Amine Ould-Hamouda

Antonio Iazzolino

Hiroko Tokoro

Shin-Ichi Ohkoshi

Eric Freysz
email: eric.freysz@u-bordeaux.fr

Large optical third-order nonlinearities in a switchable Prussian blue analogue

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

 [START_REF] Ohkoshi | Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer[END_REF]. The latter phenomenon has been demonstrated by recording the evolution of X-ray powder diffraction versus Rb content as well as by recording the second-harmonic generation (SHG) signal emitted when exciting a sample with nanosecond Nd:YAG pulses centered at λ=1.064 µm [START_REF] Ohkoshi | Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer[END_REF]. Above x=0.7, the SHG signal has been shown to steadily increase with the content of Rb. However, regardless of the content of Rb, the second-order optical susceptibility of this material remains small and is about one order of magnitude smaller than α-Quartz. Moreover, this material is photo-switchable and presents a large thermal hysteresis loop at room temperature, thus offering many other prospects, e.g., in the recording of optical data [START_REF] Tokoro | Continuous change of second-order nonlinear optical activity in a cyano-bridged coordination polymer photo-induced phase transition in RbMnFe Prussian blue analog-based magnet[END_REF]. Indeed, for x=0.94, when the temperature is decreased from T=320 K to T=240 K, one records a phase transition from a light brown noncentrosymmetric cubic (4 3𝑚) to a dark brown noncentrosymmetric tetragonal (4 𝑚2) space group. As shown in Fig. 1, this phase transition displays a broad thermal hysteresis loop, which is recorded between T~300 K and T~200 K. Since both space groups are noncentrosymmetric, an SHG signal can be recorded in both phases. However, the amplitude of the SHG signal is different in the cubic and tetragonal phases.

As a general rule, in condensed matter, the amplitude of nonphase-matched second-order nonlinear effects (such as SHG) overcomes the amplitude of nonphase-matched third-order nonlinear phenomena (such as third-harmonic generation (THG)) [START_REF] Shen | The principles of nonlinear Optics[END_REF][START_REF] Boyd | Nonlinear optics[END_REF][START_REF] Butcher | The element of nonlinear optics[END_REF]. Hereafter, we report on an efficient nonphase-matched THG in a noncentrosymetric Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O crystal powder, and study its evolution versus the excitation wavelength at different temperatures of the sample. The THG signal is found to be very large, visible with the naked eye, and largely overcoming the simultaneously generated nonphase-matched SHG signal, indicating that under our experimental conditions χ (3) E>χ (2) . The measured effective thirdorder value, we labeled 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 hereafter, is found to be ~510 -20 m 2 .V -2 , more than two orders of magnitude larger than α-Quartz, which is ~3.610 -22 m 2 .V -2 over a broad spectral range. This has to be compared to the 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 2 susceptibility previously reported for this material (𝜒 123 2 ~0.032 pm.V -1 ), which is about an order of magnitude smaller than α-Quartz (𝜒 111 2 (Quartz)~0.7 pm.V -1 ) [START_REF] Ohkoshi | Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer[END_REF]. Moreover, we will demonstrate that one can also record a photo-induced phase transition in this system, which makes it possible to modulate the amplitude of the THG signal. This clearly indicates our ability to photo-control the effective third-order optical nonlinearity of this material.

Experimental methods

Material preparation and characterization

The samples' preparation has been previously published [START_REF] Ohkoshi | Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer[END_REF]. The prepared samples of Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O consisting of cubic micro-crystals with a size of 2.1±0.7 µm.

For the measurements, a powder of Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O was inserted in between the microscope slide and cover slide, gently pressed, and heated at 330 K. As displayed in Fig. 1, when the temperature is decreased from T=330 K to T= 200 K, the color of this sample changes from light brown to dark brown. The XRD patterns and Rietveld analyses indicate that the change of color is related to the switching of the micro-crystallites from a cubic 4 3𝑚 structure, hereafter called the hightemperature (HT) phase, to a tetragonal 4 𝑚2 structure, hereafter referred to as the lowtemperature (LT) phase. Moreover, as displayed in Fig. 1, this phase transition displays a broad thermal hysteresis loop that is recorded in between ~300 K and 200 K. The evolution of the absorption and refractive index of this material measured in the visible and near IR spectral range in both the LT and HT phases and deduced from previously reported spectroscopic ellipsometry measurements are presented in Fig.

2 [START_REF] Ohkoshi | The dielectric constant in a thermal phase transition magnetic material composed of rubidium manganese hexacyanoferrate observed by spectroscopic ellipsometry[END_REF]. The evolution of the refraction index and the absorption coefficient of the sample in the LT and HT phases in the 1.1-2.4 µm spectral range were estimated by extrapolating with a polynomial fit the data obtained in the 600-800 nm spectral range. This approximation is valid, considering that the sample is weakly absorbing in the 1-2.4 µm spectral range. In the HT phase, one can notice the presence of a broad absorption peak centered at ~460 nm, which is likely due to the intervalence transfer band from the Mn III -NC-Fe II to Mn II -NC-Fe III and Jahn-Teller distorted Mn III . In the LT phase, this absorption peak is shifted toward ~410 nm and its amplitude decreases

THG experiments

The experimental set-up we used to perform our experiments is presented in Fig. 3. The sample was excited by 160 femtosecond pulses yielded by an optical parametric amplifier (OPA), which has a central wavelength that can vary from 1100-2400 nm. At the exit of the OPA, an infrared (IR) glass filter is inserted. It transmits the IR pulses produced by the OPA and blocks the visible light produced within this system. The laser pulse is then slightly focused over a beam waist of 235 µm onto the sample, and its maximal energy is 1.5 µJ. The THG signal generated at the surface of the sample was than collimated and focused on the entrance slit of spectrometer. In front of this spectrometer, another colored glass filter was used. The latter transmits the visible light and blocks the infrared excitation pulse. A thermally cooled charge coupled detector (CCD) is used to record the spectrum at the exit of the spectrometer.

Fig. 3: THG experimental set-up and pictures of the THG signal produced at the surface of the sample when excited by femtosecond pulses centered at I) λ=1400 nm, II) λ=1600 nm and III) λ=1900 nm.

Results and discussion

The THG signal is easily visible with the naked eye. Photographs of the THG signal produced at the surface of the sample in room light and in the dark are displayed in Fig. 3. These photographs are taken in the HT phase, at a temperature T=290 K, when the sample is excited by OPA pulses whose central wavelength is fixed to λ=1400 nm Fig. 3(I), λ=1600 nm Fig. 3(II) and λ=1900 nm Fig. 3(II), respectively. The sample is held in a thermally controlled cold finger in which the temperature is set at T=290 K. To switch the sample from the LT phase to the HT phase, it is heated for several minutes at T=330 K and then slowly cooled down to T=290 K. During this process, the color of the sample changes from dark brown to light brown. To bring the sample from the HT phase to the LT phase, it is cooled for several minutes by means of a nitrogen jet and slowly heated back to T=290 K, as displayed in Fig. 1. This also results in a change in the color of the sample from light brown to dark brown . The evolution of the THG signal in the LT and HT phases versus the power of the excitation pulse centered at λ=1920 nm is displayed in Fig. 4(a). In both the LT and HT phases, the intensity of the THG signal exhibits cubic power dependence. Moreover, regardless of the excitation intensity, the spectrum of the THG signal in the LT phase, displayed in the inset of Fig. 4(a), is found to be in very good agreement with the spectrum of the excitation pulses.

The normalized spectra of the THG signal recorded in the HT phase when one tunes the central wavelength of the excitation pulses from λ=1.2 µm to λ=2.4 µm are presented in Fig. 4(b). Almost identical results are recorded in the LT phase. This figure, along with Fig. 3, indicates that one can easily record a THG signal over the entire visible spectral range. As mentioned previously, our sample also exhibits a second-order optical nonlinear effect. We therefore have simultaneously record SHG and THG signals. However, in agreement with the pictures presented in Fig. 3, the amplitude of the THG signal is found to be at least one order of magnitude larger than the SHG signal. Regardless of the excitation wavelength we used, we could not detect the THG signal at the back surface of the sample. Therefore, the THG signal we record has to be generated at the air-sample interface or very near the surface of the sample. As indicated in Fig. 5(a), two different physical phenomena could give rise to this signal. At first, the THG signal may be directly generated by the surface of the sample within the surface coherence length L c,s =π/(k(3ω)+3k(ω)), where k(3ω) and k(ω) are the wave-vectors at the fundamental and third harmonic frequencies, respectively. Since the theory for THG in the limit of weak pump depletion is the same as for SHG, the irradiance of this THG signal writes 𝐼 𝑠 3𝜔 ∝ 𝐿 𝑐,𝑠 2 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 2

𝐼 3 𝜔 where 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3

is the effective susceptibility of our sample and I(ω) is the light irradiance at the fundamental frequency ω [START_REF] Kurtz | A powder techniques for the evaluation of nonlinear optical materials[END_REF][START_REF] Aramburu | Second-harmonic generation in dry powders: A simple experimental method to determine nonlinear efficiencies under strong light scattering[END_REF][START_REF] Aramburu | Second-harmonic generation by micropowders: A revision of the Kurtz-Perry method and its practical application[END_REF]. Note that, due to the very small value of L c,s (<0.1 µm), the absorption of the THG signal within this length interval can be neglected. Second, the THG signal may also be directly generated in the volume of the sample over the coherence length L c,v =π/(k(3ω)-3k(ω)). However, when the size of crystallites r is smaller than L c,v (L c,v >r>> L c,s ), the irradiance of the THG signal is only generated within the size r of the crystallites. Within a single crystallite, the THG signal writes [START_REF] Liu | Efficient third harmonic generation in a metal-organic framework[END_REF]:

