# Zeta potential and nanodiamond self assembly assisted diamond growth on
lithium niobate and lithium tantalate single crystal

Soumen Mandal<EMAIL_ADDRESS>Karsten Arts  David Morgan  Zhuohui Chen
Oliver A. Williams<EMAIL_ADDRESS>School of Physics and Astronomy,
Cardiff University, Cardiff, UK  Eindhoven University of Technology, 5612 AZ,
Eindhoven, the Netherlands  Cardiff Catalysis Institute, School of Chemistry,
Cardiff University, Cardiff CF10 3AT, U.K.  Huawei Technologies Canada Co.,
Ltd., 303 Terry Fox Drive, Kanata, Ontario, K2K 3J1, Canada

###### Abstract

This study focuses on the self-assembly and subsequent diamond growth on SiO2
buffered lithium niobate (LiNbO3) and lithium tantalate (LiTaO3) single
crystals. The zeta-potential of LNO and LTO single crystal were measured as a
function of pH. They were found to be negative in the pH range 3.5-9.5. The
isoelectric point for LNO was found to be at pH $\sim$ 2.91 and that of LTO to
be at pH $\sim$ 3.20. X-ray photoelectron spectroscopy performed on the
surfaces show presence of oxygen groups which may be responsible for the
negative zeta potential of the crystals. Self-assembly of nanodiamond
particles on LTO and LNO, using nanodiamond colloid, were studied. As
expected, high nanodiamond density was seen when self-assembly was done using
a positively charged nanodiamond particles. Diamond growth was attempted on
the nanodiamond coated substrates but they were found to be unsuitable for
direct growth due to disintegration of substrates in diamond growth
conditions.. A $\sim$100nm thick silicon dioxide layer was deposited on the
crystals, followed by nanodiamond self assembly and diamond growth. Thin
diamond films were successfully grown on both coated crystals. The diamond
quality was analysed by Raman spectroscopy and atomic force microscopy.

###### keywords:

x-cut lithium niobate, x-cut lithium tantalate, zeta potential, diamond, XPS

††journal: Carbon

##  1 Introduction

Sound waves propagate in air through mechanical vibrations which happens along
the direction of propagation. Similar effects can also be seen in solids when
a wave passes through the solid. The phonons which represent movement of atoms
in the lattice along the direction of propagation of wave are also known as
acoustic phonons (like sound wave propagating in a media). Like phonons,
another particle of interest to many applications are the photons. They have
striking similarity in the form that sound in rigid media and light in
transparent objects can travel without attenuation. However, the higher speed
of light ($\sim$ 100000 times that of sound) means that photonics devices have
large physical dimensions due to large wavelengths (centimetre to meters
depending on frequency). Replacing light by sound makes it possible to reduce
the size of devices. One such device of interest based on acoustic phonons is
the surface acoustic wave (SAW) device which play a major role in variety of
industrial and academic applications[1]. For example, SAW filters are
essential components for information and telecommunication systems[2, 3].
Conventionally SAW filters are fabricated on piezoelectric materials like
lithium tantalate (LTO), lithium niobate (LNO) etc. The 5G bands proposed in
the 5G road map[2] incorporates frequency bands above 10 GHz. This puts higher
power and frequency handling demand on SAW filters[3, 4]. The higher operation
frequency can be achieved by increasing acoustic wave velocity, which is
material dependent, or by reducing the wavelength by reducing the pitch of the
electrodes[3]. The first method requires research on newer materials with high
acoustic wave velocity, the second method is limited by the lithography
techniques and handling of the heat generated by the electrodes fabricated on
the current piezo materials like LTO and LNO. The power handling capacity of
these materials can be enhanced by attaching these materials to high thermal
conductivity material like diamond ($\sim$ 1200 - 2000 Wm-1K-1)[5]. This can
be achieved in two ways. The first is to put the diamond on the piezo material
either by direct growth[6, 7] or by direct bonding[8, 9, 10, 11, 12] and the
second, is grow the piezo electric material on top of polished diamond[13,
14]. The growth of piezo material on diamond leads formation of
polycrystalline piezo material which has been shown to effect device
performance when compared with single crystal material[14]. Furthermore, the
current state-of-the-art for direct bonding is limited to single crystal
diamond. The small sizes and high cost of single crystal diamond makes this
technology unattractive. That leaves with one alternative, that is to grow a
thick diamond layer on top of the piezo material. It has been shown earlier
that to take full advantage of superior thermal conductivity of diamond, the
diamond layers should be $\geq 10\mu$m in thickness[15].

