Etienne Sicard
email: etienne.sicard@insa-toulouse.fr

Introducing 7-nm FinFET technology in Microwind

This paper describes the implementation of a high performance FinFET-based 7-nm CMOS Technology in Microwind. New concepts related to the design of FinFET and design for manufacturing are also described. The performances of a ring oscillator layout and a 6-transistor RAM memory layout are also analyzed.

Technology Roadmap

Several companies and research centers have released details on the 7-nm CMOS technology, as a major step for improved integration and performances, with the target of 4-nm process by 2025. We recall in table 1 the main innovations over the past recent years.

Improved performances

The power, performance and area gains are an important metric for justifying a shift from older technology nodes to new ones.

Page 2/22 etienne.sicard@insa-toulouse.fr 24/06/17 As compared to 14-nm technology node, the 7-nm technology offers [Brain2017, Mistry2017]:

• More than 50 % less power consumption. This is a key feature for mobile industry for which the battery life is the top one problem. • 20 to 50 % increase in switching performance. This is equally important in server applications and smartphones, which use faster processors and higher resolution screens.

• 4 times higher density. This is a key advantage to produce the lightest and thinnest possible smartphones.

The giant cost of fab and IC design in 7-nm

The movement from node to node has been observed every 2 years, at a regular rate. In 2017, the IC manufacturing was getting into 7nm, but the transition to 5nm was predicted to appear in more that 2 years. The reason for this potential slowing down is because profitability is jeopardized by design and manufacturing costs. Until the 28-nm node, the design cost was below 100 M$. Economic gain could be ensured by high IC unit costs and high volumes, which is the case for SoC for smartphones and laptops. The consequences of the fab and chip design cost explosion have been the drastic decrease of foundries. While more than 20 foundries existed for 130nm technology, only 5 major companies are providing the 10-7nm processes (Table 2). One reason is the extraordinary fab and IC design cost on nano-CMOS designs, as illustrated in Figure 2.

Company

In 2017, no commercial processor was yet fabricated in 7nm. IBM, GlobalFoundries, Samsung and SUNY announced the first 7-nm test chip (Fig. 3). A continuous increase in switching performance has been made possible thanks to several innovations, as shown in Figure 6. Starting 14-nm, the MosFET is replaced by the FinFET, for improved current capabilities. According to Samsung and IBM, the 7-nm technology could be the last one to use Fin-FETs, which has reached its physical limits, and could be replaced starting 5-nm node by multi-bridge FETs with gate all around stacked fins, which consume far less power, according to IBM researchers.

Page 4/22 etienne.sicard@insa-toulouse.fr 24/06/17 decreased due to the thinning of the gate oxide and faster switching rates thanks to reduced voltage swings. The 7-nm technology operates around 0.6 V, while I/Os are supplied at 1.0, 1.2, 1.5 V (Fig. 5).

Key features of the 7-nm technology

Equivalent Gate oxide

The FinFET switch is made of titanium nitride gate (TiN) with a combined hafnium oxide (HfO2) and silicon oxide (SiO2) for insulator. Hafnium-based oxides were introduced as a replacement for silicon oxide for improved field-effect in the transistor channel. The dielectric constant of HfO2 is near 20, more than 5 times the dielectric constant of SiO2 (around 4). The distances between the O atoms and the Hf-atom range between 0.21 and 0.24 nm, the Si-Si distance is 0.23 nm, while the O-O distance is 0.26 nm. The formulation of the equvalent oxide thickness (EOT) if all the oxide was SiO2 is as follows:

EOT = n. d + Th × ϵ /ϵ
• EOT is around 0.65 nm for 7-nm technology [Hashemi2016], as seen in Table 3.

• d
is the distance between 2 SiO2 atoms = 0.2 nm • n is the number of SiO2 atoms (2 or 3)

• Th is the thickness of HfO2 (3 nm in 14-nm, 1.4

2D view at atomic scale

In Microwind, the 2D view of the process may be turned to an atomic scale view of the layers. As the distance between 2 Si atoms is 0.235 nm, a 7-nm fin is equivalent to 20 atoms.

Figure 6: View of the silicon lattice and atomic scale view of the fin-FET in 7-nm

Page 6/22 etienne.sicard@insa-toulouse.fr 24/06/17

Still the FinFET

The FinFET device has a different layout style than the MOS device. Instead of a continuous channel, the FinFET uses fins (Figure 7), which provide the same current at size more than 3 times smaller (Fig. 8). FinFET also provides a lower leakage current (Ioff) at the same (Ion). High density (HD) designs use 2 fins, high performance (HP) designs 4 fins or more. and Fin Length (LG).

Lambda

In Microwind, we use an integer unit for drawing, called λ ("lambda") which is fixed to 4 nm for 7-nm CMOS process (Table 4).

• The drawn gate length is 2 λ that is 8 nm.

• The fin width is 1 λ that is 4 nm.

• The lower metal pitch is 24 nm.

Transistor performances in 7-nm technology

Designing a 1µm-width FinFET

The evaluation of the equivalent FinFET channel width corresponds to the following formulation (Eq.

1). The evaluation of the current is usually expressed in mA/µm, meaning that a 1-µm equivalent width

FinFET design is needed to evaluate the current. In the proposed 7-nm technology, HFIN is 35 nm, WFIN 4 nm, so one fin has an equivalent width of 74 nm (Figure 8). Page 9/22 etienne.sicard@insa-toulouse.fr 24/06/17

An equivalent width of 1µm, as it would be designed using MosFET's, corresponds to around 14 fins in 7-nm technology. As seen in Fig. 9, the FinFET with a 1-µm width is 3 times smaller than a MosFET with the same width. We get the following I/V characteristics (Fig. 19) for n-channel FinFET and pchannel FinFET. The drawback associated with this high current drive is the leakage current which rises from 1 nA/µm (low leakage NMOS) to 10 nA/µm (high speed NMOS), as seen in the Id/Vg curve at the X axis location corresponding to Vg= 0 V. From a design view-point, the "option" menu in the MOS generator enables to switch from low leakage to high-speed. In terms of layout, the only difference is the option layer that contains the MOS option information which can be Low leakage (Regular Vt), High Speed (Low VT), or High Voltage.

Page 10/22 etienne.sicard@insa-toulouse.fr 24/06/17

P-channel MOS device characteristics

The p-FinFET drive current in 7-nm technology is quite similar to the n-FinFET thanks to the strain engineering for p-channel that nearly compensates the intrinsic mobility degradation of holes (Pchannel) vs. electrons (N-channel). The leakage current is around 1 nA/µm for the low-leakage device and nearly 10 nA/µm for the high-speed device (Fig. 11). nA/µm, is better than the one with Ion=1,2 mA/µm with the same Ioff.

However, Ion is not the best metrics to estimate the circuit delay because, in most logic cells, the current through the n-device and p-device never really reach Ion (Fig. 13). The average current Ieff reached during switching operation may be approximated as the average of Ihigh and Ilow, with the following expressions. The effective current Ieff is shown in Fig. 13. Ieff is around half of Ion.

Page 12/22 etienne.sicard@insa-toulouse.fr 24/06/17

Threshold voltage dependence on gate length

As can be seen in Fig. 14, the threshold voltage decreases when the channel length tends to its minimum value 2 λ, which is equivalent 8 nm in Microwind's 7-nm technology. Note that the minimum length for high-voltage device is 4 λ, which is 16 nm in 7-nm technology. This effect is also named

Basic gates

The cell compiler proposed in Microwind converts into layout basic cells such as inverters, AND/OR, NAND, NOR or combinations of AND/OR gates. A very regular drawing of gates and dummy gates on both sides is required for manufacturability. The fins must also be aligned from one cell to another. to the 2 nd process iteration, etc. The double patterning is required for metal layers as the pitch between tracks is smaller than 80 nm that is M3 to M6. Half the patterns go on the first patterning and half go on the second patterning. In order to ensure an easy selection of metal tracks for the first and second patterning, regular structures with straightforward orientation such as M1 east-west, and M2 southnorth are requested. The other solution is to relax the pitch constraints for an improved manufacturability, at the cost of an extended silicon area. M3-M8 with pitch of 80-nm and higher are still fabricated using simple patterning. Most often, inverters are used in the delay chain. However, NAND4 designs may also be found in the literature. In FO3 configuration (Fig. 25), each inverter of the ring oscillator is connect to the nextstage inverter (FO1) plus 2 inverter gates that have no action on the ring oscillator, but charge the inverter with 2 supplementary gate capacitances. FO4 consists in connecting the inverter output to 4 inverter inputs.

Performances

An improvement of switching performances close to a factor of 2 is observed between 14-nm and 7nm designs, although VDD is reduced from 0.85 V to 0.65 V. The performance estimation is based on the simulation of a 3-inverter ring oscillator (RO) with FO3. The tool Analysis -> Parametric Analysis of Microwind is used to monitor the oscillating frequency for varying supply voltage VDD (Fig. 26). We choose s3 as monitoring signal, and select VDD as varying parameter, from 0.3 V to nominal voltage.

We observe an oscillation starting 0.55V in 14-nm (VDD=0.85 V). For 7-nm, the oscillation starts at 0.50 V (VDD=0.65V).

