lesson 23 transport in semiconductors i intrinsic semiconductors

lesson #23: transport in semiconductors i intrinsic semiconductors case of • homogeneous crystal • without defects of impurities Solid State Physics M. Casalboni 2017/’ 18 aim: to study the carrier distribution at thermal equilibrium energy gap in common semiconductors as a function of lattice parameter 1/16

lesson #23: transport in semiconductors i density of state Solid State Physics M. Casalboni 2017/’ 18 density of state per unit volume at T=0 the occupation function implies that all state of valence band are occupied and all state of conduction band are empty 2/16

lesson #23: transport in semiconductors i at T ≠ 0 ? Solid State Physics M. Casalboni 2017/’ 18 density of holes in the valence band density of electron in the conduction band 3/16

lesson #23: transport in semiconductors i determins Solid State Physics M. Casalboni 2017/’ 18 but where ? if DOS is simmetric with respect to the middel point of the energy gap balance of electrons and holes requires that EF (and ) at any temperature lays in the center of Egap 4/16

lesson #23: transport in semiconductors i determins Solid State Physics M. Casalboni 2017/’ 18 but where ? if DOS is not simmetric with respect to the middel point of the energy gap balance of electrons and holes requires that EF (and ) moves from the center of Egap in order to equalize the number of electrons and holes 5/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 6/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 77/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 in this case Fermi-Dirac distribution can be approximate by Maxwell-Boltzman one where and 8/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 taking Log ( ) = Log ( ) for T = 0 in the middle for T ≠ 0 depends on the Do. S of the bands 9/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 and MASS-ACTION LAW 10/16

lesson #23: transport in semiconductors i in case of isotropic and parabolic band model Solid State Physics M. Casalboni 2017/’ 18 ASSIGNMENT!!! performing integral with change of variables 11/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 12/16

lesson #23: transport in semiconductors i doped semiconductors real cristals contain imperfections and impurities IDEAL CRYSTAL Solid State Physics M. Casalboni 2017/’ 18 REAL CRYSTAL no periodicity no Bloch however we can use the band wavefunctions as a starting basis set 13/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 impurity levels are LOCALIZED wavefunction (no k dependence) 14/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 15/16

lesson #23: transport in semiconductors i Solid State Physics M. Casalboni 2017/’ 18 Fermi level lies in between impurity levels and band edge 16/16