Diamond growth on non-diamond substrates is non-trivial process due to large
differences in surface energies between diamond and most substrates. With a
surface energy of $\sim$ 6J/m2[16], diamond has much higher surface energy
than common substrates like silicon ($\sim$ 1.5J/m2)[17]. This energy
difference leads to isolated island like growth of diamond crystals on
substrates[18, 19] like silicon with an island density of around 104 \- 105
cm-2. The surface energy for LNO[20] is $\sim$ 1.1J/m2. These energies were
calculated using the cleavage technique[21]. For LTO, such cleavage based
surface energies are not present, however, surface energies calculated based
on water contact angle shows LTO to have similar surface energies to
silicon[22]. Considering the large differences in surface energies, for growth
of diamond on these substrates they need to be coated with small diamond
particles. For a smooth interface the particles need to be as small as
possible. The smallest such particles are admantane and the process of coating
such small particles on any surface is quite involved[23]. The easier approach
would be to self assemble slightly bigger particles on to the substrate
surfaces using nanodiamond ($\sim$ 5-10 nm in size) colloid[24, 25]. However,
the self-assembly of nanodiamonds is only the first step in the diamond growth
process. The coated substrates are exposed to harsh diamond growth conditions
in the presence of hydrogen plasma. Normally, the growth temperatures for
diamond is of the order of 800 oC[18], which is higher than the Curie
temperature of LTO[26]. It has also been found in the case of LNO that the
crystal structure of the surface is completely destroyed/blackened when
exposed to hydrogen plasma[27]. This can be recovered to some extent by
exposing to oxygen plasma, however, if diamond is grown on the surface then
the LNO substrate is completely blanketed and no diffusion of oxygen can
happen to reform the surface. Similar, blackening effect was also observed for
LTO substrates, during this study, when exposed to diamond growth conditions.
Furthermore, the large difference in thermal expansion coefficient between the
substrates[28] and diamond[29] means that the substrate temperature has to be
kept as low as possible to manage stress in the film when cooled to room
temperature after growth. Considering all the above, it was decided to have
similar approach to $\beta$-Ga2O3 for the growth of diamond on LNO and
LTO[30]. The substrates were coated with 100nm of SiO2 by atomic layer
deposition (ALD) before self assembly of nanodiamond and growth. Diamond
growth on LNO has been attempted before[31], however the seeding technique
used for the growth was mechanical scratching. It is well known that
mechanical scratching can lead to rough interface between diamond and
substrate[18, 19]. Such rough interfaces have been shown to adversely affect
SAW performances in the past[32].

To summarise, in this work, 1) the zeta($\zeta$)-potentials of LNO and LTO
were measured, 2) self assembly of nanodiamond was studied on LNO and LTO
using AFM, 3) the substrates were coated with silicon dioxide and diamond
growth was attempted, and 4) the diamond layer on the substrates were examined
with Raman spectroscopy and atomic force microscopy.

##  2 Methods and Materials

The $\zeta$-potential of LNO and LTO surfaces were measured using Anton Paar
SurpassTM 3\. The instrument measures the $\zeta$-potential by measuring the
streaming potential, while passing an electrolyte, between the inlet and
outlet of a narrow channel formed by the sample surfaces[33]. The streaming
potential is a result of moving counterions which are sheared off the sample
surfaces by the passing electrolyte[30]. The measurement of streaming
potential as a function of electrolyte pressure can give the $\zeta$-potential
through Helmholtz-Smoluchowski equation[34]. The electrolyte used in this
study was 10-3 M KCl solution, the channel width was kept between 90 and 110
$\mu$m and the electrolyte pressure was varied between 200 and 600 mbar. The
surface charge of any solid in a liquid is heavily dependent on the pH of the
solution which in turn effects the $\zeta$-potential. To vary the pH during
the measurement, 0.05M NaOH and 0.1M HCl solution was used with the inbuilt
titrator in SurpassTM 3\. Hydrochloric acid was sourced from Fisher chemicals
(Product code: H/1150/PB15), sodium hydroxide (Product code: 28245.265) and
potassium chloride (Product code: 26764.260) were purchased from VWR. The DI
water was from ReAgent Chemical Services.

