 °C,
including the contribution due to plasma heating. T s was
measured with a pyrometer calibrated by a thermocouple
bonded to a TaN-coated MgO substrate.
TaNx (001) layer compositions were determined by Rutherford backscattering spectroscopy 共RBS兲. The probe beam
consisted of 2 MeV He⫹ ions incident at an angle of 22.5°
relative to the sample surface normal with the detector set at
a 150° scattering angle. Backscattered spectra were analyzed
using the RUMP simulation program.12 The uncertainty in reported N/Ta ratios is less than ⫾0.03.
Relaxed ␦ -TaNx (001) lattice constants and residual
strains were obtained from analyses of x-ray diffraction
共XRD兲 ␻ –2␪ scans in the powder diffraction mode and highresolution reciprocal lattice maps 共HRRLMs兲 around 113
asymmetric reflections. The powder diffractometer was operated with Cu K ␣ radiation and had an incident slit divergence of 0.05° resulting in a resolution of 0.01° 2␪. HRRLMs were obtained from a series of ␻ –2␪ scans acquired at
different ␻ offsets13 in a high-resolution diffractometer with
Ge共220兲 four-crystal and two-crystal monochromators in the
primary and secondary x-ray axes. With Cu K ␣ 1 radiation
(␭⫽0.154 0597 nm), this arrangement provides an angular
beam divergence of ⯝12 arcsec with a wavelength spread of
⌬␭/␭⯝7⫻10⫺5 .
Four-point probe measurements were used to determine
room-temperature resistivities ␳ 300 K . Temperature dependent resistivities between 2 and 400 K, as well as the critical
temperature for the superconducting transition, were obtained using a Quantum Design physical property measurement system. For this purpose, Al contacts were evaporated
through a mask with van der Pauw geometry.
The hardness and elastic modulus of ␦ -TaNx (001) layers
as a function of x were determined from nanoindentation
responses measured using a Nano Indentor II instrument. Epitaxial TiN共001兲 layers, with known H and E values,14 grown
on MgO共001兲 to the same thickness as the ␦ -TaNx (001)
samples, served as references for calibration purposes. The
maximum load was varied from 0.2 to 20 mN with a minimum of 10 indent sequences used for each load. The triangular Berkovich diamond tip was calibrated following the
procedure described in Ref. 15.
III. RESULTS AND DISCUSSION
All layers grown on MgO共001兲 at T s ⫽600 °C with a
N2 /Ar fraction f N2 ranging from 0.100 to 0.275 are singlephase epitaxial B1-NaCl-structure ␦ -TaNx as judged by a
combination of XRD ␻ –2␪, azimuthal ␾, and HRRLM
analyses. At lower f N2 values, the films are polycrystalline
and consist of both hexagonal Ta2N and ␦ -TaNx , while a
two-phase mixture of ␦ -TaNx and body-centered tetragonal
TaNx is obtained at higher f N2.
RBS results show that the N/Ta ratio in single-phase
␦ -TaNx films varies continuously from x⫽0.94 with
f N2⫽0.100 to x⫽1.37 with f N2⫽0.275. XRD ␻ –2␪ scans
exhibit only one set of TaNx peaks over the 2␪ range between
20° and 80°. A typical pattern, obtained in this case from a
layer with composition x⫽1.17, is shown in Fig. 1共a兲. The
peaks, centered at 41.59° and 41.68°, are indexed as B1NaCl structure ␦ -TaNx 002 K ␣ 1 and K ␣ 2 . The 42.92° and
43.03° peaks are MgO 002 K ␣ 1 and K ␣ 2 . XRD scans about
the azimuthal angle ␾, obtained in the parallel-beam mode
with ␻ and 2␪ angles optimized for the 220 peaks of MgO
and ␦ -TaNx at a tilt angle of 45° with respect to the surface
normal, exhibit four 90°-rotated 220 peaks at the same ␾
angles for both MgO and ␦ -TaNx 关Fig. 1共b兲兴. A combination
of these results shows that the ␦ -TaN1.17共001兲 layer is epitaxial with (001) TaN储 (001) MgO and 关 100兴 TaN储关 100兴 MgO .
