Luke A Beardslee

Fabien Josse

Stephen M Heinrich

Isabelle Dufour

Oliver Brand

Geometrical considerations for the design of liquid-phase biochemical sensors using a cantilever's fundamental in-plane mode

The influence of the beam geometry on the quality factor and resonance frequency of resonant silicon cantilever beams vibrating in their fundamental in-plane flexural mode in water has been investigated. Compared to cantilevers vibrating in their first out-of-plane flexural mode, utilizing the in-plane mode results in reduced damping and reduced mass loading by the surrounding fluid. Quality factors as high as 86 have been measured in water for cantilevers with a 20 µm thick silicon layer. Based on the experimental data, design guidelines are established for beam dimensions that ensure maximal Q-factors and minimal mass loading by the surrounding fluid, thus improving the limit-of-detection of mass-sensitive biochemical sensors. Elementary theory is also presented to help explain the observed trends. Additional discussion focuses on the tradeoffs that exist in designing liquid-phase biochemical sensors using in-plane cantilevers.

Introduction

Need For Microcantilever Sensors Quantification of liquid-phase analytes is essential in biomedical and environmental sample analysis. Example applications include, but are not limited to: (1) detection of harmful water contaminants, (2) point-of-care quantification of serum proteins, (3) chemical process monitoring, and (4) studying interactions among molecules. These four examples all require that quantitative results be obtained, preferably in real time, or with short measurement times. For the most part, these analyses are currently performed by automated analytical instruments such as mass spectrometers and UV spectrophotometers. These instruments are expensive and complicated to operate, and thus are not suited to point-of-sampling use such as at a patient's bedside or for on-site monitoring of pollutants.

Microsensors have the potential to solve many of the challenges associated with the current measurement technologies, especially when quantitative measurement of a targeted set of analytes is required on-site (e.g., point-of-care applications or in-situ environmental monitoring). Specifically, CMOS (Complimentary Metal Oxide Semiconductor) -compatible MEMS resonators are an attractive solution for several reasons. First, they can readily be batch manufactured and fabricated using the same tooling as integrated circuits; this leads to reductions in cost-per-unit and also allows system-on-a-chip or system-on-a-package solutions which have a small footprint [START_REF] Brand | Microsensor Integration Intro Systems-on-Chip[END_REF]. Moreover, resonators can produce a semi-digital output, which can be tracked with a digital counter, thus greatly simplifying system integration. Continuous operation of MEMS resonators in liquid is possible, and can be achieved using an approach that can be ported to a hand-held system. In addition, MEMS resonators are easily integrated with an applicationspecific driving/read-out circuit that can be incorporated into a system-on-a-package solution.

Because of these advantages, micromachined mass-sensitive resonant cantilevers have attracted considerable research interest. However, few studies actually operate cantilevers in liquid and continuously track the resonator's frequency. Two reasons for this are: (1) viscous damping can severely limit the resolution of cantilevers operated in liquid, and (2) when operated in the traditionally utilized fundamental out-of-plane flexural mode, there is a significant amount of mass-loading by the surrounding liquid as evidenced by the frequency shift when the devices are immersed in liquid. This leads to a higher starting mass and thus lower mass sensitivity [START_REF] Vancura | Liquid-phase chemical and biological detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems[END_REF][START_REF] Waggoner | Micro-and nanomechanical sensors for environmental, chemical, and biological detection[END_REF]. In this work, cantilevers utilizing the fundamental in-plane flexural mode are characterized in liquid and the quality factor and frequency shift due to fluid loading are measured. The experimental data are then combined with FEM (finite element method) simulations of the chemical sensor sensitivity to determine the optimal sensor geometry (of the tested devices) for creating gravimetric liquid-phase sensors.

Previous Cantilever Characterization and Sensor Work

In sensing applications in which cantilever dynamic-mode operation is used, the short-term frequency stability limits the sensor resolution. The frequency stability is correlated with the quality factor, Q, of the resonance mode. For this reason, several recent studies have measured and modeled the Q-factors of cantilevers vibrating in out-of-plane bending modes in air [START_REF] Naeli | Dimensional Considerations in Achieving Large Quality Factors for Resonant Silicon Cantilevers in Air[END_REF][START_REF] Lu | Mechanical Quality Factor of Cantilevers for Mass Sensing Applications[END_REF][START_REF] Chandorkar | Multimode Thermoelastic Dissapation[END_REF][START_REF] Cox | Generalized Model of Resonant Polymer-Coated Microcantilevers in Viscous Liquid Medium[END_REF][START_REF] Lochon | A microcantilever chemical sensors optimization by taking into account losses[END_REF]. While Q-factors up to 1,500 have been measured for the first out-of-plane bending mode in air [START_REF] Naeli | Dimensional Considerations in Achieving Large Quality Factors for Resonant Silicon Cantilevers in Air[END_REF], liquid operation becomes challenging because of the substantial viscous damping by the fluid. Besides low Q-factors, typically not exceeding 10-20 in water [START_REF] Vancura | Liquid-phase chemical and biological detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems[END_REF], a substantial reduction of the out-of-plane resonance frequency (typically in the range of 30-50%) is observed in liquid due to the large effective mass of the fluid. In addition, cantilevers that push against the fluid are more sensitive to viscosity and density changes in the liquid itself [START_REF] Vancura | Liquid-phase chemical and biological detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems[END_REF], which can be detrimental in identifying frequency shifts due to the sorption of analyte molecules from the liquid.

Few systematic studies of cantilever-based sensors operated in the liquid-phase exist, mostly because the surrounding fluid severely damps the cantilever response, thus limiting sensor resolution. Often the chosen sensing strategy is to measure a baseline sensor output in air (i.e., resonant frequency, piezoresistor resistance, etc.), expose the sensor surface to liquid-phase analytes, which are sorbed by a sensitive layer on the device's surface, and then dry the sensor and re-measure its characteristics in air [START_REF] Li | Integrated MEMS/NEMS Resonant Cantilevers for Ultrasensitive Biological Detection[END_REF]. This strategy can be problematic in practical applications because a washing step is required which necessitates additional reagents. Additionally, particles can contaminate the device surface during the drying step. Furthermore, the measurement process, including device drying, is generally not appropriate for real-time or in-situ measurements. Despite these challenges this strategy has been used to achieve ng/ml limits of detection for cancer biomarkers in liquid [START_REF] Liu | Nanogram per milliliter-level immunologic detection of alpha-fetoprotein with integrated rotating-resonance microcantielvers for early-stage diagnosis of hetocellular carcinoma[END_REF].

Optical detection of resonance modes has been employed to allow for continuous tracking of a cantilever's resonant frequency during liquid-phase operation [START_REF] Ricciardi | Integration of microfluidic and cantilever technology for biosensing applications in liquid environment[END_REF]. Generally, optical strategies require off-chip components that are incompatible with integrated systems. However, very recently, cantilever resonators with integrated optical detection components have been used to demonstrate ng/ml-range limits of detection for hepatitis virus in solution [START_REF] Urey | MEMS Biosensor for Parallel and Highly Sensitive and Specific Detection of Hepatitis[END_REF]. For continuous resonator operation in liquid using a fully integrated excitation and read-out strategy, Vancura et al. investigated cantilevers operated in their first out-of-plane flexural mode as resonant chemical sensors [START_REF] Vancura | Liquid-phase chemical and biological detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems[END_REF]. These devices are CMOS-compatible and use a magnetic excitation mechanism and piezoresistive detection scheme to achieve limits of detection in the parts-per-million (ppm) range for volatile organic compounds in water [START_REF] Vancura | Liquid-phase chemical and biological detection using fully integrated magnetically actuated complementary metal oxide semiconductor resonant cantilever sensor systems[END_REF]. Microdisk resonators supported by a clampedclamped beam and utilizing thermal actuation and piezoresistive detection are a second example of a CMOS-compatible strategy that has been used to make liquid-phase sensors [START_REF] Seo | High Q-factor in-plane mode resonant mircrosensor platform for gaseous/liquid environment[END_REF]. Toa et al. investigated a novel clamped-free cantilever structure for liquid-phase biosensors, with reported quality factors in the range of 14 in water [START_REF] Toa | Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids[END_REF]. The authors of [START_REF] Toa | Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids[END_REF] also claim a Q-factor of 249 in water (for an identical device) using a closed-loop measurement setup. However, to fairly compare the reported data, only open-loop characteristics should be considered. Direct resonator operation in liquid has also been demonstrated for sensors detecting heavy metals, whereby the metal ions are plated onto a mass-sensitive resonator, thereby altering its mass and thus the resonance frequency [START_REF] Rahafrooz | Resonant MEMS sensors for detection of aqueous heavy metal ions with sub-ppm resolution[END_REF]. The same investigators have also demonstrated silicon resonator operation in water yielding Q-factors on the order of a few hundred [START_REF] Rahafrooz | Rotational Mode Disk Resonators for High-Q Operation in Liquid[END_REF]. Unfortunately, these high-Q devices consume large amounts of power and have a large temperature rise across their surface, which may be problematic for ligands used in biochemical sensing. A final example of resonator operation in fluid is the use of piezoresistive cantilevers for mass-sensitive detection of ethanol [START_REF] Cheney | Ethanol vapor detection in saline solution using piezoresistive microcantilevers[END_REF].

