Patent Application
20240294372
The advent of Internet of Things (IoT) has given rise to a myriad of sensor-based devices used in wearables, smartphones, and remote sensing for industrial and consumer applications. Timing references are ubiquitous in these devices and help provide signals used to keep track of time, synchronize events in digital integrated circuits (ICs), and process signals. High-accuracy microelectromechanical systems (MEMS) resonators may be desirable for such high-performance electronic applications.
It is an aim of the present disclosure to achieve an improved temperature compensated MEMS device, such as a resonator. In particular, an aim of the present disclosure is to achieve a resonator design which offers second-order temperature compensation. The disclosure also provides a method to design second-order temperature compensated micromechanical resonators for various purposes.
Features, aspects, and advantages of the presently disclosed technology may be better understood with regard to the following description, appended claims, and accompanying drawings, as listed below. A person skilled in the relevant art will understand that the features shown in the drawings are for purposes of illustrations, and variations, including different and/or additional features and arrangements thereof, are possible.
The drawings are for the purpose of illustrating example embodiments, but those of ordinary skill in the art will understand that the technology disclosed herein is not limited to the arrangements shown in the drawings.
While quartz crystal oscillators have been the foundation of timing and frequency reference applications for the past century, the rapid development of sensor-based electronics has highlighted certain limitations of this technology, such as power consumption, robustness, size, and CMOS compatibility. Over the past two decades, MEMS resonators fabricated with silicon have drawn significant attention due to their small size, low cost, and integration compatibility. However, MEMS resonators still have not been able to replace their quartz counterparts in multiple applications.
A limitation of MEMS resonators that has curbed widespread adoption is the lack of temperature stability as compared to quartz. Silicon MEMS resonators have an inherent first order temperature-induced frequency drift of approximately −30 ppm/° C., resulting in a temperature stability of approximately 3,750 ppm over the industrial temperature range of −40° C. to 85° C. In comparison, AT-cut quartz resonators have a temperature stability of approximately 20 ppm over the industrial temperature range of operation. There have been several attempts made to overcome these temperature-induced frequency drifts, such as methods involving the use of highly doped silicon substrates and composite materials. However, these methods are insufficient as they provide only first order compensation of the temperature-induced frequency drift.
The change in frequency with respect to temperature of a MEMS resonator is given by the equation:
where f0 is the resonance frequency of the resonator at a reference temperature, ΔT is the deviation from the reference temperature, TCF1 is the first order temperature coefficient of frequency, and TCF2 is the second order temperature coefficient of frequency. For single crystal silicon the value of TCF2 is typically within the range of −25 to −80 ppb/° C.2 depending on the dopant type and concentration, which can result in a temperature-induced frequency drift of approximately 200-400 ppm over the industrial temperature range. While this second order temperature-induced frequency drift is relatively small compared to the uncompensated temperature-induced frequency drift of silicon (˜3,750 ppm based on −30 ppm/° C.), it is still significantly worse than the typical temperature-induced frequency drift that AT-cut quartz crystals can provide. As such, it is desirable to further reduce the temperature-induced frequency drift of fabricated silicon MEMS resonators in order enable their wide adoption in the timing market.
While it is possible to use active temperature compensation techniques to minimize temperature-induced frequency drifts, such techniques may place a significant burden on the system in terms of power consumption, circuit size, and circuit complexity. Hence it may be beneficial to find methods to passively compensate for temperature-induced frequency drifts in fabricated silicon MEMS resonators.
Various techniques have been used previously to passively compensate for temperature-induced frequency drifts. For example, fabricating composite MEMS resonators using a secondary material such as silicon dioxide (SiO2) is a well-established technique. SiO2 is known to have a large positive TCF1 (approximately 85 ppm/° C.), and due to its compatibility with silicon, it can be incorporated in silicon MEMS resonators to counterbalance the negative TCF1 of silicon. Within the industrial temperature range, total temperature-induced frequency drifts as low as sub-100 ppm have been achieved by this method. In the same temperature range, for smaller devices operating at higher frequencies (such as thin-film bulk acoustic resonators), temperature-induced frequency drifts as small as 3 ppm have been shown using this technique. However, one must take into consideration TCF2 effects of the oxide, which are not well documented in literature and difficult to measure due to its small scale, as well as the loss in resonator quality factor (Q) related to thermoelastic damping and/or surface losses. Moreover, this technique increases complexity in manufacturing and has reliability issues due to film-stresses, which lead to long-term aging issues.