Residual strain and relaxed lattice constants in the epitaxial layers were determined from analyses of HRRLMs.
Figure 2 is a typical HRRLM about the asymmetric 113 re-
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Shin et al.
J. Appl. Phys., Vol. 90, No. 6, 15 September 2001
k⬜ ⫽2r E sin共 ␪ 兲 sin共 ␻ ⫺ ␪ 兲 ,
2881
共2兲
where r E is the Ewald sphere radius given by r E ⫽1/␭. For a
113 reflection from an 001-oriented NaCl structure, the inplane a 储 and out-of-plane a⬜ lattice constants are given by
a 储 ⫽&/k 储 and a⬜ ⫽3/k⬜ . Relaxed bulk ␦ -TaNx lattice constants a 0 are then obtained as a function of x from a 储 and a⬜
values through the relationship
冉
a 0 ⫽a⬜ 1⫺
冊
2 ␯ 共 a⬜ ⫺a 储 兲
,
a⬜ 共 1⫹ ␯ 兲
共3兲
where ␯ is the film Poisson ratio. The degree of in-plane
layer relaxation R is defined as
R⫽
FIG. 1. 共a兲 ␻ –2␪ and 共b兲 220 ␾ XRD scans from an epitaxial
␦ -TaN1.17共001兲 layer grown on MgO共001兲.
flection from the ␦ -TaN1.17共001兲 layer corresponding to Fig.
1. Diffracted intensity distributions are plotted as isointensity
contours as a function of the reciprocal lattice vectors k 储
parallel and k⬜ perpendicular to the surface. k 储 and k⬜ are
related to peak positions in ␻ –2␪ space through the
relationships16
k 储 ⫽2r E sin共 ␪ 兲 cos共 ␻ ⫺ ␪ 兲 ,
共1兲
and
FIG. 2. HRRLM around the 113 reflection of an epitaxial ␦ -TaN1.17共001兲
layer grown on MgO共001兲.
a 储 ⫺a s
,
a 0 ⫺a s
共4兲
in which a s ⫽0.421 12 nm is the MgO substrate lattice
constant.17
The fact that the substrate and layer peaks in Fig. 2 are
misaligned along k 储 indicates the presence of in-plane strain
relaxation. All layers were found to be nearly fully relaxed
with only a small amount of residual compressive strain. R
ranges from 88% to 97%. Although the N-rich samples tend
to have slightly smaller relaxations, there is no clear trend in
R as a function of x.
The vertical separation between the film and substrate
diffracted intensity distributions in Fig. 2 corresponds to a
lattice constant mismatch in the growth direction of 3.14%
yielding an out-of-plane ␦ -TaN1.17共001兲 lattice constant a⬜
⫽0.4344 nm. The in-plane lattice constant a 储 is 0.4327 nm.
Substituting these values together with a Poisson ratio of
0.25 共Ref. 18兲 into Eq. 共3兲, we calculate a relaxed lattice
constant a 0 ⫽0.4337 nm for ␦ -TaN1.17.
Figure 3共a兲 shows that a 0 (x) for ␦ -TaNx (001) decreases
linearly from 0.4355 nm with x⫽0.94 to 0.4324 nm with x
⫽1.37 corresponding to a film/substrate lattice constant mismatch, (a 0 ⫺a s )/a s , ranging from 3.42% to 2.68%. Previous
reports for polycrystalline ␦ -TaNx layers give a 0 between
0.433 and 0.442 nm,2,19,20 however the film stoichiometry
and stress level were not specified. From the results in Fig.
3共a兲, it is clear that the rate of change in the normalized
␦ -TaNx (001) lattice constant as a function of x, ␨
⫽d 关 a 0 (x)/a 0,TaN兴 )/dx, where a 0,TaN is the relaxed lattice
constant of stoichiometric ␦-TaN, is quite small: ␨
⫽⫺0.015. Published a 0 versus x data from NbNx (1⭐x
⭐1.07), 4 another VB–VA TM nitride compound, yields the
same value for ␨. A linear decrease in a 0 vs x has also been
reported for the IVB–VA compounds TiNx (1⭐x⭐1.16)
共Ref. 21兲 and HfNx (0.8⭐x⭐1.18), 4 with ␨ values of ⫺0.035
and ⫺0.065, respectively.