A promising alternative strategy for liquid-phase sensing using cantilevers has been presented in [START_REF] Burg | Weighing of biomolecules, single cells and nanoparticles in fluid[END_REF]. In this work, a fluid channel is routed through the interior of the cantilever itself, which allows the beam to operate in air or even vacuum with quality factors as high as 15000, and thus mitigating the damping problem in fluids. This strategy makes extremely low limits of detection possible and quantities as small as a single particle or cell have been measured using this approach. Although the embedded fluid channel resonator offers single molecule resolution, it currently requires a complex fabrication process and can only be used with relatively low fluid flow rates (on the order of 1 µl/min at 10 bar of pressure). A piezoresistive read-out scheme has recently been demonstrated for the embedded fluid channel devices [START_REF] Lee | Suspended Microchannel resonators with piezoresistive sensors[END_REF]. A similar method for Q enhancement has also been demonstrated using flexural plate resonators [START_REF] Agache | Suspended Nanochannel in MEMS Plate Resonator for Mass Sensing in Liqudi[END_REF]. Finally, cantilever quality factors during liquid operation have been improved by placing the cantilever in a flow cell where only one side of the device is immersed, thus reducing the amount of energy loss to the fluid [START_REF] Park | Novel Type of Microcantilever Biosensor Resonating at the Interface Between Liquid and Air[END_REF]. This strategy yields Q-factors in the hundreds, but ensuring that the flow pattern is maintained without wetting the cantilever may be difficult in embedded applications.

Figures of Merit

Conventionally, the limit of detection (in ppm) of a mass-sensitive chemical sensor is defined as three times the noise-equivalent analyte concentration, which itself is given by the ratio of the short-term frequency stability ∆f min (in Hz) determined e.g. via the Allan variance method and the chemical sensor sensitivity S (in Hz/ppm):

(1)

The achievable sensitivity depends on the sorption characteristics of the enrichment membrane (or ligand in the case of biosensing) coated onto the sensor surface, which is specific to a particular analyte, and on the gravimetric sensitivity of the resonant microsensor. Alternatively, the LOD might be expressed as three times the ratio of the relative frequency stability  min to the relative chemical sensor sensitivity S R :

(2)

LOD  3 f min S LOD  3  min S R  3 f min /f S/f
As described in [START_REF] Lange | Complementary metal oxide semiconductor cantilever arrays on a single chip: masssensitive detection of volatile organic compounds[END_REF], the chemical sensitivity S (or relative chemical sensitivity S R ) may be written as the product of the gravimetric sensitivity G (or the relative gravimetric sensitivity G R ) of the coated resonant sensor, i.e., the absolute or relative change in frequency f due to a change in coating density  m , and the analyte sensitivity S A , i.e., the change in coating density  m due to a change in analyte concentration c A in the surrounding medium:

A m m A c ρ ρ f S G S        , A m m A R R c ρ ρ f f 1 S G S                (3a,b)
If the analyte concentration is given in ppm (v/v), the analyte sensitivity S A may be calculated as

6 A A m A 10 K ρ c ρ S        , ( 4
)
where   is the density of the analyte absorbed into the sensitive layer, and K is the partition coefficient of the particular analyte/membrane combination, i.e., the ratio of the analyte concentration in the sensitive film to the analyte concentration in the surrounding matrix. The factor 10 -6 accounts for the fact that c A is given in ppm.

The sensor's limit of detection as defined by equation ( 1) is particularly affected by the geometrical dependence of the minimal detectable frequency change ∆f min , a quantity that is generally improved (i.e., reduced) by increasing the quality factor of the resonance. This fact provides the main motivation behind investigating in-plane rather than out-of-plane cantilever modes. In addition, as stated earlier, utilizing the in-plane mode (in comparison to the fundamental out-of-plane mode) gives much lower mass-loading due to the surrounding fluid which helps to reduce the cantilever's starting mass and thus improves the mass-sensitivity [START_REF] Waggoner | Micro-and nanomechanical sensors for environmental, chemical, and biological detection[END_REF].

Mechanical characterization of cantilevers with twenty different length and width combinations and four different thicknesses (eighty devices in total) have been performed. The equations above in combination with FEM modeling to simulate the gravimetric sensitivity allows one to estimate which cantilever would give the lowest detection limits (at least for those beams tested), if used as a liquid-phase biochemical sensor. More broadly, examination of the characterization data allows one to examine the tradeoffs that exist in the design of biochemical sensors using inplane cantilevers.

Measurement Protocol

In order to investigate the effect of beam dimensions on the resonance frequency and quality factor of cantilevers operated in their first in-plane flexural mode, thermally actuated and piezoresistively detected single-crystal silicon cantilevers (See Fig. 1) were fabricated using a bulk-micromachining process that has been previously presented [START_REF] Seo | High Q-factor in-plane mode resonant mircrosensor platform for gaseous/liquid environment[END_REF]. For protection of the aluminum metal lines during liquid testing a stack of PECVD (plasma enhanced chemical vapor deposition) oxide/nitride layers were used. (See Fig. 2 for a diagram of the beam cross section.)

The total target thickness of the PECVD passivation layers was 1.2 m. Silicon thickness measurements were done at a 90 degree angle in a Hitachi 3500 SEM. The silicon could be differen are scall

The dev the pres resonan characte that the results. trapped

lateral (in-p cy shift of th a function of s with a leng

sets of the kness of 8µm 00 µm long hat -for a g ear when p all, the exper shift when ers get wide quency incr short-term due to mass ts the senso t of the effe due to ma [START_REF] Waggoner | Micro-and nanomechanical sensors for environmental, chemical, and biological detection[END_REF] f   where ∆f is the observed frequency decrease due to the additional mass, ∆m is the (effective) added mass associated with the target substance, m is the original effective mass of the resonator, and f o is the original resonance frequency of the device (prior to mass uptake). One can see that having a lower starting mass improves (increases) the observed frequency shift due to a given mass change from the analyte that one wishes to detect. Thus, minimizing the mass loading on the beam by the surrounding fluid is important and is one of the main motivations for using inplane rather than out-of-plane flexural modes.

While the piezoresistive detection of the first out-of-plane mode is -especially in liquid-difficult using the devices studied in this work (the piezoresistors are intentionally positioned such that signals stemming from out-of-plane flexural modes are suppressed), a small peak associated with the out-of-plane mode could be observed in liquid for some of the devices. Analyzing this data showed frequency changes on the order of 30-50% for the first out-of-plane mode in water relative to their value in air. These values were confirmed through optical measurements performed with a Polytec MSA-500 Analyzer that is able to measure in-and out-of-plane vibration amplitudes: for a 400 µm long, 90 µm wide and 20 µm thick cantilever, the optically detected first out-of-plane mode shifted from 154.6 kHz (Q = 680) to 96.1 kHz (Q = 20), i.e. by 38% when going from air to water. For the same 400 µm long, 90 µm wide and 20 µm thick cantilever, the frequency of the first in-plane flexural mode decreased from 636.7 kHz to 596.0 kHz, i.e., a shift of only 7%. Among all tested cantilever dimensions, the smallest observed frequency shifts are less than 4% when immersing the cantilever from air into water (Fig. 5).

Sensor Design Tradeoffs

The quality factor and frequency change due to mass loading in liquid do not, however, give the entire picture when it comes to fabricating effective resonant sensors. As shown above (Eq. 1), the limit of detection for closed-loop operation is a function of both the short-term frequency stability (which is correlated with the resonator quality factor) and the sensor sensitivity. The chemical sensitivity is the product of the gravimetric sensitivity G and the analyte sensitivity S A , the latter depending only on the sorption characteristics of the sensitive layer (polymer or ligand). The gravimetric sensitivity G of the cantilevers has been simulated using the finite element software COMSOL (Stockholm, Sweden). Using modal analyses, the in-plane resonance frequencies of cantilevers with different dimensions coated with a 2 µm polymer layer (density of 840 kg/m 3 ) have been obtained and the gravimetric sensitivity was extracted (see Fig. 8) by changing the polymer density. It should be noted that the thermal oxide and PECVD passivation layers were not included in the simulations, nor were the effects of the surrounding fluid. The stiffness of the polymer layer was assumed to be negligible compared to that of the silicon for the simulations. (2) the temperature increase along the length of the cantilever is problematic for (bio)chemical sensing applications because high temperatures can denature proteins and lower the partition coefficients of analytes in polymers used for chemical sensing. COMSOL (Stockholm, Sweden) simulations based on the currently used 1.5 Vpp AC excitation and ±3V DC biases show a maximum temperature rise of ≈10˚C above room temperature on the cantilever surface.

Conclusions

Twenty different cantilever length and width combinations were tested in water for the purpose of determining their resonant properties using their first in-plane flexural mode and their potential for liquid-phase biochemical sensing applications utilizing this mode. For each of the length/width combinations, up to four different silicon thicknesses were tested. Using the measured characterization data and considering resonant sensor design objectives, it was determined that the shorter, wider and thinner beams give the best sensing characteristics. Of the cantilevers tested here, the ones most promising for sensing applications are those having resonant frequencies in the 700-1200 kHz range, as evidenced by their combination of high quality factor and sensitivity, while exhibiting sufficiently low stiffness so that they could be excited thermally in liquid. In terms of thickness, the 5 m and 8 m thick beams demonstrated the greatest potential for sensing; however, one must ensure that the chosen device has a sufficiently large Q for stable closed-loop operation. Theoretical and experimental results indicate that, of the cantilevers tested, 45 μm wid, 200 μm long devices with 5 μm or 8 μm thicknesses should yield the best compromise and the lowest limits of detection.

Compared to other studies of liquid-phase operation of single-crystal silicon resonators, the achieved quality factors from this work are a factor of 3-4 times higher than most of those previously published. An exception are the high Q-factors in water achieved in [START_REF] Rahafrooz | Rotational Mode Disk Resonators for High-Q Operation in Liquid[END_REF], which however come at the expense of higher power consumption and larger temperature rise along the surface. The temperature rise on the device surface would denature ligands used for biosensing making these devices problematic for biochemical sensor applications. For the cantilevers investigated here further improvements are possible, including testing other cantilever geometries that have resonant frequencies in the 700-1200 kHz range.

