E Bustarret
email: etienne.bustarret@neel.cnrs.fr

Superconductivity in doped semiconductors

A historical survey of the main normal and superconducting state properties of several semiconductors doped into superconductivity is proposed. This class of materials includes selenides, tellurides, oxides and column-IV semiconductors. Most of the experimental data point to a weak coupling pairing mechanism, probably phonon-mediated in the case of diamond, but probably not in the case of strontium titanate, these being the most intensively studied materials over the last decade. Despite promising theoretical predictions based on a conventional mechanism, the occurrence of critical temperatures significantly higher than 10 K has not been yet verified. However, the class provides an enticing playground for testing theories and devices alike.

Introduction : half a century in a nutshell.

The notion that "doping" an insulating material by inserting or substituting atoms with a different valence state may bring about superconductivity (below an experimentally accessible critical temperature TC) is not new. It has been successfully applied to various classes of solids, whereby the resulting free carrier density became a tunable variable, as illustrated in many contributions to this special issue. However, there was a time when the occurrence of superconductivity in materials with appreciably less than one carrier per atom was an open question. The main reason for this was that a lower carrier density was expected to reduce the efficiency of dielectric screening to the point where Coulomb repulsion could not be overcome by any pairing mechanism. In this context, the idea that semiconductors chemically doped beyond the critical value nMIT for a metal-insulator transition to occur would eventually become superconductors was suggested and discussed quite early on for three-dimensional (3d) degenerate systems [1][2][3][4] . It was experimentally applied in the 60's to self-doped (with holes) narrow bandgap semiconductors, mostly tellurides such as GeTe 5,6 , SnTe [START_REF] Hein | Low Temperature Physics, LT9[END_REF][START_REF] Hein | [END_REF][9] , and the at that time more controversial PbTe 10,11 . Electron doped systems were also investigated such as La3-ySe4 12,13 and other lanthanum compounds, or the more popular reduced (or Nb-doped) SrTiO3 14,15 , a much wider bandgap semiconductor. In the case of GeTe, the "gap ratio" of the superconducting gap width 2 ( being the binding energy of the Cooper pair) to its critical thermal energy kBTC was measured 16 . The value of 4.3 was taken at the time as a confirmation of the conventional weak coupling mechanism usually referred to as 17 BCS, which predicted a gap ratio of 3.5. Probably because increasing the carrier concentration ne in these systems did not enhance the TC values above 500 mK (the TC vs ne curve even followed a "dome" shape in one case 15 , or because the observations remained restricted to "ionic" semiconductors, this initial interest did not last 16,17 .

One generation later, the observation of superconductivity (TC = 8 K) in silicon clathrates where alkaline earth metals had been inserted in the cages for doping showed that sp 3 hybridization of column IV elements was compatible with superconductivity [START_REF] Kawaji | [END_REF]20 . Such experiments were inspired by studies of superconducting alkali-doped fullerenes (see the article by A. Ramirez in this issue). Their quantitative modelling 21 by ab initio calculations and a conventional pairing mechanism illustrated the strength of the electron-phonon coupling in rigid sp 3 -bonded networks, and pointed to carbonbased clathrates as a route toward a higher TC. Although quite telling in hindsight, these findings were not the origin of the discovery published the following year 22 of type  superconductivity (TC=2.6 K, onset at 4 K) in polycrystalline boron-doped diamond grown at high pressure and high temperature (HPHT). This seminal report, which included magnetotransport and magnetic susceptibility measurements, was quickly confirmed by other groups for boron-doped polycrystalline 23 and homoepitaxial 24 diamond films grown by Microwave Plasma-enhanced Chemical Vapor Deposition (MPCVD). As reviewed a few years ago 25,26 , many groups have reproduced and extended these initial results, with transition onset temperatures soon reaching the 10 K mark in polycrystalline thick films. As for single crystal diamond, the maximum TC reported so far was 8 K in C:B epilayers 27 grown along (111), written as C(111):B in the following.

Such experimental evidence for superconductivity in boron-doped diamond motivated many theoretical quantitative studies. In order to estimate the maximum critical temperature that could be explained under the assumption of a phonon-assisted pairing mechanism, most of these resorted to numerical calculations involving the Virtual Crystal Approximation 28,29 (VCA), periodic supercells 30,31 , or both 32 . In some cases, the random incorporation of boron was taken into account [33][34][35] by using the Coherent Potential Approximation (CPA). These studies generally used the calculated electronic and vibronic band structure to derive the electron-phonon coupling spectral distribution (the so-called Eliashberg function   F()) and to compute the average coupling strength parameter  by integrating the UgF product over the Fermi surface, gF being the density of electronic states at the Fermi level EF (defining a Fermi temperature TF) and U the electron-phonon interaction potential. In diamond, because of the stiff 3d network resulting from sp 3 hybridization of the carbon atoms, U was found to be stronger than in the parent MgB2 covalent superconductor 36 , but gF was much lower, leading to calculated  values lying between 0.15 and 0.55 depending on the calculation method, for a doping level in the few at.% range. This was significantly lower than in MgB2, where  is close to 1. These theoretical works then used the McMillan formula 37 Eqn. 1

In diamond, D = 2000 K, quite a high value. As for µ*, most of the authors assumed that the values typical for metals (µ*=0.15) still applied, despite the fact that the Fermi energy EF and the average phonon energy described by kBD were comparable in superconducting diamond (see table 1). Such an approach reproduced most of the trends of the experimental results, such as the magnitude of TC or the negative sign of the pressure coefficient 38 , and provided some insight as to which phonons contributed most significantly to the coupling [30][31][32] . However, the simulations failed to reproduce the values of TC when the free hole concentration nh was reduced down to nMIT, as well as the curvature of the experimental TC vs nh variations 34,35,39,40 . Rescaling the coupling and screening parameters and µ* according to power laws close to the critical concentration has been proposed for diamond 40 and silicon 41 but remains specific and unsatisfactory. More general descriptions 42,43 of the effect of approaching the MIT in disordered metals yield TC enhancements which have not been detected in the materials under study here. Unfortunately, the powerful parameter-free approach where the Coulomb pseudo-potential µ does not need to be adjusted 44 has not been applied to any of the superconducting semiconductors so far. This situation prompted alternative theoretical approaches either based on the resonating valence bond model which assumes transport within an impurity band 45 , at the crossover between the host band and the impurity band 46 , or which relied on attractive spin-spin interactions between weakly localized holes near the Fermi level 47,48 . Meanwhile, under the assumption of optical phonon-mediated pairing, the maximum achievable TC in diamond has been tentatively estimated 49,50 . In a similar manner, it was predicted 51,52 that the rhombohedral B13C2 and cubic BC5 compounds would yield a TC value close to that observed in MgB2.

The calculated transition temperatures of a few K as detailed above for hole-doped diamond were also considered by some authors 28,53 to be in sufficient agreement with experiment to warrant predictions of p-type superconductivity in other column IV semiconducting materials, namely Si and Ge. Despite the notorious incapacity of BCS theory to predict new superconductors 54 , experimental evidence for superconductivity was gathered over the next few years, first in silicon 55 , then in silicon carbide 56 , both upon boron doping in the few at. % range, with TC soon 57 reaching 1.5 K in 3C-SiC:B and 6H-SiC:B (cubic 3C and hexagonal 6H are two of the many polytypes of silicon carbide), and more recently 41 0.7 K in Si:B. Ab initio calculations in the spirit detailed above were performed about superconductive Si:B, resulting in values which remained 41,55 below 0.45 even for 10 at.% B. Other dopants of silicon have also been investigated 58 , the calculations pointing out the detrimental influence on the electron-phonon coupling strength of the lattice contraction brought about by atomic substitution by impurities with a smaller covalent radius, so that substitutional doping (ntype) of silicon with aluminum was seen theoretically as a favorable (but notoriously unpractical) option. Similar calculations have been proposed 59,60 also in the case of SiC:B, where less energetic acoustic phonons were shown to come into play, in good agreement with specific heat measurements 61 . Further experimental studies showed that (p-type) doping 3C-SiC with aluminum 62,63 yielded a similar TC of 1.45 K.

