An analog floating-gate (AFG) inclinometer where a plurality of AFG sensors are provided to detect the presence of a discharge caused by settling of a conductive liquid droplet contained in a sealed microchannel under gravity. A plurality of sensor port electrodes associated with the AFG sensors are placed along the length of a curved sealed microchannel of the inclinometer at specific positions calibrated to corresponding angular inclinations. Discharge detected at a specific AFG sensor port during measurement due to the movement of the conductive liquid droplet under gravity is used in determining a surface inclination being measured.

FIELD OF THE DISCLOSURE

This disclosure relates generally to the field of semiconductor sensors and the methods of fabrication thereof, and more particularly, without limitation, to an analog floating-gate inclinometer and its fabrication.

BACKGROUND

An inclinometer or clinometer is an instrument for measuring angles of slope (or tilt), elevation or depression of an object or surface with respect to gravity. It is also known as a tilt meter, slope gauge, gradient meter or gradiometer, level gauge or level meter, and the like, typically depending on the field of use or application. Although mechanical inclinometers have been known for a long time, the field of electronic sensor-based inclinometers and related instrumentation is relatively recent, where improvements in performance and reliability are continually being sought. Whereas advanced tilt sensors using micro-electro-mechanical systems (MEMS)-based components such as proof masses with electrodes, springs and fixed electrodes have been developed, there remains a need for electronic inclinometers that offer better performance, for example in terms superior sensor zero offset and sensitivity, sensor linearity, hysteresis, repeatability, and the temperature drift, in a cost-effective manner. Moreover, there is a further need for tilt instrumentation that permits fast and accurate measurements of inclination in both un-powered and/or low-powered conditions, thereby enabling deployment in a variety of applications.

As the advances in the design of integrated circuits and semiconductor fabrication continue to take place, improvements in semiconductor-based sensor technologies, including electronic inclinometers, are also being concomitantly pursued.

SUMMARY

Embodiments of the present invention are broadly directed to an analog floating-gate (AFG) inclinometer and fabrication thereof, wherein a plurality of AFG sensors are provided to detect the presence of a discharge caused by the settling of a conductive liquid droplet contained in a sealed microchannel under gravity. A plurality of sensor port electrodes associated with the AFG sensors are placed along the length of a curved sealed microchannel of the inclinometer at specific positions calibrated to corresponding angular inclinations. In one implementation, discharge detected at a specific AFG sensor port during measurement due to the movement of the conductive liquid droplet under gravity is used in determining a surface inclination being measured.

In one aspect, an embodiment of an inclinometer is disclosed which comprises, inter alia, a semiconductor substrate and a dielectric layer disposed over the semiconductor substrate, the dielectric layer defining a sealed arcuate microchannel that contains a conductive liquid droplet. Access port electrodes are provided in the sealed arcuate microchannel, wherein each of the access port electrodes is associated with a reference electrode within a proximity of the respective access port electrode and disposed along a curvature of the sealed arcuate microchannel. In one embodiment, the access port electrodes are spaced from one another with an arc length that is calibrated to an angular inclination resolution. The inclinometer also includes analog floating-gate (AFG) devices formed in the semiconductor substrate, each corresponding to one or access port electrodes, wherein each of the AFG devices comprises a first conductor electrically coupled to the corresponding access port electrode and a second conductor electrically coupled to the reference electrode associated with the corresponding access port electrode. An example inclinometer may also comprise or otherwise be associated with a control circuit coupled to each of the AFG devices, the control circuit configured to: (i) detect a discharge current in at least one of the AFG devices along a conductive path between the corresponding access port electrode and the associated reference electrode interposed by the conductive liquid droplet, and (ii) determine an angular inclination measurement based on the detection of the discharge current of the at least one of the AFG devices.

In another aspect, an embodiment of a method of fabricating an AFG-based inclinometer is disclosed. The claimed method comprises, inter alia, forming a plurality of AFG sensor devices in a semiconductor substrate, wherein each of the AFG devices comprises a first conductor and a second conductor, the number of AFG devices being dependent upon, e.g., desired angular measurement resolution, maximum measurement range of angular inclination, sizing/shape of a sealed microchannel, etc., depending on implementation. In one example embodiment, the method comprises forming or otherwise defining an arcuate microchannel in a dielectric layer disposed over the semiconductor substrate containing the AFG devices, wherein the arcuate microchannel includes access port electrodes, each of the access port electrodes associated with a reference electrode formed within a proximity of the respective access port electrode and disposed along a curvature of the arcuate microchannel, the access port electrodes spaced from one another with an arc length that is calibrated to an angular inclination resolution. In one arrangement, the first and second conductors of the AFG devices are operative as corresponding access port electrodes and reference electrodes, respectively. In another arrangement, the first and second conductors of the AFG devices may be electrically coupled to corresponding access port electrodes and reference electrodes via respective conductive paths. An electrical connection path may therefore be provided for coupling each access port electrode to the first conductor of a corresponding AFG device and another electrical connection path for coupling the reference electrode associated with the access port electrode to the second conductor of the corresponding AFG device. A suitable conductive liquid droplet (e.g., having desirable electrical conductive properties, physical/chemical properties, etc.) may be injected or otherwise introduced into the arcuate microchannel, which is then sealed with a cap structure. In one arrangement, the cap structure may comprise an inverted semiconductor wafer having one or more dielectric layers. Further, the conductive liquid droplet may be dimensioned to move freely within the sealed arcuate microchannel under gravity. An example fabrication method may also comprise providing a control circuit coupled to each of the AFG devices for performing one or more functions as set forth in additional detail hereinbelow.

DETAILED DESCRIPTION OF THE DRAWINGS

In the following description, reference may be made to the accompanying drawings wherein certain directional terminology, such as, e.g., “upper”, “lower”, “top”, “bottom”, “left-hand”, “right-hand”, “front side”, “backside”, “vertical”, “horizontal”, etc., may be used with reference to the orientation of the Figures or illustrative elements thereof being described. Since components of embodiments can be positioned in a number of different orientations, the directional terminology is used for purposes of illustration and is in no way limiting. Likewise, references to features referred to as “first”, “second”, etc., are not indicative of any specific order, importance, and the like, and such references may be interchanged mutatis mutandis, depending on the context, implementation, etc. It is understood that further embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The features of the various exemplary embodiments described herein may be combined with each other unless specifically noted otherwise.

As employed in this specification, the terms “coupled”, “electrically coupled”, “connected” or “electrically connected” are not meant to mean that elements must be directly coupled or connected together. Intervening elements may be provided between the “coupled”, “electrically coupled”, “connected” or “electrically connected” elements.

