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Rohani, and A. Dynamic modeling and operation of a seeded batch cooling crystallizer. Zhang, S. Harris, and D. A, —56, Zhang, and S. On-line optimal control of a seeded batch cooling crystallizer. Grover 3. Calibration and pilot wafers can be used to characterize a process, by performing measurements during  or after  surface modification.
However, in a manufacturing setting this creates a loss of productivity, since this wafer is not used to produce any product. In contrast, optical sensors have found common use in measuring thin film properties during surface modification [2, 4, 5], because they do not directly contact the surface and are thus referred to as noninvasive. The general concept is shown in Fig. A beam of light with known properties is generated by a light source e. During in situ optical measurements, this beam is typically passed through a window, to separate and protect the light source and the processing environment from each other.
Unless the surface is completely black and at absolute zero temperature, such that it absorbs all the incident radiation and emits none, outgoing light will be produced by the interaction of the incoming beam with the surface. The properties of the light that is produced are dependent upon the properties of the surface, so by measuring the outgoing beam, one can infer properties about the surface as it evolves during processing. The details of the incoming beam depend upon the exact technique being used [3, 4]. Due to the potential for variations in this light source, the incoming beam is also typically measured by a separate detector.
In spectroscopic methods, the R.
Xiong and M. A detector also measures the intensity of the outgoing light as a function of wavelength. Ellipsometry measurements refer to the use of a polarized incoming beam, with the detector used to measure the change in polarization that occurs due to interaction with the surface . Spectroscopic ellipsometry measurements can be performed, in which both wavelength and polarization are used to infer the surface structure.
Raman techniques rely on the use of multiple wavelengths, but in this case a single wavelength is used for the incoming beam, while the detector measures the small amount of light that is emitted at different wavelengths. Depending on the technique being used, the detector may measure the outgoing beam at one or at multiple angles. The detector angle may be adjusted to match the incidence angle as it is intentionally varied, to measure the specular beam, or the detector may also measure off-specular intensity, such as light scattered by a rough surface, or diffraction patterns from a periodic surface structure.
Real-time optical measurements can be used either for detailed scientific studies such as reaction mechanisms or thin film growth mechanisms; or they can be used as a process monitoring tool for detection and control of growth rate or surface roughness. In this case, there is no actual incoming beam, but instead the detector measures the light emitted by a hot surface. This radiation, which is primarily in the infrared wavelength 3 In Situ Optical Sensing and State Estimation for Control of Surface Processing 47 range, is then measured at normal incidence by a photodetector.
The intensity of the light at one or more wavelengths is then correlated to the temperature. Like most optical measurement techniques, the pyrometer must be calibrated. The amount of radiation emitted by the surface is a function not only of the surface temperature but also the emissivity of the surface and the geometry of the measurement system, including the size of the photodetector and the distance between the surface and the detector. The emissivity is a material-dependent surface property that can be measured ex situ, while the geometric factors are specific to the particular pyrometer system being used.
Temperature control in surface processing has been successfully implemented under the name rapid thermal processing [8, 9]. Continuing challenges in implementation include the difficulty of temperature control across an entire wafer, and implementation of advanced control strategies for tracking more aggressive temperature profiles .
One limitation of the pyrometer in surface processing is that the surface emissivity may be changing as the surface is being modified. Thus, it is not possible to infer the temperature based on an ex situ measured surface emissivity. One solution that has been proposed is to additionally estimate the surface emissivity in real-time, using a normal incidence reflection measurement. This combination is referred to as the emissivity correcting pyrometer ECP  and has been successfully used for closed-loop temperature control of a chemical vapor deposition process .
The ECP measurement relies on a reflection measurement of the surface, such that a single-wavelength unpolarized beam of light is directed at the surface at normal incidence. The normal incidence reflected beam can be measured by the same detector that is used for the pyrometer: a rotating chopper is put in front of the source beam so that the reflected light for the reflection measurement can be measured independently from the emitted light for pyrometry.
