MEMS COMB DRIVE ACTUATORS AND METHOD OF MANUFACTURE

FIELD OF THE INVENTION

This invention relates to micro-electro mechanical systems (MEMS) devices, and more specifically electrostatic comb drive actuators.

BACKGROUND OF THE INVENTION

This application claims the priority of U.S. Provisional Patent Application No. 60/836,258, the specification of which is incorporated herein by reference.

Micro-electro-mechanical-systems (MEMS) devices, including resonators, mixers- filters, linear actuators, Coriolis^ased angular rate sensors and resonant linear axis accelerometers are used in a wide range of applications including gyroscopes, air bag deployment, and radio-frequency (RF) communications. Examples of such devices are given by O'Brien et al. in "Outrigger; Solid Outer Frame Lateral Accelerometer Design", Proc. 13 ^th International Conference on Solid-State Sensors, Actuators and Microsystems (Transducers'05), pl76-179, 2005, and by Geen et al. in "Single-Chip Surface Micromachined Integrated Gyroscope With 50°/h Allan Deviation", IEEE J. Solid-State Circuits, vol.37, no.12, ppl860-1866, 2002, both of which are incorporated herein by reference. These devices typically incorporate an electrostatic comb drive actuator (CDA). Examples of actuators are given by Tang and Howe in US patent 5,025,346 (the Tang patent), herein incorporated by reference. In many applications, low actuation voltage and large displacement are desirable, and actuator research has primarily been focused on these properties. Actuation voltages can be reduced by modifying fixed and moving finger designs. Examples of fixed and moving finger structures designed to reduce actuation voltage are described by O'Brien in US patent 6,307,298, herein incorporated by reference. Actuation ranges can be increased by modifying a spring constant of a suspension structure. An example of a modified suspension structure is given by Zhou and Dowd in the Journal of Micromechanics and Microengineering, vol. 13, ppl 78-183, 2003, incorporated herein by reference.

A prior art comb-drive MEMS resonator is illustrated in Figure 1. Further detail regarding prior art comb drive resonators is provided in, for example, U.S. Patent No. 5,025,346. In Figure 1, resonator 10 includes two sets 12 and 14 of movable fingers. Each

set of movable fingers includes a plurality of substantially parallel fingers, such as fingers 16, 18, 20, and 22. The sets 12 and 14 are movably mounted to a substrate 30 through anchors, such as anchor 24, by means of a folded-beam suspension 26. The sets 12 and 14 of movable fingers are electrically coupled to an electrode 28 via a path extending through the substrate 30, the anchor 24, and the suspension 26. The resonator 10 also includes two sets 32 and 34 of fixed fingers. These sets of fixed fingers include substantially parallel fixed fingers 36 and 38, among others. Each set of fixed fingers is interdigitated with its corresponding set of movable fingers. The fixed sets 32 and 34 of fingers are electrically coupled, respectively, to electrodes 40 and 42. In one exemplary use of the prior art resonator 10, the electrode 28 (and hence the movable sets 12 and 14 of fingers) are grounded, and a DC bias and AC driving potential can be applied to electrode 40 (and hence to the fixed set 32 of fingers). The electrical potential differences between fixed set 32 and movable set 12 of fingers create electrostatic forces between those sets of fingers and cause the movable sets 12 and 14 of fingers to move in a direction substantially parallel to the direction of the fingers. By taking advantage of restorative forces caused by the suspension 26, the application of properly-timed potential differences between the electrodes 28 and 40 can be used to drive the movable fingers into resonance at a frequency determined primarily by the spring constant of the suspension and the mass of the movable fingers. As the movable sets 12 and 14 of fingers are in motion, the properties of the capacitive interface between set 14 of movable fingers and set 34 of fixed fingers changes. These changes can be used in the prior art resonator 10 to measure the motion (e.g., the frequency and amplitude of resonance) of the movable sets 12 and 14 of fingers.

