Electron And Hole Equilibrium Concentrations 24 February 2014  Return and discuss Quiz 2  Chapter 4 Topics-Two burning questions: What is the density of states in the conduction and valence bands? How do you find an exact position of the Fermi Level?

2 Concentration of Electrons at Equilibrium Thermal-equilibrium concentration of electrons (#/cm 3 ) in the conduction band Assume that E F is within the energy bandgap and So for energy levels in the conduction band there is (kT ≈ 25.9 meV for T=300K). So for energy levels in the conduction band Page 87 Text, Equation 3.69

5 5 Concentration of Electrons at Equilibrium Define effective density of states in the conduction band

7 7 Concentration of Holes at Equilibrium Thermal-equilibrium concentration of holes (#/m3) in the conduction band Assume that E F is within the energy bandgap and So for energy levels in the conduction band there is then for energy levels in the conduction band

8 8 Concentration of Holes at Equilibrium Define effective density of states in the valence band

10 Carrier Concentrations in Intrinsic Semiconductors For an intrinsic semiconductor, the concentration of electrons in the conduction band is equal to the concentration of holes in the valence band is the Fermi-level for the intrinsic semiconductor, i.e., intrinsic Fermi-level For a given semiconductor, at constant temperature, n i is constant

12 The Intrinsic Fermi-Level position If

Fermi-Energy Levels In Extrinsic Semiconductors

14 Electron and Hole Concentrations in Extrinsic Semiconductor Summary For both undoped material and doped material under equilibrium condition

15 Position of Fermi Energy in Extrinsic Semiconductors Position of Fermi-level:

16 Variation of Fermi-Energy with Doping Concentration

17 Variation of Fermi-Energy with Temperature