Toth21 has attributed overstoichiometry in TM nitrides to
cation vacancies. It is unlikely, however, that the observed
decrease in a 0 with increasing x in the VB–VA nitrides, and
perhaps even in the IVB–VA TM nitrides, can be explained
by cation vacancies alone. Calculated ␨ values, obtained using ab initio density functional theory employing the generalized gradient approximation, periodic boundary conditions,
and 16-atom supercells, yield ␨ ⫽⫺0.084 for ␦ -TaNx compounds driven overstoichiometric by the addition of ran-
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Shin et al.
J. Appl. Phys., Vol. 90, No. 6, 15 September 2001
FIG. 3. 共a兲 Relaxed lattice constant a 0 and 共b兲 in-plane ␰ 储 and perpendicular
␰⬜ x-ray coherence lengths for epitaxial ␦ -TaNx (001) layers grown on
MgO共001兲 as a function of the N/Ta ratio x.
domly dispersed cation vacancies. This is more than a factor
of 5 higher than what we measure. In addition, considering
the large number of reported phases in the Ta–N system,1,2 it
seems unlikely that such vacancy-rich ␦ -TaNx compounds
would be stable in the NaCl structure with compositions up
to x⫽1.37. The cation vacancy concentration in ␦ -TaN1.37
corresponds to more than one Ta vacancy per three Ta atoms.
In the NaCl structure, this requires vacancies to have nearestneighbor sites which are also vacant, a very high energy
configuration.
We therefore propose that the deviation from stoichiometry in overstoichiometric ␦ -TaNx (001) is primarily due to N
antisite substitutions on Ta sublattice sites. Conversely, Ta
antisite substitution of N sublattice sites leads to understoichiometric ␦ -TaNx (001) layers. The antisite-controlled film
composition is also consistent with the results of our electronic transport measurements, discussed below, indicating
that even stoichiometric ␦-TaN contains antisite defects. For
this case, however, the antisite populations on cation and
anion sublattices compensate each other. The calculated
␦ -TaNx ␨ value obtained from ab initio density functional
calculations in which we assume that the overstoichiometry
is entirely due to N antisite substitution on Ta lattice sites is
within a factor of 2 of the measured value and the remaining
difference can be accounted for by small concentrations of
Ta on N antisite substitutions.
In-plane and perpendicular x-ray coherence lengths ␰ 储
and ␰⬜ were obtained from the widths of the 002 diffracted
intensity distributions perpendicular ⌬g⬜ and parallel ⌬g 储 ,
respectively, to the diffraction vector ḡ using the
relationships11
␰ 储 ⫽2 ␲ / 兩 ⌬g⬜ 兩 ⫽␭/ 共 2⌫ ␻ sin ␪ 兲
共5兲
FIG. 4. 共a兲 Room-temperature resistivity ␳ 300 K and 共b兲 temperaturedependent resistivity ␳ of epitaxial ␦ -TaNx (001) layers grown on MgO共001兲
as a function of the N/Ta ratio x. The TaN0.84 layer is a two-phase polycrystalline reference sample.
and
␰⬜ ⫽2 ␲ / 兩 ⌬g 储 兩 ⫽␭/ 共 ⌫ 2 ␪ cos ␪ 兲 .
共6兲
⌫ ␻ and ⌫ 2 ␪ are the full widths at half maximum intensities
of the 002 Bragg peak in the ␻ and 2␪ directions. The results
are plotted in Fig. 3共b兲. The highest crystalline quality, corresponding to the largest ␰ 储 and ␰⬜ values, was obtained for
␦ -TaNx (001) layers with N/Ta ratios between 1.13 and 1.22.
