James Gigliotti

Xin Li

Suresh Sundaram

Dogukan Deniz

Vladimir Prudkovskiy

Jean-Philippe Turmaud

Yiran Hu

Yue Hu

Frédéric Fossard

Jean-Sébastien Mérot

Annick Loiseau

Gilles Patriarche

Bokwon Yoon

Uzi Landman

Abdallah Ougazzaden
email: abdallah.ougazzaden@georgiatech-metz.fr

Claire Berger
email: claire.berger@cnrs.fr

Walt A De Heer

Highly Ordered Boron Nitride/Epigraphene Epitaxial Films on Silicon Carbide by Lateral Epitaxial Deposition

Keywords: graphene, boron nitride, silicon carbide, epitaxial growth, MOVPE, van der Waals heterostructures, ab initio calculations

Realizing high-performance nanoelectronics requires control of materials at the nanoscale. Methods to produce high quality epitaxial graphene (EG) nanostructures on silicon carbide are known. The next step is to grow Van der Waals semiconductors on top of EG nanostructures. Hexagonal boron nitride (h-BN) is a wide bandgap semiconductor with a honeycomb lattice structure that matches that of graphene, making it ideally suited for graphene-based nanoelectronics. Here, we describe the preparation and characterization of multilayer h-BN grown epitaxially on EG using a migration-enhanced metalorganic vapor phase epitaxy process. As a result of the lateral epitaxial deposition (LED) mechanism, the grown h-BN/EG heterostructures have highly ordered epitaxial interfaces, as desired in order to preserve the transport properties of pristine graphene. Atomic scale structural and energetic details of the observed row-by-row, growth mechanism of the 2D epitaxial h-BN film are analyzed through first-principles simulations, demonstrating one-dimensional nucleationfree-energy-barrierless growth. This industrially relevant LED process can be applied to a wide variety of van der Waals materials.

Conventional atomic layer depostion is a cyclic processes involving two different precursor molecules in the gas phase that are alternately introduced on a surface, and in which each cycle deposites exactly one atomic layer on top of the film. In contrast, in the migration-enhanced Lateral Epitaxial Deposition (LED) mechanism that we propose here, each cycle "knits" one row of atoms to the edge of the growing multilayer film. The process presented here demonsrtates that the method produces high quality BN-graphene interfaces, and provides a clear path towards further improvement.

RESULTS AND DISCUSSION

The LED process proceeds in a MOVPE growth chamber in which the TEB and NH 3 volatile molecules, that are the precursors for the h-BN films, are introduced to the extremely hot EG on SiC wafer. Contrary to most CVD processes used to grow h-BN the key steps here are the sequential introduction of the chemicals and the rest time between two injections. A growth cycle consists of first a pulsed injection of TEB that is transported in a flow of hydrogen carrier gas, followed by a purge, followed by a similar sequence for the injection of NH 3 (see Methods for details and Ref. 33). In this process, the TEB and NH 3 precursors alternatively decompose on the hot EG surface, thereby providing active boron then nitrogen atoms to form the h-BN layers.

In the following, we present properties of the h-BN films grown on EG on the (0001) Si-face and the (0001) C-face of 4H-SiC and on natural EG nanostructures on both the Si-and C-faces.

We demonstrate that the h-BN films consists of 2D sp 2 layers and that the first h-BN layers are in epitaxy with epigraphene. Figures 1a-d show cross-sectional, high-resolution transmission electron microscopy (HR-TEM) images of the h-BN/EG/SiC heterostructures, composed of h-BN on monolayer EG on the Si-terminated face (Fig. 1a-b) and h-BN on few EG layers on the C-terminated face of hexagonal SiC (Fig. 1c-d). At the interface in particular, the h-BN layers are atomically flat and very well ordered. Close examination of the HR-TEM image of Fig 1d shows AB stacking of the h-BN layers. Fast Fourier Transform (FFT) analysis confirms this stacking (Inset Fig. 1d), and also reveals some admixture of ABC stacking [START_REF] Schue | Characterization Methods Dedicated to Nanometer-Thick hBN Layers[END_REF] (see also Supplementary Information (SI) Fig. S2 andS3).

This stacking order continues throughout the film and particularly at the critically important h-BN/EG interface (Fig. 1 and Fig. S2 and S3 in SI). This is consistent with the epitaxy of the h-BN film on the graphene (see below). Extended disordered grain boundaries or discontinuities were not observed at the h-BN/graphene interface in any of the twelve 70 nm sections of cross sectional HR-TEM images spanning the 1.5µm size thin slab that was examined in detail. This suggests that during growth, h-BN sheets lock in place, rather than simply lay on top of the graphene. The local misorientation observed in the uppermost layers in thick h-BN films (Fig. 1ab), is largely caused by the HR-TEM slab preparation using a focused gallium ion beam, as evidenced by the presence of Ga in those films, (see Fig. S5), due to an insufficient protection by the deposited carbon layer.

Energy Dispersive X-ray Spectroscopy (EDX) in Fig. 1b, identifies chemical components at various depths in the film and correlates with the chemical assignments in Fig. 1a (see Fig. S5 for further analysis). The graphene layers are clearly identified and uniform composition of the h-BN layers is shown.

These results are confirmed by Electron Energy Loss Spectroscopy (EELS), see Fig. S6; in particular, the B-spectra in the film presents a narrow and intense sharp π* peak at 191.1 eV, which is a defining characteristic of sp 2 -hybridized B atoms. Composition analysis with X-ray photoemission spectroscopy (XPS) has the same line profile as a reference h-BN single crystal (see Fig. S7), and gives the same B/N ratio; the flatness of the h-BN layers also indicates 1/1 boron to nitrogen stoichiometric ratio. XPS profile analysis further indicates a carbon composition of at most about 3% in the h-BN film. This carbon content was determined after etching the spurious surface carbon of h-BN deposited on a sapphire substrate placed next to the EG/SiC substrates during the deposition runs. All the other XPS peaks are similar between h-BN on both substrates, and there is no contribution from sp 2 carbon.

The h-BN layer spacing, observed in HR-TEM in Fig. 1a and 1c is 0.345 nm, is very close to the bulk h-BN (0.333 nm), which is consistent with multilayer h-BN on sapphire. [START_REF] Jang | Wafer-Scale and Wrinkle-Free Epitaxial Growth of Single-Orientated Multilayer Hexagonal Boron Nitride on Sapphire[END_REF] On the Si-face EG, the first graphene layer is located 0.43 nm above topmost SiC, in agreement with the spacing reported for quasi-freestanding epigraphene following hydrogen passivation of the SiC surface [START_REF] Emery | Structural Consequences of Hydrogen intercalation of Epitaxial Graphene on SiC[END_REF] and lifting up of the buffer layer. Hydrogen intercalation is consistent with the XPS C1s spectra where the characteristic component of the buffer layer is not observed (Fig. S7). It also agrees with LEED observations (Fig. 2b, see below) and with preliminary measurement of a large density of positive charge carriers (≈10 13 cm -2 ) for the Si-face EG under h-BN. This indicates that a quasifreestanding bi-layer graphene is easily produced by the LED method. When helium, instead of hydrogen, is used as the carrier gas, this conversion of the buffer layer to freestanding graphene is expected to not occur, thereby conserving the pristine monolayer graphene on top of the buffer layer.

Figure 2 compiles significant characterization results that are discussed next. (See SI for details). The Scanning Electron Microscopy (SEM) image of Fig. 2a, taken for a 45 nm thick h-BN film grown on Si-face EG, shows a continuous and homogeneous film with a network of three-fold connected pleats. The quasi-hexagonal pleat pattern (see also Fig. S9d) is indicative of an isotropic uniform contraction of 2D layers upon cooling (similarly to multilayers C-face EG layers 2 ), with no sign of pinning, tearing or large defects. Note that the EG monolayer onto which the h-BN is grown has no pleats, as is common for EG on the Si-face (see Fig. S1a). Low energy electron diffraction (LEED) in Fig. 2b shows the diffraction pattern of the h-BN/EG/SiC heterostructure. The diffraction pattern was recorded with a relatively large electron energy (227 eV), to penetrate through the h-BN and graphene layers, and into the SiC, thereby producing a composite diffraction image. The h-BN diffraction spots are registered with the graphene spots; both are rotated 30° with respect to the SiC. No rings or supplementary spots are observed, that would result if the h-BN layers were rotationally disordered. This observation is consistent with the epitaxy of all three components of the h-BN/EG/SiC heterostructure. The absence of satellites around the graphene spots is consistent with buffer layer lift up by hydrogen intercalation. [START_REF] Riedl | Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation[END_REF] High resolution X-ray diffraction (HR-XRD), that quantifies the atomic layer spacing, was performed before and after the h-BN deposition on both C-face and Si-face EG. The h-BN layer spacing was found to be 0.35 nm (Fig. S4), consistent with the HR-TEM (Fig. 1d). The rocking curve measurement of the h-BN (0002) peak (Fig. 2c) gives an extremely narrow full width at half maximum of 0.04° which attests to the h-BN film high degree of parallel order that extends over the width of the X-ray beam (several mm 2 , that is about the size of the sample).

Raman spectroscopy spectra presented in Fig. 2d were performed before and after h-BN deposition. An example is given in Fig. 2d for a few layers C-face EG. Before h-BN coating, the absence of a Raman D-peak at 1350 cm -1 attests to the high quality of the multilayer EG (red trace to be compared with the SiC Raman peaks, blue trace). A large peak develops after h-BN coating at the expected energy of the h-BN E 2g peak (1370 cm -1 ). The peak is prominent on areas where the top (disordered) h-BN layers were mechanically removed, attesting to the quality of the h-BN layers closer to the SiC interface. The effect of h-BN deposition on the graphene quality was further investigated by exfoliating the h-BN layer to expose the underlying graphene layer. The Raman spectra show no significant D peak after deposition, indicating that the graphene layer was not damaged in the process (see SI Fig. S12), in agreement with the excellent h-BN/EG interface quality observed in HR-TEM.