The next column IV indirect bandgap semiconductor to be doped into superconductivity (see ref. 64 for a review) was germanium 65 , with a maximum TC of 0.5 K in Ge:Ga, again in rough agreement with ab initio calculations 66 . Further optimization 67 of the flash annealing conditions led to an increase of TC from about 0.2 to 0.5K as the Hall carrier density nH was varied from 2 to 5x10 20 cm -3 . Other annealing strategies yielded less systematic variations, among which a few higher TC values, at 1.2 K for 68 nH = 11x10 20 cm -3 , and 1K for 69 nH = 6x10 20 cm -3 . In parallel, a similar experimental process was applied by the same group on silicon, and SiO2:Ga/Si:Ga composites were shown to be superconducting 70 . However, Aluminum and Gallium being superconducting elementary metals with respective TC of 1.2K and 1.1 K, the authors have considered the possibility that the superconductivity originated from Al or Ga clusters. They have so far concluded that Ga-rich amorphous nano-inclusions are present only in the case 71 of Si:Ga. As explained in a recent summarizing overview 72 , such caveats apply to any compound containing one element (for instance Pb, In or Ga) which may form a superconducting island. This is the reason why except for the specific case of PbTe 73 , the numerous reports about PbSe, InN and In2O3, or GaAs and GaN, despite their quality, will not be mentioned in this review. We shall also discard from the present survey the numerous and in general disordered metallic compounds containing Si or Ge, either binary (for example Au:Si, Mo:Si, W:Si, CoSi2, Cu:Ge) or ternary, despite their interesting low temperature transport properties, including superconductivity. Doped cubic silicon clathrates and non-cubic high pressure superconducting phases of silicon will also be ignored, as well as the numerous superconducting carbon allotropes (such as metal-intercalated graphites and fullerites), most of which are described elsewhere in this special issue.

As a matter of fact, a high pressure phase of solid boron is also superconducting, but its presence has been consistently ruled out in the boron-doped semiconductors under consideration here. The aggregation of boron has been the object of some attention in the case of diamond, where boron pairing has been found energetically favorable 74 in heavily-doped crystals. Aggregation in boron-rich regions has been observed in grain boundaries 75,76 , without any clear correlation with superconductivity 77 . On the contrary, in cases where the grain boundaries became atomically thin, the boron-rich triple points (most probably B4C) were found to remain in the normal state 78 at low temperatures. The formation of B4C crystalline particles on the (111) surface of diamond single crystals doped during their HPHT growth by the temperature gradient method has also been reported recently 79 . Anyway, the quest for the boron-rich superconducting phases predicted theoretically 51,52,80 has not been successful so far 81 . Although the spatial distribution of boron atoms has been recognized as a source of short range disorder, and of grain-to-grain heterogeneity in polycrystalline diamond 77,82 , no such clustering has yet been reported to take place in single crystal C:B, nor in Si:B epilayers 83 . Actually, from a material synthesis point of view, it must be stressed that most of the advances just described result from the recently available possibility of circumventing the solubility limit of the dopant impurities in the host material by using out-of equilibrium processing techniques such as Gas Laser Immersion laser doping 84 or shallow implantation/flash annealing sequences 85,86 .

Coming back to some of the superconducting semiconductors which were studied most intensively half a century ago, one cannot fail to mention that single crystal SnTe is nowadays considered as a crystalline topological insulator 87,88 when it is low-doped and in the rocksalt structure (its low T phase). Moreover, In-doped SnTe is an intriguing superconductor in its own right 11,89 , as are Tldoped 73,90,91 PbTe and even more so In-doped PbTe, which features both ferroelectricity at low In content (rhomboedral phase) and 92 "topological superconductivity" above a critical In content of a few at.%, at which a structural transition to a cubic rocksalt phase occurs. Such aspects are dealt with in S. Sasaki's contribution in this volume. In the case of La3-ySe4, it is the thermoelectric properties that are drawing increasing interest 93 . As for SrTiO3, it is still the most dilute 3d superconductor by far 94 , down to free electron density values around 5 10 17 cm -3 which challenge any BCS-type of pairing mechanism 95 . It has been the object of many studies spread over the last 50 years 96 . Recently, it has been shown (see the contribution of Triscone & Gabay in this special issue) that the interface of SrTiO3 with another oxide could give rise to a 2d metal with a superconducting ground state 97,98 . Before describing in the next sections the normal and superconducting 3d states of some of the materials mentioned in this introductory historical overview, we propose to summarize in fig. 1 their TC dependence on the nominal free charge carrier density as estimated from Hall effect, (except in the case of silicon, where boron concentrations have been used) in the spirit of a previous and broader review 99 . Beside the usual uncertainties on the critical temperature values arising from an author's dependent definition, it should be stressed that the direct derivation of the apparent normal state carrier density from Hall effect data suffers from shortcomings related either to macroscopic doping heterogeneities or to the Fermi surface shape-dependent value of the Hall factor, which may differ significantly from unity. As a matter of fact, such apparent densities have been found to be larger than the chemical concentration of the doping element by 50% in 9 SnTe, and by up to an order of magnitude in diamond 27,40 . A numerical application of equation 1 to the case of silicon (D = 640 K) using a boron concentration-dependent electron-phonon coupling parameter  evaluated by ab initio supercell calculations 41 is also given in fig. 1 to illustrate the shortcomings of such a simple approach when it comes to predicting TC variations over a wide range of concentrations. Figure 1 also displays some scatter among the experimental data coming from different groups. In the particular case of silicon, TC depends on thickness (hence the two sets of points in fig. 1) in such a way that it seems to be determined by the sheet boron density rather than by its volumic concentration 41 .

3d normal state properties

Many of the standard properties of the above-mentioned materials can be found in current handbooks and databases, albeit referring mostly to their undoped semiconducting state. Some low T but normal state parameters usually deemed 11 to be relevant for the discussion of the superconductivity are listed in table 1 for the three tin and germanium and lead tellurides 91,100,101 , strontium titanate 94 , as well as for the four group IV covalent superconductors: germanium 67 , silicon 41 , silicon carbide 57,62 and diamond 27 . The cubic fcc structure of germanium telluride at high temperature becomes rhombohedrally distorted along the cube diagonal at room temperature and below. Strontium titanate has a cubic perovskite crystal structure at room temperature and undergoes a structural transition to tetragonal around 110 K or lower, depending on the self-doping level. All other materials have a cubic structure, except for the 6C-SiC polytype. The bandgap width EG as well as the Debye temperature D and the relative permittivity at low frequency r are expected to vary upon heavy doping: for example, on the basis of specific heat measurements of superconducting samples, D in 3C-SiC:B has been estimated 61 This radius provides 104,105 an estimate for the critical impurity concentration nMIT at the metalinsulator transition (MIT) according to Mott's prediction rBohrnMIT 1/3 = 0.26. This critical concentration has not been determined experimentally in all systems considered here, but is known to vary over a wide range, from below 10 16 cm -3 in SrTiO3 (a material possibly deviating from Mott's prediction) to 4 10 17 in Ge and 4x10 [START_REF] Cohen | Superconductivity[END_REF] in 106 Si:B and 3-5x10 20 cm -3 in 27,40 C(111):B and C(100):B. The critical exponents around this 3d MIT have been determined in the latter two materials 40,106 . Superconductivity was experimentally observed in these materials above a concentration nCmin which was equal to or greater than nMIT. The corresponding range of Fermi energies was estimated in table 1 by the minimum Fermi temperature TFmin calculated within a one band free electron picture (m* =1). Its ratio to the Debye temperature is larger than 10 in the tellurides, but decreases when increasing the bandgap from 4 in germanium to about one in diamond, where the applicability of the adiabatic approximation and of the usual µ* value might be questioned. As for SrTiO3, it yields a much smaller ratio, on the order of 0.1, comparable to the situation of heavy-fermion superconductors, making a phonon-mediated pairing mechanism very unlikely 94 and calling for alternative models 107 .

