Shyam Praveen Vudathu

Kishore Kumar Duganapalli

Rainer Laur

Dorota Kubalińska

Angelika Bunse Gerstner

PARAMETRIC YIELD ANALYSIS OF MEMS VIA STATISTICAL METHODS

Keywords: MEMS, process variations, Monte Carlo analysis, worst-case analysis and model order reduction

This paper considers a developing theory on the effects of inevitable process variations during the fabrication of MEMS and other microsystems. The effects on the performance and design yield of the microsystems devices are analyzed and presented. A novel methodology in the design cycle of MEMS and other microsystems is briefly introduced. This paper describes the initial steps of this methodology that is aimed at counteracting the parametric variations in the product cycle of microsystems. It is based on a concept of worst-case analysis that has proven successful in the parent IC technology. Issues ranging from the level of abstraction of the microsystem models to the availability of such models are addressed.

INTRODUCTION

With the decreasing feature sizes and increasing demand for smaller devices, the future of Micro-Electro-Mechanical Systems (MEMS) and other microsystems is increasingly depending on the ability to design and fabricate devices with smaller feature sizes. Unfortunately, even the state-of-the-art process technologies have limitations while fabricating devices in the micro and nano scales. The limitations of the processes could be; inaccurate etching rate, mask misalignments, erroneous lithographic treatment, etc. These limitations in the processes could cause unexpected variations in the device dimensions like; variation in the line-width, beam-width, thickness of the membrane, etc. The variations in the design parameters are considered to be the process or statistical parameters of the design. Many efforts [START_REF] Wong | On In-Situ Etch Rate Estimation from Interferometric Signals[END_REF][START_REF] Boning | A General Semiconductor Process Modeling Framework[END_REF] have been and are being done to accurately model the variations in the device geometry during the fabrication of MEMS structures. The modeling of processes parameters involves the consideration of different internal aspects. The process models describe the physical and geometric behavior of the process technologies.

The effect of process parameters on design yield of MEMS devices is analyzed. This is done by performing MEMS simulations that consider process models. The process models used in this work are Gaussian, Exponential or Uniform in nature. The parameters that are vulnerable to process variations are represented with their process models and the device is statistically simulated. A methodology that counteracts the effects of parametric variations on design yield of MEMS and other microsystems is briefly presented. This methodology dictates a change in the design parameter value by optimizing them in the design phase rather than the fabrication phase. It is based on the concept of worstcase analysis [START_REF] Antreich | Circuit Analysis and Optimization Driven by Worst-Case Distances[END_REF][START_REF] Director | VLSI Design for Manufacturing: Yield Enhancement[END_REF] that has proven successful in the parent IC technology. This paper tests the possibility of the adoption of worst-case methods in the yield analysis of MEMS devices.

Section 2 starts with a demonstration of the necessity for statistical analysis of MEMS. Later, a brief review on the efforts being done in this domain is presented. Section 3 throws light on a tool developed in this work for performing sensitivity analysis of MEMS. In the same section, the simulation results of a capacitive pressure sensor are also presented. Section 4 briefly introduces the yield analysis techniques using worst-case methods and relates the results obtained in this work with these methodologies. This paper finally concludes by drawing conclusions and briefly describing the future work in section 5.

Shyam Praveen Vudathu et. al Parametric Yield Analysis of MEMS via Statistical Methods

STATISTICAL ANALYSIS OF MEMS

Effect of Process Variations on MEMS

The necessity of statistical analysis of MEMS devices is being increasingly felt with the ever decreasing feature sizes. Many MEMS devices fulfill their specifications in the nominal sense (without the consideration of process variations). But the same designs when subjected to process variations in the manufacturing phase, partially fail to fulfill the specification values. This is explained with the help of a simple cantilever beam. The simple beam spring formula of 'K' is given by:

3 3 E t w K l × × = (1)
where t is the thickness of the beam, w is the width of the beam, l is the length of the beam, and E is the Modulus of elasticity.

The resonant frequency 'f r ' of the beam is extracted by changing slightly the mass at the free end of the beam. With 'f 0 ' and 'f 1 ' representing the initial and final resonant frequencies of the beam, the change in the mass can be represented as:

2 2 2 1 0 1 1 4 k m f f π ⎛ ⎞ Δ = - ⎜ ⎝ ⎠ ⎟ (2) 3 3 r w f l ⇒ ≈ (3)
The effect of process variations on this simple structure can be observed from the plot shown in Fig 2 . The beam was nominally sized to better a specification value of 49KHz. With no process variations, the beam with a width of 2.0 microns, has a resonant frequency of 50KHz, which is greater than the specification value. A '1σ' variation in the width of the beam is considered to be reasonably in par with the usually observed variations at the fabsite. Fig. 2 shows a plot between the resonant frequency and the width of the cantilever beam with a '1σ' variation. The plot shows the dependence of the resonant frequency for two different values of the beam width. From the plot, the nominal design that satisfies the resonant frequency specification is not doing the same in the entire range of the varied beamwidth. As the marked region of the line in Fig 2 indicates, a considerable amount of yield of this simple beam is affected due to process variations. Assuming a linear distribution, the yield of this design is roughly 78%. This affect of the process variation can be counteracted by increasing the beamwidth of the cantilever [START_REF] William | Enhancing MEMS Design Using Statistical Process Information[END_REF]. As the dotted curve (beamwidth = 4 microns) in the plot shows, the yield of the new design is close to 100%.

Resonant Frequency Vs. Beam Width

The yield of this design has been easily increased in this case because of:

• the presence of only two parameters • considering only a single performance • the availability of a simple and a good high abstraction model with a relatively simple structure.

Furthermore, not all devices can be blown up in size to have better yield. There are numerous devices that are ought to be small to serve a purpose (e.g. microfluidic channels, etc). All these reasons call for a better method where the device yield can be increased in a rather intelligent way.

Methods for Statistical Analysis of MEMS

This section presents a brief review on the existing statistical methods that could exploit process models in the design cycle of MEMS. The approach in [START_REF] Schenato | Process Variation Analysis for MEMS design[END_REF] estimates the performance variations for general planar suspended MEMS structure for low frequency applications. In this work they develop the capabilities to find bounds on the

Shyam Praveen Vudathu et. al Parametric Yield Analysis of MEMS via Statistical Methods

performance parameters, given the bounds on the geometric variables. In [START_REF] Ren | Statistical Optimal Design of Microelectromechanical System (MEMS)[END_REF], a comparison is drawn between various methods, and finally a mixture of methods like the Geometric Yield Optimization and the Taguchi method has been used in order to enhance the yield of an ADXL50 accelerometer. Nonetheless, Geometric yield optimization as implemented by the worst case distance (WCD) method, is employed only to bring the design closer to the target. This shows that the capabilities of the WCD methods have not been completely but only partly exploited in the design cycle of MEMS. The methodology considered in this paper can be generally applied to any MEMS device that satisfies a basic set of criterion. The chief criterion would be the level of abstraction of the model being used for the analysis. Though, principally model of any abstraction level could be analyzed, the usage of high level models is preferred because the simulation times of such models are comparatively less.

SENSITIVITY ANALYZER FOR MEMS

A sensitivity analysis can be performed on the MEMS design in order to identify the most relevant parameters, each of which influences the system performance largely. In sensitivity analysis, the system parameters are slightly perturbed and their influence on the performance is compared amongst different parameters. A Jacobian matrix is therefore a result of any first order sensitivity analysis. The Jacobian matrix when computed at the DC operation point of the device can also be used for the linearization of the performance around the DC operating point. This could later be used in the yield analysis of the design, which is about to be described in section 4.

Figure 3: Sensitivity Analyzer for MEMS -'SAM'

For performing this analysis, an interfacing tool 'SAM': Sensitivity Analyzer for MEMS was developed. The Sensitivity Analyzer for MEMS (SAM) developed in this work is based on the SUGAR simulator [START_REF] Clark | 3D MEMS Simulation Modeling Using Modified Nodal Analysis[END_REF]. In order to perform a sensitivity analysis on a MEMS device, SAM induces process statistics into the design. This is done by appending an additional ".SAM" part to the conventional SUGAR netlist. The base of a "SAM" netlist is theoretically a SUGAR netlist, which is appended with more "SAM" commands to perform a statistical analysis. To begin with, some process models like the Gaussian, Exponential and the Uniform distribution models have been included. Nevertheless, other models could be easily integrated for analysis with this tool. A simple capacitive pressure sensor was taken to be an example device in this work and has been simulated using SAM. The capacitive pressure sensor consists of a thin membrane and a chamber. More practical models of pressure sensors like that in [START_REF] Peters | Optimized behavioral model of a pressure sensor including the touch-down effect[END_REF] could be simulated using behavioral modeling languages like VHDL-AMS. On performing a sensitivity analysis, the most sensitive parameters were found to be the width and length of the membrane. Therefore, a yield plot between these two parameters in the design space is obtained by a two dimensional sweep. The force applied at the touchdown point (minimum force required for touchdown) was taken as the performance under consideration with a specification value of 5.5 micro Newtons. All the points with a '*' in the plot indicate that the point satisfied the specification value, while the points with 'o' indicate that the point doesn't satisfy the specification value. The yield of the design was observed to be 86%. The same device could be analyzed with a different material for beam, which might result in totally new yield numbers.

Shyam Praveen Vudathu et. al Parametric Yield Analysis of MEMS via Statistical Methods

STATISTICAL ANALYSIS BASED ON WORST-CASE METHODS

Amongst the various statistical methods, worst-case methods for yield analysis were highly successful in the analog and mixed signal domain of microelectronics and yielded excellent results. In this section, the considered yield analysis of MEMS using worst-case methods is briefly explained. Also, the relevance of the results obtained in section 3 to the worst-case methods is emphasized.

Using Monte Carlo analysis, the yield of the design can be calculated by performing huge number of simulations. The results of this huge number of simulations can be used in various ways. Yet there is no one single known way on how to improve yield of the design from Monte Carlo simulations. In worst-case analysis firstly, the performance of the design is linearized around the operating point. Secondly, the linearized specification boundary is used to calculate the worst-case distance from the nominal point. The advantage of the worst-case analysis lies in calculating the worst-case distance which can be directly equated to the yield of the design. Once the worst-case distance is known, larger the worst-case distance, larger is the yield of the design with respect to that particular specification.

With an assumption of a Gaussian distribution for the statistical parameters, the yield of a design 'Y', could be directly calculated from the worst-case distance 'β' using eq. ( 4).

1 1 2 2 Y erfc β ⎛ ⎞ ⎛ ⎞ ≈ + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (4)
The nominal point represented with a double lined dot in the Fig 4 represents the actual design point with zero variance. In Fig 4, the dotted line serves as discretion between the points that satisfy the specification and the points that don't. The dotted line hence is a specification boundary. The worst-case point is considered to be a point on the specification boundary and still the closest to the nominal point. Hence, the results obtained with SAM could be further extended to perform a yield analysis using worst-case methods.

CONCLUSIONS AND FUTURE WORK

The importance of the effect of process variations on MEMS devices has been demonstrated with an example of a cantilever beam. The necessity for new methods of yield analysis in the MEMS domain is becoming more obvious. SAM has been developed to meet the initial steps for yield analysis of MEMS devices using worstcase methods. SAM can be used to perform a sensitivity analysis on MEMS devices that are possible to be simulated with SUGAR.

