Patent ID: 12256641

DETAILED DESCRIPTION

One aspect of the present embodiments includes the realization that past efforts to use the Casimir force as a perpetual energy source has not been successful, as the second law of thermodynamics is a fundamental barrier by nature to realize such a behavior. Quantum fluctuation in zero-point energy (ZPE) field and the Casimir force have been validated and measured to extreme accuracy. It has been attempted in the past to devise metamaterial to create a repulsive Casimir force, which has not led to any practical realization. In the past, xenon gas has been used in a closed cavity for extracting the vacuum energy from the xenon gas flowing through the cavity and attempting to harvest electrical current from pyroelectric detectors.

Embodiments of this disclosure and contemplated variations thereof solve this problem by providing, among other things, an energy harvesting device that uses a mechanical repulsive force to counter act with the attractive Casimir force, creating an emergent oscillatory behavior. A mechanical oscillator is realized by using a set of single or multiwalled carbon nanotubes connected between two metal plates, with one metal plate being free to move towards or away from the other plate.

Some of the present embodiments use nano piezoelectric microelectromechanical system (MEMS) cantilevers to harvest the energy from the mechanical vibration of the metal plate. The moving metal plate is attached to a cantilever (or an array of cantilevers) to convert the mechanical energy released from the oscillation of metal plates to electrical current. During the energy-harvesting normal mode of operation, the cantilever harvests energy from the mechanical oscillation of the moving metal plate. During the excitement mode (e.g., initial startup or reignition), when current is applied to a MEMS nano piezoelectric cantilever by an exciter, the nano piezoelectric flexes and creates a strain on carbon nanotubes, which adds constructively to the Casimir force to start (or continue) a period of oscillation.

Some of the present embodiments overcome the limitation of energy loss due to mechanical vibration and the second law of thermodynamics by providing a mechanism to supercharge the energy harvesting device via a radio frequency (RF) or solar source on a periodic basis. Damping of oscillation, in some of the present embodiments, is compensated by harvesting RF or optical energy sources. The concept of “ignition” and supercharging the device for assuring proper energy harvesting of the device is a novel mechanism for harvesting quantum fluctuation in very small dimensions. In some embodiments, the mechanical and solar sources of energy may be added together to increase the output energy of the energy harvesting device.

Some embodiments use a two-dimensional nanostructured fractal design for the parallel metal plates that are used to harvest the mechanical energy. The fractal design maximizes the area occupied by a conductive surface, while minimizing the total mass required to cover the conductive area. Thereby, reducing the cost of the overall apparatus, in addition to adding lateral current flux across the metal plate to further increase the amount of the output energy.

Some embodiments use curved surfaces instead of parallel plates to exploit the Casimir force. This may simplify fabrication of the device and avoid maintaining two flat plates near perfectly parallel with homogenous flat surfaces and fixed separation in very small distances of nanometers. Some of the present embodiments replace one or both flat plates by a curved surface such as a lens, sphere or cylinder. Some of the present embodiments keep one flat metal plate with a flat surface and use another curved surface with conductive property. In some embodiments one or both surfaces could move freely in one direction.

Some embodiments may use multiple energy sources to combine to increase the output of the energy harvesting device. These sources are kinetic energy of moving mass and the Casimir force, radio frequency signals, and optical power. Each respective energy source is harvested and is converted to electrical current as a power source for powering electronic products and sensors. The use of the nano-technology MEMS devices allows harnessing energy in very small dimensions in the orders of micro-to-nano meters. The energy harvesting devices are highly scalable and may be connected as an array of devices to provide sufficient power level to diverse use cases.

Embodiments of this disclosure and contemplated variations thereof provide green energy harvesting methods that use renewable energy sources with no chemical reactants. Renewable energy sources are referred to energy sources which are naturally replenished and often provide energy for generating electricity. Renewable energy is taken to be clean as they do not impact global warming or harm the environment by release of pollutants such as dangerous chemicals or toxic gas. The present embodiments are at the pinnacle of hierarchy of energy producing devices to emit no gas and require no chemical in production of energy. Furthermore, the energy source used in the present embodiments are sustainable energy, which do not get expired or depleted and may be used over-and-over to meet today's demand for low power sensors and IoT devices as power supply source, when used as a singular unit fabricated together in the same package with integrated circuits. Alternatively, when used as a group of devices working together, the devices seamlessly scale and meet energy required to any application today that is powered by disposable or rechargeable batteries. The present embodiments provide sustainable energy which is green, inexhaustible, safe, as there are no greenhouse gasses, or any pollutants emitted from the device.

The energy producing device, hereinafter referred to as energy harvesting device or simply as “the device,” does not use any electrochemical reaction to produce energy. Utilization of any chemical energy is circumvented and “no-charging” is required in classical sense. Due to the second law of thermodynamics, the mechanical vibration cannot be eternal. In course of the lifetime of the device, it may be necessary to re-ignite the oscillation of the device time-to-time. The reignition process, in some of the present embodiments, is achieved by remotely injecting an RF signal which in turn is converted to mechanical energy to kick start power harvesting process. Whenever any reignition is desired, a judicious choice of an RF signal is transmitted to prime the oscillation of the energy harvesting device. The reignition (or kickstart) may be performed remotely from far field electromagnetic radiation in free space. The reignition may also be achieved through an RF energy harvesting mechanism, an optical energy harvesting mechanism, or both. This methodology does not require any coupling or cabling to any external electrical current source to recharge the energy harvesting device. In some of the present embodiments, if the RF signal or the optical signal is perpetually present, the RF power and/or the optical power may also be harvested to constructively add to the overall total output power.

One of the fundamental challenges in deployment of wireless sensor networks and IoT is cabling the device to a power source or using batteries that need to be charged periodically. The present embodiments address these limitations and lend themselves for powering electronic devices such as wireless sensors and IoT devices by providing self-powering devices without any physical interaction with or handling of the device.

In outdoor applications or in the areas where there is sufficient energy in visible light spectrum, some embodiments use light as a back-up energy source. When light is not present or when it is dark outdoor, uninterrupted power is provided to the device through the mechanical and RF energy sources. As an additional option for excitation of the energy harvesting device, some embodiments harvest the solar energy as an energy source for excitation as a forcing function to start oscillation of the moving plate, and/or to use the solar generated power as another additional source to augment to the total output power.

The remaining detailed description describes the present embodiments with reference to the drawings. In the drawings, reference numbers label elements of the present embodiments. These reference numbers are reproduced below in connection with the discussion of the corresponding drawing features.

Some of the present embodiments provide a novel system for energy harvesting in converting mechanical energy to electricity by taking advantage of the Casimir force. The Casimir force (also referred to as the Casimir effect or the Casimir-Polder force) is one of the most direct manifestations of the existence of zero-point vacuum oscillations. This effect is best conceptualized and observed in the attraction between two electrically neutral parallel conducting planes placed in vacuum. It is well established that the ground state of quantum electrodynamics causes the planes to attract each other, due to quantized electromagnetic field.

Due to the second law of thermodynamics, the mechanical vibration cannot be eternal. In course of the lifetime of the device, it may be necessary to re-ignite the oscillation of the device time-to-time. The term excitation (or reignition) used herein refers to priming the energy harvesting device (e.g., at power-up) to kick start the oscillation behavior between the two plates. The excitation may be used as frequently as necessary to either increase the period of the oscillation or re-start it from rest in ground state. The term excitation used herein, refers to a process that, in some of the present embodiments, is achieved by injecting an RF signal which in turn is converted to mechanical energy to kick start power harvesting process. For assuring steady source of energy over time, the energy harvesting device, in some embodiments, may be excited on an as needed basis with RF energy to prime the mechanical oscillation. If the RF signal is perpetually present, the RF energy may be utilized for constructively adding to the total output. In addition to, or in lieu of using the RF energy, some embodiments may complement the device by harvesting energy from solar or optical sources. In which case, the device may be advantageous for outdoor applications that use solar and optical sources as the main source of energy to provide uninterrupted power during nighttime or when dark by using the mechanical sources.

The energy harvesting devices of the present embodiments use a novel approach to a create green power from forces already existing in nature having been untapped collectively to constructively act together as an energy source. The resulting energy harvesting devices are environment friendly and do not employ any chemical agent to adversely impact the environment or produce any byproducts to pollute the air. The lifespan for these class of devices may be years without any human intervention for maintenance or replenishment needs.

With the emergence of wireless sensor networks and different classes of low-power sensing devices, prevalent in the IoT today, there is a challenge to provide power for the IoT devices. The energy harvesting devices of the present embodiments address this challenge by combining multiple power sources available in nature to provide the energy to run electronic devices. In some embodiments, these energy harvesting devices rely on fabrication in nano-scale with tolerances small enough to realize the optimal performance in emerging technologies available in the MEMS industry.

The energy harvesting mechanism of some of the present embodiments may also combine multiple energy sources, namely in addition to kinetic energy from a moving metal plate, RF power harvesting or solar power harvesting may be used to add to the output power of the device. These energy sources are additively summed together to produce an output voltage as an alternative option to increase the output power of the device.

FIG.1is a functional diagram illustrating one example embodiment of an energy harvesting device100that combines fundamental forces of kinematic and electromagnetic together to provide power supply source, according to various aspects of the present disclosure. The energy harvesting device100may utilize multiple sources and methodologies, as described herein, for harvesting energy from each source and providing the harvested energy either as output electricity or to reignite the energy harvesting device. With reference toFIG.1, the dashed line132for Vopand the dashed lime134for VRFindicate an option when it is desired to use one or both outputs, namely the output134harvested from the RF source101and/or the output132harvested from the optical source101, to further boost the overall output power. The dashed lines142and144indicate the option to use some (or all) of the energy harvested from the optical energy harvesting system130and/or to use some (or all) of the energy harvested from the RF energy harvesting system120to reignite the mechanical energy harvesting system140as needed.

In the example ofFIG.1, the energy harvesting device100may include an RF input source101, an optical input source102, and a mechanical input source103. The VRF134is the electrical voltage and/or current from an RF based energy harvesting system such as the RF energy harvesting system120described below with reference toFIG.17. VRF134is the voltage level harvested from an RF source101such as the ambient electromagnetic radiation in a prescribed radio frequency range (e.g., 200 MHz to 5 GHz) in the licensed or unlicensed bands. Some or all the energy harvested from the RF energy harvesting system120may be used (as shown by VRF-Excite144) to excite the mechanical energy harvesting system140as described below with reference toFIGS.2A-2B.

The VOP132is the electrical voltage and/or current from a solar based energy harvesting device such as the energy harvesting system130described below with reference toFIG.32. The VOP132is the voltage level harvested from solar radiation, or more precisely energy harvested in optical frequencies (e.g., 330 THz to 770 THz). Some or all energy harvested from the optical energy harvesting system130may be used (as shown by VOP-Excite142) to excite the mechanical energy harvesting system140as described below with reference toFIGS.2A-2B.

The VME133is the electrical voltage and/or current from a mechanical based (e.g., using piezoelectric and/or the Casimir force sources) energy harvesting system such as the energy harvesting system140described below with reference toFIGS.2A-2B. The Casimir force, in some embodiments, is harvested by one or more nano piezoelectric cantilevers.

In some embodiments, the energy harvesting device100may include the mechanical energy harvesting system140and only one of the optical energy harvesting system130or the RF energy harvesting system120. The output signal VOUT105, in some embodiments, may be formed by using a voltage adder110to additively sum together the voltage VME133produced by the mechanical energy harvesting system140, the voltage VOP132produced by the optical energy harvesting system130, and the voltage VRF134produced by the RF energy harvesting system120to produce the VOUT105across the output load115. In other embodiments, the voltage VME133may be used as the output voltage VOUT105without being added to the other voltage outputs. One port of the output load115may be connected to ground voltage120. The voltage from the RF sources101, the voltage from the optical sources102, and/or the voltage from the mechanical sources103(e.g., piezoelectric and/or Casimir force) may each be harvested independently.

