Victor Malherbe

Gilles Gasiot

Thomas Thery

Jean-Luc Autran

Philippe Roche

Accurate Resolution of Time-Dependent and Circuit-Coupled Charge Transport Equations: 1D Case Applied to 28 nm FD-SOI Devices

We present a 1D drift-diffusion solver for singleevent simulation. Owing to its computational speed and circuitcoupling ability, the module is embedded in our soft error rate simulation platform, enabling projections on logic cells in 28 nm FD-SOI.

I. INTRODUCTION

The physics of radiation-induced charge transport and collection is one of the key blocks in the analysis of single event effects on semiconductor devices. Because the constituting equations of electrostatics and carrier motion are tightly coupled, the formulated problem is inherently stiff and best investigated within Technology Computer Aided Design (TCAD) simulations. However, such numerical codes are computationally intensive, typically requiring several hours for a single impact simulation on a 3D structure. Thus TCAD is neither suitable for error rate prediction nor interactive feedback at circuit-design time: both of them require single event models compact enough to execute in seconds, yet physically accurate. Within the fuzzy notion of "physical accuracy", two peculiar features ought to be tackled by such models if they are to be used at analog-circuit ("SPICE") level: time dependence, and circuit coupling. The Ambipolar Diffusion with Cut-off (ADC) model [START_REF] Edmonds | A Theoretical Analysis of Steady-State Charge Collection in Simple Diodes Under High-Injection Conditions[END_REF] offered extremely valuable insight into the collection mechanisms, but the analysis was carried out under steady-state conditions only. That same idea of considering purely ambipolar transport in the absence of electric field, followed by collection from the electric field in a depletion region, gave rise to the "diffusion-collection" model [START_REF] Palau | Device simulation study of the SEU sensitivity of SRAMs to internal ion tracks generated by nuclear reactions[END_REF]: the time-dependent diffusion equation can be solved analytically, however due to the separation between diffusive and drift transport, no true circuit coupling can be implemented. The authors of [START_REF] Kauppila | A Bias-Dependent Single-Event Compact Model Implemented Into BSIM4 and a 90 nm CMOS Process Design Kit[END_REF] were among the first to tackle the question of circuit coupling, replacing the (independent) current source by a bias-dependent current-generating network comprised of a capacitor and a (dependent) current source. Circuit-element formulations have also proved to be popular for SOI technology, where bipolar amplification (i.e. additional injection due to the disturbed body potential) is commonly accounted for by injecting the primary radiation-induced current into the base of a bipolar junction transistor [START_REF] Fulkerson | Prediction of SOI single-event effects using a simple physics-based SPICE model[END_REF]. Equivalent-circuit approaches like these can offer great predictive power but only after proper calibration, which is perhaps their main weakness when compared to more physics-based models. In this paper we develop a single event model based on direct resolution of the semiconductor equations on a onedimensional mesh. The thrust behind this "1D" assumption is twofold: firstly, it greatly alleviates computational cost, allowing to meet the speed requirement for SPICE-level single event models. Secondly, it is physically relevant to advanced technologies such as Fully-Depleted SOI (FD-SOI) or FinFET, which both exhibit active silicon volumes whose dimensionality can be reduced: unlike bulk technology where the transport problem is intrinsically three-dimensional, in 28 nm FD-SOI the "thickness axis" can actually be collapsed thanks to the ultra-thin (7 nm) silicon film, and the "width axis" may also be neglected due to the electric field's orientation from drain to source. Last but not least, coupling with an external circuit is enabled thanks to the interactive mode of Mentor Graphics' Eldo circuit solver [START_REF]Eldo Classic -Foundry Certified SPICE Accurate Circuit Simulation[END_REF], which makes it possible to run a transient simulation step by step with dynamic access to the circuit parameters. The paper is organized as follows: we first go through the equations that need to be solved (including how to discretize them properly), and shed some light on practical implementation. We then validate the model against more detailed TCAD simulations, finally to integrate it inside our Monte-Carlo radiation simulator to perform cell-level soft-error studies in 28 nm FD-SOI.

II. SOLVER FORMULATION A. Physical models

Guided by Occam's razor, we wish to only include in our solver those physical models that are necessary to account for single event mechanisms, especially in FD-SOI. We thus consider the drift-diffusion transport equations (e.g. instead of more sophisticated hydrodynamic transport):

r • "F = q(p n + N d N a ) (1)
@n @t + R G 1 q r • J n = 0 (2) @p @t + R G + 1 q r • J p = 0 (3)
J n = qµ n nF n + qD n rn (4)
J p = qµ p pF p qD p rp (5)
(1) is Poisson's equation, where " is the dielectric permittivity of silicon, F = rV is the electric field obtained from electrostatic potential V , q is the elementary charge, n (resp.

p) is the electron (resp. hole) density, and N d (resp. N a ) is the donor (resp. acceptor) density assumed to be totally ionized. ( 2) and (3) are the electron and hole continuity equations, where R and G are the recombination and generation terms, and J n (resp. J p ) is the electron (resp. hole) current density. Finally (4) and ( 5) are the drift-diffusion equations for electrons and holes, where µ n , D n , µ p , D p are their respective mobilities and diffusivities. The driving fields F n,p = rV n,p = r(V ± 1 2 V bgn ) account for the spatial variations of both the electrostatic potential and the energy gap

E g,ef f = E g qV bgn ,
the latter arising because of bandgap narrowing (BGN) at high doping densities. We account for BGN with the del Alamo model [START_REF] Del Alamo | Simultaneous measurement of hole lifetime, hole mobility and bandgap narrowing in heavily doped n-type silicon[END_REF], and the 1 2 factors imply equal splitting between the conduction and valence bands. We assume Maxwell-Boltzmann statistics for the carrier concentrations (as opposed to Fermi-Dirac which are more tedious to implement), because our TCAD simulations only showed small differences in terms of radiation currents with or without Fermi statistics (and therefore, the mobilities and diffusivities are related by Einstein's relation: D = µk B T /q). On the other hand, note that overlooking bandgap narrowing leads to completely unrealistic predictions for the bipolar amplification mechanism: when the mass-action law is modified into (np

) eq = n 2 int,ef f = n 2 int exp(qV bgn /k B T )
where n int is the intrinsic carrier concentration, then with highly-doped implants the minority concentration is off by an exponential factor, yielding overly pessimistic projections for the parasitic bipolar gain and thus the total collected charge under radiation events. We also model temperature-dependent bandgap and conduction/valence band effective densities of states [START_REF] Bludau | Temperature dependence of the band gap of silicon[END_REF], [START_REF] Green | Intrinsic concentration, effective densities of states, and effective mass in silicon[END_REF], [START_REF] Lang | Temperature dependent density of states effective mass in nonparabolic p-type silicon[END_REF]. Finally, note that we define the electrostatic potential with respect to the intrinsic Fermi level, and therefore at equilibrium we have:

n eq = n int,ef f exp(qV /k B T ) (6)
p eq = n int,ef f exp( qV /k B T ) (7)
Now when outside equilibrium, more specific mechanisms that must be included are:

• Mobility: we model the temperature and doping dependence of µ n and µ p via the Arora model [START_REF] Arora | Electron and hole mobilities in silicon as a function of concentration and temperature[END_REF]. We include velocity saturation (i.e. mobility degradation with the electric field) via the Canali model [START_REF] Canali | Electron and hole drift velocity measurements in silicon and their empirical relation to electric field and temperature[END_REF], and take into account mobility degradation with carrier densities (i.e. Carrier-Carrier Scattering or CCS) via the Conwell-Weisskopf model [START_REF] Choo | Theory of a forward-biased diffused-junction P-L-N rectifier -Part I: Exact numerical solutions[END_REF]- [START_REF] Fletcher | The High Current Limit for Semiconductor Junction Devices[END_REF]. Indeed, CCS has been widely recognized as one of the driving mechanisms for radiation-induced carrier transport given the very high injection levels at play [START_REF] Dodd | Device simulation of charge collection and single-event upset[END_REF]. Therefore, it needs to be included in our solver for correct behavior at high Linear Energy Transfers (LET).