  Figure 1 bridge a

Figure

  Figure 8 for 200 thick po extracte the uppe i.e. 60W

Acknowledgements

The authors would like to thank the Georgia Institute of Technology Nanotechnology Research Center staff for fabrication support. This work was supported in part by the National Science Foundation under award number ECCS-0824017.


David Staedter

Nicolas Thiré

Laurent Polizzi

Y Mairesse

P Mayer

Valérie Blanchet

Femtosecond time-resolved Electronic Relaxation Dynamics in Tetrathiafulvalene

Keywords: numbers: 33.15 Vb, 33.50. Hv, 33.60 +q, 33.80 -b Keywords: Electronic relaxation, multiphoton ionization

come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

Since the discovery of the unusual electrical conductance in organic materials based on tetrathiafulvalene (TTF, C 6 S 4 H 4 ) in 1972, [START_REF] Wudl | Electrical conductivity by the bis(1,3-dithiole)-bis(1,3-dithiolium) system[END_REF] and metal TCNQ-TTF in 1973, 2 , TTF has been among the most studied heterocyclic systems. TTF and its derivatives are well known as efficient π electron-donors 3 with many uses in material chemistry. [4][5][START_REF] Fang | New TTF derivatives: several molecular logic gates based on their switchable fluorescent emissions[END_REF][START_REF] Canevet | Tetrathiafulvalene (TTF) derivatives: key building-blocks for switchable processes[END_REF][START_REF] Jia | Synthesis, physical properties and self-assembly of conjugated donor-acceptor system based on tetrathiafulvalene and functionalized with binding sites[END_REF] The conductivity of the non-aromatic 14π electron system with four discoordinated sulfur atoms has been rationalized by its small isomerization barrier (∼40 cm -1 ) from the nonplanar boat-like equilibrium structure of the neutral (C 2v symmetry) to a planar conformation in its cation (D 2h symmetry). [9][10][11] Both, the higher degree of aromaticity reached by the coupling between the electron removal and the 'boat' deformation and the metallic behavior enhancement with the intermolecular S-S contacts have been suggested to play a role in the mechanism of superconductivity. 10 One of the fundamental issues in designing molecular systems for photoinduced charge separation is to investigate the primary photophysical relaxation. Spectral studies of fullerenes functionalized by TTF derivatives have been reported in the ultraviolet range (UV), 12 as well as picosecond-resolved absorption spectra. 13,14 Both, the donor-acceptor system and the oligothiophene alone in liquid phase has been studied in femtosecond time-resolved spectroscopy. 15 For many of these photoactive compounds, formed by Van der Waals polarization interactions, 12 the Highest Occupied Molecular Orbital a) Electronic mail: blanchet@celia.u-bordeaux1.fr (HOMO) is mostly localized on the TTF moiety and the lowest unoccupied molecular orbital on the acceptor moiety. 16 The photoexcitation in the visible range triggers a fast energy transfer from TTF onto the acceptor moiety before the appearance of a charge transfer on the picosecond time-scale. 16 In the UV range it could be slightly different due to an efficient electronic relaxation within the TTF moiety alone.

The TTF absorption spectrum, shown in Figure 1, exhibits two close-lying intense peaks at around 317 and 303 nm [17][18][19][20] which are still without a clear assignment. It is within this framework, that the present pump-probe study of the TTF moiety alone is investigating dynamics initiated around 4 eV (≈310 nm) by time-resolved photoionization in the gas phase. The lowest energy transitions both in TTF and TTF + have been calculated by different techniques 21 and among others by time-dependent density functional theory (TD-DFT). [22][23][24] The photoelectron spectrum of TTF has been recorded by several groups reporting a vertical ionization energy, IP 1 = 6.7 ± 0.02 eV and a first excited cation state at IP 2 =8.58±0.02 eV. [25][26][27][28] The dissociative ion continuum that starts ∼ 10 eV has been studied recently up to 13 eV. 29 Following the IUPAC convention, the (x, y) axis defines the C 2 S 4 plane with the y-axis parallel to the central C=C double bond (long axis) in the C 2v geometry. On the contrary, in the D 2h geometry, the molecular plane is now (y, z) with the z-axis parallel to the long axis. By TD-DFT calculations converging to a C 2v boat geometry, Fabian et al. assigned the weak absorption band around 368 nm to a A 1 → B 1 transition (π → π * along x) and found only one state lying in the intense double structure (303/317 nm) corresponding to a A 1 → B 2 transition (π → π * along y). 30 The oscillator strengths calculated by this TD-DFT study at 368 nm and ≈307 nm are very similar, which goes strongly against the experimental observations in Figure 1. Andreu et al., as well by TD-DFT calculations, still in the C 2v geometry, assigned the two most intense excitations to the 1 1 B 2 state transition, described mainly by the HOMO to LUMO+5(b 2 , antibonding orbital) transition at 317 nm and a second one at 303 nm upto the 2 1 B 1 state described mainly by the HOMO to LUMO+4 (b 1 , bonding orbital) transition. 23 These calculations match the experimental oscillator strengths as well as the polarizations much better than the ones from Fabian et al. It is this notation that has been used in Figure 1. In this work, the weak absorption band around 368 nm, assigned as well to a 1 1 B 1 state, corresponds to the first π → π * transition with a HOMO(a 1 ) to the LUMO+1(b 1 ) excitation, while the HOMO to the LUMO+2(a 2 ) excitation is symmetry forbidden. 23 The TD-DFT calculation done by Pou-Armengo, still in C 2v geometry, differs from Andreu et al; in addition to the 1 1 B 2 and 2 1 B 1 states, they found a 2 1 B 2 state at 4.27 eV (290 nm) with an oscillator strength seven times larger than the two lower states. 22 Finally, these same authors did as well a multistate extension of a multiconfigurational second-order perturbation method (MS-CASPT2) calculation 21 with an active electron space that includes the 3s, 3p, and 3d orbitals and a TD-DFT calculation, 22 both in a D 2h optimized geometry. Using this symmetry is validated by the weak isomerization barrier towards the C 2v symmetry. In the most precise MS-CASPT2 calculation, they predict around 406 nm, a weak transition 1 1 A g → 1 1 B 2u polarized along the shortaxis (x in the C 2v → y in D 2h ) and around 309 nm, an intense transition polarized along the long axis (y in the C 2v → z in the D 2h ) to the 1 1 B 1u state. From both calculations, the authors consequently conclude that the double structure at ∼ 310 nm reveals a vibrational structure in the 1 1 B 1u band 21,31 and not an electronic structure. The central C-C vibrational mode is indeed around 1600 cm -132 and in good agreement with the energy splitting of 1460 cm -1 observed on the absorption spectrum between the two maxima. The 1 1 B 1u electronic excitation is defined at 86% by an singly excited configuration of a HOMO to LUMO+4(4b 2g ) transition. In this calculation, the Rydberg states have been predicted as low as 3.63 eV.

In the present experiment, by scanning the central pump wavelength between 307 and 322 nm, we aim to investigate if the induced dynamics change drastically through this intense UV band. To enhance the sensitivity, the photoionization is achieved at different probe wavelengths (267 nm, 398 nm and 800 nm). In addition the photoelectron spectra are recorded. In what follows, the multiphoton pump-probe pathway is denoted as (a + b'), where a and b' indicate the number of absorbed pump and probe photons, respectively, and the prime designates the probe. The remainder of the paper starts with a description of the experimental setup in section 2. Next, the time-resolved signals are presented as a function of each probe wavelengths in section 3. Finally, the results are discussed in section 4.

