5.6 Density of states (DOS)and Fermi surface 5.6.1 DOS function AZ:the number of energy states dV-dSdk located in the scope of E~E+AE d △Z DOS function: N(E)=li kx E0△E PBC tell us that N N, All of the k values are uniformly distributed in the k space 01/27
5.6 Density of states (DOS) and Fermi surface 5.6.1 DOS function Z: the number of energy states located in the scope of E~E+E DOS function: 0 ( ) limE Z N E → E = E 3 3 3 2 2 2 1 1 1 b N l b N l b N l k = + + PBC tell us that All of the k values are uniformly distributed in the k space
The volume occupied by a k spot in the k space 1) (2π) k state density: the state density indexed 2π by the momentum So,the number of wave vectors in (2x)3N2 =N the FBZ is: Ω (2π)月 The surface of E(k)=constant is a surface with the same energy. The volume enclosed by the surface of E and E+AE of is AV
3 (2 ) Vc N N = 3 3 (2 ) (2 ) The volume occupied by a k spot in the k space k state density: So, the number of wave vectors in the FBZ is: the state density indexed by the momentum The surface of E(k)=constant is a surface with the same energy. The volume enclosed by the surface of E and E+ΔE of is V
k So,the number of states is dV=dSdk V ds the perpendicular dissonance between the surface of E and E+AE is dk dkVE=AE (2π) dSdk dkV,E=AB
= dSdk V Z 3 (2 ) the perpendicular dissonance between the surface of E and E+ΔE is dk So, the number of states is
So,DOS function: Considering the spin of electrons N-2 a)For free electrons 0= h2k2 2m In the k space,the energy of spherical surface with the radius=2mE/ is equivalent
3 ( ) 2 (2 ) k V dS N E E = = E V dS N E k 3 (2 ) ( ) Considering the spin of electrons So, DOS function: a) For free electrons In the k space, the energy of spherical surface with the radius is equivalent
On the spherical surface ,小要的 m M两学”E b)The DOS of the NFE The influence of the periodic potential of the crystal on the energy is reflected near the Brilluion zones Take the 2D tetragonal lattice for example,the surface with the same energy is shown as the right image
On the spherical surface 3/ 2 2 2 2 2( ) (2 ) V m E = b) The DOS of the NFE The influence of the periodic potential of the crystal on the energy is reflected near the Brilluion zones Take the 2D tetragonal lattice for example, the surface with the same energy is shown as the right image