I. Mechanical Energy Harvesting Device

FIG.2Ais a functional diagram illustrating one example embodiment of a mechanical based energy harvesting system140, according to various aspects of the present disclosure. The mechanical based energy harvesting system140combines piezoelectric and Casimir force for generating energy.

The two near-planar interacting surfaces210and215, in some embodiments, may be required to be within distances such as for example, 1 micrometer or less, 100 nanometer or less, etc., to effectively use the Casimir force. The size of the parallel plates may range anywhere from tens of nanometer to few micrometers (e.g., 100 nanometer, 1 micrometer, 20 micrometers, etc.). The two plates may be parallel within a tolerance of a few percent, e.g., 5 percent, 1 percent, 0.5 percent, etc. With judicious choice of underlying parameters as described herein, subsequent oscillation is harvested via a piezoelectric cantilever270and converted to electrical current. In the event of damped oscillation due to thermal loss or environmental factors such as temperature variation, the system may receive, as described herein, an excitement or reignition through the RF energy harvesting mechanism, the optical energy harvesting mechanism, or an external RF energy source.

A key issue in the choice of material for the plates is the lack of surface roughness, which is required to possess a small surface roughness amplitude variation compared to the distance between the plates. The characteristics of the material such as the dielectric function, the roughness, the residual electrostatic forces, and the magnetic susceptibility must be considered. The use of liquid metal as an alternative to minimize surface roughness may be considered for applications in reconfigurable plasmonic devices. Although theFIG.2and several other examples of the present disclosure are described with referenced to metal (e.g., gold) plates, other material (e.g., liquid metal) with a small-amplitude distortion of the surface compared to the separation of the plates may be used for the plates.

In some embodiments, the Casimir attractive force between two parallel plates (also referred to as electrode plates)210and215drives the mechanical action on an array of the carbon nanotubes (CNTs)235, creating axial compression to strain the carbon nanotubes array. In realizing repulsive force to act against the attractive Casimir force to generate mechanical oscillations, different embodiment may use different elastic material such as for example and without any limitations, nanotubes (e.g., carbon nanotubes), liquid, gas, plasma to emulate nano-levitation against the interaction of attractive Casimir force. Although inFIG.2and several other examples of the present disclosure, carbon nanotube is used as the elastic material between the two plates (or between spheres and plates as described by reference toFIG.13below), other elastic material may be used to counteract the attractive force.

Some embodiments may connect more than one piezoelectric cantilever270to the moving plate215.FIG.2Bis a functional diagram illustrating an alternative example embodiment of a mechanical based energy harvesting system that uses multiple cantilevers, according to various aspects of the present disclosure. With reference toFIG.2B, the mechanical based energy harvesting system140has multiple piezoelectric cantilevers270. The embodiments of the mechanical based energy harvesting system described in the present disclosure may either use one cantilever270(e.g., as shown inFIG.2A) or several cantilevers270(e.g., as shown inFIG.2B). For simplicity, some of the examples described below may show a mechanical based energy harvesting system with only one cantilever. The same examples are equally applicable to a mechanical based energy harvesting system with multiple cantilevers.

A. Nanotubes for Creating Repulsive Action

With reference toFIGS.2A-2B, the nanotubes235may be placed between the two electrode plates210and215to counter the attraction between the two electrode plates210and215. In response to the attractive Casimir force, the carbon nanotubes235are strained, while the distance between the two parallel plates decreases until a repulsive force emerges due to the mechanical strain onto the carbon nanotubes. Mechanical energy is released due to the repulsive force and increases the distance between the plates until plates comes to rest again at which time the Casimir force induces again an attractive force and process continues indefinitely, with a reemergent oscillatory behavior, with the upper plate215oscillating back-an-forth. In some aspects of the present embodiments, the electrodes210and215may be made of gold (Au) or silver (Ag). The lower electrode's plate210may be stationary and the upper electrode's plate215may be movable.

The carbon nanotubes235are allotropes of carbon with a cylindrical (or helical) structure. Each nanotube is a hollow structure with the walls formed by one-atom-thick sheets of graphene. Individual nanotubes naturally align themselves into ropes held together by the van der Waals intermolecular force. The van der Waals force is a distance dependent interaction between atoms or molecules. Vertically aligned carbon nanotube arrays are a unique microstructure of carbon nanotubes oriented along their longitudinal axis normal to a substrate surface. The carbon nanotubes235may act as coils and provide a repulsive force to the metal plates, resulting into a harmonic mechanical oscillator.

As described herein, the density, diameter, and length of the helical carbon nanotubes may be controlled during the manufacturing process to match the design goal. The vibration energy is recovered by means of electrostatic force. Energy may be harvested by connecting the metal plates210and215, as electrodes formed, driving a voltage regulator225, which outputs the desired supply voltage VME133.

A single sheet of carbon atoms arranged in a hexagonal lattice is known as graphene. Graphite is a stack of graphene sheets held together by van der Waals forces. By rolling a graphene sheet into a cylindrical tube with a diameter of several nanometer, a single-walled carbon nanotube (SWCNT) is produced.

FIG.3Ais a perspective view of a single-walled nanotube, according to various aspects of the present disclosure. With reference toFIG.3A, a single-walled carbon nanotube350is shown. In the example ofFIG.3A, the carbon nanotube350would be under axial tension in the direction304when the carbon nanotube350is placed between the metal plates210and215.FIG.3Bis a cross section of the single-walled nanotube ofFIG.3A, according to various aspects of the present disclosure. With reference toFIG.3B, the carbon nanotube350has a one atom thickness, “d1,” an outer surface360, and an inner surface365. The carbon nanotube350has an outer radius r1340and an inner radius r2345. As shown by the scales371and372, r1and r2are typically about 0.65 and 0.5 nanometers, respectively.

Key design parameters for construction of the carbon nanotubes rely on two design parameters, namely two chiral indexes (n, m), specifically establishing the distance between each atom in a graphene sheet. A carbon nanotube is essentially a folded graphene sheet as shown inFIG.3A. Points390on the graphene's350lattice may be described by vectors of the form “n a+m b”, where n, m are integers n≥m and a, b are nonorthogonal unit vectors that may be taken as (1,0) and

(1/2,32),
respectively. The notation “n a+m b” denotes a vector multiplication with an integer and vector addition of 1×2 dimension vectors n·a and m·b. The chiral indices (n, m) determine the alignment of carbon hexagons around the circumference of the cylinder of the nanotube350. Three different geometrical classifications or “flavors” of nanotubes may be distinguished. “Armchair” configurations are characterized by indices (n, n), where both indexes are equal, while “zigzag” configurations are described by (n, 0), where the second index is 0. Chiral nanotubes have indices (n, m), with n not equal to m, and m not equal to 0. Chiral nanotubes may occur in two mirror-image forms. A nanotube structure may be designed for different indices (n, m). By way of example, inFIG.3A, the nanotube with lattice points390are chosen as a vector 8 a+3 b with n=8 and m=3.

Carbon nanotubes under a mechanical deformation may be used in energy storage. The total elastic strain energy and average energy density that can be stored in carbon nanotubes may be subject to four modes of mechanical deformation: axial tension, axial compression, pure bending and torsion. Some embodiment may consider some of these mechanical deformations, such as and without limitations, the axial tension and axial compression. One end of each carbon nanotube235ofFIGS.2A-2Bmay be connected to one of the metal plates210and215. The carbon nanotubes235may be designed such that, once compressed, the load on the carbon nanotubes does not lead to any bending of the carbon nanotubes structural integrity in axial direction. The metal plates210and215are designed to tolerate the combined loadings of arrays of carbon nanotubes235without any bending or torsion to avoid any buckling. Individual carbon nanotubes235may have diameters measured in nanometers and spring properties for energy storage. Carbon nanotubes235may be made of SWCNTs or multi-walled carbon nanotubes (MWCNTs) arranged into dense bundles of aligned tubes.

FIG.4Ais a cross section of an array configuration400A of single-walled carbon nanotubes, according to various aspects of the present disclosure.FIG.4Bis a cross section400B of an array configuration of multi-walled carbon nanotubes, according to various aspects of the present disclosure. A MWCNT includes multiple rolled layers of concentric tubes of graphene, arranged in concentric cylinders.

With reference toFIG.4A, in a group of SWCNTs350, each carbon nanotube layer is treated as a homogenous cylindrical shell's cross section350. With reference toFIG.3B, each tube350has a thickness of “d1,” an outer radius r1340, and inner radius r2345, that is r1−r2=“d1.” Typically, “d” is about 0.3 nm.

With reference toFIG.4B, each hollow cylinder430may have a thickness of “d2”, and n represents the number of cylindrical layers in the carbon nanotubes400B. Typically, “d2” is about 0.3 nm and n is greater than one in MWCNT. The distance between adjacent tubes is h490. InFIG.4A, the thickness of each tube is negligible and is not shown for simplicity. With reference toFIG.4A, with negligible thickness of the SWCNT, r1=2*r2+h. With reference toFIG.4B, r1=2*r2+h+2*“d”, where, by way of example, a two walled MWCNT array is depicted.

When strain is applied by an external tensile force, solid matter is stretched along the direction of the applied force, or contracts due to an external compression force. In the elastic region, the change of length follows Hooke's law and is proportional to the applied stress. Hooke's law, however, holds only approximately for small strains. For higher strains, the relation between normal stress and strain is nonlinear. Young's modulus represents the ratio of stress to strain for a given solid material, when the body is stretched along the direction of the applied force. This quantity depends on the material and is temperature dependent. Given the inner and outer radii of a carbon nanotube, it is possible to compute an effective Young's modulus of denoted by E, for evaluating the stiffness of a carbon nanotube.

Young's modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.

FIGS.5A-5Ddemonstrate the simulation of dynamics of a SWCNT under strain, according to various aspects of the present embodiments. By way of example, parameters for a simulation of displacement of the SWCNT is provided inFIG.5A. The displacement in z-direction is shown inFIG.5B. The parameters may be adjusted using a series of sliders541-548that adjust each parameter, namely, the initial position541, the spring constant542, the damping friction543, the mass505attached to the carbon nanotube, the forcing amplitude545, the forcing frequency546, and the time duration of the simulation548. The controls547may be used to run, pause, or replay the simulation.

With reference toFIG.5B, the spring property of the SWCNT is shown as515, the force is exerted at520to the spring model of SWCNT, and the spherical mass is shown as505. The mass of a fully loaded carbon nanotube array, in some embodiments, is a flat metal plate215ofFIGS.2A-2Binstead of the sphere505, which shall also provide sufficiently large area to support the array of carbon nanotube loads under full tension, during compression and deflection, without structural failure.

FIG.5Cillustrates the dynamics of the spring action computed from simulation parameters inFIG.5A. The waveform behaves as a damped sinusoid580, representing the position of the mass as a function of time, with the displacement denoted as z(t) in the plot ofFIG.5C.