The h-BN deposition was repeated on EG samples that were deliberately grown with incomplete graphene layers, to produce EG nanoribbon-like structures on both Si-and C-faces, without resorting to lithographic pattering (Fig. 2c -inset and Fig. S9b &S9c). After processing, the EG structures are covered with a high-quality uniform h-BN layer, while the remaining buffer layer areas are covered with poorly ordered h-BN crumpled sheets. These observations are consistent with the smooth, homogeneous and defect-free EG nanostructures with h-BN nucleation at the edges. In contrast, the buffer layer has an excess of nucleation sites (due to its inherent 6X6 corrugations) that result in the rough h-BN structure. Note that for graphene nanoelectronics a high degree of h-BN order is required only on the EG nanostructures themselves. The growth of smooth layered BN on top of EG is in stark contrast with the preferential h-BN growth on the metallic substrates instead, promoted by the graphene edges in CVD processes (see for instance Refs. 40, 41).

The h-BN dielectric quality was tested in a simple 2-probe transport measurement by measuring the I-V characteristic from graphene to a top-gate evaporated on h-BN/EG. The area of the 1 µm 2 gate is largely compatible with the size of nanoelectronics devices, providing a good indication of the h-BN property in a functional device. The resistance of the h-BN film, measured perpendicularly to the stack, is of the order of 8 GΩ, and breakdown was observed above 165 V (see Fig. S8), which is sufficient to raise the charge density on the EG to about 5x10 13 cm -2 , i.e. an order of a magnitude more than required for intended electronic applications. Nevertheless, larger values are expected with higher quality films. The tested nine top gates gave similar results, showing excellent homogeneity of the dielectric properties, despite the presence of h-BN pleats under some of them (see Fig. S8).

Turning to the growth process, Fig. 3a shows a scanning electron microscope image of the growth on C-face EG after 1200 cycles, showing several merging, quasi-hexagonal h-BN crystallites that nucleated at several random points on the graphene surface. The parallel orientation of the hexagons indicates epitaxy. The size of these crystallites correlates with the number of cycles; in this case each cycle adds on average about one and an half BN rows to the crystallite per cycle.

Growth dynamics on the surface of the EG can therefore be understood in the following way, as depicted in Fig. 3b. At the hot graphene surface where the TEB molecule decomposes after the TEB pulse injection, the liberated highly mobile boron atom migrates over the graphene surface, and attaches to the thermodynamically favorable nitrogen terminated edge of the h-BN film (see theoretical simulation below). To avoid Volmer-Weber 3D growth mode, excess boron atoms have to desorb, which is enabled by the growth-stop step where the chemical residuals (B and methyl compounds) are purged. A NH 3 pulse injection follows. The NH 3 decomposes on the surface to produce a nitrogen atom that attaches to the boron atom at the edge of the nascent h-BN film. The carrier gas desorbs other volatile decomposition products. In this way, (ideally) a single row of h-BN is added to the edge of the growing film in each cycle of the LED process. This process also applies to subsequent h-BN layer growth, mediated by the fast B and N atoms diffusion on the h-BN surface, similarly to the graphene surface.

We emphasize that the lateral growth process described above is not limited to monolayers but applies to multilayers as well, giving rise to the uniform multilayers observed in Fig. 3a. The process can be understood as follows. Once initiated at a nucleation site, a multilayer growth front will propagate laterally, where B and N atoms alternatively attach to the vertical front. B and N atoms diffusion is mediated as described above, on both on the uncoated graphene and on the growing multilayer h-BN crystal. Hence, the thickness of the film is defined by the properties of the nucleation site as is typical in crystal growth in general. For clean graphene, h-BN nucleation is initiated at the graphene edges and the lithography used to define the graphene nanostructures will need to be optimized to control the BN film thickness.

More systematic studies of different growth conditions and growth rate for fine tuning of the processes will follow in further experiments, in particular by iteratively adjusting the boron precursor flow rate. Systematic optimization for specific applications is routine in all deposition processes. The optimization of the many parameters can be efficiently guided by simulations that provide insight into the processes, as demonstrated below. In particular, the observed hexagonal grains with dendritic edges (Fig. 3a) result from diffusion limited growth conditions, as expected for ordered growth without a free-energy barrier or critical nucleus size, as demonstrated and elaborated by the computer-based simulations below. For Van der Waals material growth in general, grains can vary in shape, from triangular to truncated triangle, to hexagonal depending on the specific growth kinematics, temperature conditions and substrates. [START_REF] Stehle | Synthesis of Hexagonal Boron Nitride Monolayer: Control of Nucleation and Crystal Morphology[END_REF][START_REF] Shinde | Stacking-Controllable Interlayer Coupling and Symmetric Configuration of Multilayered MoS2[END_REF] In the process presented here, the B and N precursors are introduced in the growth chamber, separated with a purge. These growth conditions with optimized precursor ratios allowed to ultimately achieve hexagonal grains with uniform stoichiometry. In addition, the next generation of ME-MOVPE will involve higher temperatures, since an increase in the temperature is known to promote a straight growth front. This is also expected to inhibit the nucleation of subsequent layers and provide a better control of the film thickness.

To explore the structural evolution and energetics of the atomic-scale mechanisms underlying the h-BN film growth processes, we performed first-principles density-functional theory (DFT) simulations; for details see Methods and SI. To this end, we modeled the graphene surface by a periodically replicated supercell (6x12 hexagons comprising 144 C atoms, with an energy optimized interatomic distance d C-C = 1.425 Å) on which we adsorbed a partial strip of h-BN; see the configuration of h-BN/graphene in Fig. 4a. Such initial configuration could be formed by considering a graphene sheet exposing a free edge, serving to initiate the alternating adsorption of B and N rows (following the fast diffusion of the atomic constituents on the bare graphene surface). Our simulations illustrate the atomic-scale mechanisms governing such row-by-row growth process.

To simulate the growth of the h-BN film we focus on two growth modes: (I) where, subsequent to thermal decomposition of the incident (alternating) TEB and NH 3 precursors on the graphene T > 1500K heated surface, we consider low fluxes (LF) of B (boron) and N (nitrogen) atoms arriving (through low-barrier thermal diffusion (see SI) on the bare graphene surface) to the vicinity of the h-BN growth front, and (II) where for each of the growth cycles we consider (alternating) high-fluxes (HF) of B and N atoms impinge on the h-BN film growth-front. For our model system each growth cycle entails impingement of 6 B atoms followed by 6 N atoms, resulting, under optimal growth conditions, in the formation of 6 new h-BN hexagons after each cycle. In simulations of the LF mode, we divide (in each cycle) the approach of the 6 B atoms into three stages (two B atoms in each stage, 2B+2B+2B), with the system allowed to structurally and energetically relax to the lowest energy configuration after each stage of 2B atoms diffusion-andattachment to the film edge. A similar consecutive impingement-followed-by-relaxation procedure is used for the subsequent 6 N (2N+2N+2N) atoms, completing the growth cycle.

LF growth, resulting in perfect hexagonal order at the additional freshly grown h-BN film edge, is shown in the a-b-c sequence in Fig. 4. Note the bonding to graphene of the N atom at the growth edge of the h-BN film, and the debonding (compare Fig. 4b &4c) of the edge B atoms induced by the impingement of N atoms which bond to the film-edge B atoms; a detailed view of the LF growth mechanism, and corresponding structural parameters are given in Fig. S15. The binding energies, per B atom (5.86 eV) and per N atom (5.50 eV), at the end of the B and N parts of the cycle, respectively, are noted in Fig. 4b &4c; these binding energies are obtained from the calculated total energy differences corresponding to the system before and after the diffusion and attachment of the graphene-surface-adsorbed B and N atoms to the growth front of the h-BN film (see SI for details). The binding energy per BN unit in the freshly grown h-BN front row is E b (BN) = 5.86 eV + 5.50 eV = 11.36 eV. Subsequent LF cycles yield a perfectly ordered h-BN film.

Interestingly, bondings of B and N atoms is found to occur only at the edge (growth-front) of the h-BN film (see Fig. 4), whereas away from that edge, only weak interaction is found between the h-BN film and the underlying graphene surface (DFT-calculated to be 0.13 eV per BN unit). Furthermore, as observed from comparison of the edge configurations in Fig. 4a & 4b, the attachment of B atoms debonds the edge N atoms from the graphene surface. In turn, we find now graphene-surface-bonded B atoms (Fig. 4b); these atoms debond in the course of the subsequent attachment of N atom as the B & N deposition cycle completes (Fig. 4c). Such bonding-debonding processes at the growth-edge repeat and accompany, throughout, the growth process of the (essentially) perfectly ordered h-BN film. The geometrical parameters corresponding to each of the panels (a-g) are given after Fig. S14.

It is instructive to contrast the above LF results with those obtained from a simulation of the HF growth mode; also termed "inconsecutive" process. Starting from the same initial state we observe at the end of the first (6B+6N) cycle (see Fig. 4a,d,e) a disordered film edge (with a calculated E b (BN) = 11.15 eV). The subsequent cycle (Fig. 4f &4g) results in a highly disordered state, with a significantly decreased binding E b (BN) = 8.51 eV. The superiority of the low-flux (consecutive) growth mode is evident, owing to the structural relaxation/annealing, enabled by the lower rate of impingement of the film's atomic constituents.

We conclude by commenting on the 1D row-by-row growth model [START_REF] Chen | Building Two-Dimensional Materials One Row at a Time: Avoiding The Nucleation Barrier[END_REF] of the epitaxial h-BN film, illustrated by our LF simulation. Our simulations uncover ordered growth without a freeenergy barrier or critical nucleus size. Indeed, such growth "anomaly" has been long-predicted by classical nucleation theory (CNT) [START_REF] Chen | Building Two-Dimensional Materials One Row at a Time: Avoiding The Nucleation Barrier[END_REF][START_REF] Kashchiev | Nucleation: Basic Theory with Applications[END_REF] (attributed to J. Williard Gibbs), since in 1D both contributions to the free-energy-change upon phase change -the first contribution associated with decrease of the chemical potential caused by formation of a nucleus of the new phase (e.g. growth of a crystalline film), and the second one describing the increase in energy due to the interface formed between the nucleus and its surrounding -scale linearly with the length of the nucleus (unlike the case in 2D and 3D growth modes), and thus, in 1D, there is no length-scale interplay between the two contributions to the free-energy, and consequently no nucleation barrier, nor a critical-nucleus size, apply here. The above does not preclude the involvement of other activation barriers (kinetic in nature), including, barrier for dissociative adsorption of the B and N precursor molecules, diffusional barriers of the B and N atoms, or chemical attachment barriers. However, the h-BN film growth described in this work appears to not be hampered by such barriers, resulting in an effective growth of a highly-ordered h-BN film on graphene.

