Hloindo Kondo

Adjallah

Pélopé Kossi

Alexei Adzakpa

Christophe Ivanov

Noureddine Varnier

Zerhouni

Kondo H Adjallah
email: kondo.adjallah@utt.fr

Kossi P Adzakpa
email: kossi_pelope.adzakpa@utt.fr

Alexei Ivanov
email: alxei.ivanov@ens2m.fr

Christophe Varnier
email: christophe.varnier@ens2m.fr

Noureddine Zerhouni
email: noureddine.zerhouni@ens2m.fr

Approach to remote maintenance management of distributed industrial complexes

Keywords: remote, maintenance, availability, optimization, flow-time, scheduling, and allocation

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INTRODUCTION

The methods of maintenance activities management have much evolved in the last few years. Companies tend to limit corrective maintenance, rather suitable to react to equipment failures, to the benefit of preventive one. More advanced companies implement predictive or proactive maintenance [START_REF] Rao | Handbook of condition monitoring[END_REF] using monitoring tools. This strategy privileges the concept of maintenance service against classical maintenance.

In the sequel, we will focus on the maintenance management of industrial production facilities distributed on different plants. For such configuration, the technical and economic effectiveness of the maintenance requires organization and management based on network information systems, making it possible to ensure functions able to enhance distance between the plants [START_REF] Tromp | Surveillance et diagnostic de systèmes industriels complexes : une approche hybride numérique numérique/symbolique[END_REF]: communication, exchange of data and information, remote monitoring, remote diagnosis, maintenance jobs planning and tasks scheduling, risk management, etc.

In a competing context where the customers' requirements become increasingly precise and measurable in terms of the right price, the remote maintenance systems allowing management and remote control of the maintenance activities appear better adapted to obtain the best cost/effectiveness ratio. The remote maintenance management then seems well suited for large distributed industrial complexes and companies that outsource their maintenance services. It thus becomes essential to model and analyzes the remote maintenance systems for optimal management. Unfortunately, research works in this field are rare and not generic. Authors often use different system concepts and other evaluation methods. This situation complicates the comprehension of their approaches and highlights the lack of a standard model. Simultaneously, it is essential to model the maintenance processes to optimize their management in real-time, given the requirements for the equipment availabilities concerning the available means. This paper's prime objective is to examine the existing remote maintenance systems for distributed production facilities. The aim is to understand their principles, study their characteristics [START_REF] Kolski | Problems in telemaintenance and decision aid criteria for telemaintenance system design[END_REF], and deduce a model considering their particular constraints.

The second objective of the paper is to propose a first approach to modeling and optimization of maintenance processes in a context of real-time scheduling of preventive actions and real-time resource allocation to the maintenance interventions on distributed industrial complexes [START_REF] Koole | Optimal repairman assignment in two symmetric maintenance models[END_REF], [START_REF] Frostig | Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem[END_REF], (Seshardi & Pinedo, 1999).

REMOTE MAINTENANCE MANAGEMENT

2.1

Characteristics of a remote maintenance Above all, let us recall that the strategies mainly used in maintenance management are corrective, preventive, predictive, and proactive types. The two last types include conditional techniques (surveillance, detection, isolation, diagnosis, state evaluation, and decision making). Also, they have planning activities and scheduling tasks of maintenance, which require adequate and sometimes specialized resources in terms of human resources, spares, and means for interventions. The remote maintenance, which uses the same classical maintenance strategies, consists of some traditional maintenance actions' remote control. Besides, it requires technicians with the necessary and minimum qualifications and with easily adaptable skills. Remote maintenance systems are already in development in several areas: For instance, in the computer systems area, the «PCAnywhere» software was developed by SYMANTEC for remote maintenance. It allows intervening on distant workstations in distress, operating from a server. On request of the workstation in distress, the intervener uses specific software functions to remotely perform failed software reparation via a communication network, starting from a server or master-station to reach all the workstation files and applications.

In the military field, remote maintenance systems have been developed to ensure a high maintenance service level for weapon systems. They are based on integrated and intelligent sensors systems, information systems, integrated logistics, and hierarchical organization of the remotely controlled maintenance processes. For instance, following the equipment state's assessment by the integrated sensors and diagnosis systems, maintenance technicians close to the material carry out urgent interventions. In the event of no successful result, the assistance of a plant mastertechnician is requested. In the event of no-satisfaction, the data relating to the material are transmitted to a processing expert center. This center analyses the problem and proposes solutions that are used later to feed the unified information database. This center processes the data, manages the equipment's logistics support, and advises on line the maintenance operations to field technicians.

Several similar projects exist in the medical area. The SAMED project particularly aims to study, conceive, construct, and implement a generic remote infrastructure software and material for remote-medicine applications: remote monitoring, remote maintenance, and various medical and research activities. Its distant maintenance objectives are to ensure the safe operation of the multiple applications installed at the patient residence, provide automatic self-monitoring applications, and download possible news configurations in the medical equipment through telecommunications networks. The medical assistance equipment sensors are continuously «tested» by the local information system, which is equipped with tools for remote control of the equipment functions. Thus, any anomaly is transmitted to the medical expert center, which immediately sends a technical team to regulate or repair the sensor or equipment. This system reduces the non-necessary displacements of technicians.

Other remote maintenance systems are based on concepts similar to those presented above, but very few are used in the industry area. All the information and communication systems technologies are now available to develop similar systems in the industrial area. Many investigations are currently launched to develop methods suitable for the industrial requirements (IMS Center), [START_REF] Lee | Smart Products and Service Systems for e-Business Transformation", 3 ème Conférence Francophone de MOdélisation et SIMulation[END_REF].