II. EXPERIMENTAL SET-UP

The pump and probe pulses are generated from a 1 kHz-1.5 mJ regenerative amplifier centered at 795 nm delivering a fundamental pulse with a Fourier limited Full-Width at Half Maximum (FWHM) of 70 fs. A 400 nm-pumped Non-collinear Optical Parametric Amplifier (NOPA) with three-steps of amplification and a double pass prisms compressor provide a 30 µJ/p pulse, tunable between 500 and 700 nm. The duration is measured by autocorrelation via a 50 µm BBO-I crystal to ≈ 80 fs. By a subsequent second harmonic generation (SHG) of the output of the NOPA or a sum frequency mixing (SFG) with the fundamental through a 200 µm BBO crystal, a tunability of the pump pulse from 370 down to 307 nm is achieved. Typically 5-7 µJ/p are produced in this UV range by mixing 50 µJ of the fundamental beam with about 15-18 µJ/p of the visible pulse. The pulse bandwidth achieved in the UV range is around 150 cm -1 ( 2 nm), which correspond to a FWHM ∼70 fs. However, no compression is used to pre-compensate the chirp introduced by the different optics seen by the UV pump pulse before the interaction region (mostly the BBO crystal, lenses and the vacuum viewport) leading to a longer pulse duration. As probe pulse, either the fundamental pulse (50 µJ/p), its second harmonic (SHG-15 µJ/p) or its third harmonic (THG-6 µJ/pulse) is used. The Fourier limited durations expected for these probe pulses from their bandwidths are around 65 fs. The pump and the probe beams are focused in the molecular beam by 250 mm and 500 mm lenses, respectively, and combined with a 7 degrees angle between them. The TTF molecules (Aldrich, 97% without further purification) are sublimed continuously at 380 K with 200 Torr of Argon and then expanded through a 250 µm nozzle at 450 K to avoid cork formation. The skimmed molecular beam intersects the focused laser beams perpendicularly, yielding ions which are then detected at the output of an off-axial 39 cm long time-of-flight velocity-map imaging (VMI) spectrometer. The VMI spectrometer was described previously. 33 In most of the experiments presented here the polarization of both laser beams are set parallel to each other and parallel to the detector used to collect the photoions or photoelectrons. The imaging detector consists of two microchannel plates (MCPs) coupled to a phosphor screen and a 12-bit CCD camera. The transient ion signals are recorded by using a gated boxcar integrator that collects the amplified output voltage from the phosphor screen coupled by a 100 pF capacitor. For each pump-probe delay, an average over 6×10 3 laser pulses are used by averaging six scans of the delay. A typical photoelectron image was obtained by accumulating around 2×10 5 laser shots and by subtracting the background images of the pump and the probe alone. The corrected images were then Abel inverted to reconstruct the 3D photoelectron distributions, and thus to extract their kinetic energy and angular distributions. The calibration of the photoelectron energy scale was performed by using photoelectron spectra obtained from Xe pumpprobe photoionization. Typically, an energy resolution of 160 meV was obtained at 2 eV kinetic energy by using a repeller plate voltage of 4 kV. Note that any energy above 2.2 eV, the maximum kinetic energy allowed by the detector size, won't be detected. The energy distribution of photoelectrons are smoothed by a adjacent averaging of four points. The cross-correlation between the pump and the THG probe is recorded through a (1'+1) photon ionization of N,N-Dimethylaniline (DMA) resonant at 265 nm with a low 3s Rydberg state with a long lifetime. 34,35 The difference between the ionization potential and the onset of the band is indeed around 2.8 eV, a gap easily exceeded by the frequency-mixing generated pulse. This ion transient allows to determine precisely the time-overlap between the pump and probe pulses. The cross-correlation time TABLE I. The cutoff energies of the photoelectrons at E ph = (λpump=317 nm+n'), or p or p' excitation scheme based on vertical ionization potentials IP1 = 6.7 eV and IP2 = 8.58 eV. In pump-probe, due to harmonicity relationship between the different probe wavelengths, the configuration encountered at 800 nm will be a combination of the 398 nm and 267 nm ones. Note that the maximum kinetic energy detectable is 2.2 eV. extracted by fitting the step function of the DMA cation is 320 ± 20 fs as shown in Figure 2. This reveals the strong positive chirp expected for both UV pulses. The cross-correlation time between the pump and the SHG is deduced from the TTF signal itself, as discussed further, while the ones between the pump and the fundamental as probe pulse is measured through the TTF + 2 signal. Typical cross-correlation times for these two last excitation schemes are slightly reduced to around 300 fs.

λ probe [nm] Excitation E ph -IP1 [eV] E ph -IP2 [eV] 267 ( 1+1

III. RESULTS

In the present experiment, we investigate the excitation region spanning from 322 to 307 nm, in order to reveal a possible change of the electronic character via a variation of the measured decay time or the ionization probability while going through the double absorption feature. The data will be presented by separating them according to the probe pulse wavelength used (267, 398 and 800 nm). The transient ion signals recorded at each wavelength combination are fitted by assuming a resonant decay component Ψ d (t) and a non-resonant contribution inherent to this type of experiment Ψ cc (t), corresponding to a cross-correlation signal:

S ion (t) = y 0 + Ψ cc (t) + Ψ d (t) (1)
where y 0 is a background signal. Ψ cc (t) and Ψ d (t) are given by

Ψ cc (t) = b × e -4ln2 τ 2 τ 2 cc Ψ d (t) = c × e -τ τ d × [1 + erf (φ (τ, τ d ))]
where the component in the error function is expressed by:

φ (τ, τ d ) = 2 √ ln2 τ cc × τ - τ 2 cc
This allows the extraction of the decay times τ d summarized in Table III, based on the determination of the cross-correlation time τ cc and the time overlap τ = 0. As expected from the electron donor propriety of this compound, the two first vertical ionization thresholds lie quite low at IP 1 = 6.7 ± 0.02 eV and IP 2 = 8.58 ± 0.02 eV. 28 Within the Koopman's approximation, they correspond mainly to the departure of an electron from the HOMO with a symmetry b 3u and the next channel HOMO-1 with a symmetry b 2g . The seven singlet excited states calculated below 4 eV can all be described at more than 80% by singly electronic excitations. 22 All of them are single electron transitions from the HOMO to higher orbitals, except the 1 1 B 2g optically forbidden state with a principal configuration made of 53% electron removal from the HOMO and 22% from the HOMO-1. This means that photoionization is expected to take place mostly onto the ground state of the cation. Only the 1 1 B 2g state due to its 22% HOMO-1 contribution and the Rydberg states due to their peculiar strong propensity for ∆v = 0 ionization, are expected to be set apart from the other contributions in the kinetic energy distribution of the photoelectrons. 33,36 The excitation schemes for all used wavelength combinations are summarized in Figure 1. One THG photon (267 nm) is enough to probe the wave packet dynamics onto the ground state of the ion or at the threshold of the first excited state of the cation. On the contrary, when photoionization takes place with a SHG probe (398 nm), only the ground state of the cation is reached at one photon. With a 800 nm probe pulse, multiphoton ionization is required to reach any ion continuum. The onset of a higher density of cation states is ∼ 9.5 eV. 28 Table I summarizes the maximum kinetic energies expected for the photoelectrons via these different ionization schemes.

In the following, we will discuss the experimental results, starting with the easiest probe photoionization, namely at one photon (THG probe) and finishing with the most delicate one which is the multiphoton ionization at the fundamental 800 nm probe pulse.

A. A probe pulse centered at 267 nm Figure 2a displays the pump-probe signals of the parent TTF + cations recorded at different pump wavelengths. At a 1 + 1 total energy of ∼ 8.6 eV, the mass spectra is a single peak of the parent cation. There is no signal at negative delay, even if the 267 nm probe pulse is on the blue wing of the 4 eV resonance. Underneath, in Figure 2b, the typical transient of DMA + signal, through which the time overlap τ = 0 and the cross correlation time τ cc are determined, and and a C 6 S 4 H + 4 transient are shown. The main result from these C 6 S 4 H + 4 transient study is the invariance of the decay time as a function of the pump wavelength with a typical time constant of 437 ± 7 fs. This invariance could suggest that only one electronic state defines the absorption band around 4 eV, in contrast to the calculations from Andreu et al. 23 but in agreement with the ones done by Pou-Armengo et al. using the D 2h geometry. 21 The 437 fs decay time could be then assigned to a vibronic coupling from the 1 1 B 1u state onto lower electronic states. This conclusion is however too hasty. This long decay is quite unexpected taking into account the large bandwidth, characterizing this absorption band. Within the assumption of a homogeneous broadening due to pure electronic relaxation, the 437 fs decay would correspond to a bandwidth of around 12 cm -1 , namely a hundred times narrower than the bandwidths observed on Figure 1. One possible explanation to this counterintuitive invariant decay is that the ion transients reflect a vibrational relaxation. However, the ∼500 cm -1 of vibrational energy that we can expect in the 1 1 B 1u state is most likely not large enough to reach an intramolecular vibrational relaxation (IVR) threshold of this state, although this compound has 36 normal vibrational modes with strong in-plane force field coupling. Our hypothesis is that the 437 fs decay is the signature of IVR taking place in the electronic state populated by the first internal conversion (IC1) from the zeroth order state(s) (at least 1 1 B 1u ) prepared by the pump pulse. An IC rate is limited by the difference in entropy between the initial and the final electronic states. 36 When the entropy in the prepared initial state (namely 1 1 B 1u ) increases with the same rate as the entropy in the final state (to be determined), the IC rate can reach a converging limit (corresponding to a 437 fs decay) and won't vary anymore as function of the pump energy as observed over the ∼200 meV energy region investigated in Figure 2a. 36 Within this IVR interpretation, the invariance of the decay time observed in Figure 2a would mean only that the electronic state populated by IC1 is the same whatever the pump pulse, but not if one or two electronic states are prepared by the pump pulse. This hypothesis is confirmed by the photoelectron spectra which are featureless with only the integrated photoelectron intensity decaying as a function of the delay time without large spectral decay. A rotation of the probe polarisation relative to the pump one does not yield to noticeable changes on the photoelectron image apart of a lower total intensity. Whatever the delay, the photoelectrons are mainly produced with a minimum of kinetic energy. This type of energy distribution is quite an issue in time-resolved imaging due to the saturation of the MCP detectors for E kin =0 eV because everything is focused on only on few microchannels. This prevents a proper time-resolution of the photoelectron imaging at that energy. Two photoelectron distributions are displayed in Figure 3 to enlighten the pump-probe ionization process onto the IP 1 continuum. At 100 fs, when the population is expected to have still the 'zeroth order state' character prepared by the pump pulse, the photoionization is characterized by an ion with at least ∼ 1.3 eV of internal vibrational energy (E kin (e -∼ 0.5) eV). As soon as 200 fs (here shown at 400 fs) this maximal internal energy is reduced by half (E kin (e -∼ 1.1) eV). Afterward the photoelectron energy distribution changes only in intensity. This is in contrast to most time-resolved photoelectron spectroscopy studies done in large systems. In general, the photoelectron kinetic energy decreases due to the rising of the vertical ionization potential when vibrational energy increases in the neutral molecule. Our observations can be rationalized if the equilibrium geometry of the electronic excited state prepared by the pump pulse is shifted relative to the cation one and if the electronic state populated by the IC1 has a equilibrium-like geometry than the cation one. In that case, smaller internal energies of the cation would be produced once dynamics take place within the IC1 populated electronic state. In that context, it is important to remember that although computational methods failed by 0.6 eV to reproduce the experimental vertical ionization potential IP1, they predict at the optimized geometry of the neutral ground state, a ∼ 200 meV energy difference between the adiabatic and vertical ionization potentials. 21 Similar findings are observed for the one color two-photon ionizations with the pump or probe beam alone, as shown in Figure 3b. This fs-multiphoton transition should reflect ionization taking place from the vibrationally cold ground electronic state with a limiting effect from intermediate resonances. Namely, the clear energy cut-off of the IP1 threshold should appear in the kinetic energy distribution of the photoelectrons, as already observed at 800 nm with a 80 fs pulse. 29 At 2 × 317 nm, with only IP 1 accessed, the ionization probability is almost totally flat over the total 1.1 eV of vibrational energy available. A similar conclusion is reached at 2 × 267 nm, although the complete vibrational window can not be accessed in this case due to the detector size. Clearly, the intermediate resonance around 4 eV affects drastically the Franck-Condon window for a ∼200 fs chirped UV pulse. Since the flat distribution observed at a time delay of 400 fs does not fully occupy the opened vibrational window (i.e. 1.1 eV observed, instead of the 1.85 eV opened in the IP 1 continua at 1+1'), we could conclude that at this time delay, not all of the vibrational population has been detected via this 1+1' ionization. Within the current interpretation, IVR is expected to change the Franck-Condon overlap in the photoionization such that almost the entire energy range is used in the IP 1 continuum, but not completely, with a higher probability to produce ions with small internal energy at 400 fs than at 100 fs. The remaining question is what the involved IC1 electronic state is. Calculations in MS-CASPT2 in the D 2h geometry predict four triplet states and seven singlet states below 4 eV, including two Rydberg states, one 3s state at 3.6 eV and one 3p z state at 3.8 eV. 21 The angular distributions of the photoelectron images have been analyzed in two energy ranges from 0.11 to 0.36 eV and from 0.36 to 1.2 eV. With the laser polarization being linear and parallel to each other and the detector, the angular distribution is defined by a series of even Legendre polynomials up to the second order for the 1+1' photoionization:

