🔋Thermoelectric Materials and Devices Unit 7 – Semiconductor Thermoelectrics

Key Concepts and Fundamentals

• Thermoelectric materials convert temperature differences into electrical energy (Seebeck effect) and vice versa (Peltier effect)
• Semiconductors are the most commonly used materials for thermoelectric applications due to their unique electronic properties
  • Possess a bandgap that allows for the control of charge carrier concentration and type (n-type or p-type)
  • Exhibit a balance between electrical conductivity and thermal conductivity
• Thermoelectric efficiency is characterized by the dimensionless figure of merit, $ZT = \frac{S^2 \sigma T}{\kappa}$, where $S$ is the Seebeck coefficient, $\sigma$ is the electrical conductivity, $T$ is the absolute temperature, and $\kappa$ is the thermal conductivity
• Optimizing $ZT$ involves maximizing the power factor ($S^2 \sigma$) while minimizing the thermal conductivity ($\kappa$)
• Thermoelectric devices consist of multiple thermoelectric couples connected electrically in series and thermally in parallel
• Thermoelectric generators (TEGs) convert heat into electricity, while thermoelectric coolers (TECs) use electricity to pump heat from one side to the other
• The efficiency of thermoelectric devices is limited by the Carnot efficiency, which depends on the temperature difference between the hot and cold sides

Semiconductor Physics for Thermoelectrics

• Semiconductors have a bandgap between the valence and conduction bands, allowing for the control of charge carrier concentration and type through doping
• Doping involves introducing impurities into the semiconductor lattice to create excess electrons (n-type) or holes (p-type)
  • N-type doping is achieved by adding donor atoms with extra valence electrons (phosphorus in silicon)
  • P-type doping is achieved by adding acceptor atoms with fewer valence electrons (boron in silicon)
• The Fermi level determines the equilibrium distribution of charge carriers and is crucial for understanding the thermoelectric properties of semiconductors
• The density of states (DOS) describes the number of available energy states per unit energy and volume, influencing the electronic properties of semiconductors
• Charge carrier mobility ($\mu$) is a measure of how easily charge carriers move through the semiconductor under an applied electric field and affects the electrical conductivity ($\sigma = ne\mu$, where $n$ is the charge carrier concentration and $e$ is the elementary charge)
• Scattering mechanisms, such as lattice vibrations (phonons) and impurities, limit charge carrier mobility and impact thermoelectric performance
• The effective mass ($m^*$) of charge carriers influences their mobility and the density of states, with a higher effective mass generally leading to a lower mobility but a higher Seebeck coefficient

Thermoelectric Effects in Semiconductors

• The Seebeck effect is the generation of an electric potential difference ($\Delta V$) in response to a temperature gradient ($\Delta T$) in a semiconductor, with the Seebeck coefficient defined as $S = -\frac{\Delta V}{\Delta T}$
• The Peltier effect is the absorption or emission of heat at the junctions of dissimilar semiconductors when an electric current passes through, with the Peltier coefficient ($\Pi$) relating the heat flow rate ($\dot{Q}$) to the electric current ($I$) as $\dot{Q} = \Pi I$
• The Thomson effect describes the absorption or emission of heat along a semiconductor when both a temperature gradient and an electric current are present, with the Thomson coefficient ($\tau$) relating the heat flow rate per unit length ($\dot{q}$) to the electric current and temperature gradient as $\dot{q} = -\tau I \frac{dT}{dx}$
• The Kelvin relations connect the Seebeck, Peltier, and Thomson coefficients: $\Pi = ST$ and $\tau = T \frac{dS}{dT}$
• The Seebeck coefficient depends on the charge carrier concentration, with heavily doped semiconductors having lower Seebeck coefficients but higher electrical conductivities
• The sign of the Seebeck coefficient indicates the type of dominant charge carriers: negative for electrons (n-type) and positive for holes (p-type)
• Minority charge carriers can adversely affect the Seebeck coefficient, necessitating the use of heavily doped semiconductors or selective charge carrier blocking techniques

Material Properties and Selection

• Ideal thermoelectric materials should have a high Seebeck coefficient, high electrical conductivity, and low thermal conductivity
• The thermal conductivity consists of electronic ($\kappa_e$) and lattice ($\kappa_l$) contributions, with the lattice contribution being the dominant factor in most thermoelectric semiconductors
• Strategies for reducing lattice thermal conductivity include introducing phonon scattering centers (point defects, nanostructures, or interfaces) and using materials with intrinsically low lattice thermal conductivity (complex crystal structures or heavy elements)
• Band engineering techniques, such as band convergence and resonant levels, can enhance the Seebeck coefficient without significantly compromising electrical conductivity
• Nanostructuring can improve thermoelectric properties by reducing lattice thermal conductivity through phonon scattering and modifying the electronic density of states
• Common thermoelectric semiconductor materials include bismuth telluride (Bi2Te3), lead telluride (PbTe), silicon germanium (SiGe), and higher manganese silicides (HMS)
• Material compatibility and stability at the desired operating temperatures are crucial factors in selecting thermoelectric materials for specific applications
• Eco-friendly and abundant materials, such as copper sulfide (Cu2S) and magnesium silicide (Mg2Si), are being explored as alternatives to rare and toxic thermoelectric materials

