Patent Publication Number: US-10759656-B2

Title: MEMS sensor with dual pendulous proof masses

Description:
TECHNICAL FIELD 
     This disclosure relates generally to capacitive micro-electromechanical systems (MEMS) sensors. 
     BACKGROUND 
     The offset performance of capacitive MEMS accelerometers is degraded in the presence of high thermal gradients as a result of the Knudsen effect on the proof mass. High thermal gradients arise from proximity to high temperature components on a printed circuit board (PCB), such as a system-on-chip (SOC). The thermal gradient results in deflection of the proof mass from its initial position when at rest, thus creating an offset in the sensor output. This performance issue limits the placement options of the MEMS sensor inside a system (e.g., inside a smartphone). Solutions have been proposed that use a proof mass fabricated using multiple polysilicon structural layers with perforations to suppress offsets induced by vertical thermal gradients. These solutions, however, do not address offsets caused by lateral thermal gradients. 
     SUMMARY 
     A MEMS sensor is disclosed that includes dual pendulous proof masses comprised of sections of different thickness to allow simultaneous suppression of vertical and lateral thermal gradient-induced offsets in a MEMS sensor while still allowing for the normal operation of the accelerometer. In an embodiment, the structure and different sections of the MEMS sensor is realized using multiple polysilicon layers. In other embodiments, the structure and different thickness sections may be realized with other materials and processes. For example, plating, etching, or silicon-on-nothing (SON) processing. 
     In an embodiment, a micro-electromechanical systems (MEMS) sensor, comprising: a substrate; a first electrode and a second electrode having a first polarity disposed on, or formed in, the substrate; a third electrode and fourth electrode having a second polarity opposite the first polarity, disposed on, or formed in the substrate; an anchor disposed on the substrate; a first pendulous mass rotatably coupled to the anchor, the first pendulous mass having a heavy side and a light side, the heavy side having more mass then the light side, the first pendulous mass serving as a first common electrode and positioned to form a first gap between the mass and the first electrode and a second gap between the mass and the second electrode, the first pendulous mass configured to rotate about the anchor in a first direction when the first pendulous mass is subjected to an acceleration force; and a second pendulous mass rotatably coupled to the anchor, the second pendulous mass having a heavy side and a light side, the heavy side having more mass then the light side, the second pendulous mass serving as a second common electrode positioned to form a third gap between the mass and the third electrode and a fourth gap between the mass and the fourth electrode, the second pendulous mass configured to rotate about the anchor in a second direction that is opposite the first direction when the second pendulous mass is subjected to the acceleration force. 
     In an embodiment, an electronic system comprises: a micro-electromechanical systems (MEMS) sensor configured to sense acceleration of the electronic system, the MEMS sensor including dual pendulous masses having sections of different thickness and a readout circuit configured to: convert a change in differential capacitance between electrodes of the MEMS sensor to differential voltage signals; process the differential voltage signals to remove lateral, thermal gradient-induced offset; and calculate acceleration data based on the processed differential voltage signals; one or more processors; memory coupled to the one or more processors and storing instructions that when executed by the one or more processors, cause the one or more processors to perform operations comprising: obtaining the acceleration data; calculating a location of the electronic system using the acceleration data; and displaying the location on a display device of the electronic system. 
     Particular implementations disclosed herein provide one or more of the following advantages. The dual pendulous design disclosed herein allows for suppression of lateral, thermal gradient-induced offset by ensuring that forces caused by the lateral thermal gradient act on the dual pendulous proof masses in common mode to allow electronic cancellation of the offset. At the same time, the sections of different thickness allow for cancellation of the vertical gradient forces while still allowing for the normal operation of the accelerometer. 
     The details of the disclosed implementations are set forth in the accompanying drawings and the description below. Other features, objects and advantages are apparent from the description, drawings and claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIGS. 1A and 1B  illustrate a conventional MEMS accelerometer that depends on mass asymmetry and includes a proof mass with a heavy side fabricated using a second polysilicon layer. 
         FIGS. 1C and 1D  illustrate vertical and lateral thermal gradient sensitivity for the conventional MEMS accelerometer shown in  FIGS. 1A and 1B . 
         FIG. 1E  illustrates a conventional MEMS accelerometer that uses two cells oriented 180° from each other. 
         FIGS. 1F and 1G  illustrate a conventional MEMS accelerometer that depends on differential masses fabricated from a single thickness layer. 
         FIGS. 1H and 1I  illustrate vertical and lateral thermal gradient sensitivity for the conventional MEMS accelerometer shown in  FIGS. 1F and 1G . 
         FIG. 2A  is a top view of dual pendulous proof masses with multiple thickness layers, according to an embodiment. 
         FIG. 2B  is a side view of dual pendulous proof masses of  FIG. 2A , according to an embodiment. 
         FIG. 3A  is a side view of dual pendulous proof masses that use multiple polysilicon layers having perforations to suppress vertical, thermal gradient-induced offset, according to an embodiment. 
         FIG. 3B  is a side view of dual pendulous proof masses illustrating common mode rejection of forces caused by a lateral thermal gradient, according to an embodiment. 
         FIG. 4  is a top view of an alternative design using asymmetric, dual pendulous proof masses, according to an embodiment. 
         FIG. 5  is a diagram of an interface circuit for processing capacitance change extracted from a capacitive MEMS accelerometer with dual pendulous proof masses, according to an embodiment. 
         FIG. 6  is an architecture for an electronic system that uses a capacitive MEMS accelerometer with dual pendulous proof masses for various applications, according to an embodiment. 
     