There are a number of reasons why the surface emissivity will change during surface modification, and this change will affect the actual surface temperature, as well as the signal measured by the pyrometer.
A changing chemical composition will lead to a change in both the surface emissivity and the corresponding temperature dynamics. An endpoint control strategy was recently implemented for composition control in solar cell materials, by relating the emissivity to the thin film copper composition . An important optical feature of thin films is the ability to create constructive and destructive interference. When the film is at least partially transparent, then the multiple internal reflections within the film can lead to interference of light.
The ratio of the film thickness to the wavelength of the light is needed to predict the interference, and thus the interference effect can even be used to infer film thickness. This effect is illustrated in Fig. However, even with no incoming beam, the emission of radiation from the underlying substrate can also cause constructive and destructive interference , and, therefore, also an oscillation in the emission of radiation from the surface.
This oscillation due to emission has been used for film thickness control via endpoint detection . The surface roughness of a thin film can also further alter the emissivity , and emission measurements have even been used to infer surface roughness during 48 R.
Grover Constructive interference Constructive interference h R h Fig. It is also understood that patterned surfaces, such as those created by lithographic patterning for microelectronics applications, will alter the emissivity of a surface . When a beam of light having a single wavelength is directed at a transparent thin film, some light will reflect from the top surface of the film, but also some of the light will be transmitted into the film.
When the light reaches the interface between the thin film and the substrate, a portion may be transmitted into the substrate bulk, while the remainder will be reflected back into the film. Depending upon the thickness of the film and the wavelength of the light, the multiple beams of light that are transmitted back out of the film toward the detector will interfere either constructively or destructively, as shown in Fig. During surface modification a film may either become thicker during deposition or thinner during etching, and this film thickness h can be monitored using a reflectometer, if the index of refraction of the film is known.
In this case, the numbers of peaks in the reflectance measurement can be directly mapped to the thickness h. In most thin film deposition and etching processes, the nominal desired growth rate of the film is constant throughout the process. Therefore, the film thickness h is often determined by first estimating a constant growth rate G.
Once G has been determined, the time-varying film thickness h is simply the time-integral of G. To relate the measured reflection to the film thickness, the refractive index n and extinction coefficient k absorption of the film must be known. When the film is partially transparent, then the optical properties of the underlying substrate, ns and ks , must also be known.
MEMS technology ushers in a new age in optical switching
Breiland and Killeen considered the inverse problem: how to simultaneously estimate five constant parameters G, n, k, ns , and ks using 3 In Situ Optical Sensing and State Estimation for Control of Surface Processing 49 a single-wavelength normal incidence reflection measurement . One challenge articulated by this study was that these five parameters to be estimated are highly correlated with each other in the reflectance measurement. The parameter estimation was performed by minimizing the error between the model and the measurements, with no consideration of the correlations between the parameters.
Breiland and Killeen also suggested the possibility of real-time control of the growth rate. However, in their parameter fitting method they assume that all four optical constants and the film growth rate are constant, which would not be a good assumption if the chemical composition or growth rate is the quantity to be controlled.
There have been several reports of the use of reflectometry for real-time estimation of film thickness. The most common estimation strategy is the extended Kalman filter EKF , which has been applied to both film deposition by chemical vapor deposition [20, 21] and to etching for film removal . Recently we have applied moving horizon estimation MHE  to estimate film thickness in situ [24, 25] and have compared the performance and robustness of MHE to EKF in our chemical vapor deposition system . This work will be discussed in detail in Sect.
Reflectometry has also been used for real-time control of film thickness. Vincent et al. Lee et al. The previous discussion and analysis in this section on reflectometry does not take into account any inhomogeneities in the surface or film. During most surface processing, the surface of the film is not atomically smooth, and the interior of the film is not a single perfect crystal.
Polycrystalline thin films are often deposited when a film of one material is deposited on a substrate of another material. The individual crystals, or grains, may have preferred low-energy crystal facets, leading to a nonsmooth surface, with grain boundaries inside the film that alter the effective refractive index and extinction coefficient. Lithographically patterned surfaces also alter the reflectivity. Both cases are illustrated by Fig.