(b) 𝐼 𝑉 (3𝜔, 𝑟) ∝ 𝑟 2 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 2 𝑠𝑖𝑛 2 Δ 𝑘𝑟 2 +𝑠𝑖𝑛 ℎ 2 α 𝑟 4 Δ 𝑘𝑟 2 2 + α 𝑟 4 2 𝑒 -𝛼𝑟 /2 𝐼 3 (𝜔) (1)
Where Δk=k(3ω)-3k(ω) is the wave-vector mismatch, α the absorption coefficient at 3ω, and I(ω) is the light irradiance at ω within the crystallites. This volume THG signal is then reflected at the interface between the particles. Then, before reaching the detector, it has to propagate back through the crystallites. Therefore, the THG signal writes: 𝐼 𝑅,𝑉 3𝜔 = 𝑅 3𝜔 𝑒 -𝛼𝑟 𝐼 𝑉 (3𝜔, 𝑟), where R(3ω) is the reflection coefficient at the air-crystallites interface. The latter expression neglects the very small contribution of the THG signal generated by the fundamental beam reflected at the exit interface of micro-crystallites. At normal incidence, R(3ω) writes: 𝑅 3𝜔 = (𝑛-1) 2 +𝜅 2 (𝑛+1) 2 +𝜅 2 , where n and k are the real and imaginary parts of the index of refraction at 3ω, respectively. To discriminate between the volume (I R,V (3ω)) and surface (I s (3ω)) contribution, we have evaluated the ratio I s (3ω)/I R,V (3ω), and as expected, we found that regardless of the excitation wavelength, I s (3ω) is always at least an order of magnitude smaller than I R,V (3ω). In the next section of this paper, we will therefore ignore the contribution of I s (3ω) to the THG signal. In fact, the THG signal is collected from an ensemble of crystallites. For the crystallites at the bare air-powder interface, the THG signal writes [START_REF] Kurtz | A powder techniques for the evaluation of nonlinear optical materials[END_REF][START_REF] Aramburu | Second-harmonic generation in dry powders: A simple experimental method to determine nonlinear efficiencies under strong light scattering[END_REF][START_REF] Aramburu | Second-harmonic generation by micropowders: A revision of the Kurtz-Perry method and its practical application[END_REF]:

𝐼 𝑉 ′ (3𝜔, 𝑟) ∝ N 𝐼 𝑉 (3𝜔, 𝑟),
where N is the number of crystallites per unit surface involved in the THG process. However, as shown in Fig. 5(b), the beam at a fundamental frequency can also reach crystallites beneath this bare interface and generate a THG signal. The THG signals produced within this layer of micro-crystallites also contribute to the overall THG signal. If one only considers the absorption of the THG signal, together with the reflection and transmission of the beam by the crystallites at fundamental, third harmonic frequencies, it can be easily shown that the THG signal produced by M superposed layers of crystallites writes:

𝐼 𝑉 𝑇 (3𝜔, 𝑟) ∝ 𝛽(𝜔, 𝑀)𝑁 𝐼 𝑉 (3𝜔, 𝑟) , (2) with 𝛽(𝜔, 𝑀) = 𝑅 3𝜔 1 + 𝑇 2 3𝜔 𝑇 6 𝑛-1 (𝜔)𝑇 2𝑛-1 (3𝜔)𝑒 -𝑛𝛼𝑟 𝑀 𝑛=1
, where T(ω), R(3ω), T(3ω) are the transmission, reflection, and transmission coefficients at the air-crystallite interface at the fundamental and third harmonic frequencies, respectively. Due to the spectral evolution of T(ω), R(3ω), and T(3ω) the behavior of β(ω,M) in the LT and HT phases was found to be almost constant above M=64 and presents some characteristic dispersion. It must be noted that Eq. ( 2) completely neglects the light scattering induced by the micro-crystallites or the multiple reflection occurring within or in between these microcrystallites. This latter assumption results in an over-estimation of the THG signal [START_REF] Aramburu | Second-harmonic generation in dry powders: A simple experimental method to determine nonlinear efficiencies under strong light scattering[END_REF][START_REF] Aramburu | Second-harmonic generation by micropowders: A revision of the Kurtz-Perry method and its practical application[END_REF]. On the contrary, in Eq. ( 2) we also consider that all micro-crystallites are not in close contact with each other and are separated by a thin air layer. The latter assumption may result in an under-estimation of the THG signal. We will therefore suppose that, on average, this over and underestimation of the THG signal cancels out. The THG signal generated in our sample has been calibrated against the THG signal generated at the surface of a 1-mm-thick ZnSe polycrystalline plate. Thanks to the two small irises placed at the back and in the front of the lenses L 2 and L 3 , respectively, our experimental set-up makes it possible to almost perfectly set this ZnSe plate at the position of our sample. A razor blade placed on the top surface of the ZnSe plate was used to block the THG light generated in the bulk and reflected by the back surface of the plate. The THG signal we recorded in this experiment is therefore only generated within the surface coherence length 𝐿 𝑐,𝑠 𝑍𝑛𝑆𝑒 =π/(k ZnSe (3ω)+3k ZnSe (ω)) of the ZnSe particles whose micro-crystallites size distribution is centered around 50-70 µm. Regardless of the excitation wavelength, 𝐿 𝑐,𝑠 𝑍𝑛𝑆𝑒 is always two orders of magnitude smaller than the size of these particles. We can therefore consider that I ZnSe (3ω) writes:

𝐼 𝑍𝑛𝑆𝑒 (3𝜔) ∝ N 𝐼 𝑉 𝑍𝑛𝑆𝑒 𝑉 (3𝜔, 𝑟) ∝ 𝑁 𝐿 𝑐,𝑠 𝑍𝑛𝑆𝑒 2 𝜒 𝑍𝑛𝑆𝑒 3 2 𝐼 3 𝜔 (3)
Since the THG signal in our sample and in the ZnSe plate are generated from randomly oriented crystal, one can readily evaluate 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 against 𝜒 𝑍𝑛𝑆𝑒 3 by computing the square root between the THG signal generated under the same experimental conditions by computing the ratio between Eq. (1) and Eq. [START_REF] Ohkoshi | Continuous Change of Second-order Nonlinear Optical Activity in a Cyano-bridged Coordination Polymer[END_REF]. From this ratio and knowing 𝐿 𝑐,𝑠 𝑍𝑛𝑆𝑒 , the coefficients α, Δk, and R(3ω) for our sample, one can infer 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 in the LT and HT phases, considering 𝜒 𝑍𝑛𝑆𝑒 3 ~2.6510 -19 m 2 .V -2 is constant over our excitation spectral range. An interesting property of Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O is that it is bistable. Hence, within its thermal hysteresis loop that lies in between 225 K and 290 K, it can be set in either the LT or HT phase. Since the value of 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 differs in the two phases, one should be able to simultaneously switch the linear and the nonlinear optical properties of this material. As proof of this concept, we have performed the following experiment. The sample was initially set in the LT phase at 285 K. As mentioned previously, in the LT phase, the color of the sample is dark brown. The THG signal was then recorded, exciting the sample at λ=1920 nm by varying the energy of the exciting pulse in between 0.1 and 1.5 µJ. Afterwards, we increase the energy of the pulse to ~10 µJ. After several seconds, when a sequence of these more powerful pulses was used, as displayed in Fig. 7(a), the color of the area excited by these pulses turned from dark brown to light brown. This indicates the sample is likely switched from the LT phase to the HT phase [START_REF] Tokoro | Continuous change of second-order nonlinear optical activity in a cyano-bridged coordination polymer photo-induced phase transition in RbMnFe Prussian blue analog-based magnet[END_REF]. To confirm this was indeed the case, we reduced the energy of the laser pulses from 10 µJ to 0.1-1.5 µJ. The THG signals recorded for these lower energies were compared to the THG signals we previously recorded when the sample was set in the HT phase for similar laser energies. As shown in Fig. 7(b), the amplitude of these two THG signals recorded at T=285 K were found to be almost similar. This indicates that indeed we have switched the sample from the LT to the HT phase. Then, the sample was brought back in the LT phase by cooling it with a nitrogen jet. After this process, the sample recovered its dark brown color, and the amplitude of the THG signal was almost identical to the one we recorded at the beginning of this experiment. This experiment was repeated at least ten times for exciting pulses with intensities between 0.1 and 1.5 µJ. Within our experimental uncertainties (± 5%), we effectively reproduced these results. This experimental proof of concept indicates that one is indeed able to photo-switch back and forth the linear and third-order nonlinear optical properties of this sample from the LT phase to the HT phase. To understand the mechanism that gives rise to the photo-switching between the LT to the HT phase, we carried out this experiment reducing the exposure, the exciting pulse repetition rate. We found that the mechanism at the origin of the photo-switching phenomena is likely thermal. In other words, the laser beam power is absorbed and results in an increase in the local temperature of the sample. If the local temperature is strong enough, the area shined by the laser beam is brought from the LT phase to the HT phase. Within the thermal hysteresis loop, it remains in this state and can be switched back to the LT phase by decreasing the temperature of the sample beyond the thermal hysteresis loop [15].

Conclusion

In sum, we have observed and measured THG in a powder of Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O. Our THG measurements at fundamental wavelengths ranging from 1100 nm to 2400 nm show that, in this spectral range, the THG signal overcomes the SHG signal. At maximum, the effective  (3) value is comparable with that of a ZnSe poly-crystallites wave-plate and is in the 1.2-2.4 µm spectral range at least two orders of magnitude larger than that of -Quartz.

We have also demonstrated that, within its thermal hysteresis loop, the linear and third-order nonlinear optical properties of this material can be photo-switched. This demonstrates the potential of such Prussian blue analogs for nonlinear optical applications.

  coordination polymers composed of -M A -NC-M B -(M A and M B are transition metal ions), Prussian blue analogs, have the centrosymmetric face centered cubic structure of M A II [M B III (CN) 6 ] 2/3 z H 2 O [1]. When an alkali (A) ion is inserted during the synthesis, Prussian blue analogs take on the A I M A II [M B III (CN) 6 ]-type structure. It has been recently shown that above x=0.7, such a polymer of Rb x Mn[Fe(CN) 6 ] (x+2)/3 z H 2 O displays a structural change between a cubic centrosymmetric 𝑚3 𝑚 structure to a cubic noncentrosymmetric 4 3𝑚 structure

Fig. 1 :

 1 Fig. 1: Hysteresis loop of the sample revealed by the MT-T plots. The insets show that in the LT phase the color of the sample is dark brown. Its color turns light brown in the HT phase.

Fig 2 :

 2 Fig 2: Absorption spectra and refractive indices of the sample in the LT and HT phases (deduced from [S. Ohkoshi et al., J. Mater. Chem. 15, 3291-3295 (2005).]).

Fig. 4 :

 4 Fig. 4: a) Evolution of the spectra and intensity of THG signal versus the intensity at the fundamental wavelength. The experiment was performed in the LT and HT phases exciting the sample at =1920 nm. b) Normalized THG spectra recorded at different excitation wavelengths.