The knowledge of $\zeta$-potential helps in choosing the right kind of
nanodiamond colloid (positive or negative) for electrostatically driven self
assembly of nanodiamonds on LNO and LTO surfaces[24, 35, 18, 19]. Two
different types of suspensions were used in this work. The positively charged
suspension was made using hydrogen terminated nanodiamonds with average
particle size of 10nm and $\zeta$-potential of +40mV. The negatively charged
suspension was prepared with oxygen terminated nanodiamonds and had an average
particle size of 10nm with -50mV $\zeta$-potential. Full details of making the
suspensions have been published elsewhere[35, 18, 25, 19, 36]. While self-
assembly of nanodiamond on LNO and LTO is straightforward with knowledge of
surface charge, the growth of diamond thin film from the self-assembled
particles is non-trivial. The growth of diamond on these substrates, like
Ga2O3[30], is dependent on the ability of the substrates to withstand extreme
diamond growth conditions as well as the difference in coefficient of thermal
expansion between the substrates and diamond. This is due to the normal growth
conditions of diamond being 500o C or higher[18]. To work around this problem
a $\sim$100nm thick silicon dioxide layer was grown by atomic layer deposition
(ALD). An Oxford Instruments FlexAL reactor was used for this process[37] with
1100 ALD cycles with a table temperature of 300 oC. SiH2(NEt2)2
(bis(diethylamino)silane) precursor was used along with O2 plasma, generated
by an inductively coupled plasma source, as coreactant. The thickness of the
SiO2 layer was measured by J.A. Woollam M-2000D spectral ellipsometer[38]. For
the thickness measurement a small piece of silicon substrate was introduced at
the same time as the LTO and LNO substrates. Previous measurements of
$\zeta$-potential on ALD grown SiO2 have shown the surfaces to be negatively
charged in water (have negative zeta potential)[30].

For studying the self assembly of nanodiamond on LNO and LTO surfaces, atomic
force microscopy (AFM) images were taken using Bruker Dimension Icon atomic
force microscope. The microscope was operating in peak force tapping mode
using a ScanAsyst tip. For this study three pieces of each substrate were
taken. One piece from each type of substrate was dipped in diamond colloid
containing positive nanodiamond particles. The substrates were sonicated in
the colloid for 10 mins and then spin dried at 3000 rpm. The same was repeated
with a second set of pieces by dipping them in diamond colloid containing
negatively charged particles. The oxide coated substrates were dipped in
positively charged nanodiamond colloid for self-assembly of diamond particles.
The particle loaded substrates were then introduced in a clamshell microwave
chemical vapour deposition system(CVD)[39]. Growth on both substrates were
done at 5% CH4/H2 ratio, with CH4 acting as carbon source and H2 acting as
etchant for non-diamond carbon[18, 40]. However, the growth conditions were
slightly different due to difference in substrate thickness. The main aim was
to keep the substrate temperature close to 500 oC to avoid excessive stress
between grown diamond and substrates. The stress is due to difference in
coefficient of thermal expansion between diamond[29] and the substrate[28,
41]. For the thinner coated-LTO substrate the growth conditions were 3.2kW of
microwave power with 35 torr gas pressure. The coated-LNO substrates were
subjected to 3.2 kW of microwave power under 29 torr gas pressure. The lower
pressure reduces slightly the overall energy density of the plasma, thus
giving lower substrate temperature for the thicker substrate[40]. Since the
difference between the growth conditions is small, the overall growth
chemistry is not significantly affected to result in diamond layers with
dissimilar properties[40]. The diamond films on both substrates were grown for
120 mins and cooled to room temperature in hydrogen plasma. Following the
growth of diamond film was analysed using a SynapsePlus Back-Illuminated Deep
Depletion (BIDD) CCD equipped Horiba LabRAM HR Evolution. The excitation
wavelength was 532 nm. The surfaces of the films were imaged with atomic force
microscope. X-cut LTO and LNO were commercially sourced. The LTO substrates
were 5 X 5 mm in size and 0.5 mm in thickness. The LNO substrates were 5 X 5
mm in size and 1 mm in thickness. The substrate surface were examined with
X-ray photoelectron spectroscopy (XPS). The data was collected using a Thermo
Scientific K-Alpha+ spectrometer with a monochromatic Al source that was
operated at 72W, with an emission current of 6mA at a 12kV anode potential.
Survey and high-resolution spectra were obtained using pass energies of 150
and 40 eV, respectively. To neutralize the charge, a combination of electrons
and low energy Ar ions were employed. The spectra were analyzed using CasaXPS
2.3.26[42] software.