• Recombination: we consider Shockley-Read-Hall (SRH)

i.e. impurity-assisted recombination depending on the doping level, and Auger i.e. direct band-to-band recom-bination depending on the temperature. Auger recombination becomes especially important at high LET.

• Generation: we use the Van Overstraeten model [START_REF] Overstraeten | Measurement of the ionization rates in diffused silicon p-n junctions[END_REF] to account for impact ionization i.e. avalanche multiplication of the carriers under high electric fields. This mechanism is especially important for a proper rendition of bipolar amplification in FD-SOI, which is strongly "avalancheassisted" [START_REF] Malherbe | Alpha soft error rate of FDSOI 28 nm SRAMs: Experimental testing and simulation analysis[END_REF]. Last but not least, the radiation-induced generation of carriers is accounted for with

G rad (x, t) = N rad (x)g rad (t) (8)
where N rad (x) is the space-dependent deposited density and g rad (t) is the temporal rate at which deposition occurs. Finally, we assume electrothermal equilibrium at the contacts at all times. Using l and r subscripts for the left and right sides of the simulation domain, this leads to the following Dirichlet boundary conditions on the primary variables V , n, and p:

V (x l , t) = V eq (x l ) + V a,l (t) (9)
n(x l , t) = n eq (x l ) (10)
where V a stands for the voltage applied by the circuit. Equations on the right side and for p were not written for brevity.

B. Spatial and temporal discretization

In order to yield a system of equations that can actually be solved on a computer, the set of coupled partial differential equations (PDE) above needs to be discretized on a computational grid, both in space and time. The mathematical details of the discretization procedures are given in Appendix A, here we just wish to mention the main steps taken without resorting to formulae:

• The box discretization method [START_REF] Bank | Numerical methods for semiconductor device simulation[END_REF] is used to discretize (1) (2) and ( 3), based on the general non-uniform 1D mesh of variable cross section illustrated in Fig. 1. Doing so we can account for the detailed morphology of 28 nm FD-SOI transistors, whose silicon film thickness is 7 nm under the gate, but varies near the spacers and goes to 12 nm in the epitaxy-raised source/drain implants. The electric field F is easily related to the potential V via a finite-difference formula, but the current densities J n and J p cannot be obtained from a naive discretization of ( 4) and ( 5): these equations need to be discretized using the Scharfetter-Gummel scheme [START_REF] Scharfetter | Large-signal analysis of a silicon read diode oscillator[END_REF], or else the mesh has to be extremely dense to ensure convergence.

• A backward-Euler approach is used for temporal discretization, for two simple reasons: it is extremely stable (while not the most accurate), and we are anticipating on coupling with an external circuit solver: Eldo's interactive mode allows us to run a transient simulation for arbitrarily small time steps, but it is impossible to "rewind" if we want to subdivide the step further. This prohibits the implementation of a temporal discretization scheme such as the trapezoidal rule, which makes use of "two half time steps" for better accuracy. • Assembling all equations yields a non-linear system for the potentials and carrier densities, from one time step to the other. The system is solved with the Newton-Raphson method, which ultimately amounts to solving a linear system involving the Jacobian matrix of the equation residuals. LU factorization of the Jacobian is the usual procedure for 1D grids, which leads to two triangular systems solved by forward/backward sweep. • All of the above allows to propagate in time the spacedependent solution, with extrinsic boundary conditionsbut the circuit response depends itself on the device evolution. Since our circuit solver is a black box, we cannot just append the circuit equations to the device equations, and solve the entire system as one single selfconsistent entity (which is what mixed-mode TCAD often does). Therefore, additional care must be taken with the device-to-circuit communication: a basic implementation of circuit coupling is to substitute the device with a pure current source whose magnitude is calculated by the device solver, then let the circuit solver refresh the terminal voltages, and then compute a new value for the device current, and so forth. Such a coupling method was tested but exhibited mediocre stability, typically requiring time steps below 0.1 ps at all time for convergence.

Based on [START_REF] Mayaram | Coupling algorithms for mixed-level circuit and device simulation[END_REF], a much better convergence radius was then obtained by replacing the device with an equivalent current source in parallel with an equivalent conductance, as depicted in Fig. 2. Just like the current value, the conductance value is refreshed at each time step by the device solver (with negligible calculation overhead), then handed over to Eldo for circuit simulation. This allows to raise the time step to values close to the picosecond range during the impact -and much higher after -with very limited accuracy loss.

III. IMPLEMENTATION DETAILS

Our model is written in C++, in about 5,000 lines of code. During the transient run, communication with the circuit solver is implemented by redirecting the output flux of our program to the input flux of Eldo in interactive mode: using "pipe" system calls, at each time step we are able to communicate the equivalent current and conductance (device-to-circuit link), and retrieve the updated terminal potentials (circuit-to-device Fig. 2: Circuit coupling with the simulated device's equivalent conductance and current source inside the electrical solver link). Such an implementation of device-circuit connection was already presented in [START_REF] Glorieux | Random-Walk Drift-Diffusion Charge-Collection Model For Reverse-Biased Junctions Embedded in Circuits[END_REF]. Although some of the syntax is necessarily Eldo-specific, this solution can be ported to other electrical solvers as soon as they offer a commandline execution mode allowing arbitrary time increments and dynamic access to the circuit parameters. Alternatively, other works have demonstrated the use of Verilog-A models to perform a similar task [START_REF] Kauppila | A Bias-Dependent Single-Event Compact Model Implemented Into BSIM4 and a 90 nm CMOS Process Design Kit[END_REF]: these are really just different technical solutions to tackling the same challenge. Note also that before the transient simulation can be run, the solver first needs to find the equilibrium situation (zero-bias steady state, which solves (1) self-consistently with ( 6) and ( 7) starting from an initial guess based on charge neutrality), then perform a quasi-stationary ramp-up (steady state with a bias) so the device is ready to be irradiated. Now, several optimizations are needed to ensure fast execution:

• First of all, the linear system obtained for the Newton method needs to be built before it can be inverted. Calculating all of the system's protagonists is very lengthy if nothing is done to speed-up the expression evaluations. To tackle this issue, we adopt a pragmatic, hybrid strategy by caching the "clearly re-usable" arrays. For instance, the SRH recombination term is calculated with a fraction N/D on each grid point, so storing the N and D arrays allows for faster evaluation of (N 0 D ND 0 )/D 2 in the Jacobian calculations later on. This requires some hard-coding of the dependence tree in the expression evaluations, to avoid refreshing values in the wrong order. Overall, we observed a near 10⇥ speed-up when going from a careless evaluation methodology to this hybrid solution. Therefore a complete handling of expression trees -which would be required for optimal lazy reevaluation -was deemed unnecessary.

