Mamoutou Diarra
email: mamoutou.diarra@inria.fr

Walid Dabbous
email: walid.dabbous@inria.fr

Amine Ismail
email: amine.ismail@ekinops.com

Thierry Turletti
email: thierry.turletti@inria.fr

RAN-aware Proxy-based Flow Control for High Throughput and Low Delay eMBB

Keywords: TCP Congestion and Flow control, 5G millimeter wave, self-inflicted bufferbloat, eMBB, Multi-Access Edge Computing, Radio Network Information Service, Performance Enhancing Proxy

5G enhanced Mobile broadband (eMBB) aims to provide users with a peak data rate of 20 Gbps in the Radio Access Network (RAN). However, since most Congestion Control Algorithms (CCAs) rely on startup and probe phases to discover the bottleneck bandwidth, they cannot quickly utilize the available RAN bandwidth and adapt to fast capacity changes without introducing large delay increase, especially when multiple flows are sharing the same Radio Link Control (RLC) buffer. To tackle this issue, we propose RAPID, a RANaware proxy-based flow control mechanism that prevents CCAs from overshooting more than the available RAN capacity while allowing near optimal link utilization. Based on analysis of up-todate radio information using Multi-access Edge Computing (MEC) services and packet arrival rates, RAPID is able to differentiate slow interactive flows from fast download flows and allocate the available bandwidth accordingly. Our experiments with concurrent Cubic and BBR flows show that RAPID can reduce delay increase by a factor of 10 to 50 in both Line-of-Sight (LOS) and Non-LOS (NLOS) conditions while preserving high throughput.

INTRODUCTION

Over the last years, Internet content and resources have increasingly been located close to the end users by means such as Content Delivery Networks (CDN) or edge computing. In such a context and as today's cellular networks rely on well-provisioned backhaul, the radio link between the user and the base station, as illustrated in Figure 1, most often becomes the bottleneck [START_REF] Haile | End-to-end congestion control approaches for high throughput and low delay in 4G/5G cellular networks[END_REF], mostly due to the inherent characteristics and limitations of cellular Radio Access Networks (RANs). Consequently, if not managed appropriately, such a bottleneck could hinder 5G performances, especially in enhanced Mobile Broadband (eMBB) scenarios.

Moreover, traditional end-to-end Congestion Control Algorithms (CCAs) are not designed to appropriately discover cellular RAN bandwidth without introducing large delay or bufferbloat. This phenomenon is observed in startup and steady states of most CCAs (e.g., NewReno, Cubic) since they rely on probing techniques in order to gradually discover the available bandwidth. Although some end-to-end solutions such as model-based (e.g BBR [START_REF] Cardwell | BBR: Congestion-Based Congestion Control[END_REF]) and crosslayer CCAs (e.g., PBE-CC [START_REF] Xie | PBE-CC: Congestion Control via Endpoint-Centric, Physical-Layer Bandwidth Measurements[END_REF], CQIC [START_REF] Zhong | Performance evaluation of CQIC and TCP BBR in mobile network[END_REF], LCTCP [START_REF] Beshay | Link-Coupled TCP for 5G networks[END_REF], etc.) have been proposed in order to better utilize the RAN bandwidth while minimizing Round-Trip-Time (RTT) increase, the bufferbloat issues still persist since the proposed algorithms cannot perform well when competing with loss-based CCAs which keep introducing significant RTT increase due to the use of deep buffers in the base stations. Other alternatives to end-to-end solutions such as RANaware proxies (e.g., milliProxy [START_REF] Polese | milliProxy: A TCP proxy architecture for 5G mmWave cellular systems[END_REF]) have also been proposed in order to mitigate the negative effects of loss-based CCAs; however, these solutions can introduce high delay increase in case of multiple flows per user. In general, cross-layer CCAs and existing RAN-aware proxies adapt their sending rate to the RAN bandwidth allocated to the User Equipment (UE) without taking into account the number of active flows sharing this bandwidth in the UE. As a result, the per-user RLC queue (at the base station) can grow and cause self-inflicted bufferbloat when multiple flows progress in parallel in the same UE. Indeed, all the aforementioned limitations along with the diversity of congestion control algorithms on the Internet make it very challenging to address the self-inflicted bufferbloat problem at the CCA level. In such a context, it could be necessary to use a flow-level bandwidth shaping in order to limit the interference between the flows that are using different CCAs. As suggested in [START_REF] Jain | Mobile throughput guidance inband signaling protocol[END_REF], a simple solution could be to allocate equal portions of the available bandwidth to the concurrent flows; however such a solution may result in link under-utilization since some flows (e.g., slow or app-limited flows) may require just a small fraction of the total bandwidth. With that in mind, we design and evaluate a solution that minimizes RTT increase (regardless of the CCA used by the end servers) and allocates the available RAN bandwidth by taking into account the nature of the active flows in the UE. Overall, our contributions in this paper can be summarized as follows:

• We propose a RAN-aware performance enhancing proxy that intercepts TCP connections and distributes proportionally the available RAN bandwidth among the active flows. On this purpose, we rely on the MEC Radio Network Information Service (RNIS) and on packets arrival rates to estimate the aggregated RAN bandwidth and categorize the concurrent TCP flows in the UE. This approach does not involve the end user unlike existing cross-layer CCAs that introduce computational overhead and additional power consumption at the UE as they require client-side modifications in order to introduce radio information into the TCP header [START_REF] Xie | PBE-CC: Congestion Control via Endpoint-Centric, Physical-Layer Bandwidth Measurements[END_REF][START_REF] Zhong | Performance evaluation of CQIC and TCP BBR in mobile network[END_REF]. • We provide an implementation of our solution for the ns-3 network simulator on top of which we conduct various performance evaluation experiments with different CCAs under both LOS and NLOS radio conditions. We run our simulations on a cluster 1 and the scripts to reproduce all our scenarios/results are made available to the community [START_REF] Diarra | RAPID[END_REF]. • We highlight the limits of current CCAs over next-generation cellular networks and provide building blocks for their improvement. The remainder of the paper is organized as follows. In Section 2 we present the motivations of this work and shed light on the self-inflicted bufferbloat problem and bandwidth under-utilization issue introduced by traditional CCAs in cellular networks. Section 3 presents the design and implementation details of RAPID, our proposed RAN-aware proxy. Section 4 describes the simulation environment, evaluates the performance of our solution in some mobile edge scenarios and discusses some observed limitations. Section 5 explores the related work and finally, we summarize our contributions and future research directions in Section 6.

MOTIVATIONS

The use of per-user queues in cellular networks has almost eliminated the likelihood of flow interactions and CCAs interference between separate users [START_REF] Haile | End-to-end congestion control approaches for high throughput and low delay in 4G/5G cellular networks[END_REF]. However, flows of the same user may still use different CCAs, and depending on the design and TCP friendliness of the involved CCAs, a large bufferbloat can be introduced [START_REF] Jiang | Tackling bufferbloat in 3G/4G networks[END_REF][START_REF] Robert | Behaviour of Common TCP Variants over LTE[END_REF]. In fact, the probability of having multiple parallel flows on the same UE is quite high in today's cellular networks, 1 NEF cluster: https://wiki.inria.fr/ClustersSophia/Clusters_Home. mostly due to the increasing number of mobile services which create more opportunities for parallel data transfer [START_REF] Jukka | Parallel Connections and their Effect on the Battery Consumption of a Mobile Phone[END_REF]. However, this also increases the probability of self-inflicted bufferbloat since the parallel data flows on the UE may use different CCAs. This type of bufferbloat is called self-inflicted bufferbloat since it is introduced by the user itself. According to a recent study [START_REF] Mishra | The great internet TCP congestion control census[END_REF], over 30% of the top 20,000 Alexa websites are using Cubic and roughly 18% are currently based on BBR. This study also reveals that delay-based TCP variants such as Vegas/Veno and other unknown variants are used on 2.8 and 17.6% of the evaluated websites, respectively. Based on these findings, it appears that a large majority of current TCP traffic uses loss-based CCAs which are known to introduce excessive buffering in mobile networks. Furthermore, in mobile networks, due to the use of deep buffers in base stations, recent CCAs such as BBR that attempt to minimize delay increase are outperformed in terms of goodput by loss-based TCP variants when they compete for bandwidth. Other studies show that, in addition to being RTT unfair, BBR also suffers from bandwidth overestimation issues in fast-varying networks [START_REF] Chiariotti | BBR-S: A Low-Latency BBR Modification for Fast-Varying Connections[END_REF] and severe throughput collapse due to high delay variations over millimeter wave (mmWave) wireless links [START_REF] Kumar | TCP BBR for Ultra-Low Latency Networking: Challenges, Analysis, and Solutions[END_REF]. These issues along with the ever-growing number of CCAs that could potentially compete for bandwidth make it very challenging to solve the self-inflicted bufferbloat issue with a new CCA. It is also worth noting that the delay increase that may arise from these issues is particularly harmful for delay-sensitive flows and, therefore, greatly slow down web browsing as reported in [START_REF] Wang | Why Are Web Browsers Slow on Smartphones?[END_REF].

The self-inflicted bufferbloat issue becomes even more significant in mmWave bands mostly due to the inherent properties of high frequencies. According to 3GPP TS 38.104, 5G New Radio (NR) can operate in two distinct frequency ranges, Frequency Range 1 (i.e., FR1 or sub-6GHz) and Frequency Range 2 (i.e., FR2 or 24.25 GHz to 52.6 GHz) which falls in the mmWave region. In fact, frequencies in the mmWave region are prone to high penetration losses due to obstacles blocking the Line-of-Sight. Therefore, in case of NLOS conditions, the base station buffers incoming packets which eventually leads to high delay increase and/or persistent bufferbloat [START_REF] Zhang | Transport layer performance in 5G mmWave cellular[END_REF].

Our main goal with this work is to mitigate the self-inflicted bufferbloat issues that arise from parallel flows or intermittent radio links using a new approach completely independent of the CCAs in use.

RAN-AWARE PROXY-BASED FLOW CONTROL

In this section, we first present the high-level design of our RANaware proxy called RAPID, and then show how it leverages actual RAN statistics and various transport layer related information in order to categorize flows and properly allocate the available bandwidth. RAPID's main originality w.r.t. solutions presented in Section 5 is the mitigation of self-inflicted bufferbloat while preserving high bandwidth regardless of the characteristics of the CCAs involved and the number of concurrent flows sharing the per-user queues.

Proxy architecture

RAPID is a TCP proxy that seats close to the base station, in the MEC host and that leverages up-to-date radio information exposed by the Radio Network Information Service (RNIS) [START_REF] Etsi | Multi-access Edge Computing (MEC); Radio Network Information API[END_REF], similar to RAVEN [START_REF] Sabella | A Hierarchical MEC Architecture: Experimenting the RAVEN Use-Case[END_REF] and MELD (proposed in our previous work [START_REF] Diarra | Cross-layer Loss Discrimination Algorithms for MEC in 4G networks[END_REF]). The use of RNIS in real-world experimentation has been demonstrated by FlexRAN [START_REF] Foukas | FlexRAN: A Flexible and Programmable Platform for Software-Defined Radio Access Networks[END_REF], an open-source implementation of RNIS which allows a controller deployed somewhere in the network to collect radio information from some agents collocated with the deployed base stations. As illustrated in Figure 2, RAPID relies on several modules organized in layers, meaning that each module provides services to its upper module. At a basic level, RAPID first splits each incoming end-to-end TCP flow from a UE in two separate connections, referred here as 𝑇𝐶𝑃 RAN (i.e., TCP connection between the UE and RAPID) and 𝑇𝐶𝑃 WAN (TCP connection between RAPID and the corresponding end server). After that, it invokes the per-flow bandwidth estimation module in order to compute the Bandwidth Delay Product (BDP) available to each intercepted flow. Finally, the computed BDPs are used to override the Receive Window (RW) value in the TCP acknowledgements towards the corresponding end servers, thereby limiting the bytes in flight from those servers to the BDPs estimated for their respective flows. It is worth noting that while RAPID has no control over the choice of the end-server CCA, it can still control all the parameters of the connections established in the RAN segment (i.e.,𝑇𝐶𝑃 RAN ). Therefore, by default and in order to prevent excessive buffering in the proxy, 𝑇𝐶𝑃 RAN relies on a simplified CCA that always sets its congestion window to the estimated flow BDP.