An alternative approach would be to use other nodal analysis based simulators to simulate MEMS devices. This helps to implement the yield analysis techniques in a more generalized ambiance where most of the MEMS devices could be simulated. The implementation of the worst-case methods follows sensitivity analysis.

Figure 1 :

 1 Figure 1: A simple cantilever beam

Figure 2 :

 2 Figure 2: Performance sensitivity to process variations in a cantilever beam

Figure 4 :

 4 Figure 4: Design space of a capacitive pressure sensor

©TIMA Editions/DTIP 2006ISBN: 2-916187-03-0


David Ribet

Pascale Cossart
email: pascale.cossart@pasteur.fr

Ubiquitin, SUMO, Nedd8 : privileged targets of bacterial pathogens

Keywords: Ubiquitin, SUMO, ISG15, NEDD8, FAT10, host-pathogen interactions

Manipulation of host protein post-translational modifications is used by various pathogens to interfere with host cell functions. Among these modifications, Ubiquitin and Ubiquitin-like proteins constitute privileged targets as they represent regulators of pathways essential for the host cell. In particular, these post-translational modifiers control pathways that have been described as critical for infection such as pathogen entry, replication, propagation or detection by the host. Although bacterial pathogens lack Ubiquitin or Ubiquitin-like protein systems, many of them produce proteins that specifically interfere with these host post-translational modifications during infection. In this review, we will discuss the different mechanisms used by bacteria to interfere with host Ubiquitin and Ubiquitin-like proteins (UBLs), such as SUMO or NEDD8.

Highlights :

* Ubiquitin and UBLs regulate essential pathways of the host cell involved in critical steps of bacterial infections. Not surprisingly, bacterial pathogens have evolved numerous strategies to interfere with these host post-translational modifications. * Besides Ubiquitin, Ubiquitin-like proteins such as SUMO and NEDD8 have recently emerged as privileged targets of bacterial pathogens. * Strategies used by bacteria to interfere with host Ubi/UBL encompass the targeting of Ubi/UBL conjugation machineries, the modulation of the Ubi/UBL conjugation level of specific host factors and the direct targeting of Ubi/UBL proteins. * Host proteins modified by Ubi/UBL and targeted by bacteria cluster into specific host cell functions such as gene regulation, cytoskeleton dynamics or cell-autonomous immunity. * Bacteria hijack the host Ubi/UBL systems to modify their own proteins allowing a regulation of their intracellular localization, stability or interaction abilities. Outstanding questions : * Are the recently described non-canonical ubiquitination mechanisms (i.e. conjugation involving non-RING/non-HECT E3 ligases or E1/E2-independent ubiquitin conjugation) strictly restricted to bacteria? Or are there functional homologs of these bacterial enzymes encoded by human cells? * Recent improvements in proteomic analyses now allow to thoroughly monitor changes in the host ubiquitinome/"UBL-ome" in response to infection. These approaches usually generate lists of thousands of protein and/or sites modified during infection. Which strategies researchers should use to cope with this complex set of data and identify the key players affecting the outcome of infection ? * What are the mutations in the human population affecting the Ubi/UBL systems that may confer higher susceptibility to bacterial pathogens ? * Would drugs targeting bacteria-specific enzymes interfering with host Ubi/UBL conjugation be efficient to treat infectious diseases ?

Ubiquitin and Ubiquitin-like proteins constitute essential modifiers of host proteins

Post-translational modifications (PTM) of proteins encompass a wide range of chemical modifications. These PTMs include the cleavage of peptide bonds (proteolysis), the modification of specific amino acid side chains such as deamidation, eliminylation or the covalent addition of chemical moieties ranging from simple groups (such as phosphate, acetyl or methyl groups) to more complex groups such as sugar, lipids or even small polypeptides).

Ubiquitin is a small polypeptide of 76 amino acids that can be covalently linked, via its Cterminal glycine residue, to target proteins. Ubiquitination, i.e. the conjugation of Ubiquitin, usually occurs on lysine residues of target proteins although conjugation to other amino acids such as threonine, serine, tyrosine or cysteine may happen. Ubiquitin itself contains seven lysines (K6, K11, K27, K29, K33, K48 and K63) that can serve as sites for additional cycles of Ubiquitin attachment, resulting in the formation of Ubiquitin chains. The topology of these chains is very diverse, ranging from "homotypic" K48-or K63-linked chains, composed of only one type of Ubiquitin linkage, to "mixed" chains containing for example both K11 and K63 linkages [START_REF] Yau | The increasing complexity of the ubiquitin code[END_REF][START_REF] Swatek | Ubiquitin modifications[END_REF]. An additional type of chains, called "linear" chains, is generated when Ubiquitin is attached to the N-terminus of a second Ubiquitin [START_REF] Hrdinka | The Met1-Linked Ubiquitin Machinery: Emerging Themes of (De)regulation[END_REF]. Targeting of a given protein by Ubiquitin may thus result in mono-ubiquitination, multi-mono-ubiquitination (i.e. several mono-ubiquitination on different amino acids) or poly-ubiquitination. Ubiquitin is attached to substrates by a three-step enzymatic cascade involving E1 (Ubiquitin activating enzyme), E2 (Ubiquitin-conjugating enzyme) and E3 (Ubiquitin ligase) enzymes [START_REF] Swatek | Ubiquitin modifications[END_REF]. Ubiquitin is first activated in an ATP-dependent manner by E1, which links the C-terminal glycine residue of Ubiquitin via a thioester bond to a cysteine residue within the E1 active site. This activated Ubiquitin is then transferred to the catalytic cysteine residue of an E2 enzyme. E3 ligases then finally mediate the transfer of ubiquitin from the E2 enzyme to specific substrates. There are two major classes of E3s: the HECT (homologous to the E6-AP carboxyl terminus) type and the RING (really interesting new genes)/U-box type. HECT-type E3 Ubiquitin ligases form a reactive intermediate with ubiquitin before its transfer to the substrate protein whereas RING/U-box-type E3 ligases mediate transfer of ubiquitin from the E2 directly to the substrate protein, without formation of an E3-ubiquitin intermediate [START_REF] Zheng | Ubiquitin Ligases: Structure, Function, and Regulation[END_REF]. Conjugation of Ubiquitin is a reversible process as several cellular isopeptidases (called deubiquitinases or DUBs) can cleave the covalent bond between Ubiquitin and its targets and thereby remove ubiquitin [START_REF] Mevissen | Mechanisms of Deubiquitinase Specificity and Regulation[END_REF].

Besides Ubiquitin, other polypeptides such as SUMO (Small Ubiquitin-like MOdifier) [START_REF] Flotho | Sumoylation: a regulatory protein modification in health and disease[END_REF], NEDD8 (neural precursor cell expressed developmentally downregulated protein 8) [START_REF] Enchev | Protein neddylation: beyond cullin-RING ligases[END_REF], ISG15 (interferon-stimulated gene 15) [START_REF] Villarroya-Beltri | ISGylation -a key to lock the cell gates for preventing the spread of threats[END_REF] or FAT10 (HLA-F-adjacent transcript 10) [START_REF] Basler | The ubiquitin-like modifier FAT10 in antigen processing and antimicrobial defense[END_REF] can be similarly conjugated to target proteins. These polypeptides are grouped in the so-called Ubiquitin-like proteins (UBL) family and share high structural homology with Ubiquitin [START_REF] Streich | Structural and functional insights to ubiquitin-like protein conjugation[END_REF].

The mechanisms of UBL conjugation on target substrates are very similar to the ones observed for ubiquitination. The enzymes required for all these modifications (i.e. E1 UBL activating enzymes, E2 UBL conjugating enzymes and E3 UBL ligases) share highly conserved domain structures [START_REF] Streich | Structural and functional insights to ubiquitin-like protein conjugation[END_REF]. Of note, the number of UBL specific E1, E2 and E3 enzymes is usually smaller than for Ubiquitin. For example, SUMO conjugation to thousands of cellular targets seem to rely only on one single SUMO E1 enzyme (SAE1/UBA2), one single SUMO E2 enzyme (UBC9) and a dozen of SUMO E3 ligases [START_REF] Flotho | Sumoylation: a regulatory protein modification in health and disease[END_REF]. As for Ubiquitin, the formation of UBL chains (where UBLs are conjugated to internal lysines of other UBLs) has been reported for SUMO and NEDD8 [START_REF] Flotho | Sumoylation: a regulatory protein modification in health and disease[END_REF][START_REF] Enchev | Protein neddylation: beyond cullin-RING ligases[END_REF]. Finally, as for Ubiquitin, the host cell encodes several ULPs (UBL-specific proteases) that guarantee the reversibility of UBLs conjugation [START_REF] Flotho | Sumoylation: a regulatory protein modification in health and disease[END_REF][START_REF] Enchev | Protein neddylation: beyond cullin-RING ligases[END_REF][START_REF] Villarroya-Beltri | ISGylation -a key to lock the cell gates for preventing the spread of threats[END_REF][START_REF] Basler | The ubiquitin-like modifier FAT10 in antigen processing and antimicrobial defense[END_REF].

The consequences of Ubi/UBL conjugation on the fate of the modified proteins are very diverse.

Ubi/UBL can alter the half-life of the modified proteins, for example by targeting them to proteasome degradation. They can change the targets' structure thereby changing their catalytic activity. They can add new surfaces of interactions or mask internal binding domains and change the targets' interactome. The cell encodes in particular many "receptors" containing Ubiquitin-binding domains (UBDs) or UBL binding domains (such as the SUMO interacting motifs [SIMs]), that interact with proteins once conjugated to Ubi/UBL and "decode" these modifications into biochemical cascades in the cell [START_REF] Flotho | Sumoylation: a regulatory protein modification in health and disease[END_REF][START_REF] Husnjak | Ubiquitin-binding proteins: decoders of ubiquitin-mediated cellular functions[END_REF]. Besides the well-known example of K48-Ubiquitin chains conjugation that target modified proteins to proteasomal degradation, it is usually very difficult to anticipate the consequences of Ubiquitin or UBL conjugation of a given target.

Ubi/UBL are essential regulators of fundamental pathways in cell biology. Some of these pathways are critical for the outcome of infection by pathogens. For example, Ubiquitin is a major regulator of the NF-κB pathway, that triggers the expression of proinflammatory cytokines in response to pathogen detection [START_REF] Rahman | Modulation of NF-kappaB signalling by microbial pathogens[END_REF]. SUMO is a central player in the regulation of type I interferon and in anti-viral gene expression programs [START_REF] Decque | Sumoylation coordinates the repression of inflammatory and antiviral gene-expression programs during innate sensing[END_REF]. ISG15 plays several independent roles in anti-viral defense and can restrict intracellular bacteria replication in vitro and in vivo [START_REF] Villarroya-Beltri | ISGylation -a key to lock the cell gates for preventing the spread of threats[END_REF][START_REF] Bogunovic | Mycobacterial disease and impaired IFN-gamma immunity in humans with inherited ISG15 deficiency[END_REF][START_REF] Radoshevich | ISG15 counteracts Listeria monocytogenes infection[END_REF]. FAT10 was reported to be involved in xenophagy and in antimicrobial defense [START_REF] Basler | The ubiquitin-like modifier FAT10 in antigen processing and antimicrobial defense[END_REF][START_REF] Spinnenhirn | The ubiquitin-like modifier FAT10 decorates autophagytargeted Salmonella and contributes to Salmonella resistance in mice[END_REF]. It is thus not surprising that pathogens evolved strategies to target Ubi/UBL and interfere with these different cellular processes.