• Second of all, the system needs to be inverted. For this we make use of Eigen [START_REF] Guennebaud | Eigen v3[END_REF], a very complete library for linear algebra. It allows to analyze the sparsity pattern of the Jacobian matrix to accelerate its LU factorization afterwards: the non-zero entries do vary but their indices do not, so the sparsity analysis can be performed once and for all beforehand. We observed a 40% performance Fig. 3: Comparison between our model and 3D TCAD simulations for various impacts on an NMOS inside an inverter improvement with this feature -which ironically made the system faster to invert than to build. Furthermore, Eigen enables many compiler optimizations to vectorize the calculations, yielding an additional 3⇥ speed-up. We also implement some adaptive time step control tailored to our radiation context, with time step relaxation after the impact for instance. The end result of all these optimizations is that an impact takes about 1-3 seconds to run, depending on its toughness: this perfectly meets our speed requirements for Soft-Error Rate (SER) simulation.

IV. MODEL USAGE IN 28 NM FD-SOI A. Validation against 3D TCAD

As a benchmark to validate our model in FD-SOI technology, we compare the results of our 1D solver with more detailed TCAD simulations. The latter are performed by striking a 3D NMOS structure connected in mixed mode to a PMOS and a load capacitance, to simulate the context of an inverter in a CMOS network. Our 1D solver simply takes as input the 1D doping profile of the struck NMOS along its channel axis. A very important note is that in our model, we do not "erase" the NMOS in the circuit simulation, unlike what was shown in Fig. 2 for a toy circuit: we cannot realistically hope for our solver to reproduce the full behavior of a MOSFET since the influence of the gate cannot be natively treated in 1D. Therefore, for the equivalent current and conductance calculations we subtract the steady-state leakage predicted by our solver, and keep the MOSFET in parallel with those circuit elements. In other words, we leave the silicon-calibrated SPICE transistor in charge of the "normaloperation" current, and our solver is only responsible for the radiation-induced current. From a device-level perspective, our simulator is accountable for the motion of excess carriers but not the "background" electrons and holes. Fig. 3 displays the current and voltage waveforms obtained for impacts at the drain-channel junction of the transistor (where the electric field is highest), for various LET. For comparison we also include results from the behavioral model in [START_REF] Malherbe | On-Orbit Upset Rate Prediction at Advanced Technology Nodes: a 28 nm FD-SOI Case Study[END_REF], where the current waveform was simply a double-exponential pulse, of integral charge given by an LET-dependent bipolar amplification modulated by a position-dependent collection efficiency. As can be seen, the time-dependent effects are well accounted for by our new model, which natively enlarges the current pulse in high injection. On the other hand with the simple model, at high LET the decoupled current source is way off since it does not vanish when the potential drops, thus causing unphysical values for the voltage. This is not an issue for Single-Event Upset (SEU) simulation which is merely interested in whether the voltage does drop or not. But Single-Event Transient (SET) simulations would be quite coarse with the simple model, since the voltage pulse duration is mispredicted. Mention should be made that the model developed in this paper is not exempt from calibration: the TCAD simulations shown here use hydrodynamic transport equations with more complex mobility modeling (with velocity saturation and interface degradation), beside the models already listed in section II-A. Thus some adjustments are necessary, mainly by playing on the carrier mobilities and lifetimes. Note however that obtaining a good match with TCAD in not an end per se: silicon measurements -e.g. comparison with SEU cross sections on sequential cells -still have to remain the main judge to close the "model calibration" loop.

B. On the importance of circuit coupling

As a mere sanity check, in Fig. 4 we plotted the waveforms obtained with our model for a 10 MeV.cm 2 /mg impact on a pn + structure with mesh dimensions representative of a bulk-Si junction as depicted in Fig. 2, with V dd = 1.2 V, R = 10 k⌦, and C = 1 fF. As can be seen, our 1D solver perfectly captures the so-called "plateau" effect [START_REF] Dasgupta | Effect of Well and Substrate Potential Modulation on Single Event Pulse Shape in Deep Submicron CMOS[END_REF], which arises in modern bulk technologies when the time constants for charge transport and circuit response start overlapping. The n + voltage is clamped at V bi = 0.8 V, while the current lingers at the precise value of (V dd + V bi )/R = (1.2 + 0.8)/10, 000 = 0.2 mA: if the current was to exceed this value, the n + potential would drop even further and the junction would become truly forward biased, thus it would start driving a massive current in the opposite direction that would actually draw the potential back up very quickly. As a matter of fact, this phenomenon can be observed when intentionally using overly relaxed time steps during the plateau: the forward-bias current restores a dramatically high potential on the n + node, which causes spurious oscillations that sometimes stabilize, or sometimes can cause the simulation to diverge.

Voltage [V] Current [A] Time [s]

Current Voltage Fig. 4: Sanity check for circuit coupling: plateau effect for a 10 MeV.cm 2 /mg impact on a mesh representative of a bulk-Si p-n + junction connected like in Fig. 2. The plateau lasts for as long as there are charges to collect that have not recombined, and then the voltage recovers with an RC time constant.

On the other hand as can be seen in Fig. 3, in FD-SOI the plateau effect due to circuit coupling does arise, but in a less pronounced way than in bulk technology. This was expected given the reduced active silicon volumes, providing a much smaller reservoir for continued charge collection over time. More important than the current plateau however is the fact that the V ds voltage of the MOSFET is clamped at 0, much like it was clamped at V bi for a junction alone. This is of great relevance to properly capture the radiation behavior of devices connected in series. For instance, consider the robust inverter shown in Fig. 5, which uses transistors of identical function in series. Stacking is a well-known method for hardening, and its efficiency has sometimes been explained by the fact that it is highly unlikely for an impact to "turn on" both transistors at the same time, especially in SOI technology. More rigorously, the robustness comes from the fact that since V ds tends to clamp at 0 during an impact, for instance when we strike the NMOS closest to Z, the output cannot drop below 0.5 V for a long time and therefore, only short-lived SETs could propagate. For the voltage waveform obtained at 30 MeV.cm 2 /mg in Fig. 5, the glitch is likely to be filtered by the next logic stage. For comparison we also plotted the same simulation but without circuit coupling: the current was extracted under the same impact but with a constant 0.5 V hard bias across the NMOS, and then this frozen current waveform was injected in the circuit simulation to obtain a voltage waveform. As can be seen, in the non-coupled case the potential has no reason not to drop below 0.5 V, and therefore the glitch could very well propagate. This truly establishes the relevance of developing bias-dependent single event models if one is to try and predict the robustness of a given circuit design: without circuit coupling, the simulation simply misses the entire point of hardening by stacking in SOI.

