††thanks: These authors contributed equally to this work.††thanks: These
authors contributed equally to this work.††thanks:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Microelectromechanical system based design of a high-finesse fiber cavity
integrated with an ion trap

Moonjoo Lee  Institut für Experimentalphysik, University of Innsbruck,
Technikerstraße 25, 6020 Innsbruck, Austria  Minjae Lee  ISRC/ASRI, Department
of Electrical and Computer Engineering, Seoul National University, Seoul,
151-744, Korea  Seokjun Hong  ISRC/ASRI, Department of Electrical and Computer
Engineering, Seoul National University, Seoul, 151-744, Korea  Klemens
Schüppert  Institut für Experimentalphysik, University of Innsbruck,
Technikerstraße 25, 6020 Innsbruck, Austria  Yeong-Dae Kwon  Quantum
Technology Laboratory, SK Telecom, Seongnam-si, 463-784, Korea  Taehyun Kim
ICT/ASRI, Department of Computer Science and Engineering, Seoul National
University, Seoul, 151-744, Korea  Yves Colombe  Institut für
Experimentalphysik, University of Innsbruck, Technikerstraße 25, 6020
Innsbruck, Austria  Tracy E. Northup  Institut für Experimentalphysik,
University of Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria  Dong-Il
“Dan” Cho  ISRC/ASRI, Department of Electrical and Computer Engineering, Seoul
National University, Seoul, 151-744, Korea  Rainer Blatt  Institut für
Experimentalphysik, University of Innsbruck, Technikerstraße 25, 6020
Innsbruck, Austria  Institut für Quantenoptik und Quanteninformation,
Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020
Innsbruck, Austria

###### Abstract

We present a numerical study of a MEMS-based design of a fiber cavity
integrated with an ion trap system. Each fiber mirror is supported by a
microactuator that controls the mirror’s position in three dimensions. The
mechanical stability is investigated by a feasibility analysis showing that
the actuator offers a stable support of the fiber. The actuators move the
fibers’ positions continuously with a stroke of more than 10 $\mu$m, with
mechanical resonance frequencies on the order of kHz. A calculation of the
trapping potential shows that a separation between ion and fiber consistent
with strong ion-cavity coupling is feasible. Our miniaturized ion-photon
interface constitutes a viable approach to integrated hardware for quantum
information.

##  I Introduction

The trapped ion system is one of the most promising candidates for quantum
information processing Monroe and Kim (2013); Schindler  _et al._ (2013).
Recent progress includes the generation of entanglement across 20 individually
controlled ions Friis  _et al._ (2018), memory times exceeding 10 minutes Wang
_et al._ (2017), and a single-qubit gate fidelity of 99.9999% Harty  _et al._
(2014). When these advantages are combined with those of optical cavities, the
ion-cavity setting can be used to realize classical simulations Bylinskii  _et
al._ (2015); Gangloff  _et al._ (2015a); Bylinskii  _et al._ (2016) and is
expected to enable efficient quantum networks Moehring  _et al._ (2007);
Northup and Blatt (2014). Moreover, the cavity field mediates a long-range
interaction between ions, which makes the system a suitable platform to study
many-body physics such as structural phase transitions Fogarty  _et al._
(2015); Rojan  _et al._ (2016).

In order to demonstrate quantum advantage with ion-based quantum devices, that
is, to solve classically intractable problems Preskill (2012), it will be
necessary to scale up traps to store and manipulate tens or hundreds of
qubits. Coupling such ion traps to optical cavities, we can develop advanced
quantum information systems, such as a quantum repeater node comprising memory
and communication qubit ions Monroe and Kim (2013) and a modular quantum
computer distributed across a photonic network Monroe  _et al._ (2014); Kim
_et al._ (2011). To address the challenge of scalability, one solution is to
employ microelectromechanical systems (MEMS) fabrication technology to
miniaturize an ion-cavity system.

MEMS-based ion trap technology is regarded as a promising platform to build
large-scale quantum systems Kielpinski  _et al._ (2002); Cho  _et al._ (2015).
The first MEMS surface ion trap was fabricated at NIST Boulder in 2005
Chiaverini  _et al._ (2005) by evaporating Au electrodes on fused silica. A
MEMS surface ion trap has smaller trap depth than a three-dimensional Paul
trap Brownnutt  _et al._ (2006) but has the advantage of a reconfigurable
planar trapping geometry, along with extensive optical access for laser beams,
as required for a large-scale ion trap quantum computer. In 2016, a MEMS trap
called the High Optical Access 2.0 trap was developed by Sandia National
Laboratory Maunz (2016), which is widely used by many ion trap researchers
today. Topics of active research include the question of how to reduce stray
charge accumulation, e.g., on the trap sidewalls Hong  _et al._ (2018) or via
in situ cleaning Hite  _et al._ (2012, 2013), and how to build increasingly
sophisticated structures, e.g., junction traps Amini  _et al._ (2010);
Moehring  _et al._ (2011) for ion transport, and two- or three-dimensional
electrode arrays Seidelin  _et al._ (2006); Wilpers  _et al._ (2012).

MEMS-based ion traps have advantages in scalability and ease of fabrication,
and they can also be easily integrated with other type of MEMS devices. MEMS
techniques can also reduce the footprint of the optical cavity system Gollasch
_et al._ (2005); Srinivasan  _et al._ (2010), particularly for the mirror
actuators. The replacement of standard high-finesse mirrors by fiber mirrors
has already reduced the physical cavity volume significantly Hunger  _et al._
(2010); Takahashi  _et al._ (2017); however, when commercial nanopositioning
stages are used, they place significant space demands on the in-vacuum
assembly. Here, we propose and investigate a novel design for a MEMS-based
fiber-cavity system integrated with a surface ion trap. The fiber system is
studied by analyzing the mechanical stability, resonances, and stroke.
Furthermore, we calculate the trapping potential seen by the ions in order to
discuss the prospects for strong ion-cavity coupling.

Figure 1:  (a) Overview of our design for a MEMS-based fiber cavity integrated
with a surface ion trap. The central piece is the trapping chip, and the
structures on both sides correspond to the fiber cavity system. (b) Zoomed-in
view of the ion trapping site. (c) Electrode configuration of the chip, in
which the RF rails, outer DC electrodes, and inner DC rails are indicated.
Confinement along the cavity axis is achieved by voltages on the outer DC
electrodes, marked by blue boxes. The red dot in the center indicates the
ions’ position. The gap between neighboring electrodes is 8 $\mu$m. (d)
Detailed view of the fiber stage and actuators. A set of actuators control the
position of the stage in three dimensions via beams. A fiber will be glued
onto the V-shaped fiber bench.  Figure 2:  Fiber stage and stability analysis.
(a) Schematic of the fiber stage with the fiber installed on the fiber bench.
A second supporting stage can be used to relieve the load of the primary fiber
stage. Inset: Plug-and-socket structures define the position of the bench with
respect to the stage. (b) Equilibrium position of the stage, which is slightly
shifted down due to gravity (fiber not shown). The gray dotted circles
indicate the position of the minimum FOS in the whole structure. (c) Vertical
displacement (“D” in (b)) as a function of beam width w, indicated in the
inset. The beam thickness t, also indicated, is fixed at 20 $\mu$m for all
simulations in this paper. (d) Factor of safety as a function of beam width.

##  II Basic concept

The main structure consists of a surface ion trap integrated with a MEMS-based
fiber cavity system (Fig. 1(a)). The starting point is a microfabricated chip,
detailed views of which are found in Figs. 1(b) and (c), and which has
previously been described in Ref. Cho  _et al._ (2015). The chip has a linear
Paul trap configuration in which two radio-frequency (RF) rails are used to
generate a pseudopotential tube along the $y$ axis. Axial confinement of ions
is achieved by applying voltages to outer DC electrodes. The axis of the ion
string is designed to align with that of the cavity such that multiple ions
can be coupled to the cavity mode. Two inner DC rails define the principal
axes of the trapping potential to ensure that the $k$-vector of the Doppler
cooling laser has overlap with all axes. The ion height above the trap surface
may be controlled by adding RF voltages to the inner DC electrodes Boldin  _et
al._ (2018). Between the two inner DC electrodes, a slot allows for optical
access to the ions from beneath the chip.

A cavity is formed by two fiber mirrors Hunger  _et al._ (2010), each
supported by a MEMS-based fiber stage, for which actuators offer three-
dimensional position control, as shown in Figs. 1(a) and (d). A closer view of
the stage is shown in Fig. 2(a). A V-shaped bench holding a fiber is fixed to
each fiber stage, while the stage itself is suspended by thin beams, the other
ends of which are connected to the surrounding actuators. Position control of
the fiber stage is based on the mechanism of electrostatic actuation Tang  _et
al._ (1989); Legtenberg  _et al._ (1996); Gollasch  _et al._ (2005): As
described in detail in Sec. iii@, a comb drive actuator provides continuous
motion in the $xy$ plane. The fiber stage can be moved along the $z$ axis via
the electrostatic force between the stage and the fixed plate below. Such
continuous positioning is intended to enable us to compensate for misalignment
between the fiber mirrors, to align the cavity mode to the ion position, and
to scan or lock the cavity frequency. The trapping chip and the fiber stages
are fixed together using a common base plate with position-defining grooves.
The fiber stages and trapping chip are glued individually to the base plate.

Figure 3:  (a) A single cell of the comb drive, with the thickness of the
fingers $h$, the length of the gap between the two parts perpendicular to the
displacement axis $d$, the displacement $x$, and the overlappling length
between the two parts along the displacement to the displacement axis without
a voltage difference $x_{0}$. A voltage difference between the two parts
changes their relative distance via the electrostatic force. (b) Top view of
the fiber stage (center) with the plug-and-socket structure indicated. The
stage is suspended from the comb drive via two beams on each side. Both “Left”
and “Right” comb drives move the stage along the $x$ axis, and the comb drives
denoted as “Up” and “Down” are used for the positioning along the $y$ axis.
(c) Closer view of the “Up” comb structure. (d) Closer view of the blue box in
(c). (e) Exaggerated displacement along the $y$ axis. The beams in the
direction orthogonal to the movement are deflected. (f) The stage displacement
along the $y$ axis is calculated as a function of the driving voltage for beam
widths of 4 $\mu$m (black squares), 5 $\mu$m (red circles), 6 $\mu$m (blue
triangles), and 8 $\mu$m (magenta diamonds). The solid lines are obtained by
fitting with a quadratic function.