Another example of an existing passive compensation technique involves fabricating MEMS resonators using highly-doped silicon substrates. This is a well-established technique as the TCF1 of particular resonance modes, including both shear and extensional modes, change with doping concentration (note, both Lamé and face shear modes are examples of shear modes). For example, within the industrial temperature range of −40° C. to 85° C., it is possible to limit the temperature-induced frequency drift of MEMS resonators operating in the Lamé mode to the range of 200-400 ppm using highly doped silicon substrates. However, even when TCF1 becomes zero, there still exists a significant amount of temperature-induced frequency drift caused by higher order temperature coefficients of frequency.
In the existing techniques discussed above, highly-doped silicon substrates can help engineer the TCF1 of a Lamé mode MEMS resonator to be almost zero. However, existing techniques are not effective enough at compensating higher order temperature-induced frequency drifts in silicon MEMS resonators, precluding competition with quartz crystal resonators. Thus, in the new techniques described herein, the high doping of the silicon substrate compensates for the TCF2 instead of the TFC1, and modifications to the resonator element compensate for the TCF1. Examples of such modifications to the resonator element can include either one or a combination of (i) adding areas to a resonator element, (ii) subtracting areas from a resonator element and (iii) changing the orientation of a resonator element with respect to the crystal axis of silicon. Using these techniques can provide at least second-order temperature compensation of the MEMS resonator device, leading to enhanced inherent temperature stability (such as a temperature-induced frequency drift of less than 1 ppm between −40° C. and 85° C.) with proper design. Such techniques are described in further detail below.
At block 102, the method involves determining or otherwise defining an initial resonator geometry and an initial orientation with respect to the crystal axis of silicon. This choice will subsequently define a selection of eigenmodes which are supported by the resonator element. While many eigenmodes may be supported by a given resonator element, they need not be exhaustively tested, and may be narrowed by the resonator design parameters such as desired Q-factor and operational frequency range. This occurs at block 104, where a particular eigenmode is chosen for analysis. Then, at block 106, a plurality of sets of parameters are determined or otherwise established, each set of the plurality of sets defining a respective combination of (i) a type of dopant and (ii) a doping concentration.
At blocks 108 and 110, the method involves selecting a single set of parameters for analysis and calculating TCF2 for the single set, respectively. The aim of this procedure is to identify a single set of parameters that causes TCF2 to be about equal to zero for the resonator element with the particular eigenmode. As shown in block 112, if TCF2 is about equal to zero, then the method proceeds to block 114. If not, then the method returns to block 104 in order to identify an alternative set of parameters that causes TCF2 to be about equal to zero.
At block 114, once a set of parameters has been identified that causes TCF2 to be about equal to zero for the resonator element and the particular eigenmode, the method involves calculating TCF1 for the type of dopant, the dopant concentration, and the resonator element with the particular eigenmode. At block 116, if the absolute value of TCF1 is large for the type of dopant, the dopant concentration, and the resonator element with the particular eigenmode, then the method returns to block 104 in order to identify an alternative type of dopant, dopant concentration and particular eigenmode that causes TCF2 to be about equal to zero. This process can be repeated until a type of dopant, dopant concentration, and resonator element with the particular eigenmode is identified that causes TCF2 to be about equal to zero while also reducing the magnitude of TCF1, which is referred to herein as a “closely temperature-compensated” (CTC) mode. If no combination of dopant concentration, type of dopant, and resonator element with the particular eigenmode results in a CTC mode, then the particular eigenmode is discarded and the method returns to block 104.