RAN bandwidth estimation

As illustrated in Figure 2, RAPID periodically receives RAN statistics through the RNIS service. Similar to the statistics reported by FlexRAN agents [START_REF] Foukas | FlexRAN: A Flexible and Programmable Platform for Software-Defined Radio Access Networks[END_REF], these statistics include the cell bandwidth, the sub-carrier spacing, the Radio Network Temporary Identifier (RNTI), the number of allocated Physical Resource Blocks (PRBs), the computed Transport Block Size (TBS) and the selected Modulation and Coding Scheme (MCS) information for all the UEs connected to the cell. This information allows RAPID to estimate the bandwidth allocated to each UE by the base station in units of PRBs. However, the number of allocated PRBs does not always reflect the achievable bandwidth since the MAC scheduler at the base station may also take into account the RLC buffer state [START_REF] Sb Monikandan | A review of MAC scheduling algorithms in LTE system[END_REF] or the incoming data rate [START_REF] Xie | PBE-CC: Congestion Control via Endpoint-Centric, Physical-Layer Bandwidth Measurements[END_REF] when allocating resources to users. Therefore, in order to estimate the achievable bandwidth, we first calculate the number of unused PRBs, 𝑃𝑢 i (𝑡), by using the total number of PRBs in the cell 𝑁 PRB , the number of connected UE 𝑀 and the number of PRBs allocated to each UE 𝑃𝑎 i (𝑡):

𝑃𝑢 i (𝑡) = 𝑁 PRB - 𝑀 𝑖=1 𝑃𝑎 i (𝑡) , (1)
The expected number of PRBs, 𝑃𝑒 i (𝑡) for a given UE 𝑖 is then computed as follows:

𝑃𝑒 i (𝑡) = 𝑃𝑎 i (𝑡) + 𝑃𝑢 i (𝑡) , (2)
With the expected number of PRBs and the reported MCS values, RAPID computes the maximum transport block size at time 𝑡, 𝑇 𝐵𝑆 i (𝑡), for each UE as detailed in 3GPP TS 38.214. Therefore, the highest achievable throughput 𝐶 i (𝑡) (in unit of 𝑏𝑖𝑡𝑠/𝑠) for a given UE, depending on the reported MCS, is expressed as:

𝐶 i (𝑡) = 𝑇 𝐵𝑆 i (𝑡) 𝑇𝑇 𝐼 , (3)
where 𝑇𝑇 𝐼 stands for the Transmission Time Interval (e.g., TTI = 125 𝜇s for Numerology 𝜇=3). It is worth noting that this real-time RAN bandwidth estimation makes it possible to detect fast capacity variations as well as bad radio conditions (e.g., NLOS conditions in mmWave), which, to some degree, can cause excessive buffering at the base stations.

Per-flow bandwidth allocation

The major contribution of RAPID with respect to other existing solutions is its bandwidth allocation scheme. Rather than relying on a static allocation scheme, the bandwidth estimation module distributes the aggregated bandwidth of the UE according to the requirements of the active flows in terms of bandwidth. On connection start, the initial Receive Window 𝑅𝑊 ij (𝑡) of a given flow 𝑗 of a UE 𝑖 is computed by dividing the expected bandwidth estimated for the UE (in 𝑏𝑖𝑡𝑠/𝑠) by the number of active flows:

𝑅𝑊 ij (𝑡) = 𝐶 i (𝑡) 𝑁 𝑅𝑇𝑇𝑚𝑖𝑛 ij (𝑡) , (4)
where 𝑁 is the number of active flows in the UE and 𝑅𝑇𝑇𝑚𝑖𝑛 ij (𝑡) is the minimum end-to-end RTT of flow 𝑗 at time 𝑡. This initial phase is followed by a dynamic allocation phase after 𝐾 ij 𝑅𝑇𝑇 WAN , where the allocated bandwidth changes depending on flow category. We define two distinct categories of flows: slow interactive flows (i.e., browsing, instant messaging, etc.) and fast download flows (e.g., HD streaming, file transfer, Augmented and Virtual Reality AR/VR, etc.). The former are sensitive to delay but require low bandwidth while the latter may require both high bandwidth and reasonable delay variations. In such a context, allocating the same amount of bandwidth to all flows not only penalizes fast download flows (since slow flows only require a small fraction of the bandwidth) but also results in radio link under-utilization and wastage of the bandwidth allocated to the UE. With that in mind, we devise a flow categorization scheme based on a common behavior of TCP flows during startup phase. In fact, since the congestion windows of most TCP flows follow an exponential increase pattern during the initial phase, we can compute the number 𝐾 ij of RTTs it takes to reach

𝐾 ij (𝑡) = log 2 𝑅𝑊 ij (𝑡) 𝑀𝑆𝑆 + 1 , (5)
Following the same exponential increase pattern, after 𝐾 ij RTTs, the expected arrival rate 𝑅 ij at 𝑇𝐶𝑃 WAN should be:

𝑅 ij (𝑡 + 𝐾) = 𝑅𝑊 ij (𝑡) 𝑅𝑇𝑇 WANij , (6)
where MSS stands for the negotiated Maximum Segment Size and 𝑅𝑇𝑇 WANij is the current smoothed RTT of 𝑇𝐶𝑃 WANij . Therefore, after 𝐾 ij 𝑅𝑇𝑇 WANij , if the actual arrival rate, 𝑟 ij , is less than a certain percentage (set empirically to 80%) of the expected rate, the flow is flagged as slow; otherwise, it is considered as a fast download flow. The Receive Windows of slow flows are then computed as follows:

𝑅𝑊 ij (𝑡 + 𝐾) = rij (𝑡 + 𝐾) 𝑅 ij (𝑡 + 𝐾) 𝑅𝑊 ij (𝑡) , (7)
where rij (𝑡 + 𝐾) is the exponential moving average of the arrival rate 𝑟 ij at time (𝑡 + 𝐾). Using the exponential moving average of all the past arrival rates allows capturing irregular variations of the congestion window during the categorization period (i.e., during 𝐾 𝑅𝑇𝑇 𝑠). After each change of Receive Window, the available bandwidth not used by the UE is updated as follows:

𝐴 i (𝑡 + 𝐾) = 𝑍 𝑗=1 𝐴 ij (𝑡 + 𝐾) , (8)
𝐴 ij (𝑡 + 𝐾) = |𝑅𝑊 ij (𝑡) -𝑅𝑊 ij (𝑡 + 𝐾)| , (9)
where 𝐴 ij is the unused bandwidth at the flow level, 𝐴 i is the aggregated unused bandwidth at the UE level and 𝑍 , the number of slow flows identified. In order to avoid wasting bandwidth, the available unused bandwidth is evenly distributed among the fast download flows of the UE. Therefore, the Receive Windows of these flows are updated as follows:

𝑅𝑊 ij (𝑡 + 𝐾) = 𝑅𝑊 ij (𝑡) + 𝐴 i (𝑡 + 𝐾) 𝑁 -𝑍 . ( 10
)
The dynamic allocation phase is repeated for each active flow until the end of the connection in order to maximize the aggregated link utilization at the UE level. Indeed, the available bandwidth is distributed among the concurrent flows regardless of the CCA in use. However, CCAs with aggressive growth functions yield higher link utilization since they reach the target Receive Window faster.

EVALUATION

In this section, we first describe the implementation of our proxy in ns-3 [START_REF] Thomas R Henderson | Network simulations with the ns-3 simulator[END_REF]. Then, we evaluate its efficiency under some relevant scenarios that reproduce the issues mentioned in Sections 1 and 2. We repeat each scenario 10 times and show the observed results with a 95% confidence interval.

ns-3 experimentation testbed

The ns-3 mmWave module paves the way for the simulation of endto-end 5G environments. Besides providing large bandwidths in the millimeter wave band for eMBB scenarios, it also enables the simulation of low-latency communications thanks to a customizable sub-carrier spacing (i.e., supporting various numerologies) in the RAN. With that in mind and in order to evaluate the performance of RAPID, we implement all the functional modules illustrated in Figure 2 in a proxy device collocated with a mmWave base station in ns-3. The proxy is connected to the core network via a 10 𝐺𝑏𝑝𝑠 link in order to simulate a real-world fiber backhaul. Since Cubic and BBR are the dominant CCAs today [START_REF] Mishra | The great internet TCP congestion control census[END_REF], we simulate two TCP sources based on these algorithms as illustrated in Figure 3. Other simulation parameters are detailed in Tables 1 and2.

MEC Scenarios

In this paper, we focus on evaluating the performance of RAPID in mobile edge settings since it is more suitable for throughputintensive ultra-low latency applications (e.g., AR/VR, tactile Internet, etc.) that require both high throughput (e.g., from 100 𝑀𝑏𝑝𝑠 to a few 𝐺𝑏𝑝𝑠) and low latency (e.g., from 1 to 10 𝑚𝑠) [START_REF] Kumar | TCP BBR for Ultra-Low Latency Networking: Challenges, Analysis, and Solutions[END_REF]. Furthermore, although several studies have been conducted on the evaluation of recent CCAs in 4G and 5G mmWave networks, to the best of our knowledge, there is no significant work on their evaluation in mobile edge and very low latency settings. Therefore, in our different experimentation, we consider only end-to-end RTT in the range of 1 to 10 𝑚𝑠.

In order to evaluate the performance of RAPID in different RTT and flow configurations, we consider a main single user scenario Fast eMBB downloads: This first scenario aims to showcase the efficiency of RAPID in mitigating the interference between different CCAs (i.e., Cubic and BBR). To that end, the UE downloads simultaneously 200 𝑀𝐵 from two TCP servers, one using Cubic and the other BBR, in both LOS and NLOS conditions. The obtained goodput and the delay variations are observed for each flow in various end-to-end RTT configurations.

Mixed Fast and App-limited/Slow downloads: In this scenario, we highlight the negative effects of self-inflicted bufferbloat on app-limited flows (i.e., slow flows). The UE receives simultaneously a continuous flow (e.g., streaming) that uses Cubic and a slow flow (e.g., web browsing) that uses BBR. The slow flow is paced at 16 𝑀𝑏𝑝𝑠 in order to simulate a continuous web browsing activity with 2 𝑀𝐵 page sizes 3 and a Page Load Time (PLT) of 1 second, which corresponds to the limit of user's real-time perception [START_REF] Fui-Hoon | A study on tolerable waiting time: how long are web users willing to wait[END_REF]. We then evaluate the effect of bufferbloat on web browsing for different RTT values and radio conditions by monitoring the bandwidth share of the slow flow, which should remain around 16 𝑀𝑏𝑝𝑠 for a reasonable real-time perception.