Page 19/22 etienne.sicard@insa-toulouse.fr 24/06/17

Simulation of Process Variations (PVT)

Considerable differences may be observed in terms of performances, depending on the process, voltage and temperature conditions. The usual temperature range is [-50°C..+125°C], the voltage variation VDD+/-10%, and the process may also vary +/-15% for some key parameters such as the threshold voltage and mobility. Microwind gives access to "Process-Voltage-Temperature" (PVT) simulation through the command Simulate → Simulation Parameters → Process Variations. Direct access from the simulation waveform window is also possible using the button "Process Variations".

The most usual simulation consists of simulating extreme situations (Min and Max), as compared to typical conditions (Table 8).

•

In Min situation, VT is high and the mobility U0 is low. The supply is minimum and the temperature is maximum. The ring oscillating is around 100 GHz.

Compare technologies

A quick access to technology is proposed in Simulation Parameters (Fig. 28). MosFET technologies range from 0.18µm to 20nm, FinFET technologies range from 14nm to 7nm. MosFET and FinFET designs are not compatible.

Page 21/22 etienne.sicard@insa-toulouse.fr 24/06/17

Conclusions

This application note has illustrated the trends in nano-CMOS technology and introduced the 7-nm technology generation, based on technology information available from manufacturers. The key features of the 7-nm CMOS technology have been illustrated, including the FinFET, design for manufacturing and double patterning. A 3-stage ring, FinFETs wih 1-µm equivalent width as well as interconnects with 1-µm length have been used for comparison purpose.

Figure 1 :

 1 Figure 1: The spectacular reduction of feature sizes from 45 to 7nm (adapted from [Mistry2017])

Figure 2 :

 2 Figure 2: The extraordinary increase of the fab cost: more than 7 billion $ for a 10-7-nm process, and associated chip design cost as high as 270 M$ for a run in 7-nm.

Figure 3 :

 3 Figure 3: Examples of 10-nm processors and prototype 7-nm circuit by IBM

Figure 4 :

 4 Figure 4: Increased switching speed capabilities over technology nodes

Figure 5 :

 5 Figure 5: The core supply voltage in 7nm technology is 0.65 V, with typical IO voltage of 1.0 V

Figure 7 :

 7 Figure 7: 3D view of the 4-fin FinFET and illustrations of the Fin height (HF), Fin Thickness (TF)

Figure 8 :

 8 Figure 8: The equivalent width of a multi-fin FET

Figure 9 :

 9 Figure 9: The 7-nm multi-fin FET with an equivalent width of 1 µm is three times more compact than the MosFET traditional design

Figure 10 :

 10 Figure 10: Id/Vd characteristics of the low leakage and high speed n-channel FinFET devices.

Figure 11 :

 11 Figure 11: Id/Vg characteristics of the low leakage and high-speed p-FinFET devices

Figure 12 :

 12 Figure 12: Evaluation of the sub-threshold slope for a LL device: around 70mV/decade

Figure 13 :

 13 Figure 13: Difference between Ion and Ieff. The inverter switching is shown on the I/V curves.

  threshold voltage roll-off. It is anticipated that stacked nano-wires such as Gate-All-Around (GAA) FET devices will show the least amount of VT roll-off due to their superior electrostatic integrity [Zheng2016].

Figure 14 :

 14 Figure 14: The threshold voltage decreases with short-channel effects (n-channel FinFET at left, p-channel FinFET at right)

  ) may be observed by selecting the option "Monte-Carlo on process" in the Simulate > Simulation Options menu.

Figure 15 :

 15 Figure 15: Ids vs Vds calculated on 100 samples of n-FinFET with random distribution of VT and U0, with a Gaussian distribution around the nominal value.

Figure 16 :

 16 Figure 16: log(Ids) vs Vgs calculated on 100 samples of n-FinFET with random distribution of VT and U0, with a Gaussian distribution around the nominal value.

Figure 18 :

 18 Figure 18: Compilation of a 2-fin inverter (High density option) with Microwind

Figure 23 :

 23 Figure 23: Single, double and quadruple patterning as a function of interconnect pitch [Brain2017]

Figure 24 :

 24 Figure 24: Ring oscillator performance comparison proposed by [Collaert2016] on technologies ranging from 28-nm to 7-nm

Figure 26 :

 26 Figure 26: A speed improvement close to a factor of 2 is observed between 14-nm 3-stage ring oscillator and 7-nm (RO3, FO3).

  One of the most representative designs for comparing technology nodes is the static RAM cell designed using 6 transistors (6T-SRAM). High performance SRAM use 2 fins for internal inverters while high density SRAM use 1 fin.

Figure 27 :

 27 Figure 27: 6T-SRAM implementation in FinFET (SRAM-6T-7nm.MSK)

Figure 28 :

 28 Figure 28: Quick access to MosFET and FinFET technologies

Figure 29 :

 29 Figure 29: Convert MosFET design into FinFET. Only vertical gates are considered.

Table 1 :

 1 Most significant technology nodes over the past 15 years

	Technology node	Year of	Key Innovations	Application note
		introduction
	180nm	2000	Cu interconnect, MOS options, 6 metal
			layers
	130nm	2002	Low-k dielectric, 8 metal layers
	90nm	2003	SOI substrate	[Sicard2005]
	65nm	2004	Strain silicon	[Sicard2006]
	45nm	2008	2nd generation strain, 10 metal layers	[Sicard2008]
	32nm	2010	High-K metal gate	[Sicard2010]
	20nm	2013	Replacement metal gate, Double	[Sicard2014]
			patterning, 12 metal layers
	14nm	2015	FinFET	[Sicard2017]
	10nm	2017	FinFET, double patterning	[Sicard2017]
	7nm	2019	FinFET, quadruple patterning	This application note
	5nm	2021	Multi-bridge FET

Table 2 :

 2

5 major players in the 10/7/5-nm chip manufacturing Page 3/22 etienne.sicard@insa-toulouse.fr 24/06/17

7nm Low leakage RVT High speed HS High Voltage HVT Parameter in RUL file

					nm in 7-nm)
	• ϵ	= 4, ϵ	= 20
	EOT b4t2ox	b4t2ox	b4t3ox
	n-Channel FinFET (nm)	0.65	0.65	2.0
	p-Channel FinFET (nm)	0.65	0.65	2.0

Table 3 :

 3 Equivalent oxide thickness of 7-nm devices in Microwind

Microwind parameter Unit Code Name in rule file 7-nm process

	Lambda	nm	λ	lambda	4
	Core supply V	VDD	Vdd	0.65
	Fin Width	λ	WF	R301	1
	Fin pitch	λ	FP	R308	6
	Fin Height	nm	HF	thdn	35
	Gate height nm	GH	thpoly	50
	Gate length λ	GL	R302	2
	Gate pitch	λ	GP		6
	Contact size λ	CS	R401	2
	EOT	Nm	EOT	b4toxe	0.65
	M1 pitch	λ		R501+R502	6

Table 4 :

 4 Publications from foundries regarding 7-nm technology rarely give detailed numbers regarding precise currents & voltages, and usually refer to "arbitrary units" (A. U.)[Wu2016, Xie2016, Steegen2015].Another approach proposed by [Clark2016] consists in proposing a set of parameters interpolated from previous technology nodes, and tuned to available experimental data. We follow a similar approach and try to propose numbers close to average performances. Table 4 gives an overview of the key parameters for the 7-nm technological node concerning the internal MOS devices and layers. Four threshold options, namely high-Vt (HVT), regular Vt (RVT), low Vt (LVT) and Super low VT (SLVT) are usually proposed [Clark2016]: • HVT -High Threshold Voltage causes less power consumption, but switching is slow. HVT are used in power critical functions. Ioff is around 0.1 nA/µm, Idsat around 1.2 mA/µm. • RVT -Regular Threshold Voltage (sometimes called Standard VT or SVT) offers trade-off between HVT and LVT i.e., moderate delay and moderate power consumption. Ioff is around 1 nA/µm, Idsat around 1.4 mA/µm. • LVT -Low Threshold Voltage causes more power consumption and switching timing is optimized. LVT are used in time critical functions. Ioff is around 10 nA/µm, Idsat around 1.6 mA/µm.• SLVT -Super Low Threshold Voltage causes even more power consumption but switch at the highest speed. SLVT are used in time-critical functions without consideration of leakage currents. Ioff is around 100 nA/µm, Idsat around 1.8 mA/µm. Table6gives an overview of the key parameters for the 7-nm technological concerning the Input/output MOS devices and associated supply voltage. In Microwind, we only consider 1.0 V I/O supply and tune the "High-Voltage" (HV) MOS device on the median performances.

	The Idsat current for p-channel devices is almost simulare to the n-channel device. In Microwind, we
	only propose 2 types of devices :
	• Low leakage MOS (LL), close to RVT
	• High Speed MOS (HS), close to LVT
	Parameter	In Microwind
	VDD core (V)	0.65
	Effective gate length (nm)	12
	MOS variants	2
	Ion N (mA/µm) at 0.6 V	1.4 (LL) 1.7 (HS)
	Ion P (mA/µm) at 0.6 V	1.3 (LL) 1.6 (HS)
	Ioff N (nA/µm)	1 (LL) 10 (HS)
	Ioff P (nA/µm)	1 (LL) 10 (HS)
	Gate dielectric	SiO2, HfO2
	Gate stack	Al/TiN
	Equivalent oxide thickness (nm)	0.65

key parameters of the 7-nm processes used to configure Microwind rule file Cmos7n.RUL Page 7/22 etienne.sicard@insa-toulouse.fr 24/06/17 Core MOS devices Table 5: Key features of the core devices proposed in the 7-nm technology Page 8/22 etienne.sicard@insa-toulouse.fr 24/06/17 IO MOS devices

Table 6 :

 6 Key features of the I/O devices proposed in the 7-nm technology and corresponding values in Microwind

Table 8 :

 8 Variation of process parameters and effects on the oscillating frequency

Acknowledgements

The adaptation of Microwind to 7-nm FinFET technology and the development of an e-learning course on nano-CMOS cell design have been made possible thanks to the financial support of the ERASMUS+ program Knowledge Alliance "Micro-Electronics Cloud Alliance" 562206-EPP-1-2015-1-BG-EPPKA2-KA.

etienne.sicard@insa-toulouse.fr 24/06/17

Interconnects Metal Layers

The number of metal layers in nano-CMOS technology usually ranges from 8 to 15, with a trade-off between integration and cost. Layers metal5 and metal6 are a little thicker and wider, while layers metal7 and metal8 are significantly thicker and wider, to drive high currents for power supplies (Fig. 22).