Fig. 5 :

 5 Fig. 5: Micro-crystallite geometry considered for the computation of β

Fig. 6 :

 6 Fig.6: Spectral evolution of effective (3) RbMnFe and absorption of our sample in the HT (red) and LT (blue) phases. The solid lines are guides for the eyes.

Figure 6 Fig. 7 :

 67 Figure 6 displays the evolution of 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3we computed accordingly, considering that the concentration N of particles in our sample and ZnSe polycrystalline plate are similar. Note that in comparison to ZnSe, the concentration of our very slightly compacted RbMnFe sample

is likely less. Hence, here again we underestimate the value 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 . However, in both the LT and HT phases, the values of 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 range between 0.210 -19 m 2 V -2 and 1.510 -19 m 2 V - 2 . These values are smaller but still comparable with 𝜒 𝑍𝑛𝑆𝑒 3 . They are about two orders of magnitude larger than the χ (3) of α-quartz (~3.610 -22 m -2 V -2 ). However, in the LT phase, as one reaches the excitation wavelength λ=1400 nm, the 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 rapidly increases and reaches a value of ~1.510 -19 m 2 V -2 at λ=1200 nm. The latter behavior is likely related to resonant enhancement of the 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 close to the three-photon absorption centered at λ=460 nm. This resonance is not visible in the HT phase. This latter behavior is attributed to the shift of the absorption band toward lower wavelengths in the HT phase as well as the reduction of the absorption peak. However, as illustrated in Fig. 6, the wavelength at which 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 reaches it maximum does not coincide with the three-photon resonant absorption of the sample. It is shifted toward a lower wavelength. This may result from an increase in the absorption of our sample at the fundamental or third harmonic frequency through excited state absorption that is not accounted for by our model [START_REF] Christodoulides | Nonlinear refraction and absorption: mechanisms and magnitudes[END_REF].

ZnSe adopts a cubic 4 3𝑚 structure; therefore, it is optically isotropic. For THG, it exhibits two independent and non-null χ (3) elements: 𝜒 1111 [START_REF] Tokoro | Continuous change of second-order nonlinear optical activity in a cyano-bridged coordination polymer photo-induced phase transition in RbMnFe Prussian blue analog-based magnet[END_REF] and 𝜒 1212 (3) . Hence, in our experiment, the crystallites being randomly oriented, we measured an angular average of the THG over these two components, and so is the value of 𝜒 𝑍𝑛𝑆𝑒 3 in Eq. ( 3) [START_REF] Kurtz | A powder techniques for the evaluation of nonlinear optical materials[END_REF][START_REF] Aramburu | Second-harmonic generation in dry powders: A simple experimental method to determine nonlinear efficiencies under strong light scattering[END_REF][START_REF] Aramburu | Second-harmonic generation by micropowders: A revision of the Kurtz-Perry method and its practical application[END_REF]. In the HT phase the Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O also adopts a cubic 4 3𝑚 structure. It therefore also exhibits two independent and non-null χ (3) elements. Hence, the effective 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 (𝐻𝑇) value we measured in our experiment can be readily compared to the effective value of 𝜒 𝑍𝑛𝑆𝑒

3

. However, at an LT, our Rb 0.94 Mn[Fe(CN) 6 ] 0.98 .0.3H 2 O sample switches from a cubic to a tetragonal 4 2𝑚 structure. For THG, the latter structure exhibits five independent elements: 𝜒 1111 (3) = 𝜒 2222 (3) , 𝜒 3333 (3) , 𝜒 1133 (3) = 𝜒 2233 (3) , 𝜒 1122 (3) = 𝜒 2112 (3) , 𝜒 3223 (3) = 𝜒 3113

(3) [START_REF] Yang | Expression of third-order effective nonlinear susceptibility for third-harmonic generation in crystals[END_REF]. The value 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 (𝐿𝑇) is here again an angular average over these values, and it cannot be directly compared to the effective value of 𝜒 𝑍𝑛𝑆𝑒 3 .

Knowing the amplitude of 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 and 𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 2

of our sample, one can evaluate the threshold value of electric fields E th for which χ (3) E th >χ (2) , i.e., the value of E th for which the non-phase matched THG overcomes the non-phase matched SHG. One found E th ~𝜒𝑅𝑏𝑀𝑛𝐹𝑒 2 /𝜒 𝑅𝑏𝑀𝑛𝐹𝑒 3 ~10 6 V m -1 . This computation is valid when the coherence length for SHG and THG are about the same amplitude, which is the case for the sample we studied. This value of E th has to be compared to the amplitude of the electric field associated with our femtosecond laser pulses, which is about two orders of magnitude larger (E~1 10 8 V.m -1 for 0.1 µJ and E~410 8 V.m -1 for 1.5 µJ [14]). Therefore, in agreement with our observations, the electric fields associated with our laser pulses being two orders of magnitude larger than E th , we do expect the nonphase matched THG signal to overcome the nonphase matched SHG signal. Note that this phenomenon will be difficult to evidence in either -Quartz or ZnSe where E~ (2) / (3) is expected to be larger than 10 8 V.m -1 .


Sacha Loeve

Bernadette Bensaude Vincent

THE MULTIPLE SIGNATURES OF CARBON 1

Car bon is the fourth most abundant element by mass in the universe after hydrogen, helium and oxygen. The chemistry of carbon is both ancient and ubiquitous, with applications ranging from fine jewellery to heating, textiles, pharmaceuticals, energy and electronics. How can we present this familiar stuff, which has played a central role in the history of chemistry, as an exemplar technoscientific object? Wouldn't it be more adequately described as a typical scientific object?

To be sure, carbon is an object of 'pure research'. It emerged in the nineteenthcentury as a chemical substance, as an abstract albeit material substrate underlying a range of simple and compound bodies. However, this ontological perspective shows only one face of carbon. While scientific research was focused on what is conserved through change, the researchers' attention shifted to what might be changed: Carbon came back as a menagerie of allotropes -fullerenes, nanotubes, graphene and many more -which populate the 'nanoworld', making it a rich source of technological possibilities. The ontological status of carbon in a scientific perspective answers the question 'what is it?' while in a technoscientific approach, the question answered is rather 'what might be performed with it?' or, more precisely, 'what might it afford?' We could thus portray carbon as a Janus and contrast its scientific and technoscientific identities. 2 However, this contrast provides a far too purified image of carbon. Carbon has assumed so many guises over the course of the centuries that it almost seems to play various personae moving with a momentum of their own, inspiring new adventures while exhibiting surprising physical and chemical properties. Diamond, charcoal, graphite, carbon compounds, mephitic air and CO 2 are among the characters that have played -and continue to play -significant roles in science and mythology, in industry and economy alike. Carbon is too ubiquitous, too polymorphic and too important in our 1

history for being reduced to these Janus faces. Such a portrait would overlook the multiplicity of the modes of existence of carbon and their various inscriptions in daily life.

Multiple Modes of Existence

As the term 'allotropy' suggests (allos: other + tropos: manner, way or mode), 3 carbon displays a multiplicity of modes of existence. This chapter explores their coming into being in relation with human history. It tells many stories, ranging from legends about mephitic air and the key role of carbon in building the periodic table to the story of the carbon skeleton as a backbone of life and pillar of chemical industry.

Due to its disposition for creating strong bonds with itself and other atoms, carbon affords robust and stable structures and a host of potential combinations, found both in nature and in human industry. At the nanometre scale, carbon writes a kind of fairy tale. As its bulk molecular structure shrinks to pure surface, it displays a wide range of novel properties and performs a variety of mechanical, electronic, optical and magnetic functions, presented as the promises of enchanted futures.

In stark contrast to these futuristic tales, the story told by carbon deposits looks backwards and is moving inexorably towards a sad ending. Charcoal and oil, the archives of life on Earth, have been excavated and come back into existence as fire and power for human consumption needs. Two centuries after the beginning of the industrial revolution, the vestiges of life accumulated for billions of years in the soil are almost depleted. They have melted into air by a few generations of an ever-increasing population of humans under the form of carbon dioxide. As human societies realized the impacts of their carbon-based technologies, they elected carbon dioxide as a standard and 'mediating machine' to regulate the flow of exchanges between the two oikoï or 'world-houses', ecology and economy.

Carbon thus became a buzzword of economic and ecological globalization. Today, any activity correlated with greenhouse gas emissions -that is to say, most human activities -is translated in terms of 'carbon equivalent'. While the notion of 'carbon footprint' epitomizes human impacts on ecosystems, 'carbon equivalence' casts human industry as a natural force exchanging carbon with other lifeforms at a geological scale. Complementing 'carbon accountability', 'carbon trading' has been implemented: Greenhouse gas emissions are priced in carbon equivalent, which brings property titles and credit exchange rules through a series of interconnected carbon markets. Carbon thus becomes a universal unit of currency, an aerial money, a speculative product. "All that is solid melts into air" 4 .

Yet the alliance of carbon with market economy is only one of its modes of existence. Instead, we want to consider all of them at once. Carbon is reducible neither to the fashionable abstraction of carbon equivalent, nor to its chemical identity. The simple and unique definition of carbon as an element in the periodic table, like the definition of water as H 2 O questioned by Hasok Chang, is obviously too narrow to contain all its facets and roles in human history. 5 Just as Chang convincingly argues that the formula H 2 O does not deserve a monopolistic dominance, we will see that carbon calls for multiple systems of knowledge. Not only is there a plurality of views of carbon in physics, chemistry, biology, materials science and environmental science… but there are many other relevant views of carbon in lay and traditional knowledge. Carbon proves the value of 'epistemic pluralism', and invites for more 'tolerance' among the various forms of knowledge. However, this chapter goes further. It claims that there is no reason to deduce the various facets of carbon from one single fundamental definition. Carbon as a substance, standing beneath all its modes of being, is only but one of these facets. Carbon invites ontological pluralism in addition to epistemic pluralism. Although each mode of existence has an 'imperialistic' propensity for configuring the other modes in its own template, all the modes of existence coexist. Kick one of them out by the door, it comes back through the window. In paying attention to the diversity of modes of existence of carbon and their interactions along the line developed by Etienne Souriau and Bruno Latour,6 this chapter makes the case for an ontography: It considers carbon as an agent of 'graphism' in the task of writing ontologies.