I(θ) = 1 + n=2 β 2n P 2n (cos θ) (2)
with P 2 (x) = 1 2 (3x 2 -1) and P 4 (x) = 1 8 (35x 4 -30x 2 + 3). Table 2 summarizes the coefficients obtained for the four images of Figure 3.

By comparing the one color β-parameters recorded at 317 nm and 267 nm, we see that the resonance encountered at 4 eV reduces the anisotropy of the photoelectron emission regardless of the photoelectron kinetic energy. Indeed the β 2 parameters for 317 nm are about half the magnitude of those at 267 nm with minor contribution for β 4 at resonance. For a well established resonance, namely the pump-probe images, anisotropy is more important at τ = 100 fs than at 400 fs, being almost isotropic for all excitation energies at this delay with no signature of the two-photon ionization (1+1'), as revealed by β 4 ∼ 0 contribution.

TABLE II. Anisotropy parameters for the photoelectron images shown in Fig. 3 and5. The low energy range (LE) corresponds to photoelectron with kinetic energy between 0.11 to 0.36 eV, while the high energy (HE) range from 0. Note that the 3s and 3p z Rydberg states converge onto the ground state of the cation. 21 If a 3p z Rydberg state, with ∼ 100 meV of vibrational energy at 317 nm, would be populated directly or by IC1, a low anisotropy at a well-defined kinetic energy around 1.7 eV of the photoelectron would be expected, due to the interferences between the s and d outgoing waves and the conservation of vibrational energy in the ionization process respectively. The lack of a Rydberg fingerprint in the featureless energy distribution of the photoelectron spectrum let us discard a pure 3p z Rydberg state as a IC1 electronic state. 37 For the 3s Rydberg state with ∼ 300 meV of vibrational energy at 317 nm, a strong anisotropy due to the pure p outgoing wave (β 2 =2) would be expected at a kinetic energy around 1.6 eV. The decrease of anisotropy as a function of time as well as the lack of a clear component around 1.6 eV discards as well the implication of the 3s Rydberg state.

In the next two investigations, the probe wavelength is changed (to 398 and 800 nm) to confirm the long lifetime measurement and as well to enlighten the states involved in the relaxation process. The pump wavelength is kept around 317 nm.

B. A probe pulse centered at 398 nm

A probe pulse centered at 398 nm has the main advantage to be off resonance at 1 photon, while the 1+2' excitation scheme will open properly the second ionization continuum to IP 2 . Indeed, a 200 nm probe would have produce a too large background taking the high excitation cross-section at that wavelength. The TTF + transient recorded with λ probe = 398 nm, shown on Figure 4, has a typical decay time of 367 ± 11 fs which is about 16% lower than the previous one laser shot acquisitions and background free. The vertical reference lines are respectively: 317 nm + 267 nm -IP1 (green), 317 nm + 267 nm -IP2 (red), 2×317 nm -IP1 (blue) and 2×267 nm -IP2 (black). The limit for 267 nm -IP1 is at 2.55 eV, beyond the detector limit.

with a probe beam at 267 nm. The photoelectron spectra, shown in Figure 5, reveal that photoionization taking place at (1+1') energy-7 eV-only 300 meV above the IP 1 threshold is strongly shifting from 200 meV to 0 eV during the first 400 fs. A similar effect is as well observed for the 1+2' channel. For time delays of 150 fs it is worthy to note that the energy distribution is in agreement with the energy cutoff expected for the second continuum of ionization IP2 (1.56 eV). However, within the Koopman's approximation, this is only possible for photoionization taking place from an excited electronic state with a b 3g hole. There are two possible ways to get such photoionization spectrum. At one photon of the pump, this would mean that the 1 1 B 2g state (calculated at 3.41 eV 21 ) is populated by IC1 from the 'zeroth order' electronic state(s that includes 2 1 B 1u ). At 1+1'-7 eV-a Rydberg state converging to IP 2 is populated. This latter hypothesis would explain as well why no contribution for 1+2'-IP1 is observed. Rydberg states converging to IP2 have been indeed detected at 6 eV. 29 The two ionization processes (1+1') and (1+2') will be discussed independently. In the (1+1') channel, photoelectrons appear with a kinetic energy ∼ 200 meV during the first 300 fs before to be reduced. A transient from a 3p z Rydberg state would be expected at 200 meV. The angular distribution of this low energy range is quite isotropic (see Table II), consistent also with a 3p z Rydberg state. However, there is no obvious reason why a Rydberg fingerprint for that state will appear with λ probe = 398 nm and not with λ probe = 267 nm. This is the main reason why we still discard a 3p z Rydberg assignment. In the (1+2') -IP 2 /-IP 1 channel, the photoelectron energy distribution spreads almost over the entire 1.5 eV vibrational energy window with a higher probability at small kinetic energies as already observed for the (1+1') channel -IP 1 at 267 nm. The cut-off of IP2 is clearly observed, especially at 150 fs and 300 fs. This ionization onto the IP2 continuum is not expected taking into account the singly electronic excitation from the HOMO that defines most of the singlet excited state. As already discussed previously, only the 1 1 B 2g state due to its 22% HOMO-1 character is correlated to this ion continuum. Our tentative assignment is that the IC1 populates at least this state, that has been calculated at 3.41 eV. 21 The minimal vibrational energy of the cation observed at long time delays in the IP 2 continuum by (1+2') is 400 meV, which is in agreement with the 500 meV expected in the 1 1 B 2g with a 317 nm pump. In that context the 367 fs decay of the ion transient will show similarly to (1+1') at 267 nm the IVR taking place onto the the 1 1 B 2g state. Note however, that another possible explanation for the IP2 ionization is as well a Rydberg state populated at 1+1' (around 7 eV), correlated to the IP2 continuum as already observed. 29 At high energy (HE) range, the β 2 parameter slightly increases as expected for a (1+2') ionization compared to a (1+1') one. In order to take into account the three photons involved in the (1+2') scheme, the angular fit includes a β 6 contribution for the HE range. On the contrary to λ probe = 267 nm, the anisotropy of this HE range, slightly increases at longer delay. No signature of the two Rydberg states lying around 3.6 eV can be expected in this (1+2') HE range since both converged to the ground state of the cation and the kinetic energy window is limited to 2.2 eV.

