ELECTRO-MECHANICAL PROPERTIES OF PIEZOELECTRIC MATERIALS

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Electromagnetic energy conversion: development of photovoltaic and RF transducers

Solar energy conversion: photovoltaic transducers

Currently, one of the most widely used sources of energy is light. The energy coming from the sun or from the devices producing artificial light is converted into electricity with the usage of photovoltaic cells. A typical structure of a single solar cell is composed of p-type and n-type semiconductor layers with two metal contacts and a barrier layer with space-charge region placed between them. The schematic of a silicon-based solar cell and the principle of its operation are presented in Figure 1.8. When the light illuminates the silicon p-n junction from the top of the cell, a separation of photons into negatively charged electrons and positively charged holes occurs. This enables the electrons to move freely to the second level, and as a result, the electrons and holes are separated by the space-charge region. The electrons are further collected by the front contacts of the cell. When the two electrodes are connected to an external load, the electrons flow through the circuit and the electricity is created.
It has to be taken into account that when the photon energy is too low, the separation of the electron from the hole is not possible. On the other hand, when the energy is too high only some part of this energy is required to enable the separation of the particles. Hence, many photons are either reflected or pass through the cell [26].
The amount of energy harvested from the light strongly depends on an insolation. For instance, in full sun, the density of luminous power stays at around 100 mW/cm2, whereas the power density given by an artificial light source comprises in the range of 10-100 µW/cm2. A solar module with 15% of efficiency can provide 15 mW/cm2 of power when it is exposed to the sunlight. Table 1.2 shows the dependence of luminous and electric power density on the different lighting conditions.
The information placed in Table 1.2 shows, that solar panels are the efficient energy harvesting devices adapted to the applications working in luminous areas.
Due to the fact that the light is an easily accessible source of energy and that solar cells produce relatively high power as compared to the other ambient energy harvesting devices, they can be used for the wide range of applications, and they can supply both ultra-low power devices, e.g.: wireless sensor nodes, as well as high power batteries [28].
The efficiency of photovoltaic cells depends not only on the lighting conditions but also on the fabrication technology. The most common technologies are based on silicon and, in general, the efficiency of such a module is not higher than 20%. The solution alternative to silicon is the application of III-IV compounds. Due to the fact that they can be made in diverse compositions, their energy gap varies between 0.16 eV and 2.24 eV. This means that their junctions can be sensible to several parts of the solar spectrum, and as a result, they are characterized by high light absorption and high efficiency. In recent years, one could observe a rising interest in solar cells based on organic materials. Although their efficiency that currently stays at around 11%, is still relatively low, they present a very desirable feature of long lifetime.
Another interesting alternative to the standard photovoltaic cells are the structures based on photo electrochemical technology. Their main advantage is a flexible construction that opens up new opportunities for diverse applications. The module developed by EPFL presents 14,1% of efficiency [19]. Figure 1.9 depicts the time evolution of photovoltaic cells efficiency depending on their fabrication technology [NREL].

Energy conversion based on rectifying antenna: RF transducers

These energy harvesting devices extract the energy from radio frequency (RF) electromagnetic waves. Radio waves that are the part of electromagnetic spectrum, carry the information thanks to the change of amplitude, phase and frequency combination of the wave within a frequency band. The contact of electromagnetic radiation with a conductor, such as antenna, results in a generation of an electric current on the surface of the conductor [29].
Although, compared to the other energy harvesting techniques, RF transducers present the lowest energy density, the accessibility of ubiquitous radio views in proximity to humans, especially in big, crowded agglomerations, make them attractive for supplying low-power electronics. A few examples of the radiation sources, such as television set, radio, mobile phone, wireless LAN, etc. as well as the principle of typical RF energy harvesting system are shown in Figure 1.10a-b), respectively.
Figure 1.10: (a) Diverse sources of radio waves [30]; (b) principle of a of typical RF energy harvesting system.
When the signal generated by the radiation source is collected by the antenna, it passes through a matching circuit, a rectifier and a power converter that generates the voltage necessary to charge an energy storage system. In order to recover all the signals available in the ambience, and as a result, to maximize the efficiency of the system, typically the omni-directional broadband antennas are used [29].
The power densities of these transducers strongly depend on the RF source, as well as on the distance between the source and the antenna, and they are relative low, standing at around 100 μW/cm2, which imposes an application of a large surface receiving antenna [31].
The comparison of capacitive, magnetic, piezoelectric, photovoltaic and RF transducers in terms of electric power density is given in Table 1.3. It has to be taken into consideration that these values vary depending on the working conditions, as well as on the size and mechanical construction of each converter.

