Each node possesses a number and simulated with the aid of the FEM. FEM three components of rotations. Every element is associated to modeling refers to simulation of individual structures but material properties, while on nodes, constraints, called also to assembled structures, the interaction of various com- boundary conditions, and loads, called loading conditions, ponents and operation performance. Adjacent elements share their common nodes and thus boundary and loading conditions. The analysis is Finally, micro and nanomanufacturing processes includes performed on the elements by calculating nodal values which lithography and pattern transfer, mechanical microcutting, are assembled into matrices.
The assembled matrices pro- non-mechanical micromachining processes, abrasive micro duce a global matrix for the whole structure. The accuracy of and nanoprocesses. The models and simulations provided in the method depends on many parameters among which are this topic are numerous, since the processes used are quite a the geometry of the problem, the density of the mesh, the few.
FEM models are mainly predictive for the performance size of the elements, the number of nodes etc. Some special of the process and the quality of the product but also for the techniques, such as the re-meshing, a process where a new optimization of process parameters, the proposition of new mesh is applied while the analysis takes place, are suggested processes or the investigation of phenomena taking place at for further improving the technique.
For more detailed analy- the micro and nanoscale. FEM in Mechanical Micromachining In the following paragraphs the trends of modeling in mi- cro and nanotechology areas is outlined. Furthermore, a spe- Modeling and simulation of micromachining with FEM cial paragraph is delivered related to mechanical micro- shares the same background with conventional machining machining, which, as mentioned in section 2, is quite advan- and thus some common aspects will be briefly discussed.
FEM in Micro and Nanotechnology ing orthogonal cutting. In this approach the finite element mesh is spatially fixed and the material flows through it in In the field of nanotechnology FEM has been used for order to simulate the chip formation. The computational time over a decade. In Reference , a bibliographical review of in such models is reduced due to the few elements required the use of FEM in nanotechnology, with references to for modeling the workpiece and the chip and is mainly used papers is provided.
It can be seen that this method is em- for simulating the steady state condition of the cutting proc- ployed in a wide range of nanotechnology related fields and ess. The elements do not undergo severe distortion since the that there is an extensive bibliography pertaining to topics mesh is a priori known but this formulation requires com- such as: plex programming. In this approach the The conventional definition of nanomaterials describes elements are attached to the material and the undeformed them as materials having a characteristic length scale of less tool is advancing towards the workpiece.
A disadvantage of the method is connected picted where the temperature distribution and the elastic de- to the large mesh deformation observed during the simula- formation of the workpiece can be seen.
The use of smart systems that can actively and autonomously sense and control their environments has far reaching implications for a tremendous number of future commercial and industrial applications, and promises significant benefits for the United States economy and its citizens. Also, the SEM 15 can be used to measure frequency of the device during the machining process. Influence of tool wear on machining forces and tool deflections during micro milling. However, if two of each of the femto-second lasers and conventional laser were configured in a single machining system, the machining rates would be twice that of a system configuration with only one of each of these machining capabilities. The acceptance range sets the dimensional tolerances required for a given product, and by association, the resultant product performance.
The diamond cut- tion. In order to overcome this disad- and a rake angle of 0o. The models were developed with vantage, usually, continuous re-meshing and adaptive mesh- Third Wave AdvantEdge software, a Lagrangian, explicit, ing are applied, adding considerably to the required calcula- dynamic code which can perform coupled thermo- tion time.
Nevertheless, the advances in computers have mechanical transient analysis The program applies adaptive made it possible to reduce the time needed for such an analy- meshing and continuous remeshing for chip and workpiece, sis to acceptable levels. Note that, an arbitrary Lagrangian- allowing for accurate results.
Eulerian formulation ALE has also been proposed with the Fig. Three- formation in precision cutting. In this case the depth of cut is similar to the tool edge radius and signifi- cant sliding across the clearance face of the tool due to elas- tic recovery of the workpiece material is observed. Addition- ally, plowing due to the tool edge radius that presents the tool with a large effective negative rake angle is involved in the process. Note, also that, perfectly sharp cutting tools are practically impossible to be produced due to technological limitations connected to the fabrication of the tools.