As with emissivity and the pyrometry temperature measurement, it is possible to model the reflection behavior of microscopically rough thin films [4, 24—27]. A few studies have gone further, and considered the problem of estimating the surface roughness with a reflectometry measurement [29—33]. In the work of Zuiker, the thickness, surface roughness, and extinction coefficient were simultaneously estimated, although the results were mixed, with negative unphysical absorption and noisy estimates .
Recently we applied moving horizon estimation to the problem of estimating thickness, optical constants, and roughness in our chemical vapor deposition process , which we discuss in Sect. One challenge in estimating surface roughness is in selecting a sufficiently accurate optical model. Grover Fig. The lateral scale is in micrometers, while the vertical scale is in nanometers; the schematic underneath represents the crosssection of the film and substrate. The vertical and horizontal features are measured in nanometers.
Line edge roughness is visible along the lines image courtesy of Cliff Henderson and Richard Lawson For large scale features, geometric optics can be used [16, 34], while for smaller scale features, scalar scattering theory  or the effective medium model  may be more appropriate. However, despite the additional information provided, many of the same challenges seen in reflectometry also apply here. Approximate inversion relations have been proposed for certain limiting cases , as also done in reflectometry , but in general the inversion requires consideration of the full nonlinear model.
The parameters to be estimated again have significant correlations in the optical model [38, 39]. The surface roughness of a thin film can also be estimated using ellipsometry measurements; in fact ellipsometry has been used extensively in the development and validation of optical models, such as the effective medium theory [5, 40].
The original work of Aspnes established the feasibility and utility of feedback control for nanoscale graded structures comprised of compound III—V semiconductors . The measured optical properties were used to adjust the aluminum precursor flowrate in real-time to track the desired trajectory of film stoichiometry. During the past decade, more advanced control analysis has been applied. Model-based controller design for III—V layered structures [42, 43] has been used to control the thickness and chemical composition.
In the deposition of silicon— germanium alloy films, the extended Kalman filter was used for state estimation of thickness and composition , with model predictive control  implemented to enable the simultaneous control of thickness and composition. Model predictive control MPC requires an online optimization after each measurement to compute the new control action, and thus requires significantly more online computation than a precomputed feedback law such as a proportional—integral controller.
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However, MPC also holds the promise to improve tracking performance. The International Technology Roadmap for Semiconductors outlines the short-term and long-term challenges for the industry, and metrology continues to be an area of critical need . Feedback control in semiconductor processing often takes the form of run-to-run control, in which a wafer is examined after the process is completed, so that the recipe can be adjusted for subsequent wafers .
In situ sensing and control is less common, due to the difficulty of both the measurement and the adjustment, but it also holds greater promise for reducing measurement delays and correcting the process sooner, which is desired due to the high cost of each wafer that is processed. To monitor and control patterned features in microelectronics fabrication, periodic test structures are created on a small portion of each wafer. By monitoring properties of these regular structures, changes in the overall process can be detected and corrected.
The critical dimension CD , which is the characteristic length scale in a transistor, must be tightly controlled, and additionally the line edge roughness LER of these features must be minimized. Grover electron microscope while it is being processed. In contrast, scatterometry is based on an optical reflection measurement, and can be used for either run-to-run or in situ control. The detector in a scatterometer actually measures a diffraction pattern from the surface, since a regular array of nanoscale lines will cause the incoming light to be diffracted.
This diffraction pattern is very sensitive to the dimensions and shape of the pattern, and thus can be used for monitoring and for control . Fundamental optical models are used for predicting the diffraction pattern of different surface profiles, and table lookup or linear regression models are used to invert this database in order to estimate the surface profile from the measured diffraction pattern. As with the other optical measurements discussed in this chapter, a unique inverse does not always exist, due to correlations in the parameters to be estimated .
