J Dubois

C Chandre

T Uzer

Envelope-driven recollisions triggered by an elliptically polarized pulse

Increasing ellipticity usually suppresses the recollision probability drastically. In contrast, we report on a recollision channel with large return energy and a substantial probability, regardless of the ellipticity. The laser envelope plays a dominant role in the energy gained by the electron, and in the conditions under which the electron comes back to the core. We show that this recollision channel efficiently triggers multiple ionization with an elliptically polarized pulse.

Recollision [1][2][3] is the fundamental building block of many imaging techniques for the real-time motion of electrons because recolliding electrons probe the structural dynamics [4][5][6] of the target atom or molecule, giving rise to a variety of highly nonlinear and nonperturbative phenomena such as high harmonic generation (HHG), above-threshold ionization (ATI) and nonsequential multiple ionization (NSMI). The conventional semiclassical scenario of the recollisions [1,2] is split into three distinct steps where: (i) The electron tunnel-ionizes through the potential barrier induced by the laser field, (ii) travels in the laser field and gains energy, then returns to the core, and, in the case of nonsequential double ionization (NSDI), (iii) exchanges its excess energy with an electron of the parent ion and both ionize. This recollision picture can be easily understood in absence of a pulse envelope in the dipole approximation: For an elliptically polarized (EP) laser field E(t) = E 0 [x cos(ωt) + ξ ŷ sin(ωt)], given an ionization time t i , the position of the electron after ionization in the strong field approximation (SFA) is given by (atomic units are used unless otherwise stated) r(t) = r(t i ) + [p(t i ) -A(t i )] (t -t 0 ) + [E(t) -E(t i )]/ω 2 .

(1) The amplitude of the laser field is E 0 , its ellipticity is ξ and its frequency is ω. The position and the kinetic momentum of the electron are r and p, respectively. The vector potential is A(t) such that E(t) = -∂A(t)/∂t. At ionization, the electron is on the potential barrier, and p(t i ) = 0. For ξ = 0, the electron leaves the ionic core with no sideways momentum drifts, and returns close to the core at time t r , i.e., r(t r ) ≈ r(t i ), due to the laser oscillations E(t)/ω 2 . For ξ > 0, if p(t i ) = 0, strictly speaking the electron never comes back to the core, i.e., there are no times t i and t r such that r(t r ) = r(t i ) in Eq. ( 1) because of the non-vanishing drift momentum -A(t i ) which pushes the electron away from the core [1]. In this framework, the electron can only recollide and trigger NSDI when the laser field is linearly polarized (LP).

In the conventional three-step scenario, the recollision picture can, however, be extended to near LP-fields by taking into account that after ionization, the electron is near the potential barrier. The initial momentum along the transverse direction to the laser field p ⊥ is distributed [7,8] as ∝ exp(-p 2 ⊥ 2I p /E 0 ), with I p denoting the ionization potential of the atom. The initial momen-tum of the electron can compensate its initial drift after ionization, and recollisions become possible [9][10][11]. At the threshold ellipticity [11]

ξ th ≈ ωI -1/4 p / √
E 0 (which is ξ th ≈ 0.5 for the parameters we use here) and beyond, the initial momentum p ⊥ ≈ ξE 0 /ω necessary to compensate the drift momentum is poorly weighted and the probability that the electron returns to the core drops off drastically. As a consequence, for ellipticities ξ > ξ th , the NSDI probability drops off compared to its value for ξ = 0 [9]. Moreover, if the electron returns to the core, the energy it gains during the recollision is

∆E = κU p (1 -ξ 2 ), (2)
with U p = E 2 0 /4ω 2 denoting the ponderomotive energy and 0 ≤ κ 3.17. Hence, the recolliding electrons, if any, do not bring back enough energy from the laser field at ellipticities ξ close to 1 to trigger NSDI. Consequently, the three-step model in absence of laser envelope predicts that the recollisions and the enhancement of DI probability are suppressed in elliptically polarized light.

Remarkably, we find that the presence of an envelope drastically affects these conclusions: In this Letter, we unveil a highly probable recollision channel with large return energy by accounting for the effects of the pulse envelope f (t). The mechanism for this recollision channel is depicted in Fig. 1. The competition between the Coulomb force and the laser field induces ionization early after the laser field is turned on. As the electron leaves the core region, the amplitude of the vector potential is small, and therefore its sideways momentum drift -A(t i ) ∝ ŷξf (t i ) can be compensated by its momentum p(t i ) [see Eq. ( 1)], and this, regardless of the ellipticity of the laser. This recollision channel becomes highly probable if the ionization is over the barrier. The conditions under which this recollision channel is highly probable lead to the enhancement of the DI probability for specific atoms only, driven by circularly polarized (CP) pulses [12][13][14][15] and nearly-circularly polarized pulses. Furthermore, we show that this recollision channel and the return of the electron can be understood using the SFA, contrary to the prediction of the standard three-step model as summarized in Ref. [3].

We demonstrate the existence of this recollision channel, which will be referred to as envelope-driven recollisions, for the least favorable case in the recollision scenario in absence of pulse envelope, namely the circularly polarized (CP) case (ξ = 1). We describe the electron dynamics in a rotating frame (RF). In the RF, the CP field is unidirectional. The position and the momentum of the electron are r = R(t)r and p = R(t)p, with R(t) the rotation matrix of angle ωt in the polarization plane. The classical single-active electron Hamiltonian, in the dipole approximation and in the three-dimensional space with basis vectors (x, ŷ, ẑ), reads [16]

H(r, p, t) = |p| 2 2 -ω p • ẑ × r + V (r) + xE 0 f (t), (3)
where the term -ω p • ẑ × r is the Coriolis potential. We use a laser wavelength of 780 nm (corresponding to ω = 0.0584 a.u.), a laser intensity of 8 × 10 14 W • cm -2 (corresponding to E 0 = 0.151 a.u.), and the soft Coulomb potential [17]