Analyti- cal modeling indicated that the size effect in micromachining and the cutting tool geometry plays an important role and needs to be taken into account . Rounded cutting edges were introduced in machining FEM simulations , while FEM simulations dedicated to micromachining, considering the size effect, following Eulerian, Lagrangian or ALE for- mulation, have been proposed . FEM models of this kind are used to predict cutting forces, temperatures, stresses, strains and simulate chip and burr formation .
Burr formation in precision machining: a mesh of tool and workpiece and b plastic strain of workpiece and chip . All the above mentioned FEM models refer to isotropic materials; no crystallographic effects are considered in the Fig. Micromachining simulation . The latter material exhibits larger variations and nanomanufacturing in the early s . The re- of the stress than the former, due to the modeled microstruc- sults indicated that MD is a possible modeling tool for the ture.
MD models developed were used for the investigation of the chip removal mechanisms, tool geometry optimization, cutting force estimations, subsurface damage identification, burr formation, surface roughness and surface integrity prediction; some relevant works can be found in References . Nanometric cutting simulation with tool rake angle 0o . FEM is based on principles of continuum mechanics and thus modeling and simulation of bulk material machin- ing can be adequately faced. On the other hand, when nanometric cutting is considered, another method, namely Molecular Dynamics MD , appears to be more attractive, as it can simulate the behavior of materials in atomic level.
Initial setup of the MD simulation system . MD is a modeling method in which atoms and molecules are interacting for a period of time, by means of a computer Nevertheless, some disadvantages can be identified in the simulation. In order to simulate molecular systems a very big MD technique as well. MD simulation is based on calcula- number of particles is involved and a vast number of equa- tions of interatomic forces among a vast number of atoms tions occurs to describe the properties of these systems; as a that constitute the modeled system. This task requires sig- multidisciplinary method, laws and theories from mathemat- nificant computational power and in order to overcome this ics, physics and chemistry consist the backbone of the problem very small model sizes are simulated; some models method.
In order to deal with these problems, numerical are limited to nanometer or angstrom level. Another feature methods, rather than analytical ones, are used and algorithms is that cutting speed is considered to be unrealistically high, from computer science and information theory are employed. Some scientists have However, the detailed insight in material behavior in mi- crocutting provided by MD simulation has supported process even envisaged the fabrication of nanomechanical compo- nents consisting of atoms, like the planetary gear of Fig.
With the provided simulations the stability of the pro- vided information on its theoretical study. It is generally ac- posed structures can be predicted and tested. Molecular cepted that chip formation in cutting is owed to the shearing nanotechnology became known through the pioneering work effect in the cutting zone of the workpiece. When machining of D. Drexler, who has worked on establishing its basic with a depth of cut that is of the same order to the cutting edge radius, another phenomenon needs to be considered.
Regardless of the nominal rake angle of the cutting tool, the effective rake angle in nanometric cutting is always negative. Thus, a compressive stress imposes deformation in front of 7. It can be concluded that under certain cir- cumstances there is no chip formation but elastic and plastic Modeling of MEMS will be reviewed separately because deformation, as it can be seen in Fig. The subsur- of the importance of MEMS in contemporary technology and face deformation is also described by a MD model in  future trends.
Additionally, models have been proposed that com- In this area of micro and nanotechnology, the same mod- bine MD and FEM modeling techniques in order to exploit eling methods with the ones described in the previous para- the capabilities of each method and cover a more wide range graphs are used.
Modeling usually refers to design and fabri- of material behavior at nanoscale cutting [49, 50]. Usually, CAD tools are used in order to design elec- structures in nanometric scale. Additionally, CAD tools are used for the visualization of the fitting of all the Fig. Molecular dynamics simulation results from initial cutting a to exit-burr formation at final cutting d , where undeformed chip thickness is 3 nm . Computer simulation of a molecular planetary gear, a end view, b side view and c exploded view . Special CAD tools are developed for MEMS to manufacturing and function and the integration of special and are commercially available .