In this review, we will present how pathogens interfere with the host Ubi/UBL systems.

Ubiquitin and UBL systems have been shown to be targeted by diverse pathogens such as viruses, bacteria or parasites, including Plasmodium falciparum or Toxoplasma gondii [START_REF] Ribet | Pathogen-mediated posttranslational modifications: A reemerging field[END_REF][START_REF] Everett | Interplay between viruses and host sumoylation pathways[END_REF][START_REF] Wimmer | Viral Mimicry to Usurp Ubiquitin and SUMO Host Pathways[END_REF][START_REF] Maculins | Bacteria-host relationship: ubiquitin ligases as weapons of invasion[END_REF][START_REF] Ashida | Bacterial E3 ligase effectors exploit host ubiquitin systems[END_REF][START_REF] Lin | Exploitation of the host cell ubiquitin machinery by microbial effector proteins[END_REF][START_REF] Wilson | Viral Interplay with the Host Sumoylation System[END_REF][START_REF] Maruthi | Modulation of host cell SUMOylation facilitates efficient development of Plasmodium berghei and Toxoplasma gondii[END_REF].

We will focus here on pathogenic bacteria as they display the widest variety of Ubi/UBL interfering strategies known to date. Although bacteria do not have their own Ubi/UBL systems, numerous species encode virulence factors that actually manipulate host Ubi/UBL systems. These factors can be toxins secreted in the extracellular space in the vicinity of the host cell, or effectors delivered directly into host cells via specialized secretion systems such as Type III secretion systems (T3SS). We will discuss how bacterial pathogens (i) target Ubi/UBLs conjugation machineries, (ii) increase or decrease the Ubi/UBL conjugation on specific host factors, (iii) directly target Ubi/UBL polypeptides, or (iv) use host Ubi/UBL to modify their own proteins. We will enlighten how these mechanisms allow bacterial pathogens to manipulate specific host cellular pathways in order to promote infection.

Harnessing of host Ubiquitin and UBLs conjugation by bacterial pathogens

Targeting of host Ubiquitin and UBLs conjugation machinery enzymes

Targeting of host E1 or E2 ubiquitin enzymes is a conserved strategy used by pathogens to dampen ubiquitination (Fig. 1, Key figure). This strategy is used for example by Shigella flexneri, the etiological agent of bacillary dysentery. This bacterium secretes through its T3SS, an effector, named OspI, that deamidates the human E2 Ubiquitin enzyme UBC13 [START_REF] Sanada | The Shigella flexneri effector OspI deamidates UBC13 to dampen the inflammatory response[END_REF]. This deamidation inactivates UBC13 Ubiquitin-conjugating activity, leading to the dampening of the Ubiquitin-dependent TRAF6-mediated signaling pathways and to the inhibition of host inflammatory responses during infection [START_REF] Sanada | The Shigella flexneri effector OspI deamidates UBC13 to dampen the inflammatory response[END_REF]. Extracellular pathogens such as enteropathogenic Escherichia coli (EPEC) also targets the host Ubiquitin conjugation machinery. Adhesion of these bacteria to human cells leads to the degradation of UBE1 and UBA6, the two E1 Ubiquitin enzymes, and to a global decrease of host protein ubiquitination [START_REF] Lin | The Escherichia coli adherence factor plasmid of enteropathogenic Escherichia coli causes a global decrease in ubiquitylated host cell proteins by decreasing ubiquitin E1 enzyme expression through host aspartyl proteases[END_REF]. The SUMO conjugation machinery constitutes another target for bacterial pathogens.

Listeria monocytogenes, the bacterium responsible for human listeriosis, dampens SUMOylation of specific host factors by triggering the degradation of UBC9, the unique host E2 SUMO enzyme [START_REF] Ribet | Listeria monocytogenes impairs SUMOylation for efficient infection[END_REF][START_REF] Impens | Mapping of SUMO sites and analysis of SUMOylation changes induced by external stimuli[END_REF][START_REF] Ribet | Promyelocytic Leukemia Protein (PML) Controls Listeria monocytogenes Infection[END_REF]. This degradation of UBC9 is triggered by the formation of pores into the host plasma membrane by the bacterial toxin Listeriolysin O (LLO) [START_REF] Ribet | Listeria monocytogenes impairs SUMOylation for efficient infection[END_REF]. As LLO pores are not reported to affect the activity of host deSUMOylases, UBC9 degradation ultimately results in a shift in the SUMOylation/deSUMOylation equilibrium in the cell and to the deSUMOylation of host proteins such as transcription factors [START_REF] Impens | Mapping of SUMO sites and analysis of SUMOylation changes induced by external stimuli[END_REF]. The deSUMOylation events triggered by LLO were shown to promote Listeria infection [START_REF] Ribet | Listeria monocytogenes impairs SUMOylation for efficient infection[END_REF]. Of note, other toxins of the same family as LLO, and secreted by extracellular pathogens, were shown to downregulate UBC9, indicating that interference with host SUMOylation is a strategy conserved between different classes of pathogenic bacteria [START_REF] Ribet | Listeria monocytogenes impairs SUMOylation for efficient infection[END_REF]. Inhibition of the SUMOylation machinery is also observed during infection with Salmonella Typhimurium, a bacterium responsible for gastroenteritis in humans, and with Shigella flexneri but the underlying mechanisms involved here do not rely on the production of bacterial toxins. In the case of Salmonella Typhimurium, infection leads to the upregulation in the host cell of two small noncoding RNAs (miR30c and miR30e) that downregulate UBC9 level [START_REF] Verma | Salmonella Engages Host MicroRNAs To Modulate SUMOylation: a New Arsenal for Intracellular Survival[END_REF]. In the case of Shigella flexneri, infection is associated with an influx of calcium into the host cell. This ion flux activates the host proteases calpains, which cleave UBA2, one of the two components of the E1 SUMO enzyme [START_REF] Lapaquette | Shigella entry unveils a calcium/calpain-dependent mechanism for inhibiting sumoylation[END_REF]. The resulting inhibition of SUMOylation is associated with an increase in Shigella entry [START_REF] Lapaquette | Shigella entry unveils a calcium/calpain-dependent mechanism for inhibiting sumoylation[END_REF][START_REF] Fritah | Sumoylation controls host anti-bacterial response to the gut invasive pathogen Shigella flexneri[END_REF].

Secretion of bacterial effectors mimicking host Ubiquitin and UBL enzymes

Besides interfering with Ubiquitin or UBL-conjugation machineries, bacterial pathogens produce proteins that can replace or act as components of these machineries (Fig. 1). In particular, several bacterial effectors possess Ubiquitin E3-like activity. Some of these bacterial effectors share structural homologies with the two major types of eukaryotic E3 ligases, i.e. the HECT type and the RING/U-box type E3 ligases [START_REF] Maculins | Bacteria-host relationship: ubiquitin ligases as weapons of invasion[END_REF][START_REF] Ashida | Bacterial E3 ligase effectors exploit host ubiquitin systems[END_REF][START_REF] Lin | Exploitation of the host cell ubiquitin machinery by microbial effector proteins[END_REF]. These effectors may have been acquired by bacteria via horizontal transfer from diverse eukaryotic sources [START_REF] Hicks | Hijacking the host ubiquitin pathway: structural strategies of bacterial E3 ubiquitin ligases[END_REF]. In addition to these types, three other classes of bacterial effectors display structures completely distinct from eukaryotic E3 ligases: NELs (for Novel E3 ligase) [START_REF] Hicks | Hijacking the host ubiquitin pathway: structural strategies of bacterial E3 ubiquitin ligases[END_REF], XL-box-containing E3 ligases [START_REF] Singer | A pathogen type III effector with a novel E3 ubiquitin ligase architecture[END_REF] and SidC ligase [START_REF] Hsu | The Legionella effector SidC defines a unique family of ubiquitin ligases important for bacterial phagosomal remodeling[END_REF]. These ligases may represent structures evolved by pathogens to mimic the functions of these essential host enzymes. These different classes of E3 ligases enable bacteria to conjugate Ubiquitin on specific host factors, thereby altering their stability or function, subcellular localization or interaction with other cellular proteins. Bacterial E3 ligases may in particular conjugate K48-Ubiquitin chains to host proteins, thereby triggering their proteasomedependent degradation. By re-routing host factors to one of the most efficient proteolytic system of the infected cell, bacteria manage to eliminate key host components that normally interfere with their replication and propagation. Finally, bacterial E3 ligases can also target other bacterial effectors, co-delivered during infection, allowing a tight restriction of their activity during a specific time frame [START_REF] Ashida | Bacterial E3 ligase effectors exploit host ubiquitin systems[END_REF][START_REF] Lin | Exploitation of the host cell ubiquitin machinery by microbial effector proteins[END_REF][START_REF] Kubori | Legionella metaeffector exploits host proteasome to temporally regulate cognate effector[END_REF] (see below).

In contrast to bacterial effectors mimicking host ubiquitin enzymes, a family of proteins secreted by the bacterial pathogen Legionella pneumophila, the causative agent of Legionnaires' disease, was recently shown to catalyze the ubiquitination of host proteins without the need for E1 and E2 Ubiquitin enzymes [START_REF] Qiu | Ubiquitination independent of E1 and E2 enzymes by bacterial effectors[END_REF][START_REF] Bhogaraju | Phosphoribosylation of Ubiquitin Promotes Serine Ubiquitination and Impairs Conventional Ubiquitination[END_REF][START_REF] Kotewicz | A Single Legionella Effector Catalyzes a Multistep Ubiquitination Pathway to Rearrange Tubular Endoplasmic Reticulum for Replication[END_REF]. The Legionella SdeA effector belongs to this family of enzymes: it conjugates Ubiquitin on endoplasmic reticulum (ER)associated Rab GTPases and participate to bacteria virulence [START_REF] Qiu | Ubiquitination independent of E1 and E2 enzymes by bacterial effectors[END_REF]. By acting independently of E1-and E2-Ubiquitin enzymes, SdeA extents the repertoire of proteins potentially modified by Ubiquitin. Conjugation of Ubiquitin on host targets by SdeA does not rely on ATP and does not occur on lysines. Ubiquitin is instead phosphoribosylated by SdeA on a specific arginine residue, before being conjugated to a serine residue of its host target through a phosphodiester bond [START_REF] Bhogaraju | Phosphoribosylation of Ubiquitin Promotes Serine Ubiquitination and Impairs Conventional Ubiquitination[END_REF]. In addition to ER-associated Rab GTPases, the Legionella effector SdeA and other members of the Sde family ubiquitinate the host protein reticulon 4 (Rtn4), leading to ER reorganization and promoting Legionella-containing vacuoles formation [START_REF] Kotewicz | A Single Legionella Effector Catalyzes a Multistep Ubiquitination Pathway to Rearrange Tubular Endoplasmic Reticulum for Replication[END_REF]. Unconventional Ubiquitin conjugation by Sde effectors is reversible as L. pneumophila codes for a specific deubiquitinase, SidJ, that removes phosphoribosylated Ubiquitin from its substrate [START_REF] Qiu | A unique deubiquitinase that deconjugates phosphoribosyl-linked protein ubiquitination[END_REF].