V (r) = -(|r| 2 + a 2 ) -1/2 with a = 0.26. At each time, the Hamiltonian is H(r, p, t) ≥ Z(r, t), with Z(r, t) = -ω 2 |r × ẑ| 2 /2 + V (r) + xE 0 f (t).
In the right panels of Fig. 1, the gray surfaces are classical forbidden regions corresponding to the condition H(r, p, t) < Z(r, t). The boundaries of the gray surfaces are the zero-velocity surface [18] corresponding to the condition H(r, p, t) = Z(r, t). On the zero-velocity surface, p = ωẑ × r. In the adiabatic approximation, there exists three fixed points of the dynamics: at the top of the zero-velocity surface and mainly due to the laser interaction [r ≈ xf (t)E 0 /ω 2 ], around the origin and mainly due to the soft Coulomb potential (r ≈ 0), and at the saddle point r⋆ = xx ⋆ with x⋆ solution of the equation ω 2 x-∂V (x ⋆ x)/∂ x = f (t)E 0 which is due to the competition between the Coulomb potential, the laser interaction and the Coriolis potential. At time t, the energy of the saddle point is denoted Z ⋆ (t) = Z(r ⋆ , t). First, we consider a constant laser envelope with f = 1. Hamiltonian (3) is conserved in time, and its value is the Jacobi constant K = H(r, p). We apply the recollision picture in which the electron ionizes at time t i and returns at time t r such that r(t i ) ≈ r(t r ) ≈ 0 close to the core. Between time t i and t r , the electron is in the continuum. Because of the Jacobi constant, H(r(t i ), p(t i )) = H(r(t r ), p(t r )), and consequently the return energy of the electron is

|p(t r )| 2 /2 ≈ |p(t i )| 2 /2.
Hence, the electron does not gain energy during its excursion in the continuum when it is driven by CP light even in the presence of the Coulomb potential, in agreement with Eq. (2).

When the laser envelope is taken into account, however, Hamiltonian (3) is no longer conserved and the energy of the recolliding electron can vary during its excursion. We consider f (t) to be a 2-4-2 trapezoidal envelope (2 laser cycles ramp-up, 4 laser cycles plateau and 2 laser cycles ramp-down), unless stated otherwise. In Fig. 1, we show a typical recollision in CP fields seen in the rotating frame of an electron initialized with an energy H(r, p, 0) = -I p . When the laser is turned off (f = 0), the motion of the electron is bounded. The zero-velocity surface is the blue curve in Fig. 1. The maximum of the zero-velocity surface (top of the blue curve) is Z ⋆ (0) ≈ -(3/2)ω 2/3 , i.e., the Coulomb barrier is decreased in the RF since this framework naturally includes nonadiabatic effects [19]. In a zeroth-order approximation, we consider two situations: If I p < (3/2)ω 2/3 , as it is the case for the ionization potential used here, the electron is initially above the classical forbidden region, and a low laser intensity is sufficient to tear the electron off the core almost instantaneously, so t i ≈ 0. If I p > (3/2)ω 2/3 , the electron is initially topologically bounded by the zerovelocity surface. The ionization is not instantaneous, so t i > 0. For t < t i , the time-dependent term xE 0 f (t) in Hamiltonian (3) is very small, and therefore the energy is almost conserved H(r, p, t) ≈ -I p . For increasing time, the envelope increases and the energy of the saddle point decreases as

Z ⋆ (t) ≈ Z ⋆ (0) -f (t)E 0 ω -2/3 for f (t) ≪ 1.
The ionization channel is opened when the energy of the saddle point is the same as the energy of the electron Z ⋆ (t i ) = -I p . Quantum mechanically, earlier ionization times can be accessible through tunneling. In any case, the electron ionizes close to the zero-velocity surface, and the electron initial kinetic energy E i is small compared to the ponderomotive energy U p .

After ionization, at time t > t i , the electron is outside the core region and the time-dependent term xE 0 f (t) in Hamiltonian (3) starts varying significantly compared to U p . If t i is relatively small [f (t i ) ≪ 1], the effective transverse potential vector f (t i )E 0 /ω ŷ is also small, and it can be compensated by the momentum of the electron at ionization. This prevents the electron from drifting away from the core, which is the case if the ionization occurs when f (t i ) ∼ 1. During its excursion outside the core region, the electron spins around the zero-velocity surface. As we show below, the energy of the recolliding electron increases by a quantity of order U p during the ramp-up. Therefore, the electron can populate high energy states. In particular, regions of phase space where invariant structures can bring back this electron to the core region [9,15,20]. During the plateau, the electron dynamics evolves on a constant energy surface given by the Jacobi constant.

The ionization time t i determines whether or not the electron comes back: If t i is too large, there is a low probability that the momentum of the electron at ionization can compensate the sideways momentum drift -A(t i ). Two parameters influence considerably the ionization time t i : the electron initial energy -I p and the laser frequency ω. We find that the electron comes back to the core after ionizing over the barrier only if I p < I c , where I c ≈ 1.85ω 2/3 . This expression is derived using a reduced model [21] (see Supplemental Material [START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF] for details). For ω = 0.0584 a.u., the critical value is I c ≈ 7.4 eV. If I p > I c , the vector potential of the electron at ionization is too large and cannot be compensated by the electron, and it drifts away from the core without recolliding. We notice that I c /Z ⋆ (0) ≈ -1.2, which shows that the critical ionization potential is right below the saddle point energy before the laser field is turned on. Conversely, for a given I p , the laser frequency can be tuned for allowing recollisions in CP fields, as observed numerically in Ref. [START_REF] Chen | [END_REF]. Quantum mechanically, the wave packet can ionize before their classical counterparts, and therefore increasing the range of I p which allows recollisions.

In the RF with ξ = 1, the recollision picture is not so clear since the saddle moves in time even with a fixed laser envelope. The scenario, however, works the same way: The electron initiated with a sufficiently large energy can ionize over the barrier early after the laser field is turned on. After ionization, the initial momentum of the electron is relatively small and compensates the sideways momentum drift in Eq. ( 1), such that p(t i ) -A(t i ) ≈ 0. The electron does not quickly drift away from the core. Then, the electron travels in the continuum. During its excursion in the continuum, the energy gained by the electron for a slowly varying envelope is

∆E ≈ 2U p f (t r ) 2 -f (t i ) 2 + 2U p 1 -ξ 2 g(t i , t r ), (4)
where g(t i , t r ) is explicitly derived from the SFA; it depends on the parameters of the envelope and on the frequency of the laser, but is independent of ξ (see Supplemental Material [START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF] for its analytic expression). Therefore, at high ellipticities, the recolliding electron gains energy mostly through the laser envelope [first term of the right hand-side of Eq. ( 4)]. We observe that the energy of the electron can increase by an order of U p with the variations of the pulse envelope. In contrast, at low ellipticities, the recolliding electron gains energy mostly through the sub-cycle oscillations of the laser [second term of the right hand-side of Eq. ( 4)].