In some examples, a CTC mode corresponds to a mode in which the type of dopant, dopant concentration, and eigenmode of the resonator element causes TCF2 to be about equal to zero while also reducing the magnitude of TCF1 below a predefined threshold value. The predefined threshold value for TCF1 that results in a CTC mode may be a fixed value that is sufficiently lower than an uncompensated value for TCF1. For instance, because the uncompensated value of TCF1 in silicon has a magnitude of approximately 30 ppm/° C., the magnitude of the predetermined threshold value may be a lower value such as 10 ppm/° C., 5 ppm/° C., or even 1 ppm/° C. Alternatively, the threshold value for TCF1 that results in a CTC mode may not be a fixed value, but instead may be whichever calculated value for TCF1 at block 114 has the smallest magnitude. In this way, CTC modes correspond to modes that have a smaller magnitude TCF1 after compensating for TCF2 than non-CTC modes. By reducing the magnitude of TCF1 in this way, the amount of subsequent modification to compensate for TCF1 may likewise be reduced.
At block 118, once the CTC modes are identified, the next phase of the method is to apply modifications to the initial geometry and/or the initial orientation of the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the modifications thereby causing a deviation from the pure mode shape). This kind of distortion changes the initial eigenmode by changing the contribution of the elastic constants of silicon (C11, C12, and C44) to the initial eigenmode. By distorting the CTC modes by applying modifications to the initial geometry and/or the initial orientation of the resonator element, one can reduce the absolute value of TCF1, such that an at least partially temperature compensated MEMS resonator device can be designed. In some embodiments, it is possible to design a fully second order temperature compensated MEMS resonator device. The type of modifications that will result in at least partially temperature compensated MEMS resonator devices are determined using a parametric sweep approach performed with FEM.
In some examples, the method depicted in blocks 118 and 120 may be incorporated to apply in-plane rotation which alters the initial orientation of the resonator element with respect to the crystal axis of silicon. A sufficiently large set of different in-plane rotations should be tested such that the approximate angle of rotation that minimizes the absolute value of TCF1 is found.
In some examples, the method depicted in blocks 122 and 124 may be incorporated to apply geometric modifications which alter the initial geometry of the resonator element. These geometric modifications can include either one or a combination of (i) adding one or more areas to the resonator element and (ii) subtracting one or more areas from the resonator element. The geometric modifications are selected with a parametric sweep approach which entails establishing a selection of geometric shapes to be tested, systematically altering their dimensions and placement on the resonator element, and measuring the resultant TCF1. Thus, for a given resonator element, there may be multiple examples of geometric modifications that reduce TCF1.
In some examples, the method depicted in blocks 118 and 120 may be incorporated to apply an in-plane rotation to the resonator element before further modifying the geometry in blocks 122 and 124 with methods such as those described in the next section. Additionally, in some examples, the method depicted in blocks 118 and 120 may be bypassed based on resonator design requirements, while still giving the desired effect of reducing the absolute value of TCF1. Alternatively, in some examples, the method depicted in blocks 122 and 124 may be bypassed based on resonator design requirements, while still giving the desired effect of reducing the absolute value of TCF1. Finally, at block 126, the resulting design is that of a resonator having at least a second order temperature compensated mode.
It should be understood that, while the in-plane rotation and geometric modification techniques disclosed herein describe a general method for yielding second order temperature compensated MEMS resonators, the techniques can be similarly applied individually or in combination with one another. Additionally, it should be understood that the techniques disclosed herein also describe a general method for merely reducing the temperature-induced frequency drift of MEMS resonators without yielding fully second order temperature compensated MEMS resonators.