FIG.5Dcharacterizes the relationship between stress (force per unit volume) kj/m3) and strain in a material experiencing axial deformation to predict the compression and deflection that may occur when a load is applied or shortens under compression. Equation (1) is the energy density of the carbon nanotube acting as a spring in axial tension:

E=E⁢ε2⁢k⁢A2⁢ATEq.(1)

Where ε is the elastic strain, AT=πr12is the total area occupied by carbon nanotube (e.g., the total area of the circle360ofFIG.3B) and A=π(r12−r22) is total inner enclosed area (the area between the circle360and the circle365) shown in the cross-sectional area of the cylindrical tube450ofFIG.3B. Given the total inner area A, k is the fraction of the area in the bundle cross section occupied

k⁢A2⁢AT.
With densely packed shell, it is desired to maximize A/AT. For the hexagonal configuration of400A (FIG.4A), k is given by Equation (2):

k=π⁡(r+nh2)232⁢(2⁢r+n⁢h)2=91⁢%Eq.(2)

that is the bundle includes

k⁢A2⁢AT
solid CNT shells by volume. Young's modulus of is in units of kilopascals, mega-pascals (Newton/millimeter{circumflex over ( )}2) and giga-pascals (kilonewton/mm{circumflex over ( )}2) and tera-pascals (TeraPa, Meganewton/mm{circumflex over ( )}2).

The position580of the mass (i.e., the position of the plate) in the axial direction is shown inFIG.5C. InFIG.5D, the energy density585is computed from the Young's modulus and plotted in585, with the energy density axis in kJ/m{circumflex over ( )}3 units in555, as a function of the applied strain550.

Vibrating flat surface of the upper plate215ofFIGS.2A-2Bagainst the stationary flat surface of the lower plate210, may be excited into motion via a nano piezoelectric MEMS cantilever (or array of cantilevers)270which complements the Casimir force as an additive attractive force to assure sufficient downward attractive force is made to initiate oscillatory behavior between the position of the upper plate and stationary lower plate. A cantilever is a rigid beam or plate that is anchored at one end to a support surface (such as the upper plate215) from which the cantilever protrudes. Further details of a cantilever is described below with reference toFIGS.7A-7B.

The general model of a vibration energy harvester is similar to a typical mass-spring-damper system. The maximum power is achieved when the excitation frequency is equal to the natural frequency of the system. The extractable power is also proportional to the acceleration which may limit the energy available for conversion with low acceleration vibrations. The power is linearly proportional to the mass if the maximum power is achieved when the electrical damping matches the mechanical damping.

With reference toFIGS.2A-2B, in between the conducting metal plates215and210, an array of uniformly equally spaced carbon nanotubes235may be attached, manufactured in vacuum sealed packaging. The purpose of the nanotubes235is to produce a repulsive force against the overall attractive force and resulting pressure exerted from the upper plate.

The density, the diameter, and the length of the helical carbon nanotubes235may be controlled during the manufacturing process to match a design goal. Attaching vertically aligned helical carbon nanotubes to the metal plates210and215may be realized by synthesizing vertically aligned carbon nanotubes on metal plates by chemical vapor deposition of and amine such as, for example and without any limitations, ethylenediamine as a precursor. The amine serves as both etching reagent for the formation of metal nanoparticles and carbon source for the growth of aligned carbon nanotubes. The density and diameter of carbon nanotubes may be determined by the thickness of the deposited metal film. The length of the carbon nanotubes may be controlled by varying the reaction time.

The carbon nanotubes may be multiwalled with a bamboo-like graphic structure with hollow compartments. The hollow compartments of the tubes are kept separate during the process. Within 10-40 nm range, the action between the tubes keeps them growing in a well sintered to particles of suitable sizes and aligned manner.

B. Piezoelectric Cantilevers

The Piezoelectric MEMS is a proven technology for harvesting small magnitudes of energy from mechanical vibrations in nano-and-micro meter scale. Piezoelectricity is a byproduct of the lack of center of inversion symmetry in a crystal lattice. The general principle for conversion of low frequency mechanical stress into electrical energy with piezoelectric transducer is obtained through the direct piezoelectric effect. A key advantage of MEMS is the seamless fabrication process with integrated circuits. MEMS components may be fabricated using micromachining processes. During this processes, parts of silicon wafer are selectively etched away to form the mechanical and electromechanical devices. This enables fabricating single microchip with MEMS integrated in the same physical packaging with the electronic circuits.

With reference toFIGS.2A-2B, the piezoelectric cantilever beam270may require the resonance frequency of the oscillation to be wide enough to accommodate the uncertain variance of underlying mechanical vibration. In the energy harvesting device140, the vibration energy is recovered by means of electrostatic force. Energy is harvested from oscillation of the metal plate215, and the two metal plates210and215, acting as positive and negative electrodes, driving, for example and without any limitations, a rectifier220and a voltage regulator225, which may output the supply voltage VME133at a constant level. The output voltage VME133of the mechanical based energy harvesting system140may be supplied to the voltage adder110of the energy harvesting device100ofFIG.1. The two near-planar interacting surfaces210and215may be required to be within distances of less than 100 nanometer to effectively use the Casimir force.

Piezoelectric material has a crystalline structure (e.g., and without any limitations, zinc oxide or Wurtzite structure) that transforms mechanical strain to electrical charge or converts an applied electrical potential to a mechanical strain. With recent advances in microelectromechanical system, fabrication and use of nano piezoelectric components has been widely applied. Some of the present embodiments use piezoelectric cantilever(s), which operate(s) to convert the oscillation of the parallel plates210and215into an electrical energy in operating mode. In excitement mode (e.g., the initial startup or reignition), the cantilever may be used to prime the oscillation, by forcing the upper plate to exert strain on carbon nanotubes.

Some of the present embodiments may use a nano piezoelectric substance as a cantilever for compression of parallel plates with sufficient conductivity to harvest energy from oscillation of a parallel plate. Nano piezoelectric structure interacting with flat conductive plane, as electrode, drives the vibration to exert strain in the appropriate direction. Piezoelectric materials designed for power harvesting with anisotropic behavior depend upon the direction of the strain and the direction of the polarization and with respect to the position of the electrode. It is also possible to structure a bimorph piezoelectric energy harvester based on a cantilever beam. In which case, two piezoelectric layers are fixed to a non-piezoelectric elastic layer in this case

The model for the steady-state response of a piezoelectric generator connected to an AC-DC rectifier, followed by a filtering capacitance and a resistor, is herein described. The normalized voltage expressed as a function of electrical resistance, denoted as r, is as shown in Equation (3).

Vo=0.04r(r+π2)⁢0.0016r2(r+π2)4+(0.08r(r+π2)2+0.0⁢6)2Eq.(3)

The normalized power is expressed as a function of electrical resistance are as shown in Equation (4).

Po=1⁢1.1⁢1⁢r(r+π2)2Eq.(4)

FIG.6Ais the plot of the normalized voltage for a nano piezoelectric cantilever for energy harvesting, according to various aspects of the present disclosure. With reference toFIG.6A, the plot600A depicts the normalized voltage615as a function of normalized resistance630using Equation (3).

FIG.6Bis the plot of the normalized power for a nano piezoelectric cantilever for energy harvesting, according to various aspects of the present disclosure. With reference toFIG.6B, the plot600B depicts the normalized power605as a function of normalized resistance610using Equation (4).

FIGS.7A-7Bare the perspectives of two Piezoelectric cantilever structures for energy harvesting, according to various aspects of the present disclosure. The basic structures of the piezoelectric energy harvester may have bimorph or unimorph cantilever beam structures. A bimorph structure is composed of two independently polarized piezoelectric layers, and a unimorph structure is composed of a single piezoelectric layer and an elastic substrate layer attached to a mass at the end of the cantilever. InFIG.7A, in bimorph structure750with two independently polarized piezoelectric layers704,705, the layers701,702, and703are metal layers with the layers702and703acting as ground planes, metal electrodes, and the layer701acting as the voltage supply's source electrode (i.e., the voltage that is provided by the energy harvesting device and can be used as a voltage source by another device). The layers704and705are piezoelectric layers and the mass711may be the flat metal plate or a sphere.

InFIG.7B, the unimorph structure760has a single piezoelectric layer and the metal layer707acts as the ground plane electrode and the layer709acts as the voltage supply's source electrode. The layer708is the piezoelectric layer stacked over a metallic layer707with an elastic layer706at bottom of stack attached to the mass710which may be the flat metal plate or a sphere. In small scale processes in microfabrication, the unimorph configuration may be preferable as opposed to the bimorph structure, which requires depositing multiple layers of piezoelectric material.

Typical thickness of the piezoelectric layers704,705, and708may be less than 0.5 micrometer. The form factors of a piezoelectric MEMS energy harvesters may be different and is characterized by the power density, defined as the ratio of the generated power over the material volume, expressed in volume power density in units of microwatts/mm3. The design goal shall be maximizing the power density for a given volume and available area to implement the cantilever. The resonating beam structure, in some embodiments, is designed to maximize the harvested energy for a target frequency range and an acceleration rate set for design considerations, since the extractable power is also proportional to the acceleration and the mass in710and711in bimorph or unimorph structures.

FIG.8illustrates a curve800, where the Casimir force is characterized as a function of distance between two plates, according to various aspects of the present disclosure. The Casimir force may be expressed as shown in Equation (5):

Fc≈1.3*1⁢0-3⁢0d4Eq.(5)

where Fcis the Casimir force in microjoules and d denotes the distance in meters between two metal plates with infinite boundaries. As shown inFIG.8, the Casimir forces drops as the distance between the plates increases.

With reference toFIGS.2A-2B, in normal mode of operation, the metal plate215is attracted by Casimir force to the metal plate210. The strain on the carbon nanotubes235connected between two parallel plates210and215translates into potential energy. The potential energy stored in the carbon nanotubes after sufficient separation of the two metal plates210and205. A repulsive force is exerted to the upper plate215with spring action by the carbon nanotubes235, releasing the potential energy by decompressing the carbon nanotube array235to a new position. With periodic behavior of this process, a mechanical harmonic oscillator is realized.

The motion from the mass-spring action of the metal plate is harvested by the nano piezoelectric cantilever(s)270attached to upper plate215. The piezoelectric cantilever(s)270convert(s) the mechanical energy into electrical energy, which in turn is rectified by the rectifier220and stored in a storage capacitor230. The voltage level across the storage capacitor230is regulated by the voltage regulator225, producing the output voltage VME133. Optimizing the power density and efficiency of the system140requires maximizing the elastic potential energy in carbon nanotubes in235while concurrently minimizing the mechanical loss due to mismatch in mechanical impedance of carbon nanotube array235and electromechanical loss of the cantilever(s)270converting the mechanical action to electrical current. This conversion is primarily dependent on the magnitude of the electromechanical coupling factor of the piezoelectric material. The electromechanical coupling factor represents the ratio of input mechanical energy to the output electrical energy. This factor varies widely in both natural and synthetic material that exhibit piezoelectric property. The material used in nonpiezoelectric cantilever270shall be chosen judiciously for maximizing the magnitude for coupling factor, with consideration of cost and manufacturability.

InFIGS.2A-2B, the total energy is preserved in the carbon nanotubes235acting as coils, with a spring constant chosen for interaction with the Casimir force between the two plates210and215. The energy harvesting system inFIGS.2A-2Bmay be primed at power up by initially pre-charging the surface of the cantilever(s)270, such that the vibration of upper plate215is initiated at a desired displacement in axial direction of carbon nanotube arrays235. This is shown as the exciter290.

