4.5 Thermoelectric effects

Thermoelectric effects involve the conversion between thermal and electrical energy in materials. These phenomena arise from the coupling of heat and charge transport, enabling the development of devices that can generate electricity from heat or provide cooling through electrical input.

The Seebeck, Peltier, and Thomson effects form the foundation of thermoelectric phenomena. By understanding and optimizing these effects, researchers aim to improve the efficiency of thermoelectric materials and devices for applications in energy harvesting, cooling, and thermal management.

Thermoelectric phenomena

• Thermoelectric phenomena involve the direct conversion between thermal and electrical energy
• These effects arise due to the coupling of heat and charge transport in materials
• Understanding thermoelectric phenomena is crucial for developing efficient energy conversion devices

Seebeck effect

• Discovered by Thomas Johann Seebeck in 1821
• Occurs when a temperature gradient is applied across a material, generating a voltage

Seebeck coefficient

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• Quantifies the magnitude of the Seebeck effect
• Defined as the voltage generated per unit temperature difference ($S = \Delta V / \Delta T$)
• Depends on the material properties and temperature
• Higher Seebeck coefficients indicate better thermoelectric performance

Temperature gradient

• The difference in temperature between two points in a material
• Drives the flow of charge carriers (electrons or holes) from the hot side to the cold side
• Creates a built-in electric field that opposes further charge carrier diffusion

Voltage generation

• The Seebeck effect generates a voltage across the material due to the temperature gradient
• The generated voltage is proportional to the temperature difference and the Seebeck coefficient
• Can be harnessed to generate electrical power in thermoelectric generators

Peltier effect

• Discovered by Jean Charles Athanase Peltier in 1834
• Occurs when an electric current is passed through a junction between two dissimilar materials

Peltier coefficient

• Quantifies the magnitude of the Peltier effect
• Defined as the heat absorbed or emitted per unit electric current ($\Pi = Q / I$)
• Related to the Seebeck coefficient through the Kelvin relations

Current flow

• An electric current is passed through a junction of two dissimilar materials
• The direction of the current determines whether heat is absorbed or emitted at the junction
• Reversing the current direction reverses the heat absorption/emission process

Heat absorption/emission

• At the junction where current flows from material A to material B, heat is absorbed (cooling effect)
• At the junction where current flows from material B to material A, heat is emitted (heating effect)
• The Peltier effect is the basis for thermoelectric cooling and heating devices

Thomson effect

• Discovered by William Thomson (Lord Kelvin) in 1851
• Describes the heat absorbed or generated when an electric current flows through a material with a temperature gradient

Thomson coefficient

• Quantifies the magnitude of the Thomson effect
• Defined as the heat absorbed or generated per unit current density and unit temperature gradient ($\mu = Q / (J \cdot \nabla T)$)
• Related to the Seebeck coefficient through the Kelvin relations

Current density

• The amount of electric current flowing per unit cross-sectional area of the material
• Higher current densities lead to more pronounced Thomson effect

Heat generation/absorption

• When an electric current flows from a hot region to a cold region, heat is absorbed (cooling effect)
• When an electric current flows from a cold region to a hot region, heat is generated (heating effect)
• The Thomson effect is typically smaller than the Seebeck and Peltier effects

Figure of merit

• A key parameter used to evaluate the performance of thermoelectric materials
• Combines the Seebeck coefficient, electrical conductivity, and thermal conductivity

Thermoelectric efficiency

• The efficiency of a thermoelectric device depends on the figure of merit ($ZT$)
• Higher $ZT$ values indicate better thermoelectric efficiency
• The maximum efficiency is given by the Carnot efficiency multiplied by a factor related to $ZT$

Dimensionless quantity

• The figure of merit is a dimensionless quantity
• Defined as $ZT = (S^2 \sigma / \kappa) T$, where $S$ is the Seebeck coefficient, $\sigma$ is the electrical conductivity, $\kappa$ is the thermal conductivity, and $T$ is the absolute temperature
• Allows for comparison of thermoelectric performance across different materials and temperatures

Optimization strategies

• Maximizing the figure of merit requires optimizing the Seebeck coefficient, electrical conductivity, and thermal conductivity
• Strategies include doping, nanostructuring, and band structure engineering
• Trade-offs exist between these properties, making optimization challenging

Thermoelectric materials

• Materials that exhibit strong thermoelectric properties
• Typically semiconductors or heavily doped semiconductors

Semiconductors

• Semiconductors are the most common thermoelectric materials
• Examples include bismuth telluride (Bi2Te3), lead telluride (PbTe), and silicon germanium (SiGe)
• Offer a good balance between electrical and thermal properties