As previously stated, different cuts of quartz yield different temperature-induced frequency drifts, with the AT-cut quartz showing the least drift at approximately 20 ppm over the industrial temperature range. A similar approach can be used in silicon to reduce the temperature-induced frequency drift, but instead of applying different cuts to the silicon, alternative modifications can be applied in the form of in-plane rotation. Within the literature, first order temperature compensation has been achieved by applying particular combinations of doping concentration and in-plane rotation to silicon. However, existing techniques have been limited to controlling the first order temperature coefficient of frequency only, with uncompensated higher order TCFs causing significant temperature-induced frequency drifts. In contrast, in the example techniques described herein, the high doping of a silicon substrate compensates for TCF2 instead of TCF1, while in-plane rotations of a resonator element compensate for TCF1.
a. Method
Once a CTC mode has been identified, the next phase is to apply in-plane rotations to the resonator element at block 318 in order to slightly “distort” the CTC mode (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape). A sufficiently large set of different in-plane rotations should be tested such that the approximate angle of rotation that minimizes the absolute value of TCF1 is found at block 320, where the method involves selecting, from among the different applied in-plane rotations, the in-plane rotation that results in the smallest absolute value of TCF1. Then, at block 322, after applying the in-plane rotation that results in the smallest absolute value of TCF1, the resulting design is that of a resonator element having at least partial temperature compensation.
b. Example With In-Plane Resonance Modes
The values in Table 1 can be determined using FEM simulation software tools, or any other capable simulation software tools now known or later developed.
As shown in Table 1, the type of dopant, doping concentration, and eigenmode that results in a TCF1 with the smallest absolute value for the Lamé mode at TCF2≅=0 is a P-doped substrate with a direction of modal expansion in the <110> direction at a doping concentration of 2.3×1020 cm−3. By using this type of dopant, doping concentration, and eigenmode, the resonator element will require less TCF1 compensation than the other combinations of type of dopant, doping concentration, and eigenmode. In the present example, there is only a single CTC mode in which the type of dopant, doping concentration, and eigenmode results in a relatively small TCF1 value, but in other examples there may be multiple CTC modes.
Using the CTC mode identified above in Table 1, if one plots the corresponding TCF1 of the resonator element for the identified CTC mode at different in-plane rotations from 0° to 90° (in relation to the <110> direction), it can be seen that TCF1 has minima at ˜1.28 ppm/° C. for rotations of 34° and 55°, as shown in
c. Example With Out-of-Plane Resonance Modes
The method depicted in flowchart 300 may also be implemented with resonator elements having out-of-plane resonance modes. In this example, both torsional and saddle modes are considered. Similar to the previous example, by plotting the values of TCF2 versus dopant concentrations for both N-type and P-type dopants for different eigenmodes, one can identify any combinations of dopant concentration and type of dopant that cause TCF2 to be about equal to zero for a resonator element with a particular eigenmode. Subsequently, one can determine TCF1 for each of the identified combinations of dopant concentration and type of dopant that cause TCF2 to be about equal to zero to determine whether there are any CTC modes in which TCF1 is sufficiently reduced. The following table lists the CTC modes identified for the resonator elements with the particular eigenmodes considered in this example.
As before, once these CTC modes are identified, the next phase is to apply an in-plane rotation to the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape).
As discussed previously, high doping of a silicon substrate can compensate for the second order TCF2 instead of the first order TFC1, while modifications to the initial geometry of a resonator element can compensate for the first order TCF1. These geometric modifications can include adding areas to a resonator element and/or subtracting areas from a resonator element. Using these techniques can provide at least second-order temperature compensation of the MEMS resonator device, leading to enhanced inherent temperature stability (such as a temperature-induced frequency drift of less than 1 ppm between −40° C. and 85° C.) with proper design.
a. Method
The next phase is to apply geometric modifications to the resonator element in order to slightly “distort” the CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape). These geometric modifications can include adding areas to the resonator element, subtracting areas from the resonator element, or doing a combination of both. The geometric modifications that minimize the absolute value of TCF1 are selected with a parametric sweep approach. This approach entails establishing a selection of geometric shapes to be tested, systematically altering their dimensions and placement on the resonator element, and measuring the resultant TCF1. While the placement of geometric modifications may vary across embodiments, in these cases, the geometric additions are placed contiguously or at least partially overlapping with the regions of maximum displacement. The geometric subtractions may also be placed in this manner, or they may be placed along the axes of symmetry, depending on resonator design requirements.