    
    
     The same reference symbol used in various drawings indicates like elements. 
     DETAILED DESCRIPTION 
     Overview 
     A typical MEMS accelerometer is composed of a movable proof mass that serves as a common electrode to fixed outer plate electrodes. The movable mass electrode and fixed outer plates represent capacitors. The deflection of the proof mass is measured using the capacitance difference. 
     When a MEMS sensor package (e.g., a MEMS accelerometer sensor package) is proximate to external high temperature components on a PCB, such as from a nearby SOC, vertical and lateral thermal gradients can arise within the sensor cavity housing the proof mass, which is typically filled with a gas (e.g., nitrogen). The vertical thermal gradient extends in the vertical direction (e.g., Z+). The gas below the proof mass will tend to have a higher temperature than the gas above the proof mass, since the gas below the proof mass is closer to the heat source or the thermally conductive copper layers of the PCB that conduct the heat. The vertical thermal gradient creates areas of higher or lower mean velocity of gas molecules in the sensor cavity, above and below the proof mass, respectively. This disparity of mean velocity of gas molecules causes a higher force of pressure on the proof mass from the hot side (below the proof mass) that causes the proof mass to deflect from its initial position, resulting in an accelerometer offset. This temperature effect is referred to as the Knudsen Effect or Crookes Radiometer. These forces are related to the area of the proof mass, whereas the sensitivity to acceleration forces is related to the mass of the proof mass. 
     To address vertical thermal gradient-induced offset, in an embodiment, the proof mass can be fabricated to have a heavy side and a light side, where the heavy side has more mass and therefore generates a higher moment than the light side under acceleration forces. The heavy side and light side can be fabricated using multiple layers of polysilicon. Balancing the pressure force on the light side with the pressure force on the heavy side can compensate for the vertical, thermal gradient-induced offset. This can be accomplished by adjusting the holes in the polysilicon layers to adjust the pressure force on the light side. Since the force pressure F P  is proportional to the product of pressure P times area A (F P =PA), the number and size of perforations in the proof mass can increase or decrease the pressure force through increasing or decreasing the surface area A of the proof mass that is subjected to pressure due to gas molecule collisions. 
     Additionally, hole size can be adjusted on the heavy side to compensate damping changes. While adjusting the hole quantity and hole size can reduce vertical, thermal gradient-induced offset, this approach cannot reduce lateral (in x-y plane), thermal gradient-induced offset because the thermal gradients are different on opposite sides of the proof mass. 
       FIGS. 1A and 1B  illustrate a conventional MEMS accelerometer structure  100  that depends on mass asymmetry and includes a heavy side that was fabricated using a second polysilicon layer.  FIGS. 1A and 1B  illustrate normal operation of structure  100  under acceleration.  FIG. 1A  shows a top view of structure  100  having a width w, light side length (L L ) and heavy side length (L H ). Structure  100  has additional mass m formed using a second polysilicon layer and torsion bar  101 . Positive (C+) and negative (C−) electrodes  102   a ,  102   b  are also shown. 
       FIG. 1B  shows a side view of structure  100  when in detection (sensing acceleration). The force F S  exerted on the additional mass due to acceleration A Z  is given by:
 