The ␰ 储 and ␰⬜ for these layers are ⯝21 and 112 nm, respectively. Measured x-ray coherence lengths decrease with both
higher and lower N/Ta values to ␰ 储 ⫽11 nm and ␰⬜ ⫽34 nm
for TaN0.94共001兲 and ␰ 储 ⫽14 nm and ␰⬜ ⫽73 nm for
TaN1.37共001兲. The only other reported results for epitaxial
transition-metal nitrides are for the IIIB–VA compound
ScN共001兲 in which ␰ 储 ⫽15 nm and ␰⬜ ⫽57 nm. 9 Our
␦ -TaNx (001) layers with x⫽1.13– 1.22 exhibit higher crystalline quality with lower mosaicity.
Figure 4共a兲 is a plot of the room-temperature resistivity
␳ 300 K of ␦ -TaNx (001) as a function of x. For comparison,
we also show ␳ 300 K for a polycrystalline TaN0.84 film which
consists of a two-phase mixture of hexagonal Ta2N and
␦ -TaNx . The resistivity of epitaxial ␦ -TaNx (001) layers is
essentially constant at 225 ␮⍀ cm over a wide range of composition, x⫽0.94– 1.22. However, as x exceeds 1.22, ␳ 300 K
increases rapidly and approximately linearly to ␳
⫽310 ␮ ⍀ cm with x⫽1.37. ␳ 300 K for the two-phase polycrystalline TaN0.84 reference sample is 115 ␮⍀ cm, almost a
factor of 2 lower than that of epitaxial ␦ -TaNx (001) layers.
Thus, the resistivity of hexagonal Ta2N is significantly lower
than that of ␦ -TaNx .
The fact that ␳ 300 K does not vary with x indicates that
the size of the ␦ -TaNx Fermi surface remains constant over
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J. Appl. Phys., Vol. 90, No. 6, 15 September 2001
the composition range 0.94⭐x⭐1.22. This, in turn, implies
that the electron density in the Ta 5d conduction bands is
constant which, consistent with the above a 0 (x) discussion,
cannot be explained by ascribing the overstoichiometry to
vacancies alone. In stoichiometric ␦-TaN, each Ta atom provides three electrons to the N 2p bands and two electrons to
the 5d conduction bands, resulting in a charge carrier density
of n⫽9.7⫻1022 cm⫺3 in the 5d bands. Each Ta vacancy in
␦ -TaNx results in a net loss of five conduction band electrons, corresponding to a dramatic reduction in n for highly
overstoichiometric samples. TaN1.22, for example, would
have a carrier density of n⫽5.3⫻1022 cm⫺3, approximately
half that of stoichiometric ␦-TaN. This large decrease in n
would easily be detectable in ␳ 300 K(x) measurements, but is
not observed.
In contrast to the large change in carrier density associated with cation vacancies in overstoichiometric ␦ -TaNx , the
antisite substitution of N on a Ta site 共and, conversely, Ta on
a N site兲 is isoelectric. Thus, antisite defects would, to first
order, not affect the carrier density and, hence, result in
␳ 300 K remaining constant over a relatively wide composition
range as we observe.
As N/Ta becomes larger than 1.22, however, ␳ 300 K increases rapidly as shown in Fig. 4共a兲. This, we believe, is not
merely a reflection of differences in crystalline quality, since
the electron mean free path obtained from our measured resistivities ␳ 300 K using an estimated Fermi velocity of 2
⫻108 cm s⫺1 共Ref. 22兲 is ⯝2 nm, an order of magnitude less
than measured ␦ -TaNx x-ray coherence lengths. Rather, the
higher resistivity of highly overstoichiometric layers corresponds to a smaller Fermi surface which is attributed to a
change in the electronic structure of ␦ -TaNx with x⬎1.22.
Thus, the simple electron-counting argument used above, in
which the ␦ -TaNx band structure is assumed to be independent of x, is no longer valid. This is not surprising since the
density of d-band conduction electrons vanishes as x approaches 1.67, corresponding to Ta3N5. The reported resistivity of tetragonal Ta3N5 is 6 ⍀ cm,23 four orders of magnitude larger than that of ␦ -TaNx .
Typical resistivity ␳ versus temperature T curves between 2 and 400 K are shown in Fig. 4共b兲 for ␦ -TaNx (001)
layers with x⫽1.00, 1.22, and 1.37 and for the polycrystalline two-phase (Ta2N⫹ ␦ -TaN) TaN0.84 reference sample.