Referring back to the flowchart 700 in
b. Example With Initially Square Resonator Elements
Similar to the example described above in connection with
The values in Table 3 can be determined using FEM simulation software tools or any other capable simulation software tools now known or later developed.
As shown in Table 3, the type of dopant, doping concentration, and eigenmode that results in a TCF1 with a sufficiently small absolute value for both the Lamé mode and the FS mode is a P-doped substrate with a direction of modal expansion in the <110> direction at a doping concentration of 2.3×1020 cm−3 and 2.34×1020 cm−3, respectively. Thus, in the present example, there are two CTC modes in which the type of dopant, doping concentration and eigenmode results in a relatively small TCF1 value. By using either of these combinations of type of dopant, doping concentration, and eigenmode, the resonator element will require less TCF1 compensation than the other combinations of type of dopant, doping concentrations, and eigenmode.
Once these CTC modes are identified, the next phase is to apply geometric modifications to the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape). As shown in Table 3, for the identified CTC modes, the FS mode has a smaller TCF1 (˜2.93 ppm/° C.) than the Lamé mode (˜4.57 ppm/° C.). Therefore, smaller geometric modifications may be needed for the FS mode to compensate for TCF1.
It should be understood that the geometric modifications that may be applied to compensate for TCF1 are not limited to embodiments disclosed herein, but can also include embodiments where any other shape can be added or subtracted to give the desired effect of reducing TCF1 to about zero, based on resonator design requirements. Other embodiments can include adding or subtracting in different regions of the resonator besides the regions shown in
c. Example With Resonator Elements of Various Initial Shapes
To illustrate how the techniques described herein may be applicable to both resonator elements of various initial shapes and geometric modifications of various shapes, the following examples involve applying the method depicted in
As before, once these CTC modes are identified, the next phase is to apply geometric modifications to the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape).
Referring next to
d. Example With Resonator Elements Resonating in Out-of-Plane Modes
To illustrate how the techniques described herein may be applicable to resonator elements with out-of-plane eigenmodes, the following examples involve applying the method depicted in
As before, once these CTC modes are identified, the next phase is to apply geometric modifications to the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape). In this example, in order to reduce the first order temperature coefficient of frequency, the areas added to the resonator element are in the out-of-plane direction.
Additionally,
As described above in connection with
Once this CTC mode is identified and the initial orientation of the resonator element is altered with in-plane rotation, the next phase is to apply geometric modifications to the resonator element in order to slightly “distort” these CTC modes (introduce stray vibrations due to the geometric modifications thereby causing a deviation from the pure mode shape).
As further shown in
In line with the previous discussion, it may be desirable to employ various methodologies to compensate for temperature-induced frequency drifts in MEMS resonator devices. In addition to the methods previously described, it may be possible to compensate for these temperature-induced frequency drifts in a given MEMS resonator device by forming an anchor decoupler region on the resonator element of the given MEMS resonator device. The resonator element may take any of various shapes, e.g., square, rectangle, circular, oval, octagonal, hexagonal, triangular, etc.
As used herein, an “anchor decoupler region” may refer to a region of a resonator element surrounding one or more anchors, wherein the anchor decoupler region comprises one or more trench layers etched into the resonator element. The anchor decoupler region may function to reduce TCF1 to about zero, and may be combined with other methodologies previously mentioned to form a second order compensated MEMS resonator device.
In addition to reducing TCF1 to about zero, the anchor decoupler region may also function to increase the Q-factor of the resonator element (as compared to the same resonator element without the anchor decoupler region). For instance, the presence of the anchor decoupler region on the resonator element may reduce the amount of energy that is transferred to the anchor during operation of the resonator element, thereby increasing the Q-factor of the resonator element. This may be particularly valuable, as the Q-factor of anchor damping, QANC, may have a significant impact on the total Q-factor of the resonator element. For example, the total Q-factor of the resonator element may be based on the Q-factor of anchor damping, QANC, the Q-factor of thermoelastic dissipation, QTED, the Q-factor of Akhiezer damping, QAKH, and the Q-factor of squeeze film damping, QSFD, among other things, and QANC may be at least two orders of magnitude larger than other Q-factors.
