🔋Thermoelectric Materials and Devices Unit 6 – Thermoelectric Merit and Efficiency

Key Concepts and Definitions

• Thermoelectric effect converts temperature differences directly into electric voltage and vice versa
• Seebeck effect generates an electric potential in response to a temperature gradient across a material
  • Seebeck coefficient ($\alpha$) quantifies the magnitude of the voltage generated per unit temperature difference
• Peltier effect describes the heat absorption or emission at an electrified junction between two different conductors
  • Peltier coefficient ($\Pi$) represents the amount of heat carried per unit charge
• Thomson effect relates to the heating or cooling of a current-carrying conductor with a temperature gradient
• Figure of merit (ZT) measures the efficiency of a thermoelectric material
  • Higher ZT values indicate better thermoelectric performance
• Thermal conductivity ($\kappa$) quantifies a material's ability to conduct heat
• Electrical conductivity ($\sigma$) measures a material's ability to conduct electric current

Thermoelectric Effect Fundamentals

• Temperature gradient across a thermoelectric material induces charge carrier diffusion
  • Electrons in n-type materials and holes in p-type materials migrate from the hot side to the cold side
• Built-in electric field develops due to charge accumulation, counteracting further diffusion
• Steady-state condition reached when the diffusion current equals the drift current
• Seebeck coefficient depends on the material's electronic structure and charge carrier concentration
• Peltier heat absorption or emission occurs when an electric current passes through a junction of dissimilar materials
• Thomson effect arises from the interaction between charge carriers and the temperature gradient within a single material
• Thermoelectric effects are reversible, allowing both power generation and refrigeration applications

Figure of Merit (ZT) Explained

• ZT is a dimensionless quantity that characterizes the efficiency of a thermoelectric material
• Defined as $ZT = \frac{\alpha^2 \sigma T}{\kappa}$, where $T$ is the absolute temperature
• Higher ZT values indicate a material's greater ability to convert heat into electrical energy or vice versa
  • ZT > 1 is considered a good thermoelectric material
  • ZT > 2 is desired for practical applications
• Seebeck coefficient ($\alpha$) should be high to maximize the voltage generated per unit temperature difference
• Electrical conductivity ($\sigma$) should be high to minimize Joule heating losses
• Thermal conductivity ($\kappa$) should be low to maintain a large temperature gradient
• Optimizing ZT involves a complex interplay between $\alpha$, $\sigma$, and $\kappa$
  • Increasing charge carrier concentration enhances $\sigma$ but decreases $\alpha$
  • Nanostructuring can reduce $\kappa$ without significantly affecting $\sigma$

Efficiency Factors and Calculations

• Thermoelectric efficiency ($\eta$) depends on the operating temperatures and the material's ZT
• Maximum efficiency is given by $\eta_{max} = \frac{T_h - T_c}{T_h} \frac{\sqrt{1 + ZT} - 1}{\sqrt{1 + ZT} + \frac{T_c}{T_h}}$
  • $T_h$ and $T_c$ are the hot and cold side temperatures, respectively
• Carnot efficiency sets the upper limit for thermoelectric efficiency
  • Carnot efficiency is defined as $\eta_C = \frac{T_h - T_c}{T_h}$
• Thermoelectric efficiency approaches the Carnot limit as ZT approaches infinity
• Power factor ($\alpha^2 \sigma$) is another important metric for thermoelectric performance
  • High power factor materials can generate more electrical power for a given temperature difference
• Thermoelectric compatibility factor ($s$) ensures efficient heat-to-electricity conversion in segmented devices
  • Materials with similar $s$ values are more compatible and can be used together effectively

Materials and Their Properties

• Thermoelectric materials are classified as n-type (electron-conducting) or p-type (hole-conducting)
• Ideal thermoelectric materials have high Seebeck coefficient, high electrical conductivity, and low thermal conductivity
• Bismuth telluride (Bi2Te3) and its alloys are the most widely used thermoelectric materials for near-room-temperature applications
  • Bi2Te3 has a ZT around 1 at 300 K
• Lead telluride (PbTe) and its alloys are suitable for mid-temperature range applications (500-900 K)
• Silicon-germanium (SiGe) alloys are used for high-temperature thermoelectric power generation
• Nanostructured materials, such as superlattices and quantum dots, can enhance ZT by reducing thermal conductivity
• Organic and polymer-based thermoelectric materials offer advantages such as flexibility, low cost, and easy processing
  • Examples include PEDOT:PSS and carbon nanotube composites
• Doping and band structure engineering can optimize the electronic properties of thermoelectric materials

Device Design and Optimization

• Thermoelectric devices consist of multiple n-type and p-type elements connected electrically in series and thermally in parallel
• Thermoelectric modules can operate in power generation (Seebeck) mode or cooling (Peltier) mode
• Optimizing device geometry, such as the length and cross-sectional area of the elements, can improve efficiency
  • Longer elements maintain a larger temperature gradient but increase electrical resistance
  • Larger cross-sectional area reduces electrical resistance but increases thermal conductance
• Segmented thermoelectric devices use different materials optimized for specific temperature ranges
  • Segmentation allows for better overall efficiency by maximizing ZT over a wide temperature range
• Thermal and electrical contact resistances at the interfaces should be minimized for optimal performance
• Heat exchangers and thermal management systems are crucial for efficient heat transfer and maintaining the desired temperature gradient
• Impedance matching between the thermoelectric device and the load maximizes power output in power generation applications

Practical Applications

• Thermoelectric generators (TEGs) convert waste heat into electricity
  • Applications include automotive exhaust heat recovery, industrial process heat recovery, and space power systems
• Thermoelectric coolers (TECs) provide solid-state cooling for electronic devices, sensors, and small-scale refrigeration
  • Advantages include compactness, no moving parts, and precise temperature control
• Thermoelectric air conditioners and climate control systems can be used in vehicles and buildings
• Wearable thermoelectric devices can harvest body heat to power sensors and electronics
• Space applications benefit from thermoelectric devices' reliability and ability to operate in extreme temperatures
  • Radioisotope thermoelectric generators (RTGs) power deep space probes and Mars rovers
• Thermoelectric energy harvesting can power wireless sensor networks and Internet of Things (IoT) devices
• Thermoelectric materials can be used for temperature sensing and thermal management in various applications

Challenges and Future Directions

• Improving the figure of merit (ZT) of thermoelectric materials remains a key challenge
  • Trade-offs between Seebeck coefficient, electrical conductivity, and thermal conductivity limit ZT enhancement
• Developing novel materials with intrinsically high ZT, such as complex bandstructure materials and topological insulators
• Nanostructuring and band engineering to decouple the interdependent material properties and optimize ZT
  • Hierarchical nanostructuring can scatter phonons of different wavelengths to minimize thermal conductivity
• Enhancing the stability and durability of thermoelectric materials under high-temperature and cyclic loading conditions
• Reducing the cost and improving the scalability of thermoelectric material synthesis and device fabrication
• Exploring new device architectures and system integration strategies for efficient thermal management and power generation
• Investigating the thermoelectric properties of organic and hybrid materials for flexible and wearable applications
• Developing high-performance, non-toxic, and eco-friendly thermoelectric materials as alternatives to current state-of-the-art materials