Double & quadruple Patterning

The quadruple patterning is required for metal layers with a pitch smaller than 40-nm, which is the case of M1 & M2 (Fig. 23). One quarter of the patterns go on the first patterning, the second pattern


Olivier Pironneau
email: olivier.pironneau@upmc.fr

Computational Issues for Optimal Shape Design in Hemodynamics

A Fluid-Structure Interaction model is studied for aortic flow, based on Koiter's shell model for the structure, Navier-Stokes equations for the fluid and transpiration for the coupling. It accounts for wall deformation while yet working on a fixed geometry. The model is established first. Then a numerical approximation is proposed and some tests are given. The model is also used for optimal design of a stent and possible recovery of the arterial wall elastic coefficients by inverse methods.

Introduction

Hemodynamics, a special branch of computational fluid dynamics, poses many problems of modeling, data acquisition, computation and visualization. However even as of now it is a valuable tool to understand aneurisms, to design stents and heart valves, etc (see for example [START_REF] Usabiaga | Staggered schemes for fluctuating hydrodynamics[END_REF][START_REF] Formaggia | Cardiovasuclar Mathematics[END_REF][START_REF] Thiriet | Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems[END_REF]).

In this paper we shall focus on algorithms for fluid flows with compliant walls like aortic flow, their modelisation, numerical simulation and inverse techniques.

Blood in large vessels like the aorta is Newtonian and flows in a laminar regime with Reynolds number of a few thousands. The Navier-Stokes equation for incompressible fluid is a good model for it.

A blood vessel on the other hand is a complex structure for which linear elasticity is only a first crude approximation and for which the Lamé coefficients do not have a universal value and can vary with individuals.

Nevertheless, like many authors ( [START_REF] Tambaca | Mechanical Behavior of Fully Expanded Commercially Available Endovascular Coronary Stents[END_REF][START_REF] Nobile | an effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions[END_REF] for instance) we shall use Koiter's linear shell theory.

Koiter's Shell Model for Arteries

The following hierarchy of approximations for the displacement d of the aortic wall will be made:

• Small displacement linear elasticity instead of large displacement (needed for the heart).

• No contact inequalities with the surrounding organs.

• Shell model for the mean surface.

• With reference to the mean surface, normal displacement of the walls only.

Let Σ be the shell surface representing the mean position of the blood vessel.

Let n(x) be the normal at x ∈ Σ. Let d(x, t) be the displacement of the wall at x at time t. Normal displacement implies d = ηn.

In [START_REF] Nobile | an effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions[END_REF] it is shown that under such conditions, Koiter's model reduces to the following equation of η on Σ

ρ s h∂ tt η -∇ • (T∇η) -∇ • (C∇∂ t η) + a∂ t η + bη = f s , (1)
where ρ s is the density and h the thickness of the vessel, T is the pre-stress tensor, C is a damping term, a, b are viscoelastic terms and f s the external normal force, i.e. the normal component of the normal stress tensor -σ s nn . As with all second order wave type equations two conditions must be given at t = 0, for instance

η |t=0 = η 0 , ∂ t η |t=0 = η 0 . Remark 1 When [h, T, C, a] b, (1)
leads to the so-called surface pressure model

-σ s nn = bη, with b = Ehπ A(1 -ξ 2 ) , ( 2
)
where A is depends on the geometry of the artery's cross section and equal to the cross section surface when it is circular; E is the Young modulus, ξ the Poisson coefficient.

Some typical values are (in the metric system MKSA) for a heart beat of one pulsation per second:

E = 3M P a, ξ = 0.3, A = πR 2 , R = 0.013, h = 0.001, ρ f = 9.81 10 6 ,
leading to b = 3.310 7 ms -2 and giving displacements in the range of 0.1 10 -3 m and flow rates around 2 10 -5 m 3 s -1 for aortic flows.

Fluid Equations

The Navier-Stokes equations in a moving domain Ω(t) define the velocity u and the pressure p,

ρ f ( ∂u ∂t + u • ∇u) + ∇p -µ∇ • (∇u + ∇u T ) = 0, ∇ • u = 0, (3)
where ρ f is the density of the fluid and µ its viscosity. Continuity on Σ of fluid and solid velocities implies

u = ∂d ∂t := n ∂η ∂t , on Σ.
With the surface pressure model, continuity of normal stresses implies

σ f nn := n • (µ(∇u + ∇u T ) -p)n = -σ s nn := bη.
Notice that as a consequence of the hypothesis of normal displacements only of the structure, there is no provision to write the continuity of the tangential stresses.

For aortic flow there also an inflow and an outflow boundary Γ i and Γ o on which we will prescribe pressure and no tangential velocity. If S = Γ i ∪ Γ o , then the boundary Γ is

Γ := ∂Ω(t) = Σ ∪ S = Σ ∪ Γ i ∪ Γ o .
In [START_REF] Nobile | Vergana an effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions[END_REF] and many other authors, the matching conditions on Σ are written on the boundary of a fixed reference domain ∂Ω 0 because Koiter's shell model works with a fixed mean surface Σ.

With the notations of [START_REF] Decoene | Moving Meshes with freefem++[END_REF], assume that the domain of the fluid is

Ω t = A t (Ω 0 ) with A t : x 0 → x t := A t (x 0 ). Let u τ (x, t) = u(A t (A -1 τ (x)), t), ∀x ∈ Ω τ . (4)
Then in Ω t at t = τ , the Navier-Stokes equations are in ALE format

ρ f ∂u τ ∂t + (u τ -c τ ) • ∇u τ + ∇p -µ∇ • (∇u τ + ∇u T τ ) = 0, ∇ • u τ = 0, with c τ (x) = - ∂A t (A -1 τ (x)) ∂t | t=τ . (5)
3 Transpiration Conditions for the Fluid

Conservation of Energy

We begin with an important remark on the conservation of energy.

The variational formulation of (3)-divided by ρ s -is, ∀û, p

Ω(t) [û • (∂ t u +u • ∇u) + ∇p • û -p∇ • u + ν 2 (∇u + ∇u T ) : (∇û + ∇û T )] = Ω(t) f s • û. (6)
An energy balance is obtained by taking û = u and p = -p,

∂ t Ω(t) u 2 2 + ν 2 Ω |∇u + ∇u T | 2 = Ω f s • û - ∂Ω pu • n, (7)
because

∂ t Ω(t) u • w = Ω(t) ∂ t (u • w) + ∂Ω v u • w, Ω ((u∇u) • u) = ∂Ω u • n u 2 2 = ∂Ω v 2 u • u, (8)
when v = u • n, the normal speed of ∂Ω.

With transpiration conditions we intend to work on a fixed domain with zero tangential velocity but non zero normal velocity u • n = w. In that case, in order to preserve energy, (6) on a fixed domain Ω needs to be modify into

Ω [û • (∂ t u + u • ∇u) + ∇p • û -p∇ • u + ν 2 (∇u + ∇u T ) : (∇û + ∇û T )] - ∂Ω w 2 u • û = Ω f s • û; (9)
or equivalently into

Ω [û • (∂ t u -u × ∇ × u) +∇p • û -p∇ • u + ν 2 (∇u + ∇u T ) : (∇û + ∇û T )] = Ω f s • û, (10)
where p = p + 1 2 |u| 2 is the dynamic pressure. Remark 2 Notice that the difference between p and p is second order with respect to the displacement, so exchange one for the other in the shell model is a modification well within the small displacement hypothesis. However it makes a difference on Γ i , Γ o and p Γ should be changed accordingly.

From now on we drop the tilde on p.