We use this classical recollision picture to analyze NSDI with an elliptically polarized pulse [9,15].

H = 2 k=1 |p k | 2 2 + V (r k ) + r k • E(t) + 1 |r 1 -r 2 | 2 + 1 , (5)
as a function of the laser intensity. The electric field in the LF is E(t) = E 0 f (t)[x cos(ωt) + ŷξ sin(ωt)]. The electrons are initiated in the ground state of energy E g = -0.83 a.u. [15] using a microcanonical distribution of the initial conditions. In Fig. 2, the NSDI probability is also represented. A NSDI is a DI triggered by recollisions. A DI is counted as NSDI if there exist t i and t r such that the recolliding electron (labeled k = 1) leaves the core at time t i , i.e., |r 1 (t i )| > R, goes outside the core region, then returns to the core while the other electron remained bounded, i.e., |r 1 (t r )| < R and |r 2 (t r )| < R, and both ionize. We used R = 5 a.u. in our simulations. 5) leading to NSDI for Mg and CP pulses (ξ = 1). The gray areas are where electrons undergo a recollision but do not lead to NSDI. The red dashed curve is our prediction of the ionization time of the outermost electron ti [START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF] for Ip = 0.28 a.u. In the inset, the red dotted curves are tr = ti + (n + 1/2)T with n ∈ N ⋆ . The vertical dotted curve is where we expect over-the-barrier ionization, and the vertical dash-dotted curve is where we expect envelope-driven recollisions to gain enough energy to trigger NSDI [START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF].

In Fig. 2, the DI probability curves for Mg clearly exhibit knee structures as a function of the laser intensity for ξ = 0.5, 0.75, 1, signature of a recollision mechanism [15]. In order to determine the type of recollisions responsible for this knee structure, which persists at high ellipticities, we examine the ionization and return times of the recollisions leading to NSDI. Figure 3 shows the ionization and return times of all recollisions (gray areas), and the distributions of ionization and return times of the recollisions leading to NSDI (color scale) for Mg. We observe that all recolliding electrons contributing to NSDI ionize during the ramp-up of the laser pulse. Recolliding electrons which ionize during the plateau or at the end of the ramp-up cannot bring back sufficiently energy to the core to trigger NSDI [see Eq. ( 2)]. As a consequence, an absence of NSDI is observed for intensities smaller than I min ≈ 9 × 10 12 W • cm -2 (vertical dash-dotted curve) for high ellipticities, despite the presence of recolliding electrons. We observe layers for the return times of the recolliding electrons around t r ≈ t i + (n + 1/2)T with n ∈ N * . The probability of return is roughly equally distributed between n = 1, 2, 3, 4, in contrast to the predictions of Ref. [24]. At recollision time t r , the energy of the recolliding electron is E r = E i + ∆E ≈ ∆E. After the electron exchanges its energy with an electron which remained bounded, and if the energy the electron gained during the recollision ∆E is sufficiently large, both ionize.

While the recollisions from the conventional scenario do not persist at high ellipticities, or at least, are not FIG. 4: Phase diagram of the existence of envelope-driven recollisions. The black line is the critical ionization potential Ic ≈ 1.85 ω 2/3 . The white (resp. yellow) markers are where no knee (resp. a knee) is observed in the double ionization probability curves. The experimental measurements for He ( ) and Ne (△) at λ = 614 nm are reported in Ref. [12]; for Ar (⋄) and Xe (⋆) at λ = 800 nm are reported in Ref. [13]; for Mg (•) at λ = 780 nm are reported in Ref. [14]. The color code is the guiding-center energy of the electron at the saddle point E at time ti: red is where E = 2 a.u., white is where E = 0 (critical ionization potential) and green is where E = -1 a.u.

efficient due to the lack of energy boost [see Eq. ( 2)], envelope-driven recollisions manifest themselves in an efficient way regardless of the laser ellipticity and with a substantial probability, provided that I p is smaller than a critical value, e.g., I p 1.85ω 2/3 for CP. Under this condition, which corresponds to the green area in Fig. 4, manifestations of the recollisions, such as for instance in NSDI, are probable. We observe that the experimental measurements for which a knee structure is observed in CP pulses (see Refs. [12][13][14]) agree well with the conditions under which the probability of envelope-driven recollisions is substantial. Therefore, manifestations of the recollisions can also be observed at high ellipticities for specific target atoms and laser wavelengths, and therefore triggering NSDI, HHG and ATI. We observe that, by decreasing the laser wavelength, the probability of envelope-driven recollisions becomes substantial for larger ionization potentials, and therefore manifestations of the recollisions becomes measurable for other atoms than Mg, such as it was noticed in Ref. [START_REF] Chen | [END_REF].

In summary, we have demonstrated the conditions under which a large portion of electrons can both ionize and return to their parent ion regardless of the ellipticity of the laser pulse. To recollide at high ellipticity, the electron needs to ionize early after the laser field is turned on to benefit from the boost by the CP field and not to drift away from the core. We have shown that the probability the electrons undergo an envelope-driven recollision is particularly large when I p 1.85ω 2/3 . During its excursion in the continuum, the electron gains energy dominantly from the envelope of the driving laser, and can exceed 2U p , allowing for a return energy E r = E i +∆E in excess of 2U p .

FIG. 1 :

 1 FIG. 1: Typical recollision with high return energy in a CP field. The laser envelope is trapezoidal 2-4-2 (see text), the laser intensity is I = 8 × 10 14 W • cm -2 . The electron is initialized with energy -Ip = -5.8 eV. Left panel: Trajectory in the rotating frame (x, ỹ). The white and red circles are the position of the electron at the ionization and return time, respectively. The color shows the value of the zero-velocity surface during the plateau. Right panels: The trajectory projected along the position and energy of Hamiltonian (3) at ionization ti ≈ 0.3T , the end of the ramp-up 2T and return tr ≈ 2.6T (from left to right). The gray surface is the classically forbidden region for ỹ = 0 [i.e., H(r, p, t) < Z(r, t)]. The blue curve is the zero-velocity surface at time t = 0 for ỹ = 0. The saddle point is the local maximum of the zero-velocity surface for negative x. Distances and energies are in a.u.