2.2

Generalization of the remote maintenance management principles Apart from the particular applications, the existing remote maintenance systems use concepts with some common points. The remote maintenance system always consists of 3 essential and distinct parts. The structure and the composition of such a system depend on its organization [START_REF] Derman | On the optimal assignment of servers and a repairman[END_REF]. For example, the choice of the different categories of resources (material, spares, human) is determined by the performance required for the production facilities. Indeed, these resources management constitutes an important factor of the facilities' availability and the maintenance costs (Berg, 1995) [START_REF] Lam | An optimal maintenance model for a combination of secondhand-new or outdated-updated system[END_REF] [START_REF] Park | Optimal number of Minimal repair before replacement[END_REF]. One can distinguish three categories of resources: repairmen (human resources), means of intervention (intervention work equipment), spare parts, and consumables (material resources for replacement). The first type of resources can be classified by specialty and skill, which lead to job assignment and load balancing problems [START_REF] Koole | Optimal repairman assignment in two symmetric maintenance models[END_REF] [START_REF] Frostig | Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem[END_REF] (Seshardi & Pinedo, 1999). Indeed, the technician skill is an influent factor of the intervention durations and the service level, and the cost.

2.3

Technical aspects of the problem Remote maintenance of distributed industrial complexes requires the constant knowledge of the production facilities state on each plant, which implies at least three constraints related to the plants:

1) Remote monitoring and diagnosis of the facilities' state (using automatic software).

2) Transmission of information to the expert center (using appropriate communication tools).

3) Real-time decision making in job scheduling, resources allocation (using qualified people)

In this paper, the information system will be assumed to be entirely available. Design such a system remains delicate, own to the difficulties related to the integration of specific requirements: 1) High safety and reliability levels for the information system and the instrumentation (data-collection systems, integrated and intelligent sensors, database, software applications, …) 2) Reliability and robustness of the state monitoring equipment, techniques, and methods (periodic inspection, online monitoring or conditional monitoring, …) 3) Robustness of the diagnosis techniques and methods (tendencies monitoring, use of a model, pattern recognition, signature, artificial intelligence, …).

2.4

Resources management Resources management is a classical problem in maintenance management [START_REF] Frostig | Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem[END_REF] [START_REF] Koole | Optimal repairman assignment in two symmetric maintenance models[END_REF] (strategy selection, tasks planning, job scheduling, resource allocation, etc.) Although complex and fundamental, the problem of optimal management of production facilities' maintenance activities is tackled by very few scientists working in the maintenance area [START_REF] Seshadri | Optimal allocation of resources in a job shop environment[END_REF]) (Sinuany-Stern, 1999). Remote maintenance systems must thus solve three main problems in the following order: diagnosis of equipment, evaluation of information, scheduling, and allocation of tasks to resources. Therefore, we propose an original approach of real-time tasks scheduling and maintenance resources allocation in the next section.

Among the few published works on this topic, the main focus is on systems composed of single machines or machines with series-parallel configuration. In this respect, we mention the recent work of [START_REF] Bennour | Modélisation intégrée de maintenance et de production[END_REF], which is based on graph theory and integrates maintenance policies into the working cycle of the machine. [START_REF] Weinstein | Integrating maintenance and production decision in a hierarchical production planning[END_REF], on their part, proposed a mixed-integer linear model, which incorporates preventive maintenance into the production policies. This method aims at minimizing cost and the deviation of production in contrast to maintenance-free production policies. Regarding preventive maintenance, we can also mention the heuristic method of [START_REF] Qi | Scheduling the maintenance on a single machine[END_REF] based on the Shortest Processing Time (SPT) priority rule to minimize the makespan in a production policy. They studied the problem of scheduling parallel-machines where preventive maintenance jobs are performed on each machine, just as in [START_REF] Lee | Scheduling jobs and maintenance activities on parallel machines[END_REF]. [START_REF] Graves | Scheduling maintenance and semi-resumable jobs on a single machine[END_REF] and [START_REF] Qi | Scheduling the maintenance on a single machine[END_REF] proposed a branch and bound method to minimize the weighted completion time of jobs based on the partition formulation of single machines' problem.

SCHEDULING THE MAINTENANCE TASKS AND ALLOCATING RESOURCES

Let us consider an industrial complex comprising several plants working independently and in parallel (i.e., one plant's unavailability does not affect other plants' availability). Each plant is composed of several assets in serial all the plants share the resources. Thus, at any moment, a resource can be brought from a plant to another. The main problem then is to dynamically evaluate the resource needs at plant levels to establish priorities. The aim is to allocate the resources as optimally as possible at a minimum cost and minimum unavailability targets for each of the complex plants.

Note that in general, preventive maintenance job flow-time relative to one asset increases with the delay time concerning the critical starting dates of jobs for a fixed number of resources. The number M of resources is less than the total number of assets in the system Sk(Nk). But in the case of jobs having more than two assets, the scheduling, which gives the least delay concerning the critical starting dates, is not necessarily done according to the least flow time. We assume in our investigations that jobs are executed without preemption and that the setup times sik of jobs are small enough to be incorporated into the job's duration. We consider time windows over which independent plant unavailability and maintenance operation costs must be minimal in our approach.