Example semiconductor devices described below may include or formed of a semiconductor material like Si, SiC, SiGe, GaAs or an organic semiconductor material. The semiconductor material may be embodied as a semiconductor wafer or a semiconductor chip containing a number of analog floating-gate (AFG) integrated circuits, input/output and control circuitry, as well as microprocessors, microcontrollers, and/or micro-electro-mechanical components or systems (MEMS), inter alia. The semiconductor chip may further include inorganic and/or organic materials that are not semiconductors, for example, insulators such as dielectric layers, plastics or metals, etc.

Referring now to the drawings and more particularly toFIG. 1, depicted therein is an example AFG-based inclinometer100that may be fabricated in a suitable semiconductor material102as a semiconductor product or device according to an embodiment of the present invention. A sealed microchannel104fabricated in a dielectric layer over a semiconductor substrate is configured to contain a conductive liquid droplet118of a suitable dimension that is arranged to move freely within the microchannel104under the influence of gravity. Preferably, the sealed microchannel104is shaped in a curvilinear or arcuate form, which may comprise at least a portion of a suitable geometric shape, e.g., a circle, a semicircle, a quarter circle, a parabolic or ellipsoidal arc, and the like. A plurality of sensor access port electrodes106(1) to106(N) and corresponding reference electrodes108(1) to108(N) may be positioned along a curvature of the microchannel104such that the access port electrodes106(1) to106(N) are spaced from one another with a specific arc length that is calibrated to a particular angular inclination resolution, as will be described in additional detail below. In one implementation, the angular inclination may be calibrated in degrees or radians of angle. In another implementation, the angular inclination may be calibrated in a gradient or slope percentage, or tilt, and the like. A plurality of analog floating-gate (AFG) sensor devices or integrated circuits110(1) to110(N) are formed in the semiconductor substrate corresponding to the plurality of access port electrodes106(1) to106(N) and associated reference electrodes108(1) to108(N), for example in a one-to-one correspondence, wherein each of the AFG devices comprises a first conductor electrically coupled to the corresponding access port electrode and a second conductor electrically coupled to the reference electrode associated with the corresponding access port electrode for ground or discharge. By way of example, AFG sensor device110(i−1) is provided with a first conductor111A coupled to the corresponding access port electrode106(i−1) and a second conductor113A coupled to the corresponding reference port electrode108(i−1), via respective connective paths111B and113B. One skilled in the art will recognize upon taking reference to this drawing Figure in conjunction with the other drawing Figures that although elongated connective paths111B and113B are illustrated inFIG. 1, first and second conductors111A/113A of AFG110(i−1) may be fabricated in a vertically integrated process flow (e.g., for better manufacturability) to operate as corresponding access port and reference electrodes106(i−1),108(i−1), as will be set forth in reference to an example implementation with additional details hereinbelow.

Inclinometer100may further include or be otherwise associated with a control circuit112that may be formed in the same semiconductor substrate material as part of the AFG devices or separately. Regardless of how the control circuit112is coupled to or otherwise associated with the AFG devices110(1) to110(N), the control circuit112is preferably configured to perform, inter alia: detection of a discharge current in at least one of the AFG devices along a conductive path between the corresponding access port electrode and the associated reference electrode interposed by the conductive liquid droplet (e.g., when the access port electrode and the associated reference electrode coupled to the corresponding AFG devices are in an electrical conductive relationship due to a conductive path formed therebetween by the conductive liquid droplet118settled to cover at least the specific access port electrode and associated reference electrode under gravity, for instance, depending on inclination when the inclinometer is positioned on a surface for measurement). The control circuit112may also be configured to determine an angular inclination measurement based on the detection of the discharge current of the at least one of AFG devices, e.g., by way of correlation of the position of the discharging AFG device(s) and its calibrated angular inclination, interrogation of a look-up table, and the like.

In one arrangement, reference electrodes108(N) may be formed within a select proximity of the corresponding access port electrodes106(N), which may be termed inter-electrode distance115, such that the conductive liquid droplet118may be sized to cover only one access port electrode and corresponding reference electrode when the conductive liquid droplet118is settled at that access port electrode under gravity. In another arrangement, the conductive liquid droplet118may be sized to cover more than one access port electrode and corresponding reference electrodes for providing respective conductive paths therebetween when the conductive liquid droplet is settled under gravity. In such an arrangement, the control circuit112may be configured to detect discharge currents in multiple AFG devices coupled to the respective multiple access port electrodes covered by the conductive liquid droplet118and determine a specific angular inclination measurement based on respective positions of the multiple access port electrodes along the curvature of the sealed arcuate microchannel104.

Additional details concerning the functionality of the control circuit112, configuration and placement of access port and reference electrodes, fabrication of example AFG devices and associated microchannel, and calibration of an example inclinometer during manufacture will be set forth below, taking reference to the remaining drawing Figures that are illustrative of various views and embodiments of the present invention.

FIG. 2depicts an electrical circuit diagram of an AFG sensor device200that may be used in an inclinometer embodiment ofFIG. 1according to the teachings of the present invention in an example implementation. In this example, AFG sensor device200is arranged in the form of a subsystem, including integrated circuit202, in which control circuitry203that may be part of or an embodiment of, or otherwise associated with the control circuit112ofFIG. 1. As can be seen fromFIG. 2, control circuitry203may be coupled to various nodes of integrated circuit202for applying various control signals and monitor electrical parameters to carry out the functions described in further detail below. Such functions may include but not limited to appropriately biasing the integrated circuit202, (re)charging and erasure of a floating gate, and monitoring of discharge currents, for example. As noted above, control circuitry203may be realized in whole or in part as separate circuitry deployed within the subsystem of sensor device200, which may be disposed in communication with external processor circuitry and/or nodes. In some realizations, all or part of control circuitry203may be implemented into integrated circuit202itself, along with analog floating-gate functionality. In any event, it is contemplated that those skilled in the art having reference to this specification will be readily able to implement control circuitry203in the manner appropriate for carrying out the functions described herein, using the available and appropriate technology for the particular architecture to be used.

