When Electric field is applied to free electrons

When Electric field is applied to bloch electrons

Standard labels of the symmetry points of the B.Z.

Band structure of GaAs

Fermi level (chemical potential)

Extrinsic semiconductor extrinsic semiconductor : introducing small amounts of impurities  n ≠ p n-type doping IV V VI doping : 1 impurity atom per ~106 host atoms  keeping diamond crystal structure pentavalent (valency of 5) element ( As, P, Sb)  one electron left unbounded electron e− orbing around As+ ionic center  same as hydrogen atom in a silicon environment binding energy of the electron in H atom 2019-08-06 반도체물리2015_2

[o  r o (r : relative permittivity of Si)] binding energy of the electron in H atom binding energy of electron to As+ site in Si crystal [o  r o (r : relative permittivity of Si)] : comparable with average thermal energy at RT ~ 3/2 kT (~ 0.04 eV) free electron in CB  readily free the fifth valence electron donor atom : donates an electron into CB 2019-08-06 반도체물리2015_2

Nd : donor atom concentration Ed : energy required to take electron away from donor atom into CB here, Ed ~ 0.03 eV below Ec Nd : donor atom concentration in the crystal : Nd >> ni at RT, electron concentration in CB ≈ Nd  n ≈ Nd  mass action law : conductivity : 2019-08-06 반도체물리2015_2 Principles of Electronic .., S.O.Kasap (©McGraw-Hill)