In many MEMS applications, it is desirable to provide a precise control of actuator displacement, and in resonator applications, it is desirable to provide an actuator that can operate under direct current (DC) conditions only. MEMS resonators can be used as oscillator references. Present oscillator references exist as noisy silicon NAIND-gate ring oscillators or high end quartz resonators. Previously demonstrated MEMS resonators are supplied with a very high-quality, low-noise sinusoidal drive signal in order to drive them into resonance. This means that the drive signal source is generally much higher quality and lower noise than the signal intended for process via filtering, demodulation, and the like. As a result, MEMS resonators have not yet been integrated into electronic applications such as filters or demodulation intermediate frequency reference oscillators since high quality drive signals would themselves provide better frequency reference sources than is available at the

resonator output. MEMS-based automotive grade gyroscopes contain resonators that currently require the system application specific integrated circuit (ASIC) to provide closed loop blocks for both amplitude and frequency control. These ASIC control blocks consume a significant portion of the overall silicon die space and power consumption. Present MEMS resonator DC actuator research has been directed to using Electrothermal actuators. However, such devices have slow oscillation frequencies and poor reliability, making them unsuitable for many oscillator reference applications. Examples of electro-thermal actuators are given by see Gianchandani and Udeshi in US patent application 2005/0168101. It would be highly advantageous to remedy the foregoing and other deficiencies inherent in the prior art.

SUMMARY OF THE INVENTION

An actuator described in this invention disclosure, implemented, for example, into a MEMS gyroscope design, is intended to offer the potential of smaller silicon die space and lower power consumption. Such actuators enable elimination of at least some closed-loop feedback circuitry, such as that used in amplitude control, and thereby can remove noise sources associated with such circuitry.

It is an object of the present invention to provide a micromechanical oscillator actuated by a DC electrical bias only, AC electrical bias, and/or a combination of AC and DC electrical bias signals.

It is another object of the present invention to provide a micromechanical oscillator with an oscillation frequency that can be controlled by the magnitude of the applied voltage.

It is yet another object of the present invention to provide control of the magnitude of oscillation of a micromechanical oscillator through the use of linear and non-linear displacement-sensitive electrostatic force.

It is yet another object of the present invention to provide control of the oscillation waveform of a micromechanical oscillator through the use of linear and non-linear displacement-sensitive electrostatic force. These objects, either individually or in combination, are achieved in various embodiments of the MEMS comb drive actuators described herein. One such actuator comprises a support layer and at least one movable comb mounted resiliently on the support

layer. Each movable comb has a plurality of substantially parallel movable fingers. These parallel fingers pass through channels that are fixed with respect to the support layer. An AC and/or DC electrical potential difference can be applied between the channels and the movable fingers. Electrostatic forces resulting from this potential difference are capable of moving the fixed fingers through a range of motion. Over at least a portion of this range of motion, some of the movable fingers extend beyond the fixed channels. The electrostatic forces on a movable finger that terminates within a channel are different from those on a movable finger that extends beyond a channel. In designing such a MEMS actuator, the lengths of the fingers and/or channels can be selected by taking into consideration the degree to which different fingers extend beyond the channels in different portions of the range of motion. This allows tailoring the driving force on the actuator as a function not only of the driving voltage, but also as a function of the displacement of the actuator.

For example, in one embodiment, the maximum amplitude of the disclosed electrostatic actuator structure is a function of layout geometry and is relatively independent of applied voltage amplitude. Previous comb drive based electrostatic actuator maximum displacements are typically limited only by the applied voltage amplitude with the maximum applied voltage limited by ionization of actuator dielectric gap or the strength of silicon suspension springs. In certain embodiments described herein, the actuator maximum displacement can be pre-determined by well-controlled semiconductor based mask layout geometry. This allows the actuator structure to also be excited with either DC and/or and AC signal to a maximum amplitude set primarily by mask layout geometry. As a result, a relatively constant amplitude electrostatic actuator, like those used in Coriolis based MEMS gyroscopes, can be constructed which is dependent on layout geometry and relatively independent of actuation voltage amplitude using an AC and/or DC drive methodology has been demonstrated.

Preferred embodiments of the invention presented here are described below in the Brief Description of the Drawing Figures and Description of the Invention. Unless specifically noted, it is intended that the words and phrases in the specification and the claims be given the ordinary and accustomed meaning to those of ordinary skill in the applicable arts. If any other special meaning is intended for any word or phrase, the specification will clearly state and define the special meaning. In particular, most words have a generic meaning. If it is intended to limit or otherwise narrow the generic meaning, specific descriptive adjectives will

be used to do so. Absent the use of special adjectives, it is intended that the terms in this specification and claims be given their broadest possible, generic meaning.