In the excitation mode, also referred herein as the ignition mode, the exciter290drives an electrical current into the nano piezoelectric cantilever270, which in some embodiments may be an array of cantilevers, converts the electrical energy into mechanical energy, exerting a compressive force onto the carbon nanotubes arrays235. The exciter290may be any of the possible harvested energy subsystems shown inFIG.1, such as the optical energy harvesting system130from the optical source102, or the RF energy harvesting system120, driven by the RF source101. The switch295ofFIG.2Aor the switches296-297ofFIG.2Bremain(s) open during the normal mode of operation. The switch(es) is/are closed whenever excitation is desired to re-excite the device140. This can be to assure optimal harvested power level from the mechanical vibration of the moving plate215. During the design phase of the device, the required periodicity for excitation of the device is determined. The limits may be set by considering the maximum and minimum needed output power from the device and the resulting time duration taken to discharge from the maximum to minimum power level. When this duration is met, the excitation is initiated by closing the switch295ofFIG.2Aor switches296-297ofFIG.2B. In some embodiments, the switches may be coupled to a voltage dividing circuit with reference voltages as to minimum and maximum required voltage of the energy harvesting device, such that when the output voltage of the device drops below the minimum value, the switch295(e.g., a diode with forward bias mode) is thrown or shorted (to enable excitation circuit from RF or solar energy to charge the super-capacitor). Once the maximum voltage is reached, driving a comparator's reference voltages as input with the output controlling the state of the switch295, which is opened (e.g., the diode in reverse bias mode) to terminate the excitation period.

C. Fractal Metal Plates

FIG.9is a functional diagram illustrating one example implementation of the electrodes of a mechanical based energy harvesting system using fractal geometry, according to various aspects of the present disclosure. With reference toFIG.9, some of the present embodiments may employ fractal geometry in the form of space filling curves for the electrode plates910and915, which may be used in place of the metal plates210and215ofFIGS.2A-2B. A space-filling curve is a curve whose range (i.e., the set of all possible values of the curve) contains an entire n-dimensional hypercube. Some of these embodiments may utilize space filling curves in two dimensions, including but not limited to, Peano Curve or Hilbert Curve, in order to shape the flat metallic surfaces.

The energy harvesting or storage device which employs fractal geometry to embed in the flat metallic surfaces910and915, may maximize the conductive region, while minimizing the mass of the parallel metallic plates910and915. The geometry may be subject to the specific desired power level. The geometry may be subject to constraints of thickness and proximity of each region910and915to the other.

FIG.10illustrates one example implementation of the electrodes of a mechanical based energy harvesting system using a Peano1000, according to various aspects of the present disclosure. The figure shows a Peano curve that may be used for the upper plate915as well as the lower plate910ofFIG.9. The mass of a plate using the fractal geometry ofFIG.10is clearly less than the mass of a solid plate of the same dimensions. The particular geometry also maximizes the conductive region.

FIG.11illustrates one example implementation of an electrode1100of a mechanical based energy harvesting system using a Hilbert curve, according to various aspects of the present disclosure. A Hilbert curve is a continuous space-filling curve, which is a compact set homeomorphic to the closed unit interval. The same fractal pattern may be used for both the upper plate915and the lower plate910ofFIG.9. The mass of a plate using the fractal geometry ofFIG.11is clearly less than the mass of a solid plate of the same dimensions. The particular geometry also maximizes the conductive region.

The fractal geometries such as Peano curve and Hilbert curve may provide sufficient conductive surface for impinging signals to harvest electromagnetic field constructively in both lateral and vertical directions (illustrated as magnetic flux920and the Casimir force925inFIG.9), in relation to the flat surface of the two parallel electrode plates.

Employing space filling curves (such as Peano or Hilbert curves) to form a flat metallic surface exploits both lateral and vertical electrical fields to increase the force exerted per unit area. In an energy harvesting or storage device that employs fractal geometry for the vibrating electrode plate915and the stationary plate910, the conductive region is maximized, while the effect of gravity (i.e., the weight of the plates) is minimized. That is coupled to further desired constraints of thickness and proximity of each region to the neighboring region and boundary of the surface of the plates910and915.

In production phase, the thickness and length of each segment of the curve is pre-determined by design requirement for covering the available surface, with specific boundary specifications, and desired total permeability and conductivity. The fabrication of nanostructured fractals is based on a combination of anisotropic etching and corner lithography, where etching must progress perfectly vertical to the surface and corner lithography is incorporates the ability to inject sharp features in the process. The fractals emerging from repeated edge lithography can multiply and scale down to specific patterns such as the patterns shown inFIGS.10and11. Both wet or dry etching techniques for fabrication of the fractal metal plates in nanoscale are well known. In wet etching, the etch material is removed through chemical reaction between a liquid etchant (Iodine-based for gold) and the metal to be etched. In dry etching, the etch material is removed through a chemical reaction and/or physical interaction between etchant gasses and the exposed material. Alternative can be considered with wet etching using metal assisted chemical etching, or Reactive Ion Etch (RIE), a dry etching technique that uses a low-pressure plasma to remove the etch materials by means of both chemical and physical etch.

The absolute value of the vacuum energy is non-zero due to the presence of vacuum fluctuations in quantum field theory. Zero-point energies arise because the canonical quantization scheme does not fix the ordering of non-commuting operators in the field Hamiltonian. The attractive force arises due to the change in the zero-point energy of the electromagnetic field. When two parallel metal plates are sufficiently close, in orders of a few hundreds of nanometers or less, an attractive force arises from the ground state of quantum electrodynamics. Forcing the field to satisfy certain boundary conditions such as in interaction with matter or other external fields is related to the interaction of a fluctuating electromagnetic field with real materials. Essentially, the electromagnetic modes that have nodes on both plates may exist within the cavity between the two plates. The zero-point energy depends on the separation between the plates, giving rise to an attractive force. This result, in fact, may be interpreted as due to the differential radiation pressure associated with zero-point energy (virtual photons) between the plates “inside” and the “outside” of the plates, which leads to an attraction because the mode density in free space is higher than the density of states between the plates.

A key property of the Casimir effect is its highly non-trivial nature of the vacuum state in quantum field theory. Generally, the Casimir effect is the response of the vacuum of quantized fields caused by the change of the zero-point energy of a quantum field due to the presence of static, geometric boundary conditions. The concept of the Casimir energy, i.e., of physical vacuum energy as the difference of zero-point energies, has a defined counterpart for situations of quantized fields interacting with classical, static background fields, namely dielectric media, external electromagnetic and gravitational fields. The Casimir effect has been measured and proven for all the various phenomena associated with the response of the vacuum in constrained quantum fields.

Expressing analytically the expression for Casimir effect requires expressing vacuum expectation value of the energy operator in the ground state of the quantum field, between two parallel metal plates910and915inFIG.09, while considering the effective action due to the influence of the boundary condition and moving plates. The general regularization and renormalization procedures in quantum field theory under the influence of boundary conditions is well understood, where the divergent part of the vacuum state energy is found in an arbitrary quantization domain and different representations for the regularized vacuum energy are obtained and infinities dealt with re-normalization procedure for handling electrodynamics of vacuum with moving boundaries.

The following discussions assume the system is in thermal equilibrium at room temperature and the metal plates are smooth surfaces for the purpose of characterizing the field between the two plates. Among the various numerical methods, the finite difference methods have the flexibility to handle arbitrarily complex material configurations, including anisotropic and continuously varying dielectrics and using boundary element methods. Combination of finite difference and boundary element methods have the further advantage to treat bodies with arbitrarily complex shapes. In order to simulate Casimir force field between two parallel plates, the space between the two plates is divided into uniformly equally-spaced square cells, referred herein as grid cells. The square quantized grid structure in three-dimensional Euclidean space forms the underlying ambient geometry for computation of the Casmir force between the two plates where one of the plates is free to move continuously in the z-direction (i.e., towards or away from the other plate). The Casimir forces on each plate are computed using the Casimir-Polder interaction energy between two polarizable atoms i and j, which is approximated by Equation (6):

U⁡(r)≡-2⁢3⁢h⁢c⁢αi⁢αj8⁢π2⁢r7=p⁢αi⁢αjEq.(6)

Where r denotes the distance between two atoms, h is the plank constant, c is the speed of light, and a is the electrostatic polarizability of the metal. For the purpose of estimating the field strength, a grid cell is a square area that contains a fixed number of atoms. The homogenous metal plate is quantized into a square grid, indexed by i, j. U represents the energy of an atom within a grid cell as a function of electrostatic polarizability a of the metal. Let Nirepresent the number of atoms in the grid cell, the total energy for a given grid cell accounting for the interaction from all other grid cells to the i-th cell may be represented by Equation (7):

Ui=ραi⁢Ni(∑jαl⁢Nl❘"\[LeftBracketingBar]"ri-rj❘"\[RightBracketingBar]"+∑jαl+1⁢Nl+1❘"\[LeftBracketingBar]"ri-rj❘"\[RightBracketingBar]"+…)Eq.(7)

FIG.12Ais a contour map with the Casimir potential computed from the equation 7 for two metal plates with homogenous smooth surfaces, according to various aspects of the present disclosure.FIG.12Bis a table1220showing the parameters used to compute the field distribution ofFIG.12A. The contour map1200illustrates the intensity of the field for the simulation parameters ofFIG.12B, where the plate dimensions considered by way of example are 5×5×5 micrometer{circumflex over ( )}3, the number of grid points (Ni) is 500×500×500 for a given polarizability of silver with 1.88×10{circumflex over ( )}−30 m{circumflex over ( )}3/atom with a density of 5.8×10{circumflex over ( )}28 atoms/m{circumflex over ( )}3. The absolute value of the field potential in units of Newton per meter square is depicted by the contour map1200, with values taken in each contour region1201-1207are shown in the figure. This results clearly demonstrates the concentration of the force towards the center of the plate, smoothly falling off towards the boundary.

D. Using Spherical Metal Cavities Instead of Metal Plates

In some of the present embodiments, the mechanical energy harvesting may employ an array of spherical metal cavities suspended in stationary state in parallel to the flat metallic surface of the electrodes.FIG.13Ais a functional diagram illustrating one example of an energy harvesting device1300A that employs an array of spherical metal cavities1310instead of a flat metal plate, according to various aspects of the present disclosure.

In some of the present embodiments, each sphere may have a radius between 100 micrometers to a few hundred nanometers (e.g., 100 micrometers, 50 micrometers, 1 micrometer, 500 nanometers, 100 nanometers, etc.). With reference toFIG.13A, the energy harvesting device1300A may include an array of spherical metal cavities1310, connected to the carbon nanotubes1315and suspended in stationary state in parallel to the flat metallic surface of the electrodes210and215, in the form of a uniformly spaced grid in two dimensions. The role of the plate215in the embodiments ofFIG.13Ais to act as a supporting structure for suspending the spheres1310to a group of carbon nanotubes. The supporting beam1391may be used to support the cantilever1325. The supporting beam1391, in some embodiments, may be attached to the packaging or an interior protrusion of the packaging.

In the excited state, a single or multiple MEMS cantilever1325may be deployed to harvest energy from oscillations of spheres1310by moving the spheres1310towards the plate210. The attractive forces are shown as1320in the figure. While a single MEMS actuator is shown in215, some embodiments may use multiple MEMS cantilever1325and the spheres1310either individually or as separate groups may be dedicated to each MEMS actuator.

FIG.13Bis a functional diagram illustrating one example of an energy harvesting device1300B that employs an array of spherical metal cavities and an array of cantilevers instead of two parallel plates, according to various aspects of the present disclosure.

In some of the present embodiments, each sphere may have a radius between 100 micrometers to a few hundred nanometers (e.g., 100 micrometers, 50 micrometers, 1 micrometer, 500 nanometers, 100 nanometers, etc.). The spheres1310may be glued onto the end of a copper wire1381with conductive epoxy. A 200 nanometers thick film of gold with a thin chromium adhesion layer evaporated on both the sphere and the top plate1381during manufacturing process. An additional 10 nanometers layer of gold may be sputtered onto each sphere to provide electrical contact with the wire.

