cm) and the layers
were ~1µm thick. The x-ray FWHM was ~600 arc.sec on these samples.
The group III - Nitrides AlN, GaN and InN are attractive materials for optoelectronic devices and especially GaN-based laser and light-emitting diodes are already commercialised on a large scale. However, presently available devices generally are produced by doping during growth [1] and not by ion implantation like most modern electronic devices. In order to couple such devices into integrated circuits, doping by ion implantation would be highly desirable. Besides the devices mentioned above, Er doped materials are of great interest for photonic applications such as solid state lasers, optical amplifiers, lasers storage devices and displays. The Er3+ intra - 4f emission at 1.54 µm corresponds to the standard wavelength used in telecommunication. Up to now Er doping of Silicon has been intensively studied, but unfortunately the luminescence efficiency is strongly quenched at room temperature. In wide band gap semiconductors like GaN this quenching is much less pronounced [2] and thus it is hoped that Er doping by implantation might open the way to fully integrated optical circuits. Thus, a profound knowledge of the annealing process, necessary to remove the implantation induced lattice damage and activate the implanted dopants, is essential. Only a few studies exist addressing this problem [3], [4] where mainly electrical properties of the dopants were measured. Here we employ the PAC technique, which delivers information on the immediate lattice surrounding of an implanted probe atom and makes it possible to follow the reconstruction of the lattice from the initial stages on. PAC requires special properties of the probe atom. Thus the probe 181Hf(181Ta) was employed. Since its elemental properties are similar to Rare Earths like Er, is hoped it will give information also relevant to these interesting implants. Further, due to their large band gap, the group III nitrides are very suitable for high temperature electronics. A thorough knowledge of the annealing process might also stimulate progress in this direction.
The
GaN samples used were grown by Metal Organic Chemical Vapor Deposition at
1040 °C on c-plane sapphire substrates. The layers were nominally
undoped (n~5x1016 cm-3) and were ~3µm thick. Analysis
by x-ray diffraction and transmission electron microscopy showed them to be
typical of current state-of-the-art heteroepitaxial material, with rocking
curve full-width-half-maximum (FWHM) of ~280 arc.sec and defect densities of
~109 cm-2 at the surface. The InN and AlN were grown by
Metal Organic Molecular Beam Epitaxy at 650 and 900 °C,
respectively, on c-plane sapphire. The InN was strongly n-type
(~1019 cm-3) due to the presence of native point defects
and the layers were ~0.7µm thick. The x-ray FWHM was ~750 arc.sec on these
layers. The AlN was resistive (>107cm) and the layers
were ~1µm thick. The x-ray FWHM was ~600 arc.sec on these samples.
The samples were cut to 5 x 5 mm2 pieces and without further treatment implanted at room temperature at the Bonn radioactive isotope separator with 181Hf. It was produced by thermal neutron capture from the stable isotope 180Hf. The implantation energy was 160 keV and typical doses reached 1013 at./cm2 mainly due to stable 180Hf contaminating the mass 181 line. A TRIM [5] calculation yielded ranges of 460, 314, and 333 Å for AlN, GaN and InN, respectively, and corresponding typical concentrations of ~ 4 x 1018 cm-3.
Subsequently an isochronal annealing program was carried out in order to study the lattice damage recovery. The annealing steps were performed in a Rapid Thermal Annealing apparatus [6] between graphite strips under a Nitrogen atmosphere at ambient pressure. Additionally, a second, un-implanted piece of GaN was placed on the sample as a proximity cap to protect the surface. Typical holding times were 120 s and maximum temperatures of 1773 K were reached in the case of AlN.
Prior to the start of the programme and after each annealing step a PAC
spectrum was taken with 4 detectors (equipped with BaF2
scintillators) set up in a plane in a cross shaped arrangement. The PAC
technique exploits the fact that in suitable nuclei an excited nuclear state is
reached through the decay of a parent isotope and with a characteristic half
life, t1/2 = 10.8 ns in the case of
181Hf(181Ta), decays by the emission of a second nuclear
radiation. Due to the law of conservation of angular momentum, the directions
of emission of the populating and depopulating radiation in this so-called
- cascade are correlated. In the absence of hyperfine fields at
the site of the probe nucleus this correlation remains constant in time.