##  3 Results and Discussion

Figure 1: $\zeta$-potential of lithium tantalate and lithium niobate single
crystal as a function of electrolyte pH. The $\zeta$-potential for both the
crystals are negative in the pH range 3.5-9.5 with isoelectric points close to
pH $\sim$3.

Figure 1 shows the $\zeta$-potential of LNO and LTO single crystal as a
function of pH. The $\zeta$-potential is negative in the pH range 3.5-9.5 for
both the substrates. The isoelectric point for LNO is around the pH value of
$\sim$2.91 while that for LTO is $\sim$3.20. The isoelectric points were
calculated by fitting a trend-line to the curves around 0 mV mark. This
information is critical for determining the type of nanodiamond suspension
needed for high density nanaodiamond self assembly on the substrates[18, 19,
25]. It has been shown that particle in nanodiamond colloids can be positively
or negatively charged depending on the pre-treatment of the particles used for
colloid formation[25]. Since the self assembly is electrostatically driven,
nanodiamond particles with opposite $\zeta$-potential to substrate are best
suited for high density self assembly[43, 44]. In general the pH of the
nanodiamond colloid is around 4-6 and in this region the $\zeta$-potential of
LNO and LTO substrates are negative (Fig 1). So, for a high-density of
nanodiamond particle on the substrate surface a positively charged colloid is
best suited.

Figure 2: XPS spectra of LNO surface. Panel A shows the survey spectra of the
sample. The standard peaks for the crystal are indicated next to the peaks.
Panel B shows the zoomed in view of the Li1s peak region. Panel C is the zoom
in of the Nb3d peaks. Panels D and E shows the O1s and C1s peaks respectively.
Figure 3: The XPS survey spectra of LTO surface is shown in Panel A, with the
standard peaks for the crystal indicated next to the peaks. Panel B displays a
closer view of the Li1s peak region, while Panel C is a magnified view of the
Ta4f peaks. Panels D and E present the O1s and C1s peaks, respectively.

A negative zeta potential in oxides is typically observed due to the
adsorption of negatively charged species on the oxide surface, such as
hydroxyl groups (OH-) or other anions[45]. XPS was done on both LNO and LTO
surfaces to examine the crystal surfaces. The spectra for LNO and LTO are
presented in figures 2 and 3 respectively. The charge correction for the
spectra were done using the 284.8eV adventitious carbon peak[46, 47]. The
standard peaks in both LNO[48] and LTO[49, 50] crystals are indicated in panel
A of figures 2 and 3 respectively. Figure 2B shows the zoomed in region of the
Li1s peak. The peak position as determined by fitting the data using CasaXPS
was found to be 54.7 $\pm$ 0.1eV. The Nb4s peak at $\sim$60 eV is also
visible. Panel C shows the Nb3d peaks corresponding to 3d5/2 and 3d3/2[51].
The 3d5/2 peak is at 206.8 $\pm$ 0.1 eV and the 3d3/2 peak is at 209.5 $\pm$
0.1 eV. The difference in the peak position is around $\sim$ 3eV which is
consistent with what has been seen in the literature[51] for z-cut LNO. The
region of the spectra of particular interest for purpose of negative
$\zeta$-potential are the O1s and C1s peaks. These are shown in figure 2D and
E respectively. Looking at the O1s peaks three clear peaks can be seen at 530
$\pm$ 0.1 eV, 531.3 $\pm$ 0.1 eV and 532.4 $\pm$ 0.1eV. The peak at 530 $\pm$
0.1 eV corresponds to structural oxygen and the peak at 531.3 $\pm$ 0.1 and
532.4 $\pm$ 0.1 eV corresponds to adsorbed oxygen[48]. The bonding state of
the adsorbed oxygen atoms can be estimated by looking at the C1s peak from the
crystal. Since carbon does not form part of the LNO crystal, all the carbon
atoms detected on the surface are assumed to be adsorbed carbon atoms. The C1s
peak can be deconvoluted into three peaks. The peak at 284.8 eV (also the
reference peak for charge correction) is the sp3 C-C bond[46, 47]. The second
peak is at 286.5 $\pm$ 0.1 eV which is $\sim$1.7 eV away from C-C peak. This
is attributed to C-OH bonds[52, 53] confirmed also by 531.3 eV peak in O1s
spectra. Finally the third peak is at 288.5 $\pm$ 0.1 eV, which is $\sim$3.7
eV higher than C-C peak position at 284.8 eV. This is generally attributed to
carbonyl (C=O) groups on the surface[54] which is also confirmed by the 532.4
eV peak in O1s spectra[55]. The dashed lines at the bottom of each zoomed in
region shows the inelastic background. Clearly, there is irrefutable evidence
of oxygen groups (other than structural oxygen) on the surface. As has been
stated before these groups are mostly responsible for the negative
$\zeta$-potential in solid surfaces[45].