Finally we recall an identity (see [START_REF] Costabel | Singularities of electromagnetic fields in polyhedral domains[END_REF] for instance) which holds whenever u×n = 0 and shows that we can use several forms for the viscous terms,

Ω [∇ × u • ∇ × v + ∇ • u∇ • v] = Ω ∇u : ∇v = Ω [ 1 2 (∇u + ∇u T ) : (∇v + ∇v T ) -∇ • u∇ • v]. (11)
Hence a variational formulation adapted to the problem is to find u with u×n = 0 and, for all p and all û with û × n = 0

Ω [û • (∂ t u -u × ∇ × u) -p∇ • û -p∇ • u + ν∇ × u • ∇ × v] + ∂Ω pu • n = Ω f s • û. ( 12
)

Transpiration

As the wall vessel is {x + ηn : x ∈ Σ} and as, by Taylor,

u(x + ηn) = u(x) + η∇u • n(x) + o(η),
matching the velocities of fluid and structure may be written as

u + η ∂u ∂n = n ∂η ∂t + o(η) on Σ, u × n = 0. ( 13
)
On a torus of small radius r and large radius R, at a point of coordinates (R+r cos θ) cos ϕ, (R+r cos θ) cos ϕ, r sin θ), a straightforward calculation shows that

u × n = 0, ∇ • u = 0 ⇒ n • ∂u ∂n = (1 + r R cos 2 θ) u • n r .
So [START_REF] Usabiaga | Staggered schemes for fluctuating hydrodynamics[END_REF] becomes

u • n = ∂ t η 1 + η r (1 + r R cos 2 θ) -1 , u × n = 0. ( 14
)
Similarly the normal component of the normal fluid stress tensor is

σ f nn = p + 2(1 + r R cos 2 θ) µ r u • n.
Therefore for a quasi toroidal geometry, for large R, (1) is

ρ s h∂ tt η-∇ • (T∇η) -∇ • (C∇∂ t η) + a∂ t η + bη = p + 2(1 + r R cos 2 θ) µ r ∂ t η 1 + η r (1 + r R cos 2 θ) -1 . (15)
So, in fine, the domain Ω no longer varies with time but on part of its boundary

u • n = ∂ t η 1 + η r (1 + r R cos 2 θ) -1 , u × n = 0, ρ s h∂ tt η -∇ • (T∇η) -∇ • (C∇∂ t η) + a∂ t η + bη = p, ( 16
)
where a is a non linear function of η.

Remark 3 Notice that η r, i.e. large vessels, allows us to eliminate η and write everything in terms of ∂ t p and u n := u • n. It suffices to differentiate the last equation with respect to t and use the first one and integrate in time,

p = p 0 + L(u • n) := t 0 ρ s h∂ tt u n -∇ • (T ∇u n ) -∇ • (C∇∂ t u n ) + a∂ t u n + bu n . (17)

Variational Formulation and Approximation

Coming back to [START_REF] Thiriet | Biomathematical and Biomechanical Modeling of the Circulatory and Ventilatory Systems[END_REF] and using (17):

Continuous Problem Find u with u × n = 0 and, for all p and all û with û × n = 0

Ω [û • (∂ t u -u × ∇ × u) -p∇ • û -p∇ • u + ν∇ × u • ∇ × v] + Σ p 0 + L(u • n) u • n = - S p Γ û • n

Approximation in Time

From now on, for clarity, we consider only the case of the surface pressure model, i.e. h = T = C = a = 0, L(u • n) = bu • n. However everything below extends to the full model.

So define

U (t) = t 0 u(s)ds and use the integration rule U m+1 = U m + u m+1 dt. and V = {u ∈ H 1 (Ω) d : u × n = 0 on ∂Ω}, Q = L 2 (Ω).
Time discrete Problem p(t) = p 0 + bU (t) and we seek

u m+1 ∈ V, pm+1 ∈ Q, satisfying for all û ∈ V, p ∈ Q, Ω û • ( u m+1 -u m δt -u m+ 1 2 × ∇ × u m+θ ) -p m+1 ∇ • û -p∇ • u m+ 1 2 + ν∇ × u m+ 1 2 • ∇ × û + Σ [bû • n(u m+ 1 2 δt + U m ) • n] = - S p Γ û • n, (18)
where u m+ 1 2 = 1 2 (u m+1 + u m ) and θ = 0 for a semi-explicit lineat but order one scheme or θ = 1 2 for a fully implicit second order scheme in time but nonlinear.

Convergence

A convergence analysis was done in [START_REF] Chacon Rebollo | Analysis of a Simplified Coupled Fluid-Structure Model for Computational Hemodynamics[END_REF]; we recall the results. We denote u δ the linear in time interpolate of

{u m } M 1 on (0, T ) = ∪ M 1 [ (m -1)δt, mδt]. For clarity let's assume that S = ∅. Lemma 1 If Ω is C 1,1 or polyhedral and u 0 ∈ L 2 (Ω) 3 , p 0 ∈ H 1/2 (Σ), then the weak solution of the continuous problem verifies u ∈ L 2 (H 2 ), ∂ t u ∈ L 2 (L 2 ), p ∈ L 2 (H 1 ), and u×n = 0 in L 2 (L 4 (Σ)), ∂ t p = bu•n in L 2 (H 1/2 (Σ)), p(0) = p 0 .
Theorem 1 The solution of the time discretized variational problem satisfies

u δ L ∞ (L 2 ) + √ ν u δ L 2 (H 1 ) + b δt n+1 k=1 u k • n L ∞ (L 2 (Σ)) ≤ C u 0 0,2,Ω + 1 √ ν p 0 L 2 (Σ) .
Theorem 2 If Ω is simply connected, there is a subsequence (u δ , p δ ) which converges to the continuous problem in

L 2 (W) × H -1 (L 2 )
where

W = {w ∈ L 2 (Ω) | ∇ × w ∈ L 2 (Ω), ∇ • w ∈ L 2 (Ω), n × w | Σ = 0 }.

Spatial Discretization with Finite Elements

The easiest is to use penalization to enforce u×n = 0 by adding to the boundary

integral 1 Σ u m+1 × n • û × n.
Then we may use conforming triangular or tetrahedral elements P 2 or P 1 +bubble for the velocities and P 1 for the pressure.

A freefem++ implementation (see [START_REF] Hecht | New development in freefem++[END_REF]) is shown on Figure 1 Figure 1: An implementation using freefem++ for problem (18)

5 Optimization and Inverse Problems

Optimal Stents with the Surface Pressure Model

A stent is a device to reinforce part of a cardiac vessel and/or to change the topology of the flow by its rigidity. This results in a change of the coefficient b. So with a first order scheme in time we can consider

min b(x) J = Σ×(0,T ) F (p)dxdt : Subject to Ω [û • ( u m+1 -u m δt -u m+1 × ∇ × u m ) -p m+1 ∇ • û -p∇ • u m+1 ] + Ω ν∇ × u m+1 • ∇ × û + Σ [bû • n(u m+ 1 2 δt + U m ) • n] = - S p Γ û • n ∀û ∈ V h , p ∈ Q h . (19)
For instance F = |p| 4 will minimize the time averages pressure peak on Σ.

Inverse Problems

Can we recover the structural parameters of the vessel walls from the observation of the pressure? Consider the minimization problem

min b(x),x∈Σ J(u, p, b) := 1 2 Ω×(0,T ) (p m -p m d ) 2 , (20)
subject to (19) or to

Ω [û • ( 1 δt u m+1 -u m (x -u m (x)δt) -p m+1 ∇ • û -p∇ • u m+1 ] + Ω ν∇ × u m+1 • ∇ × û + Σ b(u m+1 δt + U m ) • û = - Γ p Γ ûn ∀û ∈ V h , p ∈ Q h with û × n| Γ = 0; U m+1 = U m + u m+1 δt. (21)
The difference between (19) and ( 21) is the numerical treatment of the nonlinear term: implicit Euler in the first and Characteristic-Galerkin in the second.

Calculus of Variations

To set up a descent algorithm we must do a sensitivity analysis of the problem. This is done with a "Calculus of Variations". When a parameter varies it triggers a variation of u, p which we call δu, δp. To compute them we linearise the Navier-Stokes equations. These written globally over (0,T) in weak form are,

M -1 0 δt Ω [û m+1 • ( 1 δt δu m+1 -δu m (x -u m (x)δt) -δp m+1 ∇ • ûm+1 -pm+1 ∇ • δu m+1 ] + Ω ν∇ × δu m+1 • ∇ × ûm+1 + Σ r m+1 (δU m+1 -δU m -δu m+1 δt) + Σ b(δu m+1 δt + δU m ) + δb(u m+1 δt + U m ) • ûm+1 = 0 ∀û m ∈ V h , pm ∈ Q h , r m with ûm × n|Γ = 0. ( 22
)
If ûM+1 = 0, r M +1 = 0, it can be rearranged as follows

M -1 0 δt Ω [ 1 δt ûm+1 -ûm+2 ((x + u m (x)δt) • δu m+1 -δp m+1 ∇ • ûm+1 -pm+1 ∇ • δu m+1 ] + Ω ν∇ × δu m+1 • ∇ × ûm+1 + Σ (r m+1 -r m+2 )δU m+1 -r m+1 δu m+1 δt) + Σ b(δu m+1 δt + δU m ) + δb(u m+1 δt + U m ) • ûm+1 = 0. ( 23
)

Adjoint State

To express the variations in terms of δb, we need to introduce an adjoint state v, solution of the following,

M -1 0 δt Ω [ 1 δt v m+1 -v m+2 ((x + u m (x)δt) • vm+1 -qm+1 ∇ • v m+1 -q m+1 ∇ • ûm+1 ] + Ω ν∇ × ûm+1 • ∇ × v m+1 + Σ (r m+1 -r m+2 ) V m+1 -r m+1 vm+1 δt) + Σ b(v m+1 δt + V m ) • v m+1 = M -1 0 δt Ω (p m+1 -p m+1 d )q m+1 , (24)
for all v, q such that v × n = 0 on ∂Ω.

Denote V m = r m δt ⇒ V m+1 = V m+2 -bv m+2 δt Ω 1 δt v m+1 -v m+2 ((x + u m (x)δt) • v -q∇ • v m+1 -q m+1 ∇ • v + Ω ν∇ × v m+1 • ∇ × v + Σ (bv m+1 δt -V m+1 ) • v = Ω (p m+1 -p m+1 d )q, (25)
for all v, q such that v × n = 0 on ∂Ω.