CONCLUSIONS

In summary, a potentially industrially scalable MOVPE-based lateral epitaxial deposition process has been developed to produce high quality h-BN epitaxial films on EG. The crystalline quality and uniformity of the films and the clean epitaxial h-BN/EG interface were verified using a comprehensive suite of surface probes (SEM, HR-TEM, HR-XRD, XPS, EDX, EELS, LEED, Raman spectroscopy). For short growth time, incomplete coverage reveals that the first h-BN layers have large grains that are rotationally aligned to the SiC substrate. First-principles DFT simulations have uncovered a 1D nucleation-free-energy-barrierless growth mechanism of the epitaxial h-BN film. Atomic-scale details of the row-by-row growth are calculated illustrating the role of atomic-scale relaxation processes at the 2D film growth-front, in correlation with the perfection of structural ordering of the grown h-BN film that indicates the needed control over the fluxes of the constituents (B and N) in the LED process.

The observed uniform thickness and high crystalline quality over large area offer potential for improved reliability and performance in graphene-based nanoelectronics compared to traditional LED methods. Furthermore, since the extent of the prepatterned EG devices are typically less than 100 nm in nanoelectronics, the device edges are ideally suited as nucleation sites to intitiate the line-by-line knitting film-growth, that can be completed in less than 1000 cycles. In an optimized LED process, the cycle time can be optimized further. The h-BN/epigraphene/SiC heterostructure produced here presents the added advantage to be grown on a commercial single crystal semiconductor in an industrial reactor with 3x2-inch wafer capability. Moreover, the processes can be further expanded by growing an epitaxial graphene layer on top of the BN layers, using CVD. [START_REF] Yang | Epitaxial Growth of Single-Domain Graphene on Hexagonal Boron Nitride[END_REF] In this way graphene/h-BN/graphene heterostructures can be produced. This lateral LED process represents an important enabling step towards the realization of epigraphene nanoelectronics. The technique can be readily adapted to other van der Waals materials, such as MoS 2 , to enable multilayer Van der Waals epitaxial heterostructures of them as well.

METHODS

Epigraphene was produced on commercial chemical mechanical polished (CMP) insulating 4H-SiC substrates (from CREE). Complete few layer graphene films as well as incomplete monolayer graphene domains separated by buffer layer areas were grown on the silicon terminated face (SiC-(0001)), as shown in Fig. S1. Monolayer and multilayer epigraphene domains were produced on the carbon terminated face (SiC-( 0001)) (Fig. S1). The confinement controlled sublimation growth method was used, as described elsewhere, [START_REF] De Heer | Large Area and Structured Epitaxial Graphene Produced by Confinement Controlled Sublimation of Silicon Carbide[END_REF] to ensure graphene uniformity across the SiC surface. For this, the vacuum induction furnace was pumped down to 5x10 -7 mbar prior to growth. SiC dies were outgassed at 800 °C prior to ramping to growth temperatures between 1400 °C and 1600 °C for 10-30 min, depending on the desired morphology. Incomplete graphene layers were also grown on 4H-SiC natural steps separated by large atomically flat terraces (5-20 µm). [START_REF] Berger | Epitaxial Graphene on SiC: 2D Sheets, Selective Growth and Nanoribbons[END_REF] For comparison, bare CMP 4H-SiC chips were also processed together with the graphene samples in the same MOVPE deposition runs. The above-mentioned graphene morphologies (single and multilayers, partially grown layers and nanostructures) were used for h-BN film-growth.

Migration enhanced metal organic vapor phase deposition process was applied for h-BN growth using an Aixtron close coupled showerhead 3x2" MOVPE reactor. Prior to growth, the chamber was heated to 1270°C in hydrogen environment at 85 mbar. A triethylboron (TEB) preflow (5-10 s) preceded the alternate introduction of TEB and ammonia (NH 3 ) to nucleate and grow h-BN layers. A cycle consists of first a pulsed injection of TEB (1-3 s), where the total carrier gas flow rate was maintained at 20 SLPM with a TEB flow rate of 60 µmol/min. This is followed by a 1-3 s purge of the volatile components. Then NH 3 is introduced for 3-6 s (flow rate:

1.35 SLPM, carrier gas: 20 SLPM), followed by a 1-3 s purge similarly to a standard ALD process. The cycle is repeated for full coverage. h-BN films were grown with thicknesses ranging from about 1 to 50 nm. The growth rate in the c-axis direction was 5 nm/h as determined by AFM (scratch profile). The growth rate on EG was about 1/3 of that observed on sapphire (15 nm/h), [START_REF] Li | Large-Area Two-Dimensional Layered Hexagonal Boron Nitride Grown on Sapphire by Metalorganic Vapor Phase Epitaxy[END_REF] likely due to a lower nucleation density on the graphene surface migration enhanced MOVPE process is applied to reduce excess nucleation on the surface of growing BN layers. Experience from BAlN and BGaN nitride MOVPE deposition studies indicate that simultaneous introduction of precursors leads to lower nitride quality achieved than achieved with the alternation protocol. [START_REF] Li | BAlN Thin Layers For Deep UV Applications[END_REF] For the cross-sectional HR-TEM study, 70-80 nm thick lamella were prepared by FIB milling following deposition of 50 nm of amorphous carbon (Fig. 1a-b, S2, S5, S6) or Pt (Fig. 1c-d, S3) to protect the h-BN and graphene from ion bombardment and to reduce delamination. The images were taken along the [1120] zone axis on a Titan Themis microscope at 200 kV. EDX was performed to determine the extent of Ga-ion damage, differentiate graphene and h-BN, and to examine the chemical uniformity of the film.

The first-principles electronic structure calculations were performed with the Vienna Ab initio Simulation Package (VASP). A plane-wave basis with a kinetic energy cutoff of 400 eV, projector augmented wave (PAW) pseudopotentials method [START_REF] Kresse | From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method[END_REF] with the PBE generalized gradient approximation (GGA) for the exchange-correlation potential, and including van-der Waals interactions, were used. [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] We employed a lattice parameter of 2.468 Å (C-C bond length of 1.425 Å) for the two-dimensional unit cell of a graphene's hexagonal lattice; these values were found from our DFT energy optimization (minimization) calculations. A unit cell of the graphene lattice contains two carbon atoms. We employed a graphene calculational unit cell comprised of 6×6 hexagons (72 C atoms) for the boron and nitrogen atom adsorption calculations (see SI), and a 6×12 (144 C atoms) graphene calculational cell for the h-BN film-growth simulations; the calculational cell was repeated periodically. An initial h-BN strip of 6×6 hexagons was constructed from 42 boron and 42 nitrogen atoms with the same lattice parameter as graphene, and it was positioned on the 6x12 graphene surface, and subsequently energy optimized; the initial BN strip (see Fig. 4a) comprised 912 valence electrons. Most of our calculations were performed using a single k-point sampling (that is Γ-point calculations); we checked that the results of h-BN growth remained essentially the same, by employing (3×3×1) and (6×6×1) sampling of the surface Brillouin zone (see SI).

In simulation of the h-BN film growth process, for both the low-flux (consecutive) and highflux (inconsecutive) modes, the adsorbed B or N atoms were initially located (adsorbed) on the bare graphene surface at a distance up to 5 Å from any atom of the h-BN film growth-front, to ensure no direct initial bonding to the film. The attachment of the atoms to the film-growth front occurred in the course of (unconstrained) DFT energy minimization of the total system. The Raman spectrum after h-BN growth (black) displays a large peak at 1370 cm -1 that is ascribed to the h-BN E 2g due to the absence of a D peak in the as-grown EG. (For this spectrum, the disordered top h-BN layers are mechanically removed) Inset: Lorentizan fit of the peak at 1370 cm -1 (FWHM=47.3 cm -1 ). Schematic of the formation of the epitaxial 2D heterostructure using the lateral ALD process. The process cyclically injects TEB then ammonia. In the depicted TEB phase of the cycle, TEB (1) decomposes on the hot epigraphene surface liberating ethane (2) that escapes. The free, highly mobile boron atom (3) skids on the epigraphene to an awaiting nitrogen atom at the edge of the growing film (4). The process terminates when all nitrogen sites are passivated, and is ready for the second half of the cycle where the remaining TEB and ethane are purged (5) and ammonia is introduced (6) to add a fresh row of nitrogen to the boron saturated edge by the analogous decomposition process. enlarged view taken normal to the growing film edge, illustrating the weak coupling between the h-BN film and the graphene substrate.

In (b) we depict the optimal configurations resulting from exposure of the initial configuration (in a) to a low flux (LF) of B atoms. The small flux is modeled via the consecutive adsorption of boron atoms (2B atoms at each adsorption stage), with the system allowed to relaxed to the energy-optimal configuration after each adsorption step (for a detailed view of the system after each of the three consecutive B-adsorption steps see Fig. S15). The configuration shown in (b) is the one obtained at the end of the consecutive adsorption 2B+2B+2B process (resulting in 6 adsorbed B atoms corresponding to the 6 edge-exposed N atoms). Note that in this configuration all the adsorbed B atoms are bonded to both the nearest edge-N atoms of the film, as well as anchored (to various degrees) to the underlying graphene surface.

(c) The consecutive adsorption of nitrogen atoms (low flux) results in the formation of an added row of perfect h-BN to the growing film. Five out of six of the N atoms at the bottom edge of the freshly grown hexagon row are anchored to the graphene surface.

(d-g) An inconsecutive growth process, corresponding to high flux, HF, of arriving boron atoms followed by HF of impinging nitrogen atoms; that is, in each B/N cycle all the boron, as well as all the subsequent nitrogen atoms, arrive (essentially) simultaneously to the growing edge of the h-BN film (with no, or incomplete at best, intervening structural relaxations taking place at the growth front, see initial configuration in a followed by the configurations in d), resulting in defective growth of the film (see configuration e). The subsequent HF adsorption cycle yield a disordered film edge (see g). In order to confirm that the peaks come from the h-BN film, background HR-XRD scans were taken prior to h-BN growth, and no peak is observed for monolayer graphene. Graphene peaks are only observed for few layer graphene due to the small graphene cross section. HR-XRD spectra acquired from granular h-BN films showed a significantly reduced h-BN peak, confirming that the pleated morphology observed in Fig. 2a is a characteristic of h-BN layers.

IV. h-BN Surface Morphology

Continuous h-BN films with pleated surface morphology grow on graphitized regions of both the SiC silicon and carbon faces, as shown in Fig. S9, and exhibit no dependence on the number of graphene layers. Like graphene, h-BN has a negative in-plane coefficient of thermal expansion that induces a large compressive strain upon cooling from the high temperature of h-BN growth.