Similar analysis can be done for the XPS spectra for LTO crystal. Figure 3B
shows the Li1s peak at 54.7 $\pm$ 0.1 eV[50]. Figure 3C shows the Ta4f peaks
at 27.6 and 25.7 $\pm$ 0.1 eV which correspond to oxidised Ta4f5/2 and Ta4f7/2
states respectively[49, 56]. A very small hump seen close to 22 eV can signal
the presence of some unoxidised Ta on the surface[49]. Panels D and E in
figure 3 shows the spectra for O1s and C1s peaks, respectively, from LTO
surface. Similar to LNO, the O1s peak of LTO can be convoluted into three
peaks at 530.3, 531.5 and 532.5 $\pm$ 0.1 eV. The peak at 530.3 eV corresponds
to structural oxygen (similar to LNO) and the peak at 531.5 and 532.5 eV
corresponds to adsorbed oxygen[56]. Finally, looking at the C1s peak of the
LTO surface, a picture similar to LNO surface appears. The C1s peak exhibits
three distinct peaks upon deconvolution. The first peak at 284.8 eV is
considered as the sp3 C-C bond and serves as the reference peak for charge
correction, as supported by previous studies[46, 47]. The second peak, located
at 286.4 $\pm$ 0.1 eV, is approximately 1.8 eV away from the C-C peak and is
associated with the presence of C-OH bonds[52, 53]. The third peak, which
appears at 288.4 $\pm$ 0.1 eV, is about 3.6 eV higher than the C-C peak at
284.8 eV, and is commonly attributed to carbonyl (C=O) groups present on the
surface[54]. This observation is further confirmed by the 531.5 and 532.5 eV
peaks observed in the O1s spectra[55]. It is evident that oxygen groups,
besides structural oxygen, exist on the surface of LTO substrate similar to
LNO. As has been stated earlier, these groups are primarily responsible for
the negative $\zeta$-potential exhibited by solid surfaces[45]. The LNO
crystal had trace amounts of sodium, copper, sulphur, calcium, cobalt and
silicon on the surface, the origin for which is not known. Similarly, the LTO
substrates had trace amounts of zinc, sodium and cobalt. There are still some
subtle difference in the $\zeta$-potential of LNO and LTO surfaces which
cannot be explained by the XPS study alone. Further studies are required by
preferentially terminating the surfaces with specific surface groups to
pinpoint the true effects of the surface group on $\zeta$-potential. Such
studies are beyond the scope of the current manuscript.

Figure 4: AFM images showing self-assembly of diamond nanoparticles on LNO and
LTO surfaces. The left side images (Panel A, B, C and D) are for LNO and the
right side images (Panels E, F, G and H) are for LTO. Panels A and E show the
bare solvent cleaned substrate. Panels B and F for substrates dipped in
positively charged diamond colloid. Finally, panels C and G show substrates
dipped in negatively charged diamond colloid. Finally panels D and H are for
silicon dioxide coated LNO and LTO substrates treated with positively charged
diamond colloid.

The substrates were dipped in nanodiamond suspensions(positive and negative)
and the coated surfaces were examined using AFM. The AFM images of the
surfaces (uncoated and coated) are presented in figure 4. Panel A, B, C, E, F,
and G are for the bare substrates. Panels D and H are for SLTO and SLNO
respectively. The two columns are marked on the top with the base substrate
only. Panels A and E show the image of extremely smooth LNO and LTO substrate
surfaces respectively. The scale bar on the side of the images gives an idea
of the variation in the surface. Panels B and F in the same figure show the
substrates treated with positively charged nanodiamond colloid. Evidence of
self assemble of nanodiamond is clearly visible. It is evident that there are
some agglomerates in the colloid which get deposited on to the substrates. In
contrast when the substrates are dipped in a colloid containing negatively
charged particles there is hardly any change in the roughness of the substrate
surface and this is shown in figure 4C and G. A comparison between scale bars
of panels A and C for LNO (D and F for LTO) clearly shows no self-assembly of
nanoparticles on the substrates. Finally the AFM images of the SLTO and SLNO
substrates dipped in positively charged diamond colloids are shown in panels D
and H. Clear self-assembly of nanodiamond are visible. However, when compared
with bare LTO and LNO the seed density is slightly lower. This is due to
slightly lower negative $\zeta$-potential (absolute value) of the ALD
deposited silicon surface when compared with bare substrates (LTO/LNO)[30].