##  III Fiber stage and actuator

###  III.1 Mechanical stability

The mechanical stability of the fiber stage is investigated to check whether
the stage can provide a safe support Tang  _et al._ (1992). All numerical
simulations for investigating mechanical properties are performed with COMSOL
Multiphysics. We consider a fiber of SiO2 with diameter 250 $\mu$m glued on
the fiber bench. The bench, the fiber stage, and the actuators are made of Si
Diem  _et al._ (1995); Renard (2000); Kim  _et al._ (2004); Lee  _et al._
(1999). The load for the stage is conservatively estimated as 1.8 mg,
including the fiber MEM . The mass and volume of the glue are neglected
Goettsche  _et al._ (2007). First, we numerically model the influence of the
weight on the vertical stage position, with the results shown in Figs. 2(b)
and (c). The load slightly shifts down the stage level due to gravity: The
level of the stage descends by 0.97 $\mu$m for a beam width of 5 $\mu$m. The
beams correspond to the dark brown bridges indicated in Fig. 1(d). Each
$xy$-actuator possesses 40 beams so that one fiber stage is controlled through
160 beams. For the calculations in Figs. 2(c) and (d), the width of all 160
beams is changed. Second, the factor of safety (FOS) is calculated. The FOS is
defined as the yield stress divided by the working stress and has been
commonly used to evaluate the mechanical stability of structures Miller  _et
al._ (2010). A system is considered to be a stable structure if the FOS is
larger than 3. In our system, the FOS is minimized at the position of the
largest curvature within the beams directly connected to the fiber stage (gray
dotted circles in Fig. 2(b)). In Fig. 2(d), we plot the minimum FOS as a
function of the beam width. The obtained FOS values for several beam widths
indicate that the stage is stable enough to support the fiber. Note that a
fiber feedthrough will be used to bring the fiber into the vacuum chamber in
which the system will be mounted. Tension between the fiber and the fiber
feedthrough will exert an additional mechanical stress. This stress can be
relieved by careful positioning of the fiber stage or by inserting a strain-
relieving stage, for instance, a piezoelectric element, between the fiber and
the feedthrough.

Figure 4:  The actuator for movement along the $z$ axis. (a), (b) Views of the
fiber stage (yellow) and the fixed plate underneath (grey). The thickness of
the stage and the gap between the stage and the plate are both 30 $\mu$m
(white arrows in (b)). A voltage difference between the stage and plate
displaces the stage along the $z$ axis via the electrostatic force. (c) Stage
displacement along the $z$ axis as a function of the voltage difference for a
beam width of 4 $\mu$m (black squares), 6 $\mu$m (red circles), and 8 $\mu$m
(blue triangles). The solid lines are fit to quadratic functions for
comparison. The fitting range is from 0 V to the vertical black dashed line
for 4 $\mu$m, red dotted line for 6 $\mu$m, and blue dotted dashed line for 8
$\mu$m, for which V2 scaling holds.

###  III.2 Positioning in three dimensions

We control the position of the stage in the $x$ and $y$ directions with comb-
drive actuators using the electrostatic force Legtenberg  _et al._ (1996); Liu
_et al._ (2007); Maroufi and Moheimani (2016). Two- and three-dimensional
comb-drive actuators have been demonstrated in various systems such as
microgrippers, atomic force microscopes, and scanning tunneling microscopes
Indermühle  _et al._ (1995); Kim  _et al._ (1992); Ando (2004); Maroufi  _et
al._ (2017). A single unit of the comb drive is shown in Fig. 3(a) to describe
the working principle. The comb drive has two parts: a moving part and a
stationary part. The capacitance between the two parts is given by

$C(x)=\frac{2N\epsilon_{0}h}{d}(x+x_{0}),$ (1)

where $x$ is the displacement, $x_{0}$ is the overlapping length between the
two parts along the displacement axis without a voltage difference, $N$ is the
total number of the comb units, $h$ is the thickness of the fingers,
$\epsilon_{0}$ is the dielectric constant of the vacuum, and $d$ is the length
of the gap between the two parts perpendicular to the displacement axis. If a
voltage difference $V$ is applied between the two parts, the exerted force can
be expressed as

$F=\frac{1}{2}\frac{\partial C}{\partial
x}V^{2}=\frac{N\epsilon_{0}h}{d}V^{2},$ (2)

i.e., the force is proportional to the change of the capacitance between two
comb fingers. Here we assume that $x_{0}$ is large enough that side effects
like a fringe field can be neglected. This force results in a displacement of
the moving part of

$x=\frac{N\epsilon_{0}h}{kd}V^{2},$ (3)

with the spring constant $k$ of the structure.

Our comb-drive configuration is shown in Figs. 3(b)-(e). The comb drives
indicated as Up and Down in Fig. 3(b) induce motion along the $x$ axis, and
the drives indicated as Left and Right induce $y$-axis motion. Each comb drive
has 120 teeth, such that in total the force of 240 teeth drives the motion
along a given axis. As visualized in Fig. 3(b), if the position of a moving
part is shifted, the force is transmitted between the comb drive and the fiber
stage via beams on each side. Note that the beams in the transverse directions
are deflected by this motion. Fig. 3(f) shows the simulation result of the
stroke as a function of driving voltage for three different values of beam
widths. As the width decreases, the beam becomes more elastic, which
corresponds to a decreasing spring constant $k$. Hence, for a given voltage,
the displacement is larger if the beam is thinner. As expected from Eq. 3,
this displacement follows a quadratic scaling with respect to the driving
voltage. One main benefit of MEMS actuators as compared to piezoelectric
actuators consists in the larger stroke. In our case, for a beam width of 4
$\mu$m, we can cover one free spectral range of the fiber cavity (about 400
nm) with only 20 V. We also check the mechanical stability for the
displacement along the $x$ and $y$ axes. As the displacement increases, the
working stress to the actuator also increases, resulting in the reduction of
the FOS. Our calculated FOS values at a maximum applied voltage of 300 V
correspond to 13, 21, 32, and 61 for beam widths of 4, 5, 6, and 8 $\mu$m,
respectively, showing that our actuator is stable under the maximum
displacement.

Figure 5:  Simulated mechanical modes of the fiber stage for a beam width of 8
$\mu$m, ordered by ascending frequency. The resonance frequencies without and
with fibers are calculated as: (a) 985 Hz and 633 Hz; (b) 1.53 kHz and 952 Hz;
(c) 1.62 kHz and 963 Hz; (d) 3.37 kHz and 2.15 kHz; (e) 3.58 kHz and 2.82 kHz;
(f) 7.27 kHz and 4.87 kHz.  Figure 6: Simulated trapping potential profiles
for a cavity of length 1 mm comprised of uncharged and uncoated fiber mirrors.
The black lines are the results of calculations, and the red lines are
obtained by fitting the data with quadratic functions. The fitting is done for
the data between two vertical lines. The profile is shown along $(x,0,0)$ in
(a), $(0,y,0)$ in (b), and $(0,0,z)$ in (c). The origin is the center of the
trapping chip surface.

The position of the fiber stage along the $z$ axis is controlled with the
electrostatic force between the stage and another plate fixed below (see Figs.
4(a) and (b)). This actuator for the $z$ axis also makes use of a position-
dependent capacitance. In Fig. 4(c), the simulation result shows the vertical
displacement with respect to the driving voltage for three beam widths. It is
notable that here, too, we obtain large strokes: For a beam width of 4 $\mu$m,
the stage is displaced by 5 $\mu$m with an applied voltage of 160 V. The main
difference from the comb drive is that when a voltage is applied, both the
force and the distance between two plates change simultaneously: The distance
$d$ in Eq. 2 is also a function of $V$, resulting in a deviation from the
$V^{2}$ scaling (Fig. 4(c)). To check the mechanical stability, the FOS is
calculated at the maximum applied voltage for each beam width. For beam widths
of 4, 6, and 8 $\mu$m, we obtain FOS values of 81, 95, and 99 while voltage
differences of 180, 210, and 240 V are applied for each width. These
calculation results demonstrate the safety of the $z$-axis motion. More
complicated movements could be controlled by segmenting the electrodes on the
lower plate. Separately applied voltages on these electrode segments would
apply torque to the fiber stage, enabling rolling or pitching motion.

###  III.3 Mechanical resonances

The mechanical modes of the fiber stage and their resonance frequencies are
calculated to estimate the mechanical bandwidth. For stabilizing the cavity
frequency, it is desirable to achieve high mechanical bandwidth since it
determines the maximum noise frequencies that can be suppressed Briles  _et
al._ (2010). This bandwidth is typically limited by the mechanical resonances
of the actuator: Phase shifts close to the resonance, accompanied by an
amplitude response, would cause instabilities in the frequency stabilization
Gallego  _et al._ (2016). Our simulation results are shown in Fig. 5 for a
beam width of 8 $\mu$m. We find the lowest mechanical frequency of the stage
at 985 Hz without the fiber (Fig. 5(a)) and investigated the six lowest
mechanical resonances up to 7.27 kHz. With the fiber on top, the resonance
frequency decreases due to the mass of the fiber with the lowest frequency at
633 Hz and the sixth at 4.87 kHz.

The mechanical resonance frequencies of our system are higher than those of
commercially available stages but lower than those of recently reported fiber-
cavity transducers Brachmann  _et al._ (2016); Gallego  _et al._ (2016);
Janitz  _et al._ (2017). If the resonances of our actuator are problematic for
locking the cavity frequency in a future experiment, three methods can be used
to improve the performance of the cavity lock: The first method consists of
applying a feedback signal to the piezo transducer of the optional secondary
mount (Fig. 2(a)), which would extend the bandwidth to the standard level of
the piezoactuators of several kHz. Another approach is to utilize the
photothermal effect, using which a locking bandwidth of 400 kHz has been
demonstrated in a fiber cavity setting Brachmann  _et al._ (2016). Finally,
the phase lag in the vicinity of the resonance can be electronically
compensated through digital filtering systems Ryou and Simon (2018).