3.1

Modeling of the problem Due to the system's structure (plant independence, plant composed of series assets), a constraint is imposed on asset unavailability at each plant to reduce plants downtime to the allowed minimum. A high unavailability threshold 1-αik for a given availability αik in ]0; 1[ is then defined for each asset Eik. An asset Eik that has worked for a specific time with no breakdown and whose unavailability has reached the threshold 1-αik should be shutdown for preventive actions. Under this condition, the asset is assumed to be renewed after maintenance. Subject to this constraint, the objective is to minimize the system preventive maintenance cost. At the end of the time-window [0, H1] denoted W1, the system's state gives the beginning state of the second window [H1, H2] denoted W2, and so on. Without loss of generality, we assumed exponential behavior law for the assets. Thus from the instant t0, the availability of the equipment Eik is given by the expression (1) Now, let us consider time-windows of the same length over which the maintenance cost must be minimized. Starting from time window W1, one minimizes the cost over each time window through the following steps.

1. Determine the critical instants t1 , t2 , t3 , … of assets preventive jobs over the time-window W1.

2. Allocate the resources to jobs at the critical instants.

From the initial instant t0, the unavailability condition stated above (1-Aik(t) ³ 1-aik,) gives the critical time tik from which a preventive action must be carried out on Eik. This condition could be expressed as Aik(t) £ aik, and using the asset Eik's availability expression in (1) yields the condition ,

where If no action is carried out on Eik, its unavailability will grow toward a given threshold 1-αik. Hence, in the ideal case, if the m th maintenance job on Eik ends at time Tm,ik, in the time window W1, the next intervention on Eik should be scheduled for time tm+1,ik = Tm,ik + tik. Then, assuming processing time Mtpik and set up time sik for jobs on Eik, the completion time of the (m+1) th job on Eik is Tm+1,ik = Tm,ik + tik + sik + Mtpik.

Let us assume that after the critical time, the asset will work with a higher probability of failure and that each time-unit spent by Eik in such a critical state has the cost dik. We need to minimize the total cost Ctot(W1) relative the times spent by the system in critical states over the time-window W1:

(

To simplify, let us assume that the costs dik are the same for all the assets and are equal to d, then instead of Ctot(W1), we can consider as objective-function Ctot' (W1) given by ( 4)

Instead of minimizing Ctot(W1), one just has to minimize Ctot' (W1). We then have to solve a scheduling problem with M resources, in which Tm,ik -tm,ik corresponds to jobs' flow time, and which can we can be stated as follows:

(P1):

Minimize Ctot(W1) with the M resources

This problem can also be formulated in terms of scheduling as:

(P2):

Minimize the total flow time (eventually weighted by the dik) on M parallel machines.

However, the problem (P2) is different from the classical problems of flow time minimization on a particular point. This property is the first to be considered in the following section. The problem thus formulated has other properties, which are also described in the sequel.

[ ]

) t )(t µ λ - exp µ λ λ µ λ µ (t) A ik ik ik ik ik ik ik ik ik 0 ( - + + + + = ik τ t t + £ 0 [ ] [ ] ik ik ik -1 ik ik ik ρ ρ 1 α ln ρ 1 λ τ - + + - = ) ( ) ( -1 ik ik ik λ µ ρ = ( ) åå å = = Î ÷ ÷ ÷ ø ö ç ç ç è ae - = N 1 k N 1 i W m/t ik m ik m ik 1 tot k ik m, t T d ) (W C 1 , , (
)

) (W C d t T ) (W ' C 1 tot N 1 k N 1 i W m/t ik m ik m 1 tot k ik m, 1 1 , , = ÷ ÷ ÷ ø ö ç ç ç è ae - = åå å = = Î
Propriety 1: A precedence constraint links jobs relative to the same asset. Indeed, if Tm,ik is the end of the m th preventive action on Eik, then the beginning tm+1,ik of the (m+1) st work is determined by where is as defined in expression (2).

Property 2: Problem (P1) is NP-hard.

Taking advantage of the particular case where the precedence constraint described in property 1 is not considered in problem (P2) and where jobs have the same weight dik equal to d reduces problem (P2) to problem (P2'), i.e.: (P2'): Minimize the total flow time of jobs with unequal release dates on M parallel machines.

(P2') is NP-hard [START_REF] Lenstra | Complexity of Machine Scheduling Problems[END_REF] and remains NP-hard even in the case where preemption is accepted [START_REF] Du | Scheduling Chain Structured Jobs to Minimize Makespan and Mean Flowtime[END_REF]. It has been proved that (P2') is NP-complete [START_REF] Bruno | Scheduling independent jobs to reduce mean finishing time[END_REF]. So, (P2) and (P1) are NP-hard.

Therefore, our aim is not so much to find an exact solution to problem (P1), but to find a method for its resolution the best. Now, when the precedence constraints are relaxed, and the jobs are assumed to be available at time tm,ik, one may resort the branch and bound heuristic developed in [START_REF] Yalaoui | Ordonnancement de la production en présence de machines interactives[END_REF] for its resolution.

Resolution of the problem

Let us recall that the problem under consideration consists of allocating M resources to maintenance actions on the assets of a system composed of N plants. The aim is to minimize the cost of the total time spent by the system in critical states. This problem is transformed into a flow-time minimization problem in which precedence relationships link jobs. We have proved that the problem is NP-hard. Our target now is to find the appropriate heuristic method to solve it. For this, we resort to the PRTF function (Priority Rule for Total Flow-time) initially introduced by [START_REF] Chu | One-Machine Scheduling for Minimizing Total Flow Time with Release Dates[END_REF] and [START_REF] Chu | A Branch-and-Bound Algorithm to Minimize Total Flow Time with Unequal Release Dates[END_REF] to solve the job-scheduling problem for single-machine. It has been adapted later to the problem of parallel machines. The PRTF function is defined in the following section.