C. A probe pulse centered at 800 nm

As we will see, tuning the probe wavelength to 800 nm with a typical intensity of 50 µJ/p reveals a relaxation taking place on two different timescales. The IP 1 ionization continuum is reached in a (1+2') scheme with a small excess energy of ∼ 300 meV. This is similar to the (1+1') scheme at 398 nm, seen before. Above threshold ionization (ATI) takes place from both the IP 1 and IP 2 opening the ion continuum up to 15 eV as already studied in a similar experimental conditions with a larger detector to access higher photoelectron energies. 29 In a VUV one-photon ionization, dissociative ionization onto the largest primary fragments is complete as low as 10 eV. 29 Figure 6 shows the mass spectrum recorded at τ = 200 fs. Dissociative ionization clearly dominates up to the formation of sulfur cations. In the VUV coincidence experiment, 29 the S + fragment is produced by a secondary dissociation of S 2 , formed after large rearrangement of TTF + with an appearance energy of 12.6 eV. This mass spectrum is quite similar to the helium collision-induced dissociation mass spectrum of TTF. 38 The τ = 0 fs ion image shown in Figure 6 reveals not only the main contribution from TTF but more surprising the formation of the dimer of TTF in this continuous molecular beam. There is no spectroscopic data published on this dimer. The time dependencies of the main species are shown on Figure 7. The time dependency of the dimer shows clearly a shoulder and a depleted background signal at positive delay. This is a signature of a resonance encountered at 317 nm in these dimers. The cross-correlation time as well as the time overlap is determined by fitting the negative delay part of this dimer transient. τ cc is measured to be 295 ± 7 fs and the decay time of TTF + 2 extracted from this resonant transient is 134 ± 20 fs. All decay times measured for the different masses are summarized in Table III and do not depend on the probe intensity which was varied between 30 and 90 µJ/p. The main result is that the decay time on the TTF + signal is 40% shorter than the ones measured before with a probe pulse centered at 267 nm or 398 nm. We assign this 260 fs decay to IC1 which is unrevealed in the ion transients with UV probes. The higher the appearance energy of the fragment produced by dissociative ionization, the longer is the decay time. It is as well a non-decaying step appearing in the same manner. In order to check that the dynamics are still initiated at 317 nm, a pump power dependency of C 2 H 2 S + 2 and S + is measured at τ = 4 ps which is shown in the inserts of Figure 7 for these fragments. The linear dependency observed for both fragments confirms that the dynamics are indeed initiated at 3.9 eV and no dissociation takes place from multiphoton absorption of the pump pulse, as already observed in other systems. 39 The presence of a non-decaying step at more than 6 ps can be assigned to a second internal conversion IC2 onto the ground state. In order to take into account this new contribution, an independent rising component with a typical time constant τ r is added to equation 1:

Ψ r (τ ) ∝ 1 -e -τ τr × [1 + erf (φ (τ, τ r ))] (3)
The fits converge systematically to τ d = τ r . This means that both the electronically excited state populated by IC1 and the ground electronic state have their dynamics projected onto the dissociative ionization continuum, when this later is energetically allowed, but with a lower probability for the ground electronic state. These observations are similar to the ones obtained, for instance, on Cr(CO) 6 or norbornene probed with an intense probe pulse. 40,41 Here as well the degree of fragmentation is weaker at small pump-probe delays and the decay time increases as the mass of the fragments is decreasing. Indeed, when the molecule relaxes, the electronic energy is converted into vibrational energy, which upon ionization remains in the ion. This is causing dissociative ionization once its threshold is energetically reached. Below this threshold, as observed for λ probe = 268 nm or 398 nm, photoionization takes place whatever the nuclear geometry with almost the same probability. This leads to the relative featureless photoelectron spectra observed in Figure 3 and5. This applies because the energies of the ion bonds are weaker than the binding energies of the neutral molecule. When electronic relaxation onto the ground electronic state takes place, vibrational energy becomes important. Therefore, upon photoionization, the internal energy of the ion will be more important and a fragmentation down to the smaller species will take place. This hypothesis is supported by the largest shift observed on the maximum of S + signal that requires to introduce a real time shift of 95 fs to reproduce its transient. We recall the assumption that fragments coming from the dissociation of neutral molecules, are not involved in this process. This has been checked by monitoring the VMI images of these fragments. They all show tiny kinetic energy releases as expected for dissociative ionization. Dissociative ionization allows to detect the end products of ultrafast relaxation in TTF since it gives rise to a non-vanishing signal of infinite lifetime. Figure 8 shows the time dependency of the photoelectron produced in such an excitation scheme. Taking into account the dissociative ionization, the different possible ion continua as well as the limitation of observation fixed by the size of the detector, an assignment of the time-dependent peaks is totally irrelevant. Moreover, in systems where multiphoton ionization is involved, doubly excited states can be populated at (1+1') energy, leading to Rydberg fingerprints in the photoelectron spectra. 36,37,42 IV. DISCUSSION

In the following we propose and discuss a relaxation mechanism to rationalize the three time constants observed, namely ∼ 260 fs on TTF + at λ probe = 800 nm, ∼ 400 fs on TTF + both with λ probe = 267 and 398 nm and finally for the fragments the longest timescales which are all >580 fs revealed by dissociative ionization. The shortest decay time of 260 fs is too long to be a Franck-Condon window departure and should reflect the first internal conversion IC1 onto a slightly lower electronic state that we tentatively assign to 1 1 B 2g state due to the IP2 continuum opened at 1+2' with λ probe = 398 nm. Rydberg states are discarded due to the absence of a clear vibrational or angular signature on the photoelectron spectra at λ probe = 268 nm. Since the time transients with the UV probe pulses are both fitted by a single exponential function with a decay constant of ∼ 400 fs, the electronic state reached by IC1 must be close in energy to the 'zeroth order' state prepared by the pump pulse. This is indeed the case for the 1 1 B 2g state. In addition, this newly populated state should have a similar ionization cross-section than the 'zeroth order state' to not be revealed in the ion transients of Figure 2 and4. The ∼ 400 fs decay time, revealed in these UV ion transients, reflects then the IVR taking place into the 1 1 B 2g state. By reaching higher energies in the ion continuum via multiphoton ionization at 800 nm, the transients of the dissociative ionization fragments reveal two components with similar time constants, namely a decaying one and a rising one in the range of 580 fs. This would reflect the transfer of population from 1 1 B 2g -the decaying component -to the ground electronic state -the long lifetime step showing the appearance of the end product of this photochemical reaction. This is the simplest story that can be build from the observed transients. To finish, it is quite interesting to notice that the 400 fs decay time measured with the UV probe pulses is never observed with the IR probe pulse on the parent cation, even though the three probe wavelengths are linked by the harmonic relationship. Maybe the intermediate resonance reached at (1+1') for λ probe = 800 nm, 5.45 eV, affects the Franck-Condon window of ionization.

V. CONCLUSION

The ultrafast dynamics taking place from the second band, which is optically allowed in TTF, has been revealed by both, varying the pump and the probe wavelengths. The observed time dependencies give no evidence which would indicate the presence of two different electronic states or of Rydberg states in the observed energy range, as suggested in the past. Possibly this double structure could be assigned to a vibrational pattern as suggested by Pou-Armengo et al. The ultrafast dynamics in TTF are characterized by two time scales as revealed by changing the probe wavelengths. The first internal conversion seems to be achieved in 260 fs followed by a second one onto the ground electronic state with a slightly longer time constant around 600 fs. Dissociative ionization and UV ionization allow to monitor as well the transfer from electronic to vibrational energy in all the electronic states populated by the internal conversions, namely the 1 1 B 2g state and the ground state. Monitoring similar TTF compounds, 3,30 might as well confirm the generality of this long electronic and vibrational relaxation. This approach is relevant to optimize the design of new photoactive materials incorporating a TTF core or derivatives. In this gas phase study, the formation of a TTF dimer has been as well revealed.

1 FIG. 1 .

 11 FIG. 1. (a) The different pump-probe excitation schemes used. The definition of y and z axis is relevant only for the D 2h planar geometry. (b) Absorption spectrum of TTF in acetonitrile at ambient temperature with a concentration of 5 × 10 -4 mol/l.

FIG. 2 .

 2 FIG. 2. Pump-probe time transients with a probe centered at 267 nm. (a) Femtosecond time-resolved transients of TTF + as function of the pump pulse wavelength. (b) N,N-Dimethylaniline transient at 267 +317 nm that produces a long lifetime transient through a 3s-Rydberg excitation (stepfunction) from which the time overlap (τ = 0 fs) and the cross correlation time of this UV-UV pump-probe excitation are both extracted. The T T F + time transient (shown at 317 nm full dot) can be fitted (red) by the sum of a crosscorrelation component (Ψcc(t), dash-dot) and a decay component (Ψ d (t),dashed).

FIG. 3 .

 3 photoelectron[yield[[arb.[units]

FIG. 4 .

 4 FIG. 4. Time transient of the parent molecule TTF recorded with a probe pulse at 398 nm.

FIG. 5 .

 5 FIG. 5. Photoelectron energy distribution for different pumpprobe delay and λ probe = 398nm(a) -150 and 0 fs (b) 150 and 300 fs (c) 400 and 600 fs. The image (d) and (e) corresponds to the 150 and 400 fs delays respectively. Same acquisition time than Figure 3. The vertical reference lines are respectively : 318nm+398nm-IP1 (green), 318nm+2×398nm-IP2 (red)

FIG. 6 .

 6 FIG.6. Mass spectrum recorded at +200 fs between a pump pulse centered at 318 nm and an intense probe pulse centered at 800 nm. The insert figure is the image of the mass species produced in the continuous molecular beam at τ = 0 fs.

5 FIG. 7 .

 57 FIG.7. Time transients of different cations with a probe pulse centered at 800 nm. The insert graphs show the pump power dependency of the fragments at delay 4 ps.

FIG. 8 .

 8 FIG.8. Photoelectron energy distribution as a function of the pump-probe delay. The vertical reference lines indicate the maximum kinetic energy for the different channels of ionization (1+n') onto the IP1 and IP2 ionization continuum after the absorption of one photon of the pump pulse and n' photons of the probe pulse.

  36 to 1.2 eV.

	λ / Delay	β2	β4	β6
	317 nm	LE 0.14 ± 0.01 -0.056 ± 0.007
		HE 0.39 ± 0.01	-0.003
	267 nm	LE 0.24 ± 0.01	0.03 ± 0.01
		HE 0.72 ± 0.02	0.19 ± 0.02
	100 fs	LE 0.32 ± 0.01	0.12 ± 0.01
		HE 1.18 ± 0.01	0.43 ± 0.02
	400 fs	LE 0.12 ± 0.01 -0.052 ± 0.006
		HE 0.42 ± 0.01	0 ± 0.003
	398 nm
	150 fs	LE 0.23 ± 0.01 -0.105 ± 0.01
		HE 0.74 ± 0.02 -0.06 ± 0.02 0.25 ± 0.03
	400 fs	LE 0.39 ± 0.02 -0.076 ± 0.015
		HE 1.22 ± 0.03	0.15 ± 0.04	0.45 ± 0.04

TABLE III .