Significant correlations in the fitted parameters are known to occur, yet these correlations are rarely used in the actual estimation process. Formal estimation techniques, such as the extended Kalman filter EKF and moving horizon estimation MHE , directly predict and then use these correlations, thus providing the opportunity for improved estimation . In most reported inversion studies from the surface physics community, a different approach is employed to obtain accurate estimates of multiple film properties — the sum squared error between the measurements and the model predictions is minimized, over some predefined window of past data.
The additional information provided by using multiple measurements enables a successful inversion to estimate the film properties. However, the window of data that is required may be long. In the reflectometry study by Breiland and Killeen, it was reported that the window must be at least one-fourth of an oscillation of the reflectance measurement . In the case of very thin films, this may be a significant portion of the entire deposition, eliminating the possibility for real-time correction of the process. Moreover, in this method of simple least squares fitting to the optical measurement, the variables to be estimated are constrained to be constant parameters, even though they may be varying over the time span of the window.
In our studies this substrate is a silicon wafer. In our deposition system we flow an inert gas argon through the precursor canister and into the deposition chamber. When the precursor reaches the vicinity of the hot substrate, it breaks down to form a solid thin film on the substrate. A photograph of the CVD system is shown in Fig. The deposition chamber is constructed from two four-way stainless steel crosses, and is on the left side of the oven in Fig. The right side of the oven houses the canister containing the precursor material, as well as an ultraviolet sensor used for monitoring and control of the inlet precursor concentration .
All of the lines from the precursor canister through the deposition chamber are housed in the oven so that the precursor does not re-condense in the lines or on the precursor walls. A vacuum pump and pressure control valve outside the oven are connected to the outlet of the deposition chamber, enabling the regulation of a setpoint pressure in the range of 1—10 torr. Mass flow controllers regulate the flow of argon and oxygen into the oven. The oxygen is needed to promote the chemical reaction and to provide the oxygen for the yttrium oxide Y2 O3 thin film.
Our reflectometer is mounted above the reactor and oven, as shown in Fig. This sensor is actually an emissivity-correcting pyrometer purchased from SVT Associates , although in 54 R. Grover the estimation studies described here we use only the reflection measurement not the pyrometer emission measurement. All the sensors and actuators are connected to a LabView program, which enables monitoring, data acquisition, and real-time control.
More detail on the apparatus and experimental procedure can be found in our previous publications [21, 24, 25]. Noise variables w j and v j are usually assumed to be zero mean, independent, and normally distributed for convenience, although in practice they might also represent the effects of unmodeled dynamics or correlated random disturbances.
In contrast to the simple process model, the sensor model g must be very accurate, if the sensor is to be useful. It predicts the reflectance R, which is the fraction of incident light that is reflected back to the detector at normal incidence. In our work on estimating roughness , we used the equation for multilayer reflectance response [5, 53—55], including the roughness 3 In Situ Optical Sensing and State Estimation for Control of Surface Processing 55 as a separate layer according to effective medium theory and the Bruggeman approximation [5, 40].
Thus, rab is the interface reflectivity between media a and b. Both quantities depend upon the refractive indices and extinction coefficients of the film and substrate. A model is used to compare the measured data to the model-predicted data, from 3. Ideally these two quantities would match identically, but in practice there will always be some nonideal behavior. The idea in MHE is to include additional sources of information to estimate the true value of the state, including the expected relationship between states from 3.
Only the most recent m measurements are directly included in the estimation. As each new measurement is acquired, the window of data shaded in the figure moves to the right. The quantity to be minimized has three terms, each representing a squared error in the estimate. The covariance matrix of this state estimate, P, is also calculated by the extended Kalman filter, and acts as a weighting matrix.
The second term in the minimization is the sum squared error associated with the measurement, v j. The weighting matrix for this term comes from R, which is the covariance matrix on the sensor error. The third term is the deviation from the process model at each point in the window, w j , with its corresponding covariance matrix Q. In addition to applying the general MHE method to our reflectometry measurements, we apply several limiting cases. The first is the simple least squares fitting approach over a window, as applied by Breiland and Killeen .