Likewise, the use of the words "function" or "means" in the Description of the Invention is not intended to indicate a desire to invoke the special provisions of 35 U. S. C. 112, Paragraph 6, to define the invention. To the contrary, if it is intended to invoke the provisions of 35 U.S.C. 112, Paragraph 6, to define the inventions, the claims will specifically recite the phrases "means for" or "step for" and a function, without also reciting in such phrases any structure, material or act in support of the function. Even when the claims recite a "means for" or "step for" performing a function, if they also recite any structure, material or acts in support of that means or step, then the intention is not to invoke the provisions of 35 U.S.C. 112, Paragraph 6. Moreover, even if the provisions of 35 U.S.C. 112, Paragraph 6 are invoked to define the inventions, it is intended that the inventions not be limited only to the specific structure, material or acts that are described in the preferred embodiments, but in addition, include any and all structures, materials or acts that perform the claimed function, along with any and all known or later-developed equivalent structures, materials or acts for performing the claimed function.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

Referring to the drawings: FIG. 1 is a plan view of a prior art comb drive actuator;

FIG. 2A is a schematic top view of a comb drive actuator in accordance with an embodiment of the present invention;

FIG. 2B illustrates various geometric measurements of the comb drive actuator shown in FIG. 2A; FIG. 2C is a schematic top view of a 'single side' comb drive actuator.

FIGs. 3 - 9 are schematic top views of various comb drive actuators in accordance with different embodiments of the present invention.

FIG. 10 is a schematic block diagram of a simulation for testing CDA geometries.

DETAILED DESCRIPTION QF THE INVENTION

FIG. 1 is a plan view of a prior art comb drive actuator, such as the actuator described in the Tang patent. Sets 12 and 14 of movable fingers (e.g. 16, 18, 20, and 22) are interdigitated with sets 32 and 34 of fixed fingers. The fixed fingers are connected together in the plane of motion of the movable fingers, such that displacement of a moving finger cannot exceed a distance that is physically determined by the geometry of fixed fingers.

FIG. 2A illustrates a schematic diagram showing a MEMS actuator structure 100 formed in accordance with one embodiment of the present invention. Such MEMS devices can be formed using well-known processing techniques known to those skilled in the art. The actuator 100 includes a support layer 101, a first stationary structure (or fixed finger comb) 102, a second stationary structure (or fixed finger comb) 104 and a movable structure 106 in connection with moving finger structure 108 and moving finger structure 110. The fixed finger structures 102 and 104 form channels open at two ends, such that a movable finger extends into a proximal end of each channel.

In an exemplary embodiment, support layer 101 includes a semiconductor substrate or semiconductor layer. Further, in an exemplary embodiment, support layer 101 also includes a dielectric layer overlying the semiconductor layer or substrate. As an example, the dielectric layer can be comprised of silicon dioxide. Stationary structures 102 and 104 and movable structure 106, moving finger structure 108 and moving finger structure 110 are preferably formed from the same layer of electrically conductive material. As an example, a layer of doped, crystalline or polycrystalline silicon can be patterned to form structures 102, 104, 106, 108 and 110.

Stationary structures 102 and 104 each have a comb-like configuration and comprise a plurality of elongated portions adjacent to each other and separated from each other by a gap, and are both coupled to and are located over support layer 101. Electrical connection of fingers of stationary structure 102 is achieved by electrical connector 118 formed in support layer 101. Electrical connection of fingers of stationary structure 104 is achieved by electrical connector 120 formed in support layer 101. The interdigitated fingers of FIG. 1 impose a maximum displacement of moving fingers, since the fingers are physically (and hence electrically) connected in the same plane in which the moving fingers move. In the actuator of FIG 2A ₁ in contrast, the stationary