FIG. 2 :

 2 FIG. 2: Double ionization probability curves as a function of the laser intensity. The thin dotted curves are the NSDI probability curves.

  Figure 2shows the double ionization probability curves of Mg with Hamiltonian[15]

FIG. 3 :

 3 FIG.3: Distributions of the ionization time ti and the return tr of the recollisions of Hamiltonian (5) leading to NSDI for Mg and CP pulses (ξ = 1). The gray areas are where electrons undergo a recollision but do not lead to NSDI. The red dashed curve is our prediction of the ionization time of the outermost electron ti[START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF] for Ip = 0.28 a.u. In the inset, the red dotted curves are tr = ti + (n + 1/2)T with n ∈ N ⋆ . The vertical dotted curve is where we expect over-the-barrier ionization, and the vertical dash-dotted curve is where we expect envelope-driven recollisions to gain enough energy to trigger NSDI[START_REF]See Supplemental Material for a derivation of the critical ionization potential, the critical intensity of overthe-barrier ionization, the minimum intensity for triggering NSDI, a typical NSDI trajectory, the energy gained by the electron in the elliptically polarized[END_REF].

We thank Simon A. Berman and François Mauger for helpful discussions. The project leading to this research has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sk lodowska-Curie grant agreement No. 734557. T.U. acknowledges funding from the NSF (Grant No. PHY1602823).


Damia Dekkar

Fabien Bénédic
email: fabien.benedic@lspm.cnrs.fr

Cécile Floer

Sami Hage-Ali

Ovidiu Brinza

Jocelyn Achard

Omar Elmazria

Study of low temperature deposition of nanocrystalline diamond films on ZnO/LiNbO 3 layered structures suitable for Waveguiding Layer Acoustic Wave devices

Keywords: NanoCrystalline Diamond, Waveguiding Layer Acoustic Wave, piezoelectric materials, low temperature growth

In this paper the NanoCrystalline Diamond (NCD) film low temperature deposition process on ZnO/Si, ZnO/LiNbO3 and ZnO/IDTs/LiNbO3 substrates is investigated aiming at obtaining layered structures suitable for Waveguiding Layer Acoustic Wave (WLAW) devices. The NCD synthesis is performed at 250 °C by using a Distributed Antenna Array (DAA) microwave system operating in H2/CH4/CO2 gas mixture at low pressure (<1 mbar). Since the ZnO layer is etched during the NCD growth process, the deposition of a thin AlN layer of few hundred nanometers in thickness on the considered substrates is performed and is shown to be effective as a protective layer. Diamond growth on AlN-coated ZnO/Si substrates emphasizes the ability of the DAA reactor to synthesize NCD films with properties similar to those obtained on silicon substrates. Besides adherent NCD films up to 300 nm thickness are synthesized on AlN-coated ZnO/LiNbO3 substrates but stress in the layered structure appears during the plasma process. Finally, the feasibility of a NCD/AlN/ZnO/IDTs/LiNbO3 layered structure, suitable for WLAW devices, is successfully demonstrated, even if the NCD film adherence must be further improved on the Inter-Digital Transducers (IDTs) finger zone.

1 Introduction Diamond is a material of choice for many technological applications, in particular for Surface Acoustic Wave (SAW) and Waveguiding Layer Acoustic Wave (WLAW) structures, because of its exceptionalmechanical, electrical and thermal properties [START_REF] Dischler | Low-Pressure Synthetic Diamond: Manufacturing and Applications[END_REF]. In particular, with its low surface roughness ( 20 nm) and its very high acoustic velocity ( 10 km.s -1 ), nanocrystalline diamond (NCD) is worthy of note as an acoustic material for SAW devices [2,3]. However, SAW device packaging, generally costly and bulky, remains a real bottleneck, which can be solved by using the WLAW concept. Thus, the WLAW principle is based on wave confinement in a low acoustic velocity layer enclosed between two high ve-locity materials. Moreover, one of the layers has to be piezoelectric to allow the generation of the acoustic wave.

Promising results have been obtained by using the AlN/ZnO/IDTs/LiNbO3 multilayered structure for packageless body centric sensors [START_REF] Floer | IEEE Int. Ultrason. Symp[END_REF]. In this configuration, the Inter-Digital Transducers (IDTs) are deposited on the LiNbO3 substrate; AlN and LiNbO3 have a high acoustic velocity compared to ZnO; and LiNbO3 is characterized by a high electromechanical coupling coefficient and weak acoustic wave propagation losses [START_REF] Nakahata | IEEE Int. Ultrason. Symp[END_REF][START_REF] Fujishima | IEEE Int. Ultrason. Symp[END_REF][START_REF] Aubert | [END_REF]. Recently, it was shown that the use of a sputtered AlN film of 6 µm thickness causes acoustic losses during propagation, while theoretical calculations pointed out that using only 2.5 µm of diamond films would be sufficient to confine the wave and to reduce the propagation losses [8]. Moreover, the wave confinement should be improved with the diamond layer. Besides, due to its exceptional hardness and chemical inertness, the diamond film would play a key role by protecting the SAW device from environment contaminations. Thus, the NCD/ZnO/IDTs/LiNbO3 structure is a promising layered structure to achieve high performance WLAW devices.

Most of NCD synthesis processes, especially the usual Microwave Plasma Assisted chemical Vapor Deposition (MPACVD) process, generally require substrate temperatures above 400 °C. This high substrate temperature will destroy the transducers and make ZnO and LiNbO3 lose their piezoelectric properties [9]. For these reasons, low temperature synthesis of NCD films is needed in order to overcome these inherent drawbacks.