Carbon Heteronyms

Carbon is polymorphic. Even in its elemental state it takes a variety of allotropic forms, some of them with well-ordered, crystalline structures (graphite, diamond, lonsdaleite),7 others with amorphous structures (glassy carbon, carbon black, nanofoam), in addition to mixed structures displaying various degrees of order and disorder (charcoal, soot, coke).

Yet some of the allotropes of carbon have quite different physical properties: diamond is hard and translucent, graphite friable, fragile and opaque. Diamond is abrasive, graphite lubricant. Diamond is an electrical insulator and thermal conductor, graphite an electrical conductor and a thermal insulator. Ever since the days of antiquity, diamond has been considered the hardest stone on Earth. Its name, deriving from Greek αδάμας (a: 'not' + daman: 'to tame') highlights its remarkable property of resistance to all attempts to break it, as well as to the erosion of time: it is an 'everlasting stone', which literally 'cannot be tamed'. Diamond is adamant, refusing to change or to give in. Fittingly enough, it became the symbol of an unbreakable engagement between two persons: 'diamonds are forever'. What on earth could it have in common with the black and brittle substance that leaves a dark mark on a sheet of paper? In contrast to diamond, graphite (derived from the Greek graphein: 'to write') is so fragile and soft that it has to be inserted into a hollowed wooden stick to be used. The pencil patented by Nicolas Jacques Conté in 1795 was named 'lead pencil' because graphite was initially considered to be 'plumbagol' or 'black lead', a substitute for the lead formally used for writing since Roman times. Less surprising was the connection between 'black lead' (a residue from the distillation of animal or vegetable matter in a limited supply of air), and the use of the same material to draw the pictograms of cave paintings some 30,000 years ago. Yet this artists' material was also used to heat iron in metallurgy. What does coal -the fuel of the industrial revolution extracted by the ton from mines all over Europe and in the colonies -have in common with the precious diamond?

In their chemical mode of existence, diamond and graphite are two allotropes: they are made of the same carbon atoms and differ only in the bonds between atoms. However, from an ontographic perspective, they share more than chemical allotropy. From the graphite pencil to diamond-engraving tools and the 'code of life' based on a carbon backbone, from the periodic table to the 'carbon footprint', from the carbon black tattoos of Ötzi the Iceman (5200 years ago) to the 'tons of carbon equivalent', measuring the global warming and to radiocarbon dating ( 14 C), carbon is linked with the action of scripting (graphein). It exists in inscriptions, for conservation, standardization and circulation. Human history is written in carbon. If it is true that human civilization began in prehistory with the mastery of fire, then carbon, by its very name -derived from the Latin root carbo, 'burnt' -connects nature and culture. If it is true that history began with writing, then carbon in its form of graphite kicked off cultural history. Nowadays carbon traces allow humans to read their history against the background of a wide spectrum of timescales, ranging from a few years to geological eras.

This essay presents the various modes of existence of carbon as its signatures. It lends a voice to its multiple personae and allows them to write their own narratives. Just as the Portuguese poet Fernando Pessoa had various heteronyms sign his works of fiction, carbon has several signatures for writing ever-new scripts and telling various stories that interweave human history, natural history and cosmic processes. To what extent could we consider the name 'carbon' as a multiplicity of heteronyms, each having its own signature? In considering carbon as a scribe with multiple identities, this chapter will emphasize the ways in which each persona of carbon interacting with our material and symbolic practices create togetherness and sketch the lines of our common world.

Carbon as Mephitis

In Aeneid, the Roman poet Virgil describes the valley of the river Asanto in Campania as an entry to hell.

In midst of Italy, well known to fame There lies a lake, Amsanctus is the name Below the lofty mounts: on either side Thick forests the forbidden entrance hide. Full in the centre of the sacred wood An arm arises of the Stygian flood, Which, breaking from beneath with bellowing sound, Whirls the black waves and rattling stones around.

Here Pluto pants for breath from out his cell, And opens wide the grinning jaws of hell. To this infernal lake the Erinye flies; Here hides her hated head, and frees the lab'ring skies. 8 The foaming marsh, named la Mefite by local peasants after a fury called Mephitis,9 has the largest natural non-volcanic CO 2 emission rate ever measured on Earth (about 200 tons per day). Virgil's scary description echoed and further propagated legends about the evil and pestilent nature of Mephitis. While the site is still considered potentially hazardous, especially in the absence of wind,10 the shepherds of the neighbourhood have continued to bring their sick sheep to la mefite during transhumance in order to cure them. Between Chthonian depths and Ouranian vapours, life and death, Mephitis 'stands in the middle'.11 She was a kind of pharmakon, evil and remedy at once, as well as a scapegoat. In the course of time, this ominous exhalation has been named 'mephitic air', 'pestilential vapour', 'lethal spirit', 'deadly spirit', 'fixed air', 'aerial acid', 'acid air', 'chalky acid', 'sylvester spirit', or simply, 'gas'. In fact CO 2 is the archetype of the notion of 'gas'. 12 This term, coined in the seventeenth-century by Joan Baptista van Helmont refered to, both a deadly substance and a principle of life: on the one hand, it is a kind of pneuma animating a body; on the other, because of its impetuous and elusive character, it turns into a dangerous killer when released.

To be sure, the reform of the language of chemistry promoted by French chemists in 1787, was a serious attempt to purify carbon from the 'archaic symbols' conveyed by Mephitis's avatars. The name 'acide carbonique' erased the connotations of life and death, of good and evil, borne by the ancient denominations of CO 2 . Let us see whether Mephitis's formidable power has been defeated or merely concealed by the mêlée of more modern carbon heteronyms.

Carbon as a Standard

In nineteenth-century chemistry, carbon provided a taxonomic scheme that allowed chemists to establish order within the crowd of individual substances. When chemists undertook to set up a classification of chemical elements, carbon played a decisive role in defining what was to be classified. Dmitiri Mendeleev used the case of carbon as a kind of template to define the concept of chemical elements as distinct from that of simple substances. The allotropic forms of carbon (diamond, graphite and coal) are exemplars of the concrete stuff of simple substances.

A simple body is something material, a metal or a metalloid, endowed with physical and chemical properties. The idea that corresponds with the expression simple body is that of the molecule […]. By contrast, we need to reserve the name element to characterize the material particles that constitute the simple bodies and compounds and that determine the manner in which they behave in terms of their physical or chemical properties. The word element should summon up the idea of the atom. 13 While simple substances come into existence as concrete and physical entities at the end of a process of analysis and purification, elements are the material but invisible parts of simple and compound bodies. Carbon is a hypothetical abstract entity since it can never be isolated -in stark contrast to diamond (pure carbon) and anthracene (90% pure carbon). Nevertheless the element carbon is real and identifiable by a positive individual feature: its atomic weight. For Mendeleev the atomic weight was the signature of elements. The signature of carbon was 12.

How can atomic weight be quantified when it is impossible to measure the weight of atoms? The system of atomic weights had to be set up on the basis of relative and conventional values. Carbon again played a decisive role in this process by being chosen as the standard in the mid-twentieth century. The earliest systems of atomic weights based on a conventional standard unit H=1 (hydrogen equals 1) or O=16 (oxygen equals 16) no longer worked after the discovery of isotopes. For example, physicists attributed the value 16 to one single isotope of oxygen, while chemists attributed that same value 16 to the whole range of oxygen isotopes 16, 17 and 18. In 1959-1960, the International Union of Pure and Applied Physics (IUPAP) and the International Union of Pure and Applied Chemistry (IUPAC) agreed to put an end to this troublesome discrepancy by electing the isotope carbon-12 as the standard reference for determining the atomic mass of all other elements. In 1961, an IUPAC convention defined the Dalton or UMA (Unified Atomic Mass Unit) as one-twelfth of the mass of an atom of 12 C Carbon thus acted as a diplomat, a mediator to settle a conflict between chemists and physicists.

It also provided the standard for defining the concept of mole. A mole, or N, (Avogadro's number) refers to the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kg of carbon 12 (6.0220451023). N atoms of 12 C have a mass of 12 grams. As the basis for mole, carbon acts again as mediator. This time it mediates between the nanoworld of atoms and molecules and the macroscopic world of human operations on matter, making the chemists' life easier. 14

Carbon as Substance

The periodic system has been set up by Mendeleev in an effort to discover the unique 13 Mendeleev, 'The relation between the properties of the atomic weight of the elements', 1871, reprinted in H. M. Leicester and H. S. Klickstein (eds.), Sourcebook in Chemistry 1400-1900 (New York: Dover, 1953). on p. 693. 14 C. Buès, Histoire du concept de mole : à la croisée des disciplines physique et chimie (Lille : Atelier national de reproduction des thèses, 2001). and general law governing the irreducible diversity of chemical phenomena. This law stated that the properties of simple and compound substances are a periodic function of the value of the atomic weight of elements.

Mendeleev's emphasis on the centrality of elements was maintained and reinforced in the early twentieth century with the discovery of isotopes. Carbon came to be considered an underlying substratum (sub-jactum) that persists through chemical changes. This substantialist approach was conveyed by Friedrich Paneth, a German chemist who demonstrated that radio-elements could not be isolated from the most common isotope by chemical means, and thus could be considered as true elements. In trying to identify the mode of existence of what is preserved unchanged through chemical metamorphoses, Paneth adopted a substantialist stance through his distinction between 'basic substance' (Grundstoff) and 'simple substance' (einfacher Stoff). 15 'Stuff' thus became a central concept in the philosophy of chemistry 16 , a metachemically refined version of the metaphysical 'substance'. Indeed Paneth did not come up with the typical metaphysical notion of substance, as an undifferentiated substratum of matter identified by primary qualities such as extension and impenetrability. 17 Instead of trying to reduce qualities to quantity, as philosophers did in the mechanical tradition, Paneth clearly assumed that chemists could not reduce secondary qualities to primary qualities as they had to assume the persistence of qualities in compounds.

In order to identify the 'something' that remains unchanged through chemical changes, Paneth revived the Aristotelian notion of hupokeimenon as a basic and general level of reality underlying the various particulars accessible to sense perception. Whereas the basic substance (Grundstoff) has no existence in space and time, simple substances are unique events located hic et nunc. Paneth was thus in a position to answer Aristotle's question: 'What is it (to esti) ?' And he provided a dual answer, as Aristotle did: it is both a singular phenomenal entity, an individual that you can see and point your finger at (ek-keimenon) and a universal substrate (hupokeimenon) underlying and explaining particular and changing phenomena. Carbon as substance connects modern chemistry with ancient metaphysics.

