18.1 Thermoelectric and thermophotovoltaic devices

Thermoelectric and thermophotovoltaic devices are game-changers in energy harvesting. They convert heat directly into electricity, offering new ways to tap into waste heat and improve energy efficiency. These technologies are reshaping how we think about power generation and conservation.

From the Seebeck effect to TPV cells, this section covers the principles behind these innovative devices. We'll explore how temperature differences create electrical potential and how specially designed materials can turn heat into usable power. It's all about maximizing energy conversion in clever ways.

Thermoelectric Effects

Seebeck Effect and Thermoelectric Voltage

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• Seebeck effect occurs when a temperature difference between two dissimilar electrical conductors or semiconductors produces a voltage difference between the two substances
• Electrons in the material with higher temperature have more thermal energy, causing them to diffuse to the cooler material and create a potential difference (thermoelectric voltage)
• Seebeck coefficient ($S$) quantifies the magnitude of the produced thermoelectric voltage per unit temperature difference ($\Delta V = S \Delta T$)
• Examples of materials with high Seebeck coefficients include bismuth telluride (Bi2Te3) and lead telluride (PbTe)

Peltier Effect and Thermoelectric Cooling

• Peltier effect is the reverse of the Seebeck effect, where an applied voltage creates a temperature difference between two dissimilar electrical conductors or semiconductors
• When a current flows through the junction of two different conductors, heat is absorbed or released at the junction, depending on the direction of the current
• Peltier coefficient ($\Pi$) relates the rate of heat transfer to the electric current ($Q = \Pi I$)
• Thermoelectric cooling devices (Peltier coolers) utilize the Peltier effect to create a heat flux and can be used for small-scale refrigeration applications (electronic component cooling)

Thomson Effect and Reversible Heat

• Thomson effect describes the heating or cooling of a current-carrying conductor with a temperature gradient
• When an electric current passes through a conductor with a temperature gradient, heat is absorbed or released along the conductor, depending on the direction of the current and the sign of the Thomson coefficient
• Thomson coefficient ($\tau$) relates the rate of heat production per unit length to the electric current and temperature gradient ($q = \tau I \frac{dT}{dx}$)
• The Thomson effect is reversible, meaning that the heat absorbed or released can be recovered when the current is reversed

Thermoelectric Materials and Performance

Thermoelectric Material Properties

• Ideal thermoelectric materials should have high Seebeck coefficients, high electrical conductivity, and low thermal conductivity to maximize the thermoelectric performance
• Semiconductors are commonly used as thermoelectric materials due to their optimal combination of electrical and thermal properties
• Examples of thermoelectric materials include bismuth telluride (Bi2Te3), lead telluride (PbTe), and silicon-germanium (SiGe) alloys
• Nanostructuring and doping techniques can be employed to optimize the thermoelectric properties of materials by reducing thermal conductivity and increasing electrical conductivity

Figure of Merit (ZT) and Thermoelectric Efficiency

• The thermoelectric figure of merit (ZT) is a dimensionless quantity that characterizes the performance of a thermoelectric material
• ZT is defined as $ZT = \frac{S^2 \sigma T}{\kappa}$, where $S$ is the Seebeck coefficient, $\sigma$ is the electrical conductivity, $T$ is the absolute temperature, and $\kappa$ is the thermal conductivity
• Higher ZT values indicate better thermoelectric performance, with values greater than 1 being considered suitable for practical applications
• The maximum efficiency of a thermoelectric device ($\eta_{max}$) is related to the ZT value and the temperature difference between the hot and cold sides ($\eta_{max} = \frac{T_H - T_C}{T_H} \frac{\sqrt{1 + ZT} - 1}{\sqrt{1 + ZT} + \frac{T_C}{T_H}}$)

Thermophotovoltaic Devices

Thermophotovoltaic Cell Operation

• Thermophotovoltaic (TPV) cells convert heat directly into electricity through the photovoltaic effect
• A heat source (emitter) radiates thermal energy in the form of photons, which are absorbed by a photovoltaic cell
• The absorbed photons excite electrons in the photovoltaic cell, generating an electric current
• TPV cells can utilize a wide range of heat sources, including industrial waste heat, solar thermal energy, and combustion processes

Selective Emitters and Spectral Matching

• Selective emitters are materials that emit radiation in a specific wavelength range that matches the absorption spectrum of the photovoltaic cell
• Spectral matching between the emitter and the photovoltaic cell is crucial for optimizing the efficiency of TPV systems
• Examples of selective emitters include rare-earth oxides (erbium oxide, ytterbium oxide) and photonic crystals
• Selective filters can also be used to control the spectral distribution of the emitted radiation and improve the spectral matching

Heat-to-Electricity Conversion Efficiency

• The efficiency of a TPV system depends on several factors, including the emitter temperature, the photovoltaic cell's bandgap, and the spectral matching between the emitter and the cell
• Higher emitter temperatures lead to increased power output but also higher thermal losses
• The photovoltaic cell's bandgap should be optimized to match the peak emission wavelength of the emitter for maximum efficiency
• TPV systems can achieve heat-to-electricity conversion efficiencies of up to 30% under ideal conditions, making them a promising technology for waste heat recovery and solar thermal energy conversion