A lot of work has been invested on the analytical model- ing of MEMS . In MEMS components of various kinds, 8. Mathematical models and numerical methods are The future of modeling and simulation at the micro and employed in order to predict the behavior of these systems nanoscale depends greatly on the available computational and optimize their functions without conducting long and power. More powerful systems in the future will be able to costly experimental work. Most of the designing Models with the above mentioned characteristics will be able process for producing MEMS is performed with specialized to provide more accurate results since they will be built in FEM software , or if actual devices already exist as 3D closer correlation to the existing systems they represent, al- physical objects, their static and dynamic analysis is per- lowing for models and simulations with wider fields of ap- formed with simulation in order to be improved, instead of plication.
In micro and nanoprocesses consisting of many steps, an In  a MD model of uniaxial tension in nanoscale is em- integrated simulation comprising all steps in one model pro- ployed in order to determine the mechanical properties of vides a powerful tool in the hands of the researchers. In the case of micro and nanomachining several steps can The future of modeling in MEMS and NEMS is the de- be made in order to obtain more accurate and reliable results.
Some of the topics to be that due to its setting up, takes under consideration the addressed will be the ductile mode cutting of brittle materials aforementioned feature. Nevertheless, MD simulation re- and the chip formation at the nanoscale, surface integrity quires a lot of computer power, limiting thus the size of the models, MD simulations where the cutting fluid is also con- area that is simulated.
Additionally, an experienced user of sidered and microstructure simulations. Some work has al- the MD method is required in order to provide reliable re- ready been performed on these topics  but the computa- sults. The progress in computer power is for the benefit of Modeling and simulation are of capital importance in modeling and in the future more detailed and complex mod- manufacturing. They are used widely by researchers as there els will be able to provide more accurate results and in less can be important reduction in experimentation time and cost. However, even with the available technology modeling Furthermore, modeling and simulation can provide data and and simulation is an important part of the analysis performed illuminate phenomena, a task that is difficult or even impos- in micro and nanomanufacturing.
Because of the importance of micro and nanomanufacturing in contempo-  Corbett, J. CIRP, , 49 2 , State of the art of micromachining. Micro enginee- packages that are built on the principles of these methods. Of ring. CIRP, , 52 2 , Micro and nanoprocessing techniques and applications. Recent advances in mechanical related software is suitably altered.
On the other hand, mod- micromachining. CIRP, , 55 2 , The main principles of each method and  Byrne, G. Advancing cutting technol- examples of application in micro and nanotechnology and ogy. Micro and Nanomanufacturing, Springer- manufacturing are gathered, accompanied by the relative Verlag: New York, The size effect in metal cutting. Sadhana - Acad. Special attention is given in modeling and simulation of  Kopalinsky, E.
Size effects in metal removal mechanical micromachining, a process broadly used because processes. IOP Conf. Series, No. Mechanical  Dinesh, D. An micromachining can be applied in bulk machining of silicon intrinsic size-effect in machining due to the strain gradient. An explanation for the size-effect in such as biomedical, automotive and telecommunication and machining using strain gradient plasticity, T.
ASME — J. Precision Manufacturing, Springer-Verlag: micro-displays . New York, Ductile-regime grind- Both FEM and MD models of mechanical micromachin- ing: a new technology for machining brittle materials. Computational synthe- on it due to its extensive application in modeling and simula- sis of lithographic mask layouts for silicon microcomponents.
However, this method treats the  Rajurkar, K. MD is used as an alternative simulation method  Cook, R. CIRP, , 43 1 , CIRP, , 42 1 , Effect of Tool  Mackerle, J. MD simulation of  Edelstein, A. Nanomaterials: Synthesis, Prop- exit failure in nanometric cutting. A — Struct. Mechanics of the metal cutting process, I: or-  Cheng, K. Modeling and Simulation of thogonal cutting and a Type 2 Chip, J. Mechanics of the metal cutting process, II: plastic-  Luo, X.
Bed, Int. On the size effect of micro-cutting force in  Rentsch, R. Molecular dynamics simulation of micromachining of ultraprecision machining. JSME Int. C — Dyn. Glascow, If a photosensitive material is selectively exposed to radiation e. This exposed region can then be removed or treated providing a mask for the underlying substrate. Photolithography is typically used with metal or other thin film deposition, wet and dry etching.