Integrated circuit202preferably includes an analog floating-gate circuit and structure in connection with which embodiments of the present invention may be used. Preferably, an example analog floating-gate circuit includes an electrically floating electrode, designated as floating-gate electrode210in the arrangement ofFIG. 2, which serves multiple functions. One function of analog floating-gate electrode210in the circuit202ofFIG. 2is operating as a plate of storage capacitor212. According to this embodiment, another plate of storage capacitor212receives a gate voltage VG from control circuitry203at terminal G (e.g., control gate), such that charge can be stored by storage capacitor212under suitable biasing voltages. Another function of floating-gate electrode210is operating as a gate of a metal-oxide-semiconductor (MOS) transistor204, which may be an n-channel or p-channel device, based on suitable CMOS technology. In the example ofFIG. 2depicting an n-channel device, a drain206of transistor204at drain terminal D receives drain voltage VD from control circuitry203, and a source208of transistor204at source terminal S is biased to a reference voltage, e.g., a ground reference as illustrated. In this arrangement, gate voltage VG applied at terminal G by control circuitry203will capacitively couple to floating-gate electrode210via storage capacitor212, with that voltage establishing the voltage at the gate of MOS transistor204, and thus the extent to which transistor204conducts between its drain D and its source S for a given drain-to-source voltage VD.

In the example arrangement ofFIG. 2, floating-gate electrode210also serves as a plate of each of tunnel capacitors218,220. Tunnel capacitors can apply charge to or remove charge from floating-gate electrode210, thereby “programming” it to a particular analog state. In the example of integrated circuit202, the plate of tunnel capacitor218opposite that of electrode210is connected to a terminal TP, while an opposing plate of tunnel capacitor220is connected to a terminal TN. The capacitor dielectric for tunnel capacitors218,220is contemplated to be relatively thin, to allow mechanisms such as Fowler-Nordheim tunneling to transfer charge between terminals TP, TN and floating-gate electrode210, depending on the bias. Although tunnel capacitors218,220may permit both the programming of stored charge onto floating-gate electrode210and the removal of that charge (“erase”), as noted above, it is contemplated that only one of these tunnel capacitors218,220may be implemented in some implementations.

In its general operation as an analog floating-gate device, the “programming” of floating-gate electrode210is carried out by application of a pulse of an appropriate negative voltage to terminal TN relative to the voltage at terminal TP and to the ground reference voltage at the opposite plate of storage capacitor212to cause electrons to tunnel through tunnel capacitor220. Because of the voltage divider formed by capacitors218,220,212, most of that programming voltage will appear across tunnel capacitor220, enabling electrons to tunnel through its capacitor dielectric to analog floating-gate electrode210, and become trapped at floating-gate electrode210. Conversely, electrons can be removed (“erased”) from floating-gate electrode210by applying an appropriate positive voltage at terminal TP relative to terminal TN and to the ground reference voltage at the opposite plate of storage capacitor212. Again, the voltage divider of capacitors218,220,212is operative such that most of that voltage is caused to appear across tunnel capacitor218, causing electrons that are trapped on floating-gate electrode210to tunnel through its capacitor dielectric to terminal TP. In the analog sense, the duration of the program and erase pulses can be adjusted to precisely set the charge state at floating-gate electrode210. Following programming and erasure, as the case may be, the extent to which charge is trapped on floating-gate electrode210will establish a voltage across storage capacitor212, and thus a gate voltage for MOS transistor204that controls its channel conduction.

Based on the foregoing description and fromFIG. 2, control circuitry203is coupled to the various terminals of the floating-gate device of integrated circuit202, including to terminals G, D, TP, TN so as to apply corresponding voltages VG, VD, VTP, VTN, respectively. In this example arrangement, control circuitry203monitors the drain current ID conducted by transistor204, e.g., by detecting the current drawn by its bias of drain voltage VD to directly measure drain current ID. Alternatively, transistor204may drive an analog circuit or other function, such as an amplifier, from which control circuitry203may obtain a measurement or detect the presence of drain current ID of transistor204. In an additional or alternative embodiment, control circuitry203may also include a timer function, such as a clocked counter or other conventional timer, to provide a time base for the monitoring/detection of drain current ID or its discharge, application of (re)charge pulses after a delay period, etc. as will be described below.

In the illustrated embodiment ofFIG. 2, AFG integrated circuit202also includes a conductor element216(e.g., sense conductor) that is electrically connected to floating-gate electrode210, and a reference conductor element214that is coupled to a reference voltage, such as ground, but is otherwise electrically isolated from conductor element216by a predetermined amount of separation or proximity, as well as from other nodes of the analog floating-gate device in integrated circuit202. As will be evident from the description below, conductor elements216,214may be constituted as metal pads operative as a pair of access port and reference electrodes disposed in a sealed microchannel in accordance with the teachings of the present invention.

FIG. 3Adepicts an electrical equivalent circuit300A of an example AFG sensor wherein a discharge may occur due to a conductive path effectuated by a conductive droplet disposed in the microchannel of an inclinometer according to an embodiment of the present invention. As shown inFIG. 3A, this equivalent circuit300A includes storage capacitor212receiving gate voltage VG, and transistor204having its drain biased at voltage VD and its source at ground. The conduction path between conductive element216and reference conductive element214provided by a conductive liquid droplet304(as exemplified by droplet118disposed in the sealed microchannel104ofFIG. 1) may be modeled in this equivalent circuit by the series connection of switch302and a fixed resistor (not specifically shown) that may be negligent depending on the conductive properties of the liquid droplet. For example, a highly ionic water droplet may be less resistive than a less ionic water droplet. As one skilled in the art will recognize, conductive properties of a working liquid or fluid for purposes of the present invention will effectuate a conductive path by which the charge of an energized floating gate may be discharged via the path between conductive element216and reference conductive element214at a rate proportional to the liquid's conductivity.FIG. 3Bqualitatively illustrates the operation of this equivalent circuit in terms of the discharge, where an ID discharge curve350is illustrated as a function of time in a graph300B. The initial condition of the circuit ofFIG. 3A, prior to time t0inFIG. 3B, has drain voltage VD and gate voltage VG both above the threshold voltage of transistor204(i.e., charged state), while a reference voltage, for example ground, biases each of reference conductor and source nodes. A high fraction (typically on the order of 90%) of the gate voltage VG will capacitively couple to floating-gate electrode210, turning on transistor204and resulting in drain current ID0being conducted prior to time t0. At this point in the operation, which is prior to the liquid droplet being settled at the particular AFG sensor port, there is no conduction path present between sense conductor element216and reference conductor element214. As such, floating-gate electrode210does not discharge to ground, and drain current ID remains constant at the level ID0. When the conductive liquid droplet in the sealed microchannel104settles at the particular AFG sensor port (under gravity due to the inclination of a surface at measurement), it provides a conduction path between conductor element216and one or more of reference conductor elements214, which may be illustratively shown as the switch302of the equivalent circuit300A being closed. Charge present at floating-gate electrode210will therefore conduct from conductive element216, through the conduction path of droplet304to the ground potential at reference conductor elements214. As charge is removed from floating-gate electrode210, the gate potential of transistor204drops, thereby causing drain current ID to drop following time t0, as shown in the ID current discharge curve350ofFIG. 3B.