Note that the NLOS conditions during our experiments are simulated by reproducing the positions, sizes and heights of the buildings in Jean Medecin Avenue (a famous busy avenue in Nice, France).

Results

Figures 4a,4c, 4e, 4g show a comparison of both goodput and endend latency when RAPID is not used in the fast eMBB downloads scenario. At first, it can be seen that Cubic grabs more bandwidth than BBR in all the evaluated configurations regardless of the radio conditions. This outcome was indeed expected since several studies show that loss-based CCAs outperform BBR in terms of goodput in deep buffer environments [START_REF] Cardwell | BBR: Congestion-Based Congestion Control[END_REF][START_REF] Hock | Experimental evaluation of BBR congestion control[END_REF][START_REF] Song | BBR-CWS: Improving the Inter-Protocol Fairness of BBR[END_REF]. Although most of these studies claim that the degree of fairness in this situation only depends on the bottleneck buffer size, our results show that the end-toend RTT value greatly affects the bandwidth shares of the two CCAs in mobile edge settings. As illustrated in Figures 4a and4c, the bandwidth share of BBR appears to increase as the end-toend RTT increases while Cubic follows an opposite pattern. This phenomenon is simply due to the Hystart and startup phases of Cubic and BBR, respectively. Basically, the two CCAs always start with an exponential growth; however, in case of very small RTT (e.g., 1 𝑚𝑠), the BDP of the link is quickly reached. For instance, with the following parameters: initial congestion window = 10 𝑀𝑆𝑆; RAN throughput = 850 𝑀𝑏𝑝𝑠 and RTT = 1 𝑚𝑠, the bytes in flight for each flow exceed the BDP of the link just after 4 RTTs (i.e., more than 2 BDPs of inflight data is maintained). However, since BBR's bottleneck bandwidth estimation window is around six to ten RTTs by default [START_REF] Cardwell | BBR: Congestion-Based Congestion Control[END_REF], it greatly underestimates the available bandwidth due to the large accumulation of data at the RLC buffer introduced by Cubic (more than 5 BDPs of inflight data at 10 RTTs). On the other hand, as the end-to-end RTT increases, it takes more RTTs to reach the BDP of the link, which allows BBR to get a better estimate of the bottleneck bandwidth (i.e., before Cubic introduces large buffering) but causes Cubic to leave the exponential increase phase prematurely. In fact, Cubic's Hystart exits the slow start phase after a certain increase in RTT [START_REF] Ha | Taming the Elephants: New TCP Slow Start[END_REF], meanwhile BBR's startup phase continues until it introduces more than two BDPs of inflight data [START_REF] Chiariotti | BBR-S: A Low-Latency BBR Modification for Fast-Varying Connections[END_REF]. Due to RTT increase, if BBR does not observe a lower minimum RTT (RTTmin) during a 10 seconds window, it enters a phase called probeRTT. In this phase the number of bytes in flight is reduced to 4 Maximum Segment Size (MSS) at least for 200 𝑚𝑠 in order to capture the new RTTmin. During this period, Cubic continues to grab more bandwidth as BBR decreases its sending rate, which explains why loss-based CCAs eventually outperforms BBR in deep buffer environments. However, for short to medium flows that finish before BBR's probeRTT phase takes place (i.e., for download duration around 10𝑠), as we increase the end-to-end RTT, BBR bandwidth share increases (even in very deep buffer environments) while Cubic share decreases due to the Hystart behavior. It can be seen from Figures 4e and4g that excessive buffering causes a significant increase in RTT (from 100 to over 5000%) for both BBR and Cubic especially in case of NLOS conditions.

RAPID provides both flows with relatively fair bandwidth shares under LOS conditions as illustrated in Figure 4e and the RTT increase due to Cubic overshooting becomes almost negligible (see Figure 4f) thanks to RAN-aware flow control. However, in case of NLOS conditions, although RAPID reduces the self-inflicted bufferbloat by a factor of 50 as illustrated in Figure 4h, BBR is not able to fully exploit its allocated bandwidth share, as it is subject to throughput oscillations in case of fast variations in delay [START_REF] Kumar | TCP BBR for Ultra-Low Latency Networking: Challenges, Analysis, and Solutions[END_REF]. Figures 5a through 5h show the test results for the mixed fast/applimited downloads scenario. In the cases where RAPID is not used (Figures 5a,5c), it can be seen that the app-limited flow is unable to obtain its desired bandwidth share (i.e., 16 𝑀𝑏𝑝𝑠) due to the fast download flow that overshoots more than the BDP. As a result, the slow flow is limited at less than 1 𝑀𝑏𝑝𝑠 in LOS conditions and around 5 𝑀𝑏𝑝𝑠 in NLOS. The increase in BBR goodput in case of NLOS is simply due to Cubic's sending rate decrease caused by packet losses. In fact, even after Cubic halves its congestion window, the goodput achieved by the slow flow is still 3 times less than the desired goodput. As a result, the PLT for a 2 𝑀𝐵 web page is around 3 to 16 seconds. Moreover, as depicted in Figure 5e, over 8000% end-to-end RTT increase can be observed for the slow flow in some cases. Such a large delay increase is unacceptable both for traditional web browsing and throughput-intensive ultra-low latency applications. On the other hand, in the cases where RAPID is used (Figures 5b and5d), the app-limited flow is allocated on average 11 𝑀𝑏𝑝𝑠 in LOS and 8 𝑀𝑏𝑝𝑠 in NLOS. Furthermore, unlike in the first scenario where RAPID equally shares the available bandwidth between the two download flows, here, the slow flow is automatically detected thanks to Equation 6and is allocated a Receive Window proportional to its average data rate using Equation 7. As shown in Figures 5b and 5d, this mechanism allows the fast download flow to exploit all the available bandwidth not used by the app-limited flow while remaining bounded by the actual RAN capacity. This not only improves the link utilization but also reduces the RTT increase for both flows by a factor of 10 to 50. Overall, thanks to RAPID flow categorization and bandwidth allocation schemes, the PLT is reduced by 90% (i.e., from 16s to 1.5s).

Besides evaluating RAPID's behavior under basic network conditions, we also consider other parameters that may affect its performance in real-world deployments:

Scalability: In commercial mobile networks, there is no limitations on the number of flows a user can maintain in parallel. Therefore, in order to be efficient in such networks, RAPID must exhibit good performances regardless of the number of active flows per user. Figure 6 illustrates this behavior by showing the bandwidth allocation and delay distribution of 25 Cubic flows progressing in parallel in the same UE for both 2𝑚𝑠 and 8𝑚𝑠 end-to-end RTT configurations.

Packet loss: In most cases and as Equation 5 assumes, packet loss in the backhaul network is generally negligible. This owes to the fact that, in commercial deployments, backhaul link dimensioning is done in such a way that the peak data rate or at least the average data rate of the cell is supported [START_REF] Metsälä | Planning and Optimizing Mobile Backhaul for LTE[END_REF]. After all, if the backhaul link limits the cell data rate, there would be no point for the operator to invest in large frequency spectrum. On the other hand, packet loss may still occur in the RAN segment because of bad radio conditions or buffer overflow. The latter is avoided when using the RAPID's flow control mechanism while the former is handled by RAPID's simplified CCA which always adapts its sending rate to the available RAN capacity regardless of random losses.

For space limitation reasons, we mainly focus in this paper on scenarios involving Cubic and BBR as they are currently the two main CCAs in use on the Internet. Nevertheless, we have also evaluated RAPID with other well-known CCAs such as NewReno, Vegas [START_REF] Lawrence | TCP Vegas: New techniques for congestion detection and avoidance[END_REF], Yeah [START_REF] Baiocchi | YeAH-TCP: yet another highspeed TCP[END_REF] and Westwood [START_REF] Mascolo | TCP Westwood: Bandwidth Estimation for Enhanced Transport over Wireless Links[END_REF] that still control a large portion of today's Internet traffic. For instance, a subset of these additional experiments are shown in Figure 7 where we evaluate a simple Fast-Download scenario in LOS condition involving NewReno, Vegas and Westwood in a 1𝑚𝑠 RTT configuration. As expected, our experiments show that RAPID allows delay-based TCP variants like Vegas (known for their very poor performances when competing with loss-based CCAs) to achieve similar goodput as NewReno or Westwood, while avoiding high delay increase. Figures 7a and7b show, for a single run, the bytes in flight of the 3 flows as they progress in parallel on the same UE. It can be seen from Figure 7d that RAPID equally shares the total bandwidth (i.e., 850 𝑀𝑏𝑝𝑠) between the 3 flows. All the flows get a similar completion time (around 6𝑠) as illustrated in Figure 7b and the overall delay increase is reduced by a factor of 10 to 90, see Figures 7e and7f. As illustrated in Figure 7a, without RAPID, NewReno gets by default the lowest completion time (around 2𝑠) because of its aggressive congestion growth function. In other words, it always maintains a high number of bytes in flight which negatively impacts the other competing flows, and in particular Vegas, as the latter is delay-based. As a result, NewReno always grabs a larger share of the total bandwidth (see Figure 7c) at the cost of over 7000% increase in delay (i.e. from 1𝑚𝑠 to 80𝑚𝑠) and with a high degree of unfairness to the other flows. Thanks to RAPID, a certain degree of fairness is maintained between the competing flows. Despite their different designs, all the 3 CCAs are imposed a similar number of bytes in flight, which allows them to obtain the same share and to finish approximately at the same time, as illustrated in Figures 7b and7d. Note that other additional scenarios involving the aforementioned CCAs as well as the results shown in this section can be reproduced with ns-3 using the codes and scripts that we have made publicly available [START_REF] Diarra | RAPID[END_REF].

Overhead

To work properly, RAPID requires an out-of-band control channel in the backhaul as shown in Figure 2. This control channel is necessary in order to allow the continuous retrieval of radio information, therefore, its requirements in terms of bandwidth depend both on the size of the retrieved radio information and the configured polling period. In our simulations, we use a polling period at subframe granularity (i.e., radio information is fetched every ms) and the size of the retrieved information per UE including TCP and IP headers is around 170 𝑏𝑦𝑡𝑒𝑠. In other words, each UE introduces an overhead of 1 to 1.5 𝑀𝑏𝑝𝑠 in the control channel, which is close to the FlexRAN overhead in real world deployments [START_REF] Foukas | FlexRAN: A Flexible and Programmable Platform for Software-Defined Radio Access Networks[END_REF].

We believe that such an overhead that accounts only for 0.13% of the achievable throughput (i.e., 850 𝑀𝑏𝑝𝑠 in our case) and 10 -8 % of a typical 10 𝐺𝑏𝑝𝑠 backhaul, is negligible compared to the resulting 150% and 3600% BBR's goodput increase in fast-download and web browsing scenarios, respectively (see Figures 4b and5b) as well as the overall end-to-end delay reduction in the range of 80 to 97%, see Figures 4h and5h.

Discussion

Our simulation results demonstrate that RAPID significantly mitigates the self-inflicted bufferbloat issue in mobile networks, while preserving near optimal link utilization (Figures 4b,5b). The idea is to impose a certain level of fairness on the concurrent flows depending on their nature and on the available radio bandwidth. However, even if all the flows are assigned the same Receive Window, their performance in terms of goodput and link utilization still depends on the design of their respective CCA. Indeed, depending on their growth functions, different CCAs will reach a given number of bytes in flight at different times. Therefore, CCAs with faster growth functions will yield better link utilization. In addition to that, it is worth noting that upcoming 5G and 6G networks are expected to deliver throughput in the range of several gigabits per second. So, with the design and growth functions of the current CCAs, it would be virtually impossible to reach such a high throughput in a couple of RTTs. Therefore, it becomes necessary to rethink congestion control approaches in order to maintain high link utilization with minimum latency, which is very challenging as indicated in [START_REF] Zhang | Will TCP Work in mmWave 5G Cellular Networks[END_REF], mostly because of the highly intermittent nature of mmWave capacity.