VDD = 1 V GND = 0 V A = 0 V Z = 1 V 0.5 V (a

C. Cell-level explorations

In this last section we embed our collection model within our proprietary Monte-Carlo SER simulation platform called TIARA [START_REF] Roche | Application of the TIARA Radiation Transport Tool to Single Event Effects Simulation[END_REF]. Briefly speaking, TIARA builds a 3D model of a circuit based on its layout and technological process information. Then using the circuit's netlist, a simplified Layout Versus Schematic (LVS) is run to map the devices and nodes in the schematic to physical locations in the 3D model. The user can then specify an irradiation scenario, and ions are drawn randomly and ray-traced to compute charge deposition inside the structure. Finally, the collection model is called in conjunction with the electrical solver in order to compute the circuit's response to the impacts. Some software upgrades were needed on both sides to enable smooth integration of the new collection model within TIARA. Beside general flow unification tasks to connect the API together, we had to dynamically generate the inputs for the new collector: first, automatic generation of the 1D meshes based on the impacted transistors, and then conversion of the raytracer's output into a carrier generation term. Note that for the first task, in the case of two transistors sharing a common diffusion area we generate two simulation domains with a shared boundary condition. In Fig. 6 we plotted the results of a virtual heavy-ion irradiation on an 28 nm FD-SOI SRAM cell: experimental data was obtained at RADEF [START_REF] Virtanen | Radiation effects facility RADEF[END_REF] at room temperature, but high-temperature runs were only carried out for Single-Event Latchup (SEL) testing. Our simulations show that the saturation cross section is nearly identical at 100 C, but at low LET it is increased by 60%. This prediction is compatible with our experimental neutron-SER measurements showing a 2⇥ increase at 125 C on similar bit-cells. This can be of importance for space applications, which often feature intense temperature cycles. Note that such an investigation would have been less straightforward with the simple model in [START_REF] Malherbe | On-Orbit Upset Rate Prediction at Advanced Technology Nodes: a 28 nm FD-SOI Case Study[END_REF], which is only calibrated at room temperature: it would have required a TCAD study first, then to introduce an ad-hoc temperature dependence in the collection model. In this paper we have developed a time-dependent single event model that can be interfaced with an electrical solver. The model is based on direct resolution of the semiconductor equations on a one-dimensional grid, making it computationally efficient. Furthermore this study has shown that the model is very accurate when applied to 28 nm FD-SOI devices, due to the ultra-thin silicon film in that technology. It has been integrated within our Monte-Carlo radiation simulation platform, highlighting how physics-based models can natively enable advanced sensitivity analyses at cell level. Note that the model could be applied seamlessly to more advanced nodes in FD-SOI -e.g. 22 or 12 nm -and, with some adaptation, to FinFET technology as well: using simplified 3D diffusion in the bulk beneath the fin and looking at carriers collected at the base of the fin, would allow to derive an effective generation term inside the fin and then, use 1D transport equations as shown in this article. Note that this implicitly assumes that collection inside the fin does not strongly affect transport in the bulk beneath, which seems reasonable since the electric field is mostly confined within the channel. From a physicist's perspective, compact analytical models are often preferred for the immediate insight they can offer, while brute-force numerical approaches are sometimes regarded as merely "number-crunching" routines making it hard to build one's physical intuition. However in this case we find that, owing to the solver's great speed, having the ability to get an instantaneous answer to any thought experiment -in 1D -is also extremely valuable and helps us gain a deeper understanding of the underlying mechanisms.

APPENDIX

Our goal here is to shed more light onto the mathematical details of the discretization procedure that was described succinctly in Section II-B. Suppose we want to compute the solution to our coupled PDE set on discrete grid points {x i } i=0..I 1 and discrete instants {t j } j=0..J 1 . We will note f (x i , t j ) = f i,j for short. We also scale our units to work on dimensionless quantities: all potentials are divided by the thermal voltage V T = k B T /q, all densities (carriers, doping, radiation...) are divided by the intrinsic density n int , and to close the loop, all times are divided by an arbitrary, extrinsic, reference time. First, the box method [START_REF] Bank | Numerical methods for semiconductor device simulation[END_REF] is used for spatial discretization; for all equations of the form r • F + S = 0 i.e. (1) (2) and (3), the idea is to use Ostrogradky's theorem on a local control volume (the "box" depicted in Fig. 1), yielding:

i+ F i+ i F i + v i S i = 0
In Poisson's equation for instance, this replaces the usual finite-difference formula for V with a reweighted Laplacian operator based on the local mesh cross section, natively leading to steeper potential drops in areas where the silicon is thinner. More precisely, if we denote

dx 2 i = v i (x i x i 1 )/ i and dx 2 i+ = v i (x i+1 x i )/
i+ , then the Laplacian stencil is expressed as:

i =  1 dx 2 i , ✓ 1 dx 2 i + 1 dx 2 i+ ◆ , 1 dx 2 i+
Now the current equations ( 4) and ( 5) are more specific, and need to be discretized via the Scharfetter-Gummel scheme [START_REF] Scharfetter | Large-signal analysis of a silicon read diode oscillator[END_REF]. Briefly summarized, since the electron and hole densities have exponential dependence on the potential, when using naive finite-difference formulae the equations are made locally inconsistent unless the mesh is extremely dense. The Scharfetter-Gummel method prevents this issue by anticipating the values of n and p in-between grid points, yielding e.g. for the leftward current densities:

J n,i = µ n,i [n i B(V n,i V n,i 1 ) n i 1 B(V n,i 1 V n,i )] J p,i = µ p,i [p i 1 B(V p,i V n,i 1 ) p i B(V p,i 1 V p,i )]
where the Bernoulli function:

B(x) = x e x
1 performs an optimal transition from a usual finite difference formula (which works well for diffusion-driven transport) to an upwind difference formula (which works well for driftdominated problems) depending on carrier velocity. Note that B(x) needs to be evaluated carefully to avoid overflows at large values of x and imprecision due to the indeterminate form when x ! 0 (in that case we use a Taylor series expansion evaluated to machine precision). As for temporal discretization, with the backward-Euler method all expressions of the form @g/@t+h = 0 are replaced by (g j g j 1 )/(t j t j 1 ) + h j = 0. Then when going from j 1 to j, assembling all discretized equations (with (4) and (5) substituted into (2) and ( 3)) yields a non-linear system of 3I equations for 3I unknowns -which we shall refrain from writing here in its entirety for the sake of compactness; if we denote our state vector X, then it is of the form: 0 3I = f (V 0,j ..V I 1,j , n 0,j ..n I 1,j , p 0,j ..p I 1,j ) = f (X j )

The root to the equation residuals f is computed via the Newton-Raphson method, which performs successive refinements to the solution by linearizing the system. To go from "outer" iteration k to k + 1 we compute an update candidate dX k+1 j as the solution to the linearized system:

0 3I = J f • dX k+1 j + f (X k j )
where J f stands for the Jacobian matrix of f . Then to actually refresh the solution we compute

X k+1 j = X k j + k+1 dX k+1 j
where is a damping parameter taken "as close as possible to 1", based on whether or not the update actually does improve the residuals -typically with geometrical damping for the "inner" iterations. Overall convergence is checked by ensuring the norm of the right-hand side falls below a given value.

Optionally, we could also use a criterion on the norm of the solution update, but since the Newton method converges quadratically (doubling the number of exact digits at each step) when initialized close enough to the solution, this could cause to systematically perform one useless iteration just to let the solution stabilize when it is already good enough. A last remaining mathematical aspect is the calculation of the equivalent conductance for our simulated device. It is defined as G eq = @I/@U , where the applied voltage difference is U = V l V r (V 0,eq V I 1,eq ) and current I is obtained via the mesh average of the flux of the current densities in order to minimize numerical error:

I = 1 I 1 I 2 X i=0 (J n,i+ + J p,i+ •
i+ (the displacement current I d can safely be ignored: even when the voltage drops by 1 V in 1 ps, for our L ⇡ 100 nm, ⇡ 10 ⇥ 100 nm 2 meshes it only reaches I d ⇡ " /L • @U/@t ⇡ 1 µA). Intuitively, the derivative for G eq should not have to be computed by evaluating the solution "at U + dU " -which could double the overall computation time -since the Jacobian matrix J

f already contains all the information about how the equation residuals vary around the solution. This is precisely the idea in [START_REF] Mayaram | Coupling algorithms for mixed-level circuit and device simulation[END_REF]: we can write G eq = @I @X • @X @U The first term is evaluated from symbolic differentiation, and to obtain the second term we make use of the fact that f (X(U ), U) = 0 =) J f • @X @U = @f @U @f /@U is a nearly-empty vector since U only appears at the boundary nodes, and because the Jacobian is already LUfactorized, the above system can be solved for @X/@U at almost no computational overcost.