One skilled in the art will recognize that such a drop in the ID current of an AFG sensor that is part of a plurality of AFG sensors provided at calibrated angular positions of a microchannel may be detected, monitored, measured, or otherwise processed in order to correlate or otherwise determine an angular inclination of a surface. In one example implementation, such operations may be executed as part of the functionality of an inclinometer control circuit, e.g., control circuit112, as set forth hereinabove. In one embodiment, a determination may be made immediately after a drop in the ID current is detected. In another embodiment, a determination may be made after a certain time has elapsed and/or when the ID current is dropped to a certain level. Where a conductive liquid droplet is sized to cover multiple AFG access ports when settled under the influence of gravity, an example control circuit may be configured to not only detect the presence of ID current drops in respective AFG sensors but also measure the different drop rates, actual current values, and the like, and use that information in a more advanced determination logic (e.g., weighted averages, etc.) in order to arrive at a specific angular inclination measurement based on respective positions of the multiple access port electrodes experiencing the ID current discharges at the time of measurement.

FIG. 4is a simplified rendition of an AFG inclinometer400illustrating an angular inclination measurement based on movement of a conductive liquid droplet in a sealed microchannel under the influence of gravity according to an example embodiment. As will be seen below, whereas an inclinometer comprising a plurality of AFG sensor ports disposed in a microchannel is fabricated as a planar device in a suitable semiconductor material, it may be oriented in a measurement apparatus or device such that when the apparatus is placed or positioned on a surface for measurement, the conductive liquid droplet in the inclinometer's sealed microchannel experiences a vertical gravitational force. Accordingly, when the inclinometer is placed on a flat surface, the position of the conductive liquid droplet in the sealed microchannel is indicative of 0 degrees of inclination (i.e., the “zero angle” position, also referred to as initial vertical reference line or initial plumb line). If a measurement surface has a slope, either negative or positive, the conductive liquid droplet moves within the sealed microchannel along its curvature either to the left or the right of the zero angle position under the gravitational force to define a new plumb line, whose deflection from the initial vertical reference is a measurement of the angular inclination of the surface. Assuming a simple circular geometry for the sealed microchannel (e.g., the sealed microchannel is a portion of a circle), it is known that an angle (θ) subtended by an arc length (s) of a circular arc is related to the radius (r) of the circle. More particularly, the length of an arc is equal to the radius multiplied by the magnitude of the subtended angle in radians, which can be converted into degrees given that 1 radian=180/π degrees. Accordingly, for a sealed microchannel having the shape of an arcuate portion that forms part of a circle with certain diameter, a number of sensor access ports may be provided on either side of the zero angle vertical reference line, which in a symmetrical arrangement is exactly at the mid point of the length of the arcuate portion. For an inclinometer to have a range of ±45 degrees, the sealed microchannel must therefore comprise a quarter circle that subtends to 90 degrees or π/2 radians. Likewise, for an inclinometer to have a range of ±90 degrees, the sealed microchannel needs to be at least half a circle which “subtends” to 180 degrees or π radians.

Still continuing with a circular geometry embodiment by way of illustration, angular measurement resolution may be defined as R={Maximum measurement range of angular inclination}/(N−1), where N=the number of sensor access ports provided in a sealed microchannel. For example, if the sealed microchannel comprises a semicircle for measuring ±90 degrees of angular inclination, 181 sensor access ports or electrodes are needed to achieve an angular inclination resolution of 1 degree, which may be spaced apart along the length of the sealed microchannel at a specific arc length that subtends to 1 degree. To obtain a half a degree of angular resolution, an example semicircular microchannel will therefore require 361 sensor access ports that are spaced apart along the length of the microchannel at a specific arc length that subtends to half a degree.

One skilled in the art will recognize that the length of a curvilinear, arcuate microchannel may accordingly be calibrated during fabrication based on the number of sensor access ports used for an inclinometer in conjunction with the size and shape of the specific microchannel being fabricated. Furthermore, although various examples of specific circular geometries have been illustrated herein, similar calibration methodologies may also be applied, mutatis mutandis, where non-circular microchannels, tubes, trenches, etc. having different curvatures are implemented (e.g., parabolic or ellipsoidal arcs, smoothly differentiable curves, and the like).

Turning to the example inclinometer embodiment400ofFIG. 4, a semicircular microchannel404is illustrated with a plurality of sensor access port electrodes406-1to406-12and corresponding plurality of reference electrodes408-1to408-12. Given that there are 12 electrode pairs, the angular resolution of this embodiment is 16.363°, wherein the 12 electrode pairs are spaced apart at an arc length407that subtends to 16.363° for a given radius of the microchannel404. Initially, on a flat surface, conductive liquid droplet410contained within the microchannel404is at a 0° position that defines an initial vertical reference line415. As the inclinometer400is placed on a tilted surface419that is at an angle with respect to a flat surface or horizon420, conductive liquid droplet410is moved to a new position that is 3 arc lengths away from the zero angle position, defining a new plumb line416. Because of the conductive path created between the sensor access port electrode406-9and associated reference electrode408-9, a discharge is detected by the control circuitry associated with the AFG device coupled to the electrodes406-9,408-9, which may be correlated as an angular inclination of 49.09° (e.g., by way of a lookup table, for instance), that may be read out as output via a suitable display or other user interface. Further, the subtended angle φ between the initial vertical reference line415and the new vertical reference line416is also the angular inclination φ between the tilted surface419and horizon420because of the straightforward Euclidian planar geometry involving the congruent angles caused by the intersection of the tilted surface line419and a reference parallel line418by the transversal vertical line416.