Definitions and proprieties Definition 1 (Chu, 1990)): Let us consider a set of jobs to be scheduled at time t on a machine. The job j has a release date rj and a processing time pj. The associated PRTF function is defined as follows PRTF(j, t)=2 max(rj, t)+pj

With this definition, [START_REF] Chu | One-Machine Scheduling for Minimizing Total Flow Time with Release Dates[END_REF] proved the following theorem:

Theorem 1: Consider a problem in which two jobs j and j' must be scheduled on a machine that is available after time t, and the aim is to minimize the total flow-time. We suppose that PRTF(j, t) £ PRTF(j', t). Let be a schedule in which the job j is scheduled before the job j' and be another schedule in which j' is scheduled before j, then gives a better solution than .

The PRTF also has another exciting propriety for our problem (Adzakpa et al.). The following theorem summarizes this propriety:

Theorem 2 (Adzakpa et al.): In scheduling, considering Theorem 1 implies that we also respect the order of the interventions on an asset Eik, whichever it is. In other words, for m<m' and for any asset Eik, theorem 1 allows to schedule the m th intervention on Eik before the m' th intervention.

So, comparing PRTF(tm,ik,t) and PRTF(tm',ik,t) comes to comparing tm,ik and tm',ik. Now tm,ik is less than tm',ik (because m<m'). Finally, we have . Hence, Theorem 1 allows the scheduling of jobs on any asset in the appropriate order.

Apart from the function PRTF, we also consider the emergency of the jobs scheduling as defined in the following section.

Definition 2: Let denote at time t the duration between t and the end of the last preventive job on the asset Eik before time t and let us assume that it is the (m-1) st work (cf. figure 3). Thus, we denote Urgent(t) denote at time t the job set satisfying the condition .

ik ik m, ik 1, m τ T t + = + ik τ π ' π π ' π ) , ( ) , ( , ' , t t PRTF t t PRTF ik m ik m £ ) (t ik D ik ik t t ³ D ) ( Figure 3. Definition of
We then derived a heuristic algorithm for job scheduling and allocation based on the PRTF function to solve the problem, taking advantage of theorems 1 and 2 and the emergency of the preventive actions. The aim is to find a trade-off between the cost minimization throughout the flow-time minimization and the time the equipment spent in critical states. The corresponding algorithm is summarized as follows.

Algorithm for job scheduling and resource allocation At any time t when a resource is available, the job to be scheduled is the one with the least value of the PRTF in the set Urgent(t) at that time. If the set Urgent(t) is empty, then the job to be scheduled is the one with the least value of the PRTF in the set of all the jobs not yet scheduled. If at least two resources are available at a given time, the job should assign to the resource available earlier, and if there is more than one resource, when the resource with the least index is selected.

Theorem 3 (complexity of the algorithm): The algorithm's complexity is O(N' 2 ), where N' is the total number of maintenance interventions theoretically calculated on the set of all the assets.

Let's recall that the algorithm enables dynamic online allocation decisions, taking account of the fact that the release date of a job depends on the end of another preventive action. The allocation decisions are then made online.

Numerical experimentation

The processes described in the above section have been programmed in the C language and tested on a UNIX station of the type Compaq AlphaServer ES40 DEC6600 with 2048 MB RAM.

The systems' availability parameters were randomly generated for the programs' numerical implementation and assessment. The failure rates and the repair rates have been generated according to Gauss laws. The availability thresholds must be chosen in the interval ]0, 1[ and should not be greater than the limit availability of the assets , where and are respectively the ik index equipment's failure rate and repair rate. Hence, the availability thresholds have been calculated from the failure and repair rates using relation (1). One can use allocation methods [START_REF] Calibra | Optimal reliability and maintainability allocation in manufacturing systems[END_REF] [START_REF] Elegbede | Reliability Allocation through Cost Minimization[END_REF] to apportion target reliability or maintainability to the facility components. The processing times were calculated from the repair rates and preventive actions set up times.

We programmed the algorithm in two different ways. The first program allocates the resource, considering job emergencies and job priority criteria based on the PRTF function. The second program considers only the PRTF criterion function. In both programs, only the date of the first job relative to each asset is known at the beginning. The release dates of the following preventive actions are determined each time a job is ended, enabling the online implementation of these programs. Both Prog1 and Prog2 are implemented online and correspond respectively to the proposed algorithms with emergency and without emergency criterion. The corresponding mean flow-times and the mean delay times are calculated based on the different system configurations' overall interventions. The evolutions of the mean flow-time and the mean delay-time are plotted in Figure 4. Different numerical experimentations have been performed with varying numbers of resources for each benchmark system with various configurations (systems respectively composed of 20, 30, 50, 80, and 100 assets) and taking the day as a time unit. Both programs' running time does not exceed 1 CPU second for a time-window of 365 days in all system configurations. This time is equal to 173 CPU seconds for Prog1 on a time-window of 10 000 days, in the case of a system composed of 1000 assets with 40 resources.

We use the following notations to characterize the results: Prog1 allocates the jobs considering the emergency and PRTF criterion function; Prog2 allocates the jobs considering only the PRTF criterion function. We also notice that in the particular case where, at a decision date, there is only one job to be scheduled, the decision rules of Prog1 and Prog2 are the same as the decision based on the Earliest Starting Time priority rule. However, the advantage of Prog1 against Prog2 is evident for a low number of resources. Prog1, based on job emergencies, enables the system to satisfy the availability requirement. Besides, we observe that the number of total jobs performed remains quite the same, even when the number of resources increases.

t ik 0 time t T m-1,ik t m-1,ik T 2,ik t m,ik D ik (t) ) (t ik D ) (

CONCLUSION

Let us recall that the objective of remote maintenance management, instead of adapted to large size and distributed systems, is to ensure the optimal availability of all production plants of an industrial complex through the availability of the means, competencies, and adequate resources at a lower cost. Thus, remote maintenance management of the distributed industrial complexes leads finally to considerable reductions in the operation and maintenance costs. Remote control of the maintenance interventions requires the implementation of several powerful tools, among which: 1) diagnosis tools whose effectiveness rely above all on the selection, the collection, the analysis, and the processing of suitable data to synthesize relevant decision-making information 2) reliable communication networks and information systems. The new technologies of information and communication may be coupled with the advanced Artificial Intelligence tools that enable to evaluate and predict the states of the equipment 3) computerized maintenance activities planning, and real-time resources allocation as well as maintenance interventions and tasks scheduling.