##  IV Trapping potentials

Next, we investigate the trapping potential for the ions. The total potential
$\phi(\bm{r})_{\rm{total}}$ is given by the sum of the pseudopotential
generated by an RF voltage applied to the RF rails and the static potential
$\phi(\bm{r})_{\rm{DC}}$ derived from voltages on the outer DC electrodes and
from charges on the fibers:

$\phi(\bm{r})_{\rm{total}}=\frac{q}{4m\Omega^{2}}|\vec{E}(\bm{r})|^{2}+\phi(\bm{r})_{\rm{DC}},$
(4)

where $q$ and $m$ indicate the charge and mass of a single ion, respectively.
The driving RF frequency is chosen to be $\Omega=20$ MHz, and
$\vec{E}(\bm{r})$ refers to the electric field due to the RF voltage. The
calculation is done for 171Yb+ ions using COMSOL Multiphysics. The RF
amplitude is fixed at 150 V for all simulations of the trapping potentials,
and DC voltage values for each simulation are given in MEM .

We characterize the trapping potential using two parameters: trap depth and
trap frequency. The trap depth is defined as the potential difference between
the minimum (at the trapping site) and the first local maximum of the profile
along the $x$, $y$, and $z$ axes. The trap frequency along each axis is
obtained by fitting the potential with a quadratic function. In order to
exclude anharmonic regions of the potential profile, the fitting range is
limited to $\pm 70$ $\mu$m along the $x$ axis, to $\pm 100$ $\mu$m along the
$y$ axis, and from -18 $\mu$m to +6 $\mu$m along the $z$ axis. Here, the
trapping potential is calculated for three cases: (1) uncharged and uncoated
fiber, (2) uncharged fiber with metal coating on the sidewall, and (3) charged
fiber with metal coating.

###  IV.1 Influence of fiber dielectrics

We begin with how the dielectric surface and volume of the fiber mirrors
affects the trapping potential, assuming that the fibers are uncoated and have
a neutral charge. In Fig. 6, trapping potential profiles are presented along
the $x$, $y$, and $z$ axes for a cavity length of 1 mm. The trap frequencies
obtained from fits to quadratic functions are
$(\omega_{x},\omega_{y},\omega_{z})/2\pi=(3.0,1.1,2.4)$ MHz MEM . The
deviation of each profile with respect to that of a harmonic potential is
below $<5\%$ for $|x|<86~{}\mu$m, $|y|<180~{}\mu$m, and
$-22~{}\mu$m$<z<5~{}\mu$m. The trap depth is $0.71$ eV, $0.46$ eV, and $0.33$
eV in each direction. Figs. 7(a)-(b) show the ion height above the trap and
the trap frequency as a function of the cavity length. The trapping potentials
are obtained in a step of 50 $\mu$m for a cavity length from 400 $\mu$m to
2000 $\mu$m. The height of the fibers’ centers is fixed at 169 $\mu$m,
overlapping with the height of the ion above the trap in the absence of the
fibers. As the fibers are brought closer to the trapping site in our
simulations, we find that the fibers have only a small influence on the
potential for cavity lengths up to 500 $\mu$m. For this cavity length, we
obtain trap frequencies of $(3.0,1.0,2.5)$ MHz and find that the ion height is
unchanged. Therefore, if charges are absent from the fibers or can be removed
by a discharging method Pollack  _et al._ (2010), this bare fiber becomes an
option to make a short cavity offering strong ion-cavity coupling (see Sec.
v@).

###  IV.2 Influence of metal coating

We consider a situation in which the fibers’ sidewalls are coated with a thin
metal film, as has been used to provide an ultra-high-vacuum-compatible
coating in fiber-cavity experiments with neutral atoms and trapped ions
Colombe  _et al._ (2007); Hunger  _et al._ (2010); Steiner  _et al._ (2014);
Podoliak  _et al._ (2016). This coating has two additional roles, along with
protecting the fiber: The area of dielectric surface exposed to the ion is
reduced, and a voltage can be applied to the fiber coating to compensate for
distortion caused by charges on the dielectrics. In Figs. 7(c)-(d), the
simulation result is shown for a grounded metal coating and uncharged fiber
facets. As the fibers are brought closer to the trap center, the height above
the trap surface at which the potential minimum occurs goes down, and the trap
frequency increases. This behavior can be interpreted by considering grounded
metal boundaries approaching the trapping site from far away in all
directions. The potential energy becomes more confined as the metal structures
come closer, leading to higher trap frequencies for shorter cavities. The
effect is spatially symmetric along the $x$ and $y$ axes; however, the
trapping chip makes it asymmetric along the $z$ axis. In that case, one can
consider a ground metal boundary approaching from above and shifting down the
position of the ion height.

The fiber height is fixed at 138 $\mu$m for all cavity lengths so that it
coincides with the height of a trapped ion for a 500 $\mu$m long cavity. This
height is found in the following way: Fixing the cavity length at 500 $\mu$m,
the trapping potential is calculated for fiber heights from 169 $\mu$m to 130
$\mu$m with a step of 1 $\mu$m, so that we find out the fiber height that
corresponds to the ion height. Our calculation shows that the trapping
potential for a 500 $\mu$m long cavity has frequencies of $(4.8,1.3,4.1)$ MHz,
and the most shallow trap depth is 0.29 eV in the $+z$ direction. Note that
the RF contribution to the potential along the $y$ axis is negligible with
bare fibers. In contrast, here the contribution of the RF psuedopotential is
nonnegligible along the $y$ axis since the metal coating plays a role in
determining the $y$-axis boundary conditions. This contribution would not
affect micromotion compensation for a single ion but would make compensation
difficult for a long ion string.

Figure 7:  Trapping potential simulations for cavity lengths from 300 $\mu$m
to 2.0 mm. Ion height above the trap surface and trap frequency are plotted as
a function of the cavity length for uncharged and uncoated fibers in (a) and
(b), uncharged and metal-coated fibers in (c) and (d), and charged and metal-
coated fibers in (e) and (f). The vertical navy lines indicate a cavity length
of 500 $\mu$m, at which the strong ion-cavity coupling condition can hold (see
Sec. v@). In (a), (c), and (e), the horizontal red line indicates the height
of the fiber center, which has been chosen to overlap with the height of an
ion for a cavity length of 500 $\mu$m.

###  IV.3 Influence of charges

Next, we investigate the influence of fiber charges on the trapping potential.
As in Sec. IV.2, we assume that the fiber sidewalls are metal coated. Here, we
make the additional assumption that both fiber facets are positively charged
with a surface density of 5 $q/\mu$m2. This assumption is based on a
measurement in our ion-fiber cavity setting at the University of Innsbruck:
Approaching a fiber to single ions for ion-fiber distances from 1.6 mm to 200
$\mu$m, we measured the ions’ positions and trap frequencies, affected by the
charges on the fibers, as a function of the ion-fiber distance. Reconstruction
of the charge densities shows that the fibers are positively charged with
densities of on the order of several elementary charges in an area of 1
$\mu$m2 Ong  _et al._ (2019). In the current simulation, we choose the charge
density of 5 $q/\mu$m2 that is very close to a median of the reconstructed
densities. The simulation result is shown in Figs. 7(e)-(f). The ion heights
are similar to those found with an uncharged metal coating, and the fiber
height is also fixed here at 138 $\mu$m. A notable feature is the rapid
increase of the trap frequency along the $y$ axis as the fibers are brought
close to the trap center. This increase is because the positive charging make
the potential steeper along the $y$ axis; negative surface charges would
induce the opposite effect. The trapping potential for a 500 $\mu$m long
cavity is found to have frequencies of $(4.4,2.7,3.8)$ MHz. The most shallow
trap depth is 0.13 eV along the $+z$ direction.

We would anticipate problems if the number of charges were slowly and randomly
varying, as this would result in a time-dependent potential seen by the ion.
We have previously observed timescales of such drifts to be from hours to days
Ong  _et al._ (2019). This problem could be solved either by employing a
discharging method Pollack  _et al._ (2010) or by applying compensation
voltages to the metal coating. As long as the trap frequency can be monitored
on time scales faster than those of the charge drifts, a feedback voltage can
be applied to the metal coating to stabilize the trap frequency.

Figure 8:  (a) Calculated values for $g$ (black) and $\kappa$ (red) are
plotted with with the atomic linewidth $\gamma$ (blue) for the 174Yb+
$|^{2}D_{3/2}\rangle$–$|^{3}D[3/2]_{1/2}\rangle$ transition at 935 nm. (b) The
same parameters are shown for the 174Yb+
$|^{2}S_{1/2}\rangle$–$|^{2}P_{1/2}\rangle$ transition at 369 nm, and (c) for
the 40Ca+ $|^{2}D_{5/2}\rangle$–$|^{2}P_{3/2}\rangle$ transition at 854 nm.
The color legends of (b) and (c) are identical to that of (a). The dashed
vertical lines indicate a cavity length of 500 $\mu$m, of particular relevance
for our design (see text for details).

##  V Strong ion-cavity coupling

Strong atom-cavity coupling means that the atom-cavity coupling constant $g$,
i.e., half of the coherent energy exchange rate between the atom and the
cavity field, is larger than both the atomic decay rate $\gamma$ and the
cavity field decay rate $\kappa$ Kimble (1998). The hallmark of strong atom-
cavity coupling is the vacuum Rabi splitting, which originates from new atom-
cavity eigenstates formed by the coupling Haroche and Raimond (2006). This
effect offers capabilities for exploring fundamental quantum optics Mabuchi
and Doherty (2002) and implementing quantum network protocols Reiserer and
Rempe (2015). Furthermore, if strong coupling can be achieved, then by
choosing a different cavity geometry, one also has access to the Purcell
regime, in which $\kappa\gg g^{2}/\kappa\gg\gamma$ Law and Kimble (1997);
Reiserer and Rempe (2015). The Purcell regime enables efficient single-photon
sources, a key ingredient for constructing a modular ion-based quantum
computer architecture Monroe  _et al._ (2014); Kim  _et al._ (2011); Hucul
_et al._ (2014).