 F   S   =A   Z   ·m.   [1]
 
     The forces F S_H  and F S_L  exerted on heavy side  103  and light side  104 , respectively, due to acceleration A Z  are given by Equations [2] and [3]:
 
 F   S_H   =A   Z   ·L   H   ·w·t·ρ,   [2]
 
 F   S_L   =A   Z   ·L   L   ·w·t·ρ,   [3]
 
where t is the thickness and ρ is the density of the mass material (e.g., polysilicon). A Z  is acceleration in the vertical (+Z direction), which in this example is the sensitive axis of the accelerometer.
 
     The overturning moment or sensitivity M O  of the structure  100  is given by Equation [4]: 
                       M   0     ∼         A   z     ·     [     w   ·   t   ·     ρ   ⁡     (       1   2     ⁢     (       L   H   2     -     L   L   2       )       )         ]       +       F   s     ·     L   s           ,           [   4   ]               
where L s  is the distance from the anchor to the center of mass m.
 
       FIGS. 1C and 1D  illustrate vertical and lateral gradient sensitivity for structure  100  shown in  FIGS. 1A and 1B . A vertical thermal gradient sensitivity is illustrated in  FIG. 1C . The forces exerted on heavy side  103  and light side  104  are given by Equations [5] and [6], respectively:
 
 F   G_H   =a   0   ·ΔT·w·L   H ,  [5]
 
 F   G_L   =a   0   ·ΔT·w·L   L .  [6]
 
where ΔT is a temperature change and a 0  is a constant that depends on the gas properties (e.g., density and pressure).
 
     The overturning moment/sensitivity M O  for structure  100  is given by Equation [7]:
 
 M   O   ˜a   0   ·ΔT·w ·( L   H   −L   L ).  [7]
 
     As shown by Equation [7], structure  100  requires area symmetry to suppress the offset due to the vertical thermal gradient. It is noted that the area of heavy side  103  (w·L H ) and the area of low side  104  (w·L L ) can be made the same and still preserve accelerometer performance due to the existence of the additional mass force F s . It is further noted that if sections of structure  100  are made with different thicknesses (e.g., using multiple polysilicon layers), a lumped mass m can be realized, which allows for a design space where the vertical thermal gradient sensitivity can be suppressed while still allowing for sensitivity to input acceleration. 
     Referring to  FIG. 1D , a lateral thermal gradient sensitivity is illustrated. The forces exerted on heavy side  103  and light side  104  of structure  100  are given by Equations [8] and [9]:
 
 F   G_H   =a   0 ·( T   1   −T   a )· w·L   H ,  [8]
 
 F   G_L   =a   0 ·( T   2   −T   a )· w·L   L ,  [9]
 
where T a  is ambient temperature.
 
     The overturning moment/sensitivity M O  of structure  100  is given by Equation [10]: 
     
       
         
           
             
               
                 
                   
                     M 
                     O 
                   
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                       a 
                       0 
                     
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                     w 
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                                 L 
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                   10 
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     As shown in Equation [10], the offsets induced by the lateral thermal gradient effects cannot be addressed by area symmetry alone (e.g., L H =L L ). Nor can the lateral gradient effects be addressed by using sections with different thicknesses (e.g., using multiple polysilicon layers). 
       FIG. 1E  illustrates a conventional MEMS accelerometer that uses two cells  105   a ,  105   b  oriented 180° from each other. Although a two cell structured oriented 180° can be used to reduce the effects of vertical and lateral thermal gradients, the separation between cells  105   a ,  105   b  results in different local thermal gradients for cells  105   a ,  105   b.    
       FIGS. 1F and 1G  illustrate a conventional MEMS accelerometer structure  106  that depends on differential masses fabricated from a single thickness layer.  FIGS. 1F and 1G  illustrate normal operation of structure  106  under acceleration. The differential masses allow electronic cancellation of the lateral thermal gradient effect.  FIG. 1F  shows a top view of MEMS accelerometer structure  106  having differential masses  107   a ,  107   b , where mass  107   a  has an area A H1  and mass  107   b  has an area A H2 . Structure  106  also has torsion bar  108 . Positive (C+) and negative (C−) electrodes  109   a ,  109   b  are also shown.  FIG. 1G  shows a side view of structure  106  when in detection (sensing acceleration). A Z  is acceleration in the +Z direction, which in this example is the sensitive axis of the accelerometer. Note that the differential masses are fabricated from a single layer of silicon. 
     Referring to  FIG. 1G , the net forces F S_H1  and F S_H2  exerted on the heavy side of the differential masses  107   a ,  107   b  due to acceleration A Z  are given by Equations [11] and [12], respectively:
 