Although the plurality of sensor access port electrodes and corresponding reference electrodes have been illustrated in the example inclinometer embodiments ofFIGS. 1 and 4as square pads are placed in each other's pair-wise proximity within the sealed microchannel, one skilled in the art will recognize that several variations are possible within the scope of the present invention, as will be seen in reference to one or more additional or alternative embodiments set forth in detail below. By way of example,FIG. 5depicts another simplified AFG inclinometer500illustrating an arrangement wherein five sensor port electrodes502-1to502-5disposed in sealed microchannel510are placed at a calibrated arc length508that subtends a 45° angle. Each sensor port electrode502-1to502-5is surrounded by a reference electrode ring or square band504-1to504-5that is separated by a select distance. Further, additionally or optionally, the reference electrode rings504-1to504-5may be electrically tied together, e.g., by way of electrical connectors506that couple each reference electrode to its adjacent reference electrode, thereby resulting in a continuous reference band, strip or ground ring disposed within the microchannel510in an example implementation. Skilled artisans will further recognize that a reference electrode does not have to be in any particular shape or size so long as a conductive droplet provided within the sealed microchannel of an inclinometer covers the separation distance between an access port electrode and its corresponding reference electrode such that the charge on the AFG sensor's floating-gate is discharged during inclination measurement operations.

FIG. 6depicts is an example layout diagram of an AFG integrated circuit corresponding to an embodiment shown inFIG. 2. As one skilled in the art will recognize, the layout600shown inFIG. 6is an illustrative example layout that may be implemented using a number of fabrication technologies and line widths for the construction of an analog floating-gate structure such as may be used to implement the circuit ofFIG. 2. It is therefore contemplated that the example floating-gate structure may be fabricated by way of known or heretofore unknown manufacturing technology, extending into or including sub-micron fabrication processes. It is further contemplated that those skilled in the art having reference to this specification will be readily able to adapt an example AFG integrated circuit design set forth herein in the desired manufacturing technology, without undue experimentation.

As shown inFIG. 6, a floating-gate electrode may be constructed as a polycrystalline silicon (polysilicon) element610having a specific geometry, which may extend over the surface of a semiconductor wafer (or over a semiconductor surface layer, in the silicon-on-insulator (SOI) context) in forming multiple devices or components. Polysilicon element610is typically doped to a desired conductivity type and concentration, to be conductive to the desired extent; for example, by way of n-type doping for an example n-channel MOS transistor204. In an example implementation, polysilicon element610may be provided with a widened portion at one of its ends that is operative to serve as a lower plate of storage capacitor212. Apart from forming the capacitor's lower plate, polysilicon element610may be designed as a narrower strip, for example, at a minimum feature size without violating the design rules or critical dimensions for the manufacturing technology implemented in an example process. The cross-section of storage capacitor212along X-X′ illustrated inFIG. 7shows the lower plate portion of polysilicon element610as overlying a trench isolation dielectric structure708. A gate dielectric layer706, e.g., formed of deposited or thermal silicon dioxide, is disposed between the surface of isolation dielectric structure708and polysilicon element610, which will also underlie polysilicon element610at those locations where it overlies active regions (i.e., at transistor204and tunnel capacitors218,220). A sidewall oxide702may also be provided along the vertical sidewalls of polysilicon element610. In the example embodiment shown, the surface into which isolation dielectric structure708is formed is the top surface of p-type silicon substrate710(for n-channel AFG devices). An upper plate602of storage capacitor212may be formed of a metal such as tantalum nitride (TaN), and overlies the widened portion of polysilicon element610at this location. In this embodiment of the invention, capacitor dielectric704shielding the floating gate610may be formed of one or more dielectric layers, e.g., silicon nitride, silicon dioxide, or a combination of these or other dielectric materials.

Continuing to refer toFIG. 6, transistor204and tunnel capacitors218,220may be constructed along those portions of polysilicon element610that overlie active regions (i.e., that do not overlie isolation dielectric structures708). In particular, MOS transistor204may be defined at that portion of polysilicon element610overlying an active region of p-type substrate710, with gate dielectric706disposed between polysilicon element610and that active region. The source and drain of transistor204may be formed as heavily-doped n-type source/drain regions608implanted and diffused into the p-type active region on opposite sides of polysilicon element610, e.g., in a conventional self-aligned fabrication process. Topside contacts from an overlying metal conductor, and corresponding to terminals D, S as in the circuit ofFIG. 2, may be made through an interlevel dielectric layer to source/drain regions608.

Tunnel capacitors218,220may be constructed in the conventional manner for floating-gate devices. In one example embodiment, tunnel capacitor220may be constructed essentially similarly as n-channel MOS transistor204, but where polysilicon element610overlies an instance of an isolated p-type well, e.g., a p-well isolated from the underlying substrate by a buried n-type layer and an n-well ring. Gate dielectric layer706is formed between polysilicon element610and the surface of the p-well to serve as the capacitor dielectric layer. Heavily-doped n-type source/drain regions604may be formed into the isolated p-well in a self-aligned manner. Terminal TN may be connected via a contact to the isolated p-well in which these source/drain regions604are formed, such that the resultant semiconductor structure operates as a capacitor rather than a transistor, but with source/drain regions604serving as sources of electrons when a negative bias is applied to terminal TN. Likewise, tunnel capacitor218may be constructed essentially similarly as tunnel capacitor220, but at a location at which polysilicon element610overlies gate dielectric layer706at the surface of an n-well formed into substrate710. Terminal TP is connected to this n-well by a contact structure (not specifically shown in the layout600), and p-type source/drain regions606that are formed on either side of polysilicon element610act as a sources of holes when a positive bias is applied to terminal TP. Skilled artisans should appreciate that tunnel capacitors218,220may be constructed according to such other arrangements as suitable for particular implementations and manufacturing technologies.

In the example layout embodiment600shown inFIG. 6, the difference in relative area between tunneling capacitors218,220, on one hand, and storage capacitor212, on the other hand, along with any differences in the capacitor dielectric materials and thicknesses, will be reflected in the relative capacitances between these elements. Because the capacitance of storage capacitor212is substantially larger than the capacitances of tunnel capacitors218,220(and also the parasitic capacitances of transistor204), tunneling of electrons can be achieved at reasonable bias voltages to avoid damage or breakdown. This disparity in capacitive coupling is contemplated to provide excellent (re)programming (i.e., (re)charging) and erase performance for the plurality of AFG devices provided in an example inclinometer implementation according to the teachings of the present invention.

Many variations in the electrical and physical construction of an AFG circuit, relative to that described above, are contemplated. From an electrical standpoint, an example variation may include circuits such as a reference circuit arranged as a dual floating-gate differential amplifier circuit, as known in the art. As mentioned above, examples of other analog floating-gate circuits include analog memory devices, and digital electrically programmable memory cells (including cells that may be set into one of more than two possible states, reflecting a multiple-bit data value). From a construction standpoint, such variations include other arrangements of the floating-gate device, including polysilicon-to-polysilicon floating-gate capacitors, polysilicon-to-active capacitors, and the like, and including floating-gate devices that are programmable by other mechanisms besides Fowler-Nordheim tunneling. It is contemplated that those skilled in the art having reference to this specification will be readily able to realize these, and other, variations as appropriate for particular circuit applications, without undue experimentation.