In this work, we investigate the low temperature synthesis of NCD films on various layered structures by using a distributed antenna array (DAA) system operating in H2/CH4/CO2 gas mixture at low pressure (< 1 mbar) [10]. NCD films grown at 250 °C on ZnO/Si and ZnO/LiNbO3 substrates, and finally on the ZnO/IDTs/LiNbO3 layered structure suitable for WLAW devices, are characterized in terms of morphology and microstructure, and solutions are examined in order to preserve the substrate integrity.

Experimental

Different substrate configurations were achieved: ZnO/Si, ZnO/LiNbO3 and ZnO/IDTs/LiNbO3. ZnO was deposited using Radio-Frenquecy (RF) magnetron sputtering with the following parameters: 4-inch Zn target, 150 W, 6x10 -3 mbar, 6 sccm O2 and 6 sccm N2. Two deposition temperatures of ZnO at 170 °C and 25 °C were tested. The ZnO layers were synthesized on silicon substrates ((100)oriented, thickness of around 380 µm) or on a LiNbO3 128° Y-cut substrate (MTI Corporation). Since the thickness of ZnO thin films affects strongly the device performance and the wave confinement [9], a maximum thickness of 2 µm was deposited.

In some case, a thin AlN protective coating (thickness of 150 or 300 nm) was also deposited with non-intentional heating on the ZnO surface using RF magnetron sputtering with the following parameters: 4-inch Al target, 200W, 8x10 -3 mbar and 16 sccm N2.

Considering the expected NCD-based WLAW devices, a ZnO/IDTs/LiNbO3 layered structure was realized. First 10 nm of titanium (Ti) as adhesion layer and 90 nm of gold (Au) were deposited on a LiNbO3 substrate by RF magnetron sputtering and IDTs(Ti/Au) were fabricated using the electron beam lithography process. A negative resist was used to limit the processing time. Ion Beam Etching (IBE) and O2-plasma treatment were used to finalize the IDT manufacturing. The synchronous resonator obtained has the following parameters (Figure 1):

-A period of the IDTs λ=4.4µm to reach a 868 MHz central frequency;

-100 finger pairs for the resonator and 200 fingers for the two reflectors forming the Bragg mirror; -The metallization ratio is fixed to 60% leading to a resolution of 1.32µm; -The aperture (length of the fingers) is set at the value of 269µm. NCD film deposition was carried out with a DAA microwave system which consists of 16 plasma sources arranged in 4x4 matrix. Discharge is ignited in a H2/CH4/CO2 feed gas. Such configuration, details of which can be found elsewhere [11], showed its efficiency for the NCD growth on 4-inch silicon substrates at low pressure (< 1 mbar) and low temperature (< 400 °C). Note that the addition of CO2 in the feed gas is required for low temperature synthesis in order to improve the etching of nondiamond phase, as discussed in [11] and reference therein. The main advantage of this reactor is to enable the growth of NCD films on large areas with satisfactory growth rates, while allowing an easy up-scaling and industrial implementation. For the present study, typical NCD growth conditions were employed: a microwave power of 3 kW, a 96.4%/2.6%/1% H2/CH4/CO2 gas mixture under 0.35 mbar and 50 sccm flow rate. The substrate temperature, measured with a thermocouple in mechanical contact with the bottom of the substrate holder, was controlled at 250 °C using a PID system. Before growing, the substrates were seeded by spin coating with a colloidal solution containing diamond nanoparticles produced by detonation.

Si reference and ZnO/Si (S1 sample) samples were seeded using a 25 nm grain size powder with highly negative zeta potential (SYP-GAF-0-0.05 provided by Van Moppes). The colloidal solution was diluted in water and, in order to avoid coagulation, PVA (PolyVinyl Alcohol) powder was added.

In order to improve the nucleation density on AlNcoated substrates, samples were specifically seeded by a nanodiamond aqueous solution with a grain size of 4-6 nm and a highly negative zeta potential (VOX d provided by Carbodeon). As a matter of fact, the negative zeta potential of this solution is due to its carboxylate function group surface. When AlN is immersed into the water-based colloidal diamond solution, the surface rapidly hydrolyzes by forming AlOOH and/or Al(OH). This implies the formation of hydroxyl group which forms a positively charged surface [12]. Therefore, the electrostatic attraction occurs between Copyright line will be provided by the publisher the diamond particles and the AlN surface, which leads to a high seeding density and consequently to a high nucleation density which is favorable to the NCD growth but also acts as a protective coating for the AlN and ZnO layers. Note that no other pretreatment, such as N2, O2 or CF4 plasma exposure, has been carried out when using AlNcoated substrates.

The NCD deposition time was varied from 3 up to 7 h. Table 1 summarizes the substrate characteristics and NCD deposition times, the diamond film properties of which being discussed hereafter. The film morphology was investigated by top-view Scanning Electron Microscopy (SEM) taken by a field emission ZEISS ULTRA plus SEM system. Surface topography was estimated with a VEECO Dimension 3100 Atomic Force Microscopy (AFM) system in tapping mode in air. The Raman spectra were obtained with a HR800 (HORIBA Jobyn-Yvon) apparatus operating at 458 nm excitation wavelength. It was used to analyze the phase purity of the deposited diamond films and identify the substrate contributions. X-Ray Diffraction (XRD) patterns were obtained using CuK1 radiation (= 1.54056 Å) with an incident X-ray angle of 2° in order to analyze the sample composition and crystalline properties. The NCD film grain size was estimated using a Rietveld method applied on the (111) and/or (220) diffraction peaks [13].

In order to easily estimate the NCD film thickness, the growth was systematically and simultaneously performed both on a Si substrate, as reference, and on the considered substrates (ZnO/Si, ZnO/LiNbO3 or ZnO/IDTs/LiNbO3). Indeed, the growth rate only depends on experimental parameters, regardless of the substrate nature if the deposition temperature is maintained constant [14], so that the resulting film thickness can be considered similar whatever the substrate. NCD film deposited thickness (𝑇ℎ 𝑁𝐶𝐷 ) was then estimated on Si substrate by using a UV-visible reflectometer and by measuring the weight gain after deposition according to equation [START_REF] Dischler | Low-Pressure Synthetic Diamond: Manufacturing and Applications[END_REF].