Thermal conductivity

• Low thermal conductivity is desirable for efficient thermoelectric performance
• Reduces the amount of heat that flows through the material without generating useful electrical power
• Can be reduced through phonon scattering, nanostructuring, or introducing defects

Electrical conductivity

• High electrical conductivity is necessary for efficient thermoelectric performance
• Allows for the flow of charge carriers with minimal resistive losses
• Can be increased through doping or optimizing carrier concentration

Seebeck coefficient optimization

• A high Seebeck coefficient is crucial for thermoelectric efficiency
• Depends on the material's band structure and carrier concentration
• Can be enhanced through band structure engineering, quantum confinement, or energy filtering

Applications of thermoelectrics

• Thermoelectric devices have a wide range of applications in energy conversion and thermal management

Thermoelectric generators

• Convert waste heat into useful electrical power
• Used in automotive exhaust systems, industrial processes, and space missions
• Example: Radioisotope thermoelectric generators (RTGs) power NASA's deep space probes

Thermoelectric coolers

• Use the Peltier effect to provide solid-state cooling
• Used in small-scale refrigeration, temperature control, and optoelectronic device cooling
• Example: Thermoelectric coolers maintain stable temperatures in laser diodes and infrared detectors

Waste heat recovery

• Thermoelectric generators can recover waste heat from various sources
• Examples include industrial furnaces, power plants, and geothermal sources
• Improves overall energy efficiency and reduces greenhouse gas emissions

Space exploration

• Thermoelectric devices are reliable and have no moving parts, making them suitable for space applications
• RTGs provide long-lasting power for deep space missions (Voyager probes, Curiosity rover)
• Thermoelectric coolers regulate temperatures of sensitive instruments and electronics in satellites and spacecraft

Measurement techniques

• Accurate measurement of thermoelectric properties is essential for material characterization and device optimization

Seebeck coefficient measurement

• Typically measured using a differential method
• A temperature gradient is applied across the sample, and the voltage difference is measured
• The Seebeck coefficient is calculated from the slope of the voltage vs. temperature gradient plot

Electrical conductivity measurement

• Can be measured using the four-point probe technique
• Four equally spaced probes are placed on the sample surface
• A current is passed through the outer probes, and the voltage drop is measured across the inner probes
• Electrical conductivity is calculated from the sample geometry and measured resistance

Thermal conductivity measurement

• Several methods exist, including the laser flash method and the 3ω method
• The laser flash method measures the thermal diffusivity of a sample by analyzing its temperature response to a laser pulse
• The 3ω method uses a metal strip as both a heater and a thermometer to measure the thermal conductivity of thin films

Challenges in thermoelectrics

• Despite progress in thermoelectric materials and devices, several challenges remain

Material optimization

• Simultaneous optimization of the Seebeck coefficient, electrical conductivity, and thermal conductivity is difficult
• Trade-offs exist between these properties, limiting the maximum achievable figure of merit
• New materials and strategies are needed to overcome these limitations

Thermal management

• Efficient heat transfer is crucial for thermoelectric device performance
• Thermal interfaces and heat exchangers must be designed to minimize parasitic losses
• Thermal stress and reliability issues arise from the large temperature gradients in thermoelectric devices

Cost-effectiveness

• Thermoelectric materials often contain rare or expensive elements (tellurium, germanium)
• Material processing and device fabrication costs can be high
• Improving the cost-effectiveness of thermoelectric devices is necessary for widespread adoption

Future prospects

• Advances in materials science and nanotechnology offer new opportunities for thermoelectric research

Nanostructured materials

• Nanostructuring can enhance thermoelectric properties by reducing thermal conductivity and increasing the Seebeck coefficient
• Examples include quantum dots, nanowires, and superlattices
• Nanostructured materials can decouple the optimization of electrical and thermal properties

High-temperature thermoelectrics

• Developing thermoelectric materials that operate efficiently at high temperatures (>1000 K) is an active area of research
• High-temperature applications include power generation from industrial waste heat and concentrated solar power
• Materials such as skutterudites, clathrates, and half-Heusler alloys show promise for high-temperature thermoelectrics

Flexible thermoelectrics

• Flexible thermoelectric devices can conform to curved surfaces and adapt to dynamic environments
• Potential applications include wearable electronics, personalized temperature control, and energy harvesting from body heat
• Polymer-based thermoelectric materials and composites are being developed for flexible applications

Organic thermoelectrics

• Organic semiconductors and conducting polymers are emerging as potential thermoelectric materials
• Advantages include low cost, easy processing, and the ability to tune properties through molecular design
• Challenges include improving the electrical conductivity and stability of organic thermoelectric materials