纳米结构物理学—2.pptVIP

* Reviews of Solid State Physics (1) Electronic states in a perfect crystal : Bloch wave function with: Periodically modulated plane wave, ?k = crystal momentum E(k) is also periodic in k, the period is 2?/a where (a: lattice constant) Reviews of Solid State Physics (2) Effect of periodic potential is most dramatic on states of k = Gn/2 (the boundaries of Brillouin zones): It opens energy bandgaps at k = Gn/2 separating allowed energy bands Effective mass of electrons (and holes) m*: Si: m*/m0 = 0.98, GaAs: m*/m0 = 0.067 At the top of energy bands, m* is negative! DOS (per unit length): n(E) = (d?/dk)-1 Number of electrons to fill an energy band = 2/a = 2 × Number of unit cells. The filling of bands determines electronic properties Insulators, Conductors, Semiconductors from energy band structures E valence band filled conduction band empty Forbidden region Eg 5eV Band gap E conduction band Eg 5eV Band gap + - electron hole E valence band partially-filled band Insulator Semiconductor Conductor Si: Eg = 1.1 eV Ge: Eg = 0.75 eV GaAs: Eg = 1.42 eV SiO2: Eg = 9 eV Conduction in solid: two types of carriers Electrons: electrons in conduction band of density n Holes: empty states in valence band of density p Carrier mobility: v = ? E, and Conductivity: Total current density: sum of drift and diffusion terms J = en?E + eD?n (assume n p) Einstein relation: Carrier type, density mobility determined in Hall measurements Jx B VH Ey If electron is the dominant carrier in the material, then we have: ? = 1/? = (en?e)-1, and Carrier density: n = -(eRH)-1, and the mobility: ?e = - RH/? Longitudinal conductance: Jx = ?Ex = e(n?e + p?h)Ex Longitudinal resistivity: ? = 1/? The Hall coefficient: Light Emission in Semiconductors E conduction band Band gap + - electron valence band Si: Eg = 1.1 eV, ? = 1100 nm GaAs: Eg = 1.4 eV, ? = 873 nm AlAs: Eg = 2.23 eV, ? = 556 nm hole h?