Changes of the directional correlation of the two rays indicate, that
during the lifetime of the intermediate state a hyperfine interaction between
the quadrupole moment of the nucleus and an electric field gradient (EFG) has
taken place. A PAC spectrum is extracted from the coincidence count rate N(t)
recorded for pairs of detectors, where t is the time elapsed between the
detection of the first and the second ray. In the case of pure electric
quadrupole interaction, like it is expected in the non-cubic semiconductors
studied here, N(t) has the following form:
 .
| (1) |
The leading exponential factor contains only the nuclear half life t1/2 and can be eliminated. The second factor, the perturbation function, is responsible for the modulation of a PAC spectrum. After a fit to the data it is possible to extract the parameters of the quadrupole interaction from it. The magnitude of the interaction is described by the quadrupole interaction constant:
 .
| (2) |
Apart from the elementary charge e and Planck's constant
h, 
Q is given by the product of the
nuclear quadrupole moment Q and Vzz, the principal
component of the EFG tensor at the nuclear site. The quadrupole moment Q of the
intermediate 5/2 state of the 133 - 482 keV - cascade in
181Ta has a value of Q(5/2)=(+)2.36(5) b [7]. Therefore, the magnitude of the EFG can be
derived directly from Q. Further, the PAC spectrum is
sensitive to the symmetry of the electric field gradient tensor, described by
the asymmetry parameter 
, which influences the frequency factors
cn() and the coefficients sn(
i, ) and
consequently can also be determined. Finally, if the measurement is carried out
in a single crystal, it is possible to extract the orientation of
Vzz relative to the crystal axes from the Euler angles
contained in the sn(i, ) coefficients.
The second exponential term with the additional parameter 
allows for a
Lorentzian distribution of interaction frequencies around
Q . Most of the following measurements were carried out
in a geometry where the <0001>-axis of the Wurtzite lattice is aligned with
the angle bisector of two detectors under 90°. Further details of the
application of the PAC technique to the study of solid state properties and the
data reduction procedure can be found elsewhere [8].
Internal fields at the site of probe nuclei in solids are dominated by
contributions from charges and spins within the first few atomic shells. More
distant charges and spins only contribute to an inhomogeneous broadening of the
signals from these nearby few shells, manifesting itself in an increase of the
damping parameter . As a result, hyperfine interaction frequencies
measured by PAC characterise the different local atomic environments in which
the probe atoms find themselves. Thus, PAC can be used as a tool to study the
structure and changes of local environments after different treatments of a
sample. Isochronal annealing programmes, where the sample is annealed at
increasingly higher temperatures TA with intermediate measurements
at the base temperature, here 293 K, have been proven to be particularly
successful to follow the reconstruction of a lattice after being damaged, for
instance, by implantation. Further, the onset of migration of a given defect
interacting with a probe atom can be observed or the binding energy of a probe
atom - defect pair can be determined.
After
the implantation, prior to any annealing, a damped oscillation was observed in
the PAC spectra for GaN and InN (Figs. 1a, 4a). This indicates that at the end
of the collision cascade a small fraction fs of the implanted probe
atoms stops on well defined lattice sites. Least squares fits [9] to the data yield values for fs of 36% for GaN
and 19% for InN. These relatively high values for fs as compared to
AlN can be ascribed to the higher replacement collision probability due to the
larger mass of the group III atom. However, following this argument one would
expect an even higher fs in InN than in GaN. The fact that with 19%, fs in InN
is only about half the value for GaN is most probably due to the lower crystal
quality of the InN material, which also leads to a lower final substitutional
fraction after annealing (see discussion below). In all three cases the width of the frequency
distribution is quite large, 20(1) % in GaN and 10(1) % in InN. The
following annealing process for the three compounds showed quite different
features so that in the following it will be described separately for GaN, InN,
and finally AlN.
Immediately
after implantation most (64%) of the implanted 181Hf probes are
situated in a lattice environment strongly disturbed by the implantation
induced damage. They cause the sharp drop of the anisotropy in the first few
nanoseconds in figure 1a and are characterised by a broad distribution of
quadrupole interaction frequencies around 1000 MHz. However, in the same
spectrum already a faint modulation can be observed. It is due to a fraction
fs = 36% of the implanted probes, which occupy less disturbed
lattice sites with a quadrupole interaction frequency of Q1 =
332(2) MHz (1 = 21 %, 1 = 0). Then, annealing
causes an interesting development. First, up to a temperature of TA
= 673 K, the damping parameter drops from 21 % to 11% without a strong
change in fs (see Figure 2). Subsequently continues
to decrease, although more slowly, whereas the fraction of probes on regular
lattice sites starts to grow steadily until at TA = 1373 K typically
values of fs = 70% to 80% are reached. After the annealing step at
1373 K a quadrupole interaction constant of Q1 = 338(2) MHz
(1 = 3%, 1 = 0) was derived.