FIGS. 8A-8Cdepict example layout arrangements of conductors of an AFG integrated circuit for sensing the presence of a conductive liquid droplet arranged to move freely in a sealed microchannel under gravity.FIG. 9depicts a cross-sectional view of a portion of the layout of shown inFIG. 6in additional detail. Cumulatively referencing these Figures in conjunction withFIGS. 6 and 7described above, conductor element216may formed as a metal pad at the surface of integrated circuit202to be in electrical contact with polysilicon element610(i.e., floating-gate electrode210inFIG. 2). In the conductor embodiment800A ofFIG. 8A, reference conductor element214may be formed as a concentric ring around the conductor216with a specific separation or distance802A. In the conductor embodiment800B ofFIG. 8B, reference conductor element214may be of a different geometry (e.g., a square) that surrounds the conductor element216, but spaced apart therefrom with a suitable separation802B. In a still further example embodiment800C ofFIG. 8C, one or more reference conductor elements214may be provided that are positioned in a proximity802C of the conductor element216coupled to the polysilicon floating gate610. In yet another arrangement, the reference conductor elements214of multiple AFG sensor devices may be commonly or electrically connected together to form a reference ring, band or strip or similar structure along the curvature of a sealed microchannel of an example inclinometer of the present invention, as previously noted. One skilled in the art will readily recognize that several other variations, modifications and arrangements may be provided with respect to the conductor elements of AFG sensor devices in an inclinometer implementation so long as the conductive droplet sizing is compatible for providing a conductive path as described hereinabove.

A conductor arrangement similar to the arrangements ofFIG. 8Aor FIG. B is particularly illustrated in the cross-sectional view900ofFIG. 9, wherein a cross-section taken at Y-Y′ of the layout600is exemplified. In this example, first interlevel insulator902overlies polysilicon element610, with a first conductive plug906disposed in a via in the insulator902and in contact with polysilicon element710as shown. A conductive pad908, formed of a metal (i.e., a first metal level) or another conductor material, is disposed at the surface of first interlevel insulator902and in contact with plug906. Similarly, a second interlevel insulator layer904overlies first interlevel insulator902, with a second conductive plug910formed in a via through layer904to contact conductive pad908. Conductor element216in this example is formed at the surface of second interlevel insulator904, at a location overlying and in contact with conductive plug910. As such, conductor element216is in electrical contact with polysilicon element610(which forms floating-gate electrode210inFIG. 2), by the series connections of plugs910,908and pad906. While plugs906,910and pad908are all illustrated as directly overlying one another in the example cross-sectional view900ofFIG. 9, it is also contemplated that plugs906,910may be laterally separated from one another (i.e., contacting conductive pad908at different locations along its length) if desired. In addition, while the example embodiment ofFIG. 9shows a single metal level (pad908) disposed between conductive element216and polysilicon610, it should be apparent that two or more metal levels may be included in the various layers therebetween, as known in the art. In any event, according to these embodiments, conductive element216is provided at the surface of the AFG sensor circuit, either above the top insulator layer (layer904in the example ofFIG. 9), or alternatively exposed through an opening in a protective overcoat or other overlying insulator layer.

As noted above, one or more reference conductive elements214may also be provided at the surface of the AFG sensor circuit, which may be comprise one or more metal features formed in the same conductive layer as conductive element216, and near to but spaced apart from conductive element216. In one example embodiment, reference conductive elements214may be provided in the form of metal pads that are significantly larger in area than conductive element216. Further, it is contemplated that such multiple metal pads may be arranged to surround conductive element214, similar to one or more example conductor arrangements described above so as to be capable of being covered or interposed by a droplet950, illustratively shown in two interposed arrangements inFIG. 9. In any case, reference conductive element(s)214are each separated from sense conductive element216by a particular distance or separation802A-C as previously set forth, and as such are not in direct electrical contact with conductive element214(nor in contact with any other node of the analog floating-gate circuit, for that matter, in an example implementation). It is contemplated that one or more reference conductive elements214that surround conductive element216on all sides may be designed to provide repeatable and consistent measurement results. Each reference conductive element214is preferably in contact with a conductor or a semiconductor region that will, in operation, be at a reference voltage such as ground. Further, as in the case of conductive element216, each reference conductive element214may be exposed at the surface of the AFG sensor circuit, either above the top insulator layer (layer904) in the example embodiment ofFIG. 9), or alternatively exposed through an opening in a protective overcoat or other overlying insulator layer.

FIGS. 10A-10Idepict cross-sectional views illustrative of an example process flow for fabricating an AFG inclinometer after the formation of AFG sensor circuits according to an embodiment of the present invention.FIG. 10Ashows a fabrication stage1000A with respect to a semiconductor wafer that has been processed through appropriate flows, e.g., as set forth above, to result in the formation of multiple AFG sensors per die (i.e., per inclinometer device), each comprising topside conductor elements1014,1016, one or more metal levels or layers1012-1,1012-2underlying the conductor elements, and associated floating-gate electrode1008formed over a suitable substrate1002having source/drain regions1004/1006defined therein. One skilled in the art will recognize that the exact number and spatial arrangement of the AFG sensors is dependent on various design factors such as the range of angular inclination that an inclinometer device can measure (e.g., ±45 degrees, ±60 degrees, ±90 degrees, etc.), resolution of angular inclination measurements (i.e., the smallest amount of angular inclination that can be reliably measured), size/shape of the microchannel to be formed, conductive droplet sizing, and the like, as previously noted. For example, if an inclinometer having ±90 degree range is desired at 1 degree resolution, 181 AFG sensor circuits will be required, which need to be placed along the calibrated curvature of a semicircular microchannel at appropriate arc lengths as described hereinabove.