In addition, table 2 gathers some published examples 11,39,41,55,62,67,73,91,94,95,101,108,109 of low temperature normal state transport parameters (Fermi vector kF, low T conductivity, residual resistivity ratio RRR, mean free path Lmfp and Ioffe-Regel parameter) which depend on the doping level of these materials, in the relevant range of apparent free carrier concentrations nH deduced from the Hall coefficient. The Fermi vector kF was deduced from Shubnikov-de Haas oscillations (SnTe) or Nernst effect (SrTiO3) measurements when available, and from free electron estimates for Ge, Si, SiC and diamond. Moreover, effective density of states relative masses m*dos of 2, 2.4 and 5 respectively in 11,[START_REF] Cohen | Superconductivity[END_REF] SnTe, in 6 GeTe and in 110 SrTiO3 have been deduced from the Sommerfeld coefficient determined by specific heat measurements. More recently, similar studies yielded mass values of 1.2 and 1.7 in the cases of 61 SiC:B and 102 C:B. Angle-resolved photoemission spectroscopy (ARPES) measurements of superconducting diamond epilayers have shown that their electronic band structure could not be distinguished from that of epilayers doped below the critical concentration nCmin, and that both were the same as that of the undoped crystal 111 . They yielded a few 2d projections of the Fermi surface for epilayers grown along 111,112 (111) and 113 (100). As illustrated by fig. 2, in the latter case, under a polarized incident synchrotron beam, rotating the sample surface by 45° led to two partial projections on the -X-K plane of the Brillouin zone corresponding respectively to the light and heavy hole subbands. Assuming that the boron concentration provides an estimate of the hole concentration nh at the surface of this sample led to kF = 3.3 nm -1 , in rough agreement with the green contours shown in fig. 2, despite the fact that the heavy hole subbands do not lead to a spherical Fermi surface 53 , a feature that might explain the Hall factor deviating from unity 27 . Please note that in all experiments, the photoemission of unreconstructed heavily doped diamond surfaces could be analyzed as representative of the bulk of the crystal. Finally, since most free carrier concentrations given in tables 1 and 2 correspond to a plasmon frequency p lying in the near or mid-infrared range, optical spectroscopies have also been applied to SnTe and 100 GeTe, as well as to heavily doped silicon 114 and diamond [115][116][117] . A simple interpretation of the plasmon edge within the Drude model has been found sufficient in most cases to yield carrier concentrations and damping factors = -1 typical of overdamped dilute metals, with relaxation times  in the 0.2 to 10 fs range fully compatible with the mean free path values given in table 2, generally lower than 1 nm in diamond, as confirmed by ARPES measurements 111 .

In principle, a quantitative Kramers-Kronig analysis of the optical spectral response in the infrared energy range of lattice phonon or impurity-related vibrational modes should yield the Eliashberg function   F() describing the spectral variation of the electron phonon coupling parameter. In practice, this challenge has been taken up in the case of diamond 116 , whereby the dominant contribution of optical phonons and the possible contribution of boron-related local modes predicted by ab initio numerical studies [30][31][32] were confirmed. The electron-phonon coupling was also illustrated by high resolution studies of photoemission phonon replicas of the Fermi edge in superconducting diamond 118 . Since the phonons involved in the coupling are expected to be softened, Raman studies have been performed on superconducting silicon 55 and diamond 119 and zone-center optical phonon frequencies have been extracted from first order Raman spectra, despite their polarization-and excitation energy-dependent Fano lineshape deformation 120 . The resulting softening values, 3% at most 55,119 , were significantly weaker than predicted by VCA calculations 28,29 . Before being used for estimating the electron-phonon coupling strength for these particular phonons, they should moreover be corrected for doping-induced lattice strain 119 which affects mostly the lattice parameter along the growth direction in the case of unrelaxed homepitaxial layers 27,55,120,121 . More to the point, second order Raman 123 or inelastic X-ray 124,125 scattering (IXS) allowed to detect lattice phonons away from the zone center and have confirmed that in the case of diamond the optical phonons were specifically affected in the region of the Brillouin zone occupied by free holes, as illustrated in fig. 2. However, even in that case, the softening (up to 5 %) was much weaker than predicted 124 , while the broadening of the IXS phonon lines could not be explained without invoking additional disorder effects or even macroscopic heterogeneities in these very thick epilayers. Average coupling parameter values deduced from such measurements ranged from 0.2 to 0.4 depending on the derivation method 36 , still too low for equation 1 to account for the TC values measured on the same samples.

Another striking feature common to many of the materials listed in table 2 is the low value of the residual resistivity ratio RRR = 4K/300K, around unity in GeTe, Ge, Si, and diamond. This stems from two opposite and slow variations of the normal state resistivity above and below a specific temperature at which the inelastic mean free path becomes of the order of the elastic scattering length, resulting in a broad and weak resistivity minimum. This temperature lies around 40 K in 55 Si:B, above 25 150 K and up to 22,39 300 K in C:B. Below that temperature, the resistivity increases when the temperature decreases and goes through a peak before dropping sharply at the superconducting transition temperature TC. In the range between TC and about 40K, the conductivity extrapolates to a finite temperature according to the weak localization expression 25,109,126 : (T) = 0 + AeeT 1/2 + BepT, where Aee and B ep refer respectively to interelectronic and electron-phonon interactions. As described below, the resistivity peak at low T is significantly enhanced in heavily doped nanocrystalline (nc-C:B) diamond films 127-129 while the magnetoresistance changed sign 128,130 with the field, as expected for a granular system. The weak localization observed in the granular disordered metal nc-C:B has been proposed to herald an unconventional superconductivity in that material through a spin-flip pairing mechanism 127,131 . Although presenting also a dip at intermediate temperature 91 , the variations of the resistivity of PbTe:Tl have been ascribed to a charge Kondo effect 73,91 , i.e. a totally different effect which has important consequences for the interpretation of the superconductivity in this compound 132 . The last item listed in table 2 is the Ioffe-Regel parameter kFLmfp: below unity, localization sets in, and the quasi-classical approximation is no longer appropriate. From the data of table 2, this has been observed so far only in diamond doped slightly above nMIT and grown 39,40 along (100).

3d superconducting properties

As outlined in the historical survey opening this review, the bulk nature of the superconducting transition in these materials has been attested by measuring the heat capacity anomaly associated to carrier pairing below TC in 11 SnTe, in 6 GeTe and 91 PbTe, as well as in 109 SrTiO3, in 61 SiC and 102 diamond, but not in germanium nor in silicon, while susceptibility data is lacking only in the case of germanium. However, the specific heat jump value was often significantly lower than expected from weak coupling BCS theory. In complement to the results mentioned in the introduction and to the TC(nH) data plotted in fig. 1, we illustrate also in table 3 with a few examples the experimentally determined dependence on the nominal carrier concentration nH of various additional parameters of the superconducting state of some semiconductors, such as the critical magnetic fields HC or HC2(T=0) depending on the superconductor type, the coherence lengths GL and 0 deduced from H(T) phase diagrams through GL 2 = 0/2HC2(0) = 0Lmfp, the London penetration depth L and the Ginzburg Landau parameter GL=L/GL. Whenever possible, the examples have been taken from the same references as those collected in table 2. According to these values, the only system clearly 94 in the clean limit was SrTiO3, while the only apparent type  superconductors were 3C-SiC:B and 6H-SiC:B. The fact that most of the materials under consideration are type  superconductors in the dirty limit fulfills early predictions 3 based on the long penetration depth and short mean free path expected for such systems.

Please note that in the case of diamond, a distinction was made between a bulk (and possibly polycrystalline) HPHT sample 102 , and single crystal epilayers grown by MPCVD along 39 (100) or along 116 (111), respectively dubbed C(100):B and C(111):B. As illustrated both by fig. 1 andtable 3, for a given apparent carrier density nH, the TC values are much higher in C(111):B than in C(100):B. This has been tentatively attributed to a better ordering of the substitutional boron impurities 133 when the diamond lattice grows along (111), to a higher substitutional to interstitial (or paired substitutional 134 ) incorporation ratio for (111)-oriented growth, and finally to a favorable tetragonal strain state 27 of the (111)-oriented epilayers when compared to the isotropic dislocation-rich 135 relaxed state 27 of the (100)-oriented epilayers grown in the same reactor. However, the opposite situation, where dislocations appear in (111)-oriented epilayers at a lower boron concentration than in layers grown along (100), has also been reported 136 . Anyway, a positive (tensile) strain coming from substitution by a "larger" impurity is expected to enhance TC in group IV superconducting semiconductors 21,58 , in agreement with experimental 22,137 and theoretical 38 results showing that in diamond the hydrostatic pressure coefficient of TC is negative. It is also worth noting that for strained epilayers, the band splitting of the heavy and light hole bands at  induced by the tetragonal strain is expected to modify the shape of the Fermi surface, and thus to affect both the Hall factor and the critical temperature. This strain has opposite signs in Si:B and C:B.