The weak interlayer interaction allows the sheets to slide with respect to each other to accommodate this strain without cracking, forming pleats. The pleats often radiate with tri-fold symmetry (see Fig. S9d) from sites where the h-BN is pinned, indicative of biaxial in-plane stress, 9 like for multilayer graphene. 1 The height of the pleats is 5-15nm as determined by AFM, shown in Fig. S10, in agreement with previous studies. 10 The 1260°C growth temperature of h-BN does not enable silicon sublimation from the SiC substrate, and therefore precludes additional graphene growth as the cause of the pleating. Note also that pleats are not observed on graphene grown on the Si-face before h-BN coating (see Fig. S1). The flat and pleated h-BN films are predominantly observed on EG domains. This is in stark contrast to other typical film deposition processes that do not nucleate or grow uniform films on graphene (see for instance 11 ). In fact, the inert surface of graphene is so unfavorable to film growth in general and presents so few nucleation sites that technologies have been developed using graphene as a mask for dielectric coatings. [11][12] In order to grow uniform Van der Waals materials, film growth must occur under conditions which enable sufficient adatom mobility to encourage lateral growth of each layer and platelet shifting to accommodate misalignments between impinging grains. The high temperature and carrier flow used here, in addition to eliminating vapor phase reactions by separating the precursors, contribute to low growth rate conditions (through low precursor flux and high adatom mobility), which favors selective lateral growth on the flat EG and h-BN sp 2 surfaces (see theory section, main text). Nanostructured graphene exhibits nearly pristine h-BN surfaces (Fig. S9b,c), in contrast with the bare SiC (Fig. S9a,S9c) and the buffer layer regions (Fig. S9b), where instead of the pleated morphology, a granular structure is observed. The h-BN clusters are actually crumpled sp 2 h-BN sheets, as no sp 3 hybridized BN is identified in XPS, even on highly granular surfaces (see Fig. S11). The h-BN crumpling is associated to a larger SiC lattice mismatch compared to graphene, or to higher nucleation density due to reduced adatom mobility, as expected from the corrugated surface (1 Å) of the buffer layer and the sp 3 hybridization of SiC. Further experiments conducted with low temperature TEB preflow have shown high particle densities on all surfaces, supporting that the high temperature mobility is imperative for h-BN growth. The h-BN clusters also often decorate SiC step edges in thin h-BN layers (Fig. S9b, S9c), but were not observed at the (b) graphene interface in HR-TEM cross sections confirming that they occur only on the h-BN top surface; crumpling at the graphene edges could be due to incomplete h-BN layers rearrangement during cooling. Note that, as flat h-BN growth is favored on the graphene nanostructures themselves, this will facilitate implementation into the EG nano-sized devices required for graphene-based electronics.

For thicker h-BN films (>20nm or so), clusters do not decorate step edges, as shown in Fig. S10, but the concentration and size of crumpled granules on the h-BN pleated regions increase. Stacking faults, as observed in HR-TEM (Fig. S3a), induce stress within the h-BN film that may cause the h-

V. Epigraphene Characterization

Raman spectroscopy is widely used to quantify disorder in graphene. To determine the damage caused by processing, a monolayer graphene on the Si face was measured before and after the h-BN deposition as follows. After the deposition, the h-BN layer was mechanically exfoliated to expose the underlying graphene layer so that its Raman spectrum can be measured. As shown in Fig. S12, the graphene Raman spectrum (laser excitation 532 nm) shows no D peak (at 1350 cm -1 ), confirming high graphene quality. The D-peak does not increase after deposition, indicating that the graphene layer was not damaged by the process. Significantly, the 2D peak (at 2715 cm -1 ) is slightly redshifted (2717 to 2714 cm -1 ) and broadened from (46 to 57 cm -1 ), consistent with the conversion of the buffer layer into a quasi-freestanding graphene layer (see main text) by hydrogen passivation of the SiC surface. The adsorption energy of B atom on the graphene(6x12) is 1.67 eV (gamma-point only)

The energy barrier of B atom diffusion on the graphene is 0.06 eV (gamma-point only)

The adsorption energy of N atom on the graphene(6x12) is 4.13 eV (gamma-point only)

The energy barrier of N atom diffusion on the graphene is 0.97 eV (gamma-point only)

The adsorption energy of B atom on the graphene(6x12) is 1.16 eV (6x6x1 k-points)

The energy barrier of B atom diffusion on the graphene is 0.10 eV (6x6x1 k-points)

The adsorption energy of N atom on the graphene(6x12) is 3.64 eV (6x6x1 k-points)

The energy barrier of N atom diffusion on the graphene is 0.75 eV (6x6x1 k-points)

Evaluation of binding and adsorption energies

The adsorption energy of n B atoms on the graphene area of the g/h-BN system is given by : 𝐸 !" g/ℎBN + 𝑛B = 𝐸 g/ℎBN + 𝑛𝐸 B -𝐸 g/ℎBN + 𝑛B ,

where 𝐸(g/ℎBN) is the energy of the g/h-BN system-that is, partial h-BN strip adsorbed on the graphene (g) surface and 𝐸(B) is the energy of a gas-phase B atom, and 𝐸(g/ℎBN + 𝑛B) is the energy of the g/h-BN system with n B atoms adsorbed on the graphene area.

For the B atoms that are adsorbed on the graphene surface (away from the partial h-BN strip) we can approximate 𝐸 !" (g/ℎBN + 𝑛B) as 𝐸 !" (g + 𝑛B), that is we can take 𝐸 !" (g/ℎBN + 𝑛B) ≅ 𝐸 !" (g + 𝑛B), where 𝐸 !" (g + 𝑛B) is calculated as follows:

𝐸 !" (g + 𝑛B) = 𝐸(g) + 𝑛𝐸(B) -𝐸(g + 𝑛B). As a result:

𝐸 !" g + 𝑛B ≅ 𝐸 g/ℎBN + 𝑛𝐸 B -𝐸 g/ℎBN + 𝑛B . (2)
In the following we will write 𝐸 !" (g + 𝑛B) as 𝐸 !" (𝑛B]) for simplicity 𝐸 !! 𝑛B ≅ 𝐸 g/ℎBN + 𝑛𝐸 B -𝐸 g/ℎBN + 𝑛B .

The energy of the g/h-BN system with n B atoms adsorbed on the graphene area is then 𝐸(g/ℎBN + 𝑛B) ≅ 𝐸(g/ℎBN) + 𝑛𝐸(B) -𝐸 !" (𝑛B)

The binding energy of n B atoms on the h-BN edge of the system is 𝐸 ! (𝑛B) = 𝐸(g/ℎBN + 𝑛B) -𝐸(g/ℎBN/𝑛B)

Using Eq. ( 4), Eq. ( 5

Figure 1 :Figure 2 :

 12 Figure 1: Cross-sectional HR-TEM of h-BN on epigraphene along the zone axis. (a) Colored high resolution image depicting coherence in the h-BN layer grown on one (possibly 2 layers) EG on the Si-face. Identification of the layers is obtained from the EDX analysis in (b). Disorder of the top h-BN layers is mainly due Ga ion damage from the FIB preparation. The spacing of the first graphene layer is 0.43 nm, indicating hydrogen intercalation at the SiC/EG interface. (b) EDX analysis of the HR-TEM image in (a) chemically resolving the N atoms in the h-BN layer, the Cin the graphene layer and the Si-atoms in the SiC layer (sensitivity-limited detected B is shown in Fig.S5, as well as FIB induced Ga contamination). (c) HR-TEM of another heterostructure, confirming that the h-BN layers are well ordered. (d) Zoom in the region in the red square in (c), showing an interlayer spacing of the h-BN layer of 0.345 nm and dominant AB stacking. Inset: Fast Fourier Transform showing AB stacking with some admixture of ABC stacking. (The disordered area between the well-ordered layers is a separation between layers due to delamination during the thin slab preparation.)

Figure 3 :

 3 Figure 3: (a) Colored SEM image showing a partially grown multilayer h-BN film on a multilayer C-face graphene after 1200 LED cycles. The size of the hexagonal 2D h-BN crystallites corresponds with the expected size for roughly one atomic front growth per cycle. The hexagons merge (they do not overlap) ultimately producing a single continuous sheet (see text). The large pleats on the bare graphene areas are commonly seen for the graphene on the C-face. (b)

Figure 4 :

 4 Figure 4: First-principle calculated mechanism of the growth of a h-BN film on epigraphene. The DFT model system consists of a graphene surface comprised of 6x12 hexagons, periodically replicated in the xy plane, partially covered by an h-BN strip. Boron atoms are depicted as red balls, nitrogen atoms in blue, and carbon atoms in grey color. In each of the panels (except for panel a) we include the DFT-calculated binding energy (per B or N atom) in eV units, associated with the corresponding stage of h-BN film growth shown. (a) The energy optimal initial configuration, showing a partially grown h-BN film adsorbed on the graphene surface. A top view is shown on the left. In the middle, we show a side view illustrating the 'floating' nature of the partially grown h-BN film. At the top right a zoomed view (from above) of the edge of the h-BN film is depicted, showing nitrogen termination of the growing front, with two of the N atoms bonded to the graphene surface. Below the above view we show an

FIGURE 4

 4 FIGURE 4

Fig. S1 :Fig. S2 :

 S1S2 Fig. S1: Representative atomic force microscopy images: (a-c) lateral force microscopy (LFM) and (d) topography of epigraphene. In the case of LFM, regions with tip-surface interactions near zero are graphene while the regions of higher tip interaction are buffer layer or SiC. Note that the contrast in the images was chosen to highlight the graphene features and is not consistent. (a) Monolayer graphene grown on the Si-face of SiC, exhibiting continuous graphene (bright contrast). The faint lines are SiC steps that graphene covers. No pleats are observed. (b) Graphene nanoribbons (dark lines) grown on natural SiC step edges on the Si-face. The terraces are covered with the buffer layer (c) Monolayer graphene domains (black) on the carbon-face of SiC. The light areas are bare SiC, since the graphene grows directly on the C-face, with no buffer layer. (d) Multilayer epigraphene on the carbon face, showing that graphene drapes over the entire surface with a pleated surface morphology.