Carbon as Material

In chemical textbooks carbon appears as a substance because of the ontological priority granted to atoms. However in the material world around us, artisans and engineers do not find carbon atoms. Nature affords carbon molecules and compounds, that can be 15 F. Paneth, 'The epistemological status of the concept of element', British Journal for the Philosophy of Science, 13 (1962), pp. 144-60. 16 K. Ruthenberg and J. van Brakel (eds), Stuff. The Nature of Chemical Substances (Würzburg: Verlag Königshausen & Neumann, 2008) 17 In this respect Paneth's notion of Grundstoff could not be a target for Bachelard's criticism of the metaphysical view of substances, which he contrasted to the rich metachemical notion forged through a process of realisation. Although Bachelard would object to Paneth's concern with conservation, he could not reproach him for having an intellectual view of matter as a generic entity. Such an impoverished notion, instantiated in Descartes' meditation on a piece of wax, was in Bachelard's view the counterpart of his substantialist view of the cogito. G. Bachelard, La Philosophie du non. Essai d'une philosophie du nouvel esprit scientifique, 1940 (Paris: Presses Universtaires de France, 1988), on p. 53. Engl. tr. The Philosophy of No. A Philosophy of the New Scientific Mind (New York: The Orion Press, 1968), on p. 45. used as materials. Many of them have played key roles in human industries since prehistory. For instance, bitumen -a hydrocarbon containing 80% carbon and formed from plankton slowly accumulated in sedimentary basins -was already used by Ancient Egyptians for coating roads, boats, canals, dams and tanks. Asphalt -a mixture of bitumen and aggregates which coated the streets of London and Paris around 1820was used by seventeenth-century engravers for etching and by painters to bind their pigments. Coal and bitumen have also long been known for their antiseptic properties: the Phoenicians carbonized the wooden barrels of trading ships in order to preserve drinking water on their long journeys at sea, while the Egyptians treated teeth cavities with a mixture of bitumen and clay. Carbon fibres, which are widely used today in the manufacture of composites due to their remarkable properties -resistance, flexibility and light weight -, enjoyed prior industrial success in light bulbs, when Edison and Swan used filaments obtained by the 'carbonization' of cotton and bamboo.

Such industrial uses of carbon materials did not follow from the theoretical understanding of carbon's atomic structure and of the carbon-carbon bond. Rather, the potential uses of hydrocarbon molecules were gradually explored in a complex process of de-contextualization and re-contextualization of pharmacists' and manufacturers' knowledge and know-how about carbon materials. 18 Carbon materials bridge the gap between the phenomenal world of technological applications and the theoretical world of molecular structures and models.

Carbon as Skeleton

The identification of the unique atomic structure of carbon (tetrahedral with four valence electrons) and its wide-ranging binding capabilities (C-C, C=C, C≡C, C-H, etc.) accounts for the remarkable dispositions of carbon (what it is capable of): stability, resistance, and combinatory potential to form innumerable compounds.

These dispositions have been put to work in creative processes, both in nature and in art. In nature, biomolecules such as DNA, RNA, proteins, carbohydrates and lipid membranes are all structured around a strong carbon backbone. [START_REF]We humans can be described as a compound of carbon-based molecules C E27 H E27 O E27 N E26 P E25 S E24[END_REF] Significantly, this backbone resists the current ambition of synthetic biologists to re-engineer life at the molecular level and redesign DNA. Whereas synthetic biologists are able to change the pairs of bases that carry the genetic information and recombine them in all possible ways, it seems that they cannot fix 'God's mistakes', that is, changing the backbone itself with its repeating negative charges (which look odd if not absurd to a synthetic chemist). [START_REF] Benner | Act natural[END_REF] In the realm of technology, millions of organic chemical compounds synthesized by the chemical industry are also made of a carbon backbone, albeit less complex than those made by nature. Whether natural or artificial, organic compounds are the products of the structural combinatorial game enabled by carbon binding dispositions. Thus synthetic products, usually presented as products of human design driven by social demands, are also examples of the actualization of carbon dispositions. Underlying the traditional divide between the natural productions of life and the highly artificial processes of industry runs an invisible thread, an elegant, robust, but largely unnoticed microstructure: the carbon backbone.

Carbon as Surface

Over the past twenty-five years, carbon has been the star of materials research, generating more and more exotic allotropes: nanotubes21 , fullerenes, [START_REF] Kroto | C60: Buckminsterfullerene[END_REF] graphene, [START_REF] Geim | The rise of graphene[END_REF] nanobuds, [START_REF] Nasibulin | A novel hybrid carbon material[END_REF] nano-onions, [START_REF] Rettenbacher | Radical addition of a conjugated polymer to multilayer fullerenes (Carbon Nano-onions)[END_REF] nanotori, [START_REF] Cox | New Carbon Molecules in the Form of Elbow-Connected Nanotori[END_REF] nanocones, nanohorns, 27 nanobamboos, [START_REF] Koltai | Junctions of left-and right-handed chiral carbon nanotubes -nanobamboo[END_REF] nanoribbons, [START_REF] Jiao | Narrow graphene nanoribbons from carbon nanotubes[END_REF] and so on. This weird menagerie has garnered many awards: the 1996 Nobel Prize in Chemistry for the fullerenes, the 1998 Kavli Prize in Nanoscience for carbon nanotubes, and the 2010 Nobel Prize in Physics for graphene, the individual sheet of graphite. The new avatars of carbon allotropes have prompted the coming into being of a kind of parallel world, which is invisible yet simultaneously amply visible in the media: the 'nanoworld'. Once again, after the great expectations generated by nineteenth-century synthetic chemistry, carbon appears as a cornucopia of futuristic products: screens, batteries, organic electronics, ultra-fast computers, ultra-thin sensors, traps for pollutants -and it even promises an elevator into space using a giant cable made of braided carbon nanotubes! However, these materials and their technoscientific mode of existence are far more bizarre and fascinating than their potential -and perhaps speculative -applications.

First, since these structures can be considered either as tiny crystals or as giant molecules, they challenge the boundary between organic and mineral. Second, their combinatorial potential no longer involves populations of molecules in chemical reactions; it rather refers to a game of construction involving the assembly of individual carbon molecules. Third, structure and properties matter less than the functions to perform (mechanical, electronic, photonic, chemical, magnetic). Finally, structures are viewed as configurations in an indefinite set of transformations. Since these new avatars of carbon allotropes are single or multi-layered configurations of individual graphite sheets, graphene stands as the matrix of all of them, at the frontiers of matter. It is the thinnest and the strongest material known to exist. [START_REF] Salvage | Super carbon[END_REF] Its electrons behave like massless particles, travelling at a much higher speed than in silicon. Graphene is also flexible, light absorbent, and is a chemical reactant. It is indefinitely malleable: it can be cut, bent, folded, rolled or zipped into a tube or a cone, just as in origami and kirigami art. [START_REF] García | Origami construction of 3D models for Fullerenes, Carbon Nanotubes and Associated Structures[END_REF] Graphene blurs the metaphysical divide between substance and phenomena, between primary and secondary qualities.

In this technoscientific style of research, carbon is less a source of dispositions (i.e. substantial and permanent properties waiting to be actualized) than a source of affordances, i.e. relational and functional properties that can only be performed and instantiated by the combination of material dispositions and intentional contrivance. [START_REF] Harré | The Materiality of Instruments in a Metaphysics for Experiments[END_REF] Indeed, graphene makes it possible to direct or confine electrons and photons; to change the polarity of a spin; to accelerate processes; to encapsulate molecules; to provide experimental systems for quantum field theory or 2D physics; to save information bits, or to make sensors with the help of grafted molecules-probes. In brief, graphene affords an entire playground, displayed in the thousands of papers and patents relating to graphene that appeared in 2010.

Graphene is less the surface of something, than a 'surface in itself', made of nothing else, a surface without bulk. Unlike carbon as substance, carbon as a pure surface does not stand as a permanent substratum securing an ontological identity at a deeper level of reality. Rather, it signs a new script of technoscientific research where superficiality matters.

Carbon as Memory / Carbon as Fire

'Burning buried sunshine', [START_REF] Dukes | Burning Buried Sunshine: Human Consumption of Ancient Solar Energy[END_REF] this sounds like a crazy project. It is no more a playful construction game with thin carbon sheets, but rather a mass destruction of deeply buried underground carbonaceous materials. The fate of fossil hydrocarbons exemplifies another of the interactions between the material properties of carbon and human history and politics. The layers of biomass accumulated over millions of years as sediments of hydrocarbons are like a repository of the past. They make up the material memory of life on Earth. By massively resorting to the energy of this 'buried sunshine', humans are consuming this memory at a rate of a few centuries per year. According to Alain Gras, the 'choice of fire' is the signature of our civilization, with its 'cowboy economy' and massive exploitation of fossil fuels. [START_REF] Gras | Le choix du feu : Aux origines de la crise climatique[END_REF] The peculiar set of relations that have been set up and reconfigured between the material properties of carbon, international finance, expertise and democracy is well described in Timothy Mitchell's essay Carbon Democracy. Coal played a critical role in forging democracy by encouraging social movements while oil has shaped and continues to shape the politics of Western and Middle East countries. [START_REF] Mitchell | Carbon Democracy. Political Power in the Age of Oil[END_REF] Carbon's etymology, however, suggests that its association with fire is not limited to this contingent history. Fire drove the ontogenesis of carbon as a chemical element since it has been identified through the combustion of diamond in the experiments conducted by Lavoisier, Macquer and Guyton de Morveau in Paris and by Tennant in London. [START_REF] Lavoisier | Sur la destruction du diamant par le feu[END_REF] These experiments demonstrated that burning a certain amount of diamond and burning an equivalent mass of charcoal released the same volume of 'fixed air' (carbon dioxide). Moreover, the association between carbon and fire does not necessarily mean irreversible consumption. Nineteenth-century chemists investigating the circulation of carbon through the three realms of nature -mineral, plant and animal -described animals as combustion engines releasing carbon dioxide into the atmosphere, while plants 'fix' the carbon and release oxygen. Living beings do not 'burn' calories as an internal combustion engine burns gasoline. Instead, they convert calories into 'soft energy' (known today as adenosine triphosphate) and then reuse much of the waste. Ashes can be used as a fertilizer and can participate in cosmic cycles. Jean-Baptiste Dumas's 'chemical statics of organized beings' is reminiscent of carbon exhalations as Mephitis, dispensing Life and Death. [START_REF] Dumas | Essai de statique chimique des êtres organisés[END_REF] Such 'archaic' symbols of carbon survive in today climate science and policy.