Since the pioneering tunnel spectroscopy studies 16 of GeTe, the superconducting gap of energy seen by the quasiparticles around the Fermi level has been investigated in 96,138 SrTiO3 , in 139 C(100):B, in 140 C:B, in 141,142 C(111):B and 143 Si:B. Thanks to the development of ultra-low T scanning tunnel microscopy (STM) and spectroscopy (STS), the latter studies have provided local maps of the local variations of the coherence peak intensity and of the superconducting gap 139,142,143 . In the case of C(100):B surfaces, vortex images and some evidence for localized gap states were obtained, the latter remaining a puzzle 63,139 . The temperature dependence of the local pair binding energy  deduced from the excitation gap has been also studied in diamond and silicon, and found in excellent agreement with a s-wave BCS superconductivity with a BCS ratio /kBTC = 1.75 both for a C:B plate 140 and C(100):B epilayers 123,139 , while a 20% dispersion about the BCS value was observed 143 on Si:B. Two coupled gaps had been detected earlier in SrTiO3, with a BCS ratio close to 1.76 for the larger one 96 , as well as a possible signature of the soft phonon mode at 1.9 meV involved in the low temperature structural transition 138 . Moreover, optical methods have yielded superconducting gap values for C(111):B, infrared and THz spectroscopies 116 appearing to be better suited than high resolution photoemission 109 for the purpose. The resulting  values were plotted in fig. 3 as a function of the critical temperature TC, and found to be fully compatible with a conventional weak coupling BCS description. Finally, a crucial test of the nature of the pairing attractive interaction is of course the isotope atomic mass (M) effect on TC, usually quantified by the exponent  = -dLogTC/dLog(M).  = 0.5 is considered the hallmark of a phonon-mediated BCS mechanism, although may take lower values because of Coulomb repulsion effects. Specific heat measurements 103 of isotopically substituted HPHT C:B have yielded a much higher  exponent of 1.8, while similar studies of the resistive transition led to = 1.4±0.4 for other HPHT C:B samples 144 , and to isotope exponent values of 0.6, 1.1 and 1.8 in C(100):B epilayers 145 . If the isotopic mass effect seems thus to be established in the sole case of diamond, confirming the crucial role of electron-phonon coupling in this material, its magnitude remains to be explained. Frequent Cooper pair breaking 146 , possibly triggered by the local nature of some of the coupling phonons 145 , has been considered as a plausible origin for this phenomenon 144 .

Applying the BCS model in the dirty limit within a one-band free electron picture, the slope at TC of the H(T) phase diagram (at the boundary between the vortex phase and the normal phase) may also be used to estimate the Ioffe-Regel parameter (kFLmfp). The values of -1 T/K for diamond, -0.2 T/K in silicon, and -0.02 to -0.1 T/K in GeTe lead to Ioffe-Regel parameter values in good agreement with those deduced from normal state transport measurements (table 2). Such a successful consistency check between superconducting and normal state properties brings further support to a weak coupling mechanism being at work in these three materials. No such agreement was found in the other materials, the mixed state estimate of kFLmfp being significantly smaller than the normal state estimate the case of germanium, while the opposite was true for SnTe. Another point was the relevance of the proximity of a carrier concentration-induced MIT to understand the superconducting properties of diamond close to this transition. Comparison to the parent silicon system showed that, in the latter, superconductivity was not any simpler to understand in detail 41 , despite the absence of any MIT in the doping range of interest.

Low dimensionality issues and devices

The fact that the critical doping level for the MIT and for the onset of superconductivity nCmin coincide in diamond has also given some impetus to studies aiming at controlling and studying a superconductor to insulator transition (SIT) in this system. As emphasized by theoretical studies promoting either a "fermionic" 145 or a "bosonic" 148 model for this transition, the SIT may be investigated experimentally by changing not only the carrier concentration but also the disorder and the thickness of the epitaxial film. Thickness effects on TC have been observed below about 200 nm and down to 5nm, but they appear similar for both epitaxial films doped far above 135 nMIT or much closer 149 to the MIT, so that fundamental aspects of the SIT are ruled out from their interpretation. Once normalized to the TC "bulk" value, the observed variations may be in both cases explained by a simple geometrical effect related to a weaker order parameter at the surface 150-1 , but yield a critical thickness value of 25 nm, much longer than the Thomas Fermi screening length supposed to be relevant in that case. This open question deserves further attention, at least as long as the coincidence of nCmin with nMIT is not disproved. More generally, controlled ways to change the effective disorder in these superconducting semiconductors should be sought.

Beside film thickness reduction or disorder variations, another way to induce effective dimensionality effects at a less intrinsic level is to introduce grains and to vary their size relative to the film thickness and to other physically relevant lengths. This has been performed in boron doped nanocrystalline diamond : for grain sizes smaller than the thickness and comparable to the coherence length 152 , or comparable to the thickness 81,153 , the granularity of the system takes over and percolation effects are expected. The role of the grain boundaries and intragranular metallic transport parameters, quite obvious in the normal state 130,154,155 takes another twist below TC, with an influence of the intergranular Josephson coupling, as well as that of the heterogeneity of the local superconductivity among the grains and even within the same grain, which has been assessed by scanning tunnel microscopy 77,78 . For micrometer-sized grains, the enhanced weak localization effects may be hidden at low temperatures by a sharp and pronounced "bosonic" resistivity peak occuring at a temperature close to the onset of superconductivity 129 . Such granularity-induced and percolation effects do not seem to have triggered the same interest in the other superconducting semiconductors.

Patterning of micro-or nanocrystalline superconducting diamond films into wires less than 100 nmwide preserved their superconducting properties 156 up to 1 K and 1T. Such e-beam patterned wires and loops, including a thinner region inducing a weak link, were used to make superconducting quantum interference devices (SQUID) working at magnetic fields reaching 157 4T. Similar films grown on a sacrificial silicon oxide were also patterned into double clamped suspended beams. These micromechanical resonators were driven and read out in the superconducting state at MHz frequencies 158 . Future combinations of smaller oscillators with the SQUID should soon establish the potential of superconducting nanocrystalline diamond for dissipation-free quantum opto-mechanics. Finally, in the case of diamond, the "natural" Josephson junctions occuring at grain boundaries and the "artificial" weak junctions resulting from thinning nanocrystalline wires have found 159 a single crystal counterpart in vertical SNS weak-link Josephson junctions grown epitaxially along (111). When the thickness of the normal state diamond of such structures was made much larger than the coherence length, a proximity effect could be observed. Moreover, Shapiro steps were detected under microwave irradiation 160 . This result illustrated recent improvements in the sharpness of the doping transitions upon epitaxial MPCVD growth 149,161 at the normal-superconductor interface, and opened the way for the fabrication of hybrid systems involving either optical color centers or mechanical oscillators, or both. Be it for the above mentioned quantum-limited sensing, or for quantum data processing using more elaborate devices such as Josephson field effect transistors, the ability to grow homoepitaxial Josephson junctions should improve significantly the transparency of the normal-superconductor interfaces. Similar strategies and more audacious qubits schemes have been proposed in the case of silicon 64,162 , but they have not yet materialized.

As mentioned at the end of the introduction (and in the contribution by Triscone & Gabay), low dimensionality effects quite different from the above have been demonstrated for the interface of SrTiO3 with another perovskite oxide where the 2d electron gas extending a few nm within SrTiO3 from the interface was shown to have a superconducting ground state below 97 0.2 K or 98 0.3 K. A similar 2d gas was generated at the pristine SrTiO3 single crystal surface by using the electrical double layer gate created in an organic electrolyte. When sheet carrier densities of the order of 10 14 cm -2 were obtained in this way 163 , an electric-field-induced 2d superconducting state appeared below 0.4 K, a TC value comparable to the values given in fig. 1 for Nb-doped SrTiO3.

Finally, for the sake of completeness, it should be mentioned that very high TC values (145 K) have been reported 164 for a specific type of low-dimensional silicon pyramidal sandwich nanostructures self-assembled on top of n-type (100)-oriented wafers, whereby ultra-narrow p-type silicon quantum wells were confined by heavily boron-doped superconducting delta "barriers" 165 . These amazing results, which still await an independent confirmation, have been attributed to the transport of small hole bipolarons resulting from the presence of negative-U centers associated to the boron impurities [165][166][167] . More generally, it must be recognized that at this moment, and similarly to the cases of germanium and silicon carbide, superconductivity studies of boron doped silicon lack independent confirmations by other groups.