In such a situation, we believe that providing flow-level RTT control and bufferbloat mitigation with proxy-based solutions such as RAPID will significantly simplify the design of future CCAs by allowing them to focus only on fast convergence.

RELATED WORK

Authors in [START_REF] Polese | milliProxy: A TCP proxy architecture for 5G mmWave cellular systems[END_REF] proposed milliProxy, a performance enhancing proxy for 5G mmWave scenarios that regulates the sending rate using a variable Flow Window (FW). The FW is computed using the estimated RAN data rate (derived from channel quality information), the RLC buffer occupancy and the estimated RTT. Although milliProxy significantly mitigates bufferbloat in case of single flow, its FW computation scheme is not adapted for multi-flow scenarios.

In-band throughput guidance (TG) was introduced in [START_REF] Jain | Mobile throughput guidance inband signaling protocol[END_REF]. This approach allows a functional element (TG provider) residing in the RAN to include RAN throughput information in the TCP header. This throughput information can then be exploited by a TCP server to regulate its sending rate. However, the authors indicate that, in case of multiple flows per bearer, each flow is assigned an equal share of the bearer capacity, which is not sufficient to ensure fairness since flows may have different requirements.

LCTCP proposed in [START_REF] Beshay | Link-Coupled TCP for 5G networks[END_REF] for 5G networks relies on a out-of-band signaling of queue occupancy information between the base station and the end server. The transmitted information is used by the server to adjust its sending rate so that the amount of packets queued at the base station is always aligned with the throughput and delay requirements of the application. However, although LCTCP outperforms conventional CCAs in some scenarios, it cannot deliver both high throughput and low delay simultaneously.

The authors in [START_REF] Lee | Simulation study of TCP proxy in multi-connectivity enabled 5G mmWave network[END_REF] proposed a TCP proxy for multi-connectivity enabled 5G mmWave network that speeds up congestion window growth and prevents RLC buffer overflow. The former is achieved by separating congestion events of the radio from wired segments while the latter relies on receive window modifications based on an estimation of the available proxy buffer space. Despite improving the download time in some scenarios, the proposed scheme is not adapted for bufferbloat mitigation. Indeed, the proxy buffer size is static and does not consider the actual RAN state, which could result in large delay increase especially in the mmWave band.

A proxy-based flow aggregation TCP proxy for GPRS was proposed in [START_REF] Chakravorty | Using TCP flow-aggregation to enhance data experience of cellular wireless users[END_REF]. The solution proposed relies on a static estimation of the bottleneck BDP, which is not adequate for cellular networks because of the highly varying nature of the radio conditions.

CONCLUSION

In this paper we highlight the limits of per-user flow isolation in mitigating self-inflicted bufferbloat issues in case of multiple flows per user and intermittent mmWave links. By using up-todate RAN statistics from MEC Radio Network Information Service and analyzing the behavior of active flows, the RAPID solution prevents CCAs from exceeding the RAN capacity, thus, drastically reducing the delay increase regardless of the radio conditions while preserving good link utilization.

To the best of our knowledge, RAPID is the first attempt to mitigate self-inflicted bufferbloat and interference between CCAs at the flow level. We plan to further assess its performance over a real 5G deployment in the near future.

Figure 1 :

 1 Figure 1: Bottleneck location in cellular networks.

Figure 2 :

 2 Figure 2: RAPID high-level architecture

Figure 3 :

 3 Figure 3: RAPID ns-3 experimentation testbed

Figure 5 :

 5 Figure 5: Mixed Fast and App-limited/Slow downloads scenario.

  Goodput distribution of 25 Cubic flows using RAPID

Figure 6 :

 6 Figure 6: Fast-download with 25 Cubic flows progressing in parallel in the same UE

Figure 7 :

 7 Figure 7: Concurrent NewReno, Vegas and Westwood flows

Table 1 :

 1 Global simulation parameters

	1,200
	cubic
	bbr
	Goodput (Mbps)
	RTT (ms)
	(d) Goodput in NLOS
	with RAPID

Table 2 :

 2 Mobility and blockage parameters

	Parameters	Values
	User speed	1 m/s
		mmWave3GPP Build-
	Propagation Model	ings PropagationLoss-
		Model
	Number of buildings	8
	Building sizes 2	Jean-Medecin Avenue, Nice, FRANCE
	consisting of one UE receiving simultaneously several flows from
	different end servers. Depending on the characteristics of the con-
	current flows (i.e., sheer download or slow/interactive downloads),
	such a basic scenario can highlight both the self-inflicted bufferbloat
	issue introduced by loss-based CCAs and the unfairness in terms of
	bandwidth when different CCAs compete in deep buffer environ-
	ments. Based on our main scenario, we define two sub-scenarios
	that highlight the impact of RAPID's flow-level bandwidth allo-
	cation scheme on the global achievable performance in terms of
	goodput and delay:

Google Earth TM is used to estimate the size of buildings.

The average web page size on the Internet is around 1.5 𝑀𝐵[START_REF] Johnson | Desktop and mobile web page comparison: characteristics, trends, and implications[END_REF].


Thomas Leoni

Conor Hogan

Kai Zhang

Michel Daher

Mansour §^

Romain Bernard

Romain Parret

Andrea Resta

Stefano Colonna

Yves Borensztein

Fabio Ronci

Geoffroy Prévot

Laurence Masson

Demonstration of the Existence of Dumbbell Silicene: a Stable Two-Dimensional Allotrope of Silicon

We report a combined experimental and theoretical study on the formation of dumbbell silicene structures on Ag(110). High-resolution scanning tunneling microscopy (STM) reveals a rich tapestry of adatom-free and -decorated bidimensional silicene phases covering the whole Ag(110) surface. The most thermodynamically stable silicene models obtained from densityfunctional theory (DFT) perfectly reproduce all features observed by STM. These phases correspond to different Si buckled honeycomb reconstructions ((13´4), c(18´4) and c(8´4)) composed of two periodic motifs common to all structural models. DFT calculations show that these reconstructions are stabilized by the presence of ordered arrays of Si adatoms adsorbed on top of silicene in a dumbbell configuration. Grazing incidence X-ray diffraction (GIXD) measurements confirm the growth of a dumbbell silicene layer. The structure factor values are well reproduced by a (13´4) model with 4 Si adatoms per unit cell and a slight distortion of the hexagonal unit cell. Our STM-DFT-GIXD study demonstrates the formation of dumbbell silicene, a theoretically predicted two-dimensional Si allotrope. This opens up perspectives for tuning the peculiar properties of silicene.

INTRODUCTION

Since the graphene breakthrough, two-dimensional (2D) materials have become a major field in materials research, largely motivated by their outstanding electronic and optoelectronic properties that foresee their integration in a wide range of next-generation devices. 1 2D materials beyond graphene made of elements of Group 14 such as silicon and germanium have experienced a renewed interest in the last decade due to the similarity between their valence electronic configuration and that of graphene as well as the widespread use of Si and Ge in the semiconductor industry. Indeed, theoretical studies have predicted metastable configurations of free-standing silicene and germanene, the Si-and Ge-based counterpart of graphene, consisting of 2D honeycomb low buckled structures associated with the presence of a Dirac cone in their band structure. [START_REF] Cahangirov | Two-and One-Dimensional Honeycomb Structures of Silicon and Germanium[END_REF] The considerable interest in these Group 14 2D materials, from a theoretical and experimental point of view, has been reinforced by the prediction of a much stronger spin-orbit coupling than in graphene, favoring more prominent quantum spin Hall effects and by the possibility of energy band gap engineering. [START_REF] Liu | Quantum Spin Hall Effect in Silicene and Two-Dimensional Germanium[END_REF][START_REF] Meng | Electronic Band Engineering in Elemental 2D Materials[END_REF] These peculiar electronic properties are related to the presence of a mixed sp 2 -sp 3 hybridization, which results in a low-buckled 2D structure, contrary to the sp 2 electronic configuration and flat geometry of graphene. [START_REF] Liu | Low-Energy Effective Hamiltonian Involving Spin-Orbit Coupling in Silicene and Two-Dimensional Germanium and Tin[END_REF] As widely reported, a key issue for these materials lies in their synthesis. As silicene and germanene cannot be obtained by exfoliation of the bulk material, a substrate that generally dictates the structure of the monolayer is necessarily required for the epitaxial growth of Si and Ge 2D sheets.