In order to check whether strong ion-cavity coupling can be achieved with our
design, we first plot calculated values of $g$ and $\kappa$ in Fig. 8(a), with
$\gamma$ given by the 174Yb+ $|^{2}D_{3/2}\rangle$–$|^{3}D[3/2]_{1/2}\rangle$
transition at 935 nm. The radii of curvature of both fiber mirrors are fixed
at 350 $\mu$m and the effective diameter, i.e., the diameter that is used to
form a cavity mode, at 100 $\mu$m Ott  _et al._ (2016). We assume a value of
97,000 for the cavity finesse, as reported in Ref. Ott  _et al._ (2016) for a
recent fiber-cavity experiment. The finesse is a measure of the mirror losses
and, together with the cavity length, allows $\kappa$ to be determined. For a
cavity length of 500 $\mu$m, the calculation results in
$(g,\kappa,\gamma)/2\pi=(3.0,1.0,1.5)$ MHz, proving that the strong coupling
condition can be satisfied for a length on which we have focused in the
trapping potential calculations.

In Fig. 8(b), we consider the 174Yb+
$|^{2}S_{1/2}\rangle$–$|^{2}P_{1/2}\rangle$ transition at 369 nm. The only
different assumption here is a lower cavity finesse of 10,000, as reported in
Ref. Cetina  _et al._ (2013) and attributed to oxygen depletion in the mirror
coating Cetina  _et al._ (2013); Gangloff  _et al._ (2015b); Ballance  _et
al._ (2017). For a cavity length of 500 $\mu$m, we find that the strong
coupling condition still holds, with $(g,\kappa,\gamma)/2\pi=(46,25,9.9)$ MHz.
Note that while the 935 nm transition is more suitable for optical
interconnects due to the lower absorption in optical fiber at this wavelength,
the 369 nm transition enables significantly higher cavity coupling rates.

Finally, in Fig. 8(c), we investigate the 40Ca+
$|^{2}D_{5/2}\rangle$–$|^{2}P_{3/2}\rangle$ transition at 854 nm. Assuming the
same finesse, radii of curvature, and effective diameter as in the calculation
shown in Fig. 8(a), we obtain $g/2\pi=18$ MHz, which is greater than both
$\kappa/2\pi=1.5$ MHz and $\gamma/2\pi=11.5$ MHz at a cavity length of 500
$\mu$m. Taken together, the calculation results shown in Fig. 8 verify that
our design can provide strong coupling for the transitions used in recent ion-
fiber cavity experiments Cetina  _et al._ (2013); Steiner  _et al._ (2013,
2014); Ballance  _et al._ (2017); Takahashi  _et al._ (2017, 2018). Although
the simulations of our ion trap design described in the previous sections were
carried out for 174Yb+ ions, it would be straightforward to adapt them for
40Ca+ ions.

##  VI Discussion

As presented thus far, our miniaturized ion-cavity setting exhibits safe
fiber-mirror support with a large stroke, a stable ion trapping potential, and
feasible strong ion-cavity coupling. Moreover, our approach of combining a
segmented ion trap with a cavity provides an additional advantage for
optimizing alignment of the positions of multiple ions to the cavity field.
Suppose that multiple ions are coupled to a cavity for a geometry in which the
trap axis and the cavity axis are parallel to one another, as for example in
Ref. Cetina  _et al._ (2013). Such a system would be useful for an efficient
quantum network node based on collective interactions Lamata  _et al._ (2011).
One technical challenge in realizing this ion-cavity system consists of the
incommensurability between the ion–ion distances and the spatial period of the
cavity standing wave. While the ion–ion distances are determined by the
harmonic potential and the repulsive Coulomb interaction between the ions, the
cavity-field period corresponds to one half of the resonant wavelength.
Therefore, the strength of the coupling of each ion to the cavity field will
be different, resulting in a reduced collective coupling rate as compared to
the case in which each ion is coupled to an antinode of the cavity standing
wave.

With our segmented trap design, through a particular choice of electrode
voltages, it is possible to create a periodic trapping potential such that
ions are equally spaced along the cavity axis, in order to couple each ion
with an individual antinode of the cavity standing wave Home and Steane
(2006). The number of possible potential wells increases as one makes use of
more segmented electrodes. Alternatively, a box-like quartic potential can be
engineered by adjustment of the electrode voltages Lin  _et al._ (2009). Here
the ion–ion distance is predominantly determined by the repulsive Coulomb
interaction, which aligns the ions equidistantly. Note that in a recent
demonstration, up to five ions were positioned near cavity field antinodes
based on visibility measurements as a function of trap frequency Begley  _et
al._ (2016). This method, however, would be difficult to extend for
controlling the positions of arbitrary numbers of ions.

In order to scale the ion-cavity system down even further, the surrounding
elements of the setup can be also miniaturized Kim and Kim (2009), drawing on
the technologies of microfabrication and MEMS in order to precisely integrate
optical elements, photodetectors, and parts of the control electronics. There
have been extensive experimental efforts to combine optical elements with
surface traps at the micro- or nanometer scale Merrill  _et al._ (2011);
Herskind  _et al._ (2011); Rynbach  _et al._ (2017). For example, optical
fibers VanDevender  _et al._ (2010), micromirrors, and a photodetector have
been integrated to collect the ion fluorescence Eltony  _et al._ (2013); Clark
_et al._ (2014), MEMS mirrors have been used to address individual ions
Knoernschild  _et al._ (2009); Crain  _et al._ (2014), and more advanced
optical elements like diffractive optics have also been integrated on a
nanometer scale Young  _et al._ (2014); Mehta  _et al._ (2016).

##  VII Conclusion

We have proposed and investigated a novel design for MEMS-based manipulation
of a fiber cavity integrated with a surface ion trap. The fiber stages are
shown to be mechanically stable to support the fiber mirrors. The stages move
continuously in three dimensions with strokes up to tens of micrometers. The
mechanical resonance frequencies of the stage and actuator are found to be on
the order of kHz. Furthermore, we calculate a stable trapping potential
generated for a 500 $\mu$m long cavity, which should allow us to achieve
strong ion-cavity coupling. This design for an on-chip ion-cavity system
constitutes a promising approach for constructing a scalable quantum network.

## Acknowledgments

This work has been financially supported by the Austrian Science Fund (FWF)
through Projects F4019-N23, V252, and M1964; by the U.S. Army Research
Laboratory’s Center for Distributed Quantum Information via the project
SciNet: Scalable Ion-Trap Quantum Network, Cooperative Agreement No.
W911NF15-2-0060; by the Innsbruck-Seoul ION Trap Project; and by the Ministry
of Science and ICT (MSIT), Korea, under the Information Technology Research
Center (ITRC) support program (IITP-2019-2015-0-00385), supervised by the
Institute for Information & Communications Technology Promotion (IITP).

## Open data

Our data are available at https://doi.org/10.5281/zenodo.3697922.

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Supplemental Material

## Mass of the fiber stage

Information on the materials and densities used for the fibers and stages is
given in Table 1, and information on the masses is given in Table 2. We assume
that the part of the fiber that the stage has to support has a length of 1 cm,
where we would install an additional stage for relieving a mechanical strain
to the main fiber stage or applying an additional feedback voltage to
stabilize the cavity frequency. The mass of glue is neglected Goettsche  _et
al._ (2007).

## Details of the trapping potential calculation

### Simulation parameters

The parameters common to all simulations are an RF driving frequency of 20 MHz
with an amplitude of 150 V, grounded inner DC electrodes, and a dielectric
constant of the fiber (SiO2) of 3.8. The parameters that are varied are given
in Table 3. Regarding the voltages applied to the outer DC electrodes (Fig.
S1), voltage $V_{\rm{A}}+V_{\rm{offset}}$ is applied to electrodes A and
voltage $V_{\rm{B}}+V_{\rm{offset}}$ to electrodes B. The difference
$V_{\rm{A}}-V_{\rm{B}}$ determines the trap depth in the $y$ direction, and
the offset voltage $V_{\rm{offset}}$ shifts the minimum of the DC potential in
the $z$ direction and is chosen so that the minimum of the DC potential
overlaps with that of the pseudopotential.

Figure S1:  The electrode configuration of the trapping chip. The voltage
$V_{\rm{A}}+V_{\rm{offset}}$ is applied to the outer DC electrodes A and the
voltage $V_{\rm{B}}+V_{\rm{offset}}$ to electrodes B. RF indicates the RF
rail, and GND denotes ground. The red dot in the center indicates the ion
position. The voltage $V_{\rm{A}}+V_{\rm{offset}}$ is applied to the outer DC
electrodes A and the voltage $V_{\rm{B}}+V_{\rm{offset}}$ to electrodes B. RF
indicates the RF rail, and GND denotes ground. The red dot in the center
indicates the ion position.

### Micromotion compensation

It is possible to compensate micromotion of the ions via tuning the voltages
applied to the outer DC electrodes (Fig. S2(a)). For example, in order to
shift the ion position in the $+x$ direction, the voltage applied to the DC
electrodes marked with blue solid lines has to be changed by $\Delta U_{x}$
while the voltage applied to the electrodes marked with dashed blue lines is
changed by $-\Delta U_{x}$. Similarly, shifting the ion in the $+y$ direction
by an amount $\Delta y$ requires voltage changes of $+\Delta U_{y}$ and
$-\Delta U_{y}$ on the electrodes marked by solid and dashed yellow lines,
respectively. The ion position moves along the $+z$ direction by applying
$+\Delta U_{z}$ to all outer DC electrodes. The simulation result, displayed
in Fig. S2(b), shows that the ion position can be displaced by a few microns
in each direction with voltage changes of only a few volts. This is expected
to be sufficient to bring the ions to the RF-null point for typical DC
background fields.