Concerning the last point, we presented in this paper an efficient algorithm tool based on a heuristic method for online implementation. It enables to handle preventive maintenance activities on distributed systems. Resource allocation to preventive maintenance activities is comparable to the parallel machine scheduling problem with jobs having different release dates. The problem is NP-hard. The proposed algorithm considers the jobs emergency and priority criteria to optimize the scheduling decision. The proposed algorithm has low complexity, and this was proved and confirmed through the different running times of the corresponding program fed by simulated parameters. As a logical extension of this work, future investigations will embrace other classes of resource systems, non-identical distances between the different assets, and the corrective maintenance tasks scheduling.

Figure 4 .

 4 Figure 4. Mean flow-time and mean delay times of jobs in the case of 80 assets Analysis of the flow-times and the mean delay times from critical dates: one can observe from the curves generated by Prog1 that the mean delay times of interventions show the smallest values for a low number of resources compared to those generated by Prog2. Both plots decrease monotonously toward zeros when the number of resources increases. The same observation can be done on the curves of mean delay time.

  , K. H., K. P. Adzakpa and F. Yalaoui, «Online Maintenance Job scheduling and Resource Allocation on Distributed Systems by Heuristic Based Optimization,» Submitted to Journal of Intelligent Manufacturing. 2. Berg, M.P, (1995), «The Marginal cost analysis and its application to repair and replacement policies,» European Journal of Operational Research, Vol. 82, pp. 214-224.


P Sideris
email: petros.sideris@grenoble-inp.fr

L Brunet

L Ciampolini

G Sicard

P Batude

C Theodorou

Inter-Tier Electrostatic Coupling Effects in 3D Sequential Integration Devices and Circuits

Keywords: SOI, CMOS, Fully Depleted, M3D, Monolithic 3D, 3D Sequential Integration, stacked, coupling, SRAM

This work presents for the first time an analytical study of the electrostatic coupling between bottom and top layer of 3D sequential integration devices, regarding its impact on both static and noise behavior. The effect is demonstrated experimentally through statistical measurements, and TCAD simulations are used to further examine its properties and propose ways for the limitation of inter-tier coupling. It is demonstrated that regarding digital applications, the coupling-induced fluctuations are well within the mismatch variation level.

Introduction

3D sequential integration, also named 3D monolithic integration or 3D VLSI, refers to a 3D integration scheme where the stacked devices are fabricated sequentially above each other. This process leads to outstanding high-density-contacts between the tiers (up to 10 8 3D via/mm 2 ) thanks to the high alignment precision obtained with lithography steppers [START_REF] Batude | 3D Sequential Integration: Application-driven technological achievements and guidelines[END_REF], [START_REF] Brunet | First demonstration of a CMOS over CMOS 3D VLSI CoolCube TM integration on 300mm wafers[END_REF], compared to packaging integration schemes (TSV, Copper to Copper bonding etc.). However, the ultra-thin Inter-layer dielectric (ILD) separating the sequential tiers can act as a back gate oxide of the top transistor, becoming a pathway of electrical interference for the stacked devices. Consequently, the top device is an asymmetric double-gated FDSOI MOSFET sensitive to the electrode voltage variations of the bottom device. The experiments and TCAD simulations presented in this work prove that the stacked device exhibits a shift in its electrical characteristics due to this effect. Although the electrostatic coupling effect in M3D has been already presented in principle [START_REF] Koneru | Analysis of electrostatic coupling in monolithic 3D integrated circuits and its impact on delay testing[END_REF], [START_REF] Yu | Electrical Coupling of Monolithic 3-D Inverters[END_REF], [START_REF] Hattori | Interlayer coupling effect on the performance of monolithic three-dimensional inverters and its dependence on the interlayer dielectric thickness[END_REF], [START_REF] Andrieu | Design technology co-optimization of 3D-monolithic standard cells and SRAM exploiting dynamic back-bias for ultralow-voltage operation[END_REF], and experimentally verified [START_REF] Subramanian | Parameter extraction of nano-scale MOSFETs using modified Y function method[END_REF], this is the first analytical study examining the coupling between the top and bottom tiers of 3D sequential technology stacking 28 nm FDSOI MOSFETs, under normal circuit operation (V DD = ±0.9V) and its impact on low frequency noise (LFN) performance of the stacked device.

Experimental details

The devices under study were top n-channel FDSOI MOSFETs, with EOT = 1.2 nm, t Si = 7 nm and ILD thickness t ILD = 130 nm (shown in Fig. 1) stacked above standard high temperature FDSOI CMOS devices. More details about the low thermal budget process used for top FET fabrication and the CoolCube TM process integration scheme can be found in [START_REF] Brunet | First demonstration of a CMOS over CMOS 3D VLSI CoolCube TM integration on 300mm wafers[END_REF]. The gate width of the measured devices is W = 2 μm for both tiers, whereas two different gate lengths were measured (L = 1 μm and L = 0.1 μm). The static measurements were performed with the Agilent B1500A device parameter analyzer and the low-frequency noise measurements with the NOISYS7 equipment by Synergie Concept [START_REF] Lim | Threshold Voltage of Thin-Film Silicon-on-Insulator[END_REF].