Although synthesis of silicene has been attempted on several different substrates, including ZrB2(0001), [START_REF] Fleurence | Experimental Evidence for Epitaxial Silicene on Diboride Thin Films[END_REF] Ir(111), [START_REF] Meng | Buckled Silicene Formation on Ir(111)[END_REF] ZrC(111), 8 MoS2, [START_REF] Chiappe | Two-Dimensional Si Nanosheets with Local Hexagonal Structure on a MoS 2 Surface[END_REF] Ru(0001), [START_REF] Huang | Sequence of Silicon Monolayer Structures Grown on a Ru Surface: From a Herringbone Structure to Silicene[END_REF] Au(111) [START_REF] Stpniak-Dybala | Planar Silicene: A New Silicon Allotrope Epitaxially Grown by Segregation[END_REF] and very recently NaCl/Ag(110), [START_REF] Quertite | Silicene Nanoribbons on an Insulating Thin Film[END_REF] silver surfaces have by far achieved the most success. Indeed, the synthesis of silicene has been reported on Ag(111) in 2012, [START_REF] Vogt | Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon[END_REF][START_REF] Feng | Evidence of Silicene in Honeycomb Structures of Silicon on Ag(111)[END_REF][START_REF] Lin | Structure of Silicene Grown on Ag(111)[END_REF][START_REF] Jamgotchian | Growth of Silicene Layers on Ag(111): Unexpected Effect of the Substrate Temperature[END_REF][START_REF] Enriquez | Silicene Structures on Silver Surfaces[END_REF] together with the observation in angle-resolved photoelectron spectroscopy (ARPES) spectra of electronic dispersion similar to the one of graphene. [START_REF] Vogt | Compelling Experimental Evidence for Graphenelike Two-Dimensional Silicon[END_REF] Although it was later shown that the linear features revealed in ARPES measurements were actually due to the interaction of the Si overlayer with the silver substrate rather than to the presence of Dirac cone electronic structure, [START_REF] Cahangirov | Electronic Structure of Silicene on Ag(111): Strong Hybridization Effects[END_REF][START_REF] Gori | Origin of Dirac-Cone-like Features in Silicon Structures on Ag(111) and Ag(110)[END_REF][START_REF] Chen | Revealing the Substrate Origin of the Linear Dispersion of Silicene/Ag(111)[END_REF][START_REF] Mahatha | Silicene on Ag(111): A Honeycomb Lattice without Dirac Bands[END_REF] these pioneering works have boosted the experimental and theoretical investigations of silicene on silver substrates in the years to follow. [START_REF] Grazianetti | Two-Dimensional Silicon: The Advent of Silicene[END_REF] The possibility to tune the electronic properties of graphene and especially to open a band gap has been intensively studied and demonstrated through the formation of graphene nanoribbons (NRs) [START_REF] Son | Energy Gaps in Graphene Nanoribbons[END_REF][START_REF] Cai | Atomically Precise Bottom-up Fabrication of Graphene Nanoribbons[END_REF] or doping of the 2D layer. [START_REF] Denis | Band Gap Opening of Monolayer and Bilayer Graphene Doped with Aluminium, Silicon, Phosphorus, and Sulfur[END_REF][START_REF] Usachov | Nitrogen-Doped Graphene: Efficient Growth, Structure, and Electronic Properties[END_REF] In contrast, very few experimental studies have demonstrated similar trends for silicene, in spite of the wide number of theoretical studies. In particular, although silicene NRs were widely believed to form on Ag(110), [START_REF] Aufray | Graphene-like Silicon Nanoribbons on Ag(110): A Possible Formation of Silicene[END_REF][START_REF] Lian | The Structural and Electronic Properties of Silicon Nanoribbons on Ag(110): A First Principles Study[END_REF][START_REF] Oughaddou | a Promising New 2D Material[END_REF] the observed NR reconstruction was later shown to be composed of pentamer chains of Si lying in the missing rows (MRs) of the substrate. [START_REF] Cerdá | Unveiling the Pentagonal Nature of Perfectly Aligned Single-and Double-Strand Si Nano-Ribbons on Ag(110)[END_REF] As a result, the surface electronic properties are far from those expected for lateral confinement of a silicene sheet. [START_REF] Cerdá | Unveiling the Pentagonal Nature of Perfectly Aligned Single-and Double-Strand Si Nano-Ribbons on Ag(110)[END_REF][START_REF] Hogan | Optical Properties of Silicene, Si/Ag(111), and Si/Ag(110[END_REF] An alternative way to tune the silicene properties is via the formation of dumbbell (DB) like structures. These configurations are built from the original 2D honeycomb structure by adding adatoms at selected lattice sites. DB structures have been theoretically predicted for honeycomb 2D layers of silicon, germanium, tin or phosphorus. [START_REF] Özçelik | Local Reconstructions of Silicene Induced by Adatoms[END_REF][START_REF] Borlido | The Ground State of Two-Dimensional Silicon[END_REF][START_REF] Kaltsas | Stability and Electronic Properties of Ultrathin Films of Silicon and Germanium[END_REF][START_REF] Matusalem | Stability and Electronic Structure of Two-Dimensional Allotropes of Group-IV Materials[END_REF][START_REF] Kaur | Novel Phosphorus-Based 2D Allotropes with Ultra-High Mobility[END_REF] Remarkably, they have been shown to possess a stronger cohesive energy than their pristine counterparts. In particular, DB silicene has recently been predicted to constitute the true ground state of 2D silicon. [START_REF] Borlido | The Ground State of Two-Dimensional Silicon[END_REF] Interestingly, the predicted electronic properties of DB silicene differ from those of free-standing silicene with a gap opening, a spin-polarized ground state and a very low thermal conductivity. [START_REF] Özçelik | Local Reconstructions of Silicene Induced by Adatoms[END_REF][START_REF] Borlido | The Ground State of Two-Dimensional Silicon[END_REF][START_REF] Peng | First-Principles Prediction of Ultralow Lattice Thermal Conductivity of Dumbbell Silicene: A Comparison with Low-Buckled Silicene[END_REF] Although dumbbell-like units have been proposed to form on an exotic 2D Si allotrope with a Kagome-like lattice different from the honeycomb structure expected for silicene, [START_REF] Sassa | Kagome-like Silicene: A Novel Exotic Form of Two-Dimensional Epitaxial Silicon[END_REF] an experimental confirmation of the formation of DB silicene is still lacking. Indeed, it must be noted that although DB silicene has been proposed to explain the Ö3´Ö3 phase of Si/Ag(111), [START_REF] Cahangirov | Atomic Structure of the Ö3 × Ö3 Phase of Silicene on Ag(111)[END_REF] a recent scanning tunneling microscopy (STM) and densityfunctional theory (DFT) study demonstrated that the observed phase corresponds to thicker films. [START_REF] Curcella | The Mechanism for the Stabilization and Surfactant Properties of Epitaxial Silicene[END_REF] In this article, we evidence the formation of DB silicene. We show that by adding Si atoms to the Si pentamer chain superstructure grown on Ag(110), this phase transforms into a silicene single-layer which covers the whole Ag surface and is stabilized by regular DB-like atomic units.

Through a combination of STM, DFT and grazing incidence X-ray diffraction (GIXD), we demonstrate that the silicene overlayer is composed of honeycomb structures exhibiting different buckling patterns stabilized by the presence of the adatoms. Our findings give a comprehensive demonstration of the existence of DB silicene structures.

METHODS

STM.

The STM measurements were carried out both at CINaM in Marseille and at ISM in Rome using the Scienta Omicron STM systems operating in ultra-high vacuum (UHV) (base pressure 10 -10 Torr) at T = 77 K or at room temperature (RT), respectively. No significant differences were observed by probing full or empty states in the applied bias range, or by modifying the tunneling current or measurement temperature. The STM images were successfully replicated independently in the two laboratories, demonstrating the robustness of the measurements. Sample cleaning was achieved by repeated cycles of Ar + sputtering and annealing at 780 K. Si was evaporated from a direct current heated piece of silicon wafer kept at 1520 K, after preoutgassing at 1070 K for several hours, on the Ag substrate maintained at ~ 483 K. The Si flux was ~ 1.5 monolayer (ML)/h, where 1 ML corresponds to the Ag(110) surface atom density. All images were subsequently calibrated using atomically resolved images of the (5´2)/c(10´2) Si superstructure with an accuracy of ± 5%. The lattice parameters of Ag(110) are a Ag in the [001] direction and a Ag /Ö2 in the [11 ¯0] direction where a Ag = 4.085 Å. The STM data were processed using Gwyddion software. [START_REF] Nečas | An Open-Source Software for SPM Data Analysis[END_REF] Standard plane subtraction, 1D fast Fourier transform (FFT) filter and punctually Gaussian averaging were applied to the images.

GIXD.

GIXD experiments were performed at the SIXS beamline of SOLEIL synchrotron. The Ag(110) sample was prepared by repeated cycles of Ar+ sputtering and annealing at T=780 K. Si was evaporated in the diffraction chamber from a Si rod using a commercial Scienta Omicron ebeam evaporator with a sample kept at ~ 483 K. The Si flux was kept constant during evaporation with deposition rate of ~ 2 ML/h. The sample was analyzed with 18.46 keV x-rays at a grazing incidence angle of 0.2°. The diffracted x-rays were detected by an Adaptive Dynamics hybrid pixel detector. [START_REF] Dawiec | Real-Time Control of the Beam Attenuation with XPAD Hybrid Pixel Detector[END_REF] Diffracted intensity was measured by performing rocking scans around diffraction conditions. We used the "binoculars" software to produce three-dimensional (3D) intensity data in the reciprocal space from the raw data. [START_REF] Roobol | BINoculars : Data Reduction and Analysis Software for Two-Dimensional Detectors in Surface X-Ray Diffraction[END_REF] The intensity was further integrated along the direction parallel to the surface to get the structure factors. For this purpose, the data were fitted with the product of a Lorentzian lineshape with a Gaussian lineshape, using a home-made software.

In the STM and GIXD chambers, the substrate temperature was carefully determined by calibrating the sample heater with a thermocouple. The accuracy of the temperature measurement is ± 10 K. The substrate temperature during Si deposition (483 K) was chosen to avoid the formation of the massive nanostructures called nanodikes and nanotrenches that start to appear above 490 K and completely replace the pentamer chain phase at 550 K. [START_REF] Colonna | Systematic STM and LEED Investigation of the Si/Ag(110) Surface[END_REF] As shown in Figure S1 (Supporting Information), the LEED patterns acquired in the different set-ups and associated with the Si reconstructions presented here are very similar.

Theory. DFT calculations were performed within a plane wave and norm-conserving pseudopotential framework using Quantum-ESPRESSO. [START_REF] Giannozzi | Advanced Capabilities for Materials Modelling with Quantum ESPRESSO[END_REF] The local density approximation (LDA) was used as in previous successful studies on Si/Ag(110) and Si/Ag(111). [START_REF] Hogan | Optical Properties of Silicene, Si/Ag(111), and Si/Ag(110[END_REF][START_REF] Prévot | Si Nanoribbons on Ag(110) Studied by Grazing-Incidence X-Ray Diffraction, Scanning Tunneling Microscopy, and Density-Functional Theory: Evidence of a Pentamer Chain Structure[END_REF][START_REF] Hogan | Structure and Stability of Si/Ag(110) Nanoribbons[END_REF] The kinetic energy cutoff was 30 Ry. The theoretical Ag lattice constant of 4.075 Å was used (experiment: 4.085 Å). Si/Ag slabs were modeled using asymmetric slabs containing 5 layers of Ag whose backmost two layers were fixed to the bulk positions. Structural relaxations followed a tight force threshold of 2.5 meV/A. Gaussian smearing (0.04 eV) was used to treat metallic occupancy. Supercells of size (13×4), c(18×4), (8×4), (5×4), and c(8×4) were used along with Γ-centred kpoint grids of (2×8), (2×8), (4×8), (8×8), and (8×8), respectively. These yield formation energies converged to ~1 meV/(1´1) cell. The pentamer chain reconstruction was modeled with 6 Ag layers (to accommodate the missing Ag row) in a (5×4) unit cell. Constant-current STM images were simulated using the Tersoff-Hamann approach. [START_REF] Tersoff | Theory of the Scanning Tunneling Microscope[END_REF] The surface formation energy γ of each Si/Ag slab of area A containing 𝑁 !" (𝑁 #$ ) atoms of Si (Ag) was computed with respect to the Si chemical potential 𝜇 !" using

𝛾 = *𝐸 !" #$ ⁄ ,𝑁 #$ , 𝑁 !" . -𝑁 #$ 𝐸 #$ &'() -𝑁 !" 𝜇 !" 0 𝐴 ⁄ .
Here 𝐸 !" #$ ⁄ is the total energy of the (relaxed) Si/Ag heterostructure, and 𝐸 #$ &'() is the energy of a Ag atom in the bulk. With the exception of the pentamer chain model, the number of Ag atoms 𝑁 #$ is the same in each case. Relative formation energies with respect to that of the clean Ag(110) surface were then computed for each cell size. In this way, errors related to inequivalent k-point sampling along the [001] direction in different cells were minimized via cancellation.