Whether functional homologs of SdeA exist in eukaryotes and what roles they may play remain to be determined.

Deconjugation of Ubiquitin and UBL proteins from host targets catalyzed by bacterial effectors

Another strategy used by bacteria to interfere with Ubiquitin or UBL conjugation consists in the secretion into host cells of effectors with isopeptidase activity, which remove Ubiquitin or UBL from their targets (Fig. 1). XopD, for example, is a T3SS effector secreted by the plant pathogen Xanthomonas euvesicatoria, which possesses a SUMO-specific isopeptidase activity [START_REF] Hotson | Xanthomonas type III effector XopD targets SUMO-conjugated proteins in planta[END_REF]. Upon infection of tomato cells, it deconjugates SUMO from the SIERF4 transcription factor to suppress host ethylene production, which constitutes an important pathway of plants anti-bacterial immunity [START_REF] Kim | Xanthomonas type III effector XopD desumoylates tomato transcription factor SlERF4 to suppress ethylene responses and promote pathogen growth[END_REF]. Many other bacterial proteases targeting Ubiquitin or UBLs have been identified in bacterial pathogens including Salmonella, Shigella, Chlamydia, and Legionella, some of them being specific for one UBL while others display cross-reactivity between different UBLs [START_REF] Sheedlo | Structural basis of substrate recognition by a bacterial deubiquitinase important for dynamics of phagosome ubiquitination[END_REF][START_REF] Pruneda | The Molecular Basis for Ubiquitin and Ubiquitin-like Specificities in Bacterial Effector Proteases[END_REF]. Interestingly, several bacterial effectors possessing a deubiquitinase activity display a strong preference for K63-linked chains over K48 or K11 chains [START_REF] Pruneda | The Molecular Basis for Ubiquitin and Ubiquitin-like Specificities in Bacterial Effector Proteases[END_REF]. This may reveal a significant selection pressure for bacteria to interfere with this specific Ubiquitin-modification in order to promote infection.

Direct targeting of Ubiquitin and UBL polypeptides

Ubiquitin itself, as well as other UBLs, can be directly targeted and inactivated by bacterial effectors (Fig. 1). Phosphoribosylation of Ubiquitin for example, catalyzed by the Legionella SdeA effector, was reported to interfere with multiple steps of the ubiquitination cascade [START_REF] Bhogaraju | Phosphoribosylation of Ubiquitin Promotes Serine Ubiquitination and Impairs Conventional Ubiquitination[END_REF].

The presence of phosphoribosylated Ubiquitin in chains further confers resistance to various deubiquitinases [START_REF] Puvar | Ubiquitin Chains Modified by the Bacterial Ligase SdeA Are Protected from Deubiquitinase Hydrolysis[END_REF]. SdeA, by both triggering E1 and E2-independent ubiquitination of specific host targets and by inhibiting ubiquitination of others, thus efficiently controls the host ubiquitinome.

Ubiquitin and NEDD8 are also targeted by a family of bacterial T3SS effectors called Cifs (for cycle inhibiting factors), produced by diverse pathogenic bacteria such as some EPEC or Burkholderia pseudomallei [START_REF] Taieb | Cycle inhibiting factors (cifs): cyclomodulins that usurp the ubiquitindependent degradation pathway of host cells[END_REF]. Cifs directly target NEDD8 and Ubiquitin and catalyse the deamidation of the Gln 40 residue of these polypeptides [START_REF] Cui | Glutamine deamidation and dysfunction of ubiquitin/NEDD8 induced by a bacterial effector family[END_REF]. Deamidation of Ubiquitin interferes with Ubiquitin chain formation, whereas deamidation of NEDD8 blocks the activity of neddylated Cullin-RING E3 Ubiquitin ligases (CRLs) and impairs ubiquitination of several CRL substrates in EPEC-infected cells [START_REF] Cui | Glutamine deamidation and dysfunction of ubiquitin/NEDD8 induced by a bacterial effector family[END_REF][START_REF] Yu | Gln40 deamidation blocks structural reconfiguration and activation of SCF ubiquitin ligase complex by Nedd8[END_REF]. Cifs interfere in particular with the ubiquitination of Perforin-2/MPEG1 (Macrophage-expressed gene 1), an anti-microbial host protein forming pores on bacteria cells, thereby blocking its intracellular trafficking and its bactericidal activity [START_REF] Mccormack | Enteric pathogens deploy cell cycle inhibiting factors to block the bactericidal activity of Perforin-2[END_REF].

Main host pathways targeted by bacteria and regulated by Ubiquitin or UBLs

During infection, bacterial pathogens alter the conjugation of Ubiquitin or UBLs on many different host proteins. These proteins belong to different pathways that are all essential for bacteria to efficiently enter into host cells and replicate therein, or to dampen host anti-bacterial responses. We will here detail some of the pathways tightly regulated by Ubi/UBL modifications and frequently targeted by bacterial pathogens.

The NF-κB pathway

The NF-κB pathway is an essential pillar of innate immunity and inflammation. Activation of this pathway, for example after the detection of bacteria-derived molecules by host sensors, triggers the expression of a wide range of proinflammatory chemokines and cytokines. Not surprisingly, many bacterial effectors target the NF-κB pathway to dampen the host innate immune response. One given pathogen may in particular produce several independent effectors targeting this pathway [START_REF] Rahman | Modulation of NF-kappaB signalling by microbial pathogens[END_REF]. This apparent redundancy of effectors, that all target the same signaling cascade, reflects the diversity of danger signals sensed by the host and triggering this pathway.

One common strategy used by bacterial pathogens to dampen the NF-κB signaling cascade consists in conjugating K48-Ubiquitin chains to essential components of this pathway thereby triggering their proteasome-dependent degradation. Shigella flexneri, for example, uses at least five different effectors to inhibit essential branches of the NF-κB pathway: IpaH1.4 and IpaH2.5 ubiquitinate LUBAC, a complex involved in the activation of the NF-κB pathway that conjugates linear Ubiquitin chains to the NF-κB modulator NEMO [START_REF] De Jong | Shigella flexneri suppresses NF-kappaB activation by inhibiting linear ubiquitin chain ligation[END_REF]; IpaH0722 ubiquitinates TRAF2, a factor involved in the NF-κB pathway activation following the detection of intracytosolic bacteria [START_REF] Ashida | Shigella IpaH0722 E3 ubiquitin ligase effector targets TRAF2 to inhibit PKC-NF-kappaB activity in invaded epithelial cells[END_REF]; IpaH9.8 ubiquitinates NEMO and thereby perturbs the NF-κB activation triggered by bacterial peptidoglycan detection [START_REF] Ashida | A bacterial E3 ubiquitin ligase IpaH9.8 targets NEMO/IKKgamma to dampen the host NF-kappaB-mediated inflammatory response[END_REF].

Besides triggering proteasome-dependent degradation of components of the NF-κB pathway, bacterial pathogens also interfere with the endogenous Ubiquitination of critical NF-κB regulators: as mentioned above, the Shigella OspI effector inhibits the host E2 enzyme UBC13, thereby blocking TRAF6-mediated activation of the NF-κB pathway [START_REF] Sanada | The Shigella flexneri effector OspI deamidates UBC13 to dampen the inflammatory response[END_REF]; OspG, another Shigella effector, binds to and inhibits the host E2 Ubiquitin enzyme UBCH5, involved in IκBα ubiquitination [START_REF] Kim | The Shigella flexneri effector OspG interferes with innate immune responses by targeting ubiquitin-conjugating enzymes[END_REF]; the NleB effector, encoded by EPEC, blocks TRAF2 polyubiquitination, ultimately suppressing NF-κB activation [START_REF] Gao | NleB, a bacterial effector with glycosyltransferase activity, targets GAPDH function to inhibit NF-kappaB activation[END_REF] and NleE, another EPEC effector, inhibits IκBα phosphorylation, which is a prerequisite for its subsequent Ubiquitination and degradation [START_REF] Nadler | The type III secretion effector NleE inhibits NF-kappaB activation[END_REF].

The NF-κB pathway thereby constitutes a nice example of the diverse mechanisms evolved by bacteria to promote or inhibit ubiquitination of a large number of components in a coordinated fashion, resulting in the dampening of an essential arm of the host anti-bacterial response. Of course, these interfering strategies are not restricted to the NF-κB pathway and other important signaling cascades of the innate immune response, such as the IFN response or the activation of inflammasome, can be similarly targeted [START_REF] Ashida | Bacterial E3 ligase effectors exploit host ubiquitin systems[END_REF][START_REF] Suzuki | Shigella IpaH7.8 E3 ubiquitin ligase targets glomulin and activates inflammasomes to demolish macrophages[END_REF].

Host cytoskeleton

Remodeling of the host cytoskeleton is frequently used by intracellular bacterial pathogens to enter into the targeted cells, create a niche where they can efficiently replicate, and disseminate to neighboring cells. Several components of the host cytoskeleton are regulated by Ubiquitin.

RhoGTPases, for example, which control the actin cytoskeleton dynamics, are degraded by the proteasome following Ubiquitin conjugation [START_REF] Nethe | The role of ubiquitylation and degradation in RhoGTPase signalling[END_REF]. Interestingly, the ubiquitination level of RhoGTPases can be modulated during Salmonella infection, suggesting that this bacterium may modulate RhoGTPases turn-over [START_REF] Fiskin | Global Analysis of Host and Bacterial Ubiquitinome in Response to Salmonella Typhimurium Infection[END_REF]. SUMO can be conjugated to different components of the host cytoskeleton as well, including actin itself and actin regulatory proteins, septins or intermediate filaments such as keratins and lamins [START_REF] Alonso | Emerging roles of sumoylation in the regulation of actin, microtubules, intermediate filaments, and septins[END_REF][START_REF] Ribet | SUMOylation of human septins is critical for septin filament bundling and cytokinesis[END_REF]. The role of Ubiquitin and UBL modifications in the regulation of the cytoskeleton is only in its infancy but one can anticipate that it may represent an important target for bacterial pathogens to manipulate the cell architecture.

Transcription factors

In order to exploit host functions, bacterial pathogens remodel the proteome of infected cells. This remodeling may result from deregulation of gene transcription by injection of bacterial proteins such as nucleomodulins that act directly on host nucleus [START_REF] Bierne | When bacteria target the nucleus: the emerging family of nucleomodulins[END_REF], or by interference with host transcription factors, some of them being regulated by Ubiquitin or UBLs. Listeria monocytogenes, for example, dampens the SUMOylation of numerous transcription factors during infection [START_REF] Impens | Mapping of SUMO sites and analysis of SUMOylation changes induced by external stimuli[END_REF]. As SUMO conjugation either increases or decreases transcription factors activity, this decrease in SUMOylation may modulate the expression of specific subset of genes and lead to a reprogramming of host gene expression. As mentioned above, decreasing the SUMOylation of host transcription factors is a strategy also used by the plant pathogen Xanthomonas euvesicatoria that specifically targets SUMO-SIERF4 to dampen the host ethylene-mediated antibacterial response [START_REF] Kim | Xanthomonas type III effector XopD desumoylates tomato transcription factor SlERF4 to suppress ethylene responses and promote pathogen growth[END_REF]. Finally, the colibactin toxin, produced by some Escherichia coli strains in the intestine, induces a downregulation of the SUMO isopeptidase SENP1 and an increase in the SUMOylation of the transcription factor p53. This ultimately results in the emergence of senescent cells secreting growth factors that may promote colorectal carcinogenesis [START_REF] Cougnoux | Bacterial genotoxin colibactin promotes colon tumour growth by inducing a senescence-associated secretory phenotype[END_REF].