Thermal energy conversion

Carnot cycle

Each thermodynamic system that passed through a series of different states to finally return to its initial state, performs a thermodynamic cycle. While going through this cycle, the system makes the work on its surroundings acting as a heat engine. The ideal heat engine cycle allowed by physical laws, so-called Carnot cycle, consists of two isothermal and two adiabatic processes. This cycle is a theoretical thermodynamic cycle that provides a formula enabling to determine the maximum efficiency, η, that can be achieved by every thermodynamic engine during a process of heat to work conversion. If the maximum hot temperature reached by the working fluid is given by TH and TC is the coldest temperature during the cycle, the efficiency of the heat conversion can be calculated from Eq.(1.2). = H − C Eq.(1.2)
The Carnot cycle assumes that the process performed during the heat engine cycle is reversible and that no changes of entropy occur. Due to the fact that in practice a fully reversible engine processes do not exist and all physical processes involve an entropy increase, the Carnot cycle is a theoretical construct. However, it gives a possibility of establishing the highest value of efficiency for any engine cycle operating between hot, TH, and cold, TC, temperatures.

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Thermoelectric generators: Seebeck Effect

One of the most popular methods of converting thermal energy into electricity is based on Seebeck effect that is related to a spatial temperature gradient. The value of electric power generated during the conversion depends on a temperature difference, as well as on a material forming the structure. The Seebeck effect occurs when the junction of two different conductive materials, whose endings are placed at the ambient temperature, is subjected to a source of heat. Due to the fact that the charge carriers migrate from the hot temperature zones towards the cold zones, a potential difference appears resulting in an electromotoric force generation. As the best thermoelectric properties are observed in semiconductors, a typical structure of the generator operating on the grounds of Seebeck effect is composed of two semiconductor bars, where one is doped with n and another with p carriers. Placing this structure between the hot and cold sources and loading it with a resistance, leads to an electric current generation [32]. The principle of Seebeck effect and Seebeck generator composed of pn junction are schematically illustrated in Figure 1.11a-b).
To increase the figure of merit z, it is necessary to reduce thermal conductivity of the material and at the same time to increase its electrical conductivity. As these two tendencies are contradicting, the enhancement of the generator properties is a challenge. In general, the heat transfer through the material can occur by means of electrons or phonons. The materials that express a good electric conduction due to the presence of electrons are metals. This is a positive effect in terms of thermoelectric generators. The same electrons however are the reason of high heat conduction, which means that the conductive materials are characterized by both, good electrical and thermal conductivity at the same time. As a consequence, the figure of merit of the conductors is not sufficient for energy harvesting applications. On the other hand, the electrical insulators, such as glass, present desirably low thermal conductivity, including the conductivity by phonons, but their electrical conductivity is close to zero. Thus, the ideal material for thermal generators should combine the electrical properties of metals and the heat resistance of insulators. The compromise has been reached by using semiconductor materials that present relatively high electrical and relatively low thermal conductivity. The figure of merit for semiconductors can be maximized by the control of the dopant concentration, as it is shown in Figure 1.12a). Given that the physical properties of thermoelectric materials depend also on the temperature, the figure of merit expresses the maximum value at the specific range of temperatures, which is illustrated in Figure 1.12b). It is worth to note that n-doped materials might present the optimal performances for different ranges of temperatures than the same materials doped by p-type carriers. The most efficient n-type material for the applications operating at the temperatures close to ambient is tellurium of bismuth, Bi2Te3, and its figure of merit ZT is close to 1. The p-type material that is the most suitable for the ambient temperatures is tellurium of antimony Sb2Te3. Other materials commonly used in the thermoelectric generators are Bi2(Te0.8Se0.2) and (Sb0.8Bi0.2)2Te3 operating at temperatures of 200°C and 600°C, and the alloys of silicon germanium SiGe dedicated for temperatures higher than 600°C.

Table of contents :