Results and discussion

In order to estimate the electrostatic coupling effect from the bottom to the top tier NMOS devices, a large set of experimental data was examined using different gate bias of the bottom transistor, i.e. V Gbot = 0 V (bottom device OFF), 0.9 V (upper voltage limit) and -0.9 V (lower voltage limit), as shown in Table I. The gate voltage of the top tier devices was varied from V Gtop = 0 V to 0.9 V in linear region of operation with the application of a 30 mV drain voltage, V D .

V Gbot 0 V 0.9 V -0.9 V V Gtop 0 → 0.9 V
The opposite case, i.e. an electrostatic coupling effect from the top to the bottom device does not exist, because when the bottom transistor is in operation, its gate metal layer is biased and therefore it is shielding the bottom channel from any electric field penetration from the top transistor gate bias.

A. Impact on electrical parameters of top tier device

For the purpose of this study, we selected 126 dies for the top tier device that demonstrated good input characteristics. Fig. 2a shows the I Dtop -V Gtop characteristics results of NMOS devices with L = 1 μm. An example of electrostatic coupling is shown in Fig.

2(b)

, where a visible coupling-induced threshold voltage shift, ΔV t , can be seen in both linear and log plots of I Dtop -V Gtop , whereas a slight change in the sub-threshold swing is observed in Fig. 2(c) (log-scale plot). I.

An automatic modified Y-function method [START_REF] Planes | 28FDSOI technology for low-voltage, analog and RF applications[END_REF] was applied to extract the threshold voltage, V t , values for all 126 dies. As shown in Fig. 3, the coupling-induced V t shift, ΔV t , was found to be equal to -15.6mV ± 2.87 mV and 14.7mV ± 2.38mV for a positive and a negative V Gbot bias respectively. The small difference between their mean values can be attributed to the weak bottom interface accumulation for negative V Gbot , while the ~15% variation is attributed to the variability in t ILD (estimated ±20nm for the wafer under study), that in turn affects the ΔV t variability through the SOI coupling relation, given by (1) [START_REF] Theodorou | Low-frequency noise behavior of n-channel UTBB FD-SOI MOSFETs[END_REF]:

𝛥𝑉 𝑡 𝑉 𝐺𝑏𝑜𝑡 = - 𝐶 𝑠𝑖(𝑡𝑜𝑝) 𝐶 𝐼𝐿𝐷 𝐶 𝑜𝑥(𝑡𝑜𝑝) (𝐶 𝐼𝐿𝐷 + 𝐶 𝑠𝑖(𝑡𝑜𝑝) ) (1)
where C si(top) , C ox(top) , C ILD are the top channel, the top oxide, and the ILD capacitances per unit area. The extracted average ΔV t of around 15 mV may seem significant, but it is well within the local variability limits (mismatch) of 28nm FDSOI technology [START_REF] Planes | 28FDSOI technology for low-voltage, analog and RF applications[END_REF], as can be seen in Fig. 4(a), for digital applications. Furthermore, the crossing point between mismatch and coupling reveals that even with an ILD thickness of 130nm, the maximum gate area for which the coupling-induced ΔV t does not exceed the mismatch variations is much higher than the typical gate areas used in digital circuits. Similarly to ΔV t , through Fig. 4(b) is demonstrated that both on-and off-current coupling-induced shifts ΔI off and ΔI on , are negligible compared to the calculated normalized mismatch variations of I off and I on in 28 nm FDSOI technology, for a typical range of gate areas in digital design.

B. Impact on LFN of top tier device

To study the electrostatic coupling impact on the top device LFN level, the drain current noise spectral density was measured from weak to strong inversion for all cases shown in Table I. In order to neglect the shift in the DC value of I Dtop , the measured noise was normalized by I Dtop 2 . Fig. 5 illustrates the corresponding spectra for three selected V Gtop values. Contrary to the impact on the static behavior, no noticeable coupling-induced change is observed in the LFN spectra behavior.

To further verify that the bottom-to-top coupling impact on LFN is negligible, we plotted the normalized Power Spectral Density (PSD) value extracted at f = 10 Hz versus drain current for all bias cases shown in Table I. As Fig. 6(a) shows, the LFN level for L = 1 μm can be considered unchanged whatever the bottom transistor gate bias, from subthreshold to strong inversion region. The same is true for the top devices with L = 0.1 μm, however, as shown in Fig. 6(b), the general LFN dependence on top gate bias is not the same. The latter is a typical behavior for sub-μm MOSFETs, where the noise spectra are not 1/f-like in most cases, but dominated by Lorentzian noise, responsible for the observed humps [START_REF] Ioannidis | Drain-Current Flicker Noise Modeling in nMOSFETs From a 14-nm FDSOI Technology[END_REF].

In previous studies, it has been shown that the bottom gate bias of an FDSOI MOSFET can strongly affect the remote Coulomb scattering between carriers and trapped charge [START_REF] Ioannidis | Analytical low-frequency noise model in the linear region of lightly doped nanoscale double-gate metal-oxidesemiconductor field-effect transistors[END_REF], [START_REF] Srinivasa | Compact 3-D-SRAM Memory with Concurrent Row and Column Data Access Capability Using Sequential Monolithic 3-D Integration[END_REF], leading to a change in the Correlated Mobility Fluctuations (CMF) factor Ω in the 1/f noise model expressed through (2) [START_REF] Kong | Architecting large-scale SRAM arrays with monolithic 3D integration[END_REF]:

√𝑆 𝑉𝑔 = √𝑆 𝑉𝑓𝑏 (1 + 𝛺 𝐼 𝑑 𝑔 𝑚 ) (2)
where S Vg is the input-referred gate voltage noise PSD, S Vfb the flat-band voltage noise PSD and g m the transconductance.

