page_title: Seebeck coefficient
section_title: Mott formula in semiconductors
hierarchical_section_title: Seebeck coefficient / Physical factors that determine the Seebeck coefficient / Charge carrier diffusion / Mott formula / Mott formula in semiconductors
context_page_description: The Seebeck coefficient 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, although it is more often given in microvolts per kelvin.
  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.
context_section_description: In semiconductors at low levels of doping, transport only occurs far away from the Fermi level. At low doping in the conduction band (where , where  is the minimum energy of the conduction band edge), one has . Approximating the conduction band levels' conductivity function as  for some constants  and ,
  whereas in the valence band when  and ,
  The values of  and  depend on material details; in bulk semiconductor these constants range between 1 and 3, the extremes corresponding to acoustic-mode lattice scattering and ionized-impurity scattering.
  In extrinsic (doped) semiconductors either the conduction or valence band will dominate transport, and so one of the numbers above will give the measured values. In general however the semiconductor may also be intrinsic in which case the bands conduct in parallel, and so the measured values will be
  This results in a crossover behaviour, as shown in the figure.
  The highest Seebeck coefficient is obtained when the semiconductor is lightly doped, however a high Seebeck coefficient is not necessarily useful on its own. For thermoelectric power devices (coolers, generators) it is more important to maximize the thermoelectric power factor  , or the thermoelectric figure of merit, and the optimum generally occurs at high doping levels.
caption: Seebeck coefficient of silicon at 300 K,calculated from Mott model. The crossover from hole-dominated conduction (positive 
    
      
        
          
            S
            ≈
            
              S
              
                
                  V
                
              
            
          
        
      
      {\displaystyle \scriptstyle S\approx S_{\rm {V}}}
    
  ) to electron-dominated conduction (negative 
    
      
        
          
            S
            ≈
            
              S
              
                
                  C
                
              
            
          
        
      
      {\displaystyle \scriptstyle S\approx S_{\rm {C}}}
    
  ) happens for Fermi levels in the middle of the 1.1 eV-wide gap.