FIG.13Bshows a different configuration where the lower parallel plate is replaced by individual small plates1382. With reference to the expanded section1330inFIG.13B, the flat electrode1388(as shown in the expanded section1330) is mounted below the arm of the torsion pendulum1382, while the spherical electrode1310is placed vertically at a prescribed distance from the pendulum plate1386, hereinafter simply referred to as plate. The role of the plate215in the embodiments ofFIG.13Bis to act as a supporting structure for suspending the spheres1310to a group of carbon nanotubes. The supporting beam1392may be used to support the plate215. The supporting beam1392, in some embodiments, may be attached to the packaging or an interior protrusion of the packaging.

The plate215, in the embodiment ofFIG.13Ais moving (in order for the cantilever1325to vibrate) while the plate215, in the embodiment ofFIG.13Bis stationary since the energy is harvested from the cantilevers1382.

The sphere1310may be covered by a gold film and glued onto the end of a copper wire1381with conductive epoxy and positioned close to one of side of the plate1382. The polysilicon plate1382is suspended from two of its opposite sides by thin torsional rods1386. The two fixed polysilicon1388electrodes are located symmetrically under the plate1382. The plate1382is free to rotate about the torsional rod1386in response to an external torque. The torsional rod1386provides the restoring torque to counter the external torque rotation angle, denoted as 0 about the center of the torsional rod1386. The voltage applied to the sphere1310at distance z, the distance closest approach to the sphere, attracts the plate1382, whereby the torsion rod1386counteracts the attraction and the plate1382returns to its initial position. The action of rotation of the plate1382induces an electrical current in the piezo electrical layer of the plate1382, which may be harvested for generating power. The harvested output voltage as denoted as Vss1385and Grd1386.

In some of the present embodiments, the mechanical energy harvesting device may use a nano piezoelectric based substance as a cantilever.FIG.14is a functional diagram illustrating one example of a portion of an energy harvesting device that uses a nano piezoelectric based substance as a cantilever1470, according to various aspects of the present disclosure. For simplicity, the movable electrode plate connected to the cantilever1470is not shown inFIG.14.

With reference toFIG.14, a MEMS nano piezoelectric based substance is used for harvesting power from the motion of the upper electrode plate215(FIGS.2A-2B). Utilizing a nano-piezoelectric structure interacting with the flat conductive plate215also acting as electrode is chosen for the vibration modes such to exert optimum strain in the appropriate direction, denoted as z-direction inFIGS.7A-7B. Piezoelectric materials with appropriately chosen electromechanical coupling factor for power harvesting have anisotropic behavior, which depends upon the direction of the strain and the direction of the polarization and with respect to the position of the electrode. In certain embodiments, it is possible to use a bimorph piezoelectric energy harvester based on a cantilever beam. In which case, two piezoelectric layers are fixed to a non-piezoelectric elastic layer in this case to create a cantilever. A layered perspective of the cantilever1470is shown, where the piezoelectric plate1430is mounted on a plane of silicon1445which is placed on top of a layer of gold or silver (for high conductivity), acting as electrode1450.

The electrical switch1420is closed when energy is harvested from the cantilever1470. When the switch1420is closed, the MEMS cantilever output1435drives the voltage regulator1440to maintain a constant voltage1450. The electrical switch1480is closed when the blocking oscillator1490is used to excite the system, the oscillator1490may drive a square wave. The blocking oscillator is only used during excitation period to create a square wave for synthesizing mechanical vibration to prime the carbon nanotube arrays235(FIGS.2A-2B) by forcing the upper electrode plate215to reach resonant frequency.

FIG.15illustrates an example of a simple square wave1540generated by the oscillator1490ofFIG.14. With reference toFIG.15, the square wave1540has a periodicity as shown by1545. The wave1540generated by the blocking oscillator1490may be used to drive the cantilever1470for periodically compressing the carbon nanotube array235(FIGS.2A-2B), forced by the cantilever1470. Once the piezoelectric cantilever1470reaches the resonant frequency of the oscillation mode, the switch1480is opened and the blocking oscillator1490is powered down. The device enters its normal mode of operation and the switch1420is closed to draw the electrical current from the cantilever and regulate the voltage by the voltage regulator1440connected to the output1435of the cantilever1430. The switch1480may be opened and the switch1420may be closed in order to output the voltage Vss1450harvested from the cantilever1470.

The Casimir energy and force may change at room temperature depending on the geometry of the configuration and the type of boundary conditions.FIG.16is a flowchart illustrating an example process1600for the design of the mechanical energy harvesting device, according to various aspects of the present disclosure. The process1600is an iterative method that some embodiments use to come up with a design for the mechanical harvesting device to match the performance parameters. The process uses the algorithms and formulas that are written for ideal conditions in order to come up with the design that matches a desired set of performance parameters.

The design process begins by considering the metal plates at a fixed distance. The process considers practical constraints and computes the Casimir force. The process, at block1605computes the Casimir force for plates with infinite boundary, given fixed conductivity and permittivity at minimum possible practical distance between the two plates.

Next, the process adds (at block1610) the effects of dynamic Casimir effect due to a uniformly moving plane. At block1610, the dynamical behavior of Casimir effect is considered, with one plane in stationary state and the other plate accelerates moving in the positive direction downward towards the stationary plate. For a massless scalar field, the vacuum energy density is obtained using Green's function method, after subtracting the contribution from free Minkowski space (i.e., the three-dimensional Euclidean space and time), the Casmir pressure between two plates is computed as a function of velocity.

Next, the process accounts (at block1615) for boundary size of each plate for creation of particles from the vacuum by accelerated finite boundaries with massless scalar field. Modification is made (at block1615) to account for the dynamical Casimir effect which arise from the movement of the plate (235). For a uniformly moving plane, the Casimir force acquires a velocity dependent correction. For an accelerated plane, the Casimir force is accompanied by creation of particles from the vacuum. Material boundary is viewed as a kind of concentrated external field, and moving boundaries act as nonstationary external field. The creation of particles from the vacuum by nonstationary external fields is familiar in the S-matrix (or scattering matrix) theory of particles, characterizing the temporary change in the amount of energy in a point in space. This allows the creation of particle-antiparticle pairs of virtual particles due to the uncertainty principle. While the energy conservation law accounts for creation of positive energy particles and dissipative part accounts for the energy of the remaining part of particles when the plate returns to rest. Several renormalization prescriptions may be used in order to obtain the total energy corresponding to whole trajectory of the plate displacement, and to calculate the radiation-reaction force that acts on the moving plate in emission and absorption of the particles.

The process then computes (at block1620) the total energy in all modes from classical quantum field for the number of particles in a three-dimensional cavity. In the block1620, the case of an electromagnetic field in a three-dimensional oscillating cavity is considered. In this case both the total number and the total energy of the created photons grow exponentially with time. The periodically oscillating boundary is well known to be mathematically equivalent to an external electric field periodic in time. Bosonic particles form the carriers of the field between two parallel metal plates that collectively manifest into the Casimir force. The number of bosonic particles created by such a field from the vacuum depends on time, given the condition of parametric resonance is satisfied.

Next, the geometry of flat metallic plates is modified (at block1625) to fractal geometry as described above with reference toFIG.9and the total energy is re-calculated. If the energy is sufficient, the design process may end, otherwise the design process iterates back (at block1630) to block1615, by adjusting the plate sizes and repeating blocks1620-1625until the desired energy level is reached.

II. Using RF Energy to Ignite a Mechanical Energy Harvesting Device

RF and solar energy, in some embodiments, provide effective sources for complementing the operation of device. That is to assure that energy harvesting device always outputs sufficient power for the intended application. Furthermore, whenever either sources are present, these sources may complement constructively, to add to the total power harvested from the device.

Energy harvesting from electromagnetic force is realized by converting RF signals to DC power. The RF signals may be ambient or judiciously designed waveform for power harvesting.FIG.17is a functional diagram illustrating one example embodiment of an RF based energy harvesting system120, according to various aspects of the present disclosure. The system may include an antenna1705, an impedance matching circuit1710, an RF to direct current (DC) rectifier1715, a DC-DC charge pump1720, a storage capacitor1725, and a voltage regulator1730.

An RF signal may impinge on the antenna1705as input to the impedance matching circuit1710. The output of the impedance matching circuit1710may drive the RF-DC rectifier1715, which may convert the RF to DC. The output of the RF-DC rectifier circuit1715may be input to the DC-DC charge pump1720to convert the DC to a desired voltage level, which stored in a capacitor1725. The voltage regulator1730may be used to assure a constant steady voltage level at the VRFoutput134.

In some of the present embodiments, the antenna1705(sometimes referred to as rectenna when specifically designed for energy harvesting, as described below) may be a dipole antenna (e.g., and without any limitations, a 50 ohms resistance dipole antenna). The RF-DC rectifier1715, the DC-DC charge pump1720, the storage capacitor1725, and the voltage regulator1730make a four-stage voltage amplifier. The impedance matching circuit1710may include a solenoid1735and a capacitor1740and may be used to match the impedance of the diploe antenna1705to the impedance of the voltage amplifier. The antenna1705coupled with the impedance matching circuit1710may drive the RF-DC rectifier circuit1715. The RF-DC rectifier circuit1715may include one or more rectifying devices such as Schottky diodes1750(that has a metal and n-type semiconductor junction) or a normal barrier diode (that has a p-n semiconductor junction). The RF-DC rectifier circuit1715may include one or more capacitors1755.

The DC output1760of the RF-DC rectifier circuit1715may drive the DC-DC charge pump1720. The DC-DC charge pump1720may step-up the output voltage of the RF-DC circuit1715. The output energy of the DC-DC charge pump1720may be stored in the storage capacitor1725. The storage capacitor1725may be connected to the voltage regulator1730, which may regulate the output voltage VRF134at a constant output voltage (e.g., at a voltage level required by a particular application). The output VRF134of the RF based energy harvesting system120may be supplied to the input101of the energy harvesting device100ofFIG.1.

The rectifying circuit1715may be optimized for appropriate excitation signal. Typically, the efficiency of the conversion process is related to receive antenna's1705gain, rectification efficiency, impedance matching1710, bandwidth, power and peak-to-average ratio of the excitation signal. An option by combining the antenna and rectification function is referred to as rectenna, which is a rectifying antenna, a special type of receiving antenna designed specifically for converting electromagnetic energy into direct current (DC) electricity1760. The charge pump1720also steps up the voltage to usable level and stored for driving the voltage regulator1730to maintain a constant voltage output level VRF134.

FIG.18is a graph1800depicting the amount of received RF power available for harvesting, according to various aspects of the present disclosure.FIG.18is the plot for the received power in dBm (1850) impinging on the antenna for RF power harvesting, as a function of distance1810in meters, from a source in UHF band with transmitted power of 4 Watts. This is the maximum allowable power in US in 900 MHz frequency band. With reference toFIG.18, the received RF power available for harvesting1805is plotted for the industrial, scientific, and medical radio band (ISM band) 915 MHz as a function of distance1810to the signal source of the excitation signal. The excitation signal may be expressed in Equation (8).

PR=PT(λ4⁢π⁢r)2Eq.(8)

where PRis the received power, PTis the transmitted power, λ is the wavelength of the signal, and r is the range in meters. Efficiency of percentage power from PRconverted to actual usable DC power may be dictated by a number of design selections such as the gain and reflection coefficient of the antenna and the selection of semiconductor technology, (e.g., complementary metal-oxide-semiconductor (CMOS) versus Gallium arsenide (GaAs)) and the overall design of the system shown inFIG.17to achieve target price and performance.