RESULTS

STM measurements

We start the experiments by preparing the well-known Si NR superstructure obtained upon Si deposition on Ag(110) held at 483 K (see [START_REF] Leandri | Self-Aligned Silicon Quantum Wires on Ag(110)[END_REF][START_REF] Sahaf | Formation of a One-Dimensional Grating at the Molecular Scale by Self-Assembly of Straight Silicon Nanowires[END_REF][START_REF] Ronci | Low Temperature STM/STS Study of Silicon Nanowires Grown on the Ag(110) Surface[END_REF] for the earliest articles). This 2D layer is composed of double-strand nanoribbons (DNRs) arranged in an extended (5´2)/c(10´2) superstructure. [START_REF] Colonna | Systematic STM and LEED Investigation of the Si/Ag(110) Surface[END_REF][START_REF] Bernard | Growth of Si Ultrathin Films on Silver Surfaces: Evidence of an Ag(110) Reconstruction Induced by Si[END_REF] It has been demonstrated that these DNRs correspond to twin Si pentamer chains with 12 Si atoms per 5 × 2 unit cell (see Figure S4g in the Supporting Information). [START_REF] Cerdá | Unveiling the Pentagonal Nature of Perfectly Aligned Single-and Double-Strand Si Nano-Ribbons on Ag(110)[END_REF] This atomistic model was confirmed by combining GIXD measurements with STM imaging and DFT formation energy calculations and also supported by a combined high-resolution noncontact atomic force microscopy (nc-AFM) and tip-enhanced Raman spectroscopy (TERS) study. [START_REF] Prévot | Si Nanoribbons on Ag(110) Studied by Grazing-Incidence X-Ray Diffraction, Scanning Tunneling Microscopy, and Density-Functional Theory: Evidence of a Pentamer Chain Structure[END_REF][START_REF] Sheng | The Pentagonal Nature of Self-Assembled Silicon Chains and Magic Clusters on Ag(110)[END_REF] After completion of the (5´2)/c(10´2) Si overlayer, additional Si deposition at the same temperature leads to the progressive transformation of the (5´2)/c(10´2) domains into new 2D structures. As described in the Supporting Information (see Figure S2), our STM observations strongly suggest that during this process the MR Ag(110) reconstruction associated with the (5´2)/c(10´2) structure is lifted and the new structures grow on an unreconstructed Ag(110) surface. It should be noted that these structures appear as nanostripes running along the [11 ¯0] direction, i.e, parallel to the initial pentamer chains. Thus, the pentamer chain structure acts as a guide for the growth of the new structures. Even if the nanostripes do not all have the same pattern, they all appear as a beaded surface (in blue in Figure 1) with some bright protrusions (in yellow in Figure 1) on top of it, forming locally ordered domains all having a ´4 periodicity along the [11 ¯0] direction. Considering their relative apparent height above the other atoms (~ 0.7 Å), these bright protrusions can be assigned, as demonstrated later, to the adsorption of extra atoms on top of the grown nanostripes and they will be thus denoted adatoms hereafter. As can be seen in Figure 1, the adatoms do not randomly cover the surface. Firstly, they almost exclusively form pairs (less than 10% of the adatoms are isolated); secondly, the surface separates into domains where the pairs of adatoms have formed ordered motifs, and domains free of adatoms.

In domains free of adatoms, the nanostripes display two different widths associated with three different motifs (see Figure 1 and 2). A "Ladder" motif is associated with a stripe width of 4a Ag or 5a Ag (denoted hereafter Ladder ´4 and Ladder ´5). The high-resolution STM image displayed in Figure 2a shows that the Ladder ´4 and Ladder ´5 motifs have a similar structure. They show alternating groups of two moderately bright protrusions along the [11 ¯0] direction. They differ by a line of three protrusions that appears on the right side of the Ladder ´5 motif, resulting in an extra p2 symmetry axis in the unit cell. The STM images resemble some models of zigzag silicene NRs on Ag(110) predicted by DFT. [START_REF] Lian | The Structural and Electronic Properties of Silicon Nanoribbons on Ag(110): A First Principles Study[END_REF][START_REF] Hogan | Structure and Stability of Si/Ag(110) Nanoribbons[END_REF] A second kind of adatom-free domain is shown in the highresolution STM image in Figure 2b, characterized by an octagon motif and by a width of 4a Ag (denoted hereafter Octagon). In these adatom-free domains, consecutive Ladder ´5 nanostripes are never found, while alternating Ladder ´4 and Ladder ´5 nanostripes are often found. At first glance, these STM images suggest an adlayer reconstruction composed of wide Si stripes or NRs.

However, we note here that, taking 𝑎 #$ =4.085 Å and 𝑎 !" =3.847 Å for silicene (see Table S1 and Figure S3 in the Supporting Information), there is good matching for silicene (5´3) reconstruction on Ag(4´4) (misfit of 1.9%) and silicene (6´3) on Ag(5´4) (misfit of -2.1%), as well as excellent matching for silicene (11´3) on Ag(9´4) (misfit of -0.3%) and (16´3) on Ag(13´4) (misfit of 0.4%). As it will be demonstrated below, the observed structures indeed correspond to an epitaxial silicene layer on unreconstructed Ag(110).

Concerning the domains covered with adatoms, if one assumes that the Ladder and Octagon motifs correspond to a honeycomb organization of Si atoms, the observed bright features would correspond to Si adatoms on top of a silicene plane. Indeed, such silicene+adatom sheets have been first theoretically hypothesized for free-standing silicene and silicene on Ag(111). [START_REF] Özçelik | Local Reconstructions of Silicene Induced by Adatoms[END_REF][START_REF] Cahangirov | Atomic Structure of the Ö3 × Ö3 Phase of Silicene on Ag(111)[END_REF] It has been proposed that, similar to Si adatoms on top of the (7´7) reconstruction of Si(111), adatoms form a DB configuration in which two Si atoms are vertically aligned and equidistant from the mean silicene plane. Interestingly, it has been shown that the formation of DBs is stabilizing for silicene.

In principle, it cannot be excluded that these adatoms may correspond to Ag adatoms, as it has been shown for Si growth on Ag(111) that Ag plays the role of a surfactant layer. [START_REF] Curcella | Multilayer Silicene: Clear Evidence of Ag-Terminated Bulk Silicon[END_REF] However, because of the low diffusion barriers computed for Ag on Si(111), [START_REF] Liu | Diffusion of Single Au, Ag and Cu Atoms inside Si(111)-(7×7) Half Unit Cells: A Comparative Study[END_REF] one expects a very high mobility of Ag adatoms on a silicene sheet, which would be in contradiction with the observation of very stable STM images of the adatoms-covered domains at room temperature. We anticipate here that this evidence will be confirmed by DFT calculations (see Figure 4b) reported in the following section.

As illustrated in Figure 1, the pairs of adatoms are associated to local ordered reconstructions: a c(8´4) reconstruction with 4 adatoms per unit cell (denoted c(8´4)+4adatoms hereafter), already reported by some of us, 44 a (13´4) reconstruction with 4 adatoms per unit cell (hereafter denoted (13´4)+4adatoms), and a c(18´4) reconstruction with 4 adatoms per unit cell (hereafter denoted c(18´4)+4adatoms). The presence of a 13´4 phase is interesting and not unexpected, given the excellent matching between silicene (16´3) on Ag(13´4). Figure 2c suggests that the (13´4)+4adatoms structure corresponds to Ladder motifs covered with adatoms. From Figure 1, it seems that this is also the case for the c(18´4)+4adatoms structure. Finally, the adatom pattern that covers the c(8´4)+4adatoms structure makes it difficult to resolve the atomic structure of the underlying layer (see Figure 2d).

To demonstrate the formation of silicene on Ag(110) and to precisely determine the atomic configurations of the different observed reconstructions, it is however necessary to compare the STM results with DFT simulations and to perform quantitative surface diffraction measurements.

DFT simulations

The STM measurements reveal a variety of surface reconstructions with apparently different varying the in-plane offset of the silicene layer on the Ag(110) substrate, we obtained, following geometry optimization, the variety of stable structural models shown. For comparison, we also consider the pentamer double nanoribbons (P-DNR) model (1.2 ML Si) that forms on a MR Ag substrate, [START_REF] Cerdá | Unveiling the Pentagonal Nature of Perfectly Aligned Single-and Double-Strand Si Nano-Ribbons on Ag(110)[END_REF] and a silicene-like nanoribbon (5´4)-Si NR (1.4 ML Si) discussed elsewhere. [START_REF] Lian | The Structural and Electronic Properties of Silicon Nanoribbons on Ag(110): A First Principles Study[END_REF][START_REF] Hogan | Structure and Stability of Si/Ag(110) Nanoribbons[END_REF] Our STM simulations for silicene on Ag(110) reveal the presence of two periodic motifs common to all structural models (Figure S4 in the Supporting Information). These "Ladder" and "Octagon" motifs span 4 or 5 Ag lattice constants along the [001] direction, depending on the cell size, and clearly echo the experimental findings. In Figure 3a-c we compare simulated and measured STM images for typical motifs in adatom-free domains. The agreement is excellent.

Both Ladder and Octagon motifs are found to arise from Si atoms that are buckled upwards due to their position atop Ag atoms. Dark lines along [11 ¯0] are revealed to be due to flat Si zigzag chains lying in the shallow Ag(110) troughs (see black arrows). Thus, the apparent 1D nanopattern observed by STM is due to local alignments of the continuous silicene layer with the atomically corrugated Ag(110) surface. The intensity of the corrugation alongside the troughs is also well reproduced in the calculations. Note that although isolated NRs (see Figure S4h in the Supporting Information) also naturally produce dark lines, their widths are considerably larger than those observed experimentally and theoretical STM images of these NRs do not reproduce the experimental observations. On the contrary, the silicene models reproduce all features observed.

In particular, the high-resolution image in Figure 3b also reveals weaker spots among the rungs of the Ladder motif. These are well explained by the DFT simulations as arising from lower-lying Si atoms in the buckled silicene sheet. The calculations also suggest two kinds of Ladder structure:

besides the symmetric motifs shown in Figure 3a, we also identify asymmetric Ladder ´5 motifs as indicated in Figure 3c by crooked lines. It has to be noted that the observation of these patterns in STM images is based on the presence of a slight contrast between Si atoms inside the Ladder motif, making them difficult to resolve.

These results strongly suggest the presence of a complete silicene sheet on the Ag(110) surface at high Si coverages (1.83-1.88 ML). As discussed above, the STM measurements in Figure 1 also reveal a rich tapestry of adatom-decorated domains. For epitaxial silicene, one expects that these adatoms preferentially adsorb on top of Si atoms that are already below the mean silicene plane, i.e. those located in four-fold hollow site of the Ag(110) lattice (see Figure 3f). Theoretical studies on free-standing silicene have shown that the pairs of adatoms located at opposite ends of the hexagon ring yield a stable geometry. [START_REF] Li | Defects in Silicene: Vacancy Clusters, Extended Line Defects and Di-Adatoms[END_REF] We thus considered gradual increase in adatom density via addition of adatom pairs from the lowest coverage possible in our simulations (2 adatoms per (13´4) cell) to the highest observed experimentally (4 adatoms per c(8´4) cell). For the sake of completeness, we have also computed similar structures where Ag adatoms replace Si adatoms.

Optimized geometries for the various models studied are shown in Figure S5 (Supporting Information). The presence of adatom pairs reduces the number of possible silicene geometries because they indeed lock the DBs into the four-fold hollow sites of Ag(110) (see Figure 3f).

Simulated STM images are compared in Figure 3d and 3e with high-resolution experimental scans of the (13´4) and c(8´4) domains. The agreement is again excellent, providing a clear confirmation that the pair of bright spots derive from adatom pairs on the silicene sheet forming DBs above the Ag(110) hollow sites. Underneath the adatom layer, the simulation shows that silicon atoms appear to align in Ladder formation rather than as Octagons. We note here that, from the STM simulations alone, it is not possible to determine the chemical nature of the adatoms: compare for instance Figure S5i and S5j in the Supporting Information). However, in the following we will demonstrate that models with Ag adatoms are energetically unfavored.