Fig. 1 :

 1 Fig. 1: Notations for 1D mesh of variable thickness along x

  -10 1.01E-09 1.03E-09 1.05E-09 1.07E-09 1.09E-09

Fig. 5 :

 5 Fig.5: In FD-SOI there is no strong current plateau, but the drain-source voltage of the struck FET does clamp at 0, highlighting the importance of circuit coupling: for a robust inverter that uses identical transistors stacked in series (a), the voltage drop (b) if the radiation current model does not dynamically depend on bias (30 MeV.cm 2 /mg impact).

Fig. 6 :

 6 Fig. 6: SRAM cross section simulated at elevated temperature


Alex Frame

Beyond the Cultural Turn: A Critical Perspective on Culture-Discourse within Public Relations

Keywords: Critical intercultural theory, culture, cultural appropriation, public relations, social discourse, stereotypes

Purpose

This chapter applies recent theoretical developments linked to the concept of culture to the field of public relations research and practice, notably through the prism of creativity as a vector of cultural change.

Design/methodology/approach

The chapter is theoretical in nature, and draws on relevant scientific literature in the field of public relations research, but also the social sciences more generally, and illustrates the issues being discussed with reference to relevant public relations campaigns.

Findings

While the field of public relations has moved beyond simplistic models of cultural values and characteristics, it is argued that more complex visions of culture have been neglected. Specifically, drawing on structuration theory, culture can be seen as a "system-generating mechanism" relying on creativity to uphold and renew cultural references and norms. In this perspective, public relations is both producing/reproducing culture and being produced by culture. It follows that the concept should be apprehended not as an ontological category, but as a social construct, as the source of heuristic and discursive categorisations.

Social implications

A call is issued for public relations to also question the ideological underpinnings of the production of symbols in which practitioners partake on a daily basis.

Originality/value

While the chapter fits into an emerging body of work discussing the cultural dimension of public relations, the link with creativity and the use of structuration theory to conceptualise this link contribute to its originality.

Introduction

In 1992, [START_REF] Sriramesh | Societal culture and public relations[END_REF] pointed to the importance of culture for public relations and the need for more research in this domain. Two decades later, public relations scholars answered this call in force (e.g., Bardhan & Weaver, 2011;Carayol & Frame, 2012;Edwards & Hodges, 2011;Sriramesh & Vercic, 2012). Research has thus broadly moved beyond the use of simplistic models that 'essentialise' national cultures, seeking to reduce them to distinctive sets of deterministic invariables measured along a few value-based dimensions (e.g., [START_REF] Hofstede | Culture's consequences: Comparing values, behaviors, institutions, and organizations across nations[END_REF], to a much wider range of theories and perspectives with their roots in sociology and ethnography among others.

Public relations scholars interested in culture also refer to the "mother discipline" of the conceptanthropology -and point out how practitioners can be perceived as storytellers and mythmakers, as opposed to being seen as managers or technicians [START_REF] L'etang | Thinking about public relations and culture: Anthropological insights and ethnographic futures[END_REF].

Broadly speaking, public relations scholars have so far (a) analysed culture as an antecedent for public relations practice, (b) investigated the impact of public relations on culture and society, and (c) approached public relations as culture in its own right [START_REF] Sriramesh | Culture and public relations: Formulating the relationship and its relevance to the practice[END_REF]. [START_REF] Sriramesh | Culture and public relations: Formulating the relationship and its relevance to the practice[END_REF] concludes that most research has focused on the first of these three approaches. Some studies have attempted to describe what is culture specific, while others have focused on what is common for different cultures, and yet others have focused on intercultural interaction [START_REF] Zaharna | Intercultural communication and international public relations: Exploring parallels[END_REF]. Basically, much of the research on public relations and culture has aimed to help public relations practitioners communicate in and across national and sometimes professional cultures.

In this short theoretical essay, however, we argue that the debate surrounding the place of culture in public relations research and practice should be repositioned in the context of wider discussions surrounding the concept in the social sciences. More specifically, we point to the need to take a closer look at the ideological and epistemological basis of the culture concept in public relations. First, we will argue that the way that public relations builds or maintains "cultural differences" needs critical analysis. Culture should not be reduced to a barrier for practice or something to be harnessed in pursuit of organisational effectiveness, since such approaches, when translated into public relations campaigns, may implicitly reinforce the myth underlying much populist discourse, that social categorisation is a source of inalienable difference.

Secondly, we will argue that the relationship between public relations and culture is best grasped through the lens of structuration theory [START_REF] Giddens | The Constitution of Society : Outline of a Theory of Structuration[END_REF]. It is not a question of how public relations is formed by culture or vice versa. We see public relations as both producing/reproducing culture and being produced by culture: public relations professionals attune their messages culturally, and these messages, relayed through the media, contribute to the way in which cultural representations evolve.

Culture and Criticism

While the surface meaning of the term culture implies that a group shares certain understandings or practices, there are historic (and opposing) approaches to culture as a system of values [START_REF] Parsons | Toward a general theory of action (Theoretical foundations for the social sciences)[END_REF][START_REF] Weber | The Protestant Ethic and the Spirit of Capitalism[END_REF] or meanings [START_REF] Geertz | The Interpretation of cultures[END_REF][START_REF] Swidler | Culture in action: Symbols and strategies[END_REF]. Culture is paradoxically one of the most successful concepts to have emerged in the social sciences over the course of the last century, and particularly useful to help us understand many contemporary topics of social debate, but at the same time use of the concept is strongly criticised within the social sciences themselves, where certain academics (e.g., Dervin & Machart, 2015a) reject the term outright because they see it increasingly being used to construct and maintain difference socially, rather than to try and understand interpersonal and social group dynamics. Indeed, it is in part the success of the concept itself outside the academic sphere, and the way that it is used by the media, politicians, and in the public sphere more generally, which has led to this state of affairs.

From Social and Cultural Anthropology in the early twentieth century, the concept of culture spread to other social sciences, notably from the Sixties onwards (Bauman, 1999, p. viii), rapidly moving from the domain of scientific jargon into popular discourse, to the point where, as Dervin and Machart (2015b, p. 1) note, it was declared "Word of the Year" by the Merriam-Webster dictionary in 2014. However, at the same time, critical voices were being raised in academic circles, calling for the concept to be abandoned. Indeed, from being what was already a notoriously polysemic term, according to Dervin and Machart its popularity has made it into a dangerous "floating signifier" today (2015b, p. 2), a pseudo-scientific term without a clear or fixed meaning, which leaves it open to all kinds of misuses. Already in 1999, Hannerz had denounced what he saw as increasingly pervasive "culturespeak", by which he broadly meant inappropriate and reductive or deterministic use of the concept. Culturespeak tends to understate individual differences and favour a static vision of culture, rather than a dynamic one in which culture is seen as a constantly-negotiated social process.

Although the concept was central in anthropology for many years, it has now become strongly contested within this discipline [START_REF] Anderson-Levitt | Complicating the concept of culture[END_REF][START_REF] Kuper | L'illusion des cultures[END_REF]. The idea that the members of a society or social group all share the same cultural references has revealed its limits in studies of (post-)modern societies characterised by the diversity of their populations and a certain liquidity [START_REF] Bauman | Culture in a Liquid Modern World[END_REF] in the identity choices people make. For many anthropologists, including Appadurai (2001, pp. 40-47) and Amselle (2001, pp. 205-6), the concept with its homogenising overtones is not sufficiently dynamic to capture the complex social processes and contexts within which people evolve today, and its use artificially reinforces perceptions of social distinctions.