FIG.19Ais a functional diagram illustrating one example embodiment of RF remote charging using a client device, according to various aspects of the present disclosure. Each node1930inFIG.19Amay be an energy harvesting device (e.g., the energy harvesting device140ofFIGS.1and2) and a corresponding electronic device that is using the energy harvesting device as a power source. On an as needed basis, the remote excitation system1900A ofFIG.19Amay be used for remote excitation of one or more energy harvesting devices, associated with the nodes1930, with a synthesized signal from a client device1905and/or a wireless access point (or wireless base station)1910. The client device1905may be, for example and without aby limitations, be a smartphone, a cellular telephone, a tablet computer, a laptop computer, a desktop computer, a personal digital assistant (PDA) device, etc. The client device1905and/or the access point1910may be used from a distance to excite the device for RF power harvesting.

FIG.19Bis a functional diagram illustrating one example embodiment of RF remote charging using a flying object, according to various aspects of the present disclosure. Each sensor node1930inFIG.19Amay include an energy harvesting device (e.g., the energy harvesting device140ofFIGS.1and2) and a corresponding electronic device (e.g., and without any limitations a sensor or other type of electronic device) that is using the energy harvesting device as a power source. On an as needed basis, the remote charging system1900B ofFIG.19Bmay be used for remote charging with a synthesized signal from the flying object1925such as, for example and without any limitations, a drone, a balloon, an airplane, a helicopter, or a space-based platform such as without any limitations, a satellite. The flying object1925may be used to fly by a sensor field1940in inaccessible or remote areas to energize the energy harvesting devices that are providing power to the sensors in each node1950. The periodicity of remote charging of the device may be dependent on multiple variables such as peak-power, duration of average power consumption when bursting, power profile in sleep and wake mode, operating temperature, and size and weight of the overall system.

FIG.20is a functional diagram of the triggering excitation waveform with duty cycle displayed over time, according to various aspects of the present disclosure. With reference toFIG.20, the excitation from a mobile device2005(e.g., the mobile device1905ofFIG.19A) is shown with the device antenna as2015, being driven with a square waveform, illustrating the duty cycle over time in driving the excitation with an active excitation period2020and powered down to inactive state during normal operation cycle2025.

FIG.21is a functional diagram illustrating one example embodiment of an RF based energy harvesting system, according to various aspects of the present disclosure. With reference toFIG.21, the input RF signal2110is processed by the analog front end (AFE)2120and the energy is stored in a supercapacitor2140using the supercapacitor charging circuit2130. A supercapacitor is a high-capacity capacitor with much higher capacitance values (but lower voltage limits) than the electrolyte capacitors. A supercapacitor may include two electrodes separated by an ion-permeable membrane and an electrolyte that ionically connects both electrodes.

The load2150presents the impedance for the driving the current into the target circuitry, including the piezoelectric cantilever for kick starting the oscillation of metal plates. The signal source2110for the AFE2120may be an RF signal, for example and without any limitations, in the ISM bands such as 915 MHz band, 2.4 GHz band, or solar power.

FIG.22is a functional diagram illustrating one example embodiment of a harvester analog front end circuit and a supercapacitor, according to various aspects of the present disclosure. With reference toFIG.22, the output of the antenna2210my drive the diode circuitry (e.g., without any limitations, using Schottky diodes, e.g., Skyworks SMS7630-061 diodes)2212to rectify the energy to a DC level for charging the supercapacitor2214, while the diode2219(e.g., without any limitations, a BAT54 series Schottky diode) prevents discharge back into source. For power harvesting to initiate, it is necessary to provide impedance transformation to enable charging a supercapacitor from ground state (zero volts). In some embodiments the supercapacitor charging circuit may be used in both RF and solar power harvesting circuit.

The maximum allowable energy harvested from RF energy may be dependent on the distance from the signal source to the device.FIG.23is a flowchart illustrating an example process2300for determining the optimal distance to energize an energy harvesting device, according to various aspects of the present disclosure. With reference toFIG.23, the process may determine (at block2305) the local regulatory emission limits for the Equivalent Isotropically Radiated Power (EIRP) and the target power to harvest. The EIRP is the product of the transmitter power and the antenna gain in a given direction relative to an isotropic antenna of a radio transmitter.

Next, a distance is selected (at block2310) from the source (i.e., the RF device that is providing excitation energy) to the energy harvesting device. Next, the process calculates (at block2315), the free space loss. The process then calculates (at block2320) the received power at the input of the antenna used in the emission device by taking account of the antenna gain and insertion losses associated with the particular antenna. The process then calculates (at block2325) the received power at the output of the antenna by taking the account of the antenna gain and the insertion losses associated with the particular antenna.

The process then calculates (at block2330) the power, voltage, and current to the supercapacitor computed from the power calculated at the output of the antenna2210. The process then calculates (at block2335), the amount of harvested power, the time to charge the supercapacitor, and the time to discharge the supercapacitor. The process then determines (at block2340) whether the power, the time to charge, and the time to discharge are acceptable for a particular use case. If yes, the process ends. Otherwise, the process may adjust (at block2345) the distance (e.g., by reducing the distance between the source device and the energy harvesting device). The process then returns to block2315to repeat blocks2315-2340.

Using the circuit shown inFIG.22as the model for a harvester AFE, the current and voltage may be characterized by Equation (9):

Il(t)=(Vs⁢c(t)-(Vs⁢c(t)-4⁢Es⁢P))/(2⁢Es)Eq.(9)

Where II(t) represent the current at the output2421ofFIG.24.FIG.24is a functional diagram illustrating one example embodiment of a supercapacitor charging circuit, according to various aspects of the present disclosure. With reference toFIG.24, the circuit diagram for the interface circuitry to the supercapacitor is shown. The circuit may include the resistive network2450,2425,2424, and2422to assure the capacitor2426is not discharged and the output load is not driven until sufficient voltage is accumulated across the capacitor2426. In the following equations, Vsc(t) is the voltage at the supercapacitor2426, Esis equivalent series of resistance (ESR) of the capacitor2426, and P is the power required to drive the output2421voltage or current. The voltage at the load may be expressed by the Equation (10) and the voltage at the supercapacitor may be expresses by the Equation (11):
VI(t)=(Vsc(t)−II(t)Es)  Eq. (10)
Vsc(t2)−Vsc(t1)=−II(t2−t1)/CEq. (11)

Where t2>t1≥0 and C is the capacitance in Farads and R is the resistance in ohms. The voltage across a capacitor ma be characterized by Equation (12) as a damped exponential:

Vc(t)=V⁡(t)⁢(1-e-tC·R)Eq.(12)

Thus, the charge time may be expressed by the Equation (13):

tc=-(ln⁡(1-Vc(t)V⁡(t)))·C·REq.(13)

For estimating the amount of discharge time of the capacitor the Equation (14) may be used:
tD=C/ĪEq. (14)

where Ī is the average current, the average being computed by considering maximum and minimum current. Here, tcrepresents the time duration to charge the capacitor and tdrepresents the time duration to discharge the energy into the load, which in some embodiments is the nano-piezoelectric cantilever (e.g., the nano-piezoelectric cantilever270ofFIGS.2A-2B).

With reference toFIG.24, the supercapacitor charging circuit2400may include a load switch2422and a comparator3224for power monitoring. A specific example is provided herein for selecting the components of the supercapacitor charging circuit to excite the energy harvesting device with using 915 MHz frequency band, which is the UHF ISM-band. The U.S. Federal Communications Commission (FCC) regulations allows emission of up to 4 Watts emitted EIRP in the unlicensed band in 915 MHz. For this band, the following selection of parts may made. An Infineon IRLML6401, P-Channel MOSFET load switch may be used as the load switch522and a Texas Instrument TLV3011 open drain output push-pull comparator may be used as the comparator2424. An AVX BZ05FB682ZSB, ultra-low ESR high power pulse supercapacitor may be used as the supercapacitor2426.

In excitation of the energy harvesting device from a signal source, the key parameter to consider is the distance of the signal source to the device to deliver sufficient power in the signal impinging on the antenna embedded on the device. The farther the distance, the less power is made available for the purpose of RF energy harvesting. Sample calculations are followed in a case with emission from 20 feet distance from the device. The power level at the pin in the harvester input2281ofFIG.22(which is the signal at the output of antenna2210) is 36−47+2=−9 dBm (0.126 mW) (79 mV into 50 ohms), where 36 dBm is calculated input power, 47 dB is free space loss and an antenna gain of 2 dB is considered. For determining the capacitor size using the part selected for the supercapacitor2426, 6.8 mF with 500 milli-Ohm ESR is used. Assuming fairly high and conservative choices for 100 micro Watts with one second load requirement (i.e., one second continuous delivery of excitation energy to the load), and voltage requirement with Vmax=2.7V (frequently used voltage level in low power CMOS), Vmin (frequently minimum voltage that low power CMOS can operate) equal to 2.4 V which respectively translate into a maximum current Imax=100 uW/2.4=41.7 uA, minimum current Imin=100 uW/2.7=37.1 uA, and average current Iave=39.4 uA, the voltage drop is 39.4 uA(147+0.5)=5.81 mV.

Time to discharge by 0.3V is 51.8 sec. Approx. (for 100 uW of power requirement) establishes the maximum duration of excitation period allowable in 900 MHz frequency band with the design choices described herein. From equation (13), then the time to charge the supercapacitor is calculated as (6.8 mF, 500 mohm ESR) (78 mV)=15 ms. That is the time to charge the supercapacitor (6.8 mF, 500 mohm ESR) (78 mV) is equal to 15 ms.

Calculations herein illustrates where a 4 W EIRP signal at 20 feet may charge a 6.8 mF supercapacitor in about 15 msec to 78 mV. This in turn may provide a 100 uW power to a load for 51 sec. If necessary, a voltage boost circuit may be added to the circuit2400ofFIG.24, which is a DC-to-DC power converter that steps up voltage from its input supply, to get the higher voltage levels and/or multiple capacitors may be used in series to increase the required voltage for a particular use case.

FIG.25is a graph2500depicting the duration for time-to-charge for different output voltage levels in millivolts as a function of the output voltage2510, according to various aspects of the present disclosure. Power harvesting with RF energy employing the circuit model described inFIGS.22and24, with Equations (09) to (14) are used to calculate the time-to-charge2505inFIG.25.

FIG.26is a graph2600depicting the computed path loss, according to various aspects of the present disclosure. In the example ofFIG.26, the path loss2605is calculated versus the distance2610according to block2315ofFIG.23.

FIG.27is a graph2700depicting the input power of an antenna versus the distance, according to various aspects of the present disclosure. InFIG.27, the input power2705using a 2 dB antenna is shown versus distance2710in meter.FIG.28is a graph2800depicting the harvested power versus the distance, according to various aspects of the present disclosure. The allowable maximum harvested power in micro-watts2805is shown inFIG.28as a function of distance in meters2810. This means the distance to remotely excite the energy harvesting device for re-ignition or power-up shall be adjusted to accommodate the desired power level.

FIG.29is a bar chart showing the time to discharge as a function of the required total harvested power, according to various aspects of the present disclosure. With reference to FIG.29, the time to discharge2905from 2.7 Volts for 0.3 Volts is shown as a function of required total harvested power in a bar chart.

FIG.30is a graph3000depicting the voltage into the device as a function of time, according to various aspects of the present disclosure. With reference toFIG.30, the voltage (in volts)3005into the device is depicted as a function of time3010(seconds).

FIG.31is a graph3100depicting the output current versus time according to various aspects of the present disclosure. With reference toFIG.31, the output current3105in microamps into the device is shown as a function of time3110in seconds.