To form a microchannel, a dielectric layer1020of suitable thickness, e.g., silicon dioxide, is deposited over the conductor elements1014,1016, as shown in fabrication stage1010B, wherein conductor element1014operative as an access port electrode is electrically coupled or connected to the floating gate1008while conductor element1016is provided as a reference electrode associated therewith. Fabrication stage1000C illustrates an etching process wherein an open microchannel or trench1022A is created in the dielectric layer1020. A silicon nitride liner1024is then deposited in the open microchannel1022A to line the bottom and sidewalls of the open microchannel1022A, as shown in fabrication stage1000D. In fabrication stage1000E, a nitride etch process is performed in order to create openings1026A,1026B over the conductors1014and1016, respectively. A single conductive droplet or micro-drop1026of suitable dimensions (e.g., from 1 micron to several microns) is deposited into the open microchannel1022A, using a number of microdispensing techniques, e.g., ink jet deposition, microsyringe deposition, etc. As illustrated in fabrication stage1000F ofFIG. 10F, the droplet1026is preferably sized to cover the separation between conductor elements1014and1016when settled at a particular AFG access port. A cap structure1030, which in one example embodiment may comprise a previously formed wafer of silicon substrate1032, silicon dioxide1034, and silicon nitride1036, is inverted and positioned over the wafer with the AFG circuitry (also referred to as the sensor wafer), as shown in fabrication stage1000G. In one embodiment, the silicon substrate1032of cap wafer structure1030may be thinned to a suitable thickness, with oxide and nitride layers1034,1036having appropriate thicknesses formed thereon.

In fabrication stage1000H, the inverted cap wafer structure1030is brought into contact with the sensor wafer and bonded to it so as to create a sealed microchannel1022B containing conductive droplet1026therein. Openings1042over bond pads1040provided at appropriate places in the AFG inclinometer device (e.g., formed during one or more of the metallization stages) may be created in the cap wafer1030and through the top dielectric layer by an etching process, as illustrated in fabrication stage1000I ofFIG. 10I.

Approximate dimensions for a circle-based microchannel could be a diameter of several hundred microns and widths of up to several microns, depending on resolution and/or size of the conductive droplet. Because droplet sizes as low as 1 μm are possible, various microchannel geometries may be implemented in practicing an embodiment of the present invention. By way of illustration, an example microchannel could comprise a diameter of 500 to 1800 μm and a width ranging e.g., from 2 to 25 μm for a 1-degree resolution and assuming the droplet only covers one sensor port at a time. Of course, the diameter could be made smaller and the ports moved closer together by determining the width of the droplet during calibration/reset and using that width in subsequent calculations/calibrations to determine the slope.

FIGS. 11A and 11Bare flowcharts of an example overall process flow or method1100A/B for fabricating an AFG inclinometer according to an embodiment of the present invention. At block1102, a plurality of AFG sensor devices in a semiconductor substrate may be formed, wherein each AFG device comprises a first conductor and a second conductor. A microchannel having a suitable geometry (e.g., arcuate or curvilinear shape) is formed or otherwise defined in a dielectric layer deposited over the semiconductor substrate (block1104), wherein the arcuate microchannel includes a plurality of access port electrodes and a corresponding plurality of reference electrodes formed therein. As noted above, the access port electrodes are disposed along a curvature of the arcuate microchannel, the access port electrodes being spaced from one another with an arc length that is calibrated to an angular inclination resolution. In one example implementation, the microchannel may be formed directly over the AFG sensor devices as described hereinabove, whereby the first and second conductor elements of the AFG sensor devices are respectively operative as access port electrodes and associated reference electrodes. In an alternative or additional arrangement, respective electrical connection paths may be provided for coupling each access port electrode to the first conductor of a corresponding particular AFG device and the reference electrode associated with the access port electrode to the second conductor of the corresponding particular AFG device, as set forth at block1106. At block1108, a conductive liquid droplet is deposited, injected, or otherwise introduced into the arcuate microchannel, which is then sealed with a cap structure (block1110). As noted previously, the conductive liquid droplet may be dimensioned to move freely within the sealed arcuate microchannel under gravity, e.g., when placed in a vertical orientation, placed on an incline surface, and the like. An example flow11006may further include providing a control circuit coupled to each of the AFG devices, the control circuit configured to, inter alia: (i) detect a discharge current in at least one of the AFG devices along a conductive path between the corresponding access port electrode and the associated reference electrode interposed by the conductive liquid droplet, and (ii) determine an angular inclination measurement based on the detection of the discharge current of the at least one of the AFG devices, as set forth at block1112.

FIG. 12is a flowchart of an example method of operation1200, e.g., performing angular inclination measurements, with respect to using an AFG inclinometer according to an embodiment of the present invention. At block1202, floating gate electrodes of an AFG inclinometer are charged, upon placing the inclinometer on a flat surface (e.g., a known reference horizon), by applying suitable bias voltages at the sensor circuit nodes, which voltages may be provided by an associated control circuit. The inclinometer is then moved to a position, e.g., an inclined surface, where angular inclination or slope is to be measured (block1204). When the conductive liquid droplet of the inclinometer settles at a particular access port, the AFG device coupled to or associated with the access port experiences a charge loss in its floating gate electrode, thereby causing a reduced ID current. Depending on the implementation, one or more AFG devices may exhibit charge loss (e.g., if more than one access port is covered by the conductive droplet). As the position of such discharging AFG devices is calibrated to specific angles of inclination during manufacture, the presence or detection of the charge loss is used for determining or correlating the maximum slope that the inclinometer is subjected to, which may be output via a suitable user-friendly interface such as digital readout (block1206). After the measurement process is completed, the floating gate electrodes of the AFG devices may be discharged by a suitable neutralization pulse (block1208) in order to render the inclinometer suitable for a next measurement process. In one example embodiment, a floating-gate electrode of an AFG sensor may be neutralized by tunnel capacitors (e.g., capacitors218,220in the embodiment ofFIG. 2) so as to have no residual charge. A suitable neutralization process may be performed by applying a pulse of either or both an appropriate negative voltage (e.g., on the order of −10 volts) to terminal TN and an appropriate positive voltage (e.g., on the order of +10 volts) at terminal TP, both relative to a ground reference voltage applied to all other nodes (gate G, source S, drain D). This operation is intended to remove any residual positive charge and residual electrons from floating-gate electrode210. Once neutralized in such process, floating-gate electrodes are at a known neutral state and may be then charged by the application of a bias voltage at gates G. Also, as there may be a temporary non-equilibrium depletion of charge at the sensing/access port due to the read operation, a waiting period or time delay may be needed before establishing a new equilibrium condition (block1210). Thereafter, the process is repeated (block1212) by recharging the floating-gate electrodes of the AFG inclinometer for a subsequent measurement operation.