 III The different decay times extracted by the fit procedure based on equation 1, completed with equation 3 for the fragments of dissociative ionization. The cation transients are shown in Figures2, 4 and 7. The appearance energies of the cation are extracted from29 . ( * with a delay shift of 95 ± 7 fs).

	λ probe [nm]	Ion	EA [eV]	τ d [fs]	τcc [fs]
	267 398 800 800 800 800	C6H4S + 4 C6H4S + 4 C6H4S + 4 C3H2S + 2 C2H2S + 2 S +	6.7 (IP1) --11 10 12.6	437 ± 7 397 ± 11 272 ± 3 304 ± 2 259 ± 7 295 ± 7 615 ± 21 -576 ± 9 -704 ± 13

* -

This work was supported financially by the ANR-08-JCJC-0029 HARMODYN, ANR-14-CE32-0014 MIS-FITS and l'Université Paul Sabatier. D.S. acknowledges the European Union for its PhD fellowship from the ITN-ICONIC (FP7-Grant Agreement No. 238671). We thank Elsa Baynard, Stéphane Faure and William Volondat for their expert technical assistances.


Keywords: cantilevers, ceramic, force sensor, piezoresistor, screen-printing

In this paper, the design, the fabrication and the characterization of ceramic screen-printed force sensors are described. They are based on the use of cantilevers with integrated piezoresistors. The choice of the materials constituting the cantilever and the strain gauge, so as the dimensions of the cantilever have been optimized in order to measure forces in mN range. The sensors have been fabricated using the screenprinting technique associated with the sacrificial layer technique to release the free-standing part of the cantilevers. Afterwards, they have been characterized: measurement of sensitivity, reproducibility and materials properties (Young's modulus and strain gauge factor). The performances of these sensors are compared to the existing silicon, polymer and ceramic sensors.

I. INTRODUCTION

The microsystems, generally designated by MEMS (MicroElectroMechanical Systems), have been used for some years in the fields of micro-electronic, microrobotic, microfluidic, etc. Microcantilevers are common structures for MEMS, employed for different applications (mechanical sensors, gas sensors, AFM [START_REF] Li | A novel technique of microforce sensing and loading[END_REF][START_REF] Peiner | Force calibration of stylus instruments using silicon microcantilevers[END_REF][START_REF] Lavrik | Cantilever transducers as a platform for chemical and biological sensors[END_REF][START_REF] Goeders | Sensing chemical interactions via mechanical motion[END_REF], etc.). Most of them are fabricated thanks to silicon micromachining. Nevertheless, other fabrication processes (ceramic, polymer based…) are attractive in terms of cost but also sensitivity or stability [START_REF] Johansson | SU-8 cantilever sensor system with integrated readout[END_REF][START_REF] Thaysen | SU-8 Based Piezoresistive Mechanical Sensor[END_REF][START_REF] Birol | Structuration and fabrication of sensors based on LTCC (Low Temperature Co-fired Ceramic) Technology[END_REF][START_REF] Birol | fabrication of a millinewton force sensor using low temperature co-fired ceramic[END_REF].

Low Temperature Cofired Circuits (LTCC) technology is an example of an alternative low cost ceramic process successfully applied for the fabrication of cantilever force sensors operating in mN range [START_REF] Birol | Structuration and fabrication of sensors based on LTCC (Low Temperature Co-fired Ceramic) Technology[END_REF][START_REF] Birol | fabrication of a millinewton force sensor using low temperature co-fired ceramic[END_REF]. In this LTCC technology, the piezoresistive element integrated on the cantilever for the force measurement is a screen-printed thick film resistor. Another low cost process based on the association of standard screen-printing technology with the Manuscript received October 23, 2009. R. Lakhmi is at the Université de Bordeaux, IMS Laboratory, Microsystem group, Talence, F-33405, France (e-mail: riadh.lakhmi@ims-bordeaux.fr) H. Debéda is at the Université de Bordeaux, IMS Laboratory, Microsystem group, Talence, F-33405, France (Phone : (33) 5 40 00 83 36; Fax : (33) 5 56 37 15 45; e-mail: helene.debeda@ims-bordeaux.fr), corresponding author I. Dufour is at the Université de Bordeaux, IMS Laboratory, Microsystem group, Talence, F-33405, France (e-mail: isabelle.dufour@ims-bordeaux.fr) C. Lucat is at the Université de Bordeaux, IMS Laboratory, Microsystem group, Talence, F-33405, France (e-mail: claude.lucat@ims-bordeaux.fr) sacrificial layer [START_REF] Lucat | New Sacrificial Layer Based Screen-Printing Process for Free-Standing Thick-Films Applied to MEMS[END_REF][START_REF] Castille | Free-standing piezoelectric thick-films for MEMS applications[END_REF], is suggested for the fabrication of cantilevers devoted to new force sensors.

The purpose of this paper is to show the feasibility of such sensors, using screen-printed glass ceramic cantilevers and integrated thick film piezoresistor. Comparison of their performances with those of other ceramic sensors made with LTCC technology is proposed.

The first part of this paper describes the design of force sensors working in the mN range sensitivities needed for example in robotic applications [START_REF] Perez | Fabrication, modeling and integration of a silicon technology for sensor in a piezoelectric micro-manipulator[END_REF]. The second part highlights the fabrication process of the sensors. Finally, the third part is dedicated to the materials characterization (Young's modulus of the cantilever and gauge factor of the piezoresistors) and the metrological sensor characterization.

II. SENSOR DESIGN

A. Principle

The cantilever force sensor principle and its dimensions are given in fig 1. An applied force F at the free-end induces a strain in the cantilever which is maximal closed to the clamped-end. The strain gauge integrated in this area enables the conversion of this strain into a resistance variation. The resistance variation induced by the applied force can be written [START_REF] Timoshenko | Strength of Materials, Part 1: Elementary Theory and Problems[END_REF]:

w Et Fd G G R R F l F 2 6 = = Δ ε (1)
where G F is the intrinsic gauge factor of the strain gauge, ε l the longitudinal strain, E the Young's modulus of the cantilever, w its width, t its thickness and d the distance between the strain gauge and the application point of the force.

Force sensors based on screen-printed cantilevers

Riadh LAKHMI, Hélène DEBEDA, Isabelle DUFOUR, Claude LUCAT

B. Cantilever choice (geometry and material)

The sensor force range depends on the geometry of the cantilever but also on the parameters E and G F which are linked to the materials and their fabrication process [START_REF] Ashby | Engineering Materials II[END_REF][START_REF] Cho | Characterization of Young's modulus of silicon versus temperature using a ''beam deflection" method with a four-point bending fixture[END_REF][START_REF] Prudenziati | Thick film sensors and actuators 1[END_REF]. Table I illustrates for example the characteristics of different strain gauge materials. Compared to silicon or metallic strain gauges, the thick film resistors are a good compromise in terms of sensitivity but also stability. The TCR (Temperature Coefficient Resistance) and the TCGF (Temperature Coefficient of the Gauge Factor point out the influence of the temperature on the gauge resistance.

Taking into account the geometric limitations of the screen-printing technique and the screen-printed thick layer materials properties (glass-ceramic cantilever and strain gauge), we have calculated the sensitivities S = ΔR/(RF) for different sensor dimensions (table II). The range of E and G F corresponds to what can be expected for glass-ceramic screenprinted materials. Those sensitivity values have been compared to those obtained for other existing cantilevers with piezoresistors (table III) [START_REF] Debéda | Potentialities of piezoresistive cantilever force sensors based on free standing thick films[END_REF]. The minimum detectable force linked to the electronic noise (ΔR/R minimum = 0.01%) has also been estimated. The results clearly show that the screen-printing technique can not compete with other techniques (silicon, polymer) in terms of sensitivity. They nevertheless present better sensitivities than other ceramic techniques (alumina or LTCC), and, as for the above ceramic technologies, they are interesting in terms of costs and reliability. Indeed, they have a good stability towards harsh environments (temperature, bases, acids…). Moreover, it is possible to realize a hybrid microsystem integrating the sensor and its electronic thanks to the standard thick film technology [START_REF] Haskard | Thick film technology and applications[END_REF].

C. Strain gauge design

The geometry adopted for the strain gauge is given fig 2. It is a classical geometry used in silicon force sensors [START_REF] Barlian | Review: Semiconductor Piezoresistance for Microsystems[END_REF] and it derives from the "streamer" geometry mainly used for metallic gauges. The dimensions of l, b, x and e are respectively 2.67mm/1.52mm/0.25mm/0.25mm (0.105in / 0.060in / 0.010in /0.010in) and are compatible with thick film technology. The adhesion between the piezoresistive layer and the structural layer is supposed to be perfect. In those conditions, the strain gauge's longitudinal branches will follow the cantilever's longitudinal strain and the transversal branches will follow the cantilever's transversal strain:

l F l l G R R ε = Δ (2) l F t F t t G G R R ε ν ε 0 - = = Δ (3)
where R l and R t are respectively the longitudinal and transversal branch resistances (fig. 2), ε l and ε t are respectively the cantilever's longitudinal and transversal strain and ν 0 its Poisson coefficient.

Considering the expressions (2) and ( 3), the output signal can be expressed the following way:

α α ν ε + - = Δ 1 1 0 l F G R R (4)
where α is the ratio between R t and R l .