Computation of Gradients with Respect to b

Letting v = δu m+1 , q = δp m+1 and summing in m, from 1 to M after multiplication by δt gives,

M -1 0 δt Ω (p m+1 -p m+1 d )δp m+1 = M -1 0 δt Ω 1 δt v m+1 -v m+2 ((x + u m (x)δt) • δu m+1 -δp m+1 ∇ • v m+1 -q m+1 ∇ • δu m+1 + Ω ν∇ × δu m+1 • ∇ × v m+1 + Σ (bv m+1 -r m+1 )δu m+1 δt -δU m+1 (r m+2 -r m+1 -bv m+2 ) = M -1 0 δt Ω 1 δt δu m+1 -δu m (x -u m (x)δt) • v m+1 -δp m+1 ∇ • v m+1 -q m+1 ∇ • δu m+1 + Ω ν∇ × δu m+1 • ∇ × v m+1 + Σ bv m+1 δu m+1 δt + δU m bv m+1 + (δU m+1 -δU m -δu m+1 δt)r m+1 = - M -1 0 δt Σ δb(u m+1 δt + U m ) • v m+1 = - Σ δb δt M -1 0 U m • v m , ( 26
) because U 0 = v M = 0. To minimize in H 1 -norm we solve for g ∈ H 1 0 (Σ), Σ ∇ s g • ∇ s w = - Σ δt M -1 0 U m • v m w, ∀w ∈ H 1 0 (Σ) ⇒ δJ = Σ ∇ s g • ∇ s δb (27)

Numerical Tests

We take the test case documented in [START_REF] Bukaca | Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement[END_REF]. It is a 2-d problem for the upper part of a symmetric straight vessel. The geometry is the rectangle (0, L) × (0, R) with L = 6 and R = 0.5. Pressure is imposed at both end, zero on the right and p 1 = 1 2 p max (1 -cos(2π t tmax )) with p max = 2000 and t max = 0.005. The mesh is uniform 60 × 10. The step size is δt = 210 -4 and there are 60 time steps in this simulation, so T = 0.012 = 2.4t max . The P 2 × P 1 element is used for velocity-pressure.

The objective is to see if it is possible to reconstruct b on the upper wall from the pressure in the vessel.

So we first solve the direct problem with b = b d := 2.10 5 (1 + 6 x L (1 -x L )) approximated with the P 1 element. We call the computed pressure {p m d (x)} M -1 0 . Then we solve (20) with 50 iterations of an H 1 0 -projected gradient method with fixed step size, λ = 10 6 .

Algorithmic Steps

• Compute p d by a time loop from 0 to T and store on disk.

• Optimization loop:

1. Compute u, p by a time loop from 0 to T and store on disk u, p, U . • Display results.

We choose b max = 2.10

5 (1 + 12 x L (1 -x L )), b min = 2.10 5 (1 + 2 x L (1 -x L )
). The results are shown on figures 2, 3, 4.

Preliminary 3D tests

Experiment 1 This is only a feasibility test with F = p 4 ; The geometry is a quarter of a torus with R=4 and r=1. It is discretized with 1395 vertices and 6120 elements. The number of unknown of the coupled system [u, p] is 23940 with the P 1 -bubble/P 1 element and Crank-Nicolson implicit scheme. The viscosity is ν = 0.01; we chose = ν. The final time is T = 1, the time step is dt = 0.1 and the pressure difference imposed at Γ i (top) and Γ o bottom is 6 cos 2 (πt).

The flow is stored on disk at every iteration ready to be reused backward in time for the adjoint equations.

Starting with b=200, after 3 iterations of steepest descent with fixed step size, the cost function is decreased from 1200 to 900. But as there is no constraint b is much reduced at the top near Γ i . Consquently the vessel wall becomes fragile as shown by a simulated wall motion by x → x + u m • ndt at every time step, as shown on Figure 5. The results are shown on figure 7.

Because of the computing cost, we made only an initial study; the target is not reached, but 5 iterations go into the right direction. To do better one would have to used a varying step size gradient method and a better computer (this being done on a macbook pro, takes about 15 min).

Conclusion

In this paper we have introduced a reduced fluid structure model based on a transpiration condition and applied it on a problem arising from hemodynamics.

We have shown that it has good stability property. In [START_REF] Chacon Rebollo | Analysis of a Simplified Coupled Fluid-Structure Model for Computational Hemodynamics[END_REF] a comparison study is made with full fluid-structure models on moving domains; it is shown to give very similar results. The greatest advantage of this reduced model is its computational speed and unconditional stability. As inverse problems are important in hemodynamics [START_REF] Bertoglio | Identification of artery wall stiffness: In vitro validation and in vivo results of a data assimilation procedure applied to a 3D fluid-structure interaction model[END_REF], it could be a good idea to use it. This preliminary study shows that it is indeed feasible.

2 .

 2 Compute v, p by a time loop from T down to 0 requiring to read from disk p d , u, p, U .

3 .

 3 Compute gradient by solving (27).

4 . 5 .

 45 Compute cost function and ∂ x g 2 0 . Update b by b ← b -λg.

6 .Figure 2 :

 62 Figure 2: g (left) and J (right) versus iteration number in log-log scale. Initially J = 1403 and after 50 gradient iterations J = 1.27 while g decreases from 1.210 -4 to 3.310 -9

Experiment 2 Figure 3 :

 23 Figure 3: Target b d (top curve) and computed b after 50 iterations. Initial Pressure map after one iteration (top), final pressure after 50 gradient iterations (middle) and target pressure p d (bottom). The color scales are linear from -986 to 896 except for p 0 which has a range from -680 to 782

Figure 4 :

 4 Figure 4: Flow velocity vectors u (middle) and adjoint flow velocity vectors v (bottom) at final time after 50 gradient iterations. The color scales are linear from 0 (safran) to 0.03 (red) for u and 0 (safran) to 2.9 (red) for v. The singularity at the top left corner is due to a theoretical incompatibility between the normal velocities at this corner.

Figure 5 :

 5 Figure 5: Top left: Optimization criteria versus iteration number. Top right: the coefficient b(x) after 3 iterations. Bottom Left: effect of the change of b on the dilatation of the vessel and some iso surfaces of constant pressure. Bottom right: a snap shot of the adjoint pressure and some iso surfaces.

  ter 10 iterations, similar to Experiment 1 but with a projected gradient method for the optimization, the results of Figure6are found.

Figure 6 :Experiment 3

 63 Figure 6: Left: Optimization criteria Σ×(0,T ) p 4 versus iteration number. Right: the coefficient b(x) after 4 iterations. Right: effect of the change of b on the dilatation of the vessel.

Figure 7 :

 7 Figure 7: Left: Optimization criteria Σ×(0,T ) (p -p d ) 2 versus iteration number. Right: the coefficient b(x) after 5 iterations. middle: The target b.

Acknowledgement: Special thanks to Frédéric Hecht for his help with freefem++ and Marc Thiriet and Suncica Canic for helpful discussions.


In this work we present a detailed surface science characterization of L-Aspartic acid adsorption on a Cu(110) surface. Aspartic acid is one of the main components of the tri-peptide RGD (arginine-glycine-aspartic acid). We replaced the traditional sublimation method to obtain molecular films by dosing aspartic acid directly from an aqueous solution through an Electrospray Ionization (ESI) device. X-ray Photoelectron Spectroscopy (XPS) and Polarization Modulation Reflection Absorption Infra Red Spectroscopy (PM-RAIRS) evidenced different Page 1 of 26 ACS Paragon Plus Environment The Journal of Physical Chemistry adsorption states ranging from sub-monolayer regime up to multilayers. Molecules-substrate interactions guide the creation of the pattern observed in the sub-monolayer, but moleculemolecule interactions are prevailing from a certain coverage stage, promoting the overlayer growth while leaving exposed areas of bare copper. This is evidenced by Scanning Tunneling Microscopy (STM) results, showing that single aspartic acid molecules self-organize in a 2D chiral network at low coverage and start originating new molecular layers even before a saturated monolayer has been reached.

INTRODUCTION

A better knowledge and control of biomolecule-metal interactions is a central issue for the rational design of biocompatible and/or protein-resistant materials. Fundamental research is always at the intermediate position between a fully understanding of small molecule adsorption on well-defined surfaces ("ideal" surface science approach) and "post mortem" characterization of real biological systems ("real" approach). In this context, we put our effort on the study of the adsorption of small biomolecules, namely amino acids and small di-or tri-peptides, on metallic single crystal surfaces, most often by applying a surface science approach.