FIG. 13is a block diagram of a node1300that includes an AFG inclinometer as a system, apparatus or network element operative in a network. One skilled in the art will recognize thatFIG. 13is illustrative of a high-level architecture of a sensor node or network element in which an embodiment of the present invention may be implemented. By way of example, node1300may be contemplated for deployment in a distributed network system, for instance, as an Internet-of-Things (IoT) implementation. Node1300may preferably include a programmable subsystem including embedded microcontroller unit (MCU)1302in combination with various peripheral functions. For example, node1300may be physically realized by way of a single circuit board on which MCU1302may be mounted, along with other integrated circuits and discrete components as desired, housed in an appropriate housing or enclosure suitable for its environment. Alternatively, node1300may be realized by way of multiple circuit boards, as a single integrated circuit, or as a part of a larger electronic system, depending on its functionality. In the architecture of node1300depicted inFIG. 13, communication with other nodes and perhaps with a host computer system and/or network server(s) may be carried out by way of wireless transceiver1314, constructed and operating in the appropriate manner for the particular communications facility being used. If communication is to be carried out wirelessly, any one of a number of conventional protocols and physical layer standards, including IEEE 802.11 a/b/g/n etc., Bluetooth, and Bluetooth 4.0 (i.e., Bluetooth Low Energy, or “BLE”), may serve as such communications facility. Alternatively or additionally, transceiver1304may be configured for communication over Ethernet or another type of wired network.

Node1300may also include one or more input/output (I/O) functions or interfaces for interacting with the physical environment external to the node. For example, an AFG-based inclinometer sensor device1304provided according to an embodiment of the present invention may be coupled to and controlled by MCU1302. Optionally, a control output circuit1306may also be provided as part of node1300, coupled to and controlled by MCU1302to realize a controller function. Examples of control output circuit1306may include analog output driver circuitry, serial and parallel digital outputs, pulse-width-modulated (PWM) output driver circuitry, driver circuitry for an alarm or an annunciator, and LED drivers, to name a few. As one skilled in the art will recognize, the particular numbers and functions of input/output functions may depend on the conditions and operations that node1300is to carry out in the networked system. Further, additional sensor and controller functions may also be included as part of node1300, such as, for example, temperature sensors, motion sensors, humidity sensors, transducers of various types as suitable in industrial instrumentation, cameras, thermal imaging sensors, photosensors, and the like. Node1300may also include a power manager function1312for controlling the powering of the various functions within the node. For example, node1300may be powered by any one or more sources including wired power (e.g., power over USB, DC output from a rectifier or micro-grid), battery power, solar power, wireless power transfer (e.g., over the wireless communications facility or separately), and the like.

MCU1302in node1300may be configured to include certain functions particular to the construction and operation of this embodiment of the invention, for example by way of logic circuitry programmed to execute program instructions stored in a memory resource1308or received over the communications facility via wireless transceiver1314. For example, at least a portion of the programmable logic may be represented by a logic unit ALU1310, which operates in combination with memory resource1308that is also implemented within MCU1302in this example. One skilled in the art will recognize upon reference hereto that regardless of whether node1300is provided as a network element or not, at least part of the control circuit operations relative to AFG charging, recharging, application of neutralization pulses, correlation/determination of angular inclination (e.g., in multiple measurement modes such as degrees, radians, slope/gradient percentages, etc.) may be performed by or shared with MCU1302in one example implementation.

Based on the foregoing Detailed Description, skilled artisans will appreciate that embodiments of the present invention provide a fast, accurate and low-powered inclinometer solution for taking slope measurements electronically. Typically, power consumption of an AFG inclinometer of the present invention depends on measurement rates, as there may be repeated operations of charging/recharging and neutralization pulsing. An embodiment of the present invention can also be used without power to determine a maximum slope since the AFG sensors are non-volatile (the charge on the floating-gate electrodes is trapped because of the oxide layers surrounding them) and only those sensor ports at which a conductive droplet settles exhibit a discharge condition, thereby indicating appropriate slope measurements. In an example shipping application, an AFG inclinometer can therefore provide maximum slopes that a shipment has been subjected to during transit without having to power up the device. In a further arrangement where a shipping application may be deployed in an IoT setting, an inclinometer sensor module with Internet connectivity could periodically report the maximum measured slope since reset or the current slope measurement. It could also automatically communicate the maximum slope once the shipment reaches the destination or intermediate waypoints. Other applications in which an AFG inclinometer embodiment of the present invention may be advantageously deployed include but not limited to, for example, (i) detecting zones of ground or structural movement in civil engineering projects and establish whether movement is constant, accelerating, or responding to remedial measures; (ii) monitoring and checking that deformations are within design limits, e.g., struts and anchors are performing as expected, adjacent buildings are not affected by ground movements, etc., (iii) verifying stability of dams, dam abutments, and upstream slopes during and after impoundment, and (iv) monitoring settlement profiles of embankments, foundations, and other structures (e.g., deployed as a horizontal inclinometer).

It will be further recognized that an embodiment of the present invention can be easily incorporated into a complete electronic measurement system that may be networked or operated as a discrete entity (e.g., as node1300described above in one implementation), or as part of a larger system such as gaming appliances, cameras, etc. Other advantages of the present invention may include, among others: (i) ease of determination of zero offset; (ii) high accuracy and linearity, which is basically determined by the number of AFG devices used and the geometry of a microchannel; (iii) reduced sensitivity to temperature variations and drift (typically better resistance than other conventional methods); and (iv) better long term stability than other measurement approaches.

Although circular geometries for a microchannel have been particularly exemplified hereinabove, one skilled in the art will recognize that other curvilinear geometries are also possible for purposes of the present invention, as noted previously. Further, whereas a single microchannel having a circular design that is vertically oriented has been illustratively described, it should be appreciated that two microchannels each having appropriate numbers of sensor port electrodes may be orthogonally oriented relative to each other so that inclination along two axes (e.g., both pitch and roll of a surface) may be measured. In a still further variation, a full circular microchannel having a plurality of sensor port electrodes disposed along its periphery may be horizontally oriented such that the conductive liquid droplet may settle at a particular sensor port electrode that is calibrated to inclination around both X- and Y-axes.

Accordingly, although various embodiments have been shown and described in detail, the claims are not limited to any particular embodiment or example. None of the above Detailed Description should be read as implying that any particular component, element, step, act, or function is essential such that it must be included in the scope of the claims. Reference to an element in the singular is not intended to mean “one and only one” unless explicitly so stated, but rather “one or more.” All structural and functional equivalents to the elements of the above-described embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Accordingly, those skilled in the art will recognize that the exemplary embodiments described herein can be practiced with various modifications and alterations within the spirit and scope of the claims appended below.