Indeed, the concept of culture has never been ideologically neutral. In his book Liquid Culture, Bauman (2011, pp. 1-17) identifies different uses of the notion of culture in different historical periods and distinguishes four of these: culture as Enlightenment (intellectual progress), culture as global domination [START_REF] Elias | La Civilisation des moeurs[END_REF] "civilization process"), culture as homeostasis and maintenance of group boundaries (linked to [START_REF] Bourdieu | La Distinction : Critique sociale du jugement[END_REF] "distinction"), and culture as personal invention (liquid modernity, multicultural societies). In each period, claims Bauman, the concept takes on a particular ideological nuance, linked respectively to rationalism, imperialism, elitism and then relativism. Except in its liquid version, it has been used to ethically justify various policies and attitudes towards other groups, generally judged as inferior, for example through colonialist projects. Elsewhere, Bauman describes culture as "simultaneously a man-made and a man-making entity" (Bauman, 1999, p. 28), in that it replaces, at least to some degree, supernatural rationalisations of the differences in behaviour, development, wealth, and so on between ethnic groups. Indeed, despite their historical roots, all four ideologies of culture can be found today in media discourse and public discourse in many Western countries, and must also be taken into account by public relations professionals, as the importance of culture or of culture-based discourse emerges and comes to be recognised within this field.

The Cultural Turn in Public Relations

Sriramesh and other scholars have criticized much previous public relations research for its focus on the work of Hofstede and cultural characteristics that are apparently common across countries [START_REF] Sriramesh | The relationship between culture and public relations[END_REF], rather than approaches which present culture as a social phenomenon on the level of the social group [START_REF] Frame | Cultures, Identities and Meanings in Intercultural Encounters: a Semiopragmatics Approach to Cross-Cultural Team-Building[END_REF], or as a communication resource or tool-kit [START_REF] Swidler | Culture in action: Symbols and strategies[END_REF]). Sriramesh has argued for a multi-level approach examining the political culture, economic culture, societal and organizational culture, media culture and activist culture of a country and the links between these and public relations. Culture can thus be seen as an antecedent for public relations practice, while public relations also exercises an influence on all of these cultures [START_REF] Sriramesh | Culture and public relations: Formulating the relationship and its relevance to the practice[END_REF].

Although increased attention to the question of cultures is in many ways a positive evolution in public relations theory and practice, this trend also brings with it new risks associated with increased public sensitivity towards the ways in which cultures and groups are portrayed. This can be illustrated by the "cultural appropriation" debate, when often self-designated representatives of a minority or underprivileged social group accuse non-members of trying to illegitimately appropriate its cultural codes and traditions, often in order to make a profit. The British music group Coldplay and American pop stars such as Taylor Swift, Miley Cyrus and Katy Perry have come under such criticism in recent years, for allegedly exploiting cultural traditions from other countries or minority groups 1 (here, using braids or mimicking what are seen as Afro-American dance codes) but the debate even extends to which children can legitimately wear which costumes at Halloween or for Carnival celebrations in the US and elsewhere. 2 In Norway, for example, the Minister for Finance was criticized for posing dressed in a Pocahontas costume at a party in the department. 3 Another recent example more directly relevant for public relations is the commercial released by Pepsi that featured a super model joining in a street protest and handing a policeman a can of the soft drink. A statement from the company declared that "This is a global ad that reflects people from different walks of life coming together in a spirit of harmony, and we think that's an important message to convey." 4 Given the background of recent US street rally's under the moniker "black lives matter," the commercial caused uproar and was consequently pulled. Comedian Stephen Colbert quipped "attractive lives matter." 5 Other examples of corporate cultural appropriation include the UK clothing chain Top Shop's use of the Palestinian black & white scarf design for a summer dress and the French company Chanel that included a boomerang with their logo as a part of their summer 2017 collection. 6 The former caught criticism for appropriating a symbol for the struggle of Palestinians, and the latter was criticized by aboriginal organizations. The tensions caused by the cultural appropriation by these and other corporations show just how far things can go when cultural identity claims are taken for absolute truths, and defended as such.

Cultural appropriation thus constitutes a new risk for public relations professionals, in terms of potential unwanted negative publicity attracted by brands which may be accused of trying to appropriate cultural codes for commercial reasons.

In ideological terms, referring to Bauman's classification (2011;supra), this can be analysed as revealing tensions between, on the one hand, visions of culture as homeostasis and a desire to maintain group boundaries, and, on the other hand, a liquid vision of culture as a resource for personal invention. When examining many accusations of cultural appropriation, we can also adopt a post-colonialist reading of the situation: less economically prosperous groups see themselves historically as being victims of colonial exploitation and cultural persecution, at the hands of the very same groups who appear still to be in a position of social and economic dominance, and who now seek to exploit the cultures they once denigrated, in order to make commercial profit. The situation is more acute in multicultural societies, with North-American multiculturalism constituting an extreme example, but the internet is also contributing to spread the debate, and the protests, globally. We would argue that this is symptomatic of a more general ideological tendency to see cultural identity in more "solid," essentialist (Dervin & Machart, 2015a) terms, a conception which has a very real impact on the practice of public relations all around the globe.

Indeed, in everyday public relations practice, reliance on cultural identifications is of course widespread, as we tend to unthinkingly use various categories to define ourselves and others in order to predict behaviour and anticipate reactions. In this sense, the concept of culture is a social reality, used to make sense of the social world around us and corresponds to a basic human need to think in terms of categories. As Holliday puts it, "While culture may not be real in the solid, essentialist sense, it is real in the way in which it is used and as an excuse, and very often real in the minds of those who use it" (Holliday, 2015, p. 199). It follows that this concept should be considered . This way of thinking encourages us to identify individuals as members of a particular group, and to consider them first and foremost in terms of the traits which we expect them to share, on the basis of their membership of this group, with the other members of the same group. The more different a group appears to be to our "own" group -perceived differences which we often explain away through "culture" -the more members of that group may tend to appear alike. Simplifying the complexity through the use of stereotypes is a way of making it more familiar and less frightening. In order to help us think about Otherness (considering an individual as a member of an outgroup/denying them the status of in-group membership) or communicate with individuals whom we identify as members of a (little-known) out-group, social categorisation comforts us in the idea that the members of such and such a group share a fairly homogenous culture. In other words, this natural cognitive process tends to comfort us in a falsely essentialist and reductive vision of cultures.

For public relations professionals, it is thus essential to tread the fine line between referring to cultures and social categories in order to construct meaningful messages which appeal to familiar categories, and reinforcing the underlying social stereotypes. Independently of the desire to avoid accusations of cultural appropriation, on an ethical level, public relations professionals should also think about the kind of images that they are putting into circulation in the media, since they also play a direct role in reinforcing or questioning stereotypes through their work. Public relations tends to mirror social beliefs and representations in order to resonate with audiences. This echoes an insight from ancient rhetoric: you need to take into consideration what your audience think, their values and the premises they will accept, and build on this when you try to persuade them about something.

