6.1 Definition and significance of the figure of merit (ZT)

The figure of merit (ZT) is crucial for evaluating thermoelectric materials. It combines key properties like Seebeck coefficient, electrical conductivity, and thermal conductivity into a single value that directly relates to device efficiency.

Understanding ZT helps us optimize materials for better performance. By tweaking properties and considering temperature dependence, scientists aim to boost ZT values, pushing the limits of thermoelectric technology for various applications.

Thermoelectric Properties

Key Thermoelectric Parameters

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• Seebeck coefficient measures voltage generated per unit temperature difference in a material
• Electrical conductivity quantifies a material's ability to conduct electric current
• Thermal conductivity determines heat flow through a material under a temperature gradient
• These properties collectively influence thermoelectric performance
• Optimal thermoelectric materials exhibit high Seebeck coefficient and electrical conductivity
• Low thermal conductivity enhances temperature gradient maintenance

Property Interdependence and Optimization

• Seebeck coefficient, electrical conductivity, and thermal conductivity are interrelated
• Increasing carrier concentration improves electrical conductivity but reduces Seebeck coefficient
• Thermal conductivity comprises electronic and lattice contributions
• Electronic thermal conductivity correlates with electrical conductivity (Wiedemann-Franz law)
• Lattice thermal conductivity can be reduced through nanostructuring or alloying
• Balancing these properties presents a challenge in thermoelectric material design
• Power factor, defined as $S^2\sigma$, combines Seebeck coefficient (S) and electrical conductivity (σ)

Figure of Merit (ZT)

Definition and Significance

• Figure of merit (ZT) serves as a dimensionless quantity for evaluating thermoelectric materials
• ZT combines Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ)
• Expressed mathematically as $ZT = \frac{S^2\sigma T}{\kappa}$
• T represents absolute temperature in Kelvin
• Higher ZT values indicate better thermoelectric performance
• ZT directly correlates with the efficiency of thermoelectric devices
• Typical ZT values for commercial materials range from 0.8 to 1.2 (Bi2Te3, PbTe)

Temperature Dependence and Material Optimization

• ZT varies with temperature, exhibiting material-specific peak values
• Optimal operating temperature range differs for various thermoelectric materials
• Low-temperature applications often use bismuth telluride-based materials
• Mid-temperature range employs lead telluride or skutterudite compounds
• High-temperature applications utilize silicon-germanium alloys
• Material scientists aim to enhance ZT through band engineering and nanostructuring
• Increasing power factor ($S^2\sigma$) while reducing thermal conductivity improves ZT
• State-of-the-art materials achieve ZT values exceeding 2 at specific temperatures (SnSe, PbTe-SrTe)

Efficiency Correlation and Device Performance

• ZT directly relates to the maximum theoretical efficiency of thermoelectric devices
• Carnot efficiency sets the upper limit for thermoelectric conversion
• Actual device efficiency depends on both ZT and temperature difference
• Higher ZT values enable thermoelectric generators to approach Carnot efficiency
• Efficiency calculation incorporates average ZT over the operating temperature range
• Thermoelectric coolers benefit from high ZT materials for improved coefficient of performance
• Practical applications require considering factors beyond ZT (cost, stability, manufacturability)