PML Nuclear Bodies

PML (Promyelocytic Luekemia Protein) is a protein that polymerizes in discrete nuclear assemblies known as PML nuclear bodies (NBs) and plays essential roles in many different cellular processes. Key to its function, PML can be post-translationally modified by SUMO. In addition to its role in anti-viral host defense [START_REF] Everett | Interplay between viruses and host sumoylation pathways[END_REF], PML was recently identified as a sensor for bacteria producing pore-forming toxins [START_REF] Ribet | Promyelocytic Leukemia Protein (PML) Controls Listeria monocytogenes Infection[END_REF]. Indeed, intoxication of human cells by the Listeriolysin O toxin, secreted by L. monocytogenes, triggers a massive deSUMOylation of PML. This deSUMOylation of PML, coupled to an oxidative stress-dependent multimerization of PML, initiates host cell anti-bacterial responses leading to a decrease in Listeria intracellular replication [START_REF] Ribet | Promyelocytic Leukemia Protein (PML) Controls Listeria monocytogenes Infection[END_REF]. This example of PML highlights how SUMO alterations of some specific host proteins can constitute danger signals for the cells that triggers back adapted responses. The putative role of PML in other bacterial infections targeting host SUMOylation, such as Shigella or Salmonella, remains unknown but would deserves further investigation.

Post-translational modifications of bacterial proteins during infection

Besides interfering with host proteins post-translational modifications, bacteria can hijack host Ubiquitin or UBL-conjugation machineries to modify their own components (Fig. 1). As for eukaryotic proteins, conjugation of Ubiquitin or UBL have diverse effects on bacterial effectors and may change their intracellular localization, their stability or their interaction with other bacterial or host factors. Post-translational modification of bacterial proteins couples their activity to their arrival into the host cell cytoplasm. Interestingly, post-translational modification of bacterial proteins can also be used by the host to tag exogenous proteins and target them for degradation.

Ubiquitination of Salmonella proteins constitutes a nice example illustrating the versatility of consequences of this post-translational modification on bacterial proteins activity. SopE and SptP are two Salmonella effectors that contribute to the transient remodeling of the host cell's cytoskeleton. These two effectors, which are delivered simultaneously by Salmonella, exhibit different half-lives. SopE, which is involved in actin cytoskeleton rearrangement, membrane ruffling and bacteria uptake, is rapidly polyubiquitinated and degraded by the host proteasome [START_REF] Kubori | Temporal regulation of salmonella virulence effector function by proteasome-dependent protein degradation[END_REF]. SptP, which displays an opposite activity to SopE, exhibits a much slower degradation kinetics, allowing recovery of the actin cytoskeleton's normal architecture a few hours after infection [START_REF] Kubori | Temporal regulation of salmonella virulence effector function by proteasome-dependent protein degradation[END_REF]. Conjugation of Ubiquitin to SopB, a phosphoinositode phosphatase secreted by Salmonella via T3SS, modifies its cellular localization [START_REF] Patel | Diversification of a Salmonella virulence protein function by ubiquitin-dependent differential localization[END_REF]. Upon delivery, SopB associates with the host plasma membrane where it participates to actin-mediated bacterial entry. Later on, Ubiquitination of SopB by TRAF6 leads to its translocation to the Salmonella-containing vacuoles, where it modulates vesicle trafficking and interferes with the delivery of these vacuoles to lysosomes [START_REF] Patel | Diversification of a Salmonella virulence protein function by ubiquitin-dependent differential localization[END_REF][START_REF] Knodler | Ubiquitination of the bacterial inositol phosphatase, SopB, regulates its biological activity at the plasma membrane[END_REF]. Mass spectrometry-based large-scale analysis of the Ubiquitinome of cells infected by Salmonella recently provided additional examples of bacterial proteins modified by Ubiquitin [START_REF] Fiskin | Global Analysis of Host and Bacterial Ubiquitinome in Response to Salmonella Typhimurium Infection[END_REF]. In addition to the previsouly reported SopE and SopB, several effectors were identified as being ubiquitinated during infection. Interestingly, integral outer membrane proteins were reported to be conjugated to Ubiquitin and may represent the targets forming the Ubiquitin coat surrounding cytosolic bacteria and involved in host anti-bacterial autophagy [START_REF] Fiskin | Global Analysis of Host and Bacterial Ubiquitinome in Response to Salmonella Typhimurium Infection[END_REF][START_REF] Veiga | Ubiquitination of intracellular bacteria: a new bacteriasensing system?[END_REF]. Indeed, autophagy of invasive bacteria serves as a cellular autonomous immune mechanism. During this process, a dense coat of poly-Ubiquitin chains is formed around bacteria, which serves as pathogen recognition receptor and directs intracellular bacteria for autophagic degradation [START_REF] Veiga | Ubiquitination of intracellular bacteria: a new bacteriasensing system?[END_REF][START_REF] Dikic | Proteasomal and Autophagic Degradation Systems[END_REF].

In contrast to Ubiquitination, only few bacterial proteins were reported so far to be modified by SUMO and the biological consequences of these modifications during infection often remains elusive. These SUMO-modified bacterial proteins include two effectors, TRP120 and AmpA, secreted by two intracellular pathogens, Ehrlichia chaffeensis and Anaplasma phagocytophilum respectively [START_REF] Dunphy | Ehrlichia chaffeensis exploits host SUMOylation pathways to mediate effector-host interactions and promote intracellular survival[END_REF][START_REF] Beyer | The Anaplasma phagocytophilum effector AmpA hijacks host cell SUMOylation[END_REF]. OspF, an effector secreted by Shigella flexneri, constitutes another example for which SUMO conjugation is required for the translocation of this effector into the host nucleus where it modulates the expression of proinflammatory cytokines [START_REF] Jo | Host Cell Nuclear Localization of Shigella flexneri Effector OspF Is Facilitated by SUMOylation[END_REF].

One can anticipate that recently developed techniques for large scale proteomic studies of UBL conjugation will increase the list of bacterial proteins modified by SUMO or other UBLs, and provide new insights in the role of these modifications during infection.

Concluding Remarks and Future Perspectives

Ubiquitin and UBL are essential post-translational modifiers of eukaryotic cells. Thousands of Ubi/UBL targets have been identified during these last years, suggesting that most proteins will be modified by this type of PTMs at some point in their cellular lifetime. It is thus not surprising that pathogens evolved so many strategies to interfere with these particular PTMs in order to manipulate host cell physiology. Harnessing of host Ubi/UBL systems is in particular observed both for intracellular pathogens, that tightly interact with host cell cytoplasmic components to create for example a protective niche where they can acquire nutrients from the host, and for extracellular pathogens, that manipulate host cells to favor their maintenance at the surface of the cells or dampen host immune responses.

Thanks to the continuous improvement in proteomic analyses, the list of proteins known to be modified by Ubiquitin or UBLs has greatly expanded during these last years. It is in particular now feasible to compare the variations of the ubiquitinome (or other "UBL-ome") of cells during infection by a pathogen or after exposure to a bacterial toxin [START_REF] Impens | Mapping of SUMO sites and analysis of SUMOylation changes induced by external stimuli[END_REF][START_REF] Fiskin | Global Analysis of Host and Bacterial Ubiquitinome in Response to Salmonella Typhimurium Infection[END_REF]. Some of these techniques are furthermore compatible with in vivo analysis and the comparison of the content of proteins modified by Ubi/UBL in organs from infected or control animals is now possible [START_REF] Xu | Global analysis of lysine ubiquitination by ubiquitin remnant immunoaffinity profiling[END_REF][START_REF] Becker | Detecting endogenous SUMO targets in mammalian cells and tissues[END_REF]. Interestingly, current proteomic-based approaches not only reveal the identity of the proteins modified by Ubi/UBL but also the modifications sites. These data are critical for further analysis of the role of these PTM in the function of the identified protein and hence, to decipher the consequences of bacterial alteration of these PTMs. Several recent studies on ubiquitin conjugation revealed that ubiquitination establishes a much more complex code than originally thought. Indeed, in addition to "mixed" ubiquitin chains involving different types of linkages between Ubiquitin monomers, chains mixing ubiquitin and other UBLs such as SUMO have also been reported [START_REF] Yau | The increasing complexity of the ubiquitin code[END_REF][START_REF] Swatek | Ubiquitin modifications[END_REF][START_REF] Herhaus | Expanding the ubiquitin code through post-translational modification[END_REF]. In addition, Ubiquitin has recently been found to be itself post-translationally modified by acetylation or phosphorylation, which further expands the repertoire of ubiquitination [START_REF] Yau | The increasing complexity of the ubiquitin code[END_REF][START_REF] Swatek | Ubiquitin modifications[END_REF][START_REF] Herhaus | Expanding the ubiquitin code through post-translational modification[END_REF]. We are only beginning to understand the tremendous diversity of Ubiquitin modifications and their roles in cell biology but it is very likely that bacterial pathogens have long learned how to break this so-called "Ubiquitin code" and efficiently use it for their own profit (see Outstanding Questions). Finally, while this review focused on pathogenic bacteria, some non pathogenic bacteria such as commensals of the intestinal microbiota were also reported to interfere with host Ubi/UBL systems [START_REF] Collier-Hyams | Cutting edge: bacterial modulation of epithelial signaling via changes in neddylation of cullin-1[END_REF]. For example, production of butyrate by commensal bacteria leads to the inactivation of the E2 NEDD8 enzyme in intestinal epithelial cells and was proposed to participate to the inflammatory tolerance of gut bacteria [START_REF] Kumar | Commensal bacteria modulate cullin-dependent signaling via generation of reactive oxygen species[END_REF][START_REF] Kumar | The bacterial fermentation product butyrate influences epithelial signaling via reactive oxygen species-mediated changes in cullin-1 neddylation[END_REF]. Some intestinal bacteria may even usurp host ubiquitin for their own purpose. Indeed, even though most bacteria lack Ubiquitin or UBL genes, a Ubiquitin gene has been identified in the genome of some Bacteroides fragilis strains [START_REF] Patrick | A unique homologue of the eukaryotic protein-modifier ubiquitin present in the bacterium Bacteroides fragilis, a predominant resident of the human gastrointestinal tract[END_REF][START_REF] Chatzidaki-Livanis | Gut Symbiont Bacteroides fragilis Secretes a Eukaryotic-Like Ubiquitin Protein That Mediates Intraspecies Antagonism[END_REF]. Interestingly, this eukaryotic-like Ubiquitin, which was probably acquired via horizontal gene transfer, does not seem to be involved in bacterial protein modification since it lacks the critical terminal glycine residue. This protein is instead secreted and acts as a bacterial toxin targeting and killing other intestinal bacteria [START_REF] Chatzidaki-Livanis | Gut Symbiont Bacteroides fragilis Secretes a Eukaryotic-Like Ubiquitin Protein That Mediates Intraspecies Antagonism[END_REF]. Many other surprises like this one are probably still awaiting to be discovered and, even though the first report of a bacterium post-translationally modifying a host protein occurred almost 50 years ago [START_REF] Collier | Diphtheria toxin subunit active in vitro[END_REF], the field of pathogen and host post-translational modifications is, without a doubt, still very promising.