Th NCD = ( m after -m Si ρ D ) m Si ρ Si × 1 Th Si (1)
Where 𝑚 𝑆𝑖 and 𝑚 𝑎𝑓𝑡𝑒𝑟 are the silicon weight and the weight measured after growth, respectively, 𝜌 𝑆𝑖 and 𝜌 𝐷 are the silicon and diamond densities, respectively, and 𝑇ℎ 𝑆𝑖 is the silicon thickness before growth.

Knowing 𝑇ℎ 𝑁𝐶𝐷 determined on Si substrate, the weight variation of ZnO/Si samples before and after growth permits to estimate the ZnO consumption encountered during diamond deposition from equation ( 2).

(2)

Where Th etch ZnO is the ZnO etched thickness, ρ ZnO is the ZnO density, and m before is the ZnO/Si substrate weight before the NCD growth.

The NCD film thickness was also obtained in real time by using in situ Laser Reflectance Interferometry (LRI) on the Si sample, which permits to stop the deposition process when the expected thickness is reached [15].

Results and discussion 3.1 NCD deposition on ZnO/Si and AlN-coated

ZnO/Si substrates In order to demonstrate the feasibility of NCD growth on ZnO layer, ZnO/Si substrates were first investigated (S1 sample). The synthesis was carried out for 4 h (Table 1) with growth conditions usually employed on Si substrates at 250 °C surface temperature.

The weight gain, as well as reflectometry and LRI measurements, show that the NCD film thickness deposited simultaneously in these conditions on Si reference substrate is around 170 nm. However, the weight gain is negative for the ZnO/Si sample, which indicates that the diamond synthesis did not occur and/or that the ZnO layer was partially or totally etched during the NCD growth. The SEM micrograph presented in Figure 2 exhibits a granular surface typical of NCD films produced in the DAA reactor [16], which proves that, in spite of the weight loss, the diamond growth took place. The film is homogeneous, continuous and covers the entire sample surface, and its surface roughness is about 11 nm, which is comparable to the values already reported on silicon substrate [16].

nm

The Raman spectrum of Figure 3 exhibits the characteristic peak of diamond at 1332 cm -1 , which confirms the presence of carbon sp 3 phase on S1 sample. The Full Width at Half Maximum (FWHM) of the diamond peak is around 14 cm -1 , which is typical of the nanocrystalline feature. The ZnO contribution, that appears around 1150 cm -1 [START_REF] Calizo | Proc. SPIE 6481, Quantum Dots, Particles, and Nanoclusters IV[END_REF] as shown on the Raman spectrum of the ZnO/Si bare substrate, cannot be easily identified after NCD growth. This is consistent with the fact that the ZnO layer is partially or totally consumed during the plasma process. This hypothesis is confirmed by the XRD diffraction pattern of S1 sample after NCD deposition (Figure 4), where only the diffraction peaks corresponding to diamond and silicon can been clearly observed. Indeed, the three peaks at 2 = 44.1°, 75.6° and 91.7° are relative to the (111), ( 220) and (311) crystalline plans of cubic diamond (JCPDS, No.6-0675), respectively, whereas the (311) diffraction peak of silicon appears at 2=56.2 ° (JCPDS, No.27-1402). The diamond grain size estimated from the XRD pattern is about 10 nm, which is similar to the value reported for the same growth conditions on silicon substrate [16].

This implies that the ZnO layer is etched by the deposition plasma fed with H2/CH4/CO2 gas mixture. As a matter of fact, assuming that the NCD thickness deposited on S1 sample is similar to the one measured on Si reference substrate, the ZnO etched thickness Th etch ZnO was estimated around 500 nm through equation ( 2), which corresponds to more than the half of the initial ZnO thickness (900 nm). This points out that there is a competition between NCD growth and ZnO etching. It should be also emphasized that the etching rate of ZnO layer, measured in the same conditions but in a H2 plasma (i.e. without carbon containing precursors in the gas phase), is as high as 5 μm.h -1 . It means that the 0.9 μm-thick ZnO layer of S1 sample can be completely removed after less than 15 minutes of hydrogen plasma, which shows how ZnO is sensitive to the plasma reactive species. This preliminary study thus demonstrates the feasibility of synthesizing NCD films on ZnO layers, but solutions must be found in order to avoid the ZnO consumption aiming at keeping the required thickness for the expected WLAW structure.

In order to preserve the ZnO samples from the reactive NCD deposition plasma, thin aluminum nitride (AlN) films (150 or 300 nm thickness) were tested as protective coatings. It should be recalled here that AlN was first expected as the top layer for WLAW structures and that the purpose is to replace it by a more efficient diamond layer. It can be thus assumed that the acoustic wave confinement and propagation in the ZnO layer would not be strongly affected by this thin AlN layer, while the wave confinement is supposed to be insured by a sufficiently thick NCD film deposited on AlN. All the substrates considered in the following (ZnO/Si, ZnO/LiNbO3 and ZnO/IDT/LiNbO3) were then coated with AlN and will be denominate "AlN-coated substrate". After the NCD deposition the samples will be denominate "NCD/AlN/substrate". 1). The NCD/AlN/ZnO/Si layered structure obtained after 6 h NCD synthesis is clearly visible with thicknesses of 250 nm, 150 nm and 1.2 μm for the NCD, AlN and ZnO layers, respectively. The initial thickness of AlN and ZnO on S2 sample are thus retrieved. This highlights the efficiency of the AlN coating to prevent the ZnO layer from etching due to the reactive plasma. The morphology of the growing surface is characteristics of NCD films with a granular structure homogeneously covering the entire sample surface. It should be noticed that the diamond particle size is much smaller for S2 sample than for S1 sample. This can result of a difference in the nucleation density on both samples, which could be linked to the ZnO etching in the case of S1 sample. A surface roughness as low as 10 nm is thus reached on S2 sample.