Final confirmation of our proposed models is provided by considering their thermodynamic stability. For each model we calculated the surface formation energy and compared it with those of the bare Ag(110) substrate and the pentamer DNR model (P-DNR, Figure S4g in the Supporting Information) known to be stable at low Si coverages. Results for the adatom-free models are shown in Figure 4a and demonstrate that all models of silicene on Ag(110) become more favorable than P-DNR above a certain Si chemical potential (higher Si coverage). A quasi-degeneracy is found: the energy differences between the different models are very small (< 7 meV/(1´1) cell) and close to the precision of the calculations (~1 meV/(1´1) cell). The larger c(18´4) and (13´4) models containing Ladder motifs appear slightly more stable, in alignment with the superior lattice matching demonstrated above for these cells, and correctly reflecting the relative paucity of Octagon motifs seen experimentally. The results imply that several silicene phases could coexist on the surface under Si-rich conditions. In contrast, Figure 4a

GIXD measurements

Confirmation of the long range ordered geometry of the silicene overlayer is provided by GIXD measurements. GIXD is indeed a powerful technique for the discrimination of superstructure models and for the refinement of atomic positions. It has been used to confirm silicene growth on Ag(111) and precisely determine the atomic positions in the unit cells of the various superstructures formed. [START_REF] Curcella | Determining the Atomic Structure of the (4×4) Silicene Layer on Ag(111) by Combined Grazing-Incidence x-Ray Diffraction Measurements and First-Principles Calculations[END_REF][START_REF] Curcella | Structure and Stability of Silicene on Ag(111) Reconstructions from Grazing Incidence x-Ray Diffraction and Density Functional Theory[END_REF] The (ℎ, 𝑘, 𝑙) indices used for indexing a reflection in reciprocal space refer to the Ag(110) surface basis (𝑎 #$ =4.085 Å, 𝑏 #$ =2.889 Å, 𝑐 #$ =2.889 Å, 𝛼 = 𝛽 = 𝛾 = 90°). During Si evaporation at T=483 K, we have followed the evolution of the diffracted intensity along the ℎ direction at (𝑘 = 0, 𝑙 = 0.1). The corresponding scans are shown in Figure 5a. The peak at ℎ=1 observed before evaporation corresponds to the crystal truncation rods. As soon as evaporation starts, diffraction peaks at ℎ = 𝑛 5 ⁄ are observed which are associated with the formation of (5´2)/c(10´2) domains of Si DNRs. [START_REF] Prévot | Si Nanoribbons on Ag(110) Studied by Grazing-Incidence X-Ray Diffraction, Scanning Tunneling Microscopy, and Density-Functional Theory: Evidence of a Pentamer Chain Structure[END_REF][START_REF] Bernard | Growth of Si Ultrathin Films on Silver Surfaces: Evidence of an Ag(110) Reconstruction Induced by Si[END_REF] When the intensity of these peaks starts to decrease, another peak appears at ℎ = 1.232 ± 0.005 ~ 16 13 ⁄ . The evaporation was stopped when the maximum of intensity for this peak was obtained, i.e. for around twice the evaporation time corresponding to the maximum of intensity of the (5´2)/c(10´2) peaks.

At this point, the intensity of the peaks at ℎ = 𝑛 5 ⁄ (n integer) has almost completely vanished.

This indicates that the new structure does not form on top of the Si pentamers of the DNRs, but that it replaces them. Moreover, it has been shown (see [START_REF] Prévot | Si Nanoribbons on Ag(110) Studied by Grazing-Incidence X-Ray Diffraction, Scanning Tunneling Microscopy, and Density-Functional Theory: Evidence of a Pentamer Chain Structure[END_REF] ) that the MR reconstruction of the substrate significantly contributes to the intensity of the ℎ = 𝑛 5 ⁄ peaks. The vanishing of these peaks demonstrates that the substrate MR reconstruction is lifted. This conclusion is in agreement with the growth mechanism suggested by the STM observations of coexisting (5´2)/c(10´2) and silicene phase domains (see Figure S2 in the Supporting Information). Assuming that the maximum of intensity of the peak at ℎ=1.4 corresponds to 1.2 ML, the reconstruction measured would correspond to 2.4 ML. This is higher than the coverage range [1.83-1.88 ML] of the silicene and DB silicene structures computed by DFT. However, we cannot exclude the fact that the second structure starts to form before completion of the first one, or that the Si sticking coefficient is not the same for both structures.

After the Si deposition, structure factors were measured for both in-plane and out-of-plane conditions. All measured structure factors could be indexed on the basis of a (13´4) Ag(110) reconstruction. The full width at half maximum (FWHM) of the peak at ( *+ *, , 0,0.1) is ∆ℎ = 0.023.

Note that this small value excludes the fact that the signal may arise from the superimposition of diffraction from c(18´4) and c(8´4) domains, since they would correspond to peaks at ℎ =1.222 and ℎ =1.25, which are separated by ∆ℎ = 0.028. However, we cannot totally exclude the presence of a low density of c(18´4) and c(8´4) domains, having a small size. The FWHM of the peaks is given by the size of the domains and the dispersion of the lattice parameter ∆ 𝑎 𝑎 ⁄ . From the different peaks, we estimate the domain size to be 400 Å and the lattice parameter dispersion to be 0.01. Along k, the FWHM is smaller (for example, ∆𝑘 = 0.008 for the (0, + -,0.1) peak) and other contributions to the FWHM, such as the sample size, cannot be neglected.

In the following, the (𝐻, 𝐾, 𝐿) indices refer to the (13´4) Ag( 110 show that all atoms are not at the same z value. Moreover, the rod profiles display strong differences from one rod to another, which indicates that the layer buckling cannot correspond to that of free-standing silicene. Indeed, in the latter case, the modulation of the different rods should be similar.

We The intensities of the simulated in-plane structure factors, plotted in Figure 5b, are in excellent agreement with the experimental ones. Finally, we have verified that no better agreement could be obtained with the other configurations computed by DFT and having a higher formation energy.

For instance, a model of an incomplete honeycomb stripe in a (13´4) cell, i.e. a wider NR than that shown in Figure S4h (Supporting Information), does not correctly fit the experimental structure factors, with 𝜒 / = 19.2.

The main and most important conclusion from this part is that GIXD demonstrates that the Si layer formed on Ag(110) corresponds to a DB silicene structure with a small density, equal to 0.077 adatoms per (1´1) cell, predicted by our DFT calculations and observed by STM. we observe only one structure by GIXD. These differences observed between STM and GIXD measurements could result from the inherently different growth conditions in the two experimental setups. In particular, a slightly higher substrate temperature, not exceeding 15 K, may have been used for the Si deposit analysed by GIXD. Indeed, the size of the observed domains is around 400 Å, significantly higher than the average domain width measured by STM, as shown in Figure 1.

As a result, the surface is better ordered with a large majority of (13´4)-L+4 adatoms domains.

It has been demonstrated that Si atoms strongly interact with the Ag substrate upon deposition, causing Ag atom ejection from the first layer on both the Ag(111) and Ag(110) substrates. [START_REF] Bernard | Growth of Si Ultrathin Films on Silver Surfaces: Evidence of an Ag(110) Reconstruction Induced by Si[END_REF][START_REF] Bernard | Growth Mechanism of Silicene on Ag (111) Determined by Scanning Tunneling Microscopy Measurements and Ab Initio Calculations[END_REF][START_REF] Sone | Epitaxial Growth of Silicene on Ultra-Thin Ag(111) Films[END_REF][START_REF] Satta | Silicon Reactivity at the Ag(111) Surface[END_REF] Our GIXD measurements clearly show that the MR reconstruction is lifted when the (5´2)/c(10´2)

NR structure is converted into the honeycomb structure. with the formation of novel Ag(111) terraces. [START_REF] Bernard | Growth Mechanism of Silicene on Ag (111) Determined by Scanning Tunneling Microscopy Measurements and Ab Initio Calculations[END_REF] Nevertheless, it is important to note that our GIXD experiments and DFT calculations clearly show that the Si honeycomb structure grows on an unreconstructed Ag substrate, as for the Si/Ag(111) interface. [START_REF] Curcella | Determining the Atomic Structure of the (4×4) Silicene Layer on Ag(111) by Combined Grazing-Incidence x-Ray Diffraction Measurements and First-Principles Calculations[END_REF] We have thus demonstrated the growth of DB silicene sheets on Ag(110). Although quite challenging, these layers would be of great interest if decoupled from the Ag substrate. Several approaches have been reported, both experimentally and theoretically, to achieve such decoupling.

For instance, first-principles calculations have shown that hydrogenation and calcium intercalation can be employed to break bonds between a silicene overlayer and a silver surface. [START_REF] Tsetseris | Chemical Routes to Modify, Uplift, and Detach a Silicene Layer from a Metal Substrate[END_REF] A combined STM, X-ray photoemission spectroscopy (XPS), angle-resolved photoelectron spectroscopy (ARPES) and first-principles calculations study reveals that the interaction with Ag(111) of the top layer of a bilayer silicene can be weakened by oxygen intercalation into the Si underlayer. [START_REF] Du | Quasi-Freestanding Epitaxial Silicene on Ag(111) by Oxygen Intercalation[END_REF] It has also been reported that an epitaxial silicene layer could be detached from the silver substrate and transferred onto target substrates. [START_REF] Tao | Silicene Field-Effect Transistors Operating at Room Temperature[END_REF][START_REF] Martella | Disassembling Silicene from Native Substrate and Transferring onto an Arbitrary Target Substrate[END_REF] We point out that the demonstrated higher stability of DB silicene compared to pristine silicene will favor the decoupling process of the DB silicene layer from the substrate. Since both pristine silicene 2 as well as higher-density DB phases of silicene [START_REF] Borlido | The Ground State of Two-Dimensional Silicon[END_REF][START_REF] Cahangirov | Atomic Structure of the Ö3 × Ö3 Phase of Silicene on Ag(111)[END_REF] are reported to be dynamically stable according to phonon dispersion calculations, we expect the lower density DB phases identified here will exhibit comparable stability in their freestanding form.

The synthesis of DB silicene opens new routes to tune the peculiar properties of silicene. For instance, it has been predicted that DB configuration attributes Si coverage-dependent electronic and magnetic properties to bare silicene, such as a spin-polarized semiconducting behavior with a band gap of ~ 80 meV. [START_REF] Özçelik | Local Reconstructions of Silicene Induced by Adatoms[END_REF] We thus performed band structure calculations to study the effect of the DBs on a free-standing layer with the atomic configurations identified in our study (see Figure S6 in the Supporting Information). As compared to the pristine free-standing silicene, the electronic structure for the c(8´4)-L reconstruction shows a small gap opening of 80 meV. Interestingly, a small gap value (60 meV) is also obtained for the c(8´4)-L+4 adatoms DB silicene. State projections onto p z orbitals and DB atoms show that p z contributions are located near the Fermi level while states localized on DB atoms give contributions at -1.3 eV and -1.5 eV below the Fermi level. Thus, DB atoms appear as good candidates for tuning the electronic properties of silicene by charge doping through the DB atom dangling bonds pointing outward from the silicene layer.