Figure S2:  Micromotion compensation. (a) The outer DC electrodes in the blue
boxes are used for compensation along the $x$ axis, and the electrodes in the
yellow boxes are used for compensation along the $y$ axis. The red dot in the
center denotes the ion position. (b) Simulation results. The ion displacement
along both axes is plotted as a function of the applied compensation voltages
$\Delta U_{x}$ and $\Delta U_{y}$ (see text for definition). The $x$
displacement is shown in black and the $y$ displacement in red. (a) The outer
DC electrodes in the blue boxes are used for compensation along the $x$ axis,
and the electrodes in the yellow boxes are used for compensation along the $y$
axis. The red dot in the center denotes the ion position. (b) Simulation
results. The ion displacement along both axes is plotted as a function of the
applied compensation voltages $\Delta U_{x},\Delta U_{y},$ and $\Delta U_{z}$
(see text for definition). The $x$ displacement is shown in black, the $y$
displacement in red, and the $z$ displacement in blue.

## Fabrication strategy

The fabrication process of the MEMS-based fiber stage and actuator Tang  _et
al._ (1989); Liu  _et al._ (2007); Maroufi and Moheimani (2016) is shown in
Fig. S3. The comb drive arrangement with its plug-and-socket structure is
patterned on a silicon-on-insulator (SOI) wafer with a photoresist (PR) method
Diem  _et al._ (1995); Renard (2000). The patterned structure is fabricated
with the technique of silicon deep reactive ion etching (DRIE). In parallel
with this process, the V-shaped fiber bench is prepared in the following way.
The V-groove is shaped with PR patterning and silicon wet etching. The fiber
bench is diced out afterwards with the correct dimension, followed by PR
pattering and DRIE for the plug-and-socket structure on the backside. Next,
these two parts, the comb drive and the fiber bench, are plugged and glued.
Note that the plug-and-socket structure defines the position with a precision
of few micrometers. After this assembly, SiO2 wet etching follows to complete
the development of the fiber stage Kim  _et al._ (2004). The fiber stage
structure can also be fabricated by the surface/bulk micromachining process
Lee  _et al._ (1999).

Figure S3:  Fabrication process of the fiber bench, stage, and actuator.  |  | Material |  | Density (g/cm3)
---|---|---|---|---
Fiber |  | SiO2 |  | 2.65
Fiber stage |  | Si |  | 2.57
Actuator |  | Si |  | 2.57
Table 1: The materials and densities of the dielectrics used in the simulations of mechanical properties. |  | Mass ($\mu$g)
---|---|---
Fiber stage |  | 235
…with bench |  | 806
…with bench and fiber |  | 1806
Table 2: Estimated mass of the fiber stage elements used in the simulations of mechanical properties. |  |  $V_{\textrm{A}}$ (V) |  |  $V_{\textrm{B}}$ (V) |  |  $V_{\textrm{offset}}$ (V)
---|---|---|---|---|---|---
Uncharged and uncoated |  | 24.3 |  | -65.7 |  | 0.0
Uncharged and coated |  | 26.6 |  | -63.5 |  | 0.0
Charged and coated |  | 19.4 |  | -70.7 |  | Varied from -24 to +3 V for each cavity length
Table 3: RF amplitudes and DC voltages used in the simulations of the trapping
potential in Sec. iv@ of the main text. “(Un)charged” refers to the charge
state of the dielectric fiber facets, and “(un)coated” refers to presence or
absence of a metal coating on the fiber circumference.


Version: August 27, 2024

# Epitaxial (111) Films of Cu, Ni, and CuxNiy on $\alpha-$Al2O3(0001) for
Graphene Growth by Chemical Vapor Deposition

David L. Miller, Mark W. Keller, Justin M. Shaw  Magnetics Group,
Electromagnetics Division  Ann N. Chiaramonti, Robert R. Keller  Nanoscale
Reliability Group, Materials Reliability Division  National Institute of
Standards and Technology, Boulder, CO 80305<EMAIL_ADDRESS><EMAIL_ADDRESS>Official contribution of the National Institute of
Standards and Technology; not subject to copyright in the United States

###### Abstract

Films of (111)-textured Cu, Ni, and CuxNiy were evaluated as substrates for
chemical vapor deposition of graphene. A metal thickness of $400\,\mathrm{nm}$
to $700\,\mathrm{nm}$ was sputtered onto a substrate of $\alpha-$Al2O3(0001)
at temperatures of $250\,\mathrm{{}^{\circ}C}$ to $650\,\mathrm{{}^{\circ}C}$.
The films were then annealed at $1000\,\mathrm{{}^{\circ}C}$ in a tube
furnace. X-ray and electron backscatter diffraction measurements showed all
films have (111) texture but have grains with in-plane orientations differing
by $60^{\circ}$. The in-plane epitaxial relationship for all films was
$[110]_{\textrm{metal}}$||$[10\bar{1}0]_{\textrm{Al}{}_{2}\textrm{O}_{3}}$.
Reactive sputtering of Al in O2 before metal deposition resulted in a single
in-plane orientation over 97 % of the Ni film but had no significant effect on
the Cu grain structure. Transmission electron microscopy showed a clean
Ni/Al2O3 interface, confirmed the epitaxial relationship, and showed that
formation of the $60^{\circ}$ twin grains was associated with features on the
Al2O3 surface. Increasing total pressure and Cu vapor pressure during
annealing decreased the roughness of Cu and and CuxNiy films. Graphene grown
on the Ni(111) films was more uniform than that grown on polycrystalline
Ni/SiO2 films, but still showed thickness variations on a much smaller length
scale than the distance between grains.

##  1 Introduction

Uniform growth of graphene over wafer-scale areas is a critical enabling step
for the commercial realization of various electronic, photonic, mechanical,
and other devices based upon the superlative properties of graphene [1].
Considerable progress has been made in the growth of monolayer and few-layer
graphene by chemical vapor deposition (CVD) on transition metals, particularly
Cu and Ni [2, 3]. Typically, the metal surface is heated to
$1000\,\mathrm{{}^{\circ}C}$ and exposed to a hydrocarbon gas such as methane
that decomposes catalytically to provide a source of C atoms on the surface.
In the case of Cu, growth occurs almost entirely on the surface and is limited
to a single layer for a wide range of hydrocarbon partial pressure. In the
case of Ni, growth involves C dissolution into the film at high temperature
and then precipitation to the surface as the film cools, which can result in
both monolayer and multilayer graphene [4]. Alloys of Cu and Ni offer control
over graphene thickness by adjusting the C solubility in the film [5]. The Cu
or Ni can be etched away to transfer the graphene layer to an insulating
substrate for further device fabrication steps [6].

Commercially available polycrystalline foils of Cu and Ni are commonly used
for CVD growth of graphene because they can be annealed to have millimeter
grain sizes. The best CVD graphene films to date, in terms of graphene grain
size and carrier mobility, have been achieved on foils [7], but single crystal
films offer several advantages. First, the hexagonal symmetry and small
lattice mismatch of the (111) surface should provide a more ideal template for
graphene growth than the (100), (110), or higher index surfaces. This idea is
supported by recent experiments showing less rotational disorder in graphene
grown on Cu(111) than on Cu(100) [8, 9]. Second, films typically provide a
much smoother growth surface because foils have roughness due to the rolling
process that is not fully removed by annealing. The experiments in [9] show
how surface defects on Cu(111) can cause rotational disorder either at
nucleation or during subsequent growth of graphene islands. Third, the
diffusion of C into and out of Ni is different at grain boundaries than in the
interior of grains, so better growth control and better uniformity are
expected if grain boundaries are eliminated [10, 11]. Lastly, films are
supported by a flat, rigid substrate, helping to simplify the process of
graphene transfer to other materials. Thus we anticipate that high quality
Cu(111) and Ni(111) films will enable CVD growth of graphene having improved
properties compared to graphene grown on polycrystalline foils.

A suitable substrate for the metal films must, at a minimum, promote epitaxial
growth with (111) texture and be physically and chemically stable under
graphene CVD conditions. For wafer-scale production of graphene, the substrate
should be commercially available in wafer form at a reasonable cost. The
ability to reuse substrate wafers after metal etching to release the graphene
layer is also desirable. Currently, the material that appears to best satisfy
these requirements is $\alpha-$Al2O3(0001), which is widely used by
manufacturers of radio-frequency electronics and light-emitting diodes in the
form of wafers with diameters up to $200\,\mathrm{mm}$. Given the advantages
of single crystal Cu(111) and Ni(111) films described above, achieving such
films on Al2O3 is an important step toward commercial graphene devices.

Previous investigations of Cu deposited on $\alpha-$Al2O3(0001), mainly in
ultra-high vacuum environments, found a variety of growth behaviors depending
on how the Al2O3 surface was prepared. Kelber _et al._ [12] summarized several
earlier results, discussed them in terms of multiple Al2O3(0001) surface
terminations and multiple Cu ionization states, and emphasized the role of a
hydroxyl layer bonded to the Al2O3 surface. The last point is particularly
relevant for the work presented here. When Al2O3 is exposed to ambient air,
water decomposes to form a hydroxyl (OH) layer [13] that is difficult to
remove. While bombardment with 200 eV to 1000 eV Ar ions can remove all but
$\sim 0.1\,\mathrm{monolayer}$ of OH, annealing in O2 at temperatures $\geq
800\,\mathrm{{}^{\circ}C}$ is required to recrystallize the damaged surface
[14, 15]. In typical film deposition chambers where such treatments are not
available, an OH layer is likely present on Al2O3 substrates and may interfere
with epitaxial growth. This may be why previous Cu films deposited on
Al2O3(0001) [16, 17, 18] were not single crystals but consisted of (111)
grains having in-plane orientations differing by $60^{\circ}$. While Ni on
$\alpha-$Al2O3(0001) has not been the subject of extensive experimental
studies, the OH layer can also be expected to interfere with epitaxy in this
case. As with Cu, previous Ni films on Al2O3(0001) showed in-plane
orientations differing by $60^{\circ}$ [11].