structures 102 and 104 are electrically connected by electrical connectors 118 and 120, respectively. Standard semiconductor processing techniques allows electrical connections to be made in substrate 101, and consequently a physical barrier to motion for fingers 108 and 110 in FIG. 2A is not limited by physical geometry of fixed structures 102 and 104. Electrical connectors 118 and 120 are connected to contact pads 112 and 115. (In some embodiments, pads 12 and 15 may be implemented as a single pad.) A movable structure consisting of 106, 108 and 110 is electrically connected to another contact pad 113. Contact pads 112, 115, and 113 allow a voltage from a voltage source 114 to be applied across various components of the MEMS device. Movable structure 106 is coupled to and is located over support layer 101. Movable structure 106 has a first side with movable fingers 108 located adjacent to stationary structure 102 and also has a second side with movable fingers 110 located adjacent to stationary structure 104. Movable fingers 108 and 110 also include a plurality of elongated portions located at or extending from either side of structure 106. Movable structure 106 is movable relative to stationary structures 102 and 104 and also relative to support layer 110. Movable structure 106 includes a proof mass or seismic mass 105 that is suspended over support layer 101 by suspension beams 107. Beams 107 are coupled to anchors 109, and anchors 109 are coupled to support layer 101. Beams 107 provide the mobility for movable structure 106. Stationary structures 102 and 104 actuate movable structure 106 back and forth along the direction of an axis 129. Electrostatic forces are used to provide the actuation. As illustrated in FIG. 1, axis 129 is preferably straight. However, in a different embodiment, axis 129 may be curved as in a radial coordinate system for a radial actuator. In the case of a curved axis of movement, the term "substantially parallel" should be understood to describe elements that follow substantially the same curvature. The moving finger structures (108 and 110) in connection with movable structure 106 and stationary structures 102 and 104 are inter-digitated to form an inter-digitated comb structure.

Turning now to FIG. 2B, the geometries of actuator 100 from FIG 2A are shown. Stationary structure 102 is shown as an array of fingers, with a pitch P ₁₀₂ . defining a separation of fingers of stationary structure 102. Fingers of stationary structure 102 have a width W102 and a length L ₁ ( _E -

Stationary structure 104 is shown as an array of fingers, with a pitch P ₁ 0 ₄ , defining a separation of fingers of stationary structure 104. Fingers of stationary structure 102 have a width W ₁₀₄ and a length Li ₀₄ .

Moving finger structure 108 is shown as an array of fingers, with a pitch P102, defining a separation of fingers of moving structure 108. Fingers of moving structure 108 have a width Wi ₀₈ and a length L ₁₀₈ .

Moving finger structure 110 is shown as an array of fingers, with a pitch Pi ₀₄ , defining a separation of fingers of moving structure 110. Fingers of moving structure 110 have a width WH _O and a length Lno- Stationary structure 102 and moving structure 108 define an interdigitated comb of fingers. Fingers of moving structure 108 and fixed structure 102 are separated by a gap gi. Fingers of moving structure 108 and fixed structure 102 have a zero-bias overlap distance denoted di.

Stationary structure 104 and moving structure 110 define an interdigitated comb of fingers. Fingers of moving structure 110 and fixed structure 104 are separated by a gap g ₂ .

Fingers of moving structure 110 and fixed structure 104 have a zero-bias overlap distance denoted d ₂ . Gaps gi and g ₂ are illustrated in FIG. 2A and 26 to have a constant width, but such gaps may have a non-constant or varying width.

It will be understood that other structure geometries for CDA 100 can also be used, and that the required voltage and equivalent force for operation of CDA 100 are determined by the geometry and electro-mechanical properties of materials used to form CDA 100.

FIG. 2C shows a "single side" CDA 130, formed in accordance with an embodiment of the present invention. Fixed structure 104 and movable structure 106 are electrically connected using electrical connectors 121 and 122 as shown. Electrical connector 118 connects fixed structure 102. In this configuration, CDA 130 is a single side actuator, with electrostatic actuation between 102 and 108 only.

It should be noted in the above examples, Pio ₂ =Pio ₄ , In an exemplary embodiment L ₁₀₂ and Li _O4 are chosen to be non-equal, and ends of stationary structures 102 and 104 are placed symmetrically about a center line 111 of CDA 100 (or CDA 130) to provide overlaps di and d ₂ . In another exemplary embodiment L ₁ 0 ₂ and Li ₀₄ are chosen to be equal, and ends of stationary structures 102 and 104 are placed asymmetrically (or offset) about a center line 111 of CDA 100 (or CDA 130) to provide overlaps di and U ₂ .

