Einstein's Relationship

       It is known that the drift current density is proportional to the mobility (μ) while diffusion current density is proportional to the diffusion constant (D). There exists a fixed relation between these two constant which is called Einsten's relation.
       It states that, at a fixed temperature, the ratio of diffusion constant to the mobility is constant. This is Einstein's relation. Mathematically it is expressed as,

      where T is the temperature in oK
       And k is the Boltzmann's constant = 8.62 x 10-5 eV/oK
1.1 Voltage Equipment of Temperature
       In the equation (1), the product KT is called voltage equivalent of temperature.
       The voltage equivalent of temperature is denoted by VT.

       At room temperature i.e. at 27 oC,
                  T = 273 + 27 = 300 oK
...               VT = KT = 8.62 x 10-5 x 300 = 0.02586 V = 26 mV at 300 oK
Note : The value of VT = 26 mV at 27 oC  i.e. 300 oK is very commonly used while solving the examples.
        Substituting this in equation (1) we get,
                  Dnn = Dpp = VT = 0.02586 at room temperature 
...                μn = 39 Dn    and μp = 39 Dp  at room temperature.                       ................... (3)
       In general we can express the relation between mobility and diffusion constant as,
                   μ = 39 D          at room temperature                                                .................. (4)

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