Carbon as Equivalent

In their efforts to mitigate the climate disruptions induced by the use of carbon-fire, humans have once again selected carbon as a standard. Carbon provides the 'rate of exchange' of all greenhouse gases (GhGs) according to their global warming potential (GWP), 38 just as gold or the US dollar did for currencies. And carbon dioxide, the historical archetype of all gas, became 'carbon dioxide equivalence' (CO 2 eq), the reference for devising 'green' markets and environmental finance devices. While carbon trading is meant to get the economy back down to earth, it actually turns carbon into a speculative product and renders carbon exchanges soluble into those of our current dematerialized capitalism. All that is solid… As all equivalents, carbon affords commensurability. It allows quantitative comparison between various gases39 and between heterogeneous human actions (How much carbon equivalent does your wedding party weigh? What is the carbon footprint of your alimentary diet?) Carbon globalizes the ecosystem at the planetary scale. Such system of equivalence allows considering the global ecosystem and the global economy like two oikoï exchanging carbon. Carbon thus bridges natural processes and human enterprises. It even allows equating present and future GhGs emissions or reductions. For instance planting trees, replacing a fuel generator by a wind turbine are supposed to compensate for global CO 2 emissions. A certain amount of GhGs emitted in one part of the world is thought to balance an equal reduction in another part of the world, etc. [START_REF] Fragnière | La compensation carbone : illusion ou solution ?[END_REF] Carbon markets are based on such equations. [START_REF] Mackenzie | Making things the same: Gases, emission rights and the politics of carbon markets[END_REF] The commensuration achieved by the carbon-equivalent is turned into a mechanism of compensation, which has been compared to the system of indulgences, the 'market of pardon' once established by the Catholic Church. [START_REF] Adam | You feel better, but is your carbon offset just hot air?[END_REF] An activity emitting excess gases today is declared 'carbon neutral' on the assumption that the excess will be 'neutralized' when the trees have matured in the future. This alleged neutrality depends not only on conjectures about the future but also on counter-factual estimations of the increase of emissions if the project had not been achieved. [START_REF] Schneider | Is the CDM fulfilling its environmental and sustainable development objectives? An evaluation of the CDM and options for improvement[END_REF] Buzzwords such as 'carbon neutrality', 'decarbonizing industry' or 'zero-carbon planet' make of carbon the 'bad guy'. This demonization of carbon revives the ancient identification of carbon dioxide with malefic power.

Carbon trading schemes wrongly put the blame on carbon itself. The problem is not that there is too much carbon (though there is, of course, too much CO 2 in the atmospheric air). In fact, the system of compensation nurtures the social construction of ignorance. [START_REF] Lohmann | Carbon Trading, Climate Justice and the Production of Ignorance: Ten examples[END_REF] It provides means for endlessly postponing effective measures aimed at reducing emissions. By dissociating actions from their consequences, it tends to dissolve the urgent issue of climate change into counterfactual and abstract speculation. It also serves to disconnect the present from the future by persuading people that they can be 'carbon neutral' and consequently not indebted to future generations, instead of considering how human activities have disrupted the carbon cycle over million of years as described by paleo-climate scientists.

The problem is rather that our consumption of hydrocarbons is interrupting the carbon chain, 'freezing' the carbon cycle. By consuming centuries of 'buried sunshine' per year, we create a chasm between the historical time of human activities and the geological and biological timescales. While carbon trading claims to bridge the gap between the linear timeline of economic growth and the cyclic times of carbon exchanges, it actually increases the gulf between these heterogeneous 'timescapes', 45 and neglects the work of composition that these multiple (and not necessary harmonious) temporalities require. The alledged 'bad guy' that would have to be 'neutralized' or 'sequestered' should rather be rescued, because life depends on it. After all, carbon is life -not life in its 'essence', but life it its diversity, profusion and interdependence.

Toward an Ontography of Carbon

Carbon signs the rich narrative of a persona always on the move, always binding with itself as well as with others. Endlessly metabolized, exchanged, fixed and released, it forms as many heteronyms as there are ways for carbon to be an object. In surveying the multiple identities of carbon and treating them as heteronyms -real signatures of fictitious personae -this essay sought to highlight three major features of technoscientific objects.

First, the unbounded productivity of technoscientific objects may be due to their multiple identities. Carbon is much more than a scientific object. Without questioning the central importance of the definition of carbon as a chemical element, we argued that it is only one of the many ways for carbon to sign its name (as a permanent substrate underlying various phenomenological appearances). The hierarchy of levels of reality suggested in this metaphysical perspective, even when it is 'metachemically' refined in order to guarantee the notion of chemical individuality, results from the reductive entrenchment of many modes of existence into a single one. On the contrary, our approach was to spread and to maintain the constellation of carbon's modes of existence while resisting the 'imperialist' temptation to deduce their plurality from one of them.

Is it possible to characterize the scientific approach by the question 'what is carbon?' and distinguish it from a technoscientific approach interested in the question 'what does it do?' This is a false dilemma because both questions overlook the coexistence of multiple modes of being. Neither a substantialist nor an operational definition could take into account the varieties of carbon identities revealed through the circulation of carbon atoms over the centuries. The Janus portrait is only a caricature, which occults multiple personalities. Despite the broad diffusion of scientific names such as 'carbon' and 'CO 2 ', the purification attempted by means of the reform of chemical nomenclature never succeeded in eradicating the intimate relationship we have with carbon in our vital, technical and symbolic activities. Just as carbon forms many allotropes by binding with itself in specific and different ways, each of its modes of being is able to link up with the others via analogies, metonymies, metaphors, and anaphors. For instance, carbon as a general equivalent in its economical mode plays a role analogous to the role of the mole in its chemical mode of existence, as a standard of commensuration.

Who is carbon, then? Here comes the second feature of this technoscientific object. To use the term Pessoa coined for referring to himself, the scientific name 'carbon' can be considered as the 'orthonym' of a multiplicity of heteronyms, which suggests a proper position, a degree of social 'correctness', but nothing like a deeper ontological level. But the orthonym carbon is neither object nor subject, it is a 'quasi-object' in the sense of Michel Serres. 46 Quasi-objects have no fixed essence; they are defined by the links and connections they create by circulating in local contexts. They build niches and make collectives. A striking feature of quasi-objects is that they continuously cross the boundaries between nature and culture and between the natural and the artificial. The narratives of carbon belong to natural history as well as to human history. Some of its modes of existence have been characterized as mediators, bridging the heterogeneous realms of the inorganic and the organic, of the natural and the synthetic, of ecology and economy. Through exchanges, combinations, uses and re-uses by humans and nonhumans, carbon challenges the hierarchy of ontological levels by creating a sort of bio-pedo-geo-hydro-atmo-cosmo-sphere. Besides carbon is a mediator establishing a common measure between heterogeneous regions of the world. Just as the balance in the hands of Lavoisier,47 carbon affords commensurability between the smallest and the largest scales, between the mineral, the vegetal and the animal, between the moral and the social, between the economic and the ecological. As a powerful mediating apparatus, carbon also encourages ambitious attempts at controlling the world. The balance of gains and losses, based on static equilibrium, generates a space of illusory rational control and power over the future, instantiated in carbon trading.

Finally, as carbon opens up the 'cosmopolitical' perspective of a common world shared by humans, other living beings and things, what kind of approach is the most appropriate to clarify its ontology? The narratives written by the heteronyms of carbon are at odds with the grand Promethean narrative forged by the champions of nanotechnology, synthetic biology and other ambitious technosciences. 'Shaping the world atom by atom' or re-engineering nature to improve it, are slogans that celebrate the power of human design over nature. Designers like to stress their enhanced capacity to control and shape materials thanks to their access to the molecular level. In their view, materials are no longer a prerequisite for design: fullerenes, carbon nanotubes, graphene are 'materials by design'. This phrase suggests that engineers are emancipated from all constraints of materiality. This essay, by contrast, emphasizes the affordances of materiality. As chemist Richard Smalley put it in his 1996 Nobel lecture, carbon has a 'genius wired within it':

The discovery that garnered the Nobel Prize was the realization that the carbon makes the truncated icosahedral molecule, and larger geodesic cages, all by itself. Carbon has wired within it, as part of its birthright ever since the beginning of this universe, the genius for spontaneously assembling into fullerenes. [START_REF] Smalley | Discovering the Fullerenes[END_REF] The physical and chemical properties of carbon afford opportunities for creating new lives and powerful concepts. Whether robust like the carbon backbone of DNA or delicate like the thin layer of graphene, all heteronyms of carbon are active and reactive in the hands of smart engineers. This is why an ontography seems more appropriate than an ontology for carbon. What is the difference?

We choose ontography as a genre for emphasizing the significance of 'graphism' and graphemes, of meaningful material traces printed by objects. [START_REF] Derrida | in his deconstructivist analysis of the Western logos emphasized its domination over graphein[END_REF] Ontography offers a number of advantages. First, as Lynch argues, it is an attempt to dignify a descriptive approach based on empirical study. [START_REF] Lynch | For current use of ontography in archaeology and ethnology see M. Holbraad, 'Ontology, Ethnography, Archaeology: an Afterword on the Ontography of Things[END_REF] Ontography deflates the quest for a unique substrate underlying a variety of materials. In stark contrast to ontology, it does not build a grand theory based on a hierarchy of the entities that make up the universe. Just as the term 'ontogenesis', ontography focuses on individual entities. It is compatible with pluralism. It seeks to give a voice to a plurality of beings rather than trying to silence them.

In addition, as an attempt to identify the modes of existence of particular entities, ontography does not assume a causal chain between levels of being. Nor does it single out any level of being. It opens up the possibility for humans to engage with objects as partners, thus co-creating their affordances. This process can be denoted as the 'instauration' of new identities. [START_REF] Souriau | L'instauration philosophique[END_REF] Finally, ontography allows space for a multiplicity of ontological modes. An entity such as carbon displays many different ways of being an object according to its relations, reactions and circumstances.