It will be understood other geometries for movable fingers 108 and 110, such that Wio ₈ and W _π o can be unequal, and Lirø and Lno are unequal, may also be used. Movable structure 106, 108 and 110 is designed to balance with a center of mass for the proof mass

105 and fingers 108 and 110 along a center line of CDA 100 (or CDA 130). Turning now to FIG. 3, a schematic top view of another CDA 140 formed in accordance with an embodiment of the present invention. One difference between CDA 140 and CDA 100 or CDA 130 is the electrical connection configuration. Contact pads, such as pads 112, 113, and 115 are used and connect to fixed structure 102, movable structure

106 and fixed structure 104, respectively. An electrical voltage signal across fixed structure 102 and movable structure 106, 108 and 110 is applied via contact pad 112 and 113. An electrical sense output, which can be measured as an analog or a digital output, using a displacement-dependent property such as capacitance between fixed structure 104 and movable fingers 110 can be measured via contact pad 115, and contact pad 113. Contact pad 112 and contact pad 115 can alternatively be connected to provide electrical connections to CDA 140 as shown for CDA 100.

The CDA structures described herein can have different modes of operation, depending on the zero-bias overlaps di and d ₂ chosen in the design and the applied voltages. Three of these modes of operation (and the design condition for which the mode of operation occurs) are: 1. Oscillator when (di = d ₂ );

2. Output Frequency Doubler when (di ≠ d ₂ ) and ({di > d ₂ ) or (d ₂ > di)); and

3. Displacement Limited Actuator when (di ≠ d ₂ ) and ((di » d ₂ ) or (d ₂ » di))

In the embodiment shown in FIG. 4, fixed finger widths W ₁ 0 ₂ and Wi ₀ * are chosen to be different, and correspondingly gaps gi and g ₂ between the fixed and moving finger combs are unequal. This geometrical asymmetry modifies the electrostatic actuation performance of the CDA to also be asymmetric. In the case of a push-pull actuator where contact pads 112 and 115 are connected and at the same potential, the electrostatic force of attraction for the interdigitated finger set 102 and 108 differs from that for interdigitated finger set 104 and 110. This has the effect of allowing the push and pull forces to be tailored in strength, and hence provide wave-shaping of the displacement oscillation of the moving structure 106 of CDA 140 (or CDA 100). In the case where contact pads 112 and 115 are not connected (a

force-sense mode of operation of CDA 140), higher sensitivity of the sense mode can be obtained.

FIG. 4 shows another embodiment of a CDA 160. At zero bias (and hence zero displacement of moving structure 106, and movable fingers 108 & 110) the ends of moving fingers 108 and 110 are confined within the lengths of fixed fingers 102 and 104.

For a zero-bias condition of dj >0, d ₂ >0, CDA 160 can act as an output frequency doubter.

For the cases where either di » d _∑ or d ₂ » di, CDA 160 can act as a displacement-limited actuator, providing a steady displacement state as a function of voltage. FIG. 5 shows another CDA 180 formed in accordance with one embodiment of the present invention. Fixed structure 102 consists of a finger structure wherein the finger structure includes fingers with at least two different lengths. By way of example, FIG. 7 shows a fixed structure 102 with different finger lengths, of length Uβi, Li ₈₂ and Li ₈₃ . In an exemplary embodiment, fixed structure 102 is symmetric about an axis defined in direction 129, although asymmetric finger structures for 102 can also be used. Fixed structure 104 consists of a finger structure wherein the finger structure includes fingers with at least two different lengths. By way of example, FIG. 5 shows a fixed structure 104 with three different finger lengths, of length Li ₈₄ , L ₁₈₅ and L ₁₈₆ . In an exemplary embodiment, fixed structure 104 is symmetric about an axis defined in direction 129, although asymmetric finger structures for 104 can also be used.

A zero-bias minimum overlap between fingers of 102 and 108 is di. A zero-bias minimum overlap between fingers of 104 and 110 is d ₂ . For fixed structures 102 and 104, the number of different fingers and finger lengths are shown by way of example only. It will be understood fixed structures 102 and 104 each consist of a plurality of fingers with at least two different finger lengths.

An object of asymmetric finger structures 102 and/or 104 in a CDA is to provide a tailored electrostatic force profile that can be used to tailor the displacement oscillation waveform of movable structure 106, 108 and 110.