Summarizing remarks

In summary, most of the experimental data currently available about single crystal (or large grain polycrystalline) superconducting semiconductors hint at a conventional pairing mechanism, except in the case of PbTe and SrTiO3, the latter being the only electron-doped system in the whole family. However, quantitative agreement with simple models was not yet demonstrated over a wide doping range for any of the "conventional" systems, while additional evidence is still required to assess the status and potential of germanium and silicon carbide. Except for one very recent and preliminary report 168 , the occurrence of critical temperatures significantly higher than 10 K has not been verified, despite promising theoretical predictions for sp 3 carbon clathrates 21 and cubic boron-carbon compounds [169][170] .

Diamond clearly stands out as the most studied and archetypical group IV superconducting semiconductor 64 . Ten years after its discovery, this material even shows some promise for superconducting quantum devices. In the near future, much older players with less conventional superconducting properties, PbTe and SrTiO3, and a younger one with an impressive technological maturity, silicon, will certainly provide additional opportunities for testing new and old theories, as well as futuristic hybrid devices.

Figure captions :

Figure 1 : Nominal free carrier dependence of the critical temperature TC for the superconductive transition of various heavily doped degenerate semiconductors : B-doped diamond grown along 27,39 (100) or 27 (111), B-doped silicon for two different epitaxial film thicknesses 41 , Ga-doped germanium 67- 69 , B-doped 62 or Al-doped 57 silicon carbide, self-doped or Nb-doped strontium titanate 15,94 , Tl-doped lead telluride 73 , self-doped selenium [START_REF] Hein | [END_REF]9 and germanium 5 tellurides. The lines correspond to TC estimates for three µ* values, as deduced from equation 1 for D = 640 K,  being evaluated by ab-initio supercell calculations 41 . [139][140][141] , silicon 143 , germanium telluride 16 and strontium titanate 97,138 . The straight line corresponds to the weak coupling BCS ratio.

  to estimate TC as a function of  , of a logarithmic average phonon frequency represented here by the Debye energy kBD, and of the screened and retarded Coulomb repulsion potential µ usually expressed as µ*=µ/[1+µ Log(TF/D)]. With these parameters, this formula reads: TC = D/1.45 exp[-(1.04(1+))/( -µ*(1+0.62))]

Figure 2 :

 2 Figure 2 : Color-coded intensity (bottom) and spectral shift (top) maps onto the X--K principal plane of the Brillouin zone of a boron doped diamond homoepitaxial layer(C:B), deduced respectively from (bottom) polarized Angle Resolved Photoemission Spectroscopy 113 (ARPES) and from (top) Inelastic Xray Spectroscopy 125 (IXS) measurements performed at SOLEIL (ARPES) and ESRF (IXS) synchrotron facilities. Different ARPES configurations allow to distinguish the contributions of the heavy hole (hh)and light hole (lh) subbands. The spectral shift measured by IXS is that of the optical phonons of C:B with respect to those of the undoped crystal.

Figure 3 :

 3 Figure 3 : Experimentally determined critical temperatures TC (either local or macroscopic) as a function of the pair binding energy(half-gap)  measured by tunnel spectroscopy at very low temperatures for diamond[139][140][141] , silicon143 , germanium telluride16 and strontium titanate97,138 . The straight line corresponds to the weak coupling BCS ratio.

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

  at 590 K and that of heavily doped bulk diamond 102 C:B at 1440 K, i.e. much lower than the nominal values given in table 1. It should be mentioned however that in other HPHT C:B samples, similar measurements indicated that D remained unaffected 103 . As for the Bohr radius of the acceptor or donor impurity, it is given by rBohr = rħ 2 /m*Bohre 2 within the hydrogenoid approximation parametrized by a specific effective mass m*Bohr.

Table 2 :

 2 Normal state properties of some superconducting semiconductors for various doping-induced free carrier concentrations nH deduced from the Hall coefficient, except in the case of silicon where boron concentrations (in italics) have been used. The residual resistivity ratio RRR was defined as 300K/4K = 4K/300K. The mean free path Lmfp was generally deduced from Hall mobility values within the free electron picture, and yielded the Ioffe-Regel parameter kFLmfp.

		Dopant	nH	kF	4K	RRR	Lmfp	kFLmfp	reference
			(nm -3 )	(nm -1 )	(cm) -1		(nm)
	SnTe	VSn	1	0.63	2.5x10 4	-	39	25	Ref. 11
	SnTe	VSn	2	0.78	2x10 4	-	17	13	Ref. 11
	GeTe	VGe	0.86	2.9	2x10 4	-	30	87	Ref. 11
	GeTe	VGe	0.18	1.7	1.3x10 4	1.3	40	68	Ref. 100
	PbTe	Tl	0.05	1.1	3x10 3		14	15	Refs 73 & 91
	PbTe	Tl	0.09	1.4	10 3		3.2	4.5	Refs 73 & 91
	SrTiO3	VO	5.5x10 -4	0.24	10 3	2700	140	33	Refs 94 & 107
	SrTiO3	VO	4x10 -3	0.37	4x10 3	480	140	52	Refs 94 & 107
	SrTiO3	VO	0.027	0.51	1.5 10 4	490	120	61	Refs 94 & 107
	SrTiO3	Nb	0.16	0.56	10 5	120	37	21	Refs 94 & 107
	Ge	Ga	0.53	2.5	5x10 3	1	7	18	Ref. 67
	Si	B	5	5.3	8x10 3	1.25	1.3	6.9	Ref. 55
	Si	B	0.55	2.5	8x10 3	1.2	3.2	8.1	Ref. 41
	Si	B	1.4	3.5	1.6x10 4	1.2	3.4	12	Ref. 41
	Si	B	2.8	4.4	1.4x10 4	1.3	2	8.7	Ref. 41
	3C-SiC	B	1.9	3.8	1.6x10 4	11	14	53	Ref. 62
	3C-SiC	Al	0.7	2.8	1.3x10 3	5.3	2.2	6.2	Ref. 62
	6H-SiC	B	0.25	2.3	8x10 2	4.7	3	6.9	Ref. 62
	C	B	1.8	3.8	4x10 2	0.9	0.34	1.3	Ref. 101
	C(100)	B	0.56	2.6	70	2	0.23	0.5	Ref. 39
	C(100)	B	1.3	3.3	4x10 2	1.2	0.5	1.8	Ref. 39
	C(111)	B	2.1	4	5x10 2	-	0.6	2.4	Ref. 108
	C(111)	B	13	7.3	1.4x10 3	0.9	0.5	3.8	Ref. 108

Table 3 :

 3 Carrier density-dependent superconductivity parameters for various degenerate semiconductors: critical temperatures TC and magnetic fields HC (clean limit)or HC2(T=0), coherence lengths 0 and GL, London penetration length L and Ginzburg-Landau coefficient GL, as well the type of superconductivity.

Acknowledgements

The author thanks the colleagues he has worked with on this topic over the last ten years, especially H. Guyot and M. Hoesch who allowed him to display unpublished data in fig. 2. He also thanks Dr K. Behnia and Prof. T. Klein for a critical reading of this manuscript.


F Lloret

D Araujo

M P Alegre

J M Gonzalez-Leal

M P Villar

D Eon

E Bustarret

TEM study of defects versus growth orientations in heavily boron-doped diamond

Keywords: Diamond, CVD, Heavily boron-doped diamond, defects, TEM

TEM study of defects versus growth orientations in heavily boron-doped diamond

Heavy boron doping layer in diamond can be responsible for the generation of extended defects during the growth processes [1]. As claimed recently [2], boron pair interactions rather than strain related misfit seems to be responsible for such dislocation generation.

In the present work, electron microscopy observations are used to study the defects induced by heavy boron doping in different growth plane orientations. Facets of pyramidal Hillocks (PHs) and pits provide access to nonconventional growth orientations where boron atoms incorporation is different during growth. TEM analysis on FIB prepared lamellas confirm that also for those growth orientations, the generation of dislocations occur within the heavily boron-doped diamond layers. Stacking faults (SFs) have been also observed by high resolution transmission electron microscopy (HREM). From the invisibility criteria, using weak beam (WB) observation, 1 2 ⁄ [11 ̅ 0] and 1 6 ⁄ [ 112 ̅ ] Burger vectors have been identified. Their generation behavior confirms the mechanism reported by Alegre et al. [2] where local in-plane strain effects induced at the growing surface of the diamond lattice by the neighboring of several boron atoms cause the generation of such extended defects.