Figure 1 :

 1 Figure 1 : Main strategies used by bacterial pathogens to interfere with host Ubiquitin or

Table 1 : Examples of bacterial proteins interfering with Ubi/UBL conjugation to host proteins

 1

	Ubi/UBL target	Bacteria	Extra/intracellular bacteria	Effector	Enzymatic activity	Effect

Acknowledgments

We apologize to all colleagues whose work we were unable to include due to space constraints.

Authors received support from

Institut Pasteur, INSERM, INRA, the French National Research Agency (ANR) (ERANET Infect-ERA PROANTILIS ANR-13-IFEC-0004-02), the French Government's Investissement d'Avenir program, Laboratoire d'Excellence "Integrative Biology of Emerging Infectious Diseases" (ANR-10-LABX-62-IBEID), the European Research Council (ERC) (H2020-ERC-2014-ADG 670823-BacCellEpi), the Fondation le Roch les Mousquetaires, the Fondation Louis-Jeantet and the International Balzan Prize Fondation. D.R. is a Research Associate from INSERM and P.C. is a Senior International Research Scholar of the Howard Hughes Medical Institute.


W F Faris

H M Mohammed

M M Abdalla
email: m.m.abdalla@lr.tudelft.nl

C H Ling

INFLUENCE OF MICRO-CANTILEVER GEOMETRY AND GAP ON PULL-IN VOLTAGE

In this paper, we study the behaviour of a microcantilever beam under electrostatic actuation using finite difference method. This problem has a lot of applications in MEMS based devices like accelerometers, switches and others.

In this paper, we formulated the problem of a cantilever beam with proof mass at its end and carried out the finite difference solution. we studied the effects of length, width, and the gap size on the pull-in voltage using data that are available in the literature. Also, the stability limit is compared with the single degree of freedom commonly used in the earlier literature as an approximation to calculate the pull-in voltage.

INTRODUCTION

Microsensors represent a large section of microsystems' market. Microsensors offer the advantage of replacing conventional sensors in a one to one fashion while saving weight, energy and cost [START_REF] El-Hak | The MEMS Handbook[END_REF]. Several studies have investigated the behaviour of electrostatically actuated microbeams in microsensors. Yang et al. [START_REF] Yang | macromodeling of Coupled-Domain MEMS Devices with Electrostatic and Electrothermal Effects[END_REF] modelled a clamped-clamped beam with length 350 µm. The model is test by passing four steps electrostatic voltage of 21V, 22V, 25V and 30V. The model is solved by finite differential method (FDM) then compared with the results from the reduced model generated by Karhunen-Loeve/ Galerkin approach. The macromodel method saves more time (about 502.1 speed up factor) and only contribute about 0.9% error. Hu et al. [START_REF] Hu | Some Design Considerations on the Electrostatically Actuated Microstructures[END_REF] solved a model of microcantilever beam with analytical Reileigh Riz method. The purpose of this paper is to verify the validity of neglecting the higher terms in the electrostatic force term. The result shows that it only valid when the applied voltages are below the pull in voltage. Hu also do a dynamic analysis of the beam subjected to an AC bias using Runge Kutta method to solve ordinary differential equation. Hu found that the resonant frequencies decrease with the increasing magnitude of applying voltage. Nayfeh and Younis [START_REF] Nayfeh | A New Approach to the Modeling and Simulation of Flexible Microstructures Under the Effect of Squeeze Film Damping[END_REF] presented a new approach to the modelling and simulation of flexible microstructures under the effect of squeeze-film damping. They applied perturbation methods to the compressible Reynolds equation and solved the equation using finite element method. The results compared to which get from experiment are acceptable. The further analysis was done on fully clamped and clamped-free-clamped-free plate. Abdel-Rahman et al. [START_REF] Abdel-Rahman | Characterization of the Mechanical Behavior of an Electrically Actuated Microbeam[END_REF] modelled a plate clamped at both ends and free along its width. They used shooting method to solve and compared the results from previous results. There are good agreement between them. At last, they concluded that one may use α 1 (6 x gap distance/thickness) or axial force to stiffen the microbeam. However, only α 1 are used to tune the relationship between the natural frequency and voltage. Collenz et al. [START_REF] Collenz | large Deflections of Microbeams under Electrostatic Loads[END_REF] developed an alternative approach based on a sequential field-coupling (SFC) algorithm to deal with strongly non-conservative electrostatic loads. Collenz modelled a cantilever beam with length to gap ratio of one (l/g =1). Collenz found that pull in cannot occur because the gap is as big as the beam length, therefore the beam tip cannot touch the underlying plane. Hung and Senturia [START_REF] Hung | Generating Efficient Dynamical Models for Microelectromechanical Systems from Few Finite Element Simulation Runs[END_REF] focused on obtaining macromodels based on global basis functions generation from an approach that is mathematically equivalent to Karhunen-Loeve/ Galerkin analysis of a small but representative ensemble of dynamic FEM runs. They found that macromodel speed up simulation by a factor of 37 over a FDM with less than 2% error. Faris and Abdalla [START_REF] Faris | Effect of Temperature and geometric Nonlinearity in MEMS-Based Diaphragm Devices Modelling[END_REF] used Galerkin approximation approach to solve MEMS based sensor under thermal loading.

W. Faris, H.M. Mohammed, M.M. Abdalla, and C. H. Ling INFLUENCE OF MICRO-CANTILEVER GEOMETRY AND GAP ON PULL-IN VOLTAGE.

Finite difference was not exploited in the solution of MEMS based problems, though in our opinion it is quite effective for a domain of problems which are easily formulated mathematically.

MODELING OF A MICRO-BEAM

Figure 1 Cantilever Beam with a Lumped Mass at the End Our model is a cantilever beam with a proof mass suspended at the end as shown in Figure 1. We apply Hamilton principle in developing models to analyze beam behaviour. Hamilton principle is a consideration of the motion of an entire system between two times, t 1 and t 2 . The extended Hamilton's principle:

2 0 1 ( , ) 1 ( , ) ( ) 2 2 L y x t y L t T m x dx M t t ∂ ∂ ⎡ ⎤ ⎡ ⎤ = + ⎢ ⎥ ⎢ ⎥ ∂ ∂ ⎣ ⎦ ⎣ ⎦ ∫ , (2)
and the strain energy (internal potential) is stated as:

2 2 2 0 1 (,) ( ) ( ) 2 L y x t V t EI x dx x ⎡ ⎤ ∂ = ⎢ ⎥ ∂ ⎣ ⎦ ∫ , (3)
The virtual work of the nonconservative distributed forces is expressed as:

0 ( ) ( , ) ( , ) nc L W t f x t y x t dx δ δ = ∫ (4)
Substituting into Hamilton's principle (1), we obtain:

2 2 2 2 2 2 ( , ) ( , ) ( ) ( , ) ( ) y x t y x t EI x f x t m x x x t ⎡ ⎤ ∂ ∂ ∂ - + = ⎢ ⎥ ∂ ∂ ∂ ⎣ ⎦ (5a)
and the boundary conditions at 0 x = ( , ) ( , ) 0, 0, y x t y x t x

∂ = = ∂ (5b) and at x L = 2 2 2 2 2 2 ( , ) ( , ) ( , ) ( ) 0, ( ) 0, y x t y x t y x t EI x EI x M x x x t ⎡ ⎤ ∂ ∂ ∂ ∂ = - = ⎢ ⎥ ∂ ∂ ∂ ∂ ⎣ ⎦
(5c) In the rest of the paper, we assume the I(x) and m(x) are constant over the length of the beam. It is our interest to consider the effect of electrostatic forces on the response of the microbeam. The electrostatic load depends on the beam deflection as:

2 2 ( ) 2( ) bV f x G y ε = - (6a)
Where As a result, equation ( 5) can be expressed as:

4 2 2 4 2 2 ( , ) ( , ) 2(
)

y x t bV y x t EI m x G y t ∂ ε ∂ - + = ∂ - ∂ (6b)

SYSTEM GOVERNING EQUATIONS

We consider a cantilever beam with a proof mass suspended at the end, actuated by an electrostatic force which consists of a DC component, V p and an AC component v(t). We assume that the transverse deflection of beam, y, is constant along the width of beam. The beam equation and its boundary conditions at 0 x = and at x L = can be expressed as: As a result, the beam equation can be modified as ( ) ( , ) 0, 0, at

( ) 2 4 2 4 2 2 ( ) ( , ) ( , ) 2( )
p b V v t y x t y x t EI m x t G y ε + ∂ ∂ + = ∂ ∂ - (7) ( , ) ( , ) 0, 0, 0 y x t y x t x x ∂ = = = ∂ (7a) 2 3 2 2 3 2 ( , ) ( , ) ( , ) 0, 0, y x t y x t y x t EI EI M x L x x t ∂ ∂ ∂ = - = = ∂ ∂ ∂ (
2 4 4 2 4 4 2 2 ( ) 2( ) p s s b V v t y u u EI m x x t G y u ε + ⎡ ⎤ ∂ ∂ ∂ + + = ⎢ ⎥ ∂ ∂ ∂ -- ⎣ ⎦ (
s s y y y x t EI E I M x L x x t ∂ ∂ ∂ = - = = ∂ ∂ ∂ (10b)
To solve the eigenvalue problem, we set AC forcing term in equation ( 9) equal to zero and use equation ( 10) to eliminate the term representing equilibrium position.

ε ε ⎡ ⎤ = + + + ⎢ ⎥ -- - - - ⎣ ⎦
(12) Based on the small displacement assumption, the higher order terms can be neglected, thus the nonlinear electrostatic force can be linearized as

2 2 2 2 3 1 2 2( ) 2 ( ) ( ) p p s s s bV bV u G y u G y G y ε ε ⎡ ⎤ = + ⎢ ⎥ -- - - ⎣ ⎦ (
p s bV u u EI m u x t G y ε ∂ ∂ + - = ∂ ∂ - (14)
.

FINITE DIFFERENCE SOLUTION

Refer to the grid below, by assuming that at 0 x = , 3 i = and at 0 t = ,

ε - - + + - - - - ⎡ ⎤ ⎣ ⎦ ⎡ ⎤ ⎣ ⎦ - - + - + + - = - + - + (
- - + + ⎡ ⎤ ⎣ ⎦ - + - + - = (15c) 2, 1, 1, 2, 3 , , 4 , 3 , 2 , 1 2 2 2 2
- - + + - - - - ⎡ ⎤ ⎣ ⎦ ⎡ ⎤ ⎣ ⎦ - + - + - + - + (
⎡ ⎤ = + - ⎣ ⎦ (17b) 3, 0 j y = , (17c)
⎡ ⎤ ⎣ ⎦ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ (
A y y y y i j i j i j i j G y i j y i j A C C y y y y i j i j i j i j B ⎧ ⎫ ⎡ ⎤ - - - + ⎪ ⎪ ⎢ ⎥ + + ⎣ ⎦ ⎪ ⎪ - = ⎨ ⎬ + ⎪ ⎪ ⎡ ⎤ - - + - ⎪ ⎪ ⎢ ⎥ ⎣ ⎦ ⎩ ⎭ (20d) 1 16 30 , 1, 4, 3, 2, 16 y y y y y N j N j N j N j N j ⎡ ⎤ = - + + - - - - ⎢ ⎥ ⎣ ⎦ (20e) , 4, 3, 1, 2, 4 2, 3 2, 2 2, 1 2, 2 2
11 56 114 104 35 N j N j N j N j N j N j N j N j N j y y y y D y y y y y F - - - -- -- -- -- - ⎡ ⎤ = ⎣ ⎦ ⎡ ⎤ + ⎣ ⎦ - + - + - + (20f)
.