In an alternative embodiment of CDA 180, fixed fingers 102 are all the same length and fixed fingers 104 are all the same length. Electrostatic force asymmetry can be obtained by designing movable fingers 108 and movable fingers 110 to each have at least two finger lengths. Movable fingers 108 and 110 have a center of mass along center line 111 of CDA

180. In the perpendicular direction to center line 111, movable fingers 108 are symmetric

about about an axis defined in direction 129, and movable fingers 110 are symmetric about about an axis defined in direction 129. For a zero-bias condition of di >0, d ₂ >0, CDA 180 can act as an output frequency doubler.

For the cases where either di >> d ₂ or d ₂ » d _lt CDA 180 can act as a displacement-limited actuator, providing a steady displacement state as a function of voltage.

FIG. 6 shows another CDA 200 formed in accordance with an embodiment of the present invention. By way of example, FIG. 6 shows fixed fingers 104 on one side only of CDA 200 connected by connector 201, although it will be understood that fixed fingers 102 could be connected by a connector instead of fixed fingers 104. An overtravel stop 202 may be used to limit the maximum displacement of the moving fingers, and hence prevent contact between active electrodes under normal operation. Overtravel stop 202 can also be implemented in any CDA formed in accordance with the present invention.

In CDA 200, interdigitated fingers 102 and 108 provide a comb-drive limited travel capacitor or actuator. Interdigitated fingers 104 and 110 provide a parallel plate capacitor or actuator. Geometries of fingers and gaps can be chosen as described before, and various additional embodiments are shown in FIGs. 7-9. Overlap distances di and d ₂ are important in operation of such CDAs.

If d ₂ >> di (FIG. 7), interdigitated fingers 102 and 108 provide a limited travel Capacitor/Actuator. Interdigitated fingers 104 and 110 provide an unlimited travel capacitor/actuator .where the actuator maximum displacement is much smaller than d ₂ .

FIG. 8 shows another embodiment of a CDA formed in accordance with an embodiment of the present invention.

FIG. 9 shows yet another embodiment of CDA a formed in accordance with the present invention. This embodiment can be used as an oscillator through the application of an AC and/or DC bias by a voltage source 114.

FIG. 9 shows a schematic diagram showing a MEMS actuator structure and 280 formed in accordance with an embodiment of the present invention. Contact pad 112 and contact pad 115 are coupled by resistor 204. Contact pad 115 and contact pad 113 are coupled by resistor 206. A single voltage source 114 can be used to provide a potential difference across 112 and 115 and a potential difference across 115 and 113, the ratio of the potential differences determined by the values of resistors 204 and 206.

Proposed geometries of CDA structures according to embodiments of the invention can be tested through simulation, as illustrated in FIG 10. Different driving voltage profiles

301, 302, 303 can be selected. Based on the input voltage and on the displacement (305) of the movable structure, the total electrostatic force on the movable structure can be calculated. Using parameters based on the mass (m) of the movable structure, a damping constant (μ), and the spring coefficient (k) of the suspension structure, the time change in displacement can be calculated. (In FIG. 10, the circles represent addition and subtraction, the triangles represent multiplication, and 1/s represents integration with respect to time.)

A CDA is designed such that an applied voltage, such as a step voltage or the like displaces moving structure 108 in a direction along the length of fingers of moving structure 108 in direction 129 to beyond an equilibrium displacement of the structure. Application of a voltage decreases overlap di and comb drive 108 overshoots the end of fixed structure 102 by extending past the channels formed by the fixed structure (di changes sign) to a distance beyond a stable equilibrium displacement. A restoring force is generated on the opposite side of CDA between fixed structure 104 and moving structure 110.

In one exemplary simulation, di = 2μm and d ₂ = 2μm. A step voltage is applied using voltage source 114 with an equivalent lOμN unit-step input forcing function. A double-sided push-pull comb drive in accordance with the present invention generates an oscillating displacement as a function of time.

Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement that is calculated to achieve the same purpose may be substituted for the specific embodiments shown. This application is intended to cover any adaptations or variations of embodiments of the present invention. It is to be understood that the above description is intended to be illustrative, and not restrictive, and that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Combinations of the above embodiments and other embodiments will be apparent to those of skill in the art upon studying the above description.

The scope of the present invention includes any other applications in which embodiment of the above structures and fabrication methods are used. The scope of the embodiments of the present invention should be determined with reference to claims associated with these embodiments, along with the full scope of equivalents to which such claims are entitled.