Sometimes, photolithography is used to create structure without any kind of post etching. One example is SU8 based lens where SU8 based square blocks are generated. Then the photoresist is melted to form a semi-sphere which acts as a lens. Electron beam lithography often abbreviated as e-beam lithography is the practice of scanning a beam of electrons in a patterned fashion across a surface covered with a film called the resist ,  "exposing" the resist and of selectively removing either exposed or non-exposed regions of the resist "developing".
The purpose, as with photolithography , is to create very small structures in the resist that can subsequently be transferred to the substrate material, often by etching. It was developed for manufacturing integrated circuits , and is also used for creating nanotechnology architectures. The primary advantage of electron beam lithography is that it is one of the ways to beat the diffraction limit of light and make features in the nanometer range. The key limitation of electron beam lithography is throughput, i. A long exposure time leaves the user vulnerable to beam drift or instability which may occur during the exposure.
Also, the turn-around time for reworking or re-design is lengthened unnecessarily if the pattern is not being changed the second time. It is capable of generating holes in thin films without any development process. Structural depth can be defined either by ion range or by material thickness. Aspect ratios up to several 10 4 can be reached. The technique can shape and texture materials at a defined inclination angle. Random pattern, single-ion track structures and aimed pattern consisting of individual single tracks can be generated. X-ray lithography is a process used in electronic industry to selectively remove parts of a thin film.
It uses X-rays to transfer a geometric pattern from a mask to a light-sensitive chemical photoresist, or simply "resist", on the substrate. A series of chemical treatments then engraves the produced pattern into the material underneath the photoresist. A simple way to carve or create patterns on the surface of nanodiamonds without damaging them could lead to a new photonic devices. Diamond patterning is a method of forming diamond MEMS. It is achieved by the lithographic application of diamond films to a substrate such as silicon.
The patterns can be formed by selective deposition through a silicon dioxide mask, or by deposition followed by micromachining or focused ion beam milling. There are two basic categories of etching processes: wet etching and dry etching. In the former, the material is dissolved when immersed in a chemical solution. In the latter, the material is sputtered or dissolved using reactive ions or a vapor phase etchant. Wet chemical etching consists in selective removal of material by dipping a substrate into a solution that dissolves it.
The chemical nature of this etching process provides a good selectivity, which means the etching rate of the target material is considerably higher than the mask material if selected carefully. Etching progresses at the same speed in all directions. Long and narrow holes in a mask will produce v-shaped grooves in the silicon. The surface of these grooves can be atomically smooth if the etch is carried out correctly, with dimensions and angles being extremely accurate. Some single crystal materials, such as silicon, will have different etching rates depending on the crystallographic orientation of the substrate.
Therefore, etching a rectangular hole in a -Si wafer results in a pyramid shaped etch pit with They were first used in medieval times for glass etching. It was used in IC fabrication for patterning the gate oxide until the process step was replaced by RIE. Hydrofluoric acid is considered one of the more dangerous acids in the cleanroom. It penetrates the skin upon contact and it diffuses straight to the bone.
Therefore, the damage is not felt until it is too late. Electrochemical etching ECE for dopant-selective removal of silicon is a common method to automate and to selectively control etching. An active p-n diode junction is required, and either type of dopant can be the etch-resistant "etch-stop" material.
Boron is the most common etch-stop dopant. In combination with wet anisotropic etching as described above, ECE has been used successfully for controlling silicon diaphragm thickness in commercial piezoresistive silicon pressure sensors. Selectively doped regions can be created either by implantation, diffusion, or epitaxial deposition of silicon. Its etch selectivity to silicon is very high, allowing it to work with photoresist, SiO 2 , silicon nitride, and various metals for masking. Its reaction to silicon is "plasmaless", is purely chemical and spontaneous and is often operated in pulsed mode.
Models of the etching action are available,  and university laboratories and various commercial tools offer solutions using this approach. Modern VLSI processes avoid wet etching, and use plasma etching instead. Plasma etchers can operate in several modes by adjusting the parameters of the plasma. Ordinary plasma etching operates between 0.
This unit of pressure, commonly used in vacuum engineering, equals approximately The plasma produces energetic free radicals, neutrally charged, that react at the surface of the wafer.