Thus, the only term retained in 3. With these simplifications, only the initial state at the beginning of the window is varied during the optimization, since the remaining states are computed using the process model. This greatly reduces the dimension of the minimization problem. We find that this approach provides good state estimates compared to MHE, due to the slowly drifting nature of our disturbances, but that the computation associated with the optimization is significantly reduced .
In other words, the use of the state estimate at the beginning of the window computed with the EKF is helpful in avoiding overfitting 3 In Situ Optical Sensing and State Estimation for Control of Surface Processing 57 of noisy data in the window, by including a priori knowledge of the state based on the earlier measurements. Regardless, the EKF does not achieve the same robustness as the estimation methods based on a longer window of data, which can better account for the nonlinearities in the sensor model.
Implicit in this discussion is that our nonlinear state space system will be observable, i. Significant correlations exist in the states to be estimated. Moreover, both the extinction coefficient k and the surface roughness he cause a decay in the amplitude of the reflectance oscillation, so it may also be difficult to separate out these two effects using the measurements. A common test of local observability is based on the linearization of the system about a single operating point, but for any single operating point, the observability matrix for our system is not full rank, suggesting that the state is not observable.
However, this is not a necessary condition for nonlinear observability . Here we use the notion of strong local observability , meaning that any two trajectories that start nearby can be distinguished from each other, given a sufficiently large window of measurements.
We find in our simulation studies that the EKF can converge under near-ideal conditions, but that the other three methods using a window of data at each iteration are much more robust to realistic noise levels and disturbances. Even though this surface roughness is an order of magnitude less than the wavelength of light, the surface roughness can still affect the normal incidence surface reflectance R. We have confirmed this point using ex situ ellipsometry measurements, after removing the films from the deposition chamber.
The ellipsometry software uses the effective medium model to fit a roughness layer that is approximately 50 nm. The thickness of the effective rough layer predicted by the effective models has previously been correlated to be twice the root-mean-square roughness . Since our effective layer is 50 nm and our root-mean-square roughness is 20—30 nm half 58 R. Grover 0. Comparison of thin film reflectance R with and without the effective roughness layer, for various levels of roughness of 50 nm , it may be possible to estimate the actual surface roughness measured by AFM from our in situ reflectometry measurements.
Since roughness does in fact alter the reflectometry measurement, we can ask two specific questions: 1 by neglecting the effect of roughness on the measurement, can we still accurately estimate the film thickness? We consider both questions in this chapter. We addressed the first question in , where we did not include a roughness optical model in the moving horizon estimation. Instead, we viewed the roughness effect as an unmodeled disturbance, and showed that the modified moving horizon estimates of film thickness and refractive index are significantly more accurate, compared to the simple least squares method and to the extended Kalman filter.
We addressed the second question in a separate publication , using our nominal sensor model in 3. Before actually implementing the estimator, we consider what effect the roughness would have on the reflectivity, based on the effective medium approximation. This prediction is shown in Fig.
This plot is a simulation of an ex situ spectroscopic reflectometry measurement, for a film with a thickness of nm, 3 In Situ Optical Sensing and State Estimation for Control of Surface Processing 59 which is typical for our CVD thin films. Note that the two wavelengths of our in situ sensor are nm and nm, which are both contained within the wavelength range on the plot.
During film growth, we observe oscillations due to the changing thickness at a constant wavelength, while in Fig. Clearly the effect of surface roughness is significant in the effective medium model, even at roughness values much less than the measurement wavelength. Another important trend in Fig. For example, at nm we should expect our measured reflectance to be more altered than at nm. For a roughness layer of 30 nm, and a measurement at nm, R should be altered only near the maximum in the oscillation constructive interference , while at a higher roughness of 60 nm, R will be altered at all phases of the interference.