Of course, values and premises should not be reproduced unthinkingly. Public relations professionals should be held professionally and socially accountable for the implicit cultural models and beliefs underlying the materials they produce. However, this question is only very rarely included in discussions of professional ethics by professional bodies. Bringing this aspect in would be in line with many of the calls that have been issued in critical public relations over the years (L'Etang, McKie, Snow & Xifra, 2015). Practitioners should "always question the nature of their own institutions and strive to improve them and make them more just" (Holtzhausen, 2012, p. 234). For the most part, however, such scholarship has addressed, for instance, whether "the democratic, deliberative and decision-making roles of civil society" have been opened up or closed down as a consequence of public relations activity (Motion & Leitch, 2015, p. 148) or public relations has been urged to engage with the public interest [START_REF] Johnston | Public relations and the public interest[END_REF]. As Sriramesh (2012) points out, the impact of public relations on culture and society has not been widely studied.

Culture, Public Relations, and Creativity

The preceding discussion enables us to pinpoint the relationship between culture, public relations and creativity. Culture can be understood as the supply of symbols, stories, rituals, and world-views on which people draw to create strategies of action [START_REF] Swidler | Culture in action: Symbols and strategies[END_REF]. Creativity in public relations relies on these symbolic resources which constitute the foundations and building blocks, from which a message is shaped in a new and original way.

In order to better characterise this relationship, it is important to take into account the fundamental duality of what we call "culture", in that it both structures our social interactions and is performed through them. Paraphrasing [START_REF] Hall | The Silent Language[END_REF], cultures shape our communication, and our communication in turn shapes our cultures. 7 Bauman expresses this idea, focusing on the tensions between conformism and non-conformism underlying our everyday social interactions, when he observes that culture as praxis:8 is as much about inventing as it is about preserving; about discontinuity as much as about continuation; about novelty as much as about tradition; about routine as much as about pattern breaking; about norm-following as much as about the transcendence of norm; about the unique as much as about the regular; about change as much as about monotony of reproduction; the unexpected as much as about the predictable. (Bauman, 1999, p. xiv) Here, Bauman is echoing Giddens' vision of the duality of structure, which the latter expressed in the form of Structuration Theory (1984), reminding us that when individuals produce symbolic acts (speech, actions), they are unconsciously referring to various rules and norms, but the fact of doing so means that the rules and norms themselves are being maintained and possibly updated. The system which structures behaviour is itself reproduced through the behaviour it structures.

If we consider it as structure, then, it is important to note that culture is not stable, but a dynamic process. As Desjeux points out:

Culture is both structure and something dynamic, which is what makes it so hard to observe and analyse. As structure, it includes stable elements which can give the impression that it has an essence, whereas in fact this stability results first and foremost from the fact that historically things change over long periods. As a dynamic process, it is indeed subject to historical change [authors' translation] (Desjeux, 2002, p. 2).

This dynamic nature of culture as a structuring process in communication helps us foreground the links between public relations and creativity, and indeed the role of public relations professionals as cultural mediators [START_REF] Schoenberger-Orgad | Transcending boundaries: The public relations practitioner as cultural mediator[END_REF] for society at large. As already pointed out, public relations professionals often seek to draw upon social representations familiar to the publics they are targeting, in order to express new ideas in what is likely to be perceived as a convincing way. While doing so, they are acting in a context of intertextuality, where the audience is supposedly able to draw on knowledge from a variety of sources in order to interpret the messages being produced. They are also themselves contributing to enriching this context through the material they produce, which can in turn be used as a new reference in interpreting subsequent messages. Thus the "Like a Girl" campaign by Always, for example, clearly sought to build on audience members' existing representations and widespread social discourse about what it means do something "like a girl", while reconfiguring these representations to a small degree: the campaign 'works' thanks to the cultural context, and aims to influence the context itself. Similarly, the company Bodyform has recently played on the intertextual codes of female hygiene product advertising, and notably the conventional use of "blue fluid" by many brands to promote the absorbancy of sanitary products. 9 These ads follow on from pioneering viral YouTube marketing in 2012 by the same company, 10 which 'work' because people recognise this convention, and possibly affect the way they will react to other such adverts in the future. The inherent creativity of public relations campaigns resides in professionals' capacity to produce forms which reflect existing representations, structures and ideas within a particular cultural or societal frame, in order to ensure that their messages resonate with the target publics, while renewing the underlying cultural conceptions in a way that allows the brand to stand out and be noticed, often to appear "modern". These representations, structures and ideas may thus be implicitly criticised, questioned or reinforced by the campaign, as it constitutes its own contribution to the discourse "out there" about such and such a topic. The pressure for campaigns to be "creative", i.e., to remain recognisable while challenging communicational conventions, is one of the motors of cultural change on the societal level.

It follows that the notion of creativity in public relations does not suppose total artistic freedom, rather it refers to the ability of creatives and other public relations professionals to adopt and adapt existing cultural frames of reference, to play the role of "cultural mediators" by expressing concepts and ideas in forms which resonate with their audiences' representations while associating them with a message which is new and different. Public relations in this sense molds taste and creates identification between producers and consumers [START_REF] Curtin | International public relations: Negotiating culture, identity, and power[END_REF][START_REF] Edwards | Exploring the Role of Public Relations as a Cultural Intermediary Occupation[END_REF].

With reference to structuration theory, public relations professionals rely on dominant structures to make sense to their audiences, while often seeking to breaking away from them for effect (to increase notoriety or work on image) or to convey a particular message. Indeed, public relations is more often about influencing and changing dominant representations than it is about reinforcing them, though both are of course possible. In both cases, creativity is the key, but a form of creativity which is firmly grounded in existing cultural representations.

If culture is the underlying structure, in Giddens' sense, public relations messages are thus one of the many ways (materialised forms) in which the structure is dynamically updated and caused to evolve, thanks to the creative work of the public relations teams. The impact of public relations messages are all the more powerful when they are released through mass media outlets, exposing many individuals simultaneously to the same stories and symbolic stimuli. The creative development of the aforementioned Pepsi commercial was explained this way by the company:

The creative showcases a moment of unity, and a point where multiple storylines converge in the final advert. It depicts various groups of people embracing a spontaneous moment, and showcasing Pepsi's brand rallying cry to 'Live For Now,' in an exploration of what that truly means to live life unbounded, unfiltered and uninhibited. 11 Sometimes creative minds go further, playing on stereotypes and cultural taboos for maximal sensationalist effect though at the same time they may create ugly examples, for instance of a misogynist character. Despite US discussions of rape culture, the retailer Bloomingdale issued an infamous ad which read "Spike your best friend's eggnog when they're not looking". 12 Whether such campaigns and the outcry they often provoke actually reinforce or rather call into question what many people deem to be dominant negative cultural representations is wide open to debate, though it would appear to be an important issue which needs addressing by the ethics bodies of the public relations profession.

In contrast to the preceding examples, a campaign that received praise is the one instigated by the personal care brand Dove with the slogan "Real beauty". In what has been called of the biggest conceptual ad campaigns of the decade" narrow definitions of female beauty were challenged. 13 Through ads depicting women with shapes and figures different from the typical slim models, Dove, with the help of the public relations agency Edelman, "sought to start a conversation about beauty". 14 The contrast to the campaign from Victoria's Secret called "The Perfect 'body'" is striking. 15 The latter was also hijacked by the smaller competitor Dear Kate, showing pictures of ordinary women. In this way, public relations professionals as cultural mediators contribute to upholding, challenging, and renewing cultural values and representations within the societies in which they work. It also illustrates a point that by now has grown old; namely that public relations can be used for both positive or negative purposes, and as a profession needs to come to grips with this [START_REF] Fawkes | Public relations ethics and professionalism: The shadow of excellence[END_REF][START_REF] Ihlen | A public relations identity for the 2010s[END_REF].

