Seebeck coefficient

The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material, as induced by the Seebeck effect. The SI unit of the Seebeck coefficient is volts per kelvin (V/K), although it is more often given in microvolts per kelvin (μV/K). − d f ( E ) d E = 1 4 k B T sech 2 ⁡ ( E − μ 2 k B T ) {displaystyle -{frac {df(E)}{dE}}={frac {1}{4k_{ m {B}}T}}operatorname {sech} ^{2}left({frac {E-mu }{2k_{ m {B}}T}} ight)} The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material, as induced by the Seebeck effect. The SI unit of the Seebeck coefficient is volts per kelvin (V/K), although it is more often given in microvolts per kelvin (μV/K). The use of materials with a high Seebeck coefficient is one of many important factors for the efficient behaviour of thermoelectric generators and thermoelectric coolers. More information about high-performance thermoelectric materials can be found in the Thermoelectric materials article. In thermocouples the Seebeck effect is used to measure temperatures, and for accuracy it is desirable to use materials with a Seebeck coefficient that is stable over time. Physically, the magnitude and sign of the Seebeck coefficient can be approximately understood as being given by the entropy per unit charge carried by electrical currents in the material. It may be positive or negative. In conductors that can be understood in terms of independently moving, nearly-free charge carriers, the Seebeck coefficient is negative for negatively charged carriers (such as electrons), and positive for positively charged carriers (such as electron holes). One way to define the Seebeck coefficient is the voltage built up when a small temperature gradient is applied to a material, and when the material has come to a steady state where the current density is zero everywhere. If the temperature difference ΔT between the two ends of a material is small, then the Seebeck coefficient of a material is defined as: where ΔV is the thermoelectric voltage seen at the terminals. (See below for more on the signs of ΔV and ΔT.) Note that the voltage shift expressed by the Seebeck effect cannot be measured directly, since the measured voltage (by attaching a voltmeter) contains an additional voltage contribution, due to the temperature gradient and Seebeck effect in the measurement leads. The voltmeter voltage is always dependent on relative Seebeck coefficients among the various materials involved. Most generally and technically, the Seebeck coefficient is defined in terms of the portion of electric current driven by temperature gradients, as in the vector differential equation where J {displaystyle scriptstyle mathbf {J} } is the current density, σ {displaystyle scriptstyle sigma } is the electrical conductivity, ∇ V {displaystyle scriptstyle {oldsymbol { abla }}V} is the voltage gradient, and ∇ T {displaystyle scriptstyle {oldsymbol { abla }}T} is the temperature gradient. The zero-current, steady state special case described above has J = 0 {displaystyle scriptstyle mathbf {J} =0} , which implies that the two current density terms have cancelled out and so ∇ V = − S ∇ T . {displaystyle {oldsymbol { abla }}V=-S{oldsymbol { abla }}T.}