Epitaxy and film adhesion are relevant to graphene growth for several reasons.
For Cu, which has a bulk melting point of $1084\,\mathrm{{}^{\circ}C}$,
evaporation can cause roughness or even complete loss of the Cu film [19].
Previous work on Cu [18] showed that epitaxial and highly textured films with
large grains survive graphene CVD conditions better than polycrystalline films
with small grains. Ni evaporation under growth conditions is negligible, since
the bulk melting point is $1453\,\mathrm{{}^{\circ}C}$, but Ni films can be
damaged by the annealing in H2 which typically precedes graphene growth [20].
An additional consideration for Ni is that films thinner than
$100\,\mathrm{nm}$ are desirable in order to limit the total amount of C that
is available to precipitate to the surface, since $\approx 35\,\mathrm{nm}$ of
Ni at $1000\,\mathrm{{}^{\circ}C}$ can absorb enough C to form a monolayer
[21]. Such thin Ni films, even when epitaxial and highly textured, can be
damaged by graphene CVD conditions [11]. Given the various factors summarized
here, the properties and limitations of Cu and Ni films must be considered,
alongside the kinetics and thermodynamics of graphene formation from a
hydrocarbon precursor, when optimizing a recipe for graphene growth by CVD.

This paper reports a study of sputtered Cu, Ni, and Cu/Ni films that have been
exposed to typical graphene CVD conditions. We used x-ray diffraction (XRD)
and electron backscatter diffraction (EBSD) to measure crystallinity, atomic
force microscopy (AFM) to measure surface morphology, transmission electron
microscopy (TEM) to image the metal/substrate interface, and optical
microscopy to show film properties over large areas. We also report results
for graphene growth by CVD on these films, characterized by scanning electron
microscopy (SEM) and Raman spectroscopy.

##  2 Film Preparation

Wafers of $\alpha$-Al2O3(0001) were prepared by annealing at
$1000\,\mathrm{{}^{\circ}C}$ in O2 at atmospheric pressure for 24 h to remove
scratches due to polishing and give atomically flat terraces. Chips of
$5\,\mathrm{mm}\textrm{ x }6\,\mathrm{mm}$ were cleaned by ultrasonic
agitation in acetone and isopropanol, mounted on a resistively heated Cu puck,
and placed in a cryopumped vacuum system with a base pressure below
$10^{-5}\,\mathrm{Pa}$ $(10^{-7}\,\mathrm{Torr})$. Metal films were deposited
by dc magnetron sputtering from 76 mm targets of 99.99+ % Cu or Ni in
$0.67\,\mathrm{Pa}$ $(5\,\mathrm{mTorr})$ of Ar. Sputtering powers between
$50\,\mathrm{W}$ and $200\,\mathrm{W}$, corresponding to deposition rates
calibrated using a profilometer of $0.3\,\mathrm{nm/s}$ to $1\,\mathrm{nm/s}$,
produced no significant differences in film properties. For some films, a
“seed layer” of Al2O3 was deposited immediately before the metal by reactive
sputtering from a 76 mm target of 99.999 % Al in a mixture of 40 % O2 in Ar
(both 99.999 %) at a total pressure of $0.67\,\mathrm{Pa}$
$(5\,\mathrm{mTorr})$ and a power of $50\,\mathrm{W}$. The target-to-substrate
distance in all cases was 10 cm.

The use of a reactively sputtered seed layer to improve film adhesion and
epitaxy was motivated by a desire to remove OH without using ion bombardment
and high temperature annealling. Sputtering with high O2 content causes
“resputtering” of the substrate due to bombardment by O– ions generated at the
target and accelerated across the plasma sheath [22]. This results in a low
net deposition rate, $<0.01\,\mathrm{nm/s}$ in our case, and should remove the
OH layer from the substrate. The TEM results discussed below show that the
reactive sputtering did not damage the surface. For the films reported here,
this step was done at a substrate temperature of $650\,\mathrm{{}^{\circ}C}$
to promote crystallinity, but the technique was also successful at
$500\,\mathrm{{}^{\circ}C}$.

Metal film properties were strongly influenced by the substrate temperature
during sputtering. The deposition temperature $T_{\textrm{d}}$ reported here
was measured using a thermocouple clamped to the side of the puck facing away
from the sputter gun. For fixed $T_{\textrm{d}}$ and without a seed layer, the
films did not adhere to the Al2O3 substrate above $\approx
400\,\mathrm{{}^{\circ}C}$ for Cu and $\approx 600\,\mathrm{{}^{\circ}C}$ for
Ni. Most films reported here were deposited at
$T_{\textrm{d}}=275\,\mathrm{{}^{\circ}C}$ for Cu and
$T_{\textrm{d}}=475\,\mathrm{{}^{\circ}C}$ for Ni. Cu/Ni bilayer films were
formed by depositing $50\,\mathrm{nm}$ of Ni and then $350\,\mathrm{nm}$ of
Cu. These films formed a homogeneous alloy upon annealing (see below) and we
refer to them as “Cu-Ni” in the rest of the paper. When the Al2O3 seed layer
was used, better film adhesion allowed higher $T_{\textrm{d}}$. These films
were deposited using a linear ramp of $T_{\textrm{d}}$ during deposition, from
$275\,\mathrm{{}^{\circ}C}$ to $400\,\mathrm{{}^{\circ}C}$ for Cu and from
$475\,\mathrm{{}^{\circ}C}$ to $600\,\mathrm{{}^{\circ}C}$ for Ni.

In order to evaluate survivability, the films were annealed in a hot-wall tube
furnace before characterization. The annealing conditions were similar to
those used for graphene CVD, but without the hydrocarbon precursor: duration
10 min to 15 min, temperature of $1000\,\mathrm{{}^{\circ}C}$, flowing 5 % H2
in Ar at a total pressure of $270\,\mathrm{Pa}$ to $5300\,\mathrm{Pa}$
($2\,\mathrm{Torr}$ to $40\,\mathrm{Torr}$). The temperature of the furnace
was measured using a thermocouple mounted just outside the quartz tube.

##  3 Film Characterization

The overall crystalline structure of the films without a seed layer, as
characterized by XRD using Cu $K\alpha$ radiation with a spot size of several
mm2, is shown in Fig. 1. The $\theta-2\theta$ curves in Fig. 1a, with
intensity plotted on a logarithmic scale, show a peak at $41.6{}^{\circ}$ from
the Al2O3(0001) substrate and a peak corresponding to (111) orientation of the
metal film. These peaks are located at $43.4{}^{\circ}$ for Cu,
$43.8{}^{\circ}$ for Cu-Ni, and $44.6{}^{\circ}$ for Ni. The peaks between
$90{}^{\circ}$ and $100{}^{\circ}$ are higher-order reflections, and the lack
of any other peaks indicates all films are exclusively (111) textured. The
rocking curves in Fig. 1b were fit with a gaussian function, yielding a full-
width-at-half-maximum of 0.334° for Cu, 0.533° for Cu-Ni, and 0.393° for Ni.
The single peak observed for the Cu-Ni alloy film indicates complete mixing of
the two metals during annealing. Its position corresponds to an alloy
composition of Cu70Ni30, whereas the Cu and Ni film thicknesses predict a
composition of Cu87Ni13. We attribute this difference to the preferential
evaporation of Cu during annealing.

Figure 1: Xray diffraction data for $400\,\mathrm{nm}$ films of Cu, Cu-Ni, and
Ni, deposited without Al2O3 seed layer, after annealing at
$1000\,\mathrm{{}^{\circ}C}$ and $270\,\mathrm{Pa}$ ($2\,\mathrm{Torr}$). (a)
$\theta-2\theta$ curves, plotted on a logarithmic intensity scale, show that
all films are exclusively (111) textured. (b) Rocking curves with Gaussian
fits yielding full-width-at-half-maximum of 0.334° for Cu, 0.533° for Cu-Ni,
and 0.393° for Ni. (c, d, e) (111) pole figures plotted on a logarithmic color
scale. The six innermost spots come from the substrate and the other spots
come from the metal film. The six outer spots of roughly equal intensity
indicate each film contains two families of (111) grains differing by an in-
plane rotation of $60^{\circ}$.

Figures 1c, d, and e show pole figures measured at the peak of the (111)
reflection and plotted on a logarithmic color scale. In each pole figure, the
six innermost spots come from the substrate, the other spots come from the
metal film, and the rotational alignment of the two sets of spots indicates
the film is epitaxially aligned with the substrate. The measured epitaxial
relationship for all films can be expressed as
$(111)_{\textrm{metal}}$||$(0001)_{\textrm{Al}{}_{2}\textrm{O}_{3}}$ and
$[110]_{\textrm{metal}}$||$[10\bar{1}0]_{\textrm{Al}{}_{2}\textrm{O}_{3}}$,
consistent with prior results for several fcc metals on Al2O3 [23]. For a
(111) film with a single in-plane orientation, the pole figure would show only
three spots. The six spots with similar intensity shown in Fig. 1c indicate
roughly half the Cu film is rotated in-plane by $60^{\circ}$ with respect to
the rest of the film. The second set of spots appears with lower intensity in
Figs. 1c, d, indicating that only a minority of the Cu-Ni and Ni films are
rotated by $60^{\circ}$. Comparing the integrated intensities for the two sets
of spots, we estimate the fraction of the film composed of these $60^{\circ}$
twin domains to be 50 % for Cu, 15 % for Cu-Ni, and 25 % for Ni. The Cu-Ni
film also shows faint spots in between the six stronger spots, indicating that
a small minority (< 1 %) of the film is rotated in-plane by $\pm$30°. Overall,
the XRD characterization shows that all films are (111) textured but have some
degree of in-plane rotational disorder. This is not unexpected because there
are two equivalent orientations for a cubic film deposited on a hexagonal
substrate.