Introduction
1. STATE OF THE ART
WASTE ENERGY RECOVERY
ENERGY HARVESTING SOURCES
ENERGY HARVESTING METHODS
1.3.1. Mechanic energy conversion: development of kinetic transducers
1.3.1.1. Electrostatic energy conversion: capacitive transducers
1.3.1.2. Magnetic energy conversion based on Faraday’s Law
1.3.1.3. Energy conversion based on piezoelectric effect: piezoelectric transducers
1.3.2. Electromagnetic energy conversion: development of photovoltaic and RF transducers
1.3.2.1. Solar energy conversion: photovoltaic transducers
1.3.2.2. Energy conversion based on rectifying antenna: RF transducers
1.3.3. Thermal energy conversion
1.3.3.1. Carnot cycle
1.3.3.2. Thermoelectric generators: Seebeck Effect
1.3.3.3. MEMS-based micro heat engines
1.3.3.4. Vapor-based generator operating due to micro-vibrations
1.3.3.5. Pulsating Heat Pipes
1.3.3.6. Concept of thermal energy transducer applying two-phase energy conversion
SUMMARY OF THE CHAPTER
2. ELECTROMECHANICAL CONVERSION APPLYING PIEZOELECTRIC MATERIALS HISTORICAL DEVELOPMENT AND APPLICATIONS OF PIEZOELECTRIC MATERIALS CLASSIFICATION OF PIEZOELECTRIC MATERIALS
2.2.1. Inorganic piezoelectric materials
2.2.2. Organic piezoelectric materials
2.2.3. Piezoelectric composites
ELECTRO-MECHANICAL PROPERTIES OF PIEZOELECTRIC MATERIALS
2.3.1. Boundary conditions
2.3.2. Properties of piezoelectric materials and piezoelectric coefficients
2.3.2.1. Elastic properties and coefficients of piezoelectric materials
2.3.2.2. Electrical properties and coefficients of piezoelectric materials
2.3.3. Piezoelectric equations
SUMMARY OF THE CHAPTER
3. ANALYSIS OF PIEZOELECTRIC CONVERTERS EXPOSED TO PULSE OF PRESSURE EXPERIMENTAL SETUP DESCRIPTION ANALYSIS OF FLEXIBLE PVDF TRANSDUCERS
3.2.1. Electrical response of PVDF to the pressure pulse: cantilever mode
3.2.2. Electrical response of PVDF to the pressure pulse: strain mode
3.2.3. Comparison of PVDF films operating in cantilever and strain mode
3.3.1. Piezoelectric material determination
3.3.2. Electrical response of PZT to the pressure pulse: stress mode
3.3.3. Electrical response of PZT to the pressure pulse: strain mode
3.3.4. Comparison of PZT-based ceramics operating in stress and strain mode
COMPARISON BETWEEN PVDF AND PZT-BASED TRANSDUCERS NUMERICAL MODELING
3.5.1. Comparison between simulation and experimental results
3.5.2. Size optimization
3.5.2.1. Influence of PZT thickness
3.5.2.2. Influence of PZT radius
3.5.2.3. Miniaturization
SUMMARY OF THE CHAPTER
4. CONCEPT OF A THERMAL ENERGY CONVERTER BASED ON PHASE-CHANGE PHENOMENON
THE PROTOTYPES APPLYING PHASE-CHANGE PHENOMENON TO HARVEST THERMAL 4.1.ENERGY
4.1.1. Microfluidic heat engine based on explosive boiling
4.1.2. Self-Oscillating Fluidic Heat Engine (SOFHE)
4.1.3. Thermo-mechanical oscillating system at macroscale
CONCEPT OF THE SILICON-BASED DEMONSTRATOR IN MICROSCALE
4.2.1. Technological challenges
4.2.1.1. Type of the working fluid
4.2.1.2. Channel design
4.2.1.3. Filling ratio
4.2.1.4. Hot surface temperature
4.2.1.5. Type of piezoelectric
SUMMARY OF THE CHAPTER
5. TECHNOLOGICAL REALIZATION OF THE SILICON-BASED DEMONSTRATOR SELECTION OF TECHNOLOGICAL PROCESSES
5.1.1. Silicon etching process
5.1.1.1. Dry etching approach
5.1.1.2. Wet etching approach
5.1.2. Surface wettability
5.1.3. Silicon bonding
5.1.3.1. Wafer preprocessing
5.1.3.2. Silicon bonding techniques
5.1.3.3. Adhesive bonding
5.1.4. PZT montage – challenges and limitations
PROCESS FLOW OF ENERGY HARVESTER FABRICATION
SUMMARY OF THE CHAPTER
6. CHARACTERIZATION OF THE PROTOTYPE STRUCTURES PARAMETERS OF INFLUENCE: HIERARCHY OF IMPORTANCE
6.1.1. Ranking of the parameters
PRELIMINARY EXPERIMENTS
6.2.1. Determining the working conditions ensuring oscillation mechanism
6.2.1.1. Fixed parameters: device structure
6.2.1.2. Variable parameters: oscillations nature
6.2.2. Working conditions summary
OPERATION OF THE DEVICE WITH A COOLING SYSTEM
6.3.1. Uncertainty analysis and experimental repeatability
6.3.2. Experimental setup description
6.3.3. Electric response to the pressure pulses
6.3.3.1. Impact of TH for 10% filling ratio
6.3.3.2. Impact of TH for 20% filling ratio
6.3.3.3. Impact of TH for 30% filling ratio
6.3.3.4. Summary of the experiments
OPERATION OF THE DEVICE WITHOUT A COOLING SYSTEM
SUMMARY OF THE CHAPTER
Conclusions 

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