1 Introduction Synthetic diamond is known as a promising material for high power electronic devices due to its exceptional properties [3]. However, electronic devices require metallic diamond, getting it by doping. In fact, when boron concentration in diamond increases up to 5x10 20 atm/cm 3 , their properties change drastically from an insulating behavior to a metallic one [4]. Unfortunately homoepitaxial boron doped layer usually contain planar and one-dimensional defects [5,6]. The origin of these defects is not well understood yet but they have an undesirable impact on the posterior diamond based devices [7,8]. The understanding of the mechanism of defects generation during the heavily boron doped diamond growth and its relationship to boron incorporation will help to understand and to improve the boron-doped diamond growth. This is one of the required technological steps to develop well designed commercial electronic devices. Under these premises, Alegre et al. [2] reported an original mechanism of dislocations generation that established a critical boron-doping levels in diamond. In line with that work, an extensive study of defects in heavily boron-doped layers for different growth planes orientations is presented here.

Experimental

In order to determine where defects occur, within the heavily doped layer or at interfaces with the substrate or with a layer of different doping level, as well as its relationship with the layer thickness, a multilayer structure has been studied. Therefore, under exactly the same growing conditions summarized in table 1, a stack of nine undoped and heavily boron-doped (10 20 at/cm 3 ) diamond bilayers was grown by microwave plasma chemical vapor deposition (MPCVD) on a <100> oriented polished CVD diamond 3x3 mm 2 substrate. An initial 2h-long pure hydrogen plasma was used to eliminate residual contamination Similar to a previous work [9], methane concentration of 0.5% in purified H2 was then used to grow the nine boron doped layers with 7000 ppm B2H6/CH4. After a short hydrogen flush, the CH4/H2 ratio was raised to 0.75% and oxygen added during the nominally undoped growth. Substrate temperature and pressure were kept at 910 o C and 33 Torr throughout the growth without interrupting the plasma. Focused ion beam-prepared lamellas have been obtained for cross sectional transmission electron microscopy (TEM) observations using a dual beam FEI QUANTA 200 3D microscope and following the lift-out method [10]. TEM diffraction contrast study was realized with a 120kV JEOL 1200 EX microscope and high resolution TEM observation with a 200kV JEOL 2010F microscope.

3 Results and discussion Fig. 1 shows weak beam (WB) micrographs in two beam conditions for two different reflections (g=022 and g=111) recorded at the [011] pole of the sample. This region presents a high density of defects. For an easier identification, doped layers have been marked by arrows with p ++ labels. From the orientation of the lamella planes and the angles observed in the micrographs, the growth plane facet orientations are deduced (see dashed lines in Fig. 3d). First observation is that the <111> facets of the triangular shaped pit defects on the substrate (probably coming from etching before CVD-growth) induce the <111> growing orientation of the first p ++ layers and also for first nanometres of the underneath layer (undoped buffer layer) undoped layer, instead of the expected <100> growing. That is, growing orientation is clearly conditioned by the existence of superficial defects on the substrate. As is shown in micrographs, extended defects are generated in (111) growth plane of the first doped layer becoming parallel to the <100> growing orientation some nanometres later on.

Dislocations coming from strain related or lattice mismatch usually occur at the interface between doped and undoped layers [11]. However, Fig. 2 shows an annular dark field (ADF) micrograph, recorded at 20 cm camera leght, where dislocations are generated at different positions with respect to the doped layers. In order to confirm this behaviour, different orientations have been compared. For this purpose, 3D-superficial defects generated during the growth process have been used.Growth defects such as pyramidal hillocks (PH) or flat hillocks (FH) are commonplace on the surface of epitaxial diamond samples growth by CVD [12]. The formation of these defects has been thorough studied by authors as A. Tallaire et al. [13] who attributed their formation to a crystalographic defect. Although the defect at the source of the PH could not be identified here, due the conditions of our experiments and the similarities between the ones studied by Tallaire and the one here studied, we assumed that the same mechanisms take place during the formation of the PH studied. Fig. 3 shows dark field (DF) micrographs of the PH in two beam conditions for g=400 (Fig. 3a), g=022 (Fig. 3b) and g=111 (Fig. 3c) reflections. Images have been recorded at [011] pole. PH had a squared shaped base with their side parallel to the 〈011〉 and 〈01 ̅ 1〉 directions. As expected, each face of the hillock shows different growth direction at the surface of the sample. They have been identified and marked in the bright field (BF) micrograph presented in Fig. 3d. The high density of defects generated at initial growth planes is shown in DF micrographs. Three different regions of defects have been identified and they have been marked by white dashed circles. Doped layers show multiple growth orientations during PH formation. These changes in the growth directions curved the dislocation lines. Fig. 3d shows that growth orientation changed at least twice per edge during the PH generation. (28 ̅̅̅̅ 1 ̅ 1) and (33 ̅̅̅̅ 2 2 ̅ ) planes started to grow following the <100> direction. After around 400nm, the growth orientation changed to the 〈1 ̅ 1 ̅ 1〉 and 〈1 ̅ 1 1 ̅ 〉, respectively. In fact, the dislocations density, defined as sum of the dislocations length per volume:

𝜌 = ∑ dislocation length 𝑣𝑜𝑙𝑢𝑚𝑒 , (1)
has been calculated for each one of the growth planes identified in the sample. A higher density of dislocations was obtained for the (111) family planes. This situation confirms the particular afinity of defects to be generated in (111) planes against any other less packed plane orientation, showing that the distance between atoms is the main reason of its formation.

In order to identify the Burger vectors and to determine the family of defects observed in the micrograph, invisibility criterion has been employed. It is well known [START_REF] Williams | Transmission Electron Microscopy[END_REF] that the visibility of edge dislocations observed in TEM is complicated by the strain field component normal to the slip plane for edge dislocations. Consequently, complete invisibility of edge dislocations is only achieved under conditions of g•b=0 where g is the normal to the TEM diffracting planes and b is dislocations burger vector. Table 2 shows the result of applying this criterion (g•b=0) for the reflections used in this work (g=220, g=111 and g=400) which allows to determine the burger vector orientations along <011> direction. Fig. 4 shows weak beam (WB) micrographs in two beam conditions in the same region of the sample recorded at Fig. 2. Micrographs were recorded at the [011] pole for three reflections: g=220 (Fig. 4a), g=111 (Fig. 4b) and g=400 (Fig. 4c). Defects with 𝒃 = ± [11 ̅ 0], marked with label "B", have been observed. Similar dislocations have been previously reported [START_REF] Matthews | [END_REF].This criterion has been used also for dislocations contained in Fig. 3 where the same Burger vectors were observed. They are also marked with labels "A" and "B" in the corresponding micrographs.

Table 2 Results of the g•b invisibility criterion for the usually observed Burger vectors (b) using the reflections (g) present at the 110 pole. The shadows and the letters "A" and "B" remark the cases corresponding with the results from the micrographs. [16], these planar defects correspond with the ∑3 coincident-sizelattice structure. In addition, a Fourier transform performed on the defects (white dashed square on Fig. 5a) shows that they correspond to the {111} type. These structures are twins boundaries-like and they have been observed in polycrystalline diamond [17,18]. Preferred grain boundary planes are the closest packed planes of the corresponding CSL that is, (111) planes. Here, an additional observation of the preferential planes for extended defects generations is shown.

g b (𝟒𝟎𝟎) (𝟎𝟐 ̅ 𝟐) (𝟏𝟏𝟏 ̅ ) ± 𝟏 𝟔 [𝟏𝟏𝟐 ̅ ] ± 2 3 ±1 ± 2 3 ± 𝟏 𝟔 [𝟏𝟐𝟏] ± 2 3 ± 1 3 ± 1 3 ± 𝟏 𝟔 [𝟐𝟏𝟏] ± 4 3 0 ± 1 3 ± 𝟏 𝟑 [𝟏𝟏𝟏] ± 4 3 0 ± 1 3 ± 𝟏 𝟐 [𝟏𝟎𝟏] ±2 ±1 0 ± 𝟏 𝟐 [𝟏𝟎𝟏 ̅ ] ±2 ±1 ±1 ± 𝟏 𝟐 [𝟎𝟏𝟏] 0 0 0 ± 𝟏 𝟐 [𝟎𝟏𝟏 ̅ ] 0 ±2 ±1 ± 𝟏 𝟐 [𝟏𝟏𝟎] ±2 ±1 ±1 ± 𝟏 𝟐 [𝟏𝟏 ̅ 𝟎] ±2 ±1 0
Edge dislocations were also observed by HREM as shown in Fig. 5a and 5b at higher magnification. In this case it corresponds to a threading edge dislocation with a 1 2 ⁄ [11 ̅ 0] Burger vector.