The anchor decoupler region may affect the TCF1 and Q-factor to various extents, depending on the configuration of the anchor decoupler region. As used herein, an anchor decoupler region “configuration” refers to a unique set of values for a number of variables that define the anchor decoupler region. These variables may take any of various forms.
One anchor decoupler region variable may be the number of trench layers surrounding the anchor of the MEMS resonator device. In some implementations, the anchor decoupler region may comprise a single trench layer, while in other implementations, the anchor decoupler region may comprise two or more trench layers.
Another anchor decoupler region variable may be the number of trenches within each trench layer. In some implementations, a given trench layer may comprise a single trench, which may at least partially, but not completely, surround the anchor of the MEMS resonator device. Further, in some implementations, a given trench layer may comprise multiple trenches, and each trench may at least partially surround the anchor of the MEMS resonator device.
Yet another anchor decoupler region variable may be the distance between the anchor of the MEMS resonator device and a trench layer. For example, a first trench layer may surround (e.g., partially surround) the anchor at a first distance (e.g., a first radial distance), and a second trench layer may surround (e.g., partially surround) the anchor at a second distance (e.g., a second radial distance). Relatedly, yet another anchor decoupler region variable may be the distance between two trench layers, e.g., in implementations where the anchor decoupler region includes multiple trench layers.
Yet another anchor decoupler region variable may be a trench width. For instance, trenches may be etched at various widths. In some examples, each trench may be etched at the same trench width. However, in other examples, some trenches may be etched at a first trench width, while other trenches may be etched at a second trench width, etc. For instance, trenches of a first trench layer may have a first trench width, and trenches of a second trench layer may have a second trench width. Various other examples may also exist.
Yet another anchor decoupler region variable may be a trench shape. The trenches of the anchor decoupler region may take various shapes, examples including linear trenches, curved trenches, and possibly other irregular shapes and combinations thereof (e.g., curved trenches with portions extending outward at various positions).
The anchor decoupler region may be defined by other variables as well.
In line with the previous discussion, there may be various anchor decoupler region configurations, and each configuration may correspond to a unique set of values for the anchor decoupler region variables. The extent to which the anchor decoupler region (i) reduces the TCF1 and (ii) increases the Q-factor of the resonator element may vary, e.g., based on the configuration of the anchor decoupler region. For instance, one anchor decoupler region configuration may reduce the TCF1 to about zero, but may only nominally increase the Q-factor, while another anchor decoupler region configuration may have a limited effect on the TCF1, but may significantly increase the Q-factor. It should be understood that these examples are non-limiting, and anchor decoupler region configurations may affect the TCF1 and the Q-factor to various other extents as well.
It may be desirable to identify an anchor decoupler region configuration that simultaneously (i) reduces the TCF1 to about zero and (ii) increases the Q-factor, e.g., so that the Q-factor satisfies a given threshold value. The given threshold value may take any of various forms, and may be defined by a user, e.g., such that the QANC of the resonator element is not the limiting factor for the total Q-factor of the resonator element, in line with the previous discussion. As described in greater detail below, FEM simulation software tools or the like may be utilized to identify such an anchor decoupler region configuration, which may then be formed on a resonator element.
Additionally,
A second top view 2004 is also shown, where the anchor 2002 is now surrounded by an anchor decoupler region comprising a first trench layer 2006. As shown, the first trench layer 2006 includes four curved trenches surrounding the anchor 2002. In line with the previous discussion, the anchor decoupler region shown in the second top view 2004 may be configured in various ways depending on what values are selected for the anchor decoupler region variables previously described.
A third top view 2008 is also shown, where the anchor 2002 is now surrounded by an anchor decoupler region comprising a first trench layer 2010 and a second trench layer 2012. As shown, the first trench layer 2010 includes four trenches having a substantially curved shape, but with portions extending outward from the anchor 2002 and toward the second trench layer 2012. The second trench layer 2012, on the other hand, includes four curved trenches that do not include portions that extend outward from the anchor 2002. In line with the previous discussion, the anchor decoupler region shown in the third top view 2008 may be configured in various ways depending on what values are selected for the anchor decoupler region variables previously described.