The intrinsic gauge factor G F of a material (semiconductor, metallic or thick film) does not take in account the geometry of the gauge. From the relation (4), the effective gauge factor K j can be extrapolated:

α α ν + - = 1
1 0 F j G K (5)
Considering a Poisson ratio ν 0 = 0.2, an effective gauge factor K j = 0.73G F is found for the chosen dimensions of the screen-printed gauge. The equation [START_REF] Johansson | SU-8 cantilever sensor system with integrated readout[END_REF] shows the importance of the strain gauge geometry on the sensor performances.

III. FABRICATION PROCESS

A. Screen-printing

The screen-printing process is widely used in hybrid microelectronic for the fabrication of interconnections, thick layer passive components (conductors, resistors, dielectrics…) and the packaging of hybrid circuits. It enables the realization of any pattern (minimum line width 100μm) with a controlled thickness (from a few micrometers to a few tens of micrometers per deposit). Thick layers are generally screenprinted on alumina substrate.. Once it is screen-printed, the ink is dried at 120°C and then fired at high temperature (classically 850°C) to give the layer its final electrical and mechanical properties (adhesion to the substrate, cohesion thanks to the sintering) [START_REF] Haskard | Thick film technology and applications[END_REF].

The standard thick film process has been associated to the sacrificial layer technique for the obtaining of free-standing structures. The sacrificial layer, used as a support for the deposition of the active layer, is removed at the end of the process in order to set the active layer free from the substrate. The sacrificial layer is realized at the IMS laboratory from a polymer ink epoxy type loaded with strontium carbonate (SrCO 3 ). After the screen-printing step, the layer is polymerized at 120°C before the printing of the active layer. The samples are fired at temperature above 850°C. Then, the sacrificial layer is removed by dissolution in an acid phosphoric (H 3 PO 4 ) solution (pH = 1) [START_REF] Lucat | New Sacrificial Layer Based Screen-Printing Process for Free-Standing Thick-Films Applied to MEMS[END_REF].

B. Application to cantilever type force sensor

The following materials have been chosen for the sensor fabrication:

an alumina substrate (96%Al 2 O 3 ) is used as a support for the structures. The substrate has been pre-cut by laser for the collective fabrication of sensors.

a glass-ceramic ink has been used for the cantilever because of its good dielectric properties, its good aptitude to sintering, its good adherence to the alumina substrate and its relatively low Young's modulus (a few tens of GPa). The dielectric ink from ElectroScience Laboratory ESL4702, mainly based on alumina, silica and barium oxide, has been chosen.

the strain gauge, realized from a resistive ink (ESL3414), has been chosen for its piezoresistive properties (G F = 17, TCR ≈ ±100ppm/°C, resistance per square R /□ ≈ 4kΩ/ for a thickness of 10µm).

the gauge electrical contacts are realized with the conductive gold ink ESL8836.

The fabrication steps are described in fig 3. The different layers of the sensor have been successively screen-printed with a drying at 120°C between each deposit. A co-firing at 850°C has been performed once all the layers have been printed. In fig 3, we can notice the presence of two piezoresistors on the cantilever: the active gauge described part II-C integrated in the free-standing part of the cantilever, and the passive one placed on the fixed part of the cantilever. These resistances can be integrated in a Wheatstone bridge to eliminate temperature effect.

IV. CHARACTERIZATION OF THE FORCE SENSOR

A. Experimentation

Applications of known forces F at a distance 0.5mm from the free-end of the cantilever allows the determinations of sensitivity S = ΔR/(RF), Young's modulus E and gauge factor K j. The force is either obtained thanks to home-calibrated SnAgCu solder balls (from 20mg to 430mg) or thanks to the stylus of a mechanical Tencor profilometer (from 5mg to 100mg). During the force application, the deflection is measured with an optical profilometer Altisurf 500 (range 3mm, resolution 0.5µm). This deflection, which depends on the stiffness of the material and consequently on E, is given by the following relationship [START_REF] Timoshenko | Strength of Materials, Part 1: Elementary Theory and Problems[END_REF]:

w Et F L G F 3 3 4 = δ (6)
The Young' modulus can be thus calculated, providing that cantilever's dimensions are accurately known.

The dimensions L, w and t used in the calculations are measured by two methods. The length of the cantilever and its width are obtained thanks to the Altisurf 500 optical profilometer (range 300µm, resolution 0.1µm). The thickness is estimated with a manual micrometer (resolution ± 2μm). The cantilever roughness (R=4.5±1.2µm) and the micrometer resolution induce an uncertainty on the thickness measurement evaluated to 5µm.

B. Material characterization (E and K j )

Young's modulus and gauge factor are respectively obtained thanks to the slope measurement of the curve F(δ) (fig 4) and the curve ΔR/R(ε). The determined mean Young's modulus is 36GPa ± 4GPa [START_REF] Lakhmi | Determination of Young's Moduli for free-standing screen-printed thick film layers[END_REF]. The mean value measured for the effective gauge factor is K j = 11.8 ± 0.9 is closed to the calculated one K j = 12.1 (from the constructor data G F = 17).

C. Metrological sensor characterization

The main static metrological characteristics, among which the detectable forces range, the hysteresis, the linearity and the sensitivity, have been determined.

The limit of force detection is chosen when the ratio (signal noise /resistance variation) reaches 50% (fig 5). The minimum and the maximum detectable forces are linked to the cantilever dimensions. Minimum detectable forces of 100µN have been determined. Besides, the maximum detectable force (also called scale load),defined as the limit force for which the sensor properties are guaranteed are close to 4mN for the chosen cantilever dimensions. Indeed, for most of them, the properties are guaranteed even for a force corresponding to 4.3mN; but a few ones break under this last force value.

The resistance variation of the strain gauge, consecutive to the force application, has been evaluated for increasing and decreasing forces varying in the range 0.2 -4.3mN (fig. 6). An hysteresis value of 1.7% and a linearity error of 3.5% have been found. IV). Within the range 0.97 -2.33 N -1 , measured sensitivities match the predicted ones except for the P6 cantilever. For this cantilever, the measured gauge factor is K j = 10, whereas the calculations gives K j = 12.1. The fabrication reproducibility has been evaluated on 3 cantilevers P2 type. A good reproducibility linked to the fabrication process is observed (fig 7). The differences are related to the uncertainty on cantilever dimensions but also to measurement uncertainties related to the application point. V. CONCLUSION

The feasibility of force sensors based on screen-printed glass ceramic cantilevers with the low cost thick film process has been demonstrated. Compared to ceramic LTCC cantilevers force sensors, sensors studied in this paper exhibit a lower measurable force of 100μN [START_REF] Birol | fabrication of a millinewton force sensor using low temperature co-fired ceramic[END_REF]. Moreover, good fabrication reproducibility has been observed.

The size and the shape of cantilevers could be optimized with the main objective of forces detection in mN range and to improve the sensitivity [START_REF] Wilkinson | Nanomechanical properties of piezoresistive cantilevers: Theory and experiment[END_REF][START_REF] Harley | High-sensitivity piezoresistive cantilevers under 1000 Å thick[END_REF]. According to the resolution obtained with screen-printing process, width of 100µm and thickness of a few microns are reasonable for our cantilever. This size reduction should allow a better integration in microsystems. In agreement with microrobot application [START_REF] Perez | Fabrication, modeling and integration of a silicon technology for sensor in a piezoelectric micro-manipulator[END_REF], where the microgripper are made with different micromachining technologies, our process could be a simple and cost effective alternative process, for a whole "screenprinted microrobot" fabrication [START_REF] Castille | Free-standing piezoelectric thick-films for MEMS applications[END_REF].

Fig 1 .

 1 Fig 1. Geometry of cantilever structures

Fig 2 .

 2 Fig 2. Geometry of the strain gauge and equivalent circuit

Fig 3 .

 3 Fig 3. Fabrication steps of the force sensor

Fig 4 .

 4 Fig 4. Applied force F as a function of the cantilever free-end deflection δ

Fig 5 .

 5 Fig 5. Resistance measurement during the application of a force F on the tip cantilever (stylus test)

Fig 6 .

 6 Fig 6. Cantilever hysteresis evaluation (cantilever dimensions: 10mm/2mm/75µm) Sensors sensitivities deduced from the slope of the curve ΔR/R = f(F) have been determined for different cantilever dimensions (tableIV). Within the range 0.97 -2.33 N -1 , measured sensitivities match the predicted ones except for the P6 cantilever. For this cantilever, the measured gauge factor is K j = 10, whereas the calculations gives K j = 12.1.

Fig 7 .

 7 Fig 7. Fabrication reproducibility of the P2 type cantilevers (15mm/2mm/75µm)

TABLE I CHARACTERISTICS OF STRAIN GAUGES MATERIALS Material G F TCR (ppm/°C) TCGF (ppm/°C) Stability

 I

	Metallic
	sheets and	1-2	20	100	Excellent
	films
	Silicon single crystals	50-80	1000	-1500	Good
	Thick Film Resistors	2-35	50 -200	-300	Very Good

TABLE II CALCULATED

 II

			L (mm)	15	10	15	10
			w (mm)	2	3	2	3
			t (µm)	50	50	100	100
			E=10GPa /	63	28	16	7.0
	S	) (N -1	G F =35 E=100GPa /	0.35	0.15	0.10	0.05
			G F =2
			E=10GPa /	1.6	3.5	6.3	14
	Fmin	(µN)	GF=35 E=100GPa /	276	624	1108	2500
			G F =2

SENSITIVITIES S AND MINIMUM FORCE F MIN FOR DIFFERENT SIZES OF SCREEN-PRINTED CANTILEVERS