Fig. S3 :

 S3 Fig. S3: Cross-sectional HR-TEM of a thick h-BN film on epigraphene prepared by FIB using a Pt coating (a) Large scale image showing the whole h-BN/EG/SiC heterostructure. Inset FFT of the h-BN region boxed in blue (b) zoom on the region boxed in yellow in (a), showing atomic resolution and the parallel layers close to the interface. (c) FFT of the region boxed in red close to the interface, showing h-BN (AB) stacking with some admixture of r-BN (ABC).

FFT

  (d)-(e) numerical simulation of diffraction for (d) h-BN (AB) stacking and (e) r-BN (ABC) stacking.High resolution X-ray diffraction (HR-XRD) scans covering the entire sample (about 15 nm h-BN on a few layer graphene on the C-face), as shown in Fig.S4, confirm the highly ordered h-BN were completed in triple-axis configuration with monochromatic Cu-Kα radiation on a Panalytical X'pert Pro MRD. The h-BN (0002) peak is located at 2θ = 25.35 ° corresponding to an interlayer spacing of 3.5 Å. This represents a 4.8% expansion over bulk h-BN (3.33 Å), and agrees with the HR-TEM results. The interplanar spacing of graphene is nearly identical to h-BN.

Fig. S4 :

 S4 Fig. S4: Representative HR-XRD taken from a 15 nm thick h-BN film deposited on few layer graphene grown on the C-face. The h-BN (0002) peak is located at 2θ=25.5°. The sharp, quasi-forbidden SiC peaks (SiC(0001) and its multiple orders) were used to ensure alignment to the substrate.

Fig. S6 :

 S6 Fig. S6: Electron Energy Loss Spectroscopy (EELS) on the same thin h-BN/EG/SiC slab as Fig. S5, and Fig. 1a-b confirms the EDX results, and the sp 2 character of the BN film. The red spectrum close to the EG interface presents an intense and sharp π* peak at 191.1 eV that is a fingerprint of sp 2 -hybridized B atoms in the hexagonal BN network, (i.e., a trigonal BN 3 bonding environment). The blue spectrum (7 nm above the SiC) and green spectrum (12 nm above the SiC) show the emergence of three additional features related to defective boron nitride film with some oxygen substitution to nitrogen. The yellow spectrum (20 nm above the SiC) presents the signature of a heavy BO 3 contamination 2-3 , due to thin slab processing.

Fig. S9 :

 S9 Fig. S9: Scanning electron images of the surface morphology of h-BN deposited on partially graphitized SiC. (a) h-BN on bare SiC, (b) h-BN on partially grown graphene structures on Si-face natural (disordered) steps (graphene is the smooth darker areas, outlined in red, the rest is the buffer layer), (c) h-BN on partially grown monolayer graphene on the C-face (graphene is the smooth darker areas, outlined in red, the rest is SiC), and (d) h-BN on uniformly covered monolayer Si-face graphene. The h-BN exhibits selective growth with a flat pleated surface morphology on graphitized regions and a granular structure on the SiC and buffer layer. The granular structure on the buffer layer is larger than on SiC.

Fig. S10 :

 S10 Fig. S10: (a) AFM topography 10 µm x 10 µm scan showing pleated h-BN morphology on monolayer Si-face graphene (25 nm thick h-BN). (b) profile along the white horizontal line in (a) across a pleat. The h-BN pleat heights are 5-15 nm.

  BN sheets to crumple. For these thick h-BN films, Raman spectra of as-deposited films show a broad band instead of the large peak shown in Fig 2d, which may be related to the disordered top layers.

Fig. S11 :

 S11 Fig. S11: XPS taken from the granular h-BN surface shown in the SEM image in the inset indicating sp 2 bonding, even in this case.

Fig. S12 :D

 S12 Fig. S12: (three upmost spectra) Raman spectra of the graphene before (red) and after (black) h-BN growth on a monolayer graphene on the Si-face, in comparison to bare SiC (blue). (bottom most pair) Same as above, but with the SiC spectra subtracted. The absence of a D peak, within the precision of the subtraction, clearlyshows that the LED process did not damage the graphene. For the red spectra, the h-BN layer was removed by mechanical exfoliation to expose the graphene.

7 )

 7 ) becomes𝐸 ! 𝑛B ≅ 𝐸 ! !!" + 𝑛𝐸 B -𝐸 !" 𝑛B -𝐸 g/ℎBN/𝑛B ,(6)with 𝐸 !" 𝑛B = 𝑛𝐸 !" B ,𝐸 ! 𝑛B ≅ 𝐸 ! !!" + 𝑛𝐸 B -𝑛𝐸 !" B -𝐸 g/ℎBN/𝑛B . (For n N atoms the formula for the binding energy of n N atoms to the h-BN growing edge is:𝐸 ! 𝑛N ≅ 𝐸 ! !!" + 𝑛𝐸 N -𝑛𝐸 !" N -𝐸(g/ℎBN/𝑛N).(8)In our calculation, 𝐸 B , 𝐸 N , 𝐸 !" B , and 𝐸 !" N are -0.25eV, -0.35 eV, 1.67 eV, and 4.13eV, respectively.

Fig. S14 :

 S14 Fig. S14: Geometrical structures and energies for one-dimensional h-BN growth in low-flux (consecutive) and high-flux (inconsecutive) growth modes. For the reader's convenience we include here Fig. 4 of the main text. (see detailed caption in the main text).

ACKNOWLEDGMENTS

Financial support was provided by the AFOSR under grant #FA9550-13-0217 and NSF #1506006. The work of UL and BY was supported by the AFOSR grant # FA9550-15-1-0519. Calculations were carried out at the GATECH Center for Computational Materials Science. This work was also made possible by the French American Cultural Exchange council through a Partner University Fund project. CB, VP, FF. and AL acknowledge funding from the European Union's Horizon 2020 research and innovation program under grant agreements No. 696656 (Graphene Core 1) and No 785219 (Graphene Core 2).

SUPPORTING INFORMATION

Additional data on (1) epigraphene morphology, (2) h-BN crystal structure, (3) h-BN chemical and dielectric characterization, (4) h-BN surface morphology, (5) epigraphene characterization, (6) theory.

The authors declare no competing financial interest.

Supporting Information

Highly Ordered Boron Nitride/Epigraphene Epitaxial Films on Silicon Carbide by Lateral Epitaxial Deposition

I. Epigraphene Morphology

The morphology and electronic properties of epigraphene 1 depend on its growth conditions and growth face, as shown in Fig. S1. On the silicon-terminated face of 4H-SiC (that is (0001)), the buffer layer is the first graphene-like layer at the interface with SiC. It exhibits strong interactions to the SiC substrate, which induces structural corrugation and semiconductor properties. The subsequent layer has the iconic graphene band structure. Graphene on the Si-face is flat and shows no pleats. It covers uniformly the SiC wafer and traces of bilayer are observed, at steps edges. If graphitization is stopped before graphene grows onto the SiC terraces, graphene nanoribbons can be formed on sidewall of SiC steps, separated by buffer layer on the terraces. On the carbonterminated face (SiC(0001)), multilayer graphene (with rotational layer stacking) is produced, yielding a pleated structure due to the negative in-plane coefficient of thermal expansion and weak interlayer forces. 1

II. h-BN Crystal Structure

Cross sectional HR-TEM images in Fig. S2 andS3 show a layered h-BN structure with a pristine graphene-h-BN interface and no visible grain boundaries. Fast Fourier Transform (FFT) analysis confirms BN layer stacking. The atomic positions can be seen within the graphene and h-BN layers in Fig. S3b, confirming epitaxy between the h-BN, graphene, and SiC.

Energy dispersive X-ray spectroscopy (EDX) and Electron Energy Loss Spectroscopy (EELS) were performed on cross sectional samples (same as Fig. 1a-b, main text), as shown in Fig. S5 and S6. A sharp interface between the SiC, graphene, and h-BN is observed. The cross-section was produced by a gallium ion beam (FIB) that penetrated through an amorphous carbon protection layer, contributing to the layer distortion. Thus, high gallium and carbon and oxygen are incorporated in the top h-BN layers.


Raphael Remonnay
email: remonnay@lyon.fnclcc.fr

Nathalie Havet

Magali Morelle

Marie-Odile Carrere

Raphaël Remonnay

ANALYZING THE DETERMINANTS OF WILLINGNESS-TO-PAY VALUES FOR TESTING THE VALIDITY OF THE CONTINGENT VALUATION METHOD. APPLICATION TO HOME CARE COMPARED TO HOSPITAL CARE

Keywords: contingent valuation, validity, protest responses, censored data, home care

The contingent valuation (CV) method is an attractive approach for comparing home care to hospital care in which the only difference is patients' well-being during the treatment process and not health outcomes. We considered the empirical situation of blood transfusion (BT) in cancer patients and collected willingness to pay (WTP) values among BT users.

Our main objective was to test the validity of the CV method, namely its ability to elicit true preferences. Firstly, possible determinants of WTP values and their expected influences were identified, from both economic and non economic literature and from the findings of a pilot study.

Secondly, they were compared to predicted influences resulting from appropriate econometric analysis of WTP values elicited by a bidding process. From the health economics literature it appeared that the double-hurdle model is the most appropriate approach to account for zero values and protest responses. However, because the number of protest responses was too small, we used a truncated regression model.

None of the 7 hypothesized influences was invalidated by econometric results. The anchoring bias hypothesis was confirmed. The WTP for home BT compared to hospital BT increased with household income, with previous experience of home care, with living far from the hospital and with low quality of life. Conversely, it was lower for advanced-stage (palliative or terminal) than for early-stage (curative) patients.

We conclude that the CV approach is acceptable to severely ill patients. Moreover, WTP values demonstrate good validity given that influences predicted by our model are consistent with expected determinants.

INTRODUCTION

In recent years, a growing number of studies conducted in the health care field have used contingent valuation (CV), as reported in several literature reviews [START_REF] Diener | Health care contingent valuation studies: A review and classification of the literature[END_REF][START_REF] Olsen | Theory versus practice: A review of willingness to pay in health and health care[END_REF][START_REF] Smith | Construction of the contingent valuation market in health care: a critical assessment[END_REF][START_REF] Yeung | Empirical implications of response acquiescence in discrete-choice contingent valuation[END_REF]. The CV method has been used for evaluating all types of health care strategies, either preventive, diagnostic or therapeutic.

Meanwhile, its ability to provide the "true" preferences of the respondents has been extensively questioned. Accordingly, numerous validity properties such as criterion validity, content validity and construct validity have been defined and empirically tested using willingness-to-pay (WTP) responses.