The orientation of the corresponding EFG was checked by taking not only spectra with the sample's <0001>-axis oriented in the standard direction (Figure 3a) as described above, but also with the <0001>-axis perpendicular to the detector plane (Figure 3b) or pointing towards one detector (Figure 3c). The results, a doubling of the period in the first case and a practically vanishing oscillation in the second, are in perfect agreement with the assumption that Vzz, the principal component of the EFG, is oriented parallel to the <0001>-axis of the Wurtzite structure. The small contribution of the second and first harmonic in figure 3 b and c can be explained by a slight deviation from the perfect orientation.
Since GaN crystallises in the hexagonal Wurtzite structure an axially symmetric EFG with its principal component oriented along the <0001>-axis is expected at a regular lattice site. Thus, the observation of a unique EFG with this orientation indicates that the corresponding fraction fS of probe nuclei occupies regular sites. Due to the large difference in the covalent radii of Hf (rC=1.44 Å) and N (rC=0.75 Å) the incorporation of Hf on N sites is very improbable and the incorporation on Ga sites (rC= 1.26 Å) is more likely. This was confirmed by recent RBS measurements, which show that implanted Hf fully replaces Ga in GaN [10].
Dividing the measured QIF by the quadrupole moment Q = 2.36 b [7] of the 5/2
intermediate state of the - cascade in 181Ta and the
Sternheimer antishielding factor (1-
) = 62 [11] of the Ta ion the lattice EFG at the Ga
site can be calculated to be Vzzlatt=0.96
x 1016 V/cm2. This agrees well with the value of
Vzzlatt=0.65 x 1016 V/cm2 derived in the same way from NMR
measurements for Ga in GaN [12],
further confirming the complete substitutionality of the Hf probe.
At low annealing temperatures a second quadrupole interaction frequency
Q2 = 1378(9) MHz with an asymmetry parameter 2 =
0.63(2) is necessary to describe the spectra. A fraction of fD = 25%
of the probe atoms is subjected to the corresponding EFG (Figure 2a). Immediately
after implantation this EFG is highly non-unique resulting in large frequency
distribution parameter 2 = 23 %, but 2
drops parallel to 1 (Figure 2b) and after annealing at
773 K the frequency is clearly visible in the PAC spectrum (Figure 1b). The
fraction fD reaches a maximum of 28% at 573 K and disappears after
annealing above 1000 K (Figure 2b). The large value of Q2 is
characteristic for a deviation from the regular lattice structure in the
nearest neighbourhood of the probe atoms. The low value of 2
implies that this deviation has a regular structure, i.e. does not correspond
to an amorphous environment. Similar situations have been observed in other
semiconductors and are indicative of a unique defect trapped at the probe atom
[13]. Since no diffusion in the Ga
sub-lattice is expected in GaN below 1273 K [14], and the defect - probe atom complex
breaks up below 1000 K, we suggest that a Nitrogen vacancy, trapped at the
slightly oversized Hf probes, causes the corresponding quadrupole interaction.
Estimates for a nearest neighbour vacancy in the point charge model [15] yield a magnitude of the observed EFG which
is in good agreement with the experimental value. However, it seriously
underestimates the lattice EFG at the Ga site and therefore cannot explain the
large asymmetry parameter 2.
Summarising, the PAC data lead to the following picture of the annealing
process. For a fraction corresponding to the initial fS after the
implantation no defect remains in the immediate vicinity of the probe atom.
Thus the lattice EFG is only slightly disturbed by more distant defects leading
to the observed frequency distribution. Annealing leads to a partial recovery
of these defects thus narrowing 1. Due to the larger mobility
of Nitrogen - Nitrogen loss has been observed well below 1273 K [14] - these
are most probably defects of the Nitrogen sub-lattice. For the remaining
fraction, defects in the nearest neighbourhood seriously disturb the lattice
EFG. It takes temperatures well above 1000 K, where also diffusion in the Ga
sub-lattice sets in, to restore the surrounding lattice leading to a unique EFG
at over 80% of the Hf probe sites. A small fraction of probes traps a Nitrogen
vacancy at a nearest neighbour site. The corresponding quadrupole interaction
frequency also narrows until at 1000 K complete de-trapping occurs and the
substitutional fraction is increased. Assuming in a simple model, that the
de-trapping is a one step process, a binding energy EB 
3 eV
can be estimated. Here a Debye temperature of 586 K was used [16].