RESULTS AND ANALYSIS

In this paper, we study the behavior of a microbeam under a nonlinear electrostatic force. First, we present a numerical procedure to solve the static behaviour or boundary value problem of a microbeam under DC electrostatic force. We are interested in finding the pull-in voltages corresponding to static deflection at different beam lengths. Second, we determine the natural frequencies and mode shapes of microbeam under DC electrostatic force. Equations (10) describe the microbeam static deflection under static electrostatic force. We use finite difference method to solve the problem numerically for s y .

2( )

p s s bV y EI x G y ε ∂ = ∂ - (21) 0, 0, at 0 s s y y x x ∂ = = = ∂ (21a) 2 3 2 2 3 2 ( , ) 0, 0, at s s y y y x t EI EI M x L x x t ∂ ∂ ∂ = - = = ∂ ∂ ∂ (21b)
We initially set 0 s y as zero and iterate until it converge to a value within 0.1%. Considering a cantilever beam with a mass suspended at the end made of silicon. The geometries and material parameter are given in table 2330 kg/m 3 Free Space Permittivity (ε) 8.8541878 x 10 -12 (F/m) Table 1 The Geometric and Material Parameters of the Microbeam We solve equations (21) for a range of electrostatic forces by changing the applied voltage. Then, we will change the length (L) to see its effect on static with respect to applied voltages (V p ). Figure 3 shows the deflection along the microbeam with dimensions L = 300 µm, W = 50 µm, t = 3 µm, G = 3 µm at voltage = 10 V. The beam is fixed at one end. The more distance the point from the fixed end is, the larger will be the deflection. .

W. Faris, H.M. Mohammed, M.M. Abdalla, and C. H. Ling INFLUENCE OF MICRO-CANTILEVER GEOMETRY AND GAP ON PULL-IN VOLTAGE.

CONCLUSIONS

In this paper, we formulate the problem of a cantilever beam with proof mass at the end which is used in many applications, most notably is MEMS based accelerometer. We used Hamiltonian principle as a tool of this formulation. Also, we explained the solution using finite difference technique. We solved the static part of the problem and decided the pull-in voltage for different geometric parameters of the beam. The parameters studied were beam length, thickness, width, and gap. The finite difference method proved to be effective and easy to code for solving such problems. The length and thickness were found to have a great influence on the pull-in voltage while the width was found of no influence on the pull-in voltage. The gap also was found to have a significant influence on the pull-in results as well. Also, it was found that the stability limits from the single degree of freedom approximation is quite erroneous compared to full geometry calculations. .

ACKNOWLEDGEMENT

The first author would like to thank the Research Center at IIUM for the financial support to carry out this work..

W. Faris, H.M. Mohammed, M.M. Abdalla, and C. H. Ling INFLUENCE OF MICRO-CANTILEVER GEOMETRY AND GAP ON PULL-IN VOLTAGE.

where A is the area of the capacitor. The electric force and spring constant with fixed potential may be obtained by differentiations, ( ) ( )

2 3 2 3 PI m V A K G ε = ( 7 )

  start derive the beam bending equation by write the kinetic energy expansion of the beam:

2

 2

  : E = Young Modulus, m = mass per unit length of beam, I = bh 3 /12 = cross section area moment of inertia, b = width of beam, h = height of beam, G = gap distance, ε = free space permittivity or dielectric constant of vacuum, t = time.

  7b) Where: E = Young Modulus, m = mass per unit length of beam, I = bh 3 /12 = cross section area moment of inertia, b = width of beam, h = height of beam, G = gap distance, ε = free space permittivity or dielectric constant of vacuum, t = time. The microbeam deflection under an electric force is composed of static component due to the DC voltage, termed as ( ) s y x and dynamic component due to the AC voltage, termed as ( ) , u x t that is: W. Faris, H.M. Mohammed, M.M. Abdalla, and C. H. Ling INFLUENCE OF MICRO-CANTILEVER GEOMETRY AND GAP ON PULL-IN VOLTAGE.

  9)To calculate static deflection, s y , we put time derivation and the AC forcing term in equation (9) equal to zero and obtain

  Expanding the nonlinear electrostatic force term by Taylor series with respect to equilibrium position,

Figure 2

 2 Figure 2 Grid Point for the Dynamic Behavior Proble( )

  15d) According to the assumption stated above, at 0 x = , 3 i = , from the boundary condition (22a) and (22b)

  19b) To facilitate in programming, we assume that

Figure 3

 3 Figure 3 Static Deflection of Microbeam ( L = 300 µm, W = 50 µm, t = 3 µm, G = 3 µm and Voltage = 10 V) Figure 4 shows the variation of the maximum static deflection of microbeam, max ( ) s s W Y y x L = = = , with applied voltages for L=200 µm, 225 µm, 250 µm, 275 µm and 300 µm. Other geometry dimensions are remaining same. The dashed line represents the stability limit, W max = / 3 G predicted by the single-degree-offreedom spring-mass model. As applied voltage increases, the maximum deflection increases. The slope of maximum deflection, max p y V ∂ ∂ , increases as the voltage increases and finally approach infinity when it reaches pull in voltage. Beside this, maximum deflection is also larger for longer beam. This relationship is linear at low voltage and becomes increasingly nonlinear when the voltage applied is increased. The slope of maximum deflection, max p y V ∂ ∂ , is larger for longer beam at specific voltage. As a result, microbeam with shorter length can sustain larger voltage before it collapses. Variations of the maximum deflection with voltage for various thicknesses are shown in figure 5. As voltage increases, static deflection increases. At specific voltage, maximum deflection increasing as thickness is reduced. The slope of maximum deflection, max p y V ∂ ∂ , increases more rapidly for thin beam. This proves that the pull in voltage is larger for thicker beam.

Figure 4

 4 Figure 4 Variation of maximum Deflection with applied Voltage until Pull-In for L=200 µm, 225 µm, 250 µm, 275 µm and 300 µm.

Figure 5

 5 Figure 5 Variation of the Maximum Deflection with Voltage until Pull-In for t=2 µm, 2.5 µm, 3 µm, 3.5 µm and 4 µm. Gap distance has influence on the static deflection too.As represent in Figure6, static deflection will be reducing when the gap between microbeam and support is increased..

Figure 6

 6 Figure 6 Variation of the Maximum Deflection with Voltage for until Pull-In for G=2 µm, 2.5 µm, 3 µm, 3.5 µm and 4 µm..

  voltage driven electro-mechanical systems. It may equally well be written as of the elasticity. For linear cases 1 γ = by definition. Equation (4) provides a starting point for the pull-in iteration scheme.In the one-dimensional case the electric field has an analytical solution, ()E V G y = -, where G is the initial aperture between the mass and the ground level. The electric energy now yields

  the above formulas in Equation (4) and solving for the pull-in position gives 3 y G =. The relative displacement of 1/ 3 is a characteristic value for this one-dimensional case. Also more complicated cases have values independent of the scale and of the material parameters.The pull-in voltage can be obtained from equation (1) by equating electric and mechanical spring constants,

W. Faris

In addition, for 2, i N =we have to consider another two boundary condition to find

Appendix One-Dimensional Pull-In Voltage Analysis

When a voltage is applied between two electrodes, the electrostatic force between them pulls them together. The restoring force of the beam, arising from the beam's stiffness, resists the electrostatic force. When the voltage is increased, a point is reached where the electrostatic force equals the spring restoring force of the beam. If this point, known as pull-in voltage, is passed, the beam will snap to the substrate.

In one-dimensional geometries, the pull-in phenomenon is greatly simplified and the basic dependencies are easily visible. Now, the displacement field is just a scalar y, and the mechanical force, m


J Lu

T Ikehara

T Kobayashi

R Maeda

T Mihara

QUALITY FACTOR OF PZT THIN FILM TRANSDUCED MICRO CANTILEVERS

Keywords: quality factor, PZT film, micro cantilever, micro resonator, MEMS

In this paper, quality factor (Q-factor) of piezoelectric Pb(Zr,Ti)O 3 (PZT) thin film transduced micro cantilevers were investigated under atmospheric pressure. The mechanisms for energy loss during cantilever vibration were analyzed and discussed. It was found that Q-factor increases with the increase of PZT thickness while keeping other cantilever geometries unchanged. Shorter cantilever, especially when cantilever length to width ratio less than 2, results in preferred larger Q-factor, which can be as high as 450 when using 1.04µm-thick PZT film as the electromechanical conversion medium. Moreover, our results indicate that dielectric loss in PZT film and thermoelectric loss are significant as well as air damping even when PZT cantilever was actuated at atmospheric conditions.

INTRODUCTION

Piezoelectrically transduced micro resonators have become an attractive research topic in recent years since it has potential applications in ultra-small mass detectors, bio-sensors, RF filters and high frequency micro oscillators [START_REF] Yan | High frequency filters based on piezoelectrically transduced micromechanical resonators[END_REF]~ [START_REF] Shih | Simultaneous liquid viscosity and density determination with piezoelectric unimorph cantilevers[END_REF]. Compared with electrostatically actuated and sensed capacitive silicon micro resonator [START_REF] Hao | VHF singlecrystal silicon elliptic bulk-mode capacitive disk resonators --part I: design and modeling[END_REF] [START_REF] Pourkamali | VHF singlecrystal silicon elliptic bulk-mode capacitive disk resonators --part II: implementation and characterization[END_REF], piezoelectrically transduced micro resonator exhibits better impedance matching with electronics so that sub-100nm gap spacing can be avoided in device fabrication. Piezoelectrically transduced micro resonator also provides better power handing capability than capacitive type since low driving-voltage of several hundreds of millivolts is enough for resonator actuation [START_REF] Adams | Nanowatt chemical vapor detection with a selfsensing, piezoelectric microcantilever array[END_REF], which facilitates the integration of micro resonators with CMOS signal processing circuits.

To achieve ultra-high resonator sensitivity, high quality factor (Q-factor) is most desirable in resonator design and fabrication. However, up to date, Q-factor of piezoelectrically transduced micro resonator is still lower than that of conventional capacitive type even under atmospheric pressure [START_REF] Pourkamali | VHF singlecrystal silicon elliptic bulk-mode capacitive disk resonators --part II: implementation and characterization[END_REF] [START_REF] Ye | A 1.14GHz piezoelectrically transduced disk resonator[END_REF], where air damping is believed much larger than other energy dissipation mechanisms. It limits its application on occasions when both ultra-high sensitivity and atmospheric environment are required, such as chemical vapor/molecule detection [START_REF] Adams | Nanowatt chemical vapor detection with a selfsensing, piezoelectric microcantilever array[END_REF] and living cells observation [START_REF] Gogers | High speed tapping mode atomic force microscopy in liquid using an insulated piezoelectric cantilever[END_REF].

