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In a pn-junction, the difference in Fermi level between the p doped and the n doped regions causes the apparition of a built-in electric field at equilibrium. This electric field goes from the n to the p, (so the positive carriers, for example, would not feel anymore the Coulomb attraction from the ionized atom donors), meaning that the Fermi level of the n doped region is below the one of the p doped, but I don't see any elementary argument explaining that.

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Before the p-doped and n-doped materials are joined, maybe we can think that their conduction and valence bands are aligned (although that's probably a dubious assumption). We know that when they join the Fermi-levels must be flat so we need to lower the n-type material down in energy. We lower the n side because electrons row down hill, that is to say we are minimising their energy. Or you could say we move the p-side up because hole roll up hill. The result is the same: the n-side is lower than the p-side. A semiconductor material p-doped and n-doped

After the charge has equilibrated, the end result is the bands bend to accomodate the flat Fermi level. Formation of pn-junction.

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In equilibrium the Fermi level (or chemical potential ) must not change across the junction - this is exactly the thermodynamic condition of equilibrium.

When n doped semiconductor is set into contact with the p-doped semiconductor it is true that an intrinsic field is set up at the junction and this is exactly what serves to align the chemical potentials. Thus the Fermi level of n-doped semiconductor should be exactly the same of the p-doped semiconductor that it is on contact with (in equilibrium conditions).

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Yes, this part I had understood, my question is: the fermi levels must be equal at equilibrium, thus the apparition of an electrostatic potential, which is higher in the n region than in the p; implying that before equilibrium the fermi level of the n region was lower than the fermi level of the p region (as seen before realizing the junction), why so? – Learning is a mess Jan 31 at 17:07
Fermi level represents electrochemical potential of electrons in a solid. Electrochemical potential is a thermodynamic intensive property which dictates which way charged matter will flow. It is like heat flows down a temperature gradient, charged matter flows down the electrochemical gradient. So before making a junction the n-type material has higher Fermi level than the p-type. During equilibration electrons migrate (diffuse) from n to p bringing a Fermi level balance but in the process setting up an electric field in the junction that prevents further diffusion – Sankaran Jan 31 at 17:13
also.. it is important to remember that charged particles respond to "electro"-chemical potential meaning they respond to both concentration and electrical potential gradients. so initially there is a concentration gradient (n-type has more electrons) but later the electric field builds up such that the combined effect of chemical gradient (n to p) and electrical gradient (p to n for electrons) is a net equilibrium balance. This is what one means when one says thermodynamic equilibrium at the junction – Sankaran Jan 31 at 17:16

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