Therefore, in order to verify if the bottom transistor gate bias under normal operation can affect the CMF factor Ω, we plotted the square root of the input-referred gate voltage noise, S Vg , versus I d /g m . As one can observe in Fig. 7, in all three cases (Table I), there is the same linear dependence, and the extracted Ω factor (inset) can be considered constant with V Gbot . I.

C. Comparison with numerical simulations and proposed solutions for improvement

TCAD simulations were performed using the ATLAS Silvaco software, applying the same bias conditions as for the measurements (see Table I), as well as the same channel and gate oxide thickness values.

Fig. 8(a) shows the dependence of ΔV t with t ILD revealing a good agreement with the experimental results for a t ILD of 130nm.

From the same diagram we can conclude that decreasing tILD (for example up to 75 nm) the coupling-to-mismatch margin is maintained in an adequate level while the 3D contact aspect ratio is improved. In addition, the inter-tier coupling impact may be efficiently reduced when there is a misalignment between top and bottom device positions. Indeed, as shown in Fig. 8(b), our simulations revealed that in cases where the bottom-to-top overlapping area ratio is lower than 0.5, the coupling-induced ΔVt can be decreased by a factor of 3. This observation may function as a guideline for 3D design rules in the near future. ).

Monolithic 3D SRAM Analysis

Within the More than Moore context, 3D sequentially fabricated SRAM cells are framed as an extremely appealing architecture as they can provide denser and faster memory blocks, being co-integrated among various components (heterogeneous integration). Related work [START_REF] Srinivasa | Compact 3-D-SRAM Memory with Concurrent Row and Column Data Access Capability Using Sequential Monolithic 3-D Integration[END_REF]- [START_REF] Srinivasa | ROBIN: Monolithic-3D SRAM for Enhanced Robustness With In-MemoryComputation Support[END_REF] clearly demonstrates the virtues of this option. Therefore, in order to study the possible impact of the coupling-induced V t shift on a circuit's operation, we chose the 6T SRAM cell as a reference. In particular, we examined the configuration of a monolithic 3D (M3D) 2-bitcell SRAM, i.e. two stacked SRAM cells that are identical in layout design, so that the inter-tier coupling effects are maximized. Fig. 1 shows the stacked M3D SRAM structure under consideration.

A. Methodology

As shown before, the inter-tier coupling is sensitive to both the ILD thickness and the layout design of the top/bottom cell with respect to each other. Except for using coupling advantageously [START_REF] Batude | 3D CMOS integration: Introduction of dynamic coupling and application to compact and robust 4T SRAM[END_REF], previous work considering undesirable coupling impact [START_REF] Fan | Stability and performance optimization of heterochannel monolithic 3-D SRAM cells considering interlayer coupling[END_REF] has been carried out only for a single M3D SRAM bitcell having half of the transistors in each tier. Fig. 9 shows a schematic layout representation of the M3D 2-bitcell SRAM under study. Because the top transistors have an asymmetric double-gate SOI structure, one can consider that the Interlayer dielectric functions as their buried oxide and therefore their back gate terminalis indeed the front gate terminal of the respective bottom tier transistors. In order to assess whether the bottom SRAM cell operation can significantly alter the top SRAM cell performance some of the most common stability metrics were investigated: the Read and Write Static Noise Margin (RSNM & WSNM) and the Supply Read Retention Voltage (SRRV), that can provide a profound overview of the top SRAM cell dynamic stability [START_REF] Guo | Large-Scale SRAM Variability Characterization in 45 nm CMOS[END_REF], [START_REF] Singh | Robust SRAM designs and analysis[END_REF]. The impact of coupling was studied in conjunction with the mismatch induced variations, using SPICE implementation of the equivalent circuit. The model chosen to describe the behavior of the top tier transistors is the LETI-UTSOI MOSFET model (version 2.11) that accurately captures the device characteristics. Furthermore, an appropriate parametrization was done to match the experimental coupling-induced behavior, analyzed in the previous sections.

The results (Fig. 10) show very good fitting between measurements and model for the static characteristics for the required transistor biasing. In detail both linear and saturation behavior as well as the 15.6mV shift of the top transistor's threshold voltage due to bottom gate coupling, are accurately captured. For the bottom SRAM cell operation we can distinguish 3 cases: 1) no operation (zero power supply), 2) a stored '0'

(V CLbot =0V, V CHbot =1V), 3) a stored '1' (V CLbot =1V, V CHbot =0V).
V PULbot 0 V 1 V 0 V V PURbot 0 V 0 V 1 V V PDLbot 0 V 1 V 0 V V PDRbot 0 V 0 V 1 V

B. SRAM stability metrics analysis

The RSNM represents the maximum tolerable DC noise voltage at each storage node before causing a read upset. The extraction of the RSNM was performed by applying mismatch-related Monte Carlo simulations to capture the impact of the mismatch variations. The SRAM cell can be repeated over 1 million times in memory circuits resulting in 6σ of mismatch variations. However, the 3σ limit is critical enough to compare it with the coupling induced shift and requires 1000 runs rather than over 1 million in the case of the 6σ limit. From the obtained butterfly curves (Fig. 11a), the mean represents the typical behavior while the blue curve shows the worst case of mismatch among the 1000 runs. The largest square was fit for the worst set to estimate the mismatch related RSNM degradation. Additionally, the mean RSNM was extracted and comparing the two values, the impact of the V t mismatch is a RSNM reduction of 27%.