In correspondence with the dislocation generation model published by M. P. Alegre et al. [2], the following aspects are observed: (i) in plane dislocations (Fig. 4b and5) are generated exclusively insight the heavily doped layer, (ii) such dislocations (observed as points) changes then their orientation to follows the growth directions.

In general, regions of the sample where the growth plane is along the <100> direction are almost free of defects. Therefore, a special tendency to generate defects at (111) growth plane in opposition to <100> orientation with exactly the same growth conditions is evidenced. This behaviour is in according with the mechanism reported by Alegre [2]. Neighbouring effects between boron atoms might be higher for (111) family planes than for (100) since these (111) planes have smaller planar distance. Local strains due the distance between the substitutional boron pairs and their neighbours have a higher influence on the generation of dislocations than interface strain related effects [2,[START_REF] Matthews | [END_REF].

4 Conclusions Highly boron-doped diamond epilayers grown along <100> direction have been characterized by TEM. Additional growth directions have been also characterized thanks to local changes in the growth directions

due the presence of etch-pits at the initial stage of growth and pyramidal hillock formed during the growth. A large number of defects have been obtained along the <111> growth direction, in contrast with other directions using the same growth conditions. In this way, the dependence of the dislocation generation on the growth orientation has been shown. Threading dislocations observed had 1 6 ⁄ [ 112 ̅ ] and 1 2 ⁄ [11 ̅ 0] Burger vectors and stacking faults with the structure Σ3 {111} coincident-site-lattice (CSL) have been identified.

All these results are consistent with the model proposed by Alegre et al. [2].

Figure 1

 1 Figure 1 Weak beam micrographs in two beam conditions for the 022 (a) and 111 (b) reflections. Doped layers are marked by arrows and p ++ label. Plane of growth where the defects are generated are marked by dashed lines in (b) and corresponds with [1 ̅ 1 ̅ 1] and [1 ̅ 11 ̅ ].

Figure 2 .

 2 Figure 2. Annular dark field (ADF) micrograph recorded at 20cm camera length where defects marked by white dashed circles are placed at diferent position of the boron-doped layers. White arrows and p ++ labels show doped layers.

Figure 3 . 6 [ 2 [

 362 Figure 3. Dark field micrographs in two beam conditions for (a) g=400, (b) g=022 and (c) g=111 reflections of a cross section of a pyramidal hillock (PH). Groups of defects are encircled and labeled according with its Burger vector, "A" defects correspond to 𝒃 = ± 1 6 [112 ̅ ] and "B" ones to 𝒃 = ± 1 2 [11 ̅ 0]. (d) Bright field micrograph of the PH whose different growth orientations are marked by white dashed lines and identified by labels. Doped layers are marked by arrows and p ++ labels. They show different orientation during growth. Six of these intermediate growth directions are indicated by white/black dashed lines where they are revealed by the doped layers and planes are identified by labels.

1 6[

 1 112 ̅ ], marked with label "A", and𝒃 = ±1 2

Figure 4

 4 Figure 4 Weak beams micrographs under two beam conditions for the 220 (a), 400 (b) and 111 (c) reflections. Arrows and labels are used to identify the defects. "A" corresponds to a 1 6 ⁄ [ 112 ̅ ] Burger vector and "B" with 1 2 ⁄ [11 ̅ 0] one. Doped layers are mainly observed for reflexion 400.

  will be provided by the publisher 5Copyright line will be provided by the publisher

Fig. 5

 5 Fig.5shows a high resolution transmission electron microscopy (HREM) micrograph of a doped region of the sample recorded at the [011] pole. Stacking faults are observed forming an angle of 70.53º. As previously reported[16], these planar defects correspond with the ∑3 coincident-sizelattice structure. In addition, a Fourier transform performed on the defects (white dashed square on Fig.5a) shows that they correspond to the {111} type. These structures are twins boundaries-like and they have been observed in polycrystalline diamond[17,18]. Preferred grain boundary planes are the closest packed planes of the corresponding CSL that is, (111) planes. Here, an additional observation of the preferential planes for extended defects generations is shown.

Figure 5

 5 Figure 5 HREM micrographs recorded at the [011] pole of sample growth in 100 direction. Planar defects such as stacking faults (SFs) as well as dislocations are showed. SFs show to form an angle close to 70º consistent with the ∑3 type in the CSL model. Inset Fourier transform, corresponding to the white dashed square in (a), demonstrated that SFs are {111} type. Also some dislocations were observed. Enlarged in figure (b) a threading edge dislocation is shown.

Table 1

 1 Summary of the growth conditions of the studied sample (stack of nine bilayers).

	Non intentionally doped	Boron doped p ++
	CH4/H2 (%)		0.75	CH4/H2 (%)	0.5
	O2/H2 (%)		0.32	B2H6/CH4 (ppm)	7000
	Flow (sccm)	rate	200	Flow rate (sccm)	200
	Pressure (Torr)	33	Pressure (Torr)	33
	Time (min)		11.8	Time (min)	11.3
	Tsub ( o C)		910	Tsub ( o C)	910
	H2 Flush duration (sec)	10
	Flow rate H2 flush (sccm)	2000

Acknowledgements F. Lloret would like to acknowledge Prof. K. Zekentes for his financial support by the European project LAST-POWER (2009SE01380012, Program ENIAC, GSRT). Authors are also grateful for the project TEC2009-11399 of the Spanish Government.


Aymen Jmal
email: aymen.jmal@ecoledubois.fr@33240181222.

Amadou Ndiaye

Franck Michaud

Mark Irle

How to transfer scientific knowledge in recovered wood from research to industry

Keywords: knowledge transfer from research to industry, scientific knowledge, knowledge representation, recovered wood valorisation

The creation and the use of scientific knowledge on recovered wood allow industry to refine their skills on recovered wood management and to propose an ecologically responsible choice as the future of this waste respecting the environment. Nowadays, numerous scientific results are generated and published by university but little quantities are translated to the practice. This limitation is due to the difficulty to transfer this knowledge in its typical format i.e. scientific papers. In this paper, a new channel transfer in the form of the electronic knowledge book (k-book) on the recovered wood is proposed which facilitate the transfer of scientific knowledge from research to industry. It contains a new approach for representing scientific knowledge adapted to the industrial word. The declarative scientific knowledge has been represented by concepts maps and the procedural scientific knowledge has been represented by a knowledge-sheets.

The tests realized have demonstrated that the user of the k-book experiences has a low disorientation and a cognitive load level, which promotes the absorption and the use of the transferred scientific knowledge.