In this process, objects are not just materials. We have seen that carbon has become a matter of concern and a matter of affairs. May we suggest that the pattern of relations displayed by each heteronym of carbon has to become a matter of care as well? We would well be advised to take care of its multiple modes of existence in order to better inhabit the common world that we share.

Allotropy refers to the ability of an element to form different simple bodies made up of the same atoms bounded together in multiple specific ways.

K. Marx and F. Engels, Manifesto of the Communist Party (1848).

H. Chang, Is Water H 2 0? Evidence, Realism and Pluralism (Heidelberg, London, New York: Springer, 2012).

E. Souriau, Les différents modes d'existence, 1943 (2 nd ed. Paris: Presses Universtaires de France, 2009) with a presentation by Bruno Latour and Isabelle Stengers. B. Latour, Enquête sur les modes d'existence. Une anthropologie des modernes (Paris: la découverte, 2012). Eng. tr. Cathy Porter, An Inquiry into Modes of Existence (Cambridge, MA: Harvard University Press, 2013).

Lonsdaleite, named in honour of crystallographer Kathleen Lonsdale, is a polymorph of diamond.

Virgil, Aeneid, VII, on pp. 562-71. Trans. John Dryden (New York: P.F. Collier and Son, 1909).

A. Di Lisio, F. Russo and M. Sisto, 'Un itinéraire entre géotourisme et sacralité en Irpinie (Campanie, Italie)', Physio-Géo, 4 (2010) pp. 129-49, on p. 142. Furies or Erinyes are mythical entities personifying revenge and persecution.

In 1986, a giant CO 2 bubble explosion killed all animals -including hundreds of humans -in an area of a few square kilometres around the lake Nyos, in Cameroon's volcano region. The inhabitants attributed this stealth kill to Mazuku, the God of lakes. See J. Soentgen, 'On the history and prehistory of CO 2 ', Foundations of Chemistry, 12:2 (2010) pp. 137-48.

A. Di Lisio et al. , 'Un itinéraire entre géotourisme et sacralité en Irpinie, on p. 143.

J. Soentgen, 'On the history and prehistory of CO 2 '.

S. Iijima, 'Helical microtubules of graphitic carbon', Nature, 354:6348 (1991) pp. 56-58.

For instance, one ton of methane weighs 23 tons of CO 2 eq or 6.27 Carbon equivalent. To convert CO 2 eq into Carbon equivalent, one multiplies it by the approximate mass of carbon atoms contained in one ton of CO 2 that is, 0.2727. Thus, for methane: 23 x 0.2727 = 6.2721. In this respect, the role of Carbon eq in carbon accounting is analogous to the role of the mole in chemistry.

L. Lohmann et al., Carbon Trading. A critical Conversation on Climate Change Privatization and Power (2006), at http://www.thecornerhouse.org.uk/sites/thecornerhouse.org.uk/files/carbonDDlow.pdf (accessed September 2014)

M. Serres, The Parasite. Trans. Lawrence R. Schehr (Baltimore, London: Johns Hopkins University Press, 1982).

B. Bensaude-Vincent, 'The Balance: Between chemistry and politics', The Eighteenth Century, 33:3 (1992), pp. 217-37; N. Wise, 'Mediations: Enlightenment Balancing Acts, or the technologies of rationalism', in P. Horwich (ed.), World Changes, Thomas Kuhn and the Nature of Science (Cambridge, MIT Press, 1992), pp. 207-56.


Luigi Dilillo
email: dilillold3@ecs.soton.ac.uk

Paul Rosinger

Bashir M Al-Hashimi

Patrick Girard

Minimizing Test Power in SRAM through Reduction of Pre-charge Activity

In this paper we analyze the test power of SRAM memories and demonstrate that the full functional precharge activity is not necessary during test mode because of the predictable addressing sequence. We exploit this observation in order to minimize power dissipation during test by eliminating the unnecessary power consumption associated with the pre-charge activity. This is achieved through a modified pre-charge control circuitry, exploiting the first degree of freedom of March tests, which allows choosing a specific addressing sequence. The efficiency of the proposed solution is validated through extensive Spice simulations.

Introduction

Reducing power dissipation during testing of complex Systems-on-Chip (SoC) has been acknowledged as a major concern. Industrial research has shown that the power dissipation during test mode can be several times larger than in normal functional mode [START_REF] Shi | How power aware test improves reliability and yield[END_REF][START_REF] Girard | Survey of Low-Power Testing of VLSI Circuits[END_REF]. We have chosen to focus our attention on memories because, as indicated by the ITRS'03 [START_REF]International Technology Roadmap for Semiconductors (ITRS)[END_REF], over 90% of SoC area in 2008 will be employed by memories. Minimizing test power in embedded memories is important since they are becoming the main contributor to the overall IC power dissipation.

Whilst numerous papers on constraining power dissipation during test exist [START_REF] Rosinger | Scan architecture with mutually exclusive scan segment activation for shift and capture power reduction[END_REF][START_REF] Larsson | Efficient test solutions for core-based designs[END_REF], there appear to be only few publications that address reducing test power in memories. In [START_REF] Bhattacharjee | LPRAM: A Novel Low-Power RAM Design with Testability[END_REF] and [START_REF] Ohler | Low power embedded DRAMs with high quality error correcting capabilities[END_REF], the authors outline techniques that mainly reduce power during functional mode and they indicate how their technique can be employed during test or error correction. In this paper, we propose a new method that minimizes the test power in SRAM memories, by exploiting the predictability of the addressing sequence. It is known that [START_REF] Liu | Power Consumption Estimation in CMOS VLSI Chips[END_REF][START_REF] Nirshl | High Speed, Low Power Design Rules for SRAM Pre-charge and Self-Tming under Technology Variation[END_REF] the pre-charge circuits are the principal contributor to power dissipation in SRAM.

These circuits have the role of pre-charging and equalizing the long and high capacitive bit lines. This action is essential to ensure correct memory operation. In this work we have developed a technique that reduces the pre-charge activity during test. This technique is based on the fact that in functional mode the cells are selected in random sequence, and therefore all pre-charge circuits need to be always active, while during the test mode the access sequence is known, and consequently, only the columns that are to be selected need to be pre-charged. We implemented this low power test mode by using a modified pre-charge control circuitry.

The rest of the paper is organized as follows. In Section 2, we describe the SRAM pre-charge operation in functional mode. In Section 3, we present the new method that allows reducing the pre-charge activity during test mode, and its implementation in Section 4. Experimental validation of the proposed low power technique for SRAM is presented in Section 5. Conclusions and future work directions are given in Section 6.

Background: SRAM functional mode

In random access memories during functional mode, the addressing sequence is unpredictable. Consequently, all bit lines need to be pre-charged (to VDD) in order to have all the array columns ready for a new operation. When a cell is selected for a read/write operation, the corresponding pre-charge circuit is normally turned off during the time required for the operation. For the columns that are not involved in the operation, the precharge circuit is commonly left ON and the corresponding cells undergo a stress called RES (Read Equivalent Stress), as it has been demonstrated in [START_REF] Dilillo | Efficient March Test Procedure for Dynamic Read Destructive Faults detection in SRAM Memories[END_REF]. For example, in an 8kx32 SRAM, organized as an array of 512 rows x 512 column, when a read/write operation is performed on a cell, the other 511 cells of the same row undergo RESs. This is illustrated in Figure 1. When the cell C i,0 is selected for a read/write operation, the word line selection signal WL i is activated and all the cells of the i th row are selected, and thus connected with their bit lines.

Figure 1 -Functional mode of an SRAM array

The actual operation is performed on cell C i,0 , while all the other cells in the row undergo RESs. With the precharge circuits (Pr j ) active and the word line command being high on the unselected columns, the cells fight against the pre-charge circuits, that pull-up the voltage level at VDD. In Figure 2, we show the operational diagrams of a pre-charge circuit of a selected and an unselected column. In the following, we will identify the two main sources of power consumption in the unselected columns related to the pre-charge activity. Firstly, the cells in the unselected columns consume power due to the RES. Secondly, there is power dissipation in the pre-charge circuits of these columns because they are always ON. In the normal operation mode of a random access memory, this pre-charge activity is essential and the RES is tolerated, because at the end of each operation all the columns of the array, including the current selected column, need to be ready for the next operation, whose location is unpredictable.

During the memory test mode, however, the addressing order to access the cells (and the columns) is known. Consequently the power dissipation due to pre-charge and RESs could be significantly reduced by pre-charging only the necessary columns as it will be shown in the following section.

Reducing power dissipation during test

Memories are mainly tested with fault-oriented algorithms, such as March tests [START_REF] Van De Goor | Testing Semiconductor Memories: Theory and Practice[END_REF]. All March tests are characterized by six Degrees Of Freedom (DOF) and the first one states: any arbitrary address sequence can be defined as an ⇑ sequence, as long as all addresses occur exactly once (⇓ is the reverse of ⇑). The fault detection properties are independent of the utilized address sequence [START_REF] Niggemeyer | Integration of Non-classical Faults in Standard March Tests[END_REF][START_REF] Nicolaidis | An Efficient Built-In Self-Test Scheme for Functional Test of Embedded Memories[END_REF]. This means that we can choose the addressing sequence of a March test without changing its capability to cover the target faults, for most March algorithms. We exploit this property of March tests in order to minimize power dissipation during test by eliminating the unnecessary precharge activity.

For this purpose, we choose the addressing sequence 'word line after word line'. For example, consider an SRAM organized as an array of n rows x m columns. The read and write operations of each March element need be operated first on all the m cells of the first word line, then on the m cells of the second word line, and so on, as shown in Figure 3. With this particular addressing sequence, when one March element is operated on a certain cell, and thus in a certain column of the array, the following cell to be selected is placed in the column that immediately follows. This means that the pre-charge action is required only in two columns of the entire memory array:

-In the selected column, because the bit line restoration is needed for each following operation of the current March element. -In the column that immediately follows, because the next cell to be accessed is placed there. Considering the scenario of a 512x512 SRAM array configuration, we have:

-In the selected column: pre-charge is OFF during the first half of the cycle. Pre-charge is ON during the second half of the clock cycle, see Figure 2a and2b. -In next column to be selected, the pre-charge is ON during the entire clock cycle, see Figure 2c and2d.