Figure 6 exhibits the Raman spectrum obtained on S2 sample after NCD growth. It is comparable to what is usually obtained on silicon substrates treated in the DAA reactor [16]. The FWHM of the diamond peak observed at 1332 cm -1 is slightly narrower than S1 sample with a value of 12 cm -1 . The band at 1150 cm -1 could be assigned to trans-polyacetylene [START_REF] Ferrari | [END_REF] but is more probably due to the contribution of the ZnO substrate as observed on the AlNcoated ZnO/Si substrate before growth (Figure 6). This is consistent with the SEM micrographs of Figure 5 showing that the ZnO layer is still present in the sample with its initial thickness of 1.2 μm. It should be noted that no AlN contribution is identified before or after NCD growth on the considered Raman spectra, whereas the XRD patterns Copyright line will be provided by the publisher 220) crystalline plans of cubic diamond, respectively. The NCD grain size is estimated at 13 nm, which is close to the value reported for S1 sample. The XRD patterns definitely confirm that the ZnO layer is successfully preserved owing to the protective coating of AlN. In this part, the effectiveness of the AlN coating for protecting the ZnO layer from plasma etching was demonstrated for the ZnO/Si layered structure. In the next section, the investigations are focused on the deposition of NCD films on AlN-coated ZnO/LiNbO3 substrate, which is the suitable configuration for the WLAW structure.

NCD deposition on AlN-coated ZnO/LiNbO3

substrates In this part the sample composed of a 300 nm thick AlN layer deposited on a 2 µm thick ZnO film achieved at ambient temperature on LiNbO3 substrate is considered (S3 Sample, Table 1).

The surface morphology of a 300 nm-thick NCD film grown on the AlN-coated ZnO/LiNbO3 substrate is exhibited through the SEM image of Figure 8. A completely homogenous film, showing dense NCD grains, is observed. The surface roughness obtained on the S3 sample, which is about 19 nm, is nearly twice higher than S2 sample (10 nm). It should be noticed that for NCD films thicker than 300 nm, a weak adherence, that may lead to the film delamination, is observed. The Raman spectra of S3 sample before and after NCD growth presented in Figure 9 are composed of three main component responses. The first range (150-875 cm -1 ) corresponds mainly to the LiNbO3 contributions [20][21][22][23], which intensities are well visible without NCD and significantly decrease after the growth. The Raman peak at 437 cm -1 could also be related to the ZnO layer [24], that can be overlapped with LiNbO3 Raman peaks occurring at 426 and/or 448 cm -1 . The Raman peak of ZnO at 1150 cm

Silicon

well defined on AlN-coated ZnO/LiNbO3 substrate but tends to disappear after the NCD growth. Finally, the FWHM of the diamond peak at 1332 cm -1 is estimated at 13 cm -1 , which is consistent with S2 sample. The principal Raman peak of AlN usually reported at 650 cm -1 [25] is not appreciably visible for such a low thickness (300 nm) used for S3 sample. The change of the diffraction peak positions can be mainly attributed to the film strain. For an identical NCD synthesis temperature (250 °C) for S2 and S3 samples, the residual stress is more noteworthy when achieving NCD/AlN/ZnO deposits on LiNbO3 (S3 sample) than on Si (S2 sample). The grain size measured for S3 sample is about 16 nm, which is higher than S1 and S2 samples and leads to the raise of the surface roughness reported before. Nevertheless, S3 sample characterization highlights the successful feasibility of NCD growth on AlN-coated ZnO/LiNbO3 substrate using the DAA system. The ability of the considered NCD deposition process for achieving NCD/AlN/ZnO/IDTs/LiNbO3 WLAW device was then examined.

NCD deposition on AlN-coated ZnO/IDTs/LiNbO3

substrates for WLAW devices The NCD-based WLAW device achieved on S4 sample is shown in Figure 11. The NCD film covers homogeneously and continuously all the device parts. The adherence of the NCD layer is satisfactory everywhere except on the IDTs finger zone as it is observed in the SEM micrograph of Figure 12 showing the frontier between the IDTs base (on the left) and the IDTs fingers (on the right). Indeed, some cracks are visible on the frontier and the film is bulge on the IDTs finger zone, which in not observed elsewhere. This is due to a lower and inhomogeneous nucleation density resulting from the local topography of the IDTs fingers. Indeed, for such 3D patterns the spin coating method used for nanodiamond particle seeding leads to an inhomogeneous distribution of the nanodiamond particles both on the top and in the space between IDT fingers. Thus, the ex situ pretreatment used for enhancing the diamond nucleation must be adapted and optimized for such structure. The AFM micrograph given in Figure 13 shows the NCD deposited on the IDTs finger zone. In spite of the successive deposition of ZnO, AlN and NCD layers, the shape of the IDTs fingers can be still distinguished. Especially the period  = 4.4 µm measured from Figure 12 is identical to the value of the initial IDTs/LiNbO3 SAW de-vice (Figure 1). The width of a single coated finger is now 2 μm instead of 1.32 μm, which shows a filling of the inter-finger volume owing to a conformal growth of the different materials. Even if some aspects of the NCD synthesis must be further controlled, the feasibility of achieving NCD/AlN/ZnO/IDTs/LiNbO3 layered structure suitable for WLAW device is thus demonstrated.

Conclusion

In this paper we investigated the NCD deposition on ZnO/Si, ZnO/LiNbO3 and ZnO/IDTs/LiNbO3. The synthesis was carried out in a Distributed Antenna Array microwave system convenient for large area and low temperature deposition, compatible with industrial requirements and temperature sensitive substrates.

The NCD deposition on ZnO substrates necessitates a protective coating in order to prevent the material from plasma etching since a very high etching rate of ZnO is yielded when using H2/CH4/CO2 feed gas. The deposition of a thin AlN layer of few hundred nanometers in thickness was shown to be effective to limit the ZnO consumption during the NCD growth process.

First attempts of diamond growth on AlN-coated ZnO/Si substrates pointed out the ability of the DAA reactor to synthesize NCD films with similar properties to those obtained on silicon substrates. The NCD synthesis on AlN-coated ZnO/LiNbO3 substrates showed that the materials involved in the layered structure are stressed. However, adherent NCD films up to 300 nm thickness were synthesized on the considered structure.

Finally, the NCD/AlN/ZnO/IDTs/LiNbO3 layered structure was successfully realized and is promising for WLAW devices. The NCD film adherence is satisfactory, except on the IDTs finger zone.

From the point of view of diamond growth on the AlNcoated ZnO/IDTs/LiNbO3 layered structure, forthcoming works will deal with the improvement of the nucleation enhancement on the IDTs finger zone, and with the reduction of the structure strain during NCD deposition. The characterization of operating NCD-based WLAW devices will also be the subject of future research efforts.