Analyzing the determinants of WTP values can be a valuable way of assessing the validity of the CV method. Indeed, possible determinants and their expected influences can be derived from theoretical predictions or empirical literature, then confirmed or not using WTP data.

For example, the respondent income should positively influence WTP values according to construct validity (Donaldson, 1999; Smith et al., 1999 b ; Drummond et al., 2005). However, analyzing the determinants of WTP has received limited attention in health economics. The empirical literature about WTP has focused more on the method used for data collection and on possible consequences on the monetary values obtained (Smith 2003; Smith 2006; Smith 2007 a, b ).

The technique used for econometric analysis of WTP data is nevertheless an important issue because an inappropriate choice can lead to erroneous inferences about the determinants of WTP and consequently about validity. Econometric modeling should fit the type of WTP question asked [START_REF] Donaldson | Willingness to pay for antenatal carrier screening for cystic fibrosis[END_REF][START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF][START_REF] Dalmau-Matarrodona | Alternative Approaches to obtain optimal bid values in contingent valuation studies and to model protest zeros. Estimating the determinants of individual's willingness to pay for home care services in day case surgery[END_REF][START_REF] Kurth | The Benefit of Health Insurance Coverage of Contraceptives in a Population-Based Sample[END_REF]. A closed-ended approach and a dichotomous choice with follow-up provide qualitative binary responses while a payment scale approach, an open-ended question and a bidding process generate continuous monetary WTP values [START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF]. In the 3 latter cases, the WTP distribution is usually censored so that the data may contain a large proportion of zero values, for which there is a range of possible explanations such as protest responses or real zeros consistent with economic decisions.

The objective of the present study was to analyze the determinants of WTP values in the framework of a CV survey aimed at comparing hospital care to home care. Home care is a promising alternative to hospital care in many health care situations. However, to our knowledge, the two options have never been compared using the CV approach.

We shall first present the empirical situation studied, the CV study design, the WTP questioning process, the selection of possible determinants of WTP values and sample characteristics. Secondly, the health economics literature on the econometric methods currently used for analyzing determinants of WTP data will be investigated, with a special focus on censored data and protest responses. Thirdly, the WTP values obtained will be analyzed using appropriate econometric modeling, and results will be compared to the expected influences of pre selected possible determinants. In conclusion, we will discuss the implications of our study regarding the validity of the CV method.

EMPIRICAL SITUATION, CV STUDY DESIGN AND DATA COLLECTION

Empirical situation

CV is an attractive alternative to the Quality-adjusted life years (QALYs) approach when it comes to comparing two types of health care management which differ only in patients' wellbeing during the treatment process and not in health outcomes [START_REF] Ryan | Assessing the benefits of health care: how far should we go?[END_REF][START_REF] Olsen | Theory versus practice: A review of willingness to pay in health and health care[END_REF]. This is the case for some treatments which can be delivered at home or in the hospital day-care unit, such as blood transfusion (BT) in cancer care. BT is currently administered to advanced-stage cancer patients for curative, palliative or terminal intent. BT is simple to administer, with identical effectiveness and safety at home, in the framework of a homecare network, or in the hospital [START_REF] Idri | La transfusion à domicile ? Une alternative à l'hôpital de jour[END_REF][START_REF] Madgwick | A home blood transfusion programme for betathalassaemia patients[END_REF].

Administration at home requires neither transportation between home and hospital nor waiting time in the hospital and may decrease the patient's tiredness; however, it may also increase the feeling of insecurity and isolation. As a result, home administration compared to hospital administration may be viewed differently from one patient to another.

Study design

A CV survey conducted in the Comprehensive Cancer Centre of the Rhone-Alps Region in Lyon, France, compared hospital BT to home BT. As said before, our analysis focused on WTP values. Willingness-to-accept (WTA) values were also collected for further analysis.

A prospective pilot study using the same design as the main study was conducted in 40 eligible patients to assess whether a CV survey was feasible in this situation, i.e. among patients personally involved in the treatment under consideration, most of them severely ill. situation under investigation.

The pilot study demonstrated the feasibility of the CV survey: of the 44 patients planned, only 4 did not consent to participate because they felt too tired for the 45-minute interview.

Therefore, a prospective study was conducted on a 12 months period in 2003 and 2004. All cancer patients needing a BT and aged more than 18 years were asked to participate. All were eligible to receive BT either at home or in the hospital. They were allocated between home BT and hospital BT according to organizational possibilities. For example, home BT was only available in a few well defined geographical areas. After obtaining informed consent, and less than 48 hours after BT administration, face-to-face interviews were conducted by a trained interviewer on the basis of a detailed guide. Although costly, this type of interview was chosen for minimizing hypothetical biases and improving the quality and rate of responses (Mitchell and Carson, 1989; NOAA, 1993, 1994; Smith et al., 1999 a ).

Patients were first asked whether they had already undergone home BT (including the current procedure when it was administered at home) and whether they had already received home care, other than BT. They were then given a detailed presentation of the two BT managements, either at home or in the hospital, and were told that effectiveness and safety were identical in both cases. Finally, they were asked where they would choose to receive their next BT, would they need another one in the future and would the two BT managements be available.

WTP questioning process

Once they have chosen the BT arrangements, all patients were given a general presentation of the CV method, which was introduced as a way of measuring their preference for the type of BT management they had chosen, as compared to the other one, without consideration of the corresponding costs for the health care system. Then they were asked to imagine a hypothetical future situation where they would need another BT and where the only freely available management would be the one they had not chosen. Then the interviewer asked them how much they would be willing to pay to get their preferred BT management rather than the free alternative. We chose out-of-pocket expenditure which is the recommended payment vehicle when respondents are personally involved [START_REF] Smith | Construction of the contingent valuation market in health care: a critical assessment[END_REF][START_REF] Mitchell | Using Surveys to Value Public Goods: The Contingent Valuation Method[END_REF][START_REF] O'brien | When do the "dollars" make sense?[END_REF]. Thus, in reference to prospect theory [START_REF] Kahneman | Prospect Theory: An Analysis of Decision Under risk[END_REF], WTP was framed as a gain (Sayman and Öncüller, 2005). Indeed, we considered that framing the WTP question as a gain rather than a loss would be easier to understand.

For asking WTP questions we preferred using a bidding process rather than closed-ended questions because of our small sample size [START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF]. The process involved three steps. First, an initial bid of money was proposed to the patients. If they agreed to pay, we proposed a higher bid, whereas if they did not we proposed a lower one. This step was repeated twice. Patients were randomly assigned to two initial bids of money (38€ and 76€) to test for a possible anchoring bias affecting content validity (Herriges and Shogren, 1994;[START_REF] Flachaire | Starting point bias and respondent's uncertainty[END_REF]. The range from 38€ to 76€ was chosen because it was close to the range of fees normally covered by social insurance in France for a home visit by a specialist (including call-out charges).

Selection of possible determinants of WTP values

As said before, a possible anchoring bias was tested: according to health economics literature, choosing a higher initial bid value could increase WTP responses, but would in no way decrease them (Smith et al., 1999 b ). Apart from this possible influence related to the framing of questions, we also investigated some personal characteristics of the patients, selected on the basis of previous knowledge of their possible influence on patients' preferences and WTP values.

The health economics literature suggests that income positively influences WTP values (Donaldson, 1999; Smith et al. 1999 b ; Drummond et al., 2005). Hence patients were asked their household incomes.

The medical literature indicates that previous experience of home care promotes preference for home care compared to hospital care. A Cochrane Collaboration literature review by Shepperd and Iliffe compared home care to hospital care in randomized studies [START_REF] Shepperd | Hospital at home versus in-patient hospital care (Cochrane Review)[END_REF]. They concluded that patients who had no a priori preferences (since they agreed to participate in a randomized trial) generally expressed higher satisfaction after experiencing home care compared to hospital care. Accordingly, we asked our patients whether they had previously experienced home care, either for BT or any other procedure.

In the pilot study, patients were asked which BT management they preferred, and why. More precisely, they were proposed a list of possible reasons for their choice and were asked to state the importance of each reason using a 5-point Likert scale ranging from "not important at all" to "very important". Reasons were statistically compared according to importance using a Friedman's test, and a follow-up multiple comparison test. On the one hand, the most important reasons for preferring home BT were that it avoided disruption in daily life and that it spared transportation and waiting time in the hospital. On the other hand, hospital BT was mainly preferred because it allowed to clearly separate daily life from health care and because it was perceived as safer.

We assumed that, all other things being equal, patients would be all the more willing to spare transportation and waiting time as they lived far from the hospital and as their quality of life (including tiredness) was low. We thus selected two possible determinants of patients' preferences: distance between home and hospital, and a health-related quality of life index including tiredness as measured by the Functional Assessment of Cancer Treatment General scale (FACT-G) [START_REF] Cella | The Functional Assessment of Cancer Therapy Scale: development and validation of the general measure[END_REF].

Considering safety, we assumed that patients would be all the more sensitive to this concern as their life was threatened, which was taken into account by collecting information on their disease stage. Three stage levels were used: curative, palliative and terminal.

Regarding daily life, patients' preferences referred to contradictory reasons. Some wished to avoid disruptions in daily activities, whereas others wanted to clearly separate daily life from health care. We collected data on patients' characteristics which could influence their feelings about daily life, i.e. marital status and having children at home or not, without foreknowledge of their influence on preferences. Other variables like standard demographics, gender, age and employment status were collected as controls, with no a priori assumption whatsoever on their possible influences.

Sample characteristics

On the study period, all 153 eligible patients consented to participate. However, 14 people could not be interviewed within the 48 hours following their BT either because of lack of availability or because they felt too tired. As a result, 139 patients were enrolled, which corresponds to a 90% response rate. Their characteristics are presented in Table I.

All patients' characteristics were documented by the patients themselves, except stage of disease which was assessed as curative, palliative or terminal by the oncologist in charge of the Home Care Unit at the Cancer Centre. The quality of life index measured using the FACT-G scale varied from 0 (worst possible situation) to 108 (best possible situation).

[Insert Table I over here] Median monthly household income was between 1500€ and 2300€. Almost one in two respondents had previous experience of home BT on the one hand, and of home care (except home BT) on the other (43.2% and 45.3% respectively). Distance from home to hospital was close to 35 km in average, with a high 100% variation coefficient. Quality of life according to the FACT-G scale was rather poor, with an average index of 61.7 (range 0-108). Regarding stage of disease, patients were almost equally distributed between curative stage on the one hand and palliative or terminal stage on the other.