III. Using Solar Energy to Ignite and/or to Complement a Mechanical Energy Harvesting Device

FIG.32is a functional diagram illustrating one example embodiment of a solar based energy harvesting device130, according to various aspects of the present disclosure. The solar based energy harvesting device130may be integrated with the RF based energy harvesting system1700ofFIG.17, and the mechanical based energy harvesting system200ofFIGS.2A-2Bin a single package (e.g., as described below with reference toFIG.33).

The visible light may also be considered as an optional source for outdoor applications for maximizing total harvested energy. In some embodiments, augmenting any solar cell with the kinetic energy harvesting, enables the solar panel to continue to act as a power source even when dark or clouded, effectively acting as an energy storage module backing up the power produced by the solar cell.

Some embodiments may use for graphene as a conductive anode in a solar cell, featuring a flexible organic photovoltaic cell. The main performance parameter is power conversion efficiency (Pce) for any solar cell is given by Equation (15):

Pc⁢e=Vmax⁢JmaxPinEq.(15)

Where Pinis the incidental optical power density, Vmaxand Jmaxare the voltage current density at the maximum power operating point respectively. A power conversion efficiency of 10.04% has been achieved with appropriate choice of parameters for doping, thickness of various layers and fill factor of the graphene sheet. The I-V characteristic of the junction is a linear function of the contact area between the graphene layer and the doped semiconductor technology used in the process, with GaAs having demonstrated superior performance.

In some embodiments, the size of the metal plates210and215ofFIGS.2A-2Bis set to reach the desired power level for the specific application (e.g., the power required by an electronic device that is receiving power from the energy harvesting device that is using the metal plates210and215. If the solar cell exceeds the size of the metal plates for energy harvesting, the individual support system needs to anchor and keep each individual solar cell at a sufficient distance from the moving plate215to deter any interference with the mechanical oscillation of the plate and piezoelectric cantilever. The process of structural parameters includes GaAs thickness, graphene work function and transmittance, and n-type doping concentration in GaAs crystal.

With reference toFIG.32, the solar based energy harvesting device130may use the impinging light on the device130to harvest energy. In some of the present embodiments, a layer3225of graphene3290may be used as the primary conduit to harvest optical energy illuminating the surface of the device130. As described above, graphene is a form (or allotrope) of carbon that is formed from a single layer of carbon atoms arranged in a hexagonal lattice. Graphene conducts heat and electricity efficiently and is nearly transparent. The device's top layer may be covered with a transparent coating layer3295(e.g., titanium deuteride TiD2) to protect against any damage to the layer of graphene underneath.

Graphene, in some embodiments, may be the primary component which interacts with incident photons and extract energy from impinging light. The electrodes3211-3212are connected to the graphene over a layer3280of gold (or silver) and may be used to drive the output stage, which may include a storage capacitor3215and a voltage regulator3220.

For bonding material, the metallization layer3280plays important roles in bonding reliability. The gold or silver may be utilized for metal-dielectric-metal (MDM) nanostructure. For example, a thin solar cell structure may be comprised of graphene deposited on two shallow gold gratings acting as metallic plasmons. Metallic plasmons are metals that support surface plasmons and oscillation of electron density with respect to the fixed positive ions in a metal. It has been demonstrated that the traveling direction of the surface waves may be controlled. A dielectric or semiconductor spacer3230of explicit thickness may be unified beneath metal gratings. The graphene layer3225may be stacked on top of a layer3230of dielectric or semiconductor (e.g., silicon dioxide, SiO2) stacked on top of a bottom layer3235of material such as titanium (Ti) or silver. The graphene layer3225may have dual contact with metallic gratings3280and dielectric spacer3230that may offer a channel for incident light to accelerate through and transfer the entire stored induced current loops harvested from incident wave, from the spacer to the semiconductor layer3230placed between the dielectric spacer and the back metal reflector layer3235. The electrodes3211-3212connected to the graphene are used to drive the output stage, which may include the storage capacitor3215and the voltage regulator3220.

The output Vop132of the solar based energy harvesting device130may be supplied to the input102of the energy harvesting device100ofFIG.1. In applications that use solar based energy, when the environment is dark (e.g., at night in an outdoor environment), the energy harvesting device may cease to harvest sufficient energy to power a corresponding electronic device. Using the energy harvesting device100ofFIG.1provides for continuous operation by relying on the alternative power sources as described herein.

IV. Packaging

FIG.33illustrates an example packaging for the energy harvesting device3300that combines the RF, solar, and mechanical harvesting devices ofFIGS.2A,2B,17, and32, according to various aspects of the present disclosure. With reference toFIG.33, the energy harvesting device3300may include some or all components of the energy harvesting device100ofFIG.1. The packaging for the device3300may be organized as a three-dimensional stack, where the optical energy harvesting layer3305may be placed on the top layer, followed by the radio frequency energy harvesting layer3310, followed by the mechanical harvesting layer3315, coupled to one or more cantilevers3370as described above with reference toFIGS.2A-2B. In some embodiments, two near-planar interacting surfaces in the mechanical harvesting layer3315is required with distances less than 100 nanometer to effectively create a platform for manifestation of Casimir force. The interior of the package3300may be vacuum sealed.

The output of the device3300is the voltage supply source, Vss3350and ground connection, Grd3360. In application for wireless sensor networks, the RF harvesting circuit embedded in RF layer3310may be complemented with a transceiver3390coupled with an RF antenna3320, and power level reporting circuit embedded in the RF harvesting layer3310. There may be multiple uses of a transceiver in the system, including remote power monitoring of the device and collection of telemetry data produced by wireless sensors or IoT type devices. In some embodiments, in the same package with the device, sensors, for example and without any limitations, temperature sensors, gyros, magnetometer, accelerometer, chemical sensors, electrical sensors, nuclear sensors, or optical transducers are included for environmental or location monitoring and transmission of the telemetry data to a base station.

By way of example, the telemetry data payload in addition to power level of the device may include sensory data, ranging from an identification code to ambient temperature or pressure, and the device may be quarried wirelessly on a as needed basis or transmitted periodically.

FIG.34is a functional diagram illustrating one example implementation of the voltage adder110ofFIG.1, according to various aspects of the present disclosure. The voltage adder110and the output load115ofFIG.1are implemented by the operational amplifier3430and resistors3432-3435to provide the output voltage VOUT105. VOP132, VME133, and VRF134may be equalized to the same voltage level with different currents by using the resistors3431-3433and adding the currents together to produce a combined output VOUT105(the current in the resistor3435is the sum of the currents in the resistors3432-3434).

The VOP132may be the voltage level harvested from solar radiation or optical sources, for example, energy harvested in optical frequencies (e.g., 330-770 THz). The VME133may be the voltage level harvested from mechanical sources by combining piezoelectric and Casimir force. The Casimir force may be accounted for and harvested to constructively add to the efficiency of the overall device output power. The VRF134may be the voltage level harvested from the RF sources such as the ambient electromagnetic radiation in a prescribed radio frequency range (e.g., 200 MHz to 5 GHz) in the licensed or unlicensed bands. With reference toFIG.33, the voltage adder110may be included in any of the layers3305,3310, or3315.

FIG.35is a functional diagram illustrating one example of the use of the energy harvesting device ofFIG.33as a power supply source for electronic devices such as transducers, sensors, communication devices, and/or IoT devices, according to various aspects of the present disclosure. With reference toFIG.35, the device3300may be employed to energize and act as a power supply source to one or more electronic devices3510such as transducers, sensors, communication and/or IoT devices. As an example, the device3300may provide sufficient power to act as a power supply for a low power transducer or sensor device3510to conduct chemical/optical/ambient transduction of transforming a reaction in the transducer or sensor to an output signal3520. With the option of using the RF energy circuitry, with addition of an optional transceiver integrated in the energy harvesting device3300, the electronic device3510may conform to waveforms defined in international standards (e.g., ISO-6805) to transmit back to a base station, using the antenna3550, a telemetry signal (e.g., an information bearing signal such as temperature, pressure, toxicity, etc.) produced by the transducer or sensor3510.

In large scale, the device3300ofFIG.33may be replicated and housed in large packages, such as blades and racks to scale and produce sufficient energy for residential or industrial applications such as, for example and without any limitations, home appliances, computer networks for businesses and homes, office buildings, small office/home of office (SOHO), etc.FIG.36is a functional diagram illustrating the replication of energy harvesting devices, according to various aspects of the present disclosure. With reference toFIG.36, multiple energy harvesting devices3300are replicated to form a blade3605. Multiple blades3605are replicated to form a rack3610. Multiple racks3610may be used to provide power for residential and/or industrial applications.

In some aspects of the present embodiments, multiple energy harvesting devices may be fabricated into a single die.FIG.37illustrates a conceptual diagram for a multicell configuration of energy harvesting devices, according to various aspects of the present disclosure. With reference toFIG.37, multiple energy harvesting devices3705are cascaded and are fabricated on a single die in a two-dimensional configuration. The die may sum up the voltages generated by all the individual energy harvesting devices3705to provide the aggregate output voltages Vss3710, with respect to the ground pin3715.

V. Temperature & Vibration

In some embodiments, the energy harvesting device may operate at room temperature and used in an environment without any physical vibration. In other embodiments, the energy harvesting device may operate in environments with more extreme temperatures or high temperature gradients. In these embodiments, the re-ignition of the energy harvesting device may be required more frequently.

In design of the nano piezoelectric cantilever (e.g., the cantilever270ofFIGS.2A-2B), it is possible to further enhance the energy harvesting efficiency by considering ambient vibrations present around where the device is used. This additional energy may be harvested, as vibration may add constructively to the overall oscillation experienced by the cantilever architecture. These vibrations may be present from multiple sources, such as a human motion in walking or running, vehicle or aircraft movements, structural movements such as bridges or tunnels due to periodic stress, industrial movements such as conveyors, pumps and fans. Design considerations may be taken into account in the nano piezoelectric cantilever for additional acceleration and oscillation modes due to ambient vibration present in the environment where the device may be used.

It has been successfully demonstrated that the synthesis of vertically aligned carbon nanotubes may be achieved on iron, cobalt or nickel-deposited quartz plates by chemical vapor deposition with ethylenediamine as a precursor to act as both the etching reagent for the formation of metal nanoparticles and carbon source for the growth of aligned carbon nanotubes. The deposited metal film determines the density and diameter of carbon nanotubes. The duration of the reaction time impacts the thickness of and the length of the tubes. The synthesized carbon nanotubes are multiwalled with a bamboo-like structure confirmed by electron microscopy and Raman spectroscopy.

Fabrication of vertically aligned carbon nanotubes between two parallel plates may be realized by catalytic chemical vapor deposition (CVD). The most common and efficient catalysts are the mono- or bimetallic transition metals (Fe, Co, Ni), while Al2O3, SiO2 or MgO are generally applied as supports. Careful consideration is given to choosing the catalyst layer and the support. The properties of both the support and the catalytic layer considerably affect the properties of carbon nanotube arrays in terms of density, orientation, length, thickness and graphitization of the product. High density carbon nanotube arrays may also be fabricated by using high quantity of iron oxide clusters to enable the growth in the desired orientation perpendicular to both plates. The objective in some of the present embodiments may be to have a geometry of the carbon nanotube array that is aligned in the axial direction with no deformation between two end points. It is well known that the alignment of carbon nanotube forests is mainly due to van der Waals interactions between growing nanotubes, and the steric hindrance between neighboring carbon nanotubes. In the carbon nanotube growing process, during the early stage of CVD, the growth begins in random directions to the substrate surface. Sufficient reaction time may be needed to reach desired orientation and length of the array.