Figure 2: Optical and atomic force microscopy images showing the morphology of
the same films as in Fig. 1. Top row (a, b, c) shows optical images
($50\,\mathrm{\mu m}$ scale bar, shown in (c)) and bottom row (d, e, f) shows
AFM images ($10\,\mathrm{\mu m}$ scale bar, shown in (f)) Dark spots in the
optical images indicate areas of dewetting. The Cu surface becomes rough,
while the Ni surface remains much smoother.

The morphology of the films without a seed layer is shown in Fig. 2. The Cu
film shows a rough surface in both optical and AFM images. The black spots in
the optical image are areas of the film that have dewetted from the substrate,
and these spots increase in size and density for longer annealing times. Both
the roughness and the dewetting indicate the Cu film is only marginally stable
at $1000\,\mathrm{{}^{\circ}C}$. Such instability has been noted previously
[24, 19] and can be attributed to the rapid evaporation of Cu when heated near
its bulk melting temperature in rough vacuum. This is discussed further below.
The Cu-Ni film is smoother than the Cu film and shows a lower density of
dewetting spots. The Ni film is smoothest of all and has the fewest dewetting
spots. The AFM image of the Ni shows areas of several $\mu\textrm{m}^{2}$ that
are atomically smooth (rms roughness $0.2\,\mathrm{nm}$ to $0.4\,\mathrm{nm}$
for a $1\,\mathrm{\mu m}\times 1\,\mathrm{\mu m}$ area). The EBSD
characterization discussed below suggests that the dark lines in the optical
images for Cu-Ni and Ni are boundaries between the $60^{\circ}$ twin domains
revealed in the XRD data. These grain boundaries are wider for the Cu-Ni film
than for the Ni film, and are obscured by roughness for the Cu film. In the
AFM images for Cu-Ni and Ni, the grain boundaries appear as trenches. These
trenches, which do not appear in the as-deposited films, likely form when
grain boundaries move during annealing. These morphological characterizations
show that the Ni film clearly survives the annealing better than the Cu film,
as expected from the higher melting point of Ni.

Figure 3: Electron backscatter diffraction data for the same films as in Fig.
1 and for a polycrystalline Ni foil. (a, b, c) Orientation maps using a color
scale that represents in-plane direction only: blue and green regions differ
by $60^{\circ}$. The scale bar shown in (c) is $50\,\mathrm{\mu m}$. (e, f, g)
(111) pole figures with a logarithmic color scale. The Cu film shows equal
amounts of each orientation, while the Cu-Ni and Ni films show a majority of
one orientation in the regions shown. (d) Orientation map for a
polycrystalline Ni foil after annealing to $1000\,\mathrm{{}^{\circ}C}$. Wedge
color scale represents out-of-plane orientation. Scale bar is
$400\,\mathrm{\mu m}$. (h) (111) pole figure for the polycrystalline Ni foil.

The micro-crystalline structure of the films can be characterized by EBSD, as
shown in Fig. 3 for films without a seed layer. Because the films are fully
(111) textured, we use a color scale for in-plane direction only: blue and
green regions differ by a $60^{\circ}$ rotation about the [111] axis. The
upper images are therefore spatial maps of the $60^{\circ}$ twin domains
revealed in the XRD data. The lower images are (111) pole figures with a
logarithmic color scale. The spatial map for the Cu film shows a broad
distribution of grain sizes, and the pole figure shows equal intensity for
both in-plane orientations. For the Cu-Ni film, both the spatial map and the
pole figure indicate that one orientation dominates in the region shown here.
Comparing the orientation map of Fig. 3b and the optical image of Fig. 2b, we
conclude that the dark lines enclosing small areas in the optical image are
boundaries between $60^{\circ}$ twin domains. A less pronounced preference for
one in-plane orientation is apparent in the spatial map and pole figure of the
Ni film. For comparison with our (111) films, Figs. 3d, h show EBSD data for a
polycrystalline Ni foil, also annealed at $1000\,\mathrm{{}^{\circ}C}$. In
this case we use a color scale for out-of-plane orientation. The foil shows a
broad distribution of grain sizes and orientations.

Figure 4: Crystallinity and morphology of $400\,\mathrm{nm}$ Ni film deposited
with Al2O3 seed layer, after annealing at $1000\,\mathrm{{}^{\circ}C}$ and
$270\,\mathrm{Pa}$ ($2\,\mathrm{Torr}$). Optical image in (a) and EBSD map in
(b) ($50\,\mathrm{\mu m}$ scale bars) show fewer grains than the corresponding
images for Ni without the seed layer (Figs. 2c and 3c, respectively). AFM
image in (c) shows an ordered surface and shallower trenches between grains
than in Fig. 2f ($10\,\mathrm{\mu m}$ scale bar). XRD (111) pole figure in
(d), plotted on a logarithmic intensity scale, shows a single in-plane
orientation over 97 % of the film. Line profile in (e), taken along the black
line in (c), shows steps $\approx 1\,\mathrm{\mu m}$ wide and $\approx
5\,\mathrm{nm}$ high.

We now turn to the effect of the Al2O3 seed layer and other measures that
improved the metal films in terms of epitaxy and/or survivability under
graphene CVD conditions. The seed layer improved the adhesion of all films, as
indicated by a reduced density of dewetting areas after annealing. For the Cu
films, the seed layer had little effect on crystallinity: the XRD pole figure
(not shown) has six spots of similar intensity, indicating roughly equal
amounts of each $60^{\circ}$ twin orientation, as in the data of Fig. 1c. For
the Ni films, the seed layer increased grain size and reduced $60^{\circ}$
twin formation, as shown in Fig. 4. The second set of spots in the XRD pole
figure of Fig. 4d is faint even on a logarithmic scale, and from their
integrated intensity we estimate that only 3 % of the film area is composed of
$60^{\circ}$ twin domains. The optical image in Fig. 4a shows fewer lines due
to grain boundaries, and the lines are less distinct than in Fig. 2c. Finally,
the AFM image in Fig. 4c shows the detailed morphology of the improved Ni
film. The surface shows a regular series of atomically flat terraces, also
seen in the profile of Fig. 4e, that are $\approx 1\,\mathrm{\mu\text{m}}$
wide and separated by steps $\approx 5\,\mathrm{\text{nm}}$ tall. This profile
corresponds to a slope of 0.3°, consistent with the $\pm 0.5^{\circ}$ miscut
specification of the Al2O3 wafer. The trenches between $60^{\circ}$ twin
domains are shallower than for Ni without the seed layer, which is consistent
with less grain boundary motion during annealing due to the higher deposition
temperature.

Figure 5: Cross-sectional transmission electron microscopy of Ni on Al2O3. (a,
b) Without seed layer. (c, d, e) With seed layer. In (a), a $60^{\circ}$ twin
boundary in the Ni is seen at the edge of an extra (0003) Al2O3 lattice fringe
that may indicate a dislocation or step at the surface. The focused probe
diffraction pattern corresponding to the region of the Ni twin boundary is
shown in (b), where the subscript “T” labels spots from one of the twin
grains. In (c), the lattice fringes of the film with the seed layer are
continuous and smooth, indicating the surface was not damaged by the
resputtering process. Selected area diffraction patterns are shown for the Ni
in (d) and for the Al2O3 in (e).

To further investigate the effect of the seed layer, TEM was performed on a
cross-section of the Ni/Al2O3 interface from unannealed samples with and
without the seed layer. The bottom half of each image in Figs. 5a,c shows
Al2O3(0003) lattice fringes, which are kinematically forbidden but dynamically
allowed and are observed due to double diffraction. Ni lattice fringes are not
resolved because the distance between Ni(111) planes, 0.203 nm, is beyond the
0.28 nm point resolution of the microscope. For the Ni film without the seed
layer, Fig. 5a, the last Al2O3 fringe shows a lateral intensity modulation
that could indicate a fractional-unit-cell island or dislocation near the
surface. At the edge of the extra fringe, there is a vertical grain boundary
in the Ni (darker region near the center of the image). The focused probe
diffraction pattern corresponding to this region, shown in Fig. 5b, indicates
both grains share the [111] out-of-plane and [110] in-plane directions. This
can only occur for a twin boundary with a $60^{\circ}$ in-plane rotation about
the [111] direction. The presence of a Ni grain boundary at the edge of an
extra (0003) Al2O3 lattice fringe was not uncommon, so the extra fringe is
likely correlated with the mechanism for grain boundary formation. Thus the
TEM results independently confirm the EBSD results and provide a microscopic
view of the origin of the $60^{\circ}$ twin domains.

For the Ni film grown with the seed layer, we found far fewer grain boundaries
for an equivalent length of cross-sectional interface. Fig. 5c shows a typical
image for this film. The Al2O3 lattice fringes are continuous and smooth,
indicating the reactive sputtering produced a seed layer with an undamaged
surface. Selected area electron diffraction patterns show the Ni (Fig. 5d) and
the Al2O3 (Fig. 5e) are highly ordered.

While the Al2O3 seed layer did not significantly affect the amount of
$60^{\circ}$ twin domains or other properties of the Cu films, the roughness
of these films was strongly affected by the annealing conditions. The rough
surface shown in Fig. 2a, produced by annealing for 15 min at
$1000\,\mathrm{{}^{\circ}C}$ in a total pressure of $270\,\mathrm{Pa}$
($2\,\mathrm{Torr}$), offers a poor substrate for graphene growth. Increasing
the total pressure during annealing reduced the overall roughness of Cu and
Cu-Ni films, as shown in Table 1. We attribute this improvement to the reduced
evaporation rate of Cu at higher pressure. Table 1 also shows that roughness
was further decreased by placing a Cu foil $\approx 1\,\mathrm{\text{mm}}$
above the surface of the Cu film. This improvement is presumably due to a
higher vapor pressure of Cu near the film, and is likely related to the
improvements seen in graphene CVD when the Cu foil was folded and crimped to
make an enclosure [25]. With both higher total pressure and a foil cover, a
Cu(111) film annealed at $1065\,\mathrm{{}^{\circ}C}$ for 15 min showed a
roughness only slightly larger than that of the Ni film in Fig. 4c. Thus thin
Cu(111) films on Al2O3 can survive graphene CVD conditions, even those
approaching the Cu melting point, if the total pressure is high enough and
there is a nearby source of Cu vapor.

