Olivier Mongin

Marina Charlot

Claudine Katan

Laurent Porrès

Manuel Parent

Thomas Pons

Jerome Mertz

Mireille Blanchard-Desce
email: mireille.blanchard-desce@univ-rennes1.fr

Nanoscale multipolar chromophores for optical limiting in the visible-NIR range based on multiphoton absorption

Keywords: Two-photon absorption, multipolar structures, nanoscale systems, branched-structures, optical limitation

A series of structurally-related multipolar chromophores of different symmetry (dipolar, quadrupolar, octupolar, dendritic…), and shape (rod-like, Y-shaped…) propeller-shaped, were investigated for optical power limiting based on multiphoton absorption processes. Their design is based on the functionalization of nanoscale linear or branched conjugated backbones with electro-active (i.e. electron-releasing or electron-withdrawing) peripheral and core/node groups. Their two-photon absorption (TPA) spectra were determined by investigating their two-photon-excited fluorescence properties in the NIR region using pulsed excitation in the femtosecond regime. These studies provide evidence that the charge symmetry plays an important role, the quadrupolar chromophores leading to giant TPA crosssections in the visible red. Furthermore, modulation of the nonlinear absorptivity/transparency/photostability trade-off can be achieved by playing on the nature of the electroactive groups and of the spacers. Interestingly, higher-order charge symmetries and branched structures provide an innovative route for TPA amplification and/or spectral broadening in the NIR region.

INTRODUCTION

Multiphoton absorption has attracted considerable attention for optical power limiting applications. [START_REF] He | Two-photon absorption and optical-limiting properties of novel organic compounds[END_REF][START_REF] He | Optical limiting effect in a two-photon absorption dye doped solid matrix[END_REF][START_REF] Ehrlich | Two-photon absorption and broadband optical limiting with bis-donor stilbenes[END_REF][START_REF] Perry | Two-photon and higher-order absorptions and optical limiting properties of bis-donor substituted conjugated organic chromophores[END_REF] This nonlinear process offers the possibility of maintaining high transparency in ambient light and achieving efficient and instantaneous protection against the high intensity delivered by high power lasers. Key ingredients for such purpose are a high transmission at low intensity (i.e. weak linear absorption) and high multiphoton absorption cross-sections (i.e. high nonlinear responses). In this context, we have focused on the design of chromophores showing very large two-photon absorption (TPA) cross-sections (σ 2 ) while maintaining wide transparency in the visible and/or NIR spectral range. Large one-photon excited-state cross-section (σ e ) and long excited-state lifetime are also desirable to allow two-photon induced excited-state absorption phenomenon to arise, leading to synergic effects of TPA and excited-state absorption and improved optical limitation behavior in the nanosecond regime. [START_REF] Perry | Two-photon and higher-order absorptions and optical limiting properties of bis-donor substituted conjugated organic chromophores[END_REF][START_REF] Albota | Design of organic molecules with large two-photon absorption cross sections[END_REF] Until recently, optimization of molecular TPA has focused mainly on one-dimensional dipolar, [START_REF] He | Nonlinear optical properties of a new chromophore[END_REF][START_REF] Reinhardt | Highly active two-photon dyes: design, synthesis, and characterization toward application[END_REF][START_REF] Ventelon | New quadrupolar fluorophores with high twophoton excited fluorescence[END_REF][START_REF] Belfield | New Two-Photon Absorbing Fluorene Derivatives: Synthesis and Nonlinear Optical Characterization[END_REF][START_REF] Kim | New Class of Two-Photon-Absorbing Chromophores Based on Dithienothiophene[END_REF][START_REF] Strehmel | The influence of σ and π acceptors on two-photon absorption and solvatochromism of dipolar and quadrupolar unsaturated organic compounds[END_REF][START_REF] Antonov | A systematic femtosecond study on the two-photon absorbing D-π-A molecules-π-bridge nitrogen insertion and strength of the donor and acceptor groups[END_REF] or quadrupolar [START_REF] Albota | Design of organic molecules with large two-photon absorption cross sections[END_REF][START_REF] Reinhardt | Highly active two-photon dyes: design, synthesis, and characterization toward application[END_REF][START_REF] Kim | New Class of Two-Photon-Absorbing Chromophores Based on Dithienothiophene[END_REF][START_REF] Strehmel | The influence of σ and π acceptors on two-photon absorption and solvatochromism of dipolar and quadrupolar unsaturated organic compounds[END_REF][START_REF] Ventelon | Nanoscale push-push dihydrophenanthrene derivatives as novel fluorophores for two-photon-excited fluorescence[END_REF][START_REF] Mongin | Synthesis and Photophysical Properties of New Conjugated Fluorophores Designed for Two-Photon-Excited Fluorescence[END_REF][START_REF] Abbotto | Novel Heterocycle-Based Two-Photon Absorbing Dyes[END_REF][START_REF] Iwase | Synthesis and photophysical properties of new two-photon absorption chromophores containing a diacetylene moiety as the central π-bridge[END_REF][START_REF] Silly | Optical limiting in the red-NIR range with soluble two-photon absorbing molecules[END_REF] structures. However, it has been realized lately that two-dimensional, [START_REF] Drobizhev | Drastic enhancement of two-photon absorption in porphyrins associated with symmetrical electron-accepting substitution[END_REF][START_REF] Drobizhev | Resonance enhancement of two-photon absorption in porphyrins[END_REF][START_REF] Pyun | Synthesis and twophoton absorption property of phenylacetylene macrocycles[END_REF] branched [START_REF] Joshi | Energy transfer coupling of two-photon absorption and reverse saturable absorption for enhanced optical power limiting[END_REF][START_REF] Chung | Cooperative Enhancement of Two-Photon Absorption in Multi-branched Structures[END_REF][START_REF] He | Two-Photon Excitation and Optical Spatial-Profile Reshaping via a Nonlinear Absorbing Medium[END_REF][START_REF] Chung | Two-Photon Absorption and Excited-State Energy-Transfer Properties of a New Multibranched Molecule[END_REF][START_REF] Cho | Two Photon Absorption Properties of 1,3,5-Tricyano-2,4,6-tris(styryl)benzene Derivatives[END_REF][START_REF] Beljonne | Role of dimensionality on the two-photon absorption response of conjugated molecules: the case of octupolar compounds[END_REF][START_REF] Yoo | Bis-1,4(p-diarylaminostyryl)-2,5dicyanobenzene Derivatives with Large Two-Photon Absorption Cross-Sections[END_REF][START_REF] Abbotto | Novel heteroaromatic-based multi-branched dyes with enhanced two-photon absorption activity[END_REF][START_REF] Mongin | Synthesis and Two-Photon Absorption of Triphenylbenzene-Cored Dendritic Chromophores[END_REF][START_REF] Mongin | Synthesis and two-photon absorption of highly soluble three-branched fluorenylene-vinylene derivatives[END_REF][START_REF] Porrès | Enhanced Two-Photon Absorption with Novel Octupolar Propeller-Shaped Fluorophores Derived from Triphenylamine[END_REF][START_REF] Porrès | Two-Photon Absorption and Fluorescence in Nanoscale Multipolar Chromophores: Effect of dimensionality and charge-symmetry[END_REF][START_REF] Porrès | Two-Photon Absorption and Fluorescence with Quadrupolar and Branched Chromophores. Effect of Structure and Branching[END_REF] and dendritic [START_REF] Mongin | Synthesis and Two-Photon Absorption of Triphenylbenzene-Cored Dendritic Chromophores[END_REF][START_REF] Porrès | Two-Photon Absorption and Fluorescence in Nanoscale Multipolar Chromophores: Effect of dimensionality and charge-symmetry[END_REF][START_REF] Adronov | Novel Two-Photon Absorbing Dendritic Structures[END_REF][START_REF] Drobizhev | Dendrimer molecules with record large two-photon absorption cross section[END_REF][START_REF] Drobizhev | Strong Cooperative Enhancement of Two-Photon Absorption in Dendrimers[END_REF][START_REF] Spangler | New organic dendrimers with greatly enhanced multi-photon absorption for photonics applications[END_REF] structures could lead to highly effective multiphoton absorption. In this context, we have been interested in the elucidation of the role of dimensionality and charge-symmetry on molecular TPA. We have investigated a series of structurally-related chromophores of different symmetry (dipolar, quadrupolar, pseudo-dipolar, octupolar, dendritic...) and shape (rod-like, propeller-shaped, Y-shaped…). Their design is based on the functionalization of semirigid linear or branched conjugated backbones with electro-active (i.e. electron-releasing or electron-withdrawing) peripheral and core/node groups (Fig. 1). In addition to investigating structure-property relationships, our aim was to identify appropriate structural combinations to optimize the TPA/transparency/solubility/photostability trade-offs. The series includes quadrupolar molecules (Fig. 2) built from the symmetrical functionalization of a biphenyl core that is either free (Q 1 ,Q 2 ) or planarized when using dinonylfluorene (Q 3 -Q 8 ). Quadrupolar chromophores bearing either electron-releasing (Q 1 -Q 4 ) or electron-withdrawing (Q 5 -Q 8 ) peripheral groups were investigated in order to assess the role of both end-groups on molecular two-photon absorptivity (Fig. 2). Arylene-vinylene and phenylene-ethynylene rods were used as connecting spacers between the core and the electroactive end-groups to ensure effective electronic conjugation while tuning the nonlinearity/transparency range.

All compounds show excellent solubility in apolar or weakly polar solvents (typically higher than 300 g.L -1 ) due to the presence of the long alkyl chains on the core and/or the end-groups. This is of particular interest for optical limiting applications for which high concentrations are required. We also note that the linear nonyl chains (n-C 9 H 19 ) grafted on the fluorenyl core not only provide excellent solubility but also hamper tight π-stacking between chromophores in concentrated solution. Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937 Branched structures TPB 1 -TPB 3 where 1,3,5-triphenylbenzene (TPB) units (i.e. a trigonal analogue of the biphenyl core) are used as trigonal cores and nodes moieties (Fig. 3) have been studied in order to investigate branching and charge symmetry effects. In addition a branched structure TPA(Q 4 ) built from the assembly of three chromophores Q 4 via a common donating nitrogen has been investigated (Fig. 3).

