Week 2: Fill the states (D(E) and mu)

Fill the states: density of states D(E) and the water line μ (Datta Sec. 2.1, Ch. 6)

D(E) is the shape of the container: how many seats (states) each energy floor has. Electrons fill seats from the bottom, one per seat. The electrochemical potential μ is the water line, where seats are half full (f = ½).

Container shape:

Number of electrons Temperature T

Water line μ–

Seats at the water line D(μ)–

Fraction of seats filled–

Thermal blur kT–

Electrons in material A (before contact) Electrons in material B (before contact) Battery voltage V (after connecting)

μ of A–

μ of B–

μ_A − μ_B–

Net electrons moved A → B–