Blocks 2118-2122 may be performed repeatedly to determine an anchor decoupler region configuration that (i) reduces the TCF1 of the resonator element to about zero and (ii) increases the Q-factor of the resonator element to satisfy a threshold value, in line with the previous discussion. Starting at block 2118, an anchor decoupler region configuration may be selected for testing, e.g., by selecting values for the anchor decoupler region variables previously described. Then, the anchor decoupler region configuration may be tested using FEM simulation software tools or the like to determine how the anchor decoupler region configuration affects the TCF1 and Q-factor of the resonator element. At block 2120, the method may include determining whether the TCF1 has been reduced to about zero, and at block 2122, the method may include determining whether the Q-factor of the resonator element satisfies a threshold value. If either or both of these conditions are not met, then the method 2100 may return to block 2118 and select another anchor decoupler region configuration for testing.
In some implementations, once it is determined that a selected anchor decoupler region configuration satisfies both conditions, the method 2100 may proceed to block 2124, as described below. However, it may be possible for the method 2100 to continue to iterate through blocks 2118-2122 until a set of anchor decoupler region configurations is determined, wherein each anchor decoupler region configuration of the set both (i) reduces the TCF1 to about zero and (ii) increases the Q-factor to satisfy the threshold value. Once the set of anchor decoupler region configurations has been determined, the method 2100 may then proceed to select one of the anchor decoupler region configurations from the set (e.g., the anchor decoupler region configuration from the set that best satisfies the conditions) and proceed to block 2124 with the selected anchor decoupler region configuration.
At block 2124, the selected anchor decoupler region configuration may be formed on the resonator element of the MEMS resonator device, resulting in an at least second order temperature compensated MEMS resonator device, with the added benefit of the MEMS resonator device having an improved Q-factor, in line with the previous discussion.
Blocks 2318-2324 may be performed repeatedly to determine a combination of an anchor decoupler region configuration and one or more geometric modification(s) that (i) reduces the TCF1 of the resonator element to about zero and (ii) increases the Q-factor of the resonator element to satisfy a threshold value, in line with the previous discussion.
Starting at block 2318, an anchor decoupler region configuration may be selected for testing, e.g., by selecting values for the anchor decoupler region variables previously described. Then, at block 2320, one or more geometric modifications may be selected for testing, in line with the previous discussion. The combination of the selected anchor decoupler region configuration and the selected one or more geometric modifications may then be tested using FEM simulation software tools or the like to determine how the combination affects the TCF1 and Q-factor of the resonator element. At block 2322, the method may include determining whether the TCF1 has been reduced to about zero, and at block 2324, the method may include determining whether the Q-factor of the resonator element satisfies a threshold value, in line with the previous discussion. If either or both of these conditions are not met, then the method 2300 may return to block 2318 and/or block 2320 and select another anchor decoupler region configuration and/or one or more geometric modifications for testing.
In some implementations, once it is determined that a combination of a selected anchor decoupler region configuration and one or more selected geometric modifications satisfies both conditions, the method 2300 may proceed to block 2326, as described below. However, it may be possible for the method 2300 to continue to iterate through blocks 2318-2324 until a set of combinations of anchor decoupler region configuration and geometric modification(s) is determined, wherein each combination of the set both (i) reduces the TCF1 to about zero and (ii) increases the Q-factor to satisfy the threshold value. In some implementations, this may comprise exhaustively testing each possible combination of anchor decoupler region configuration and geometric modification(s), while in other implementations, less than all of the possible combinations may be tested. Once the set of combinations of anchor decoupler region configuration and geometric modification(s) has been determined, the method 2300 may then proceed to select one of the combinations of anchor decoupler region configuration and geometric modification(s) from the set (e.g., the combination from the set that best satisfies the conditions) and proceed to block 2326 with the selected combination.