METHODOLOGY

Optical measurements

UV/VIS spectra were recorded on a Jasco V-570 spectrophotometer.

Fluorescence measurements were performed at room temperature in diluted solutions (ca. 10 -6 M) using a PTI spectrometer (LPS-220B) in photon counting mode. Emission spectra were obtained, for each compound, at λ ex = λ max (abs) with Aλ ex = 0.1 to minimize internal absorption. Fluorescence quantum yields were measured on degassed samples at room temperature; fluorescein in 0.1 N NaOH was used as a standard (Φ = 0.90 at λ ex = 470 nm) and refractive index correction was performed. [START_REF] Demas | The Measurement of Photoluminescence Quantum Yields. A Review[END_REF] The lifetime values were obtained from the reconvolution fit analysis of the decay profiles with the F900 analysis software and the fitting results were judged by the reduced chi-square value.

Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937

TPEF measurements

The TPA cross-sections of the quadrupolar molecules were determined by investigating their TPEF properties. This procedure provides the TPEF action cross-sections σ 2 Φ from which we can derive the corresponding σ 2 values. The TPEF excitation spectra of quadrupolar molecules were measured following the experimental protocol described in detail by Xu and Webb, [START_REF] Xu | Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm[END_REF] using a mode-locked Ti:sapphire laser operating between 700 and 990 nm and delivering 80 fs pulses at 80 MHz. TPEF measurements were calibrated relative to the absolute TPEF action cross-section determined by Xu and Webb for fluorescein in water (pH = 11) in the 690-1050 nm range. [START_REF] Xu | Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm[END_REF][START_REF] Albota | Two-photon fluorescence excitation cross sections of biomolecular probes from 690 to 960 nm[END_REF] The quadratic dependence of the fluorescence intensity on the excitation intensity was verified for every data point, indicating that the measurements were carried out in intensity regimes in which saturation or photodegradation do not occur. The experimental uncertainty is estimated to ± 10%.

Calculations

Calculations and especially geometry optimization were conducted using the Gaussian 98 package [START_REF] Frisch | Gaussian 98, Revision A.11[END_REF] with the B3LYP [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] density functional and the 6-31G* basis set. For the sake of simplicity, calculations have been conducted on chromophores where the alkyl solubilizing chains have been replaced by methyl substituents. Illustrations have been obtained with MOLEKEL. 44

RESULTS AND DISCUSSION

The photophysical data of the chromophores are collected in Table 1.

λ cut-off a (nm) τ b (ns) λ TPA (nm) σ2 c (GM) N d σ 2 /N

Structure-property relationships in quadrupoles

End-groups' effect

As noted from Table 1 and illustrated in Fig. 4 (Q 3 , Q 8 ) and Fig. 5 (Q 4 , Q 5 ), push-push chromophores always show larger TPA cross-sections in the NIR region than corresponding pull-pull derivatives, in correlation with a definite Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937 red shift of the one-photon absorption spectra. Push-push derivatives thus offer interesting potentialities for optical limitation in the red-near IR region. Indeed numerical simulations performed with compounds Q 1 and Q 2 (which also exhibit an intense excited-state absorption band overlapping the two-photon absorption band in the red-NIR region) demonstrate a strong nonlinear absorption behavior, suitable for optical limiting of nanosecond pulses (with threshold values down to 1.5 Í 10 -2 J cm -2 for 0.55 ns pulses). [START_REF] Silly | Optical limiting in the red-NIR range with soluble two-photon absorbing molecules[END_REF] Comparison of pull-pull derivatives Q 5 -Q 7 (Fig. 6 and Table 1) indicates that increasing the electronwithdrawing strength of the end-groups (CHO: σ p = 0.42, CN: σ p = 0.66, SO 2 Me: σ p = 0.72) [START_REF] Hansch | A Survey of Hammett Substituent Constants and Resonance and Field Parameters[END_REF] results in a decrease of the TPA cross-section in the NIR region. Since pull-pull compounds are blue-shifted as compared to push-push derivatives, pull-pull derivatives offer promising alternative for optical limiting in the visible blue region.

Core effect

Comparison of push-push derivatives built from different core moieties and bearing similar end-groups demonstrates that the nature of conjugated core significantly influences the TPA spectra. From Fig. 7 (left) and Table 1, we observe that replacing the twisted biphenyl core (BP) by the planarized fluorene unit (Fl) results in both a red shift and a significant enhancement of the TPA cross-section close to the red region. In addition we observe that chromophore Q 3 shows a low energy TPA maximum at 774 nm (i.e. at 2λ max OPA ). This indicates that the lowest excited state is both one-photon and two-photon allowed in the case of chromophore Q 3 . Such phenomenon is not observed in the case of chromophore Q 1 and is most probably related to the slight loss of symmetry caused by the fluorenyl moiety as compared to the symmetrical biphenyl unit. Such effect is responsible for the much more pronounced TPA efficiency in the NIR region (at λ> 800 nm) as illustrated in Fig. 7 (right).

Linker effect

As observed from the comparison of homologous push-push derivatives Q 1 and Q 2 , replacing a phenyleneethynylene linker (PE) by a phenylene-vinylene one (PV) leads to larger TPA cross-sections in the 720-900 nm range (Fig. 8), in relation with a bathochromic shift of the TPA band. This effect is also visible when comparing the homologous PE and PV pull-pull derivatives Q 8 and Q 7 (Fig. 9). However, for push-push derivatives, the TPA crosssection become comparable close the red region (see for instance compounds Q 3 and Q 4 in Table 1). Moreover, the use of PE linkers lead to higher transparency in the visible range, as well as improved photostability (due to the lack of photoisomerization), as indicated by the absence of photodegradation either upon pulsed-laser or prolonged lamp irradiation. [START_REF] Mongin | Synthesis and Photophysical Properties of New Conjugated Fluorophores Designed for Two-Photon-Excited Fluorescence[END_REF][START_REF] Porrès | Enhanced Two-Photon Absorption with Novel Octupolar Propeller-Shaped Fluorophores Derived from Triphenylamine[END_REF] In view of their improved nonlinearity/transparency/stability trade-off, push-push derivatives with PE linkers thus represent interesting candidates for optical power limitation in the visible region.

Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937

Branching effect

Recently following pioneering work by P. N. Prasad and coll., several experimental and theoretical [START_REF] Macak | Electronic and vibronic contributions to two-photon absorption of molecules with multi-branched structures[END_REF] studies have focused on the effect of branching on TPA. These studies lead to different outcomes: cooperative enhancement, [START_REF] Chung | Cooperative Enhancement of Two-Photon Absorption in Multi-branched Structures[END_REF][START_REF] Abbotto | Novel heteroaromatic-based multi-branched dyes with enhanced two-photon absorption activity[END_REF][START_REF] Drobizhev | Dendrimer molecules with record large two-photon absorption cross section[END_REF][START_REF] Drobizhev | Strong Cooperative Enhancement of Two-Photon Absorption in Dendrimers[END_REF] , additive behavior [START_REF] Chung | Two-Photon Absorption and Excited-State Energy-Transfer Properties of a New Multibranched Molecule[END_REF][START_REF] Adronov | Novel Two-Photon Absorbing Dendritic Structures[END_REF] or even decrease of TPA. [START_REF] Chung | Cooperative Enhancement of Two-Photon Absorption in Multi-branched Structures[END_REF] It should be emphasized that these results were obtained, in most cases, at one single wavelength, which might explain the different conclusions. In that context, we have been interested in investigating the wavelength dependence of the branching effect in various types of multipolar branched systems. Our goal was both to identify the origin of the discrepancies, and to assess the influence of charge symmetry. Indeed, a number of factors influence the TPA magnitude, such as electronic delocalization and intramolecular charge transfer phenomena, symmetry and dimensionality. A correlation between the square of the number of π-electrons in the conjugated systems (N) and the maximum TPA that can be reached has been reported recently. [START_REF] Kuzyk | Fundamental limits on two-photon absorption cross sections[END_REF]

Branching of quadrupoles

In this perspective, comparison of the TPA spectra of quadrupolar chromophores Q 4 and its three-branched analogue TPA(Q 4 ) is quite informative. First of all, chromophore TPA(Q 4 ) exhibits a larger normalized maximum TPA cross-sections (σ 2 /N 2 ) than its quadrupolar branch Q 4 (Table 1) and one of the highest measured in the femtosecond regime for a branched structure. [START_REF] Abbotto | Novel heteroaromatic-based multi-branched dyes with enhanced two-photon absorption activity[END_REF] In addition it maintains similar excited-state lifetime. These features are important for optical power limiting in the nanosecond regime since excited-state absorption subsequent to two-photon excitation is known to be responsible for the strongly nonlinear absorption behavior of quadrupolar chromophores. [START_REF] Perry | Two-photon and higher-order absorptions and optical limiting properties of bis-donor substituted conjugated organic chromophores[END_REF][START_REF] Silly | Optical limiting in the red-NIR range with soluble two-photon absorbing molecules[END_REF] Fig. 10. Effect of branching of quadrupoles on TPA.

In addition, the ratio between the TPA cross-sections of quadrupolar chromophore Q 4 and its three-branched derivative TPA(Q 4 ) significantly depends on the wavelength (Fig. 10). At lower wavelength, the contribution of the three quadrupolar branches to the TPA amplitude of TPA(Q 4 ) seems roughly additive. The ratio significantly increases at higher wavelength, branched chromophore TPA(Q 4 ) overcoming chromophore Q 4 . This effect is correlated with a definite TPA spectral broadening further to the NIR region where new TPA bands appear to emerge. Such phenomenon might be originating from an electronic coupling between the quadrupolar branches via the TPA core. In that respect, we note from Table 1 that the one-photon absorption band of TPA(Q 4 ) is red-shifted with respect to that of chromophore Q 4 , suggesting that such coupling takes place.