 F   S_H1   =A   Z   ·A   H1   ·t·ρ,   [11]
 
 F   S_H2   ·A   Z   ·A   H2   ·t·p,   [12]
 
where A H1  and A H2  are the areas of the differential masses  107   a ,  107   b , respectively.
 
     Since the two masses are configured electronically for differential operation, the equivalent differential sensitivity M O  of structure  106  is given by Equation [13]:
 
 M   O   ˜A   Z   ·t ·ρ( A   H1   ·L   H1   +A   H2   ·L   H2 ),  [13]
 
where L H1  and L H2  are the moment arms from the anchor to the center of mass of masses  107   a ,  107   b , respectively. The sign change in sensitivity is because masses  107   a ,  107   b  work differentially.
 
       FIGS. 1H and 1I  illustrate vertical and lateral thermal gradient sensitivities for structure  106  shown in  FIGS. 1F and 1G . Referring to  FIG. 1H , a vertical thermal gradient sensitivity is illustrated. The net forces on the heavy sides of the differential masses  107   a ,  107   b  are given by Equations [14] and [ 15 ]:
 
 F   G_H1   =a   0   ·ΔT·A   H1 ,  [14]
 
 F   G_H2   =a   0   ·ΔT·A   H2 ,  [15]
 
     Again, due to the fact that the masses are configured for differential operation, the net equivalent differential sensitivity M O  is given by Equation [16]:
 
 M   O   =a   0   ·ΔT ·( A   H1   ·L   H1   +A   H2   ·L   H2 ),  [16]
 
where ΔT is a temperature change and a 0  is a constant that depends on the gas properties (e.g., density and pressure). Sensitivity term (A H1 ·L H1 +A H2 ·L H2 ) appears in both the vertical gradient sensitivity and the sensitivity under normal operation shown in Equation [13]. Therefore, the vertical gradient sensitivity cannot be made to be zero without also making the sensitivity under normal operation also equal to zero. Accordingly, MEMS accelerometer structures that have only a single thickness layer cannot be made to eliminate vertical gradient sensitivity without impacting performance.
 
     Referring to  FIG. 1I , a lateral temperature gradient sensitivity is illustrated. The net differential forces on differential masses  107   a ,  107   b  are given by Equations [17] and [18]:
 
 F   G_H1   =a   0 ·( T   1   −T   a )· A   H1 ,  [17]
 
 F   G_H2   =a   0 ( T   2   −T   a )· A   H2 ,  [18]
 
where T 1 &lt;T a &lt;T 2 .
 
     The net equivalent differential sensitivity is given by:
 
 M   O   =a   0 ·( T   1   −T   a )· A   H1   +a   0 ·( T   2   −T   a )· A   H2 .  [19]
 