The substrates with the nanodiamond particles were then introduced in a CVD
reactor to directly grow diamond. As has been seen in the case of Ga2O3[30],
both LNO and LTO substrates were heavily etched in the hydrogen plasma thus
inhibiting growth of diamond. As a result SiO2 coated substrates were used to
self-assemble diamond nanoparticles followed diamond growth process. It has
been shown in the past that ALD grown SiO2 layer have negative charge when
dipped in water[30]. As a result positively charged diamond solution was used
to achieve high nanodiamond density on the substrates[25, 30]. The diamond
films were imaged using AFM and their quality tested using Raman spectroscopy.
In general scanning electron microscopy(SEM) is used for imaging diamond
layers, however on this occasion due to highly insulating nature of the
substrate and the resulting diamond it was not possible to use SEM due to
excessive charge accumulation on the samples.

Figure 5: AFM images of the thin diamond films grown on SLNO and SLTO. The
crystalline facets of the small diamond grains are clearly visible with
average grain size of $\sim$ 80nm for both samples.

The AFM images of thin diamond films are shown in figure 5. The films grown on
both the substrate show good crystalline quality as clear diamond facets are
visible in the images. The presence of well faceted crystals indicate good
quality of the diamond film. The average grain size is $\sim$ 80nm for both
the films as seen from AFM images. The growth of diamond form nanoparticle
follows a Volmer-Weber growth model[57, 58] until coalescence and then follows
a competitive columnar growth as explained in Van der Drift model[59, 60].
Assuming there is no secondary nucleation, the thickness of the films are
close to the grain size seen at the surface. In this case, the films thickness
as seen from grain size is close to $\sim$ 80nm. Considering the growth was
done for 120mins, the growth rate of diamond on these substrates is of the
order of $\sim$40 nm/hr. The thin films were then analysed using Raman
spectroscopy and the results for the same are presented in figures 6 and 7.

Figure 6: Raman spectroscopy of the LNO substrate, SiO2 coated LNO (SLNO) and
the thin diamond film grown on SLNO are shown here. In all three spectra the
peaks from the LNO are clearly seen. The bottom panel shows the zoomed in
region between 1100 and 1800 cm-1 clearly showing a Raman peak around 1332
cm-1.

Figure 6 shows the Raman spectra of LNO, SiO2 coated LNO (SLNO) and diamond
film grown on SLNO. The top panel shows the full spectrum while the bottom
panel shows the zoomed in view of the spectra between 1100 and 1800 m-1. The
curve shown in blue solid line is for the bare substrate. The substrate shows
all the characteristic peak for LNO grown with lithium-7 (7Li)[61, 62]. The
observed peaks, as reported in literature[62], are 155, 180, 238, 255, 265,
276, 325, 334, 371, 431, 582, 633 and 610 cm-1. In this case the 180 cm-1 is
not present, instead a small shoulder can be seen at $\sim 196$ cm-1. This
peak have been theoretically calculated by Repelin etal.[62] in their work and
can appear at 180 cm-1 instead. Furthermore, the peaks at 255 and 265 cm-1
appears as one broad band around $\sim 250$ cm-1. The curve in green dashed
line in the figure shows the spectrum for SLNO. In this case the relative
intensities between various peaks are markedly different from the relative
intensities of LNO spectrum. This has been seen earlier in the case of
$\beta$-Ga2O3[30]. Finally, the data for thin diamond film grown on SLNO is
shown at the top in red dotted lines. The data shows all the peaks
characteristic of LNO. The signature of the thin diamond film is not visible
in the zoomed out view. This is due to thin diamond film and low signal
intensity when compared with the LNO single crystal substrate. The bottom
panel in figure 6 shows the expanded view around the 1332 cm-1. A clear
diamond peak can be seen in the inset along with some signature for D and G
peaks. No such peaks could be seen for the Raman spectra on LNO and SLNO. The
diamond peak position as determined by a Gaussian fit is $\sim$ 1331.4 cm-1.
Based on various models to calculate stress from Raman shift
($\sim$0.4GPa/cm-1) and the ideal diamond peak at 1332 cm-1[63, 64], the
stress in the film is around $\sim$0.24 GPa[65, 66, 67]. The origin of the
stress in the diamond films is the difference in coefficient of expansion
between substrate[28] and diamond[29]. Higher the growth temperature, higher
would be the stress in the diamond film once the film is cooled to room
temperature from growth temperature (normally around 800 oC). In this case the
growth temperature was $\sim$500oC which resulted in lower stress.