Influence of charge symmetry and branched character

The series of structurally-related multipolar chromophores -Q 2 (quadrupolar), TPB 1 (pseudo-dipolar), TPB 2 (octupolar) and TPB 3 (dendritic) -built from the (linear) biphenyl or (trigonal) triphenylbenzene core/nodes was examined in order to investigate both the role of branching and charge symmetry. HOMO-LUMO calculations reveal that multipolar derivatives show pronounced intramolecular charge transfer phenomena upon excitation (Fig. 111213). A charge density shift from the electron-releasing peripheral groups to the biphenyl (Q 2 ) or triphenylbenzene (TPB 2 ) core is observed both in 1-D quadrupolar chromophore Q 2 and in 2-D octupolar chromophore TPB 2 . For Y-shaped pseudo-Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937 dipolar chromophore TPB 1 , a directional intramolecular charge transfer from the donating end-groups towards the acceptor moiety is observed even though the donating and accepting moieties are not conjugated. Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937

Interestingly, we observe from Table 1 and Fig. 14 that increasing the branched character leads to improved transparency: a clear blue-shift of the absorption band is observed with increasing number of branches in the chromophores. As a result branched chromophores TPB 1 -TPB 3 retain wide transparency in the visible region. We observe from Fig. 15 that the 1-D quadrupolar chromophore Q 2 shows the highest TPA cross-section close to the visible red while all 2-D branched structures become more efficient two-photon absorbers at λ > 780 nm. Indeed the branched structures show broader and red-shifted TPA band in the NIR region. Hence, the branched-structures exhibit both improved transparency in the visible region (as a result of a blue-shift of the OPA bands) and superior TPA efficiency further to the NIR region as compared their 1D-quadrupolar analogue (as a result of a red-shift of the TPA bands). For instance, the dendritic chromophore TPB 3 shows a three times larger TPA cross-section at 800 nm than chromophore Q 2 while being more transparent (Table 1). Hence increasing the branched character in multipolar structures built from the triphenylbenzene core seems to be a promising route for improving the TPA-transparency tradeoff in the context of broadband optical limitation in the NIR region. To compare the efficiency of the various branched structure in view of optical power limiting, it is helpful to consider the normalized TPA molecular efficiency σ 2 /MW (Fig. 15 right). Interestingly, in the NIR region both the twobranched pseudo-dipolar chromophore TPB 1 and the three-branched octupolar chromophore TPB 2 appear as the best candidates in terms of normalized TPA-transparency trade-off. On the other hand, comparison of the normalized TPA efficiency of octupolar chromophore TPB 2 and of its second-generation dendritic analogue TPB 3 shows that in that particular case, increased branching character does not bring a net gain in normalized TPA efficiency (Fig. 15). This is most likely related to more confined intramolecular charge transfer phenomena in dendritic structures like TPB 3 , as compared to pseudo-dipolar and octupolar structures (TPB 1 and TPB 2 ).

Proc. SPIE 5516, Nonlinear Optical Transmission and Multiphoton Processes in Organics II, (15 October 2004); doi: 10.1117/12.559937

CONCLUSION

The present work shows that modulation of the nonlinear absorptivity/transparency/photostability trade-off in 1D-quadupolar structures can be achieved by playing on both core and spacer structures. In particular, the replacement of the double bond by a triple bond in the conjugated spacers in push-push derivatives yields optimized TPA/transparency/photostability features for optical power limiting in the visible red region. In contrast, pull-pull derivatives are good candidates for optical power limiting in the visible blue. Both push-push and pull-pull quadrupolar chromophores also display very high solubility in apolar or weakly polar solvents. Such behavior is particularly attractive in the context of the search for optimizing multiphoton absorbers for broadband optical power limitation. Indeed nonlinear transmission experiments in the visible region conducted in solution in the nanosecond regime yield similar structure-TPA relationships as those derived from TPEF measurements in the NIR, and indicate that quadrupoles Q 1 -Q 4 show pronounced optical limiting properties. 48 The present study also demonstrates that the branching strategy provides a useful route for TPA enhancement and/or spectral broadening in the NIR region. In addition, by playing on the nature of the core/nodes and the charge symmetry, the transparency/nonlinearity trade-off can be tuned via control of the intramolecular charge transfer phenomena.

Fig. 1 .

 1 Fig. 1. Molecular engineering of multipolar chromophores for two-photon absorption and optical limitation.

Fig. 2 .

 2 Fig. 2. Series of quadrupolar chromophores investigated in the present work.

Fig. 3 .

 3 Fig.3. Series of structurally-related branched chromophores built from triphenylbenzene (TPB) and triphenylamine (TPA) nodes.

Fig. 4 .

 4 Fig. 4. TPA spectra of fluorophores Q 3 and Q 8 in toluene. Fig. 5. TPA spectra of fluorophores Q 4 and Q 5 in toluene.

Fig. 6 .

 6 Fig. 6. TPA spectra of fluorophores Q 5 -Q 7 in toluene.

Fig. 7 .

 7 Fig. 7. TPA spectra of fluorophores Q 1 and Q 3 in toluene.

Fig. 8 .

 8 Fig. 8. TPA spectra of fluorophores Q 1 -Q 2 in toluene. Fig. 9. TPA spectra of fluorophores Q 7 -Q 8 in toluene.

Fig. 12 .

 12 Fig. 11. Frontier orbitals of Q 2 .

Fig. 13 .

 13 Fig.13. Frontier orbitals of TPB 2 .

Fig. 14 .

 14 Fig. 14. Normalized absorption spectra of Q 2 and TPB 1 -TPB 3 in toluene.

Fig. 15 .

 15 Fig. 15. Effect of branching on TPA in multipolar structures built from TPB core/nodes.

Q 1 Q 2 Q 3 Q 4

  [START_REF] Ranger | New Base-Doped Polyfluorene Derivatives[END_REF]

	Hex 2 N			NHex 2	OHC			CHO
						Non	Non
						Q 5
	Hex 2 N			NHex 2
					NC			CN
						Non	Non
						Q 6
	Hex 2 N	Non	Non	NHex 2	MeO 2 S	Non	Non	SO 2 Me
						Q 7
	Bu 2 N	Non	Non	NBu 2	OctO 2 S	Non	Non	SO 2 Oct
						Q 8

Table 1 .

 1 One and two-photon absorption properties of multipolar chromophores

	Compd	X	Connector Core/node	OPA (nm) λ max

ACKNOWLEDGEMENTS

This work was supported in part by the Centre National de la Recherche Scientifique and Rennes Métropole. M. C. received a fellowship from the Direction Générale pour l'Armement and L. P. a fellowship from the Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche. We also wish to thank M. H. V. Werts for important help in TPEF experiments. Calculations were supported by the "Centre Informatique National de l'Enseignement Supérieur" (CINES-France).


Sylverin Kemmoé-Tchomté
email: sylverin.kemmoe_tchomte@udamail.fr

Damien Lamy
email: lamy@isima.fr

Nikolay Tchernev
email: nikolay.tchernev@udamail.fr

Job-shop like manufacturing system with time dependent energy threshold and operations with peak consumption

Keywords: job-shop, energy consumption, energy threshold, linear programing

In this study the Job-shop scheduling problem with energy considerations is considered. At each moment of the schedule an energy threshold must not be exceeded. This energy threshold is not fixed all along the schedule and can vary. The variation of energy is handled by inclusion of dummy operations. Furthermore, the operations that must be scheduled have a power profile presenting a high energy consumption (peak) at the beginning and a lower consumption after the peak's end. A mathematical formulation of the problem is proposed. This model is experimented on a short example with the CPLEX 12.4 solver. The schedules obtained show the relevance of the model. This study shows that new approaches for scheduling are no longer avoidable and that it is possible for enterprises to schedule efficiently their tasks according to energy constraints.

Introduction

A linear model is proposed in this paper which goal is to extend a previous work [START_REF] Kemmoe | A Job-shop with an Energy Threshold Issue Considering Operations with Consumption Peaks[END_REF] concerning the scheduling in a job-shop like manufacturing environment with an energy threshold which must not be exceeded. Operations presenting two distinct energy consumptions are considered as follows: a peak consumption at the beginning of the process and a nominal consumption after the peak's end. The previously proposed linear model [START_REF] Kemmoe | A Job-shop with an Energy Threshold Issue Considering Operations with Consumption Peaks[END_REF] is extended in order to manage variations in the allowed energy threshold. Thus, the objective is to find the best feasible schedule of the problem where operations need electricity in order to be realized and where the instantly usable energy is constrained and varies with time. The model of the problem could have many applications especially in scheduling operations efficiently according to price variations during given periods, or avoid exceeding predefined consumption peaks that have been negotiated with the electricity supplier. The rest of the paper is as follows. In the next section a literature review of articles including energy constraints is proposed. In the third section, the assumptions made in this study are presented. The fourth and fifth sections introduce a linear program modelling the problem and experiment results. Finally we conclude and give some directions for future research.

Related Work

In the literature, industrial problems such as minimizing the total completion time (makespan), the cost, and other objective functions have been widely studied. Although the energy efficiency in manufacturing is well-addressed in the literature (see for survey [START_REF] Gunasekaran | Sustainability of manufacturing and services: Investigations for research and applications[END_REF] only a few works addressed the energy consumption as an important constraint in scheduling [START_REF] Trentesaux | Sustainability in Manufacturing Operations Scheduling: Stakes, Approaches and Trends[END_REF]. However, several papers have spread on this subject concerning the "Green Manufacturing" these past years and a non-exhaustive review is proposed in this section. [START_REF] Mouzon | Operational methods for minimization of energy consumption of manufacturing equipment[END_REF] proposed several methods and operational tools to minimize the energy consumption of factories. They present a mathematical formulation aiming at minimizing the total completion time of a set of operations while minimizing the total energy consumption. Their model handles the different states a machine can be in: idle, running, switch ON or OFF. [START_REF] Salido | Energy-aware Parameters in Job-shop Scheduling Problems[END_REF] showed that a more energy efficient system is more robust and thus less sensitive to breakdowns. They worked on the correlation between makespan, energy and robustness. By inclusion of variable speeds in the operation processes, a machine which is processing a task quickly will consume more energy but the treatment time will be reduced. Thus if a breakdown occur, the lost time could be caught up by increasing processing speed. The model of [START_REF] Fang | A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction[END_REF] consists in minimizing the carbon footprint, the makespan and the consumption peaks in a Flow-shop. In their work [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] authors proposed a solution which consists in avoiding consumption peaks on a production system, modelled as a Flexible Flow Shop. They use an Energy Aware Scheduling (EAS) on the existing schedule obtained with an APS (Advanced Planning and Scheduling). They finally note the fact that their model could be better, integrating variability of costs and energy need of machines which is constant in their study. [START_REF] Luo | Hybrid flow shop scheduling considering machine electricity consumption cost[END_REF] took into account the variable prices of electricity during a day, including Time-of-Use (TOU) rates in a Flexible Flow-shop. It is observed that a few work have been done concerning the Job-shop with energy constraints and thus they proposed a Job-shop where both the total energy consumption and the total tardiness are minimized.