We explicitly modeled and estimated this surface roughness to simultaneously estimate the optical constants, film thickness, and roughness . Because the micro-mirror must have multiple possible positions, a sophisticated analog-driving scheme is implemented to ensure that the mirrors are in the correct positions at all times. Although MEMS technology can produce 2N 3-D mirror arrays with impressive stability and repeatability by using a simple open-loop driving scheme, closing the loop with active feedback controls is fundamental to achieving the long-term stability required in carrier-class deployment of an all-optical crossconnect.
Using a closed-loop control scheme implies that monitoring the beam positions must be implemented in conjunction with computation resources for the active feedback loop and very-linear high-voltage drivers. Of the many possible methods of actuating a MEMS optical switch, two have emerged as possible solutions for commercial optical products: electrostatic and magnetic. The electrostatic method relies on the attraction of oppositely charged mechanical elements.
It is one of the main actuation methods used for all types of MEMS devices. Its many advantages include repeatability, ease of shielding, and well-understood behavior. Magnetic actuation relies on attraction between magnets and typically one or more electromagnets. While magnetic actuation can generate larger forces with high linearity, the MEMS community generally has not taken to its use because of the complications of integrating the magnets and the near impossibility of shielding neighboring devices from actuator crosstalk.
The shielding problem is particularly difficult in non-laboratory situations where, for example, someone might be running a large electric motor nearby, thus generating huge and repeated magnetic disturbances. Additionally, magnetic actuators on the MEMS scale have yet to prove reliable. Many developers are also concerned with hysteresis, both in the magnetic domain and in the structural properties of the magnetic materials.
The only way to ensure reliability is through long-term testing and field use. So far, electrostatic is the only mass-produced and fielded MEMS actuation method. For many years, a large amount of effort went into solving the problems of electrostatic behavior, and many products using electrostatic actuation have reached the market in demanding fields. Modern electrostatic MEMS devices often have positioning accuracy measured in fractions of an angstrom somewhat smaller than a single hydrogen atom , with reliability greater than that of the electronics supporting them.
However, not everyone employs electrostatics due to its relatively low force potential. An appropriate structure combined with the right process is necessary to design structures that work well in this regime. If the structure is too stiff, for example, greater force may be needed, dictating the use of magnetic actuation. The MEMS designer makes tradeoffs, choosing either to accept the weaker forces of electrostatics or to fortify the system shielding and packaging and tackle the long-term reliability issues associated with magnetics.
Because many open-ended questions remain in the use of magnetics, the electrostatic actuation method remains the optimum choice today for reliable devices required in high volumes. Even when designers employ electrostatic actuation methods, optoelectronic packaging remains a considerable challenge. The traits that make MEMS so well matched with optical switching-most importantly, small size-can also present some of the biggest obstacles in making MEMS devices robust and manufacturable.
With the compact scale of MEMS structures, a drop of water can seem like a typhoon and a speck of dust like a landslide. To keep these potentially destructive forces from causing harm, it is imperative to hermetically seal the MEMS chips. One solution is to integrate the electronics of a MEMs optical-switch subsystem with the optics and micro-mirrors in the same hermetically sealed ceramic packages see Figure 7.
This integration radically improves reliability and drastically simplifies manufacturability. By internally packaging the optics, whether it is collimating lenses or waveguides, they become considerably less susceptible to shifting or misalignment due to environmental effects that can wreak havoc on exposed optical components. But if the manufacturing process is not closely controlled, the benefits of internally packaging optics and electronics with the MEMS switch can be offset by new vulnerabilities introduced by the need for multiple fiber feedthroughs through the hermetic package.
Each fiber or pin entering or exiting the package represents a possible point of compromise to the package's hermeticity. Careful attention must be paid to this issue in the manufacturing process. The key to controlling manufacturing processes and ensuring hermeticity in the high volumes required for current and future applications is the development of automation in manufacturing. The manufacture of the actual MEMS-based switch core exploits established, highly automated silicon foundry processes in use for more than a decade.
The remaining challenge lies in fiber integration and module packaging. Aleksandar Zecevic Dragoslav D.
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