Since neutral particles attack the wafer from all angles, this process is isotropic. Plasma etching can be isotropic, i. Such anisotropy is maximized in deep reactive ion etching. The use of the term anisotropy for plasma etching should not be conflated with the use of the same term when referring to orientation-dependent etching. The source gas for the plasma usually contains small molecules rich in chlorine or fluorine. For instance, carbon tetrachloride CCl 4 etches silicon and aluminium, and trifluoromethane etches silicon dioxide and silicon nitride.
A plasma containing oxygen is used to oxidize "ash" photoresist and facilitate its removal. Because the etching is performed by ions, which approach the wafer approximately from one direction, this process is highly anisotropic. On the other hand, it tends to display poor selectivity. In reactive-ion etching RIE , the substrate is placed inside a reactor, and several gases are introduced. A plasma is struck in the gas mixture using an RF power source, which breaks the gas molecules into ions. The ions accelerate towards, and react with, the surface of the material being etched, forming another gaseous material.
This is known as the chemical part of reactive ion etching. There is also a physical part, which is similar to the sputtering deposition process. If the ions have high enough energy, they can knock atoms out of the material to be etched without a chemical reaction.
It is a very complex task to develop dry etch processes that balance chemical and physical etching, since there are many parameters to adjust. By changing the balance it is possible to influence the anisotropy of the etching, since the chemical part is isotropic and the physical part highly anisotropic the combination can form sidewalls that have shapes from rounded to vertical.
In this process, etch depths of hundreds of micrometres are achieved with almost vertical sidewalls. The primary technology is based on the so-called "Bosch process",  named after the German company Robert Bosch, which filed the original patent, where two different gas compositions alternate in the reactor. Currently there are two variations of the DRIE. The first variation consists of three distinct steps the original Bosch process while the second variation only consists of two steps.
Both variations operate similarly. The C 4 F 8 creates a polymer on the surface of the substrate, and the second gas composition SF 6 and O 2 etches the substrate. The polymer is immediately sputtered away by the physical part of the etching, but only on the horizontal surfaces and not the sidewalls. Since the polymer only dissolves very slowly in the chemical part of the etching, it builds up on the sidewalls and protects them from etching.
As a result, etching aspect ratios of 50 to 1 can be achieved. The process can easily be used to etch completely through a silicon substrate, and etch rates are 3—6 times higher than wet etching. After preparing a large number of MEMS devices on a silicon wafer , individual dies have to be separated, which is called die preparation in semiconductor technology.
For some applications, the separation is preceded by wafer backgrinding in order to reduce the wafer thickness. Wafer dicing may then be performed either by sawing using a cooling liquid or a dry laser process called stealth dicing. Bulk micromachining is the oldest paradigm of silicon based MEMS. The whole thickness of a silicon wafer is used for building the micro-mechanical structures.
Anodic bonding of glass plates or additional silicon wafers is used for adding features in the third dimension and for hermetic encapsulation. Bulk micromachining has been essential in enabling high performance pressure sensors and accelerometers that changed the sensor industry in the s and 90's. Surface micromachining uses layers deposited on the surface of a substrate as the structural materials, rather than using the substrate itself. The original surface micromachining concept was based on thin polycrystalline silicon layers patterned as movable mechanical structures and released by sacrificial etching of the underlying oxide layer.
Interdigital comb electrodes were used to produce in-plane forces and to detect in-plane movement capacitively. This MEMS paradigm has enabled the manufacturing of low cost accelerometers for e. Analog Devices has pioneered the industrialization of surface micromachining and has realized the co-integration of MEMS and integrated circuits. To control the size of micro and nano-scale components, the use of so-called etchless processes is often applied.
Thermal oxidation processes are used to produced diverse silicon structures with highly precise dimensional control. Devices including optical frequency combs,  and silicaon MEMS pressure sensors,  have been produced through the use of thermal oxidation processes to fine-tune silicon structures in one or two dimensions. Thermal oxidation is of particular value in the fabrication of silicon nanowires , which are widely employed in MEMS systems as both mechanical and electrical components. Both bulk and surface silicon micromachining are used in the industrial production of sensors, ink-jet nozzles, and other devices.