     Since T 1 &lt;T a &lt;T 2 , (T 1 −T a ) and (T 2 −T a ) are opposite signs and there is cancellation. As shown in Equation [19], the differential mass design allows for electronic cancellation of the lateral gradient effect. 
     Dual Pendulous Mass Design 
       FIG. 2A  is a top view of dual pendulous masses  200  with multiple thickness layers, according to an embodiment. The structure shown in  FIG. 2A  is designed to overcome the shortcomings of the conventional MEMS accelerometer structures described above in reference to  FIGS. 1A-1I . 
     A first pendulous mass  201  has a heavy side and a light side. A second pendulous mass  202  has a heavy side and a light side. The heavy sides of pendulous masses  201 ,  202  have more mass than the lighter sides of the masses  201 ,  202 , and therefor generate higher moments than the lighter sides when subjected to an external acceleration. The pendulous masses  201 ,  202  are rotatably coupled to anchor  203  using, for example, torsion bars. Pendulous masses  201 ,  202  are not coupled together and therefore rotate independent of each other about anchor  203 . Anchor  203  is attached to a substrate (e.g., substrate  104 ) in a MEMS sensor package (e.g., MEMS sensor package  100 ). Anchor  203  provides a fulcrum that allows the dual pendulous masses  201 ,  202  to “teeter-totter” in opposite directions in response to an external acceleration force. 
       FIG. 2B  is a side view of the dual pendulous masses  200  shown in  FIG. 2A , according to an embodiment. As shown, when subjected to an external acceleration force (A Z+ ), and due to the heavy/light sides, pendulous mass  201  pivots clockwise about anchor  203  (torsional movement), and at the same time, pendulous mass  202  pivots counterclockwise about anchor  203 . As can be observed in  FIG. 2B , when pendulous mass  201  pivots clockwise, mass  201  (a moving common electrode) becomes closer to fixed positive electrode  205   a  and further from fixed negative electrode  204   a . Likewise, when pendulous mass  202  pivots counterclockwise, mass  202  (a moving common electrode) becomes closer to fixed positive electrode  205   b  and further from fixed negative electrode  204   b . These pivots result in a change in differential capacitance, which can be extracted and processed by readout circuitry, as described in reference to  FIG. 5 . 
       FIG. 3A  is a side view of dual pendulous proof masses that use multiple polysilicon layers having perforations to make the heavy side and light side areas symmetric and suppress vertical, thermal gradient-induced offset, according to an embodiment. As illustrated in  FIG. 3A , the hole quantity and hole size in a polysilicon layer of the pendulous masses  201 ,  202  can be adjusted to balance dual pendulous masses  201 ,  202  by creating a net torque of zero on pendulous masses  201 ,  202 . That is, the vertical component F of the pressure force caused by the vertical thermal gradient can be nullified by changing the area, by adjusting the hole quantity and hole size, exposed to the gas molecules in an amount sufficient to create a net torque of zero. The holes alone, however, cannot balance pressure force components F 1  and F 2  due to the lateral thermal gradient. 
       FIG. 3B  is a side view of dual pendulous proof masses illustrating common mode rejection of lateral pressure force components F 1 , F 2 , caused by a lateral thermal gradient, according to an embodiment. When subjected to a lateral thermal gradient, pendulous mass  201  pivots about anchor  203  in the clockwise direction causing mass  201  (a moving common electrode) to move closer to positive fixed electrode  205   a  and further from negative fixed electrode  204   a . Under the same lateral thermal gradient, pendulous mass  202  pivots about anchor  203  in the same clockwise direction causing mass  202  (a moving common electrode) to move away from positive fixed electrode  204   b  and towards negative fixed electrode  205   b . This pivoting results in a net output of zero (ΔC+=ΔC−). Accordingly, dual pendulous proof masses that include a number and size of perforations adjusted to achieve symmetric areas in order to achieve a zero net torque, suppress offset caused by both vertical and lateral thermal gradients. 
       FIG. 4  is a top view of an alternative design of dual pendulous masses with asymmetric masses, according to an embodiment. A first pendulous mass  401  and a second pendulous mass  402  are rotatably coupled to anchor  403  by, for example, torsion bars. Pendulous mass  401  includes finger portion  406 , which overhangs pendulous mass  402 . Electrodes  404   a  (C−) and  405   a  (C+) are disposed on, or formed in, a substrate supporting pendulous mass  401 . Pendulous mass  402  includes finger portion  407 , which overhangs pendulous mass  401 . Electrodes  404   b  (C−) and  405   b  (C+) are disposed on, or formed in, the substrate. This alternative design allows for a stiffer suspension, which makes it less susceptible to stiction. 
       FIG. 5  is a flow diagram illustrating a readout circuit for a differential capacitance MEMS accelerometer, according to an embodiment. Readout circuit  500  implements a synchronous demodulation technique to reduce noise, increase linearity and dynamic range. In an embodiment, readout circuit  500  includes differential capacitors  501  (electrodes  204   a ,  204   b ,  205   a ,  205   b ), reference signal generator  502 , amplifier  504 , synchronous demodulator  506 , low-pass filter  508  and analog-to-digital converter (ADC)  510 . The reference signals (PM 1 , PM 2 ) can be AC voltage signals that can be a square-wave or sinusoidal signal. The reference signals PM 1  and PM 2  are applied onto pendulous proof masses  201 ,  202 , respectively where the masses form differential capacitive pairs with sensing electrodes  204   a ,  204   b ,  205   a ,  205   b . Amplifier  504  is used to convert the differential sensing capacitance value to an amplified AC voltage and can be, for example, a trans-impedance amplifier. The amplified AC voltage is input into synchronous demodulator  506 , which operates at the excitation frequency f e  and is controlled by control signal X c (t). The output voltage of synchronous demodulator  506 , V out  is proportional to the product of the differential capacitance (C + −C − ) and feedback capacitor C f  of amplifier  504 , according to Equation [20]: 
     