In this paper, in order to better understand the energy dissipation mechanisms in piezoelectrically transduced micro resonators at atmospheric conditions, which is believed more complex due to electromechanical coupling in piezoelectric thin film and multi-layered device structure, Pb(Ti, Zi)O 3 (PZT) thin film transduced micro cantilevers with different PZT thicknesses and cantilever geometry were fabricated. Then their Q-factors under atmospheric pressure were investigated and compared. Here, (100) oriented PZT thin film was chosen as the electromechanical conversion medium due to its excellent mechanical and piezoelectric properties. Furthermore, the affections of cantilever structure as well as PZT film on performance of PZT cantilever were analyzed and discussed.

EXPERIMENTS

Fig. 1 shows the structure of our PZT thin film transduced micro cantilever. It is composed of SiO 2 structure layer, Platinum(Pt)/Titanium(Ti) bottom electrode (Ti was used as adhesion layer between SiO 2 and Pt), PZT thin film, Ti/Pt/Ti top electrode and SiO 2 electric passivation layer. The fabrication process starts from thermal oxidized silicon wafer. The thickness of SiO 2 is 2.3µm. Fig. 2 In this study, Q-factor of the PZT cantilever was defined as the ratio of cantilever resonant frequency resonance f to bandwidth at -3dB power 3dB -

f ∆ : 3dB - resonance f f Q ∆ = Eq.1
Although PZT cantilever has self-sensing function as well as self-actuation, Q-factor of the cantilevers were detected by a Laser Doppler Vibrometer (LT7901, GRAPHTEC Co.) then analyzed by a Network Analyzer (HP4395A, Agilent Technogies Inc.) to avoid extra noise from following PZT induced current detection circuits and make the measured results comparable. Fig. 3 shows the schematic drawing of our Q-factor measurement system.

RESULTS AND DISSCUSION

In this study, two kinds of PZT cantilevers were fabricated, which marked as A (without triangle tip) and B (with 50µm-long triangle tip), respectively. Fig. 4 shows the SEM images of the fabricated PZT cantilever. Type A is commonly used for the application of molecule sensing while type B is often used for micro probe structures. The measured resonance-peak of the 150µm-long B-type cantilever when actuated by integrated 390nm-thick PZT film was shown in Fig. 5.

In order to investigate the Q-factor dependence on cantilever geometry as well as PZT thickness, measured Q-factors of these cantilevers were summarized in Fig. 6. Obviously, cantilever exhibits preferred larger Q-factor when actuated by thicker PZT film, which increases almost 2 times when PZT thickness varies from 390nm to 1.04µm. Besides, shorter cantilever without triangle tip results in larger Q-factor, especially when cantilever (cantilever-150A), Q-factor was found as high as 450 when using 1.04µm-thick PZT film as the electromechanical conversion medium. It is coincide with the theoretical analysis on single-layered silicon cantilever by F.R.Blom et al. [START_REF] Blom | Dependence of the quality factor of micromachined sillicon beam resonators on pressure and geometry[END_REF], which concluded that thick and short cantilever seems to be more appropriate to obtain a large Q-factor. Since the measurement was performed under atmospheric pressure, air damping is believed essential to energy consumption than other mechanisms [START_REF] Blom | Dependence of the quality factor of micromachined sillicon beam resonators on pressure and geometry[END_REF], such as thermoelastic loss [START_REF] Houston | Thermoelastic loss in microscale oscillators[END_REF], support loss [START_REF] Hao | An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations[END_REF] and surface loss [START_REF] Yang | Investigation surface stress-Surface loss in ultrathin single-crystal silicon cantilevers[END_REF]. Accordingly, Q-factor of the PZT cantilever will be proportional to its peak kinetic energy peak E during vibration, which can be expressed as follows:

2 r peak 2 1 A K E = Eq.2
where A is the vibration amplitude and r K is elastic constant of the cantilever. For multi-layered cantilever, r K is determined by:

∑ ∑ = = - - + = n i i j i j i i i i t t Z t t w Y L K 1 1 2 nt 2 r } )] 2 ( [ 12 { 3 3 Eq.3
where i Y is Young's modulus of layer i ; i t is thickness of layer i ; i w is width of layer i and nt Z is the distance from zero-stress interface in PZT cantilever to its top surface, which can be calculated from equation

∑ ∑ ∑ = = = - = n i i j n i i i i j i i t Y t t t Y Z 1 1 1 nt / ]} 2 [ { . Therefore, thicker
PZT film and shorter cantilever length will contribute to larger cantilever Q-factor through improving cantilever elastic constant r K . It is believed one of the major reasons for Q-factor dependence at atmospheric conditions as shown in Fig. 6.

Besides, we found by wafer-bending stress measurement method that residual stress in PZT film decreases notably when the film thickness increases from 390nm to 1.04µm. It gives us another possible reason on PZT thickness dependent as shown in Fig. 6. Further experiments are under consideration to prove this analysis.

(-6) (+10) (+5) (+8) (-3 ) (+13) (-3) (+37) (+39) (+15 ) (-3) (+9) (+12) (+10 ) (+16) (+6)
Other than air damping, dielectric loss in PZT thin film is another important energy dissipation mechanism for PZT transduced micro cantilevers. According to Don L.DeVoe's study, transfer function of PZT transduced resonator can be expressed as follows [START_REF] Devoe | Piezoelectric thin film micromechanical beam resonators[END_REF]:

2 1 21 ) ( ) ( γ ω ω ωγ = j F j Z j Y
Eq.4

where 1 γ stands for the electromechanical conversion from driving signal to PZT induced mechanical force F for actuation; 2 γ stands for the electromechanical conversion from cantilever deformation Z to PZT induced piezoelectric current output for sensation; and

) ( / ) ( ω ω j F j Z
describes the transfer of mechanical force F to cantilever deformation Z. In order to investigate the affections of dielectric loss in PZT thin film during electromechanical conversion, the fabricated cantilevers were actuated by an external vibrator and the measured Q-factors under atmospheric pressure were shown in Fig. 7. Similar Q-factor dependence on PZT thickness as well as cantilever geometries can be found in the curve, whereas, the differential value in bracket indicates that Qfactor of the cantilever increases a few percent when actuated by external vibrator. When cantilever was actuated by integrated PZT thin film, electromechanical conversion of both 1 γ for actuation and 2 γ for sensation will be involved, while actuated by external vibrator, only 2 γ for sensation will exists. This difference in measured Q-factor reveals that dielectric loss in PZT thin film during electromechanical conversion from driving signal to cantilever deformation is noticeable even under atmospheric conditions.

Moreover, it seems that differential value in the brackets as shown in Fig. 7 decreases with the increase of PZT thickness. Characterization on PZT film's electric properties, piezoelectric properties and microstructures at different film thickness may give us reasonable explanation, while it's still under going.

For multi-layered piezoelectric transduced resonators, thermoelastic damping can be quite significant because internal friction seems easier to happen near interfaces of each layer as well as within crystallographic defects [START_REF] Houston | Thermoelastic loss in microscale oscillators[END_REF] [START_REF] Duwel | Experimental study of thermoelastic damping in MEMS gyros[END_REF]. Fig. 8 shows the measured Q-factor of the fabricated cantilever with different layer structures. Similar Q-factor dependence as shown in Fig. 6 can be found in SiO 2 cantilever (TYPE_A) and SiO 2 +Pt/Ti cantilever (TYPE_B), while after 1.04µm-thick PZT film deposition, Q-factor of the SiO 2 +Pt/Ti+PZT cantilever (TYPE_C) decreases even the thickness of the cantilever increases from 2.5µm to 3.5µm. These differences in the Q-factor can be explained by including the contributions of thermoelastic damping especially in polycrystalline PZT ceramic thin films. After covered by Pt/Ti top electrode and SiO 2 electric passivation layer, Q-factor of the PZT cantilever (TYPE_D) increases again due to improved cantilever elastic constant r K , which includes both Young's modulus and thickness as shown in Eq.3.

Recent [START_REF] Battiston | A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending readout[END_REF]. Piezoelectrically transduced micro resonator is one of the most promising candidates for array application due to its ability to serve as both actuator and sensor. This paper gives us a preliminary impression on energy dissipation mechanisms in piezoelectric PZT thin film transduced micro cantilevers. Further study, especially in reduced pressure to find the intrinsic Q-factor of the PZT cantilever, is keeps going to describe the principle more precisely. Moreover, as described in literature [START_REF] Blom | Dependence of the quality factor of micromachined sillicon beam resonators on pressure and geometry[END_REF], cantilever thickness and width should be chosen as small as possible to obtain a large critical pressure c P . In that case, Q-factor reaches a pressure-independent value in viscous region. How to optimize the device design is still challenging and needs our further efforts.

CONCLUSIONS

In this paper, piezoelectric PZT thin film transduced micro cantilevers with different cantilever geometries and PZT thicknesses were fabricated to investigate its energy dissipation mechanisms at atmospheric conditions. It was found that Q-factors of the cantilever can be increased by increasing the thickness of the PZT thin film. Besides, dielectric loss in PZT thin film as well as thermoelastic loss is quite significant even when PZT cantilever was actuated at atmospheric pressure. These results will help us better understand the energy dissipation mechanism in piezoelectrically transduced micro resonators, and then facilitates its design.

Fig. 1

 1 Fig.1 Structure of our piezoelectric PZT thin film transduced micro cantilever.

Fig. 2

 2 Fig.2 PZT cantilever fabrication process: (a) Pt/Ti bottom electrode layer, PZT film and Pt/Ti top electrode layer deposition; (b) PZT film and top/bottom electrode layer patterning; (c) SiO 2 passivation layer deposition; (d) electrode contact hole and cantilever shape patterning; (e) electric contact line deposition and patterning; and (f) cantilever release.

Fig. 3

 3 Fig.3 Schematic drawing of our PZT thin film transduced micro cantilevers' Q-factor measurement system.

  Fig.4 SEM images of the fabricated PZT cantilever (a) Type A: without triangle tip and (b) Type B: with 50µm-long triangle tip.

Fig. 5

 5 Fig.5 Measured resonance-peak of the 150µm-long B-type cantilever when actuated by integrated 390nm-thick PZT film.

  Fig.6 Measured Q-factors of the PZT thin film transduced micro cantilevers with different PZT thicknesses and cantilever geometries when self-actuated under atmospheric pressure.

Fig. 7

 7 Fig.7 Measured Q-factors of PZT film transduced micro cantilevers under atmospheric pressure when actuated by external vibrator. The bracketed number indicates the differential value to the results when actuated by integrated PZT thin film.

Fig. 8

 8 Fig.8 Measured Q-factors of the fabricated cantilevers which composed of different layer: TYPE_A: SiO 2 cantilever; TYPE_B: SiO 2 +Pt/Ti cantilever; TYPE_C: SiO 2 +Pt/Ti+PZT (1.04µm-thick) cantilever; TYPE_D: complete layered PZT (1.04µm-thick) cantilever as shown in Fig.4.

  Lu, T.Ikehara, T.Kobayashi, R.Maeda, T.Mihara Quality Factor of PZT Thin Film Transduced Micro Cantilevers array to provide more useful and reliable information by multiplicity responses from individual element

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