Standard demographics were as follows: patients were 57.5 year old in average (SD=12.8) and 3.2% had a professional occupation. Finally, patients were equally distributed between males and females.

HEALTH ECONOMICS LITERATURE SURVEY: ECONOMETRIC MODELS FOR ANALYZING DETERMINANTS OF WTP VALUES RESULTING FROM A BIDDING

PROCESS

For [START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF], the appropriate technique for econometric analysis of WTP data depends firstly on the type of question asked. For example, closed-ended questions and dichotomous choice with follow-up valuation only generate qualitative responses for WTP. This is why it is advised to use discrete choice models such as binary logit and probit for regression analysis [START_REF] Johannesson | Willingness to pay for antihypertensive therapy-results of a Swedish pilot study[END_REF][START_REF] Johannesson | Willingness to pay for antihypertensive therapy -further results[END_REF]. For data elicited by using a payment scale, the most appropriate econometric methodology is grouped data regression, also called interval regression or ordered logit/probit [START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF][START_REF] Yasunaga | Willingness to pay for health care services in common cold, retinal detachment and myocardiac information: an internet survey in Japon[END_REF][START_REF] Bärnighausen | Willingness to pay for social health insurance among informal sector workers in Wuhan, China: a contingent valuation study[END_REF]. When using an open-ended question or a bidding process -as was the case in our study -the WTP values obtained are quantitative and several modeling methods have been proposed in the literature.

For responses obtained through the bidding process, the first regression analysis studies conducted in the health care field began in the 1980s and mostly estimated standard linear models by ordinary least squares (OLS) [START_REF] Berwick | What do patients value? Willingness to pay for ultrasound in normal pregnancy[END_REF][START_REF] Thompson | Willingness to pay and accept risks to cure chronic disease[END_REF]O' Brien and Viramontes, 1994;Miedzybrobzka et al., 1995). 1 However, the observed data for WTP responses are generally censored. When analyzing the distribution of WTP, we generally observe that the WTP variable does not take values below zero and has positive density at zero. The large proportion of zeros calls into question the continuity of the dependent variable and consequently the use of the classical multiple regression model. In the presence of data censoring, OLS estimation yields biased and inconsistent estimates because 1 The dependent variable of WTP values could be expressed in level, in logarithm or in square roots. Besides, [START_REF] Amin | A contingent valuation study to estimate the parental willingness-to-pay for childhood diarrhoea and gender bias among rural households in India[END_REF] used a linear specification for WTP values, but supposed that they followed a log-normal distribution. Consequently, their estimations were based on maximum likelihood estimators instead of OLS. it fails to account for the qualitative difference between limit (zero) observations and nonlimit (continuous) observations. Consequently, all conclusions on the determinants of WTP are potentially erroneous. The Tobit model is the correct alternative frequently proposed for such censored data in contingent valuation literature in health economics [START_REF] Donaldson | Willingness to pay for antenatal carrier screening for cystic fibrosis[END_REF][START_REF] Kurth | The Benefit of Health Insurance Coverage of Contraceptives in a Population-Based Sample[END_REF].

However, the underlying assumption in the Tobit model is that the same specification is used both for the continuous and the zero decision processes. This implies that the Tobit specification is relevant only if all zero realizations represent an economic decision, i.e. a real zero preference for the health care program under evaluation. Other quite reasonable determinants of zero observations, such as the presence of protest zeros which are common in contingent valuation surveys, also exist. Protest responses do not reflect individual patient preferences and have no economic significance [START_REF] Lindsey | Market models, protest bids, and outliers in contingent valuation[END_REF][START_REF] Jorgensen | Protest Responses in Contingent Valuation[END_REF]. They may reflect participants' objection to being asked to complete the questionnaires, or indicate an ideological position about the inappropriateness of placing monetary values on health.

Protest patients refuse to reveal their real willingness even though it is positive. On the contrary, respondents genuinely place zero value on the WTP question, through stating that they have no strong (nil or very small) preference for it or they cannot afford to pay. Their responses have true economic significance. The issue at stake in the literature has thus been the development of appropriate empirical models to treat protest responses in addition to censored data. Several approaches have been proposed.

The simplest and most frequently used solution is to discard protest zeros. Nevertheless, this approach is generally incorrect from a statistical point of view: a sample selection bias is introduced if the socioeconomics and other personal characteristics of the protest patients are significantly different from the rest of the sample. Under such conditions, discarding protest responses produces biased estimates, which are not interpretable and unusable to test validity.

The second solution is to indirectly address the issue of protest responses. Because zero responses may have explanations other than a genuine zero WTP, [START_REF] Donaldson | Limited dependent variables in willingness to pay studies: applications in health care[END_REF] considered that positive WTP values and zero values could significantly differ in their determinants. In fact, positive WTP values stem from an economic decision-making process whereas zero values are a mixture of significant economic responses and protest responses.

They proposed a specification of the censoring mechanism more flexible than Tobit, called the type II Tobit model [START_REF] Amemiya | Tobit models: a survey[END_REF]). 2 This model permits the coexistence of different patterns for the question of how much and whether to pay for the care under evaluation. One set of parameters determines the impact of the characteristics on the probability to record a positive WTP value, and the second set characterizes the determinants of the positive WTP amount:

⎩ ⎨ ⎧ > + = =
), ( 0 The third econometric approach, the double-hurdle model used by [START_REF] Dalmau-Matarrodona | Alternative Approaches to obtain optimal bid values in contingent valuation studies and to model protest zeros. Estimating the determinants of individual's willingness to pay for home care services in day case surgery[END_REF], represents an interesting modification of the type II Tobit model by explicitly emphasizing protest responses. 3 It decomposes the behaviour of individuals in the decisionmaking process in two parts: first, the reasons for deciding to participate or not in the contingent market offered, i.e. to give or not a protest response (participation equation: first hurdle), and second, the decision on the amount to consume, that is how much they are willing to pay for the procedure (consumption equation: second hurdle).

) ( 0 1 1 1 1 *
Participation equation: For a general presentation of this model, see [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF][START_REF] Jones | A Note on Computation of the Double Hurdle Model with Dependence with An Application to Tobacco Expenditure[END_REF], [START_REF] Blundell | Unemployment and female labour supply[END_REF].

⎩ ⎨ ⎧ > + = = ; 0 ) ( 0 1 * else responses protest u Z P if P i i i i γ Consumption equation: ⎩ ⎨ ⎧ = = = = > = , 0 1 0 0 1 0 * * * i i i i i i i
double-hurdle methodology. Consequently, the consumption equation in the double-hurdle model allows to obtain unbiased and efficient estimations for the determinants of WTP for the whole sample. 4 This is why the double-hurdle model seems to constitute the most robust approach for empirically testing validity in contingent valuation in the presence of censored data and protest responses.5

Even if the double-hurdle approach is attractive, it cannot provide reliable estimates when the number of protest responses is too small. In that case, the most appropriate econometric methodology is a truncated regression model [START_REF] Mahmud | Contingent Valuation of Mortality Risk Reduction in Developing Countries: A Mission Impossible[END_REF]

ANALYZING THE DETERMINANTS OF OUR WTP VALUES

Choice of modeling

As reported in Section 2, WTP data were collected in 139 patients. Forty-two patients responded that they would prefer to receive BT in the hospital versus 97 at home, i.e. 30%

versus 70%, respectively. Given that a large majority of patients preferred home BT to BT, we decided to favour WTP data associated with preference for home BT.

Accordingly, the 42 patients preferring hospital BT were considered to have real zero or negative WTP values for home BT.

Of the 97 patients preferring home BT, 3 expressed comprehension problems with the WTP question and their responses were eliminated from empirical analysis. Of the 94 remaining patients, 74 provided a strict positive WTP response and 20 chose a zero value indicating either protest responses or real zeros. The identification of protest zeros was based on responses to a follow-up question on the reasons for unwillingness to answer. Eight respondents reacted negatively to the payment vehicle and gave reasons for their zero WTP value such as "I have paid health insurance premiums all my life and I should not have to pay anything more", "the goal of this kind of study is that we pay more and more for care", "I do not want to pay for blood when the donors are voluntary". These 8 respondents were considered protest bidders. The other 12 patients who stated a zero response without any justification or because of low income were considered as real zeros. Apart from the 3 unusable and the 8 protest WTP responses, the mean WTP for home BT (as compared to hospital BT) among the 86 remaining patients was approximately 60€ (60.9€) with a standard deviation close to 55€ (54.8€).

Censored data should receive a particular attention in our empirical analysis because, with the 42 patients who expressed a preference for hospital BT and were treated as real zero or negative WTP values and the 20 patients who preferred home BT but also stated a zero value (8 protest and 12 non protest responses), they represented 45% of the whole sample (62/139).

Since only 8 protest bidders were identified, it was not reasonable to estimate the participation equation of a double-hurdle model, i.e. to identify the variables influencing the choice of a respondent to reveal or not its real preferences. Nevertheless, discarding protest responses, even in limited number, could produce biased results. In this case, and as discussed above, the most appropriate econometric methodology is a truncated regression model. This model specifies the probability to observe the amount of WTP, conditional on the expression of a positive willingness to pay. The dependent variable y i was defined as the logarithm of the expressed WTP value in the model equation:

i i i i i i u X y with y if y y + = > = β * * 0 (1)
where y i is the value of the ith observation on the dependent variable log(WTP) and its corresponding latent value, described by the relation with

X * i y i i i u X y + = β * i the independent
variables that influence the WTP amount, β the unknown parameters and u i the error term such as . The likelihood function can be written as follows:

) , 0 ( 2 s N u i → ∏ ∏ + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ - = > = = s X F s X y f s y y y P L i i i i i i β β 1 ) 0 ( * (2)
where ∏ refers to the product over positive observations for y + i and F(.) and f(.) refers to the standard normal cumulative distribution function and density function, respectively. The unknown parameters are the solution to the maximization of the likelihood function.

Results

The results of the truncated model are reported in Table II.

[Insert Table II over here] According to the truncated regression model, several patient characteristics were significantly associated with the WTP value for home BT (as compared to hospital BT): income, experience of home care, distance from home to hospital, stage of disease, marital status (living with a partner) and professional occupation (p < 0.05), as well as health-related quality of life (FACT-G) and age (p < 0.1).

Initial bid was also significantly associated with WTP (p < 0.01).