The temperature coefficient of resistivity 共TCR兲 of TaN0.84 is
slightly positive, due to phonon scattering, between 10 and
400 K where ␳ increases from 115.0 ␮⍀ cm at 10 K to 115.8
␮⍀ cm at 400 K. However, the TCR is negative for all epitaxial ␦ -TaNx (001) layers. We attribute the negative TCR to
a weak localization of conduction electrons as a result of the
perturbation in the periodic crystal potential associated with
randomly distributed point defects.24,25 This is true even for
stoichiometric ␦-TaN (N/Ta⫽1), where the antisite defects
on cation and anion sublattice sites compensate each other.
The T⫽20 K resistivity ␳ 20 K of ␦ -TaNx (001) increases with
N/Ta, from 279 ␮⍀ cm with x⫽1 to 345 ␮⍀ cm with x
⫽1.22 to 497 ␮⍀ cm with x⫽1.37. The increase in ␳ 20 K(x)
is due to the increasingly higher point defect density, resulting in a smaller elastic scattering length, and thus stronger
localization. At T⬍20 K, the ␳ (T) curves exhibit slightly
Shin et al.
2883
FIG. 5. Superconducting transition temperature T c of epitaxial ␦ -TaNx (001)
layers grown on MgO共001兲 as a function of the N/Ta ratio x. The TaN0.84
layer is a two-phase (Ta2N ␦-TaNx ) polycrystalline reference sample.
positive TCR values due to the effects of virtual Cooper pairs
and/or superconducting fluctuations.26 –28
␦ -TaNx (001) superconducting transition temperatures
T c are plotted in Fig. 5 as a function of x. The highest critical
temperature, T c ⫽8.45 K, was obtained from the slightly understoichiometric TaN0.94共001兲 layer. T c continuously decreases with increasing N/Ta ratio to a value of 4.6 K with
x⫽1.37. The two-phase polycrystalline TaN0.84 reference
sample becomes superconducting at an even lower temperature, T c ⫽3.0 K. We interpret the decrease in T c for
␦ -TaNx (001) as a function of x as resulting from a decrease
in the attractive electron–electron interaction strength since
the increased density of point defects leads to a corresponding localization of vibrational modes which in turn reduces
the phonon-mediated long-range effective electron–electron
coupling. The large difference in mass involved in the N 共14
amu兲 on Ta 共181 amu兲 antisite substitution and the lower
lattice constants associated with overstoichiometric ␦ -TaNx
may also contribute to the observed trend. A similar composition dependence, with the highest T c obtained for layers
with the largest lattice constant near stoichiometry, has been
reported for other TM nitrides and carbides including TiNx ,
HfNx , VNx , NbNx , NbCx , and TaCx . 29
Figure 6共a兲 is a typical load-displacement curve, with 3
mN maximum load, obtained from an epitaxial
␦ -TaN1.22共001兲 layer. The initial loading segment contains an
elastic-plastic displacement. In order to minimize the effects
of time-dependent plasticity on the measured hardness, the
hold time at maximum load was 10 s for all loads. Thermal
drift was calculated from a hold segment of 100 s at 95%
unloading and used to automatically correct the loaddisplacement data through the instrument software. The measured hardness H and elastic modulus E values for
␦ -TaNx (001) films with x⫽1.13, 1.22, and 1.35 are shown
in Fig. 6共b兲. Measured hardness values H were found to be
constant as a function of load up to the maximum displacement, ⯝80 nm. At higher loads, H decreases continuously.
This behavior is expected when the plastic zone associated
with the indentation measurement penetrates through a significant fraction of the film thickness resulting in an apparent
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2884
Shin et al.