Fabrication Techniques

• Powder metallurgy is a common fabrication method for thermoelectric semiconductors, involving the compaction and sintering of powdered materials
  • Mechanical alloying (ball milling) is used to produce fine-grained and homogeneous powders
  • Spark plasma sintering (SPS) enables rapid and high-density consolidation of powders while minimizing grain growth
• Melt growth techniques, such as Bridgman and Czochralski methods, are used to produce single-crystal thermoelectric materials with high purity and structural perfection
• Thin-film deposition methods, including sputtering, evaporation, and pulsed laser deposition (PLD), are employed for fabricating thermoelectric thin films and superlattices
• Chemical synthesis routes, such as solvothermal and hydrothermal methods, offer precise control over composition, morphology, and nanostructure of thermoelectric materials
• Additive manufacturing techniques, like 3D printing, enable the fabrication of complex thermoelectric device geometries and functionally graded materials
• Post-processing treatments, such as annealing and hot pressing, can improve the thermoelectric properties and mechanical stability of fabricated materials
• Scalability, cost-effectiveness, and reproducibility are important considerations in selecting fabrication techniques for commercial thermoelectric devices

Device Design and Optimization

• Thermoelectric devices consist of multiple p-type and n-type semiconductor legs connected electrically in series and thermally in parallel
• The geometry and arrangement of thermoelectric legs influence device performance, with longer and thinner legs generally improving efficiency but reducing power output
• Thermal and electrical contact resistances at the interfaces between thermoelectric legs and metal interconnects can significantly impact device performance and must be minimized through proper material selection and interface engineering
• Thermal management strategies, such as heat sinks and thermal interface materials, are crucial for maintaining the desired temperature gradient across the device
• Segmented thermoelectric devices, which use different materials optimized for different temperature ranges, can enhance overall efficiency by leveraging the temperature dependence of thermoelectric properties
• Cascaded or multi-stage thermoelectric devices, where each stage operates at a different temperature range, can improve heat pumping capacity and temperature control
• Flexible and wearable thermoelectric devices require materials and designs that can withstand mechanical deformation while maintaining performance
• Numerical modeling and simulation tools, such as finite element analysis (FEA), are used to optimize device geometry, material selection, and operating conditions
• Device-level optimization must consider the balance between efficiency, power output, and other application-specific requirements (weight, size, and cost)

Performance Metrics and Characterization

• The figure of merit ($ZT$) is the primary performance metric for thermoelectric materials, with higher values indicating better performance
  • $ZT$ is calculated from the Seebeck coefficient ($S$), electrical conductivity ($\sigma$), thermal conductivity ($\kappa$), and absolute temperature ($T$) as $ZT = \frac{S^2 \sigma T}{\kappa}$
  • $ZT$ is often reported as an average value over the operating temperature range of the device
• The power factor ($PF = S^2 \sigma$) is another important metric, representing the electrical performance of a thermoelectric material
• The thermoelectric conversion efficiency ($\eta$) of a device depends on the $ZT$ of the materials and the temperature difference between the hot and cold sides, with the maximum efficiency given by $\eta_{max} = \frac{T_h - T_c}{T_h} \frac{\sqrt{1 + ZT_{avg}} - 1}{\sqrt{1 + ZT_{avg}} + \frac{T_c}{T_h}}$, where $T_h$ and $T_c$ are the hot and cold side temperatures, respectively
• The coefficient of performance (COP) is used to characterize the efficiency of thermoelectric cooling devices, defined as the ratio of the heat removed from the cold side to the input electrical power
• Experimental characterization techniques for thermoelectric materials include:
  • Seebeck coefficient measurement using a differential temperature and voltage setup
  • Electrical conductivity measurement using a four-point probe method
  • Thermal conductivity measurement using laser flash analysis or the 3ω method
  • Hall effect measurement to determine charge carrier concentration and mobility
• Spectroscopic techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM), are used to study the structural and compositional properties of thermoelectric materials
• Thermal stability and cycling tests are performed to evaluate the long-term performance and reliability of thermoelectric devices under operating conditions

Applications and Future Trends

• Waste heat recovery is a major application area for thermoelectric generators, with potential sources including industrial processes, automotive exhaust, and power plants
• Space applications, such as radioisotope thermoelectric generators (RTGs), use thermoelectric devices for reliable, long-lasting power generation in remote or hostile environments
• Thermoelectric cooling finds applications in temperature-sensitive electronics, such as laser diodes and infrared detectors, as well as in portable refrigeration and localized climate control systems
• Wearable thermoelectric devices can be used for personal thermal management, harvesting body heat to power small electronics or providing localized cooling or heating for comfort
• Internet of Things (IoT) and wireless sensor networks can leverage thermoelectric generators for self-powered operation, eliminating the need for batteries or external power sources
• Flexible and stretchable thermoelectric materials are being developed for integration with textiles, skin patches, and other conformable surfaces
• Nanostructured and low-dimensional thermoelectric materials, such as quantum dots and nanowires, are being explored for their potential to decouple electrical and thermal transport properties and achieve high $ZT$ values
• Computational materials discovery and machine learning techniques are being employed to accelerate the identification and optimization of novel thermoelectric materials
• Transient and pulsed thermoelectric effects, such as the Ettingshausen and Nernst effects, are being investigated for potential applications in thermal management and energy harvesting
• Integration of thermoelectric devices with other energy conversion technologies, such as photovoltaics and thermophotovoltaics, can enable hybrid systems with improved overall efficiency and functionality