In a previous work [START_REF] Kemmoe | A Job-shop with an Energy Threshold Issue Considering Operations with Consumption Peaks[END_REF], a linear model for the Job-shop with Energy Consumption Threshold (JS-ECT) is proposed where each operation has two different energy consumption: a high energy consumption at the beginning of the operation, called a peak consumption, and a lower energy consumption for the rest of the operation. In this mathematical formulation, the energy threshold is constant during the schedule. Thus, an improved linear program where this energy threshold could change over time is proposed. In the next section the assumptions used in this paper concerning the Jobshop with a Variable Energy Consumption Threshold (JS-VECT) where the operations to be scheduled present an electricity consumption peak at their start are presented.

Assumptions Used

Physical Assumptions

This study is based on the Job-shop theoretical model which is known to be a NP-Hard problem (see for review [START_REF] Jain | Deterministic Job-shop scheduling: Past, present and future[END_REF]). The Job-shop problem consists in scheduling a set of n jobs that have to be sequenced on m machines. Each job involves a set of operations, which must be processed in a pre-determined order. Each operation has to be processed on a given machine during a processing time and no pre-emption is allowed. A commonly used objective in Job-shop problem is the minimization of completion time of all jobs (makespan) by managing machine disjunctions.

Energy Assumptions

While doing the literature review concerning energy optimization on production systems, two things appeared. First, the operations are generally represented with constant energy consumption as shown in [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] where operations have a unitary consumption. However, it can be seen in the literature that machine operations have complex energy behavior where most of the time operations present an energy consumption peak at the start of processing as shown in the work of [START_REF] Kellens | Energy and Resource Efficiency of Laser Cutting Processes[END_REF] In the Fig. 1, it can be easily understood that considering a constant energy consumption for the operations imply a possible loss of time while scheduling since some operations cannot be planed earlier because of an operation consuming more energy than really needed. Considering this assumption, it has been chosen to divide the operations into two sub-operations: one concerning the high energy consumption peak, and the other concerning the operating energy consumption. Finally, a variable energy threshold that must never be exceeded is introduced (i.e.: from 0 to 50 time units, 70kW are allowed; from 50 to 80, 50kW are allowed; etc …). An example of a schedule including a varying energy threshold and operations considering peak consumption is given in Fig. 2 Energy Threshold starts at 60

J 1 ,M 1 J 2 ,M 1 J 1 ,M 2

Fig. 2. A Gantt chart of a schedule involving energy threshold variations

In Fig. 2, two jobs must be processed: Job J1, which routing pass through Machine M1 and M2, and job J2 passing through M2 and M1. Vertical dotted lines represent the separation between peak consumption of operations and nominal consumptions. In this example, second operation of J2 cannot be started earlier because of a reduction in the available energy threshold. This variation will be modelled with use of dummy operations which starting dates correspond to the moment of energy threshold change and energy consumption equal to the variation (i.e.: between threshold valued 60 and threshold valued 25, a dummy operation will need 35 energy units).

In this section the different energy assumptions used in this study are presented. In the next section the mathematical formalization of the JS-VECT is introduced. : energy required for processing the operation i; Emax : maximum energy that must never be;

Variables

Cmax : completion date of all operations also referred as the makespan of the schedule; si : starting time of sub-operation i; xi,j : binary variable equal to 1 if sub-operation i is realized before sub-operation j and equal to 0 otherwise; yi,j : binary variable equal to 1 if there is a non-null energy flow from suboperation i to the sub-operation j and equal to 0 otherwise; j , i  : denotes the number of energy units transferred between entities of the system (could be real or dummy operations);

Linear Formulation

max C Min (1) V i , C p s max i i     ( 2
)
k i l k j i i , l k , j , k i , O O , O O , l k , j i / V l , k , j , i , x x             1 ( 3
)
j i i i j J J , j i / V ) j , i ( , p s s       (4) j i i i j O O , j i / V ) j , i ( , p s s       (5) 1 2 0 2           ) , j mod( , ) , i mod( , , O O / V j , i , H p Hx s s j i j i i j , i i j   (6) max V j E j ,     0  (7) j i / V j , E j V i j , i          (8) j i / V i , E i V j j , i          (9) j i j i O O , j i / V ) j , i ( ), E , E min( j , i       (10) V V k , T s V k k \      (11) j i / V j , i , y . H j , i j , i       (12) j i / V i , y j , i j , i       (13) j i i j , i i j J J / V ) j , i ( , H p Hy s s         (14) j i i , j J J , j i / V ) j , i ( ,      0  (15)
The first line (1) refers to the objective of the problem: minimizing the completion time of all operations (makespan). Constraints [START_REF] Gunasekaran | Sustainability of manufacturing and services: Investigations for research and applications[END_REF] give the expression of the makespan. Constraints (3) represent the precedencies for sub-operations occurring on the same machines (i.e.: whether the first sub-operation of a global operation scheduled before a second sub-operation on another global operation, or vice versa). Constraints (4) define the starting dates of operations according to job's sequence. Constraints [START_REF] Salido | Energy-aware Parameters in Job-shop Scheduling Problems[END_REF] ensure that, if i and j are two sub-operations referring to the same global operations, then j is processed directly after the end of the sub-operation i. Constraints (6) adjust the starting dates of operations that belong to different jobs but need the same machine. Constraint [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] avoids to exceed the maximal energy threshold when processing the operations. Constraints [START_REF] Luo | Hybrid flow shop scheduling considering machine electricity consumption cost[END_REF] ensure that the sum of energy flowing from dummy operations, sub-operations and energy threshold is equal to the energy needed for the sub-operation j. Constraints [START_REF] Jain | Deterministic Job-shop scheduling: Past, present and future[END_REF] ensure that the sum of energy flowing from dummy operations or the sub-operation i to the other ones never exceeds the energy that was used for its processing. Constraints [START_REF] Kellens | Energy and Resource Efficiency of Laser Cutting Processes[END_REF] is a cut corresponding to a flow of energy between first and second sub-operation of the same global operation. Constraints (11) fix the starting dates of the dummy operations that represent the variation of the energy threshold over time. Constraints (12) ensure that if there is an energy flow from i to j then yi,j =1. If yi,j=0 then no flow is possible from i to j. Constraints (13) stipulate that if there is no need of a flow from i to j (φi,j=0), then necessarily yi,j = 0, however if yi,j=1 then necessarily φi,j>0. Constraints (14) adjust the starting dates of sub-operations which need to wait before the end of previous operations in order to not exceed the energy threshold available at the moment. Constraints (15) stipulate that no flow is possible between two sub-operations i and j, if i and j belong to the same job and if i is processed before j.

Results

The validity of the above linear program has been tested on a set of small examples (including the one presented in Fig. 2) randomly generated. The linear model is solved using CPLEX 12.4 solver. In Fig. 3 is presented the Gantt diagram of a problem without any energy consideration and the Gantt diagram of the same problem extended with energy consumptions and an energy threshold varying over time. In this figure, it is also plotted the energy consumed by each operation to show the impact of the threshold on the schedule. On Fig. 3 it can be stressed that third operation of J3 is the most consuming one and can only be scheduled during a given time-window, thus all its predecessors on the job must be scheduled before. The other operations start only if enough energy is available. Finally, it can be clearly seen that two things can affect the schedule while considering a variable energy threshold: the moment energy threshold change and the value of allowed energy after a change. According to chosen values it is possible that no schedule will fit the energy threshold profile.

Conclusion and Future Work

In this study the problem of the Job-shop with a Variable Energy Threshold Constraint (JS-VECT) is addressed. The linear model considers operations that have two types of energy consumption: a huge energy consumption, and a nominal energy. Furthermore, the available energy at each moment of the schedule could change over time. This is modelled by inclusion of dummy operations which have a predefined energy consumption and whom starting dates are fixed. The linear model provides exact solutions for small scale instances, but is quickly overtaken with the increasing of jobs and machines. In the future larger scale instances for the problem will be treated with the use of a metaheuristic. Several perspectives appear as future works. Indeed, the energy threshold is considered as a parameter in this study, and it could be really interesting to consider it a variable to be calculated thus leading to a bi-criteria problem where the objective is to display a Pareto graphic of the possible solutions.

Another perspective is to consider due dates since starting dates of operations are modified in order to respect the energy threshold, and with them the ending dates of operations or jobs. Finally, it could be interesting to add other objectives such as minimizing the cost of the production by inclusion of time-of-use considerations, or minimizing the total energy needed in the planning.

Fig. 1 .

 1 Fig. 1.Power profile of a machine and its representations[START_REF] Kemmoe | A Job-shop with an Energy Threshold Issue Considering Operations with Consumption Peaks[END_REF]

Fig. 3 .

 3 Fig. 3. Impact of the energy threshold on schedules

  .

	Energy
	Threshold
		Energy Threshold
		is increased to 35
	Energy Threshold
	fall down to 25	Energy Threshold
		fall down to 17
	J 2 ,M 2

Acknowledgments. This work was financially supported by the French Public Investment Bank (BPI) and granted by the ECOTHER project.