Nanoscale printing for patterning of surfaces in two or three dimensions with at least one feature on the submicron length scale has been developing rapidly. Fabrication of fractal pattern metal plates on gold may be realized by electron-beam lithography and polymer-based “soft” nano-fabrication methods to transfer arbitrary metallic nano-patterns to the substrates. The spacing resolution is limited only by the resolution of electron-beam lithography. This approach avoids residual doping from ion implantation, as occurs in focused-ion beam milling.

Nanoimprint lithography (NIL) has been used in the production of nanostructured supercapacitors (micro-supercapacitors, MSC). Liquid sucrose- and lignin-precursor are used in printing to produce patterns with liquid-carbon-precursor. NIL-printing approach enables nitrogen doping to achieve an increased supercapacitor performance for aqueous electrolytes.

In a first aspect of the present embodiments, an energy harvesting device comprises: first and second substantially parallel plates; a plurality of nanotubes connected between the first and second plates along an axial direction of the nanotubes; a piezoelectric cantilever connected to the first plate; and a device packaging housing the first and second plates, the plurality of nanotubes, and the cantilever; where the second plate is fixedly connected the device packaging; where the first plate and the cantilever are free to move towards and away from the second plate; where the cantilever oscillates by being attracted towards the second plate in response to the Casimir force and by being repelled from the second plate by a spring action on the axial direction of the nanotubes; and where the oscillations of the cantilever cause the piezoelectric cantilever to convert the oscillations to electrical current.

In an embodiment of the first aspect, the device packaging is vacuum sealed.

In another embodiment of the first aspect, the nanotubes are carbon nanotubes.

In another embodiment of the first aspect, the plates are metallic.

In another embodiment of the first aspect, the plates have a small surface roughness amplitude variation compared to a distance between the plates.

An embodiment of the first aspect further comprises an electrical switch comprising first and second connections, the first connection connected to the piezoelectric cantilever; and a radio frequency (RF) exciter connected to the second connection of the electrical switch, the RF exciter comprising: an antenna for receiving RF signals; a capacitor; and an RF to direct current (DC) rectifier for converting energy from the RF signals received by the antenna into electrical current and charging the capacitor for delivering an electrical current to the piezoelectric cantilever through the electrical switch to initiate or reignite the cantilever oscillations.

In another embodiment of the first aspect, the device packaging houses and vacuum seals the electrical switch and the RF exciter.

Another embodiment of the first aspect further comprises a voltage adder, comprising: a first input for receiving a voltage from the piezoelectric cantilever; a second input for receiving a voltage from the RF exciter; and an output for providing a sum of the voltages received at the first and second inputs to drive an electronic device.

In another embodiment of the first aspect, the antenna is configured to receive the RF signals from one or more of a smartphone, a cellular telephone, a tablet computer, a laptop computer, a desktop computer, a personal digital assistant (PDA) device, and one or more flying object comprising a drone, a balloon, an airplane, a helicopter, and a space-based platform.

In another embodiment of the first aspect, the electrical switch is a first electrical switch, the energy harvesting device further comprising: a second electrical switch comprising first and second connections, the first connection connected to the piezoelectric cantilever; a capacitor; and an optical exciter connected to the second connection of the electrical switch, the optical exciter comprising: a solar cell for receiving optical signals and charging the capacitor for delivering an electrical current to the piezoelectric cantilever through the second electrical switch.

In another embodiment of the first aspect, the device packaging houses and vacuum seals the first and second electrical switches, the RF exciter, and the optical exciter.

Another embodiment of the first aspect further comprises a storage capacitor for storing the electrical energy as a first voltage; a voltage adder comprising: a first input for receiving a voltage from the piezoelectric cantilever; a second input for receiving a voltage from the RF exciter; a third input for receiving a voltage from the optical exciter; and an output for providing a sum of the voltages received at the first, second, and third inputs to drive an electronic device.

In another embodiment of the first aspect, the solar cell is configured to receive signals in optical spectrum comprising one or more of ambient light and solar light.

Another embodiment of the first aspect further comprises a voltage dividing circuit for determining a level of a voltage output of the energy harvesting device; and a transceiver for transmitting the level of the voltage output of the energy harvesting device.

Another embodiment of the first aspect further comprises a transceiver for transmitting telemetry data collected from one or more temperature sensors, gyros, magnetometer, accelerometer, chemical sensors, electrical sensors, nuclear sensors, and optical transducers.

Another embodiment of the first aspect further comprises an electrical switch comprising first and second connections, the first connection connected to the piezoelectric cantilever; and an optical exciter connected to the second connection of the electrical switch, the optical exciter comprising: a capacitor; and a solar cell for receiving optical signals and charging the capacitor for delivering an electrical current to the piezoelectric cantilever through the electrical switch.

Another embodiment of the first aspect further comprises a voltage adder, comprising: a first input for receiving a voltage from the piezoelectric cantilever; a second input for receiving a voltage from the optical exciter; and an output current for providing a sum of the voltages received at the first and second inputs to drive an electronic device.

In another embodiment of the first aspect, the electronic device is one of a sensor and an Internet of things (IoT) device.

In another embodiment of the first aspect, the device packaging houses and vacuum seals the electrical switch and the optical exciter.

In another embodiment of the first aspect, the piezoelectric cantilever is a microelectromechanical system (MEMS) nano piezoelectric cantilever.

In another embodiment of the first aspect, the piezoelectric cantilever is a first piezoelectric cantilever, the energy harvesting device further comprising a plurality of piezoelectric cantilevers connected to the first plate, the plurality of cantilevers comprising the first piezoelectric cantilever.

Another embodiment of the first aspect further comprises a plurality of electrical switches, each electrical switch comprising first and second connections, the first connection of each electrical switch connected to a corresponding piezoelectric cantilever in the plurality of piezoelectric cantilevers; and a radio frequency (RF) exciter connected to the second connection of each electrical switch in the plurality of electrical switches switch, the RF exciter comprising: an antenna for receiving RF signals; a capacitor; and an RF to direct current (DC) rectifier for converting energy from the RF signals received by the antenna into electrical current for charging the capacitor for delivering an electrical current to each of the plurality of piezoelectric cantilevers through the corresponding electrical switch.

In another embodiment of the first aspect, the first and second plates are fractal shape plates.

In another embodiment of the first aspect, the first and second plates are solid plates.

In another embodiment of the first aspect, a distance between the first and second plates is less than a micrometer.

In a second aspect of the present embodiments, a power supply comprises: an output connection for connecting to an electronic device; and a plurality of energy harvesting devices, each energy harvesting device comprising: first and second substantially parallel metallic plates; a plurality of nanotubes connected between the first and second plates along an axial direction of the nanotubes; a piezoelectric cantilever connected to the first plate; and a device packaging housing the first and second plates, the plurality of nanotubes, and the cantilever; where the second plate is fixedly connected the device packaging; where the first plate and the cantilever are free to move towards and away from the second plate; where the cantilever oscillates by being attracted towards the second plate in response to the Casimir force and by being repelled from the second plate by a spring action on the axial direction of the nanotubes; and where the oscillations of the cantilever cause the piezoelectric cantilever to convert the oscillations to electrical current; where the power supply adds the electrical energy of the plurality of energy harvesting devices and provides an electrical voltage to the output connection as a voltage source for the electronic device.

In a third aspect of the present embodiments, an energy harvesting device, comprises: first and second plates; a plurality of nanotubes, each nanotube comprising first and second connections, the first connection of each nanotube connected to the first plate; a piezoelectric cantilever connected to the first plate; a plurality of metallic spheres, each metallic sphere connected to the second connection of a nanotube; a device packaging housing the first and second plates, the plurality of nanotubes, the plurality of spheres, and the cantilever; where the second plate is fixedly connected the device packaging; where the first plate, the cantilever, the plurality of nanotubes, and the plurality of spheres are free to move towards and away from the second plate; where the cantilever oscillates by being attracted towards the second plate in response to the Casimir force and by being repelled from the second plate by a spring action on an axial direction of the nanotubes; and where the oscillations of the cantilever cause the piezoelectric cantilever to convert the oscillations to electrical energy.

In a fourth aspect of the present embodiments, a method of determining a distance between a radio frequency (RF) exciter and an RF energy harvesting device for delivering a predetermined amount of RF power by the RF exciter to the energy harvesting device, the energy harvesting device comprising an antenna and a super capacitor, the method comprising: a) selecting a distance between the RF exciter and the energy harvesting device; b) determining an amount of RF energy lost in free space due to travelling of RF signals from the RF exciter to the RF energy harvesting device; c) calculating an amount of power received at an input of the antenna from the RF exciter based on the RF energy loss; d) calculating an amount of power output from the antenna to the energy harvesting device based on the power received at the input of the antenna; e) calculating, based on the amount of power output from the antenna, an amount of power charged into the super capacitor to reach a predetermined power level; and when the amount of power charged into the super capacitor is below a predetermine level, decreasing the distance between the RF exciter and the energy harvesting device and repeating b) to e) until the power charged into the super capacitor reaches the predetermined level.

An embodiment of the fourth aspect comprises: calculating an amount of power at an input of the super capacitor; where calculating the amount of power charged into the super capacitor further comprises using the amount of power at the input of the super capacitor.

Another embodiment of the fourth aspect comprises: calculating a duration of time to charge the super capacitor; calculating a duration of time to discharge the super capacitor; where calculating the amount of power charged into the super capacitor further comprises using the amount of time to charge the super capacitor and the amount of time to discharge the super capacitor.

Another embodiment of the fourth aspect comprises: determining frequency modes in an oscillatory behavior of the RF energy harvesting device.

In a fifth aspect of the present embodiments, a method of designing a mechanical energy harvesting device comprising first and second plates comprises: calculating a Casimir force between the first and second plates with infinite boundaries; adjusting the Casimir force for effects of the first plate uniformly moving towards the second plate; selecting a finite boundary size for the first and second plates; adjusting the Casimir force for the selected finite boundary size for the first and second plates; computing the Casimir force in a plurality of modes from quantum electrodynamics methods considering a three-dimensional volume between the first and second plates based on the selected finite boundary sizes for the first and second plates; and computing a power level generated by the energy harvesting device based on the computed Casimir force.

An embodiment of the fifth aspect further comprises increasing the finite boundary size for the first and second plates when the power level generated by the energy harvesting device is below of a threshold; and repeating the computing of the Casimir force and increasing the finite boundary size until the power level generated by the energy harvesting device reaches the threshold.

Another embodiment of the fifth aspect further comprises when the power level generated by the energy harvesting device reaches a threshold, selecting a fractal design for the first and second plates; computing the Casimir force in the plurality of modes from quantum electrodynamics methods considering the three-dimensional volume between the first and second plates based on the selected finite boundary sizes for the first and second plates and the fractal design; and computing the power level generated by the energy harvesting device based on the computed Casimir force.

The above description presents the best mode contemplated for carrying out the present embodiments, and of the manner and process of practicing them, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which they pertain to practice these embodiments. While the invention has been described with reference to numerous specific details, one of ordinary skill in the art will recognize that the invention can be embodied in other specific forms without departing from the spirit of the invention. In addition, a number of the figures (includingFIGS.16and23) conceptually illustrate processes. The specific operations of these processes may not be performed in the exact order shown and described. The specific operations may not be performed in one continuous series of operations, and different specific operations may be performed in different embodiments. Furthermore, the process could be implemented using several sub-processes, or as part of a larger macro process. Thus, one of ordinary skill in the art would understand that the invention is not to be limited by the foregoing illustrative details, but rather is to be defined by the appended claims.