Conclusion

Although the "cultural turn" in public relations has been salutary in many respects, it finds its (opposing) limits in (a) accusations of cultural appropriation or viral communitarian backlashes, and (b) essentialising identities and reinforcing imagined (homogenous) communities. In this paper, we have argued the need for a more complex vision of culture, its role in society and notably the essential role that it plays in the creative process. Building on work done by [START_REF] Giddens | The Constitution of Society : Outline of a Theory of Structuration[END_REF] or [START_REF] Bauman | Culture as Praxis[END_REF] on culture as a structuration process, we have focused on its social role as a "systemgenerating mechanism" that creates "knowledge-making groups […] within which individual choice and creativity are produced" (Hartley & Potts, 2014, p. 23). Such process-based perspectives place communication and story-telling, indeed, public relations, at the centre of their analysis and, in this sense, public relations can itself be studied as a process of cultural reproduction [START_REF] Frame | PR and Global Interculturation. Methodological Challenges for (Cross)Cultural PR Research[END_REF]. As such, studying public relations and culture is also a study of how public relations is influenced by and influences society.

Public relations plays a role in building/maintaining social consciousness of "cultural differences" both in the way it classifies audiences along cultural lines (structural determinism) and through the messages it produces which often tend to flatter audiences' (stereotyped) preconceptions of society. It is thus essential for public relations theorists and practitioners alike to adopt a critical stance towards their own and their colleagues' uses of "culture discourse" within the field, questioning their epistemological and ideological underpinnings.

What next? We would obviously encourage more research, focusing on, for instance, the cultural toolbox of culture comes into play in public relations on many different levels, or the impact of various types of messages, which appear to reinforce or challenge positive and negative representations, on various audiences. Cultures and identities are national, regional, ethnic, organisational and professional, among others, and these different levels of identification and of symbolic recognition mean that public relations practitioners need to take into account many different potential readings of the same message, in the light of what it might mean for many different groups. Naturally, the more complexity one seeks to take into account, the more unwieldy the models become. This, however, promises a fruitful future for scholarship on public relations and culture.

  , deterministic and reductive 1 Cf. https://www.theguardian.com/music/2015/apr/17/hunger-games-amandla-stenberg-criticises-mileycyrus-taylor-swift-cultural-appropriation. Page consulted on 31/03/2017. 2 Cf. https://www.washingtonpost.com/news/parenting/wp/2016/10/10/cultural-misappropriation-and-mydaughters-halloween-costume/?utm_term=.d5cfc803e17f. Page consulted on 31/05/2017. 3 http://www.newsinenglish.no/2017/10/17/sivs-pocahontas-stunt-backfired/ . Page consulted March 26, 2018. 4 http://people.com/food/pepsi-responds-kendall-jenner-backlash-protest-ad/. Page consulted on 31/05/2017. 5 http://time.com/4728979/stephen-colbert-kendall-jenner-pepsi-attractive-lives-matter/. Page consulted on 31/05/2017. 6 http://www.commisceo-global.com/blog/how-to-avoid-cultural-appropriation-promote-cultural-awarenessinstead. Page consulted on 31/05/2017.

  13 http://www.huffingtonpost.com/2014/01/21/dove-real-beauty-campaign-turns-10_n_4575940.html. Page consulted on 31/05/2017. 14 http://www.huffingtonpost.com/2014/01/21/dove-real-beauty-campaign-turns-10_n_4575940.html. Page consulted on 31/05/2017. 15 http://www.huffingtonpost.com/2014/11/06/victorias-secret-perfect-body-campaign_n_6115728.html. Page consulted on 31/05/2017.

In the Silent Language, Hall famously states, "Culture is communication and communication is culture"(Hall, 1959, p. 186).

The term praxis, as in Bauman's book Culture as Praxis, is used here to refer to culture which exists through practice: it is only through behaviour marked by culture that culture is maintained, passed on and renewed.


Xueru R Yan

Alexandre Favard

Stéphane Anguille

Jean-Luc L Seguin

Marc Bendahan

Philippe Moulin

Membrane SF: Hybrid membrane process to remove emerging pollutants

Keywords: Hybrid membrane process, Remove VOCs, Separation, Regeneration

Introduction

The removal or/and recovery of volatile organic compounds (VOCs) from gas or liquid is a major issue in terms of minimizing the environment impact of numerous industrial processes. No destructive VOCs capture technologies are preferentially used to enable the recycling of a large ratio of the emitted compounds. Our work relates to new membrane processes "Membrane SF" for extraction of pollutants by multichannel tubular membrane coupled with ionics liquids (ILs) [START_REF] Anguille | Device for extraction of pollutants by multichannel tubular membrane[END_REF]. This process will find applications for the treatment of traces of pollutants in a liquid or gaseous fluid, for example, the removal of small pollutants from an aqueous stream in industrial waste water, separation of aromatic compounds from a hydrocarbon feed in petrochemical applications and the removal of water traces in products of high added value as pharmaceutical, cosmetic or bio-carburant. Moreover, this hybrid membrane process improves the membrane separation technology allowing specific separation (functions of the ILs used) and easy manufacture and regeneration. It provides a high-efficiency and environmentally friendly device and process to purify wastewater and industrial waste gas.

Material and Methods

The membrane we used is tubular multichannel ceramic membrane. At least one channel enables the fluid to go through and at least one channel is filled with ILs. Channels, which contain the ILs, were sealed by glue on each extremity to keep the ILs inside. The experimental devices and the structure of membrane SF are presented in Figure 1. There are several steps of processes to remove pollutants, including the step of extraction and the step of regeneration. Different pollutants were used (VOCs, water, CO2) to demonstrate the feasibility of this new concept for gas and liquid effluents. The influence of operating conditions including temperature, flow rate, and pressure was studied. Moreover, this new concept "membrane SF" was compared to adsorption or absorption processes for some applications. This new concept was also used to protect VOCs sensors [START_REF] Favard | Highly Sensitive WO3 Thin Films Integrated on Microsensor Platforms for ppb BTEX Detection in a Gas Mixture with High Rate of Humidity[END_REF] from humidity, which currently is one of the weaknesses of chemical sensors for low concentration detection

Results and Discussion

The removal of VOCs was estimated as a function of the mass of ILs from toluene, benzene, xylene and chloroform. For batch application, the removal factor decreased versus time due to the ILs saturation but the outlet concentration was very low during long time. For removal of humidity, it was demonstrated that "membrane SF" can remove a high quantity of water and a good reproducibility is obtained in terms of adsorption (error range lower than 10%) but also in terms of "membrane SF regeneration". The operating conditions (temperature, pressure and flow rate) were studied to optimize this regeneration step. As can be seen in Figure 2, the response of a metal oxide gas sensor used to measure the concentration of BTEX was influenced by the environmental humidity. The "membrane SF" placed upstream has a double action, on the one hand it greatly reduces the humidity dependence of the sensor response, on the other hand it improves the sensor response stability. (Figure 2).

Conclusions

For membrane application, we have developed a new concept "membrane SF" which provides a membrane separation technology enabling specific separation, and improvement in the fabrication and regeneration processes.

Figure 1 .

 1 Figure 1. Steps of extraction with the Membrane SF Process

Figure 2 .

 2 Figure 2. Sensor response for 500 ppb of BTEX without membrane SF a) in dry air b) in wet air (50% RH) and with membrane SF c) in dry air, d) in wet air (50% RH)