       
         
           
             
               
                 
                   
                     V 
                     out 
                   
                   ∝ 
                   
                     
                       1 
                       
                         C 
                         f 
                       
                     
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                       ( 
                       
                         
                           C 
                           + 
                         
                         - 
                         
                           C 
                           - 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   20 
                   ] 
                 
               
             
           
         
       
     
     The output voltage, V out , of synchronous demodulator  506  is input into low-pass filter  508 , which outputs a DC output signal with an amplitude and phase corresponding to the sensed capacitance change. Low-pass filter  508  (e.g., a Bessel filter) limits the bandwidth, and thus increases the resolution of the voltage signal. ADC  510  converts the filtered DC output signal into a digital value, which can be used by various applications, as described in reference to  FIG. 6 . ADC converter  510  can be implement using, for example, a delta-sigma ADC. In an embodiment, a feedback can be included to increase the dynamic range of circuit  500 . 
       FIG. 6  is an architecture for an electronic system that uses the capacitive MEMS accelerometer with dual pendulous masses for various applications, according to an embodiment. Architecture  600  can be included in any electronic device that uses motion sensors, including but not limited to: smart phones, tablet computers, wearable devices (e.g., a smart watch) and automotive systems. 
     Architecture  600  includes processor(s), memory interface  602 , peripherals interface  603 , motion sensors  604   a  . . .  604   n , display device  605  (e.g., touch screen, LCD display, LED display), I/O interface  606  and input devices  607  (e.g., touch surface/screen, hardware buttons/switches/wheels, virtual or hardware keyboard, mouse). Memory  612  can include high-speed random access memory and/or non-volatile memory, such as one or more magnetic disk storage devices, one or more optical storage devices and/or flash memory (e.g., NAND, NOR). 
     Memory  612  stores operating system instructions  608 , sensor processing instructions  609  and application instructions  610 . Operating system instructions  608  include instructions for implementing an operating system on the device, such as iOS, Darwin, RTXC, LINUX, UNIX, WINDOWS, or an embedded operating system such as VxWorks. Operating system instructions  608  may include instructions for handling basic system services and for performing hardware dependent tasks. Sensor-processing instructions  609  perform post-processing on motion sensor data (e.g., averaging) and provide control signals to motion sensors. Application instructions  610  implement software programs that use data from one or more motion sensors  604   a  . . .  604   n , such as navigation, digital pedometer, tracking or map applications. At least one motion sensor  604   a  is the capacitive MEMS accelerometer with dual pendulous masses, as described in reference to  FIGS. 1-5 . 
     For example, in a navigation application executed on a smart phone, acceleration data is provided by the capacitive MEMS accelerometer to processor(s)  601  through peripheral interface  603 . Processor(s)  601  execute sensor-processing instructions  609 , to perform further processing of the acceleration data (e.g., averaging). Processor(s)  601  execute instructions for the navigation application, which draws a map on display device  605  including a location marker that shows the location of the smartphone on the map. The acceleration data is used to determine the speed and direction of the smart phone on the map. If a user is walking with the smartphone, the acceleration data can be used to count steps using known digital pedometer techniques. The step count can be multiplied by the user&#39;s stride length to determine a distance traveled by the user. Accordingly, the applications benefit from the dual pendulous design in that the acceleration measurements provided by the capacitive MEMS accelerometer are more accurate than without the design due to the common mode rejection of vertical and lateral thermal gradient-induced offset. 
     While this document contains many specific implementation details, these should not be construed as limitations on the scope what may be claimed, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can, in some cases, be excised from the combination, and the claimed combination may be directed to a sub combination or variation of a sub combination. Logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other implementations are within the scope of the following claims.