However, neither having children at home, previous experience of home BT, nor gender seemed to influence WTP values.

Compared with econometric results, none of the expected influences of pre selected possible determinants was invalidated (Table III).

[Insert Table III over here]

Considering patients characteristics, the WTP value increased with higher income, as commonly reported in the health economics literature on contingent valuation. Even if the WTP value did not seem to depend on previous experience of BT at home, it did depend on experience of home care other than BT. As said before, this is consistent with non-economic literature findings according to which previous experience of home care favours further preference for home care compared to hospital care.

Regarding the possible determinants selected on the basis of the results of our pilot study, we observed, as expected, that patients living far from the hospital stated a higher WTP for home BT (compared to hospital BT) than the others. Likewise, those with a higher health-related quality of life stated a lower WTP for home BT, which means that home BT was all the more appreciated, as compared to hospital BT, as patient quality of life (including tiredness) was low. This is in agreement with the results collected in the pilot study, which identified sparing painful transportation and waiting time as strong reasons for preferring home BT. WTP for home BT was higher at early stages of the disease (curative) than at advanced stages, i.e. palliative or terminal. Referring to the safety concern expressed in the pilot study by patients preferring hospital BT, receiving hospital BT instead of home BT was all the more appreciated as patients' lives were threatened.

We could not hypothesize on the possible influences of other patients characteristics on WTP values. They were thus introduced in the model as control variables. Econometric results did not show any influence of either gender or having children at home. However, lower WTP values for home BT were obtained for patients living with a partner, which means that these appreciated hospital BT (compared to home BT) more than the others. This could result from a wish of clearly separating daily life from healthcare, as stated in the pilot study by patients.

All other things being equal, WTP for home BT was higher for older people, and it was lower in patients with a professional occupation. These findings are not counterintuitive but could not be anticipated from what was known at the beginning of study.

Finally, the anchoring bias hypothesis was confirmed: all other things being equal, the WTP value for home BT increased when the initial bid was higher, which is consistent with results published in the health economics literature.

DISCUSSION/CONCLUSION

Home care may be an interesting alternative to hospital care, especially in chronic diseases.

Accordingly, it is more and more used for cancer care, particularly for severely ill patients, including those at a palliative or terminal stage of their disease (Francks et al., 2000;[START_REF] Emanuel | Cost saving at the end of life. What do the data show?[END_REF]Zimmerman et al., 2008). Home care has been extensively studied as a possible substitute for hospital care, regarding either costs or patients' quality of life and satisfaction [START_REF] Brumley | Increased Satisfaction with Care and Lower Costs: Results of a Randomized Trial of In-Home Palliative Care[END_REF]Shepperd and Illife, 2001).

To our knowledge, the CV method had never been used for comparing home care to hospital care. However, it is an attractive approach for evaluating different types of health care management that differ only in patients' well-being during the treatment process and not in health outcomes [START_REF] Ryan | Assessing the benefits of health care: how far should we go?[END_REF][START_REF] Olsen | Theory versus practice: A review of willingness to pay in health and health care[END_REF].

We considered the empirical situation of BT in cancer patients and we collected WTP values among BT users. In so doing, we chose to elicit use value, and not externality or option values. Indeed, we wanted to know whether a WTP questioning would be acceptable to severely ill patients, i.e. whether they would be willing not only to participate in the survey, but also to give non protest responses.

Protest responses could result from emotional and ethical concerns, as well as from social responsibility considerations [START_REF] Jorgensen | Fairness in the Contingent Valuation of Environmental Integrated knowledge for ecological economics: a database to support ecosystem services evaluation[END_REF]Sayman and Onçüller, 2005 ;[START_REF] Meyerhoff | Protest Beliefs in Contingent Valuation: Explaining Their Motivation[END_REF], all dimensions which were encountered in our situation. Emotional and ethical aspects could be particularly important for patients at palliative or terminal stages; some of them even claimed that "health is invaluable". Social responsibility could also be an important concern since a survey using a WTP approach could call into question the principle of solidarity under which the cost of cancer care is completely covered by national health insurance in France.

The response rate of our study was high (90%) and most patients (70%) expressed a preference for home BT. Of the 94 patients who preferred home BT and who did not express understanding problems, only 8 gave protest responses, which corresponds to a less than 10% protest responses rate. Overall acceptability was thus high among BT users.

Our main objective was to test the validity of the CV method, namely its ability to elicit true preferences. For so doing, we chose a two-step approach. First, we identified possible determinants of our WTP values and their expected influences, on the basis of both economic and non economic literature. We also extrapolated from the findings of a previous pilot study.

Second, we compared them to predicted influences as resulting from appropriate econometric analysis. The choice of appropriate econometrics for analyzing WTP values resulting from a bidding process is essential for obtaining relevant results. One must take into account that censored data at zero value correspond either to real zero values or to protest responses. As a consequence, suitable modeling should (1) involve the whole sample (including non zero responses, protest zeros and real zeros), (2) take the different behaviors at work into account (protest versus non protest responses). Based on a health economics literature survey, we concluded that the double-hurdle model would be the most appropriate approach to fulfill these two conditions. However, the estimation of the separation equation requires a sufficient number of protest responses. Because we had only few protest responses, we used a truncated regression model rather than a type II Tobit model in which estimated parameters for zero values would not be interpretable.

None of the 7 hypothesized influences was invalidated by our econometric results. First, the anchoring bias hypothesis was confirmed. Regarding the possible influence of patients' characteristics, the WTP for home BT compared to hospital BT increased with the household income, with previous experience of home care, with living far from the hospital and with low quality of life. Conversely, the WTP for home BT was lower for advanced-stage (palliative or terminal) patients than for early-stage (curative) patients.

These results first underline the interest of using all a priori relevant sources of information for selecting possible determinants of WTP values. Second, because of the good consistency between expected and predicted influences of patients' characteristics on WTP values, our results may have some implications for policy-making. They suggest that, all other things being equal, home care should be considered in priority for people living far from hospital and people with low health-related quality of life. Regarding the stage of the disease, preference for home seemed to be lower among patients receiving palliative or terminal care than among those receiving curative care. This result may seem to contradict other medical literature findings according to which home care could improve satisfaction or quality of life in palliative patients [START_REF] Zimmermann | Effectiveness of specialized care : A systematic review[END_REF]Shepperd and Illife, 2001). However, we believe that there is no contradiction between the different conclusions since these authors did not compare patients' opinions across the different stages of disease.

From our study we conclude that, based on WTP values, the CV approach is acceptable to severely ill patients. Moreover, WTP values even demonstrate good validity, given that predicted determinants are consistent with expected ones. the CV approach, but it might be important to investigate also the potential role of WTA. For a number of reasons, the use of WTA for decision making is not recommended. Studies investigating given health care programs have shown that WTA is generally higher and more scattered than WTP (Smith et al., 1999 b ; Brown, 2005; Sayman and Onçüler, 2005; Whynes and Sach, 2007). On the basis of the WTA values also collected in our CV survey, we aim to investigate, in a further analysis, the potential role of WTA for testing CV validity.

  approach does not differentiate zeros generated by economic decisions (genuine zero values) from zeros generated by non-economic decisions (protest zeros), which makes interpretation difficult. 2 This econometric specification is also called the sample selection model. The two-part model is a special case of the type II Tobit model.

  type II Tobit model, the main advantage of the double-hurdle model is that the participation equation allows not only to determine the socioeconomic and personal characteristics of the protest respondents, but also to better define the WTP equation. In fact, in the type II Tobit model, the expression of the WTP equation depends on a selection equation which determines whether a positive WTP value is recorded. In the double-hurdle model, the WTP equation depends on the participation equation. But, because opposing protest responses to responses that reflect true preferences has more economic sense than opposing zero values to positive values, the selection is better taken into account in the 3

Table II . Results of the truncated regression model of WTP (log) values

 II

	Explanatory variables	Coefficient	SE	p-value
	Intercept	3.17630	0.514	0.000 ***
	Income (1= 2 300 € or more)	1.02655	0.142	0.000 ***
	Experience of home BT (1=yes)	0.16635	0.160	0.298
	Experience of home care, except BT (1=yes)	0.41905	0.124	0.001 ***
	Distance to hospital (continuous scale)	0.00365	0.002	0.045 **
	FACT-G (continuous scale)	-0.00944	0.005	0.060 *
	Stage of disease (1=curative; 0=palliative or terminal)	0.30030	0.128	0.019 **
	Living with a partner (1=yes)	-0.45585	0.162	0.005 ***
	Children at home (1=yes)	0.21794	0.133	0.102
	Gender (1=male)	0.17425	0.130	0.180
	Age (continuous scale)	0.01247	0.006	0.053 *
	Professional occupation (1=yes)	-0.49574	0.146	0.001 ***
	Initial Bid (1=76 €; 0=38 €)	0.37818	0.125	0.003 ***
	σ	0.46671	0.040	0.000 ***
	Number of observations	68
	Log likelihood	-44.66932

Table III . Expected and predicted influences of possible determinants of WTP (log) values

 III

		Expected	Predicted
	Explanatory variables	influence	influence
	Income (1= 2 300 € or more)	+ a	+ ***
	Experience of home BT (1=yes)	+ b	NS
	Experience of home care, except BT (1=yes)	+ b	+ ***
	Distance to hospital (continuous scale)	+ c	+ **
	FACT-G (continuous scale)	-c	-*
	Stage of disease (1=curative; 0=palliative or terminal)	+ c	+ **
	Living with a partner (1=yes)	? c	-***
	Children at home (1=yes)	? c	NS
	Gender (1=male)	?	NS
	Age (continuous scale)	?	+ *
	Professional occupation (1=yes)	?	-***
	Initial Bid (1=76 €; 0=38 €)	+ a	+ ***

a According to health economics literature. b According to medical literature. c According to pilot study results * p<0.1; ** p<0.05; *** p<0.01

The double-hurdle model can be viewed as a tobit method with selectivity.

* p<0.1; ** p<0.05;*** p<0.01

ACKNOWLEDGEMENTS

Special thanks go to Dr Yves Devaux, without whom this study would not have been possible. Yves Devaux is head of the oncology home care-coordination unit located at the comprehensive cancer center of Lyon.

We are also grateful to Valerie Kante, Josette Chalencon and the home care coordination team for their help in patient recruitment, to Marie-Dominique Reynaud for editorial assistance, and to Izabela Jelovac for valuable comments.

Our study received financial support from the French Ministry of Health.