More generally, DB silicene structures open new perspectives for tailoring the chemical, physical and mechanical properties of silicene sheets with molecular attachment. Indeed, numerous experimental and theoretical works have been devoted to the reactivity of silicene towards molecular adsorption. [START_REF] Xu | Effects of Oxygen Adsorption on the Surface State of Epitaxial Silicene on Ag(111)[END_REF][START_REF] Du | Tuning the Band Gap in Silicene by Oxidation[END_REF][START_REF] Feng | Gas Adsorption on Silicene: A Theoretical Study[END_REF] For example, the adsorption of NO, O2, NH3, and SO2 opens the band gap of silicene, rendering silicene a narrow gap semiconductor. [START_REF] Feng | Gas Adsorption on Silicene: A Theoretical Study[END_REF] The possibility of tuning the electronic properties of silicene by molecular adsorption makes silicene a promising candidate as molecular sensor. [START_REF] Hu | Silicene as a Highly Sensitive Molecule Sensor for NH 3 , NO and NO 2[END_REF][START_REF] Prasongkit | Highly Sensitive and Selective Gas Detection Based on Silicene[END_REF] From a mechanical point of view, adsorption of H and F reduces the Young's and bulk moduli of silicene. [START_REF] Goli | Influence of F and H Adsorption on the Elasto-Plastic Properties of Silicene: A DFT Investigation[END_REF] Whereas a silicene sheet already presents a high reactivity, it has been shown that its reactivity is enhanced at defects sites, such as Stone-Wales defects. [START_REF] Feng | Gas Adsorption on Silicene: A Theoretical Study[END_REF] Interestingly, the high reactivity of DB silicene to hydrogen has already been noted and thus one should expect an equally strong molecular adsorption on the Si adatoms of the Si layer. [START_REF] Ding | Tunable Electronic Structures of Hydrogenated Zigzag and Armchair Dumbbell Silicene Nanosheets: A Computational Study[END_REF] One may expect enhanced detection performances for DB silicene deriving from specific adsorption sites.

CONCLUSION

In conclusion, our combined STM-DFT-GIXD study demonstrates the formation of silicene phases on Ag(110), stabilized by DBs adsorbed at four-fold hollow sites of the Ag substrate. DFT calculations show that the different structures have similar formation energies, in agreement with the coexistence of various 2D domains of small size observed by high-resolution STM.

Figure 1 .

 1 Figure 1. STM image (77 K), (370´330) Å 2 , of the Ag(110) substrate after Si deposition at 483 K, above completion of the pentamer chain overlayer. Ladder ´4, Ladder ´5 and Octagon motifs are observed in domains free of adatoms, while c(18´4)+4adatoms, (13´4)+4adatoms and c(8´4)+4adatoms structures are observed on the rest of the surface (the white dashed rectangles highlight the unit cells). The primitive unit cell of the c(8´4)+4adatoms and c(18´4)+4adatoms structures are indicated by yellow parallelograms. I = 20 pA, V sample = 100mV.

Figure 2 .

 2 Figure 2. High-resolution STM images of adatom free motifs: (a) Ladder ´5 and Ladder ´4 motifs (I = 100 pA, Vsample = 100 mV), (b) Octagon motif (I = 5 nA, Vsample = 200 mV). High-resolution STM images of adatom-covered structures: (c) (13´4)+4adatoms structure (I = 460 pA, Vsample = -570 mV), (d) c(8´4)+4adatoms structure (I = 460 pA, Vsample = -570 mV). The STM images were acquired at 77 K in (a), (c), (d) and at RT in (b).

  periodicities along [001], making atomistic simulations difficult. Guided by the aforementioned matching conditions along both [001] and[11 ¯0] as well as the presence of distinct c(8´4), c(18´4), and (13´4) domains in the STM images, we performed DFT calculations of periodic silicene adlayers placed atop c(8´4), c(18´4), and (13´4) slabs of bulk-truncated Ag(110). Due to their number and size, we report the full set of models in FigureS4(Supporting Information). They correspond to Si coverages of 1.83-1.88 monolayers (ML) in Ag(110) surface atom density. By

  Figure4ashows, above a certain Si chemical potential, a clear gain in energy for the adatom-

Figure 3 .

 3 Figure 3. Experimental (blue-yellow colormap, top) and simulated (greyscale, center) STM images and corresponding structural models (bottom). Simulated images are computed at the experimental bias. The contrast of the experimental STM images has been magnified with respect to Figure 2. (a) c(18´4) phase showing Ladder motifs. Dotted circles indicate a "rung" due to pairs of up-buckled Si atoms. (b) A high-resolution image of a Ladder ´4 region. Dotted features indicate weaker spots from lower Si atoms. (c) Partial (13´4) image showing the Octagon motif alongside a Ladder structure. Note the presence of asymmetric features indicated by crooked lines.(d) Full (13´4) image with 4 adatoms per cell. (e) c(8´4) pattern at maximum adatom coverage (4 per cell). (f) Local adatom geometry showing DB pair formation at 4-fold hollow site. Unit cells

Figure 4 .

 4 Figure 4. Phase diagram of silicene reconstructions on Ag(110). See Figure S4 and S5 (Supporting Information) for a full explanation of each geometry. Formation energy γ is plotted with respect to that of clean Ag(110). The Si chemical potential μ is given with respect to a suitable reference value, here taken to be the average energy per atom in an isolated Si pentamer nanoribbon. (a) Pure silicene phases. The range of stability of the pentamer double nanoribbon phase (P-DNR) is indicated by the left shaded area. (b) Silicene phases decorated with adatoms. (c) Dependence of formation energy on adatom coverage for the most stable phase of each cell size at a typical value of Δμ=-1.19eV. Energy range is indicated by the blue double arrow within inset of (b). The pathway that maximizes the formation energy for increasing coverage is indicated by dotted lines.

  FigureS7in the Supporting Information).[START_REF] Curcella | Multilayer Silicene: Clear Evidence of Ag-Terminated Bulk Silicon[END_REF]

Figure 5 .

 5 Figure 5. (a) Evolution of the diffracted intensity measured along the ℎ direction at (𝑘 = 0, 𝑙 = 0.1) during Si evaporation. From blue to red: scans at 𝑡 = 0 s, 18 min, 36 min, 59 min and 76 min. The peak at ℎ = 1 is indicated with a dashed line, the peaks at ℎ = 6/5 and ℎ = 7/5 are indicated with a dotted line while the peak at ℎ = 16/13 is indicated with a continuous line. The maximum of intensity of the ℎ = 7/5 and ℎ = 8/13 peaks are obtained for 𝑡 =38 min and 𝑡 =78 min, respectively. (b) In-plane structure factors. Comparison between experimental (red half-disks) and simulated (black half-disks) structure factors (the substrate structure factors for integer values of h and k have not been drawn for clarity). (c) Experimental Patterson map of the (13 × 4) Si/Ag(110) structure. A quasi hexagonal unit cell (𝑎 = 3.837Å, 𝑏 = 3.852Å, 𝛾 = 120.1°) is drawn in green.

19 .

 19 have compared the measured structure factors to theoretical structure factors simulated from various atomic configurations relaxed by DFT calculations. For this purpose, we have used only 7 free parameters: a scale factor and two sets of Debye-Waller factors for Si and Ag atoms along the H, K, and L directions. The agreement between experimental (𝐹 678 ) and simulated (𝐹 th ) structure factors is estimated by the value of 𝜒 / = * ; pts <; par ∑ `=th <= exp > exp a ; Pts / where 𝑁 pts is the number of experimental structure factors, 𝑁 par is the number of free parameters and 𝜎 exp is the experimental uncertainty, which takes into account the statistical uncertainty given by the number of counted photons and an overall 10% uncertainty. We have first tested the most stable (13´4) configurations identified by DFT. Whereas a good agreement is already obtained with the two adatom-free silicene configurations tested, Figure S8 (Supporting Information) shows that the best fit is obtained for the (13´4)-L+4adatoms structure, with 𝜒 / = 4.7. It corresponds to a R-Factor value 𝑅 = = ∑ F= th <= exp F The comparison between experimental and simulated structure factors is shown in Figure 6. The (13´4)-L+4adatoms model reproduces well all variations of intensities along the diffraction rods, whereas the fit is poorer for the (13´4)-LO configuration.

Figure 6 .

 6 Figure 6. Structure factors for various rods of the (13´4) structure. Comparison between experimental (red dots) and computed values, using the (13´4)-LO (dotted blue line) or (13´4)-L+4adatoms (continuous black line) models simulated by DFT.

  It is not surprising since this MR reconstruction is intimately linked to the Si NR superstructure and becomes thermodynamically unstable when this superstructure is removed, as shown by our DFT calculations. Based on our STM observations, a mechanism is proposed, where Ag atoms of the MR reconstruction are released, leaving bare unreconstructed Ag(110) areas, and new Ag(110) terraces are concomitantly formed (see the Supporting Information). It cannot be excluded that additional Ag atom ejection occurs during the growth of the Si honeycomb structure, as observed for Si deposited on Ag(111)

Conor Hogan: 0000-0002-0870-6361 Kai Zhang: 0000-0002-6124-8793 Michel Daher Mansour: 0000-0001-6319-2650 Romain Bernard: 0000-0002-2944-142X Romain Parret: 0000-0003-0662-6373 Andrea Resta: 0000-0002-0614-1192 Stefano Colonna: 0000-0001-9994-4287 Yves Borensztein: 0000-0002-1570-732X Fabio Ronci: 0000-0002-7424-4046 Geoffroy Prévot: 0000-0001-7960-5587 Laurence Masson: 0000-0003-0587-2468

DISCUSSION

We obtain an excellent agreement between STM observations and simulated images of silicene and DB silicene phases as well as between the DFT calculation for the (13´4)L+4adatoms structure and the diffraction data. This demonstrates that the Ag(110) surface is entirely covered with a silicene layer, which is itself partially covered with adatoms in DB configurations. The ordering of the observed structures originates from both a local registry between the silicene lattice and the substrate along Ag [11 d 0] with a ratio equal to 3/4 and along Ag[001] with ratios equal to 5/4, 11/9 or 16/13 for the c(8´4), c(18´4) and (13´4) reconstructions, and a periodic organization of adatom pairs. Moreover, the different structures are shown to have a very similar formation energy, in agreement with the coexistence of various domains of small size observed by STM.

DFT computations show that the formation energy of the silicene adlayer is lowered by adding adatoms up to a maximum density which depends on the unit cell (see Figure 4c). The simulations also show that the silicene layer is distorted to accommodate the DBs on top of four-fold hollow sites of the Ag substrate. The gain in cohesive energy from DB formation is thus balanced by the energy of deformation of the silicene layer. This is clearly visible for the (13´4) reconstruction for which the most favored number of adatoms is 4 per unit cell instead of 6, implying a larger deformation penalty in the latter case. It also explains why we find a low DB density compared to the density of host sites on the silicene sheet (see the FDS or LHDS silicene phases proposed by Cahangirov et al. [START_REF] Cahangirov | Atomic Structure of the Ö3 × Ö3 Phase of Silicene on Ag(111)[END_REF] or the Si-VI phase of Borlido et al. [START_REF] Borlido | The Ground State of Two-Dimensional Silicon[END_REF] ), as DBs prefer to form at the fourfold hollow sites of the Ag substrate. This finding is in agreement with both STM observations and GIXD measurements. While we cannot rule out that better models of the system exist, they should only be refinements of the proposed geometries as the presence of a single-layer honeycomb geometry is demonstrated by GIXD.

Nevertheless, GIXD measurements indicate that the control of the growth conditions can lead to the formation of an extended DB silicene structure whose orientation is guided by that of the Si pentamer chain domains initially grown on Ag(110). This opens up interesting perspectives for practical applications such as gas sensing and may offer a realistic platform for exploring predicted novel topological properties of DB silicene. [START_REF] Zhang | Dumbbell Silicene: A Strain-Induced Room Temperature Quantum Spin Hall Insulator[END_REF]