-In all the other 510 columns the pre-charge circuit can be turned OFF, because the cells of these columns are not involved in the immediately following operation. This leads to a significant saving in cell array power consumption, as it will be shown in the experimental section. Figure 4 shows the previously described scenario when in the memory array column '0' is selected. For the 510 columns where the pre-charge circuit is inactive, the cells are still selected by the common word line selection signal. This implies that these cells are still interacting with their corresponding bit lines. These bit lines behave like floating capacitors, which are not driven any longer by the pre-charge circuits, but by the cells. We have studied this interaction with Spice simulations using the following parameters: technology: 0.13µm; clock cycle: 3ns; voltage supply: 1.6 V. The scheme used in the simulation is depicted in Figure 5, while the results are shown in Figure 6.

Figure 5 -Scheme of interaction between unselected cells and bit lines

The scheme in Figure 5 shows two cells C i, j and C i+1, j placed in the same column. Cell C i, j stores '1' (node S at '0'and node SB at '1') and C i+1, j stores the opposite value '0' (node S at '1'and node SB at '0'). In the first part of simulation, cell C i j is selected (WL i at VDD) and interacts with the bit lines. After a certain delay, cell C i, j is deselected (WL i at '0'), and cell C i+1, j selected (WL i+1 at VDD).

Figure 6 -Spice simulations of the interaction between unselected cells and bit lines

The waveforms in Figure 6a and 6b show that the contact between node SB of cell C i,j and bit line BLB has no effect on the voltage levels of BLB and node SB, because both of them are at VDD. On the other hand, the contact between cell node S active at '0' and bit line BL floating at VDD produces the progressive discharge of BL to 0V (logic value '0') in nearly nine clock cycles. This implies that, after a short time, in all the unselected columns, the cells are not stressed anymore by the bit lines. The consequence is that in the unselected cells there is no more power consumption associated with RES, as shown in Figure 6b. The transition from the current array row i to i+1 may lead to a problem as shown in Figure 7. Cell C i, j , storing a '0', has driven its bit lines BL and BLB respectively at '0' and '1'. In the transition from the i th row to the (i+1) th row, these same bit lines are connected to cell C i+1, j that stores an opposite value ('1'). This event causes the faulty swap of cell C i+1, j . This is because the bit lines drive the value of the cell C i+1, j , since their equivalent capacitances are much larger than the cell nodes capacitances. The occurrence of this faulty swap is shown in Figure 6c. The solution that we propose for this problem is: in the last operation on the last cell on the current row, the bit line level of all columns is restored at VDD by activating their pre-charge circuits for only this clock cycle (Figure 7). The advantage of this solution is that it preserves the data background independency, which means that any value can be stored in the cells.

Pre-charge control modification

According to the proposed low power test technique the SRAM memory can operate in two different modes: a functional mode in which the memory acts normally and a low power test mode in which the addressing sequence is fixed to 'word line after word line' and the pre-charge activity is restricted to two columns for each clock cycle: the selected column and the following one. During the last operation on the last cell of each row, the memory returns to functional mode for only one clock cycle, in order to restore voltage level of all the bit line at VDD, for the operations in the next row. We propose a practical implementation of this method consisting in a modification of the pre-charge control circuitry, which allows switching between the functional mode and the low power test mode. In the low power test mode, the pre-charge is active for the selected column j and the following one, and for this purpose, we use as pre-charge signal (NPr j ): the column pre-charge signal (Pr j ) when the column j is selected; the previous column selection signal ( 1 j CS -) when the column is not selected; the new pre-charge control logic is depicted in Figure 8. The modified pre-charge control logic contains an additional element for each column. This element consists of one multiplexer (two transmission gates and one inverter) and one NAND gate. The additional cost of the added logic is ten transistors. The signal LPtest allows the selection between the functional mode and low power test mode. The signal Pr j is the former pre-charge signal, while j CS is the complementary of column selection signal.

The multiplexer acts the mode selection, while the NAND gate forces the functional mode for the column when it is selected for a read/write operation. When LPtest is ON, the signal j CS of a column j drives the pre-charge of the next column j+1. Note that the pre-charge is active with the input signal at '0'. The CS signal of the last column is not connected to the first column pre-charge control, because it is not necessary. As stated above, for the transition from a row to the next one, the functional mode is restored for one clock cycle, making the first column ready to be accessed for a read/write operation, and avoiding faulty cell swaps in the other columns.

We have studied the effect of the modified pre-charge logic and we have found that it has negligible impact in terms of performance during normal operation. The switching between the functional mode and the low power test mode is achieved by a multiplexer implemented by two transmission gates (Figure 8). When the functional mode is selected the transmission gate on the right in Figure 8 allows signal Pr j to drive the pre-charge circuit. We have chosen the transmission gate (two transistors), instead of a single pass transistor, to ensure the minimum delay in the transitions (0→1 and 1→0) of the Pr j signal during the normal functional mode, as well as CS j-1 signal during low power test mode.

The proposed method assumes 'word line after word line' addressing sequence. It should be noted that for algorithms that require different addressing sequence or rely on normal operation power consumption [10, 12, 14 and 15], the normal function mode can be selected.

Experimental results

In this section, we first analyze the sources of power consumption in the traditional and proposed test scenario. Next, based on this analysis we show how the power dissipation of the two scenarios is computed. Finally, we present and discuss the experimental results. Our analysis shows hat there are five main sources of power dissipation during test:

1.

Pre-charge circuits. Apart from the selected column, (n-1) pre-charge circuits are ON in functional mode, while only one pre-charge circuit is ON in low power test mode.

2. Array row transition. The activation of the normal mode, for one clock cycle at the row transition, involves significant power dissipation, due to the restoration at VDD voltage level for about 50% of all the bit lines in the array. This is because half of the bit lines have been driven to '0' by the indirect selected cells, with few of them not completely discharged, as shown in Figure 6a. Note that, even though this event involves significant power dissipation, its impact on the average power per clock cycle is reduced because of its unfrequent occurrence. This line is charged and discharged only once for each row transition, thus its frequency is very low: F(Row transition) =1/(#March element operations)* *(#memory columns)

Considering a one operation March element and n=512, the signal there is a row transition once for each 512 (=512*1) clock cycles. For a four operations element it happens once every 2048 (=512*4) clock cycles. For its low occurrence the average power increment per clock cycle can be neglected.

3.

Driver of signal LPtest. The line that carries this signal has the same equivalent capacitance of a word line, because it has the same length and it drives the same number of MOS transistors. This line is charged and discharged only once for each row transition, thus its frequency is very low (see point 2) and therefore its contribution to the average power per clock cycle that it brings can be neglected.

4.

Read Equivalent Stress consumption. The (n-1) cells undergo RESs in functional mode, while, in low power test mode, only one cell undergoes a full RES. This cell is the one placed in the column immediately after the selected one. Moreover, few other cells (<10), undergo a reduced RES, as shown in Figure 6a and 6b. We identify with α (2<α<10) the average number of cell that undergo to a RES in low power test mode. We have performed Spice simulations showing that the cell power dissipation during a RES is three orders of magnitude smaller than the pre-charge power dissipation during the RES. Consequently the cell power dissipation can be neglected.

5.

Modified pre-charge control logic. The gates that used to realize this logic are designed with minimal dimensions because their output load is very low. The capacities driven by these gates are about three orders of magnitude smaller than a single bit line capacitance. Moreover, there is only one control element switching for each column changing. For these reasons, the contribution of the new control elements to the overall power dissipation can be considered negligible. Based on the previous analysis, it can be concluded that the power dissipation reduction depends on the memory array organization (#row and #col) and on the March algorithm that is being run (#elements and # operations per element). Also the number of read (#read) and write operations (#write) of the algorithm is important in the computing, because the power dissipation of a read action is lower than that of a write action. On the other hand, the power reduction per operation offered by the method is independent on the type of performed operation. The average power dissipations per clock cycle during functional mode and low power test mode (respectively P F and P LPT ) are given by: To give insight into the test power reduction, we have run a set of well-known March tests in the functional and low power test modes, on a 512x512 0.13µm SRAM. We have chosen these algorithms, because they consist of different number of elements and operations. The Spice simulation results, with the following operational parameters (3ns clock cycle and 1.6V voltage supply), are shown in Table 1. The experimental results show that this method leads to a significant reduction in terms of overall power consumption (∼50%) for the considered SRAM memory. This result can be extended to all SRAM memories because it reduces the pre-charge circuitry activity, which represents up to 70%-80% of the overall power dissipation of SRAM memories, as demonstrated in [START_REF] Liu | Power Consumption Estimation in CMOS VLSI Chips[END_REF].

Algorithm

Conclusions

In this work we have presented a method that minimizes the test power in SRAM memories by reducing the precharge activity. This was achieved by exploiting the fact that the addressing sequence during test is predictable, and hence only two columns need to be pre-charged in each clock cycle. We have implemented this low power test mode by using a modified pre-charge control logic. Spice simulations used to validate the proposed method show significant power reduction in the cell array (~50%). It has been shown that the effect of the modified pre-charge logic on the normal functional mode is negligible.

In this study we have considered only bit-oriented memories. We are currently extending the method to word-oriented memories. Also, we will consider the capability of the proposed method to reduce power consumption during test when applied to other types of memories.

Figure 2 -

 2 Figure 2 -Pre-charge action for a selected and an unselected column

Figure 3 -

 3 Figure 3 -Access order "word line after word line"

Figure 4 :

 4 Figure 4: Proposed pre-charge activation

Figure 7 -

 7 Figure 7 -Preserving faulty cell swap during row transition

Figure 8 -

 8 Figure 8 -The modified pre-charge control logic

  Power consumption of one pre-charge circuit during a RES; P B : Power consumption of a column restoration during the row transition; P r : Memory power consumption during a read operation; P w : Memory power consumption during a write operation.We define the Power Reduction Ratio (PRR) as

Table 1 -PRR for different March algorithms

 1

		# elm	# oper	# read	# write	PRR
	March C-	6	10	5	5	47.3 %
	March SS	6	22	13	9	50.0 %
	Mats+	3	5	2	3	48.1 %
	March SR	6	14	8	6	49.5 %
	March G	7	23	10	13	50.5 %

Acknowledgements

L. Dilillo, P. Rosinger and B. M. Al-Hashimi acknowledge the Engineering and Physical Sciences Research Council (EPSRC) for funding this work under grant no. GR/S05557.