Figure 1

 1 Figure 1 Top view of a microfabricated SAW device formed of IDTs(Ti/Au)/LiNbO3 before ZnO deposition.

  . The properties of these synthesized NCD films, deposited at 250 °C, are investigated and discussed in section 3. ThAlN and ThZnO are respectively the aluminum nitride (AlN) and zinc oxide (ZnO) deposited thicknesses measured by profilometer and checked by SEM cross-sectional images, and TZnO is the ZnO deposition temperature.

Figure 2

 2 Figure 2 SEM micrograph of NCD film deposited on S1 sample (ZnO/Si).

Figure 3

 3 Figure 3 Raman spectra of S1 sample (ZnO/Si) before and after NCD growth.

Figure 4

 4 Figure 4 XRD pattern of S1 sample (ZnO/Si) after NCD growth.

Figure 5

 5 Figure 5 presents the SEM micrograph (cross section and top view) of a NCD film deposited on the AlN-coated ZnO/Si substrate corresponding to S2 sample (150 nm AlN, 1.2 μm ZnO, seeTable1). The NCD/AlN/ZnO/Si layered structure obtained after 6 h NCD synthesis is clearly visible with thicknesses of 250 nm, 150 nm and 1.2 μm for the NCD, AlN and ZnO layers, respectively. The initial thickness of AlN and ZnO on S2 sample are thus retrieved. This highlights the efficiency of the AlN coating to prevent the ZnO layer from etching due to the reactive plasma. The morphology of the growing surface is characteristics of NCD films with a granular structure homogeneously covering the entire sample surface. It should be noticed that the diamond particle size is much smaller for S2 sample than for S1 sample. This can result of a difference in the nucleation density on both samples, which could be linked to the ZnO etching in the case of S1 sample. A surface roughness as low as 10 nm is thus reached on S2 sample.Figure6exhibits the Raman spectrum obtained on S2 sample after NCD growth. It is comparable to what is usually obtained on silicon substrates treated in the DAA reactor[16]. The FWHM of the diamond peak observed at 1332 cm -1 is slightly narrower than S1 sample with a value of 12 cm -1 . The band at 1150 cm -1 could be assigned to trans-polyacetylene[START_REF] Ferrari | [END_REF] but is more probably due to the contribution of the ZnO substrate as observed on the AlNcoated ZnO/Si substrate before growth (Figure6). This is consistent with the SEM micrographs of Figure5showing that the ZnO layer is still present in the sample with its initial thickness of 1.2 μm. It should be noted that no AlN contribution is identified before or after NCD growth on the considered Raman spectra, whereas the XRD patterns

Figure 5

 5 Figure 5 SEM micrographs (cross section and top view) of a NCD/AlN/ZnO/Si sample after NCD growth (S2 sample). shown in Figure 7 highlights the presence of a crystalline AlN layer. Indeed, different diffraction peaks corresponding to AlN, ZnO and Si are clearly observed on the XRD spectra of S2 sample before and after NCD growth. The most important contribution is due to the (103) diffraction peak of ZnO film at 2 = 62.4 ° (JCPDS, No.36-1451) [19], which is slightly shifted after NCD growth. The three peaks at 2 = 34.2 °, 35.8 ° and 65.7° are relative to the (100), (002) and (103) crystalline plans of hexagonal AlN (JCPDS, No.25-1133). The other two peaks observed at 2 = 43.6 ° and 74.8 ° after growth are relative to the (111) and (220) crystalline plans of cubic diamond, respectively. The NCD grain size is estimated at 13 nm, which is close to the value reported for S1 sample. The XRD patterns definitely confirm that the ZnO layer is successfully preserved owing to the protective coating of AlN.

Figure 6

 6 Figure 6 Raman spectra of S2 sample (AlN-coated ZnO/Si) before and after NCD growth.

Figure 7

 7 Figure 7 XRD patterns of S2 sample (AlN-coated ZnO/Si) before and after NCD growth.

Figure 8

 8 Figure 8 SEM micrograph of NCD film deposited on S3 sample (AlN-coated ZnO/LiNbO3).

Figure 9

 9 Figure 9 Raman spectra of S3 sample (AlN-coated ZnO/LiNbO3) before and after NCD growth. The characteristic peaks of AlN (100) and ZnO (103) observed in XRD diffraction patterns of S3 sample after NCD deposition (Figure 10) prove that both materials are still present after the plasma treatment. These peaks are shifted compared to S3 sample before NCD growth. Indeed, AlN(100) diffraction peak appears at 2= 36 ° instead of 2 = 34.6°, and ZnO (103) is at 2 = 61.8 ° instead of 2 = 63°. The diamond diffraction peaks ((111) at 2=42°, (220) at 2=74.7°) observed after deposition are also slightly shifted with respect to S2 sample ((111) at 2=43.6°, (220) at 2=74.8°).

Figure 10

 10 Figure 10 XRD diffraction patterns of S3 sample (AlN-coated ZnO/LiNbO3) before and after NCD growth.

Figure 11

 11 Figure 11 SEM micrograph (back-scattered electrons) of the NCD/AlN/ZnO/IDTs/LiNbO3 WLAW device achieved on S4 sample: (a) global view; (b) focus out of the device; (c) focus of the IDTs finger zone.

Figure 12

 12 Figure 12 SEM micrograph (secondary electrons) of the IDTs base (on the left) and the IDTs figers (on the right) of the NCD/AlN/ZnO/IDTs/LiNbO3 WLAW device achieved on S4 sample.

Figure 13

 13 Figure 13 AFM micrograph of the IDTs finger zone of the NCD/AlN/ZnO/IDTs/LiNbO3 WLAW device realized on S4 sample.

Table 1

 1 Substrate characteristics and NCD deposition times

Copyright line will be provided by the publisher

Acknowledgements

The authors wish to thank V. Bockelée from LSPM, for technical support and fruitful discussions about NCD film characterization. This work has received support by ANR through projects ANR-11-LABX-086. It was also partially supported by Direction Générale de l'Armement (DGA), the French PIA project "Lorraine Université d'Excellence" (ANR-15-IDEX-04-LUE) and the Institut Carnot en Lorraine (ICEEL).