At block 2326, the selected anchor decoupler region configuration may be formed on the resonator element of the MEMS resonator device and the one or more geometric modifications may be applied to the resonator element of the MEMS resonator device, resulting in an at least second order temperature compensated MEMS resonator device, with the added benefit of the MEMS resonator device having an improved Q-factor, in line with the previous discussion.
Although not shown in the figures, forming an anchor decoupler region on a resonator element may be combined with applying rotations (in-plane or out-of-plane) to the resonator element to reduce TCF1 to about zero. For instance, the TCF1 of a resonator element may be reduced to about zero using any combination of (i) forming an anchor decoupler region on the resonator element, (ii) applying a geometric modification to the resonator element, and/or (iii) applying a rotation (in-plane or out-of-plane) to the resonator element.
Further, the MEMS resonator devices described herein should be understood to have the ability operate as a dual-output MEMS resonator device. Specifically, the MEMS resonator devices may be configured to operate in both an in-plane mode of vibration as well as an out-of-plane mode of vibration.
It should be understood that the techniques described herein to reduce TCF2 or TCF1 to zero or about zero do not necessarily involve reducing TCF2 and TCF1 to exactly zero. Rather, it is sufficient to reduce TCF2 and/or TCF1 to be as close to zero as is practically possible. In some embodiments, this may involve reducing TCF2 to be less than 1 ppb/° C.2 and/or reducing TCF1 to be less than 1 ppm/° C. In other embodiments, this may involve reducing TCF2 to be less than 0.1 ppb/° C.2 and/or reducing TCF1 to be less than 0.1 ppm/° C. Still in other embodiments, this may involve reducing TCF2 to be less than 0.01 ppb/° C.2 and/or reducing TCF1 to be less than 0.01 ppm/° C.
Additionally, it should be understood that, while the techniques disclosed herein are described in connection with square, circular, and octagonal resonators, the techniques can be similarly applied in connection with resonators of other shapes as well, such as rectangular resonators, elliptical resonators, or any other shape of resonator. In addition, while the techniques disclosed herein that involve subtracting areas from resonator elements are described in connection with subtracting square-shaped areas, the techniques can be similarly applied to other shapes as well, such as rectangular, circular, or elliptical subtracted areas.
The techniques described herein can be used to design a microelectromechanical resonator device and fabricate a microelectromechanical device according to the design. For instance, once the MEMS resonator device has been designed using the techniques described herein, the device may be fabricated using any semiconductor fabrication techniques now known or later developed; such a MEMS resonator device can include a support structure such as a silicon substrate, a resonator element capable of resonating at least partly with an in-plane resonance mode, at least one anchor coupling the resonator element to the support structure, at least one driving electrode and at least one sensing electrode. In some examples, the device can be configured to operate as an oscillator.
Further, when carrying out the techniques described herein, the actual resulting values of the compensated TCF1 as a result of forming an anchor decoupler region, modifying the geometry, and/or modifying the orientation of the resonator element may differ slightly from the theoretical values gleaned from the simulation tools. For instance, extrapolation errors in the simulation model may cause the theoretical values of the compensated TCF1 to be offset from the actual values of the compensated TCF1 by some amount. Other inaccuracies in the simulation model or imperfections in a real-world MEMS resonator device may also contribute to this difference. As such, when using the techniques described herein to design a MEMS resonator device, the extent of the actual anchor decoupler region, geometric modification and/or rotation of the resonator element applied during the manufacture of the device may be varied from the theoretical values by some amount. The extent of this amount may be determined in various ways, such as through experimentation, e.g., by varying the theoretical values by various amounts until the desired compensated TCF1 is achieved, or any other applicable technique.
While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.
This application is a continuation-in-part of, and claims priority under 35 U.S.C. § 120 to, U.S. application Ser. No. 17/973,896, filed Oct. 26, 2022, which claims priority to U.S. Provisional Application No. 63/271,956, filed Oct. 26, 2021, the contents of each of which are incorporated herein by reference in their entirety.
| Number | Date | Country | |
|---|---|---|---|
| 63271956 | Oct 2021 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 17973896 | Oct 2022 | US |
| Child | 18647923 | US |