Figure 7: Raman spectroscopy of the LTO substrate, SiO2 coated LTO (SLTO) and
the thin diamond film grown on SLTO are shown here. In all three spectra the
peaks from the LTO are clearly seen. The inset shows the zoomed in region
between 1100 and 1800 cm-1 clearly showing a Raman peak around 1332 cm-1.

Raman spectra for LTO, SiO2 coated LTO (SLTO) and diamond film grown on SLTO
were also taken, similar to the data on LNO, and the results are presented in
figure 7. Like before, the bottom spectra (shown in blue solid line) is for
bare substrate. The crystal shows the characteristic features for a x-cut LTO
crystal[68, 62, 69]. The observed peaks from the literature[68, 62] for LTO
are 140, 180, 201, 206, 251, 253, 316, 356. 383, 462, 597, 660 and 750 cm-1.
In the data presented in figure 7, peaks are seen at $\sim$ 142, 191, 207,
252, 318, 358, 384, 463, 597, 659 and 751. The peak at 191 cm-1 is close to
the calculated frequency of 199.9 cm-1[62]. This frequency has been reported
to appear at 180 cm-1 in many studies. The peak at 597 cm-1 generally include
the calculated peaks at 595, 599.4 and 617 cm-1[62]. The curve in green dashed
in figure 7 shows the Raman spectra for SLTO. The relative intensities of
various peaks from the substrate are markedly different, as has been seen in
the case of LNO. Finally the curve in red dotted line shows the spectrum for
diamond grown on SLTO. The characteristic peaks for LTO are all present and as
seen for diamond on SLNO, the signal from the diamond layer is weak and can
only be seen in the zoomed in version shown in the inset. Similar to LNO and
SLNO, no such peaks were seen in the LTO or SLTO spectra and hence the
expanded view have not been shown for the same. The diamond peak position is
$\sim$1330.84 cm-1 as determined by a Gaussian fit. The stress in the diamond
film on SLNO is around $\sim$0.46 GPa[65, 66, 67].

##  4 Conclusion

In conclusion, we have measured the $\zeta$-potential of LNO and LTO single
crystal and studied electrostatic driven self assembly of nanodiamonds on
these crystal. The $\zeta$-potential of both the substrates are negative. The
presence of oxygen groups, as determined by XPS, on the surface are most
likely reason for the negative $\zeta$-potential. The self assembled
nanodiamonds were used to grow thin diamond layers on these substrates. It was
found that the substrates could not survive the harsh diamond growth
condition. As a result a protective SiO2 layer was deposited for diamond
growth experiments. It has been shown here that it is possible to successfully
grow thin diamond layers on buffered LNO and LTO. However, the growth rate in
both the cases is really slow (around 40nm/hr). This growth rate is not ideal
for growing tens of microns of diamond needed for effective thermal management
in acoustic wave devices. Furthermore, it is important to have large grain
size to benefit from good thermal property of diamond and also to reduce
losses in acoustic wave filters. Finally, even if diamond is grown at such
slow growth rates to get thicker diamond layers, the layers peel-off from the
substrate in-spite of low stress seen in thinner layers. It is quite possible
that as the diamond layer grows thicker the stress between diamond and the
substrate also increases. The thin diamond layers were analysed with AFM and
Raman spectroscopy and were found to be of good crystallinity with minimal
stress. The alternative to this would be to directly bond piezo material to
poly-diamond substrates which has its own complexities due the requirement of
low surface roughnesses ($<$1nm over large area).

## Acknowledgment

The authors would like to acknowledge financial support from Huawei.

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