Film | Thickness (nm) | Temp. (${}^{\circ}\textrm{C}$) | Press. (Torr) | Foil cover | Roughness (nm)
---|---|---|---|---|---
Cu | 400 | 1000 | 2 | No | 27
Cu | 700 | 1000 | 20 | No | 9.5
Cu | 700 | 1000 | 40 | No | 6.8
Cu | 700 | 1000 | 20 | Yes | 5.8
Cu | 700 | 1065 | 40 | Yes | 5.0
Cu-Ni | 350/50 | 1000 | 2 | No | 18
Cu-Ni | 350/50 | 1000 | 20 | No | 13
Ni | 400 | 1000 | 2 | No | 3.3
Table 1: RMS roughness of metal films on Al2O3(0001) under different annealing
conditions. Annealing time was 15 min in all cases. All roughness values were
measured from a $30\,\mathrm{\mu m}\times 30\,\mathrm{\mu m}$ AFM image.

##  4 Graphene Growth and Characterization

Graphene was grown using CH4 as the precursor gas in a hot-wall tube furnace
with an inner diameter of 80 mm and an overall length of 1.5 m. The tube was
evacuated using a scroll pump (base pressure of $2.5\,\mathrm{Pa}$) and all
gases were 99.99+ % pure. For growth on Ni, the films were annealed at
$1000\,\mathrm{{}^{\circ}C}$ in a flow of $27\,\mathrm{\mu mol/s}$
($36\,\mathrm{sccm}$) of Ar and $27\,\mathrm{\mu mol/s}$ of H2 for 15 min,
cooled to $900\,\mathrm{{}^{\circ}C}$, and then exposed to $27\,\mathrm{\mu
mol/s}$ of H2 and $27\,\mathrm{\mu mol/s}$ of CH4. Growth conditions were
maintained for 30 min to ensure full C saturation, and the film was cooled at
$4\,\mathrm{{}^{\circ}C/min}$ in the same gas flows used for growth. A total
pressure of $2700\,\mathrm{Pa}$ ($20\,\mathrm{Torr}$) was maintained
throughout the process. For growth on Cu, the films were annealed at
$1035\,\mathrm{{}^{\circ}C}$ in $370\,\mathrm{\mu mol/s}$
($500\,\mathrm{sccm}$) of Ar and $7.4\,\mathrm{\mu mol/s}$
($10\,\mathrm{sccm}$) of H2 for 15 min. A flow of $27\,\mathrm{\mu mol/s}$
($36\,\mathrm{sccm}$) of CH4 was then added to the Ar and H2, growth lasted 4
min, and the film was cooled at approximately $(50\textrm{ to
100)}\,\mathrm{{}^{\circ}C/min}$ in the same gas flows used for growth. A
total pressure of $5300\,\mathrm{Pa}$ ($40\,\mathrm{Torr}$) was maintained
throughout the process.

Figure 6: Scanning electron microscopy (SEM) images of multilayer graphene
grown on Ni films. (a, c, e) $400\,\mathrm{nm}$ epitaxial Ni(111) on Al2O3.
(b, d) $400\,\mathrm{nm}$ polycrystalline Ni on SiO2. Scale bars are
$40\,\mathrm{\mu m}$ for (a) and (b), $4\,\mathrm{\mu m}$ for (c) and (d), and
$10\,\mathrm{\mu m}$ for (e). (f) Raman spectroscopy indicates there is at
least a monolayer of graphene at all points. Darker regions correspond to
thicker growth.

Scanning electron microscopy (SEM) at low accelerating voltage (5 kV) was used
to image graphene on the Ni and Cu surfaces. Figure 6 compares growth on
$400\,\mathrm{nm}$ films of epitaxial Ni(111) on Al2O3 (Fig. 6a,c,e) and
polycrystalline Ni on SiO2 (Fig. 6b,d). The graphene films were grown
simultaneously to ensure identical treatment. We attribute variations in the
grey-scale to variations in graphene thickness, with darker areas presumably
corresponding to thicker graphene. Although contrast variations from the
polycrystalline Ni film itself could exist due to channeling, we expect this
effect to be minimal because the images were taken with an in-lens detector.
The most striking feature in these images is the different relationship
between graphene thickness changes and Ni grain boundaries for the two films.
For the polycrystalline Ni film, most changes in thickness occur at grain
boundaries, leading to mostly faceted edges for regions of a given thickness
(Fig. 6d). For the Ni(111) film, the graphene thickness varies dramatically on
a length scale much smaller than the size of the grains shown in the EBSD data
of Fig. 4b. Thus while graphene growth on Ni(111) is indeed more uniform than
growth on polycrystalline Ni, it is not nearly as uniform as one would expect
if thickness variations are simply caused by faster precipitation of C at
grain boundaries than within the interior of grains. This suggests there is an
additional source of thickness variations that remains to be identified.
Similar thickness variations occured for a variety of growth parameters.

The higher resolution SEM images in Fig. 6c,e show detailed features of the
thickness variations that are worth mentioning. In some places, thicker
graphene follows the boundary between a minority grain and the surrounding
majority grain (red arrows in Fig. 6e). This has been reported previously for
growth on Ni [11] and is likely due either to faster precipitation of C or to
trapping of C atoms at these boundaries. In other places, the boundaries of
minority grains have no change in graphene thickness (green arrow in Fig. 6e).
In many of the thicker graphene regions, straight, bright lines may indicate
buckling of the graphene from differential contraction during cooling (yellow
arrow in Fig. 6c). Some of the thinnest graphene regions show a network of
bright lines that may indicate a discontinuous mosaic of graphene patches
(blue arrows in Fig. 6c). The variety of growth features on a substrate of
such high quality highlights the need for a better understanding of how
graphene grows on Ni.

Raman spectroscopy using an excitation wavelength of 633 nm was done to verify
the existence of graphene and as a rough characterization of defects. The
thickest graphene ($\gtrsim 4$ layers) on Ni films appears darker in an
optical microscope. Raman spectra with a spot size of $\approx 1\,\mathrm{\mu
m}\times 3\,\mathrm{\mu m}$ were taken in between these darker patches to
preferentially sample the thinnest regions. Fig. 6f shows typical spectra,
which have the _G_ and _G_ ’ peaks characteristic of few-layer graphene [26].
No places were found that did not have these peaks, indicating the films were
fully covered by graphene. The lack of a significant _D_ peak in the Raman
spectra for graphene on Ni indicates there are few defects.

The graphene grown on Cu is primarily monolayer, as shown by the Raman
spectrum in Fig. 6e, and therefore SEM images (not shown) reveal little about
the growth. The large _D_ peak is likely due to a high density of graphene
nucleation sites, resulting in a large number of graphene grain boundaries.
When graphene growth is interrupted before a complete layer forms, the
nucleation sites can be seen directly in SEM images [7]. Nucleation sites were
separated by roughly $1\,\mathrm{\mu m}$, much less than the distance between
Cu grain boundaries in Fig. 3a. As with Cu foils [7], we expect that
optimization of growth conditions can improve the quality of graphene on
Cu(111) films.

##  5 Conclusion

The metal films reported here have many of the properties needed for wafer-
scale growth of graphene by CVD. They can be deposited epitaxially with a pure
(111) texture on commercially available $\alpha-$Al2O3(0001) substrates. The
films fall short of being single crystals only due to grain boundaries between
(111) regions that differ by an in-plane rotation of $60^{\circ}$. For Ni, a
film that is 97 % single orientation and has a smooth, well ordered surface
can be achieved by reactive sputtering of an Al2O3 seed layer immediately
before metal deposition. This process, which probably helps by removing the OH
layer typically found on Al2O3 after exposure to air, does not require ion
bombardment or temperatures above $650\,\mathrm{{}^{\circ}C}$ and thus can be
implemented in many commercial sputtering systems if they are fitted with a
basic substrate heater. Cu films do not show significant improvement from the
seed layer process, but the roughness of these films caused by evaporation
under graphene CVD conditions can be reduced by a combination of higher total
pressure and proximity of a Cu foil. Cu-Ni films deposited as bilayers become
homogeneous alloys when annealed at $1000\,\mathrm{{}^{\circ}C}$,
demonstrating the possibility of tuning C solubility through alloy composition
and thereby controlling graphene thickness. The evaporation of Cu during
annealing can have a significant effect on the final alloy composition.

Further improvements are needed to reach the goal of wafer-scale, single
crystal thin films of Cu, Ni, and Cu-Ni alloys. Optimization of the reactive
sputtering process and the use of a sputtering system with lower base pressure
may result in fewer grain boundaries than demonstrated here. The improvements
found in the Ni films may be transferable to Cu films through the use of a few
nanometers of Ni deposited before the Cu. Another possible route is the use of
MgO substrates. In recent work, both Cu [27] and Ni [28] deposited on MgO(111)
showed a (111) texture without apparent in-plane rotational disorder, and the
films did not noticeably degrade under graphene CVD conditions. These
measurements may have been less sensitive to in-plane rotations than the XRD
pole figures presented here, but if these films do contain a small fraction
that is rotated in-plane, they may also benefit from a reactively sputtered
seed layer. Unfortunately, wafers of crystalline MgO are not widely available.

Independent of progress on film quality, there is clearly room for improvement
in our understanding of graphene CVD on metal substrates, be they foils, films
or ingots. The work presented here implies that even a single crystal metal
film free of grain boundaries may not be sufficient to achieve the graphene
uniformity needed for commercial applications. The identification of other
mechanisms for graphene nonuniformity remains an important topic of research.

##  6 Acknowledgments

We thank Dustin Hite and David Pappas for advice on metal film growth,
Lawrence Robins and Angela Hight-Walker for assistance with Raman
spectroscopy, and Stephen Russek for helpful discussions about magnetron
sputtering.

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