Are they same? I read some of the post in RG regarding this question but didn't get a clear idea.
Thank you for your time.
Yes. Basic level of the energy in temperature near 0 K we can describe by Electrochemical potential (area of chemistry for example analytical chemistry but not only) or Fermi level if you consider physical properties of matter.
Fermi level is strictly defined as the electrochemical potential at T=0. But physicists tend to call the electrochemical potential Fermi level at any temperature, informally.
Ef=µ=µc+qΘ which is an expression for the electrochemical potential which is same as the Fermi level. if we consider a p-n junction this occurs due to the difference the chemical potential (concentration gradient). While these carriers move, they leave back ions, which gives the intrinsic E field that opposes the movement of these carriers. This intrinsic field is qΘ. Now, the equilibrium is attained, when both the above process becomes equal. (i.e) when their electrochemical potential is same. Thus at equilibrium we name this electrochemical potential as the fermi level to indicate the equilibrium distribution of the carriers.
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