Jacky Even
email: jacky.even@insa-rennes.fr

Daniel Sapori

Laurent Pedesseau

Alain Rolland

Mikael Kepenekian

Roberto Robles

Shijian Wang

Yong Huang

Alexandre Beck

Olivier Durand

C Katan

Theoretical insights into multibandgap hybrid perovskites for photovoltaic applications

Keywords: hybrid perovskite, solar cell, rashba, tandem, silicon, dielectric

This paper reviews some of the recent theoretical investigations on the Rashba Dresselhaus spin effects and dielectric properties of CH 3 NH 3 PbI 3 hybrid perovskites and CsPbI 3 all-inorganic perovskites using Density functional theory. The spin vectors rotate in the non-centrosymmetric P4mm tetragonal phase, respectively clockwise and counterclockwise, in a manner that is characteristic of a pure Rashba effect. The high frequency dielectric constants ε ∞ of MAPbI 3 and CsPbI 3 are similar as anticipated, since large differences are only expected at very low frequency where additional contributions from molecular reorientations show off for the hybrid compounds. A first simulation of a perovskite on silicon tandem cell, including a tunnel junction, is also investigated. Effect of halogen substitution (I/Br) is inspected, revealing limitations for short-circuit current and open-circuit voltage electrical characteristics.

INTRODUCTION

A scientific breakthrough for solar cells was achieved in the last three years using 3D Hybrid Organic Perovskites (HOP) with the chemical formulae MAMX [START_REF] Kojima | Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells[END_REF] , where MA is an organic cation CH 3 NH 3 + , X is a halogen atom (X=I, Br, Cl) and M a metal atom (M=Pb, Sn). The efficiency of hybrid perovskites solar cells rose rapidly from 3.8% in 2009 with DSSClike technologies to about 10% in 2012 using new concepts. These record values steeply increased to about 15% in 2013 thanks to new deposition techniques. At the end of 2014, optimized conversion efficiency amounts to 19.3% and then 20% in the last (2014) NREL efficiency chart. Over 21% efficiency was announced for a perovskite on silicon tandem cell at the HOPV Roma conference in May 2015. Clearly, understanding physical properties of operational HOPs and the design of novel devices with improved performances will greatly benefit from theoretical work. Prior to 2013, most theoretical studies either focused on layered HOP, purely inorganic 3D perovskites, and 3D HOP, but, in the latter case, missing inherent physical properties such as effect of spin-orbit coupling. In 2013, a few theoretical papers have appeared on 3D HOP in relation with the breakthrough in the field of photovoltaics, followed by a large number of papers in 2014. Significant progress has been made toward a better understanding of the unusual physical properties of this new class of semiconductors. This paper reviews some of the recent theoretical investigations using the SIESTA Density functional theory code that may contribute to gain better physical understanding of HOP materials, especially focusing on MAPbX3 compounds. Besides, a primary study of a perovskite on silicon tandem cell, including a tunnel junction, is presented, based on the SILVACO code dedicated to optoelectronic device simulation.

ELECTRONIC PROPERTIES AND RASHBA DRESSELHAUS SPIN INTERACTION

A giant spin-orbit coupling (SOC) operates on the conduction band (CB) of lead-based HOPs, leading to SOC splittings consistent with metal atomic energy level tables and to a spin-orbit split-off state at the bottom of the CB (figure 1). The optical transitions are related to a direct electronic band gap located at the R point of the Brillouin zone (BZ) of the reference high temperature Pm-3m centrosymmetric cubic phase. Besides SOC, time reversal symmetry (T-symmetry) is also important for spin effects, whether or not combined with inversion symmetry close to high symmetry points. For conjugated spinor states, T-symmetry yields the general conditions: E n ↑(k)=E n ↓(-k) and E n ↓(k)=E n ↑(-k). Inversion symmetry yields additional conditions: E n ↑(k)=E n ↑(-k) and E n ↓(k)=E n ↓(-k). Combining both symmetries leads to a double spin degeneracy, E n ↑(k)=E n ↓(k), across all the dispersion diagram within the BZ of the Pm-3m crystal structure. However, the room (high)-temperature crystal structure of 3D lead-based hybrid perovskites remains under debate. Recent single crystal X-ray diffraction experiments, performed on MAPbI 3 close to room temperature, support a noncentrosymmetric tetragonal space group (P4mm), which might lead at low temperature to another non-centrosymmetric I4cm tetragonal phase. A first effect of the Pm-3m to P4mm space group change is the folding of the CB and valence band (VB) states from the R-point to the A point (figure 1). Besides electronic band folding effect, the most important transformation of the diagram is due to atomic displacements. Lattice tetragonal strain leads to an increase of the band gap and a partial splitting of the CB when the SOC is neglected. When inversion symmetry is lost in the P4mm phase, the spin degeneracy condition En↑(k)=En↓(k) is lost as well for a general wave vector, except for special high symmetry points like the A-point (figure 1). In 3D HOPs, it has been shown that even a small P4mm and I4cm symmetry breaking can lead to a strong spinor splitting, since the SOC effect is giant, as compared to conventional semiconductors. Such a k-dependent band splitting, also designated under Rashba/Dresselhaus, Dresselhaus, and Rashba effect, was confirmed by many theoretical groups, but still deserves experimental evidence in HOP. Indeed, the electronic band diagram of the P4mm phase of CH 3 NH 3 PbI 3 close to the critical point A of the BZ exhibits a splitting of the spinor bands. This effect is larger in the tetragonal I4cm phase. A linear mixed Rashba-Dresselhaus effect close to a degenerate high symmetry point can be studied by considering the spin-dependent Hamiltonian: λ are constants related to the magnitudes of the Rashba and Dresselhaus terms, respectively. For the Amm2 space group, both terms coexist, but D λ vanishes by symmetry for the P4mm case. Thus, the wavefunctions eigenvectors can be computed for the P4mm bands close to the A-point as:

( ) ( ) x y x D x y x R RD k k k k H y y σ σ λ σ σ λ ) ) ) ) ) + + - = Proc. SPIE
ϑ π i r i k R ie e t m h 1 2 2 . = Ψ ±
where k t and θ are the wavevector and wavevector orientation angle, in the (k x ,k y ) plane. A classical representation of the the splitted spin states is afforded by the expectations < σ > vectors of the σ = (σ x , σ y , σ z ) vector of Pauli spin matrices for the two eigenvectors. Each < σ > spin vector is represented by a small arrow at a point defined by the corresponding eigen-energy and θ. Such a computation was performed for the CB and VB states of the P4mm phase of MAPbI 3 (figure 1). The spin vectors rotate respectively clockwise and counterclockwise on the inner and outer circles, in the typical manner of pure Rashba effect.

FIRST PRINCIPLES SIMULATION OF THE DIELECTRIC PROPERTIES

The dielectric constant is related to the response of the medium to local charges or external electric field, and thus plays an important role in the optoelectronic properties of hybrid perosvkites. For MAPbI 3 , it has been shown experimentally that the high frequency dielectric constant ε ∞ amounts to 6.5, and shows a smooth variation with temperature up to 20-30 in the medium frequency range (~90GHz). Comparison to purely inorganic 3D perovskites suggests that the difference between these two regimes stems from contributions related to polar optical phonons. Above the critical temperature Tc, the low frequency value (~1KHz) of ε increases, and reaches about 60 at room temperature. We attributed this to the thermal activation of the collective tumblings of MA cations. Recently, giant dielectric constants have been reported in the low frequency regime: in the order 1000 in the dark and an additional factor of 1000 upon illumination under 1 sun. This effect has been attributed to very slowly moving photoinduced carriers assisted by molecular rotations. Herein we apply a new DFT-based method, already tested for colloidal nanoplatelets of CdSe, to determine the high frequency dielectric constant ε ∞ of MAPbI 3 and CsPbI 3 . The first step consists in the determination of the electronic density induced by an external electric field ext E applied to slabs in a direction (z) perpendicular to the surface (figure 2). The induced polarization profile across the slab ) ( z p ind is thus computed from nanoscale average of the induced charge density profile. Subsequently, the dielectric constant profiles are computed from:

) ( ) ( 0 0 z p E E z ind ext ext - = ε ε ε (figure 2).
Proc. SPIE 9552, Carbon Nanotubes, 95520Z; doi:10.1117/12.2191953; http://dx.doi.org/10.1117/12.2191953 ε ∞ amounts to 5.5 in the central part of the MAPbI 3 slab, in reasonable agreement with the experimental value (6.5) for the bulk compound at room temperature. The MAPbI 3 slab was built from the low-temperature orthorhombic Pnma phase, since the dynamical disorder of the MA cations in the Pm-3m phase prevents from using atomic positions for C, N, and H atoms in the DFT simulation without implicit bias. A small anisotropy of the dielectric constant in the Pnma phase is thus expected and might contribute to the difference between the theoretical and experimental estimates. The high frequency dielectric constant ε ∞ for the CsPbI 3 compound is of the same order of magnitude (4.8). Indeed, it is related to a similar response of the electronic gas to the external field ext E . The two compounds should also exhibit similar values in the intermediate frequency range, where the ionic contribution yields an increase of the dielectric constant. However, at very low frequencies only the hybrid compound MAPbI 3 undergoes a further increase of the dielectric constant in relation with molecular dipoles reorientations.

