Lecture 6

E1 n z amounts to nding the number of lapce points on

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Unformatted text preview: at the soluIon for single parIcle energies: En = 2 mL2 •  We can say the highest occupied level is: ! 2 ! 2 ( N / 2 )2 ! 2 ! 2 N 2 EF = = 2 2 mL 8 m L2 called the “Fermi energy” The density of electrons in a 1 ­D well is N/L ! 2!2 2 EF = ne 8m 8 EF m If we measure the Fermi energy we know the carrier density: ne = ! 2!2 That was 1 ­D, but bulk objects (metals, semiconductors) are 3 ­dimensional 11 Fermi energy in 3 ­D •  Imagine confining an electron to a box of volume L3. •  The wavefuncIons for each Euclidean dimension are independent, and so the energy of the electron is simply: z E n x , n y , nz ! 2!2 2 2 = (nx + ny + nz2 ) 2 mL2 Ground state = nx L x L L = 1, ny = 1,...
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This document was uploaded on 02/04/2014.

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