1-INTRODUCTION

Knowledge transfer here is the process where scientific knowledge (SK) is transmitted across a transmission channel so that it might be absorbed and used by the receiver (industrialists) [START_REF] Davenport | Working knowledge-How Organization Manage What They Know[END_REF]. The absorptive capacity of industry is its ability to recognize the value of new, external information, assimilate it, and apply it to commercial ends [2]. It is dependent on a person's prior knowledge and also on the format of the knowledge. The transfer of SK generated by universities on recovered wood to industry will help the sector to develop [START_REF] Agrawal | University-to-industry knowledge transfer: literature review and unanswered questions[END_REF][START_REF] Herrara | Mobility of public researchers, scientific knowledge transfer, and the firm's innovation process[END_REF] and encourage the responsible recycling of waste wood. The European commission has highlighted the importance of improving knowledge transfer between public research and industry [5]. In its typical format, i.e. scientific papers, SK is not readily accessible nor easily understood by industrialists, partly due to the fact that the scientific language can be very specific and then difficult to comprehend without specific training. Knowledge transfer to industrialists can be facilitated by the existence of dedicated structures e.g. R&D departments, within the company [START_REF] Dowling | Prodcut development success through cooperation : a study of entrepreneurial firms[END_REF], employee training and/or using Industry Mediators [START_REF] Braun | knowledge transfer from research to industry[END_REF]. These structures require a large investment and so are largely inappropriate to the wood sector, which consists mainly of small or medium-sized enterprises that cannot afford such investment. This study is therefore looking for alternative ways of transferring SK on recovered wood to the industry. For a successful transfer, SK must be acquired and represented into a formalism adapted to the knowledge domain of the industrialist. The representation depends on the nature of the knowledge. The SK on recovered wood is an explicit knowledge, and by the way can be acquired, represented and transferred through an electronic medium. It consists of both declarative and procedural knowledge. The declarative knowledge corresponds to the theoretical knowledge such as facts, rules and laws. The procedural knowledge corresponds to necessary knowledge for the achievement of tasks, e.g. sub-tasks, parameters and conditions etc. The SK on recovered wood also is granular and fragmented. The relevant SK includes the technical, environmental and economic data associated to the two broad types of use: recycling into new materials or energy production. In this paper, a new transfer channel of SK on the recovered wood from research to industry is developed in the form of an electronic knowledge book (k-book). Below is a description of the proposed framework for the SK acquisition and representation and its application to recovered wood. This is followed by an evaluation of the absorptive capacity from the k-book as assessed by the disorientation and cognitive load when exploring the k-book.

2-MATERIALS AND METHODS

The knowledge book (k-book) is a web-based medium dedicated to the transfer of knowledge, here SK about recovered wood. Its development started with the acquisition of SK. Firstly, the recovered wood valorisation process was identified and modelled. The model of the valorisation process (Figure 1) is a succession of unit operations and it corresponds to the industrial process of recovered wood valorisation. This model defines the scope of the knowledge domain (necessary and sufficient knowledge to determine the optimal use of the recovered wood). Then, the second step consists in collecting the available SK for each process unit operation. In order to do this, individual unstructured and semi-structured interviews were organized with a set of researchers who had complementary skills covering the knowledge domain. An adapted knowledge models (trees, semantic network etc.) [START_REF] Milton | Knowledge acquisition in practice: A step-by-step Guide[END_REF] has been used to model each collected knowledge; and then propkindsosed to the knowledge provider for the validation of its accuracy. Thereafter, the collected data were structured and represented. The declarative scientific knowledge has been represented using the concept maps formalism [START_REF] Novak | The theory underlying concept maps and how to construct them[END_REF]. The nodes represent the scientific concepts and the links the relationships existing between them. Only taxonomical, meronimical and domain relationships have been used in the representation of declarative knowledge according to a specific canonical form of concept maps [START_REF] Moon | Rapid and accurate idea transfer: Evaluating concept maps against other formats for the transfer of complex information[END_REF]. The canonical form is a tree which declare at a sufficient level a concept (the root) through three ontological axes: 1) a taxonomic axe to declare what is the principal concept across the generalization/specialization relationship "is-a", 2) a meronimic axe to enumerate the parts of the principal concept across the part-whole relationship "has-parts" and 3) a SK domain axe to declare how the concept is observed, measured, characterised or studied across the relationships "is-observed-by", "is-measures-by", "is characterised-by" or "is-studied-by". The procedural scientific knowledge has been represented through knowledge sheets (ksheet). A k-sheet is composed of several information fields including: title, illustration, explanation of the illustration, author of the k-sheet, keywords, related k-sheets and references (see Figure 3). The set of concept maps and k-sheets has been proposed to the knowledge providers during interviews for the validation of the correctness of the knowledge representation.

In the k-book, the network of concepts maps and k-sheets, a hypertext, has been implemented. Three kinds of hyperlinks are used: concept to concept-map (the declaration of the concept), concept to k-sheet (a procedural knowledge associated to the concept) and k-sheet to k-sheet (a related k-sheet). The model of the valorization process (Figure 1) which is the industrial recovered wood valorization process is used as transfer structure in the k-book in the form of a clickable menu. To each unit operation is associated a concept map, through a hyperlink, that declare what is the operation. The associated concept map will provide access to more detailed information (more specific concept maps and k-sheets) through the hyperlinks contained within. The ease of absorbing knowledge from the k-book was evaluated using 45 under-graduates from the Ecole Supérieure du Bois. The evaluation was based on the disorientation and the cognitive load required whilst exploring the k-book. The cognitive load was measured with the 7-points rating scale of mental effort [START_REF] Jmal | Structuring and representation of scientific knowledge for a transfer through an electronic knowledge-book[END_REF]. The disorientation was measured using the disorientation scale method [START_REF] Pass | Measurement of cognitive load in instructional research[END_REF]. The participants were divided into 2 groups: the first group was informed of the canonical form of the k-book prior to navigation and the second was not informed about the form. An assessment of mental effort and disorientation was performed after 2 navigation tasks of 25 minutes using a questionnaire with a response scale of 1 (extremely low) to 7 (extremely high) to a set of questions.

3-RESULTS AND DISCUSSION

The k-sheets have been created using a specific computer program developed to facilitate the creation of k-sheets. So far, 39 concepts maps and 100 k-sheets have been created. An illustration of a concept map representing the relevant declarative knowledge related to the concept of "recovered wood" is shown in Figure 2. An example of a k-sheet is shown in Figure 3. The results of mental effort and disorientation tests are presented in Table 1 and show that the use of k-book generates a low level of disorientation (M = 3.4, SD = 1.27) and requires low level of mental effort (M = 3.8, SD = 1.49) while exploring the k-book. The disorientation and cognitive load observed are mainly due to the use of the network of concepts maps and k-sheets. This network and its main menu, the k-book main page, promote knowledge transfer because it offers to user the possibility to explore the k-book from multiple perspectives and navigate freely in the k-book content [START_REF] Ahuja | Perceived disorientation: an examination of a new measure to assess web design effectiveness[END_REF].

Figure 2 : Concept map of the recovered wood

The representation of the information space using concept maps and hypertext minimize the disorientation and cognitive load of users of the k-book. The use of concept map with hierarchical structure creates a favorable situation to absorb external SK [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF]. Therefore, it allows the creation of a mental representation which reduces disorientation and cognitive load [START_REF] Amadieu | Effects of prior knowledge and concept-map structure on disorientation, cognitive load, and learning[END_REF]. The recovered wood valorization process used as a transfer structure should reduce the disorientation and cognitive load of the industrialists who has some knowledge of recovered wood because he will navigate the k-book according to his prior knowledge. At the same time, he will be acquiring new SK related to each operation in the process.

A one factor ANOVA indicated no significant effect (all p > 0.05) between the average mental effort rating for the first group of participants who had the canonical form (PCF) compared to those without the canonical form (PWCF). This implies that the two kinds of participants are investing the same effort mental. Another ANOVA applied on disorientation scores of two kinds of participants also indicates no significant effect (all p > 0.05) which means that all participants (PCF and PWCF) had the same disorientation level. According to these results, we can conclude that the canonical form of concept map is intuitive. During navigation, the participants (PWCF) rapidly understood the form. In fact, it offers a standardized, simplified and uniform reading for the set of maps and a direct access to the relevant information.

4-CONCLUSIONS

A new transmission medium in the form of the electronic knowledge book on the recovered wood is proposed. The first results tend to show that it will facilitate the transfer of scientific knowledge from university to industry. It contains a new approach for representing scientific knowledge adapted to the industrial word. The tests realized have demonstrated that the user of the k-book experiences low disorientation and cognitive load level, which promotes the absorption of the transferred scientific knowledge. In addition, the developed k-book provides a review on scientific knowledge generated in the domain of recovered wood, which helps users of recovered wood to find answers to their technical problems. In addition, the k-book provides an opportunity to identify knowledge gaps and therefore aids researchers in the development of new, relevant research projects. The next aim of this study is to enrich the kbook with industry knowledge (know-how) and determine its better representation in order to develop a decision support tool for industrialists when deciding on the optimal solutions for their recovered wood streams.

Figure 1 :

 1 Figure 1 : Representation of a valorization recovered wood process

Figure 3 :

 3 Figure 3 : Example of a k-sheet

Table 1 :

 1

Means (M) and standard deviations (SD) of the mental effort and disorientation rating

th International Conference on Engineering for Waste and Biomass ValorisationSeptember 10-13, 2012 -Porto, Portugal