DRIFT-DIFFUSION MODELLING OF PEROVSKITE ON SILICON TANDEM SOLAR CELLS WITH TUNNEL JUNCTIONS

Single HOP cells have been used to demonstrate over 20% solar to electricity conversion efficiency. One attractive solution to further enhance these performances is to stack multiple solar cell junctions, which combine absorbers with different electronic bandgaps to optimize solar light-harvesting. This concept has been recently tested in a tandem configuration, using either CIGS or silicon as a small band-gap material and the MAPbI 3 HOP as a large band gap material. In this paper, we present a numerical simulation of a two terminal perovskite-based tandem cell monolithically integrated on silicon (Si) and including a Si interband Tunnel Junction (TJ) to electrically interconnect the top and the bottom sub-cells (figure 3, left). The purpose of this preliminary study is to identify some key parameters of this architecture, as well as to explore the influence of HOP chemical engineering (figure 3, right). Figure 3 shows the device structure of the perovskite tandem solar cell monolithically integrated on a n-type silicon substrate. The structure consists in a 850 nm thick Hole Transport Material layer (HTM), a perovskite methyl ammonium MAPbX 3 lead tri-iodide (X=I) or tri-bromide (X=Br) absorbing layer, a 300 nm thick TiO 2 electron transport layer, a 2x20 nm thick Si(n ++ )/Si(p ++ ) tunnel junction, a 280 µm thick n-type Si substrate and a 100 nm thick heavily ndoped Si layer for the backside contact. The doping level for the silicon tunnel junction has been set to 10 20 cm -3 . This doping level ensures a nice electrical serial connection between the top perovskite cell and the bottom Si cell. The classical tunnel junction model implemented in the Silvaco Atlas device simulator was used. An identical single Si cell exhibits an efficiency of 15% under AM1.5 illumination, with a short-circuit current density J SC = 49.0 mAcm -2 and an open-circuit voltage V OC = 0.50 V. For the HOP materials, n-type and p-type carrier mobilities were set to 2 cm 2 V -1 s -1 in agreement with previous perovskite solar cell modeling. The single MAPbI 3 (MAPbBr 3 ) cell efficiency amounts to 13% (6%) under AM1.5 illumination, with a short-circuit current density J SC = 22.0 mAcm -2 (6.0 mAcm -2 ) and an open-circuit voltage V OC = 0.85 V (1.7V). By comparing the short-circuit current densities of single Si and perovskite cells, we can already conclude that the perovskite cell limits the current especially in the case of MAPbBr 3 HOP material. The tandem cell short circuit current limitation is expected to be compensated by an enhancement of the V oc for the whole structure. Figure 3 (right) shows that for the MAPbI 3 based tandem cell, the short circuit current is indeed limited by the perovskite part of the structure, however a large V oc (1.6V) is obtained. The tandem cell efficiency is thus increased to a value of 17%, larger than the values of 13% (MAPbI 3 ) and 15% (Si) for each single cell. On the other hand, the drastic reduction of the short-circuit current in the MAPbBr 3 based tandem cell (figure 3, right) with respect to a single Si solar cell, is not fully compensated by the very large value of V oc . The tandem cell efficiency in this configuration is indeed equal to 11%, and thus does not exhibit any improvement by comparison to a single Si solar cell.

Figure 1 .

 1 Figure 1. Electronic band structure of MAPbI3 in the P4mm crystal phase with (straight lines) and without(dotted lines) the spin-orbit coupling (SOC) interaction. The downward shift of the CB is indicated by three arrows. The spin vectors rotate, in the CB and the VB, respectively clockwise and counterclockwise on the inner and outer circles, in the typical manner of pure Rashba effect (DFT computation with the GGA functional and the SIESTA code).

Figure 2 .

 2 Figure 2. Nanoscale dielectric constant ε ∞ (z) as a function of the position along the stacking axis (z) for isolated slabs of MAPbI 3 (red dashed line) and CsPbI 3 (black straight line) in vacuum (DFT computation with the LDA functional and the SIESTA code) .

Figure 3 .

 3 Figure 3. (left) structure of a perovskite tandem solar cell monolithically integrated on n-doped silicon substrate. (right) J-V characteristics of the tandem cell including either the iodine MAPbI 3 (straight line) or the bromide MAPbBr 3 (dashed line) hybrid perovskite as an absorber.

  9552, Carbon Nanotubes, 95520Z; doi:10.1117/12.2191953; http://dx.doi.org/10.1117/12.2191953

	where R λ and D

Proc. SPIE 9552, Carbon Nanotubes, 95520Z; doi:10.1117/12.2191953; http://dx.doi.org/10.1117/12.2191953


Rengarajan Ragavan
email: rengarajan.ragavan@irisa.fr

Benjamin Barrois
email: benjamin.barrois@irisa.fr

Cedric Killian
email: cedric.killian@irisa.fr

Olivier Sentieys
email: olivier.sentieys@inria.fr

Pushing the Limits of Voltage Over-Scaling for Error-Resilient Applications

Voltage scaling has been used as a prominent technique to improve energy efficiency in digital systems, scaling down supply voltage effects in quadratic reduction in energy consumption of the system. Reducing supply voltage induces timing errors in the system that are corrected through additional error detection and correction circuits. In this paper we are proposing voltage over-scaling based approximate operators for applications that can tolerate errors. We characterize the basic arithmetic operators using different operating triads (combination of supply voltage, body-biasing scheme and clock frequency) to generate models for approximate operators. Error-resilient applications can be mapped with the generated approximate operator models to achieve optimum trade-off between energy efficiency and error margin. Based on the dynamic speculation technique, best possible operating triad is chosen at runtime based on the user definable error tolerance margin of the application. In our experiments in 28nm FDSOI, we achieve maximum energy efficiency of 89% for basic operators like 8-bit and 16-bit adders at the cost of 20% Bit Error Rate (ratio of faulty bits over total bits) by operating them in near-threshold regime.

I. INTRODUCTION

Scaling techniques have evolved and been explored in greater extent over the time to unlock the opportunities of higher energy efficiency by operating the transistors near or below the threshold voltage [START_REF] Kuroda | Variable supply-voltage scheme for lowpower high-speed cmos digital design[END_REF], [2]. After the advent of inherent low-leakage technologies like FDSOI (Fully Depleted Silicon On Insulator), near-threshold computing has gained more importance in VLSI due to improved resistance towards various variability effects like Random Dopant Fluctuations (RDF). Body-biasing technique in FDSOI provides greater flexibility to control trade-off between performance and energy efficiency based on the application need. In spite of the improvement in techniques and technology, near-threshold computing is still seen as no go zone for conventional subnanometer designs, due to timing errors introduced by the supply voltage scaling and need for additional hardware such as double-sampling registers [START_REF] Nicolaidis | Double-sampling design paradigma compendium of architectures[END_REF] to detect and correct such timing errors. There are techniques, like algorithmic noisetolerance based error correction approach proposed in [START_REF] Hegde | Soft digital signal processing[END_REF], which contain error correcting circuit along with computing circuit to handle errors due to drastic reduction in V dd .

Error-resilient computing is an emerging trend in VLSI, in which accuracy of the computing can be traded to improve the energy efficiency and to lower the silicon footprint of the design [START_REF] Han | Approximate computing: An emerging paradigm for energy-efficient design[END_REF]. Emerging classes of applications based on statistical and probabilistic algorithms used for video processing, image recognition, text and data mining, machine learning, have the inherent ability to tolerate hardware uncertainty. Such error-resilient applications that can live with errors, void the need for additional hardware to detect and correct errors. Also, error-resilient applications provide an opportunity to design approximate hardware to meet the computing needs with higher energy efficiency and tolerable accuracy loss. In error-resilient applications, approximations in computing can be introduced at different stages of computing and at varying granularity of the design. Using probabilistic techniques, computations can be classified as significant and non-significant at different design abstraction levels like algorithmic, architecture, and circuit levels. In this paper, we are targeting circuit-level approximation, which can further be extended to algorithmic level by using the proposed statistical model for approximate operators. This work makes the following contributions:

• We characterize energy efficiency and accuracy of different adder configurations using several operating triads (supply voltage, body-biasing voltage, clock period). • We formulate a framework to model the statistical behavior of arithmetic operators subjected to voltage over-scaling that can be used at algorithmic level. • Simulation results show that a maximum of 89% energy reduction is achieved at the tolerable output bit error rate of 20%.

The paper is organized as follows, Section II presents some of the existing approximate operators and modelling techniques. Characterization of arithmetic operators is discussed in Section III, followed by modelling of approximate operators in Section IV. Section V charts out the experimental setups and results, finally Section VI gives the conclusion and perspectives.

II. APPROXIMATION IN ARITHMETIC OPERATORS

Approximations in arithmetic operators are broadly classified based on the level at which approximations are introduced [START_REF] Han | Approximate computing: An emerging paradigm for energy-efficient design[END_REF]. This section reviews methods proposed in the literature at physical and architectural levels.

In [START_REF] Tziantzioulis | Lazy pipelines: Enhancing quality in approximate computing[END_REF], operators of a Functional Unit (FU) are characterized by analyzing relationship between V dd scaling and BER (Bit Error Rate, ratio of faulty output bits over total output bits). Based on the characterization, for every FU in the pipeline, one more imprecise FU running at lower V dd is designed. According to the application's need, selected set or all the FUs in the pipeline are accompanied by an imprecise counterpart in the design. Based on the user defined precision level, computations are performed either by precise or imprecise FU in the pipeline. Instead of duplicating every FU with an imprecise counterpart, a portion of the FU is replaced by imprecise or approximate design as discussed in [START_REF] Han | Approximate computing: An emerging paradigm for energy-efficient design[END_REF]. Fig. 1 shows this principle where least significant inputs are processed by approximate operator and most significant inputs are processed by accurate operator to increase the energy efficiency at the cost of acceptable accuracy loss. In [START_REF] Soares | Near-threshold computing for very wide frequency scaling: Approximate adders to rescue performance[END_REF] n-bit RCA adder based on near-threshold computing is proposed with two parts; k-bit LSBs approximated while (n -k) bits computed by precise RCA.

Another class of physical-level approximation is achieved by applying dynamic voltage and frequency scaling to an accurate operator, as depicted in Fig. 2. Due to the dynamic control of voltage and frequency, timing errors due to scaling can be controlled flexibly in terms of trade-off between accuracy and energy. This method is referred as Voltage Over-Scaling (VOS) in [START_REF] Tziantzioulis | Lazy pipelines: Enhancing quality in approximate computing[END_REF]. Similar to VOS, clock overgating based approximation is introduced in [START_REF] Kim | Designing approximate circuits using clock overgating[END_REF]. Clock overgating is done by gating clock signal to selected flip-flops in the circuit during execution cycles in which the circuit functionality is sensitive to their state. In all the approximation methods at physical level, in addition to the deliberate approximation introduced, impact of variability has to be considered to achieve optimum balance between accuracy and energy. Decoupling the data and control processing is proposed in [START_REF] Akturk | Decoupled control and data processing for approximate near-threshold voltage computing[END_REF] to mitigate the impact of variation in near-threshold approximate designs. Also, technologies like FDSOI provide good resistance towards the impact of variability. Approximation at architectural level is discussed in [START_REF] Li | Joint precision optimization and high level synthesis for approximate computing[END_REF], where accuracy control is handled by bitwidth optimization and scheduling algorithms. Also other forms of architecturallevel approximations are discussed in [START_REF] Lingamneni | Energy parsimonious circuit design through probabilistic pruning[END_REF], where probabilistic pruning based approximation method is proposed. In this method, design is optimized by removing certain hardware components of the design and/or by implementing alternate way to perform the same functionality with reduced accuracy. In [START_REF] Kim | Inexact computing for ultra low-power nanometer digital circuit design[END_REF], a probabilistic approach is discussed in the context of device modeling and circuit design. In this method, noise is added to the input and output nodes of an inverter and the probability of error is calculated by comparing the output of the inverter with a noise-free counterpart. In [START_REF] Schlachter | Near/sub-threshold circuits and approximate computing: The perfect combination for ultra-low-power systems[END_REF], new class of pruned speculative adder are proposed by adding gatelevel pruning in speculative adders to improve Energy Delay Area Product (EDAP). Though there is claim that the pruned speculative adder will show higher gains when operated at sub-threshold region, no solid justification is given in [START_REF] Schlachter | Near/sub-threshold circuits and approximate computing: The perfect combination for ultra-low-power systems[END_REF]. In general, approximations introduced by pruning methods are more rigid in nature, which lacks the dynamicity to switch between various energy-accuracy trade-off points.