Directly
after the implantation a fraction fS = 19 % of the implanted
181Hf probes show a well defined quadrupole interaction frequency of
Q1 = 668(5) MHz (1 = 13%, 1 =
0) (Figure 4a). Annealing causes a continuous increase of this fraction, until,
after the 1173 K step, 43 % of the probes occupy regular lattice sites (Figure 5a). drops rapidly to 3.5 % at 1173 K (Figure 5b). A final value for
Q1 = 666(1) MHz (1 = 3.5 %,
1 = 0) is reached. An orientation measurement yielded the same
orientation of the electric field gradients principal axis as in GaN, i.e.
parallel to the c axis.
The data suggest that like in GaN a small fraction fS of the
implanted probes comes to rest on substitutional In sites at the end of the
collision cascade. However, the lower value of is indicative of less
severe implantation damage in this case. Unlike in GaN, here annealing causes a
steady increase of fS up to 44%, whereas remains essentially
constant up to 600 K before it drops to its final value at 1200 K. The maximum
of 43% of Hf incorporated into an undisturbed InN lattice is only about half
the value reached in GaN. This can be either due to the lower crystal quality
of the InN sample (due to the higher lattice-mismatch with sapphire) or to the
not yet optimised annealing procedure and will be subject of further
investigations. No evidence for the trapping of a was found in this lattice.
Since the covalent radii of Hf and In are equal (rC=1.44 Å), this can be explained by the lack of any attractive strain
introduced by the Hf probe.
Directly
after the implantation all probe atoms come to rest in a highly damaged lattice
environment resulting in a strong damping of the PAC spectrum (Figure 6a). This
can be described by a broad quadrupole frequency distribution around
Q1 = 922(11) MHz (1 = 40%). Annealing leaves
the spectrum unchanged until at 773 K a second, much narrower, frequency
distribution (Q2 = 323(10) MHz, 2 = 0,
2 = 9%) appears in the spectrum (Figure 6b). Its fraction fs
increases only slightly to 13% at 1173 K and then decreases again (Figure 7). The
damping parameter 2 remains virtually constant in the
temperature range investigated, indicating that no further annealing of the
implantation damage occurs. Considering the high melting point TM =
3273 K of AlN and the fact that lattice damage recovery stages are usually
correlated to it, the temperature where Q2 appears is
quite low. So the frequency is probably due to the annealing of correlated
damage, i.e. Hf probes moving into Al vacancies which remained in their
vicinity at the end of the collision cascade. The highest annealing
temperatures reached in this study correspond to only about half the melting
point, a temperature where in GaN the incorporation of Hf onto Ga sites only
starts. Therefore in the case of AlN much higher temperatures seem necessary to
restore the lattice order. Such annealing seem feasible since no signs of
lattice destruction due to the out - diffusion of N (or decomposition of the
surface) was observed up to the highest annealing temperature.
Measurements for different orientations of the sample did not show significant differences, which due to a near polycrystalline structure of the AlN films, is not surprising.
From the quadrupole interaction frequencies the following values of the electric field gradients for the Hf probe on a group III lattice site can be derived as described above: GaN 9.5(2) x 1015 V/cm2, InN 18.9(3) x 1015 V/cm2 and AlN 9.2(2) x 1015 V/cm2 . Estimates in the point charge model mentioned above [15] yield values of 0.27, 0.43 and 1.56 x 1015 V/cm2, respectively. Here lattice constants given by Nakamura and Fasol [17] and a charge of Z = +1 for the cation and -1 for N were used. Assuming first order exponential kinetics and de-trapping of the vacancy in a one step dissociation process, a binding energy of EB ~ 3 eV can be estimated. However, it is probable that the bad agreement is not only due to the known inadequacies of this model but also to uncertainties in the crystallographic data [16], mainly the so called u parameter.
Implantation of 181Hf into GaN, AlN and InN was studied by PAC. After implantation, substitutional fractions of 36% for GaN, 19% for InN and 0% for AlN were found. Subsequent annealing increased these values to ~80% for GaN, 43% for InN and 12% for AlN. The PAC data provides strong evidence for the role of defect reactions in controlling the recovery of implantation damage in the group III-nitrides.
© 2000 The Materials Research Society