We have recently shown that molecules dosed via an electrospray ionization (ESI) device are adsorbed intact and in a chemical state close to that in solution. [START_REF] Méthivier | UHV Deposition of the Gly-Pro Dipeptide on Cu(110) by Sublimation or Electrospray Ionization[END_REF][START_REF] Méthivier | Tuning the Surface Chirality of Adsorbed Gly-Pro Dipeptide/Cu(110) by Changing Its Chemical Form via Electrospray Deposition[END_REF] Compared to the traditional Knudsen cells, ESI allows an adsorption from an aqueous solution at room temperature; high sublimation temperatures are thus avoided and molecular films of delicate biomolecules can be obtained without any molecular damage. Our next objective is to unravel the interaction modalities of more relevant peptides, like RGD, which plays a determining role in the context of biotechnologies for its capacity to promote cell adhesion or other peptide sequences for specific Page 2 of 26

ACS Paragon Plus Environment

The Journal of Physical Chemistry molecular recognition or cell interactions on metallic or oxidized surfaces [START_REF] Zhang | Effects of Immobilizing Sites of RGD Peptides in Amphiphilic Block Copolymers on Efficacy of Cell Adhesion[END_REF] . RGD is currently employed for biomaterials functionalization and knowledge of RGD adsorption mechanisms on different surfaces is of paramount importance for its implementation. The tri-peptide RGD is constituted of three amino acids, namely arginine, glycine and aspartic acid (ASP). Arginine and ASP, differently from glycine, [START_REF] Hasselström | The Adsorption Structure of Glycine Adsorbed on Cu(110); Comparison with Formate and Acetate Cu(110)[END_REF][START_REF] Zhao | Self-Assembled Structures of Glycine on Cu(111)[END_REF][START_REF] Löfgren | Glycine on Pt (111): a TDS and XPS Study[END_REF][START_REF] Gao | Chemistry of Glycine on Pd(111): Temperature-Programmed Desorption and X-ray Photoelectron Spectroscopic Study[END_REF][START_REF] Zhao | Physisorption-Induced Surface Reconstruction and Morphology Changes: Adsorption of Glycine on the Au(110) 1 × 2 Surface[END_REF][START_REF] Rankin | Structures of Dense Glycine and Alanine Adlayers on Chiral Cu(3,1,17)[END_REF] have not given rise to extended investigations of their interaction with a metal surface.

As a first step in the characterization of RGD interaction with a copper surface, we studied ASP adsorption on a Cu(110) surface. Moreover, considering that RGD, a rather heavy tripeptide, will not be easily sublimated in the UHV chamber, an ESI device will probably be necessary to introduce RGD with no damage. Therefore, we have already used the ESI device for ASP in order to keep similar evaporation conditions. ASP, C 4 H 7 NO 4 (Figure 1), is mostly known for being one of the main ingredients of the artificial sweetener aspartame, together with L-phenylalanine. What is maybe less known is that is one of the most abundant amino acids in nature, it has fundamental biological and biomedical/biotechnological functions [START_REF] Azevedo | The Aspartic Acid Metabolic Pathway, an Exciting and Essential Pathway in Plants[END_REF][START_REF] Liu | Efficient Delivery of Antitumor Drug to the Nuclei of Tumor Cells by Amphiphilic Biodegradable Poly(L-Aspartic Acid-co-Lactic Acid)/DPPE Co-Polymer Nanoparticles[END_REF]12,[START_REF] Zhao | Shape-Controllable and Versatile Synthesis of Copper Nanocrystals with Amino Acids as Capping Agents[END_REF][START_REF] Tan | Aspartic Acid Synthesis of Crystalline Gold Nanoplates, Nanoribbons and Nanowires in Aqueous Solutions[END_REF][START_REF] Rafey | Growth of Ag-Nanoparticles Using Aspartic Acid in Aqueous Solutions[END_REF] and, last but not the least, is the C-ter end of RGD. Studies of ASP on metallic substrates and in ultra-high vacuum (UHV) conditions are quite rare. ASP has been adsorbed on Ni(111) surfaces, from solution [START_REF] Wilson | Understanding the Surface Chemistry of Enantioselective Heterogeneous Reactions: Influence of Modification Variables on the Interaction of Methylacetoacetate with (S)-Aspartic Acid Modified Ni{111}[END_REF] and by sublimation, [START_REF] Wilson | Interaction of the Pro-Chiral Molecule, Methylacetoacetate, with (S)-Aspartic Acid Modified Ni{111}[END_REF] as a surface chiral modifier to investigate the enantioselective hydrogenation of β -ketoesters. More recently, Gellman and co-workers have studied ASP films evaporated (in racemic mixture or as pure D or L enantiomers) in UHV conditions, to characterize the enantiomer nature of ASP molecules on chiral and achiral copper surfaces. [START_REF] Yun | Enantioselective Separation on Naturally Chiral Metal Surfaces: D, L-Aspartic Acid on Cu(3,1,17)(R&S) Surfaces[END_REF][START_REF] Yun | Adsorption-Induced Auto-Amplification of Enantiomeric Excess on an Achiral Surface[END_REF][START_REF] Reinicker | Influence of Step Faceting on the Enantiospecific Decomposition of Aspartic Acid on Chiral Cu Surfaces Vicinal to Cu{111[END_REF][START_REF] Yun | Enantiospecific Adsorption of Amino Acids on Naturally Chiral Cu{3,1,17}(R&S) Surfaces[END_REF][START_REF] Mhatre | Explosive Enantiospecific Decomposition of Aspartic Acid on Cu Surfaces[END_REF] All these studies have in common the conclusion that ASP chemical form after adsorption on a surface depends on the film coverage. However, this form is different according to the substrate. On Ni surfaces, ASP is in its zwitterionic (COO -/NH 3 + ) form at lower coverages, and in its anionic (COO -/NH 2 ) form at high coverages. [START_REF] Wilson | Interaction of the Pro-Chiral Molecule, Methylacetoacetate, with (S)-Aspartic Acid Modified Ni{111}[END_REF] On Cu surfaces, ASP is found with two COO -groups and a neutral (NH 2 ) amine group for lower coverage and in its zwitterionic form for higher coverage. [START_REF] Mhatre | Explosive Enantiospecific Decomposition of Aspartic Acid on Cu Surfaces[END_REF] The doublydeprotonated carboxylic groups and the neutral amine group of the lower coverage are considered the responsible for the ASP anchorage on the surface.

ݏ1ܥܫ 2ݑܥܫ = ܶ ଵ௦ ܶ ௨ଶ ߪ ଵ௦ ߪ ௨ଶ ߣ ଵ௦ ௗ ܥ ଵ௦ ௗ ቈ1 -ݔ݁ ቆ -݀ ߣ ଵ௦ ௗ ߠݏܿ ቇ ߣ ௨ଶ ௦௨ ܥ ௨ଶ ௦௨ ݔ݁ ቆ -݀ ߣ ௨ଶ ௗ ߠݏܿ ቇ [1]
where cosθ is 1 because the photoelectron collection angle θ is equal to zero. T C1s and T Cu2p are the relative sensitivity factors of C and Cu, respectively, provided by the spectrometer manufacturer. The Scofield photoionization cross sections σ are 1 for C 1s and 2.48 for Cu 2p.

The superscripts ad and su designate the adsorbed layer and the copper substrate, respectively.

ܥ ௫ ௬
represents the concentration of the element x in the matrix y. The electron inelastic mean free paths λ were calculated using the Quases program based on the TPP2M formula. 26 For more details on equation [1], see Supp. Info section.

PM-RAIRS. Spectra were recorded using a Nicolet 5700 spectrometer equipped with a nitrogen-cooled MCT wide-band detector. A ZnSe grid polarizer and ZnSe photoelastic modulator to modulate the incident beam between p and s polarization were placed prior to the sample. The spectrometer was interfaced to the UHV chamber via ZnSe windows. The reflected light was focused onto the detector at an optimal incident angle of 85°. All spectra were obtained after 1024 scans with a resolution of 8 cm -1 .

XPS. Photoemission analysis was

RESULTS AND DISCUSSION

PM-RAIRS spectra obtained after a 2, 5 and 7 minutes dosing by ESI are shown in Figure 2a, together with the peak assignment (Figure 2b) in agreement with previous ASP infrared studies [START_REF] Roddick-Lanzilotta | An In-Situ Infrared Spectroscopic Study of Glutamic Acid and of Aspartic Acid Adsorbed on TiO 2 : Implications for the Biocompatibility of Titanium[END_REF] and with the infrared analysis of ASP solutions at different pHs (see the Supporting Information section, Figure S1). One can notice three main features at 1427 cm -1 , 1391 cm -1 and 1352 cm -1 , present on the PM-RAIRS spectra at all examined coverages. The sharp bands at 1427 cm -1 and 1391 cm -1 are attributed to the symmetric stretching vibrations of, respectively, the α-carboxylate (closer to the amine group) and the distal carboxylate functionalities (Figure S1). The not symmetric position of the amine group in the molecule breaks the degeneracy of the two otherwise equivalent COO -groups and leads to two distinguishable contributions. The observed vibrations also furnish a direct evidence of the carboxylic acids deprotonation. As already reported for other copper surfaces, [START_REF] Tabatabaei | The Detailed Kinetics of the Desorption of Hydrogen from Polycrystalline Copper Catalysts[END_REF] The third rather intense band at 1352 cm -1 can be ascribed to the CH 2 wagging mode. [START_REF] Wilson | Interaction of the Pro-Chiral Molecule, Methylacetoacetate, with (S)-Aspartic Acid Modified Ni{111}[END_REF] Increasing the molecular coverage on the substrate, one observes two other bands growing. The C=O stretching mode and the NH 3 + asymmetric deformations, visible in the 7 minutes adsorption spectrum in Figure 2a, are responsible for the broad features at 1733 cm -1 and 1630 cm -1 , respectively. Additional information concerning the (protonated or not) nature of the amino group will be given by analyzing the XPS data.