On contrast, voltage scaling based approximations are more flexible, easy to implement and offer dynamic control over energy-accuracy trade-off. Approximation introduced by sup-ply voltage scaling offers dynamic approximation, by changing the operating triad (combination of supply voltage, bodybiasing scheme, and clock frequency) of the design at runtime, which makes the user to control the energy-accuracy trade-off efficiently. In [START_REF] Lingamneni | Designing energyefficient arithmetic operators using inexact computing[END_REF], limitations of voltage over-scaling based approximate adders such as need for level shifters and multiple voltage routing lines are mentioned. These limitations can be overcome by employing uniform voltage scaling along the pipeline or at larger granularity.

III. CHARACTERIZATION OF ARITHMETIC OPERATORS

In this section, characterization of arithmetic operators is discussed for voltage over-scaling based approximation, as shown in Fig. 2. As adder is the most common operator used in datapaths, we consider Ripple Carry Adder (RCA) and Brent-Kung Adder (BKA) configurations. Fig. 3: Carry Chain of Brent-Kung Adder [START_REF] He | CMOS VLSI Design: A Circuits And Systems Perspective[END_REF] Ripple carry adder is a sequence of full adders with serial prefix based addition. RCA takes n stages to compute n-bit addition. In contrast, Brent-Kung adder is a parallel prefix adder. Fig. 3, shows the carry chain of Brent-Kung adder. BKA takes 2 log 2 (n -1) stages to compute n-bit addition. In BKA, carry generation and propagation are segmented into smaller paths and executed in parallel. Black and gray cells in Fig. 3 represent carry generate and propagate, respectively. This additional timing prevents timing errors due to variability effects. Due to the limitation in availability of design libraries for near/sub-threshold computing, it is necessary to use SPICE simulation to understand the behaviour of arithmetic operators in different voltage regimes. By tweaking the operating triads, timing errors e are invoked in the operator and can be represented as

e = f (V dd , V bb , T clk ) (1)
Characterization of arithmetic operator helps to understand the point of generation and propagation of timing errors in arithmetic operators. Among the three parameters in the triad, scaling V dd causes timing errors due to the dependence of operator's propagation delay t p on V dd , such as

t p = V dd .C load k(V dd + V t ) 2
(2)

Body-biasing potential V bb is used to vary the threshold voltage (V t ); thereby increasing the performance (decreasing t p ) or reducing leakage of the circuit. Due to the dependence of t p on V t , V bb is used solely or in tandem with V dd to control timing errors. Scaling down V dd improves the energy efficiency of the operator due to its quadratic dependence to total energy.

E total = V 2 dd .C load .
Mere scaling down F clk does not reduce the energy consumption, though it will reduce the total power consumption of the circuit. Therefore, F clk is scaled along with V dd and V bb to achieve high energy efficiency.

Behaviour of arithmetic operator in near/sub-threshold region is different from the super-threshold region. In case of an RCA, when the supply voltage is scaled down, the expected behaviour is failure of critical path(s) from longest to the shortest with respect to the reduction in the supply voltage. Fig. 5 shows the effect of voltage over-scaling in 8-bit RCA. When the supply voltage is reduced from 1V to 0.8V, MSBs starts to fail. As the voltage is further reduced to 0.7V and 0.6V more BER is recorded in middle order bits rather than most significant bits. For 0.5V V dd , all the middle order bits reaches BER of 50% and above. Similar behaviour is observed in 8-bit BKA for different values of V dd . This behaviour imposes limitations in modelling approximate arithmetic operators in near/sub-threshold using standard models. Behaviour of arithmetic operators during voltage over-scaling in near/subthreshold region can be characterized by SPICE simulations. But SPICE simulators take long time to simulate exhaustive set of input patterns needed to characterize arithmetic operators.

IV. MODELLING OF FAULTY ARITHMETIC OPERATORS

As stated previously, there is a need to develop models that can simulate the behavior of faulty arithmetic operators at functional level. In this section, we propose a new modelling technique that is scalable for large-size operators and compliant with different arithmetic configurations. The proposed model is accurate and allows fast simulations at the algorithm level by imitating the faulty operator with statistical parameters.

As VOS provokes failures on the longest combinatory datapaths in priority, there is clearly a link between the impact of the carry propagation path on a given addition and the error issued from this addition. Figure 6 illustrates the needed relationship between hardware operator controlled by operating triads and statistical model controlled by statistical parameters 6: Functional equivalence for hardware adder

P i .
As the knowledge of the inputs gives necessary information about the longest carry propagation chain, the values of the inputs are used to generate the statistical parameters that control the equivalent model. These statistical parameters are obtained through an offline optimization process that minimizes the difference between the outputs of the operator and its equivalent statistical model, according to a certain metric.

In this work, we used three accuracy metrics to calibrate the efficiency of the proposed statistical model:

• Mean Square Error (MSE) -average of squares of deviations between the output of the statistical model x and the reference x. • Hamming distance -number of positions with bit flip between the output of the statistical model x and the reference x. • Weighted Hamming distance -Hamming distance with weight for every bit position depending on their significance.

In the rest of the section, we develop a proof of concept by applying VOS on different adder configurations. All the adder configurations are subjected to VOS and characterized as shown in Fig. 4. In the case of adder, only one parameter P i for the statistical model is used and is defined as C max , the length of the maximum carry chain to be propagated. Hence, given the operating parameters (T clk , V dd , V bb ) and a couple of inputs (in 1 , in 2 ), the goal is to find C max , minimizing the distance between the output of the hardware operator and the equivalent modified adder. This distance can be defined by the above listed accuracy metrics. Hence, C max is given by:

C max (in 1 , in 2 ) = Argmin C∈[0,N ] x (in 1 , in 2 ) , x (in 1 , in 2 )
where x, y is the chosen distance metric applied to x and y. As the search space for characterizing C max for all sets of inputs is potentially very high, C max is characterized only in terms of probability of appearing as a function of the theoretical maximal carry chain of the inputs, denoted as P C max = k|C th max = l . This way, the mapping space of 2 2N possibilities is reduced to (N + 1) 2 /2. Table I gives the template of the probability values needed by the equivalent modified adder to produce an output. The optimization algorithm used to construct the modified adder is shown in Algorithm 1. When the inputs (in 1 , in 2 ) are in the vector of training inputs, output of the hardware adder configuration x is computed. Based on the particular input pair (in 1 , in 2 ), maximum carry chain C th max corresponding to the input pair is determined. Output x of the modified adder with three input parameters (in 1 , in 2 , C) is computed. The distance between the hardware adder output x and modified adder output x is calculated based on the above defined accuracy metrics for different iterations of C. The flow continues for the entire set of training inputs. After the off-line optimization process is performed, the equivalent modified adder can be used to generate the outputs corresponding to any couple of inputs in 1 and in 2 . To imitate the exact operator subjected to VOS triads, the equivalent adder is used in the following way:

1) Extract the theoretical maximal carry chain C th max which would be produced by the exact addition of in 1 and in 2 .

2) Pick of a random number, choose the corresponding row of the probability table, in the column representing C th max , and assign this value to C max . 3) Compute the sum of in 1 and in 2 with a maximal carry chain limited to C max . Fig. 7 shows the estimation error of model of different adders based on the above defined accuracy metrics. SPICE simulations are carried out in 43 operating triads with 20K input patterns. Input patterns are chosen in such a way that all the input bits carry equal probability to propagate carry in the chain. Fig. 7a plots the Signal to Noise Ratio (SNR) of 8-and 16-bit RCA and BKA adders. MSE distance metric shows higher mean SNR, followed by Hamming distance and weighted Hamming distance metrics. Since MSE and weighted Hamming distance are taking the significance of bits into account, their resulting mean SNRs are higher than for the Hamming distance metric. Fig. 7b shows the plot of normalized Hamming distance of all the four adders. In this plot, MSE and Hamming distance metrics are almost equal, with a slight advantage for non-weighted Hamming distance, which is expected since this metric gives all bit positions the same impact. Both the 8-bit adders have same behaviour in terms of the distance between output of hardware adder and modified adder. On the other hand, 16-bit RCA is better in terms of SNR compared to its BKA counterpart. These results demonstrate the accuracy of the proposed approach to model the behavior of operators subjected to VOS in terms of approximation.