J. Appl. Phys., Vol. 90, No. 6, 15 September 2001
FIG. 6. 共a兲 Typical load-displacement curves, using maximum loads of 2
and 3 mN, obtained during nanoindentation measurements of a 0.5 ␮m thick
epitaxial ␦ -TaN1.22共001兲 layer grown on MgO共001兲. Hold segments are labeled and the arrows indicate the load/unload directions. 共b兲 Hardness H and
elastic modulus E of ␦ -TaNx (001) as a function of the N/Ta ratio x.
decrease in H for hard films on softer substrates, the case
here, where H for MgO共001兲 is 9.0⫾0.3 GPa. 14
␦ -TaNx (001) layers with x⫽1.13 and 1.22 have essentially the same hardness (H⫽30.9⫾1.9 GPa) and elastic
modulus (E⫽455⫾27 GPa). However, both H and E decrease significantly to 27.5⫾1.4 and 404⫾19 GPa, respectively, for ␦ -TaN1.35共001兲. While it is tempting to explain the
decrease in hardness for ␦ -TaNx (001) layers with large x as
being due to reduced crystalline quality 关Fig. 3共b兲兴, the parallel decrease in E suggests that the changes are primarily
due to electronic effects associated with the large deviation
from stoichiometry. This is consistent with the ␳ 300 K(x) results which show that the electronic structure of
␦ -TaNx (001) is nearly independent of the composition over
the range x⫽0.94– 1.22, but changes considerably above x
⫽1.22. The hardness of ␦ -TaNx (001)(1.13⭐x⭐1.22) is
54% higher than that of TiN共001兲.
hence the charge carrier density, is independent of composition. We attribute this to the compositional change being primarily due to the isoelectronic substitution of N on Ta sites
共Ta on N sites兲 for overstoichiometric 共understoichiometric兲
layers, respectively. The substitutional antisite defects are
also responsible for the rather small change in relaxed lattice
constant as a function of x, which is far too small to be
explained by cation and anion vacancies alone. In contrast,
the resistivity of ␦ -TaNx (001) layers with higher N/Ta ratios
(x⬎1.22) increases approximately linearly to ␳ 300 K
⫽310 ␮ ⍀ cm with x⫽1.37, indicating a change in the character of the electronic structure due to the high antisite density which leads, in turn, to antisite–antisite interactions and,
perhaps, to the initiation of ordering.
All ␦ -TaNx (001) layers exhibit negative temperature coefficients of resistivity at temperatures between 20 and 400
K. We ascribe the negative TCR to a weak localization of the
conduction electrons caused by the perturbation in the periodic crystal potential associated with randomly distributed
point defects. The temperature dependence of ␳ becomes
more pronounced at larger x, due to the higher density of
antisite defects resulting in a stronger perturbation of the
crystal potential. ␦ -TaNx (001) is superconducting throughout the entire phase field composition range with the highest
critical temperature, 8.45 K, obtained for layers with x
⫽0.94.
The hardnesses and elastic moduli of ␦ -TaNx (001) layers with x⭐1.22 are H⫽30.9 GPa and E⫽455 GPa. Both H
and E decrease significantly at higher x to 27.5 and 404 GPa,
respectively, for ␦ -TaN1.35. This is also consistent with the
presence of composition-induced changes in the electronic
structure for x⬎1.22.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial support
of the Department of Energy, Division of Materials Science,
under Contract No. DEFG02-ER9645439 during the course
of this research. The authors also appreciate the use of the
facilities of the Center for Microanalysis of Materials, which
is partially supported by DOE, at the University of Illinois.
Two of the authors 共C.S.S. And P.D.兲 were partially supported by Hynix Semiconductor Inc. 共Korea兲 and the Natural
Sciences and Engineering Research Council 共Canada兲, respectively.
1
IV. CONCLUSIONS
Single-crystal metastable B1-NaCl-structure ␦ -TaNx layers with x ranging from 0.94 to 1.37 were grown on
MgO共001兲 at T s ⫽600 °C by UHV magnetically unbalanced
reactive magnetron sputter deposition. All layers exhibit an
epitaxial cube-on-cube relationship with the substrate:
(001) TaN储 (001) MgO and 关 100兴 TaN储关 100兴 MgO .
The relaxed lattice constant of ␦ -TaNx (001) decreases
linearly from 0.4355 nm with x⫽0.94 to 0.4324 nm with x
⫽1.37 while the room-temperature resistivity ␳ 300 K remains
constant at 225 ␮⍀ cm for compounds with 0.94⭐x⭐1.22.
The constant ␳ 300 K indicates that the Fermi surface, and
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