The N1s and O1s XPS spectra obtained at the three investigated dosing times are shown in Figure 3. The spectra and the subsequent analysis are in perfect agreement with a previous study of ASP sublimated on Cu(110), [START_REF] Mhatre | Explosive Enantiospecific Decomposition of Aspartic Acid on Cu Surfaces[END_REF] confirming once again that ESI is as accurate and reproducible, in term of sample preparation methods, as traditional sublimation. For nitrogen, Figure 3b, in the 2 minutes adsorption spectrum, the Binding Energy (BE) of the N1s peak at 399.9 eV is The fitting procedure to disentangle the contributions of the different species to the core level spectra is also shown.

At the same time, the presence of the NH 2 peak, alone, suggests that the initial interaction of the molecule with the surface induces a deprotonation of all NH 3 + groups existing in the gas phase.

Consistently, for oxygen (Figure 3a), a unique O1s peak at 531.7 eV, ascribed to the COO -group oxygen, indicates a deprotonation of COOH groups, confirming the interaction of the carboxylate groups with the surface, as deduced from infrared data (Figure 2). One has to point out that the cationic state of ASP molecules obtained through ESI is an assumption based on the ESI working principles. In fact, in lacking of gas phase measurements on the ESI beam, we cannot exclude the possibility that molecules are in a different state. In particular, the obtained data would be also consistent with neutral (COOH/NH 2 ) ASP molecules arriving on the surface.

For the 2 minutes results, this would simply imply that no deprotonation occurs in the amine group, while keeping the same interaction mechanisms for the carboxylic groups. After 5 minute dosing, the N 1s spectrum displays two peaks, indicating that the NH 3 + groups now exist in the adsorbed molecules. Together with this change in the N1s peak, two peaks on the high binding energy tail of the COO -peak start to be visible on the O1s spectrum, at 532.9 and 533.6 eV respectively. These are the contributions from C=O and C-OH oxygen atoms, [START_REF] Vallée | Adsorption of Di-and Tripeptides on Au(110) under Ultrahigh Vacuum Conditions. 1. Polarization Modulation Reflection Page 24 of 26 ACS Paragon Plus Environment The Journal of Physical Chemistry Absorption Infrared Spectroscopy and X-Ray Photoelectron Spectroscopy Characterization[END_REF][START_REF] Gonella | UHV Deposition of L-Cysteine on Au(110) Studied by HR XPS: From Early Stages of Adsorption to Molecular Organization[END_REF] suggesting the presence of COOH. Note that these two contributions have equal intensities, and their relative intensities increase from 5 to 7 minutes (12 % to 16 % of the total O1s intensity). The C 1s spectra for the three dosing times, shown in the Supporting Information section (Figure S2), are in agreement with O1s data, confirming COOH complete deprotonation for low coverage and COOH neutral state, coexisting with some COO -, for higher coverages. Eventually, the values of the average coverage values, calculated from the attenuation of the copper signal (Equation 1), lead to the following numbers: 3.2 Å, 6.7 Å and 10 Å after 2, 5 and 7 minutes of dosing, respectively. Estimating a maximum size for ASP molecules of 5 Å (maximum gas phase elongation), one may think that after 2 minutes of exposures, only a fraction of monolayer is on the surface whilst multilayer starts to grow after 5 minutes of exposure. This will be later confirmed by STM images.

Page 10 of 26

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The appearance of the NH 3 + , C-OH and C=O peaks after 5 minute dosing is in agreement with the building of multilayers where molecules do not interact directly with the surface, thus do not undergo a deprotonation of COOH and NH 3 + groups. Alternatively, in the presence of neutral gas phase molecules, the 5 and 7 minutes results would infer the creation of a zwitterionic network in the multilayer, with one deprotonated carboxylic group in interaction with the positively charged amine group and the second carboxylic group still in its neutral state. Another possibility would be the NH 2 group of the monolayer turning into NH 3 + and interacting with a COO -group of the second layer. Both situations are consistent with the high binding energy contributions observed in O, N and C 1s spectra for higher coverages. The process determining the state of the amine (carboxylic) group would not be an actual protonation (deprotonation) but a delocalization of the proton, favored by the amine (acid) nature of the functional group.

Gathering all the information obtained so far and considering the strict RAIRS dipole selection rules, which allow observing only vibrational modes with a dynamic dipole moment non-parallel to the surface, [START_REF] Greenler | Infrared Study of Adsorbed Molecule on Metal Surfaces by Reflection Techniques[END_REF] we can deduce some characteristics of the geometries of adsorbed ASP molecules depending on the coverage. In the submonolayer regime (2 minutes dosing), the intense symmetric COO -band and the almost absence of absorption at ca 1600 cm -1 suggest that the four oxygen atoms from the COO -groups are anchored to the surface in a bidentate configuration. A similar geometry was observed for bitartrate [START_REF] Lorenzo | Creating Chiral Surfaces for Enantioselective Heterogeneous Catalysis: R,R-Tartaric Acid on Cu(110)[END_REF] and bisuccinate [START_REF] Humblot | Local and Global Chirality at Surfaces: Succinic Acid versus Tartaric Acid on Cu(110)[END_REF] on Cu(110) and it is also in agreement with the geometry proposed in previous ASP studies. [START_REF] Yun | Enantiospecific Adsorption of Amino Acids on Naturally Chiral Cu{3,1,17}(R&S) Surfaces[END_REF][START_REF] Mhatre | Explosive Enantiospecific Decomposition of Aspartic Acid on Cu Surfaces[END_REF] Besides that, looking at the different intensities of the carboxylate bands at 1391 and 1427 cm -1 (Figure 2a), we can say that the OCO planes positions, even if close to be normal to the surface plane, are slightly different, with the distal carboxylate plane less perpendicular than the α-carboxylate plane with respect to the surface and thus less contributing to the infrared spectral intensity. Differently from studies from Gellman's group, [START_REF] Yun | Enantiospecific Adsorption of Amino Acids on Naturally Chiral Cu{3,1,17}(R&S) Surfaces[END_REF][START_REF] Mhatre | Explosive Enantiospecific Decomposition of Aspartic Acid on Cu Surfaces[END_REF] we hypothesize that the NH 2 amine group is not interacting with the surface. In fact, since no contribution from the NH 2 group is visible in corresponding infrared data, we deduce that, at low coverage, its plane is parallel, or almost parallel, to the surface. Besides, N1s 2 minutes spectrum (Figure 3a) denotes the absence of interactions between NH 2 and Cu, otherwise a peak at lower binding energies would have been visible, due to hydrogen bonds, -N-H-Cu, between the amine group and the Cu surface, as already been observed in similar studied on copper1 and on gold surfaces. [START_REF] Feyer | Adsorption of Histidine and Histidine-Containing Peptides on Au(111)[END_REF][START_REF] Feyer | Adsorption of Histidine and a Histidine Tripeptide on Au(111) and Au(110) from Acidic Solution[END_REF] After 5 minutes adsorption the α-carboxylate band increases, while the distal carboxylate band remains constant (Figure 2a), thus suggesting a slight reorientation of the former carboxylate in a more perpendicular position and of the latter carboxylate in a more parallel position with respect to the substrate. Finally, the appearance of the C=O stretching mode and of the NH 3 + asymmetric deformations bands and the decreasing of the CH 2 wagging band intensity in the 7 minutes adsorption infrared spectrum suggests that, once the multilayer regime is reached, molecules are found in various orientations, some letting COOH and NH 3 + planes more perpendicular and CH 2 planes more parallel to the surface. Changes in molecular arrangement when the coverage increases is a commonly observed phenomenon, already encountered, for alanine, [START_REF] Barlow | Supramolecular Assembly of Strongly Chemisorbed Size-and Shape-Defined Chiral Clusters: Sand R-Alanine on Cu(110)[END_REF] tartaric acid, [START_REF] Lorenzo | Creating Chiral Surfaces for Enantioselective Heterogeneous Catalysis: R,R-Tartaric Acid on Cu(110)[END_REF] lysine 40 and methionine [START_REF] Méthivier | L-Methionine Adsorption on Cu(110), Binding and Geometry of the Amino Acid as a Function of Coverage[END_REF] on Cu(110). As pointed out from infrared results, OCO planes of the two ASP carboxylate groups are characterized by a different angle with respect the substrate, being the α-carboxylate --OOC-NH 2 group more perpendicular than the distal -COO -group to the surface. In this way, the two extremities of the molecule are forced to be at a different distance (i.e. height) from the surface.

Therefore, we propose that the two lobes at different z position revealed by STM profiles correspond to the two ends of a single ASP molecule, with the highest lobe being the end with the distal α-carboxylate --OOC-NH 2 . An analogous situation has been observed for methionine on Au(111) [START_REF] Humblot | Characterization of Two-Dimensional Chiral Self-Assemblies L-and D-Methionine on Au(111)[END_REF] where a single methionine molecule appeared as two bright spots, due to the fact that, as evidenced by DFT calculations, the sulfur moiety and the carboxylic acid groups had different orientations, pointing towards and away from the surface, respectively. Besides, the distance between the two lobes in ASP is comparable to the distance between the two bright dots in methionine, while is half the distance observed, for example, between the two bright spots characterizing lysine pattern on Cu(110). 40 However, differently from methionine, lysine tends to self-organize in dimers. So the bigger distance between its two double features confirms the hypothesis of ASP single-molecule assembly.