V. EXPERIMENTS AND ENERGY EFFICIENCY RESULTS

In our experiments, we characterized 8-and 16-bit ripple carry adder (RCA) and Brent-Kung adder (BKA) using LVT (Low V t ) transistor libraries of 28nm-FDSOI technology. Table II shows the synthesis results (area, static plus dynamic power, critical path) of different adder configurations at 1V V dd without body bias. Post synthesis, SPICE netlist of all the adders are generated and simulated using Eldo SPICE (version 12.2a). Table III shows the different operating triads used to simulate the adders. Clock period (T clk ) of the adders is chosen based on the synthesis timing report. Supply voltage (V dd ) of all the simulations are scaled down from 1.0V to 0.4V in steps of 0.1V and body-biasing potential (V bb ) of -2V, 0V, and, 2V. Pattern source function of SPICE testbench is configured with specific input vectors to test the adder configurations. Circuit under test is subjected to 20K simulations for every different operating triad with same set of input patterns. Energy per operation corresponding to different operating triads is calculated from the simulation results. Output values generated from the SPICE simulation are compared against the golden (ideal) outputs corresponding to the input patterns. Automated test scripts calculate various statistical parameters like BER (ratio of faulty output bits over total output bits), MSE and bit-wise error probability (ratio of number of faulty bits over total bits in every binary position) for all the test cases. Fig. 8a and Fig. 8b show the plots of BER vs Energy/Operation of 8-bit RCA and BKA adders. Likewise plots of BER vs Energy/Operation of 16-bit RCA and BKA adders are shown in Fig. 8c and Fig. 8d respectively. The label of x-axis of the plots show the operating triads in the format T clk (ns), V dd (V), and V bb (V) respectively. In all the adder configurations, energy/operation decreases and BER increases in sync with the supply voltage over-scaling. Table IV shows the maximum energy efficiency (amount of energy saving compared to ideal test case) achieved by 8-bit and 16-bit RCA and BKA in different BER ranges. Due to the parallel prefix structure, BKA adders show staircase pattern in BER plot shown in Fig. 8b and Fig. 8d. On other hand, RCA adders based on serial prefix show exponential pattern in BER plot.

Energy/operation curve of all the four plots show two patterns corresponding to 0% BER, and BER greater than 0%. Effect of voltage over-scaling is visible in the left half of the plots, where energy/operation is gradually reduced in sync with reduction in V dd while BER is at 0%. Another important observation is that the effect of body-biasing is helping to keep the BER at 0% in this region of the plot. Both the 8-bit RCA and BKA adders operated at 0.5V V dd with forward body bias of 2V V bb , achieve maximum energy efficiency of 76% and 75% respectively at 0% BER. Similarly, 16-bit RCA and BKA achieve maximum energy efficiency of 60% and 59% respectively at 0% BER, while operating at 0.6V for V dd with forward body bias V bb of 2V. This set of operating triads provides high energy efficiency without any loss in accuracy of the computation by taking advantage of near-threshold computing and body-biasing technique.

On the right half of the BER vs Energy/Operation plots, where the BER is greater than 0%, energy curve starts in three branches and tapers down when the BER reaches 40% and above. In those three branches, operating triads with bodybiasing are most energy efficient followed by triads without body-biasing and finally triads with overclocking. In 8-bit BKA adder, 28 out of 43 operating triads operate within 0% to 25% BER. Similarly, 36 triads operate within 0% to 25% BER in 8-bit RCA adder. In 16-bit BKA and RCA adders, correspondingly 30 and 38 operating triads operate within BER range of 0% to 25%. For an application with acceptable error margin of 25%, 8-bit RCA, 8-bit BKA, 16-bit RCA, and 16bit BKA can be operated at 0.4V V dd with forward body bias V bb 2V to achieve maximum energy efficiency of 92%, 89%, 90.8%, and 84%, respectively.

Approximation in arithmetic operators based on voltage over-scaling, provides dynamic approximation, which makes the user to control the energy-accuracy trade-off efficiently by changing the operating triad of the design at runtime. In this method, dynamic approximation can be achieved without any design-level changes or addition of extra logic in the arithmetic operators unlike accuracy configurable adder proposed in [START_REF] Kahng | Accuracy-configurable adder for approximate arithmetic designs[END_REF]. Dynamic speculation techniques like in [START_REF] Ragavan | Adaptive overclocking and error correction based on dynamic speculation window[END_REF] can be used to estimate the BER at runtime to switch between different triads to achieve high energy efficiency with respect to user defined error margin. 8-bit RCA and BKA can be dynamically switched from accurate to approximate mode by merely scaling down V dd from 0.5V to 0.4V at the cost of 8% BER to increase energy efficiency from 76% to 87%. Similarly in 8-bit RCA, switching from accurate to approximate mode is possible by reducing V dd from 0.5V to 0.4V at the cost of 16% BER to increase energy efficiency from 75% to 89%. BKA adder configuration records more BER compared to RCA because of more logic paths of same length due to parallel prefix structure. Likewise in 16-bit RCA, accurate to approximate mode can be switched by scaling V dd from 0.6V to 0.4V at the cost of 6% BER to increase energy efficiency from 60% to 84%. In 16-bit BKA, accurate to approximate mode can be switched by scaling V dd from 0.6V to 0.4V at the cost of 9% BER to increase energy efficiency from 59% to 84%. Both 16-bit adders provide leap of 24% increase in energy efficiency at the maximum cost of 9% BER compared to accurate mode.

VI. CONCLUSION

In this paper, we have proposed to use voltage over-scaling to highlight possible trade-off between energy efficiency and approximation in arithmetic operators that can be used for error-resilient applications. In this work, we characterized different configurations of adders using different operating triads to generate statistical model for approximate adder. We have laid down the framework to construct statistical model by characterizing approximate operators based on voltage overscaling. We have achieved maximum energy efficiency of 76% in 8-bit RCA while operating at 0.5V V dd without any accuracy loss. By increasing the effect of voltage over-scaling from 0.5V to 0.4V, energy efficiency is increased to 87% at the cost of 8% BER. All the adder configurations have shown maximum energy gains of up to 89% within 16% of BER and 92% within 22% of BER. Dynamic approximation can be used in these adders by employing dynamic speculation methods to monitor the errors at runtime.

Fig. 1 :

 1 Fig.1: Accurate approximate configuration of[START_REF] Han | Approximate computing: An emerging paradigm for energy-efficient design[END_REF]

Fig. 4 :

 4 Fig. 4: Flow of arithmetic operator characterization Fig.4shows the characterization flow of the arithmetic operators. Structured gate-level HDL is synthesized with userdefined constraints. The output netlist is then simulated at transistor level using SPICE (Simulation Program with Integrated Circuit Emphasis) platform by varying operating triads (V dd , V bb , T clk ), where V dd is supply voltage, V bb is body-biasing voltage, and T clk is clock period. In ideal condition, the arithmetic operator functions without any errors. Also, EDA tools introduce additional timing margin in the datapaths during Static Timing Analysis (STA) due to clock path pessimism.

Fig. 5 :

 5 Fig. 5: Distribution of BER in output bits of 8-bit RCA under voltage scaling

begin P ( 0 :

 0 N bit adder | 0 : N bit adder ) := 0; max dist := +∞; C max temp = 0; for variable in 1 , in 2 ∈ training inputs do x := add hardware(in 1 , in 2 ) C th max := max carry chain(in 1 , in 2 ); for variable C ∈ C th max down to 0 do x := add modif ied(in 1 , in 2 , C); dist := x, x ; if dist <= max dist then dist max := dist; C max temp := C; end end P (C max temp |C th max ) + + end P (: | :) := P (: | :)/size(training outputs); end Algorithm 1: Optimization Algorithm

Fig. 7 :

 7 Fig. 7: Estimation error of the model for different adders and distance metrics

TABLE I

 I

	: Carry propagation probability table of modified 4-
	bit adder
	X X Cmax X	X X C th X max X 0	0 1	1 P (0|1)	2 P (0|2)	3 P (0|3)	4 P (0|4)
		1	0	P (1|1)	P (1|2)	P (1|3)	P (1|4)
		2	0	0	P (2|2)	P (2|3)	P (2|4)
		3	0	0	0	P (3|3)	P (3|4)
		4	0	0	0	0	P (4|4)

TABLE II :

 II Synthesis Results of 8 and 16 bit RCA and BKA

	Benchmarks	Area (µm 2 )	Total Power (µW)	Critical Path (ns)
	8-bit RCA	114.7	170	0.28
	8-bit BKA	174.1	267.7	0.19
	16-bit RCA	224.5	341	0.53
	16-bit BKA	265.5	363.4	0.25

TABLE III :

 III Operating triads used in Spice simulation

	Benchmarks	T clk (ns)	V dd (V)	V bb (V)
	8-bit RCA	0.5, 0.28, 0.19, 0.13	1 to 0.4	-2 to 2
	8-bit BKA	0.5, 0.19, 0.13, 0.064	1 to 0.4	-2 to 2
	16-bit RCA	0.7, 0.53, 0.25, 0.20	1 to 0.4	-2 to 2
	16-bit BKA	0.7, 0.25, 0.20, 0.15	1 to 0.4	-2 to 2

TABLE IV :

 IV Energy Efficiency and BER in 8-bit and 16-bit Ripple Carry and Brent-Kung Adders

	BER Range	8-RCA	Number of Triads 8-BKA 16-RCA	16-BKA	8-RCA	Max. Energy Efficiency (%) 8-BKA 16-RCA 16-BKA	BER at Max. Energy Efficiency (%) 8-RCA 8-BKA 16-RCA 16-BKA
	0%	16	14	15	18	76	75.3	60.5	73.3	0	0	0	0
	1% to 10%	15	7	15	9	87	65.3	83.6	84	8	8.8	6	9.1
	11% to 20%	2	5	6	3	74	89	86.2	73.3	11	16.1	17.5	18.1
	21% to 25%	3	2	2	-	92	82.8	90.8	-	22	25	22.1	-

.2 8 ,0 .5 ,±

2 0 .2 8 ,0 .6 ,± 2 0 .2 8 ,0 .7 ,± 2 0 .1 3 ,0 .8 ,± 2 0 .2 8 ,0 .8 ,± 2 0 .2 8 ,0 .9 ,0 0 .1 9 ,0 .8 ,± 2 0 .2 8 ,1 .0 ,0 0 .1 3 ,0 .9 ,± 2 0 .2 8 ,0 .9 ,± 2 0 .1 9 ,1 .0 ,0 0 .1 9 ,0 .9 ,± 2 0 .5 0 ,1 .0 ,0 0 .1 3 ,1 .0 ,± 2 0 .2 8 ,1 .0 ,± 2 0 .1 9 ,1 .0 ,± 2 0 .1 9 ,0 .7 ,± 2 0 .2 8 ,0 .8 ,0 0 .1 9 ,0 .9 ,0 0 .2 8 ,0 .