This in fact is how the fermi level equilibrates more

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Unformatted text preview: piece of material, a different probability of occupancy at a given energy would lead to a net mo[on of carriers toward the region with a lower probability •  A net mo[on of carriers would lead to a net current, which cannot be present in equilibrium –  Comment: Pay a5en[on to the word “net” – carriers can be in mo[on due to drim and diffusion as long as the mo[on is balanced. (This, in fact, is how the Fermi level equilibrates.) More on this later. 6 Fermi Level Misalignment: Net Flow •  “Across a piece of material, a different probability of occupancy at a given energy would lead to a net mo[on of carriers toward the region with a lower probability” •  Generalized: “Across a piece of material, a different probability of occupancy would lead to a net mo[on of carriers” Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉Ÿ༉ Ÿ༉ Ÿ༉Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ Ÿ༉ EF1 Ÿ༉ Ÿ༉ Ÿ༉ EF2 1 2 Carrier Diffusion (pre equilibrium) •  For any given E: f1(E) > f2(E) 7 Another Explana[on In Equilibrium, there is: •  No net current •  No net charge transport •  For 2 joined materials (1 and 2), the transfer of electrons from material 2 to 1 must exactly balance the transfer from material 1 to 2 Ÿ༉ Ÿ༉ è༎ = ç༎ 8 Case 1: Electrons Moving From 1 to 2 •  At a given energy “E” the mo[on of an electron from material 1 to material 2 requires a full state in material 1 and an empty state in material 2 •  The rate of mo[on is propor[onal to the product of the number of electrons at energy “E” in material 1 and the number of empty states...
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