A further statistical analysis revealed the distances between ASP molecules along the main symmetry directions of the 2D pattern (line profiles 2 and 3 of Figure 4b, shown in Figure 4c), which are, on average, (10.7±0.5) Å and (13.0±0.5) Å. The distance between 2 neighboring ASP molecules, bigger than the weakest hydrogen bond (roughly 4 Å 42 ), and their anionic (COO -/NH 2 ) state on the surface, prevent the creation of any intermolecular hydrogen-bonding network. A similar situation with methionine adsorbed on Cu(110) led to a total absence of the 2D array. [START_REF] Méthivier | L-Methionine Adsorption on Cu(110), Binding and Geometry of the Amino Acid as a Function of Coverage[END_REF] Therefore, given the lacking of intermolecular directions, we propose that molecule-substrate interactions, rather than molecule-molecule interactions, are the driving force of the supramolecular assembly. The strict geometry adsorption via the four O atoms, indicating a not-negligible ASP-Cu interaction, seems to corroborate this suggestion.

It has to be noted that ASP molecules are accommodated along nonsymmetry directions, destroying the symmetry planes of the underlying substrate. In this way the surface is bestowed not only of point chirality due to the intrinsic chirality of ASP molecules, but also of chirality at the organizational level. Besides, since domains of different chirality are not present on the surface, we can conclude that the supramolecular assembly originated by ASP is able to modify an achiral surface such as Cu(110) into a truly chiral surface with a global chirality, as also observed, for example, in the adsorption of Gly-Pro on Cu(110). [START_REF] Lorenzo | Creating Chiral Surfaces for Enantioselective Heterogeneous Catalysis: R,R-Tartaric Acid on Cu(110)[END_REF][START_REF] Barlow | Supramolecular Assembly of Strongly Chemisorbed Size-and Shape-Defined Chiral Clusters: Sand R-Alanine on Cu(110)[END_REF][START_REF] Cruguel | Surface Chirality of Gly-Pro Dipeptide Adsorbed on a Cu(110) Surface[END_REF] Page 15 of 26

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The Journal of Physical Chemistry When the coverage increases (5 minutes dosing), ASP 2D pattern gradually covers the whole surface (Figure 6a). In the high resolution image shown in Figure 6b, we can identify the lighter areas as the beginning of the multilayer and fuzzy and not well-resolved areas (indicated by dashed arrows), ascribable to Cu(110) surface. We do not have enough elements to examine properly the multilayer pattern which, nonetheless, seems to be the characterized by more than one structure, as indicated by solid arrows in Figure 6b. However, we can clearly see that, even if the substrate is not still completely covered by the adsorbates, ASP molecules prefer accommodating on other molecules rather than on the bare surface. Line profile of Figure6c traced along the solid line of Figure 6b shows the simultaneous presence of the substrate, the monolayer and the starting overlayer. The multilayer way of growth can be explained considering that, since molecules in the overlayer are not interacting with the surface, there is no deprotonation of COOH/NH 3 + groups in the case of cationic gas phase molecules or of COOH groups in the case of neutral gas phase molecules. Thus, differently from what seen in submonolayer regime, they have the possibility of hydrogen bonding creation that can favor the overlayer growth over the reaching of a saturated monolayer. Thus, this second stage of growth is characterized by a prevalence of ASP-ASP interactions over ASP-Cu interactions. undergo to a deprotonation process. As evidenced by our XPS and PM-RAIRS characterizations, when the molecular coverage increases, molecules are adsorbed in their gas phase state. This infers that the interaction with Cu is responsible for the hydrogen loss in the molecule. Besides, the higher presence of hydrogen facilitates the growth of the multilayer, with the formation of a NH 3 + --COO-hydrogen bonding network.

STM images, taken in the submonolayer regime (2 minutes dosing), show the creation of ASP islands inside Cu terraces. Each island is made of ASP molecules arranged along a nonsymmetry direction, diagonally crossing the close-packed rows and creating a chiral 2D network. In the 5 minutes dosing images, we can see both the substrate and the first structures of the overlayer growing on the top of the underlying layer rather than on Cu. In the monolayer regime, the selfassembly is guided by molecule-substrate interactions, while intermolecular interactions become predominant for higher coverage, even before monolayer reached saturation.

The knowledge of ASP adsorption mechanisms and of ASP coverage-dependent behavior will allow us to disentangle the contribution of ASP moiety in RGD and will help in the comprehension and interpretation of RGD characterization.

ASSOCIATED CONTENT

Supporting Information

Infrared spectra of solutions of Aspartic Acid in water at different pH C 1s core level spectra as a function of dosing times Thickness evaluation detailed calculations

Figure 1 .

 1 Figure 1. Schematic representation of an L-aspartic acid molecule.

  performed using a SPECS (Phoibos 100 1D Delay Line Detector) hemispherical analyzer and a monochromatized aluminum K α X-ray source (hν = 1486.6 eV). The acquired spectra were calibrated according to the Cu Fermi level. The experimental uncertainty on the position in biding energy of the XPS peaks is 0.1 eV. STM experiments were conducted in an Omicron Vakuumphysik XA VT-STM chamber with facilities for STM, LEED and sample cleaning. All STM images were acquired in constant current mode. The STM scanner was calibrated using the Cu(110)-O-(2×1) missing/added rows (interspacing distance = 0.51 nm).

Figure 2 .

 2 Figure 2. (a) PM-RAIRS spectra obtained after a 2, 5 and 7 minutes dosing by ESI; (b) Peak assignment table.

32 Figure 3 .

 323 Figure 3. Evolution of ASP O1s (a) and N1s (b) XPS peaks, for increasing molecular coverage.The fitting procedure to disentangle the contributions of the different species to the core level spectra is also shown.

Figure 4

 4 Figure 4 presents the STM images corresponding to a submonolayer of ASP on the Cu(110)

Figure 4 .

 4 Figure 4. (a) Islands of ASP molecules, characteristics of the submonolayer regime. (b) Bilobate elements inside ASP islands. (c) Profiles extracted from dashed lines in (b). Image conditions are: (a) 84 nm x 85 nm, V = 1.1 V, I = 100 pA, (b) 25.2 nm x 25.5 nm, V = 1.1 V, 120 pA.

Figure 5 .

 5 Figure 5. (a) ASP molecules 2D pattern from a high-resolution STM image (left, image conditions: 8.4 nm x 8.5 nm, 1.1 V, 120 pA) and depicted on copper rows in a schematic representation, together with the unit cell (right). (b) Adsorption model of ASP molecules, showing unit cell dimensions and the angles between the main symmetry directions of ASP pattern and Cu(110) crystallographic axis.

Figure 6 .

 6 Figure 6. (a) Higher coverage (5 minutes dosing) of ASP: the ASP islands increase in number until reaching an almost complete covering of the underlying substrate. (b) High resolution STM image showing the co-existence of the multilayer (brighter areas) and of the Cu substrate, indicated by dashed arrows. Solid arrows indicate different co-existing multilayer structures. (c) Profile along the solid line traced in (b) to evidence the three elements present on the surface, substrate, monolayer and multilayer, and their different z position. Image conditions are: (a) 60.8 nm x 58.5 nm, 1.1 V, 50 pA; (b) 40.5 nm x 39 nm, 1.1 V, 50 pA.

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  The thickness d of the obtained molecular layer could be estimated by means of the intensities ratio IC1s/ICu2p of C1s and Cu2p XPS spectra, related by the formula:

	showing the creations of a chiral 2D network for submonolayer coverage, determined by
	molecule-substrate interactions, and the growth of the overlayer before reaching a saturated
	monolayer, with a prevalence of molecule-molecule interactions.
	EXPERIMENTAL SECTION
	All measurements were performed in UHV conditions, i.e. with a base pressure better than
	1x10 -10 mbar, with the sample kept at room temperature. PM-RAIRS and XPS measurements
	were realized in situ. STM images were acquired after dosing using a different experimental
	equipment.
	Materials. Before ASP adsorption, the Cu(110) crystal (Surface Preparation Laboratory, The
	Netherlands, purity of 99.99% (4N) and alignment accuracies of 0.1°) was prepared for the
	experiments through several cycles of Ar + sputtering (500 eV, P Ar =3x10 -6 mbar) and annealing at
	850 K. XPS and LEED (Low Energy Electron Diffraction) were used to check surface
	cleanliness and reconstruction. L-ASP was purchased by Fluka (99%) and used without further
	purification.
	Dosing. ASP adsorption has been realized from a 1 mM solution of ASP in a methanol/water
	75:25 ratio by means of an ESI device. Explanations on ESI mode and principles of operation
	This work aims at studying the adsorption mechanisms of L-ASP after deposition by ESI on can be found elsewhere. 1,2Error! Bookmark not defined. Dosing of 2, 5 and 7 minutes for XPS and 2 and
	Cu(110) surfaces. The chemical state and the anchoring points of the molecules on the surface, 5 minutes for STM were used to obtain different ASP coverage. The pressure during the dosing
	deduced through X-ray Photoelectron Spectroscopy (XPS) and Polarization Modulation Infrared varied in the range 1x10 -7 to 5x10 -7 , with a base pressure of 7x10 -8 after opening the gate valve
	Reflection Absorption Spectroscopy (PM-RAIRS) revealed, also in this case, changes in the between the ESI vessel and the experimental chamber. A positive voltage of 1.5 kV was applied,
	chemical state, charge and configuration of ASP molecules, with the coverage. Scanning with ASP gas phase molecules nominally in their cationic state, i.e. COOH/NH 3 + .
	Tunneling Microscopy (STM) furnished complementary information about the layer structure,

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ACKNOWLEDGMENTS

This work was supported by French state fund managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE ACS Paragon Plus Environment The Journal of Physical Chemistry

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Notes

The authors declare no competing financial interest.

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