The same steps were followed after the addition of the coupling due to the operation of the bottom SRAM, the RSNM was extracted. As shown in Fig. 11b, the coupling-induced V t shift can further reduce the RSNM by 1% more. Following the same methodology as for the RSNM, we also extracted the WSNM that characterizes the write-ability of the SRAM bitcell (Fig. 12). Once again the reduction of the WSNM window due to the addition of the inter-tier coupling is 1% more. Regarding the SRRV, it is defined as the maximum allowed reduction of cell supply voltage for which the read stability is not affected. It is an equally important stability metric for SRAM cells [START_REF] Guo | Large-Scale SRAM Variability Characterization in 45 nm CMOS[END_REF]. It can be estimated measuring the bitline current I BL while the power supply of the cell (V CELL ) is ramped down. At a specific value of the V CELL (called V flip ), the stored bit is flipped and I BL drops suddenly. Then the SRRV is extracted as SRRV= V DD -V flip =1-V flip Fig. 13 (a) shows the simulation results for a typical cell with the 3 cases of the bottom operation. It is apparent that the most critical case is when a '1' is stored at the bottom cell. By further adding for this case the mismatch variations with 1000 Monte-Carlo runs, we obtain is an additional SRRV reduction of 3.5%.

CONCLUSIONS

A study of coupling-induced effects in the static and noise behavior of 3D sequential top tier transistors has been presented.

Through both measurements and simulations, it was shown that the coupling-induced ΔV t , ΔI off and ΔI on have high values considering analog applications, however they are well within the local variability limits of 28nm FDSOI technology for digital circuits, where sub-μm devices are used. Concerning the low frequency noise performance of the top tier transistor, no couplinginduced impact was observed regardless the transistor area. In addition, it was demonstrated that the coupling effect can be limited either by increasing the ILD thickness or through a top/bottom transistor misalignment. Finally, a circuit example of a M3D 2bitcell SRAM proved the validity of our analysis as all of the metrics were altered negligibly (1 to 3.5%) by the inter-tier coupling compared to the mismatch-induced variations.

Fig. 1 .

 1 Fig. 1. a) TEM picture of two stacked transistors fabricated in M3D technology. The top device channel is separated from the bottom device gate by 130nm dielectrics. b) Schematic of the experimental configuration studied in this work. The applied gate voltages are shown in Table I along with VDtop=30mV and VSbot,VDbot floating.

Fig. 2 .

 2 Fig. 2. (a) Drain current versus gate voltage for NMOS devices stacked on top of another NMOS, both with 2 μm 2 area (total of 126 dies). (b) Drain current versus gate voltage for an n-MOSFET (W = 2 μm, L = 1 μm) in linear scale and (c) in log scale, for all cases shown in TableI.

Fig. 3 .

 3 Fig. 3. Threshold voltage shift of top tier NMOS devices for linear regime (VDtop = 30 mV).

Fig. 4 .

 4 Fig. 4. a) Coupling-induced shift and mismatch-related variations (28 nm FDSOI versus reciprocal of gate area square root) for a) threshold voltage and b) Ioff and Ion current shift. The vertical marker in figure 4(a) indicates the mismatch standard deviation for the minimal transistor surface in 28 nm FDSOI (W = 80nm, L = 30 nm).

Fig. 5 .

 5 Fig. 5. Normalized drain current power spectral density vs frequency for a top NMOS with W = 2μm, L = 1μm in three different bias conditions of the bottom.

Fig. 6 .

 6 Fig. 6. Normalized power spectral density at f = 10 Hz vs drain current for a top NMOS with W = 2 μm, L = 1 μm (a) L = 0.1μm (b) and all bias cases of TableI.

Fig. 7 .

 7 Fig. 7. Square root of input-referred gate voltage PSD SVg versus Id/gm (b) for a top NMOS with W=2μm, L=1μm and all bias cases of TableI.

Fig. 8 .

 8 Fig. 8. (a) Coupling-induced threshold voltage shift vs ILD thickness for drain bias 30mV and ΔVGbot=-0.9V, compared with threshold voltage mismatch level for 28 nm FDSOI technology. (b) Threshold voltage shift vs overlapping gate area of bottom gate poly to top channel ( Overlapping area Total top channel area

Fig. 9 .

 9 Fig. 9. Schematic layout representation of the M3D 2-bitcell SRAM under study.

Fig. 10 .

 10 Fig. 10. Drain current versus gate voltage for the top tier NMOS device (L=100nm). Circles and lines denote experimental and simulation results respectively.

Fig. 11 .

 11 Fig. 11. (a) Impact of Vt mismatch on RSNM of top tier SRAM, (b) Addition of the static coupling because of the bottom tier SRAM operation

Fig. 12 .

 12 Fig. 12. (a) Impact of Vt mismatch on WSNM of top tier SRAM, (b) Addition of the static coupling because of the bottom tier SRAM operation

Fig. 13 .

 13 Fig. 13. Bit-line current versus cell supply voltage for (a) the three cased of the bottom SRAM operation and (b) Monte Carlo simulation with mismatch variations only or (c) adding also the static coupling induced shift.

TABLE I

 I

	.	CASES OF BOTTOM TRANSISTOR GATE BIAS
		Bottom	Bottom ON
		OFF	Upper limit	Lower limit

  TableIIsummarizes the bottom transistor gate bias for each one of the 3 cases. These conditions were applied in the back gates of the respective top transistors to emulate the inter-tier coupling effect.

Acknowledgement

This work was partially supported by the LabEx Minos ANR-10-LABX-55-01 program.