林雁英8283A41.docVIP

CHAPTER 3 The Semiconductor in Equilibrium Exercise Problem EX3.3 Determine the intrimsic carrier concentration in GaAs at ()T=200K and at ()T=400K.[.()1.48cm-3,( )3.22109cm-3 ] 3.14 The Intrinsic Fermi-Level Position We have qualitatively argued that the Fermi energy level is located near the center of the forbidden bandgap for the intrinsic semicoductor. We can specifically calculate the intrinsic Fermi-level position.Since the electron and hole concentrations are equal,setting Equations(3.20)and(3.21) equal to each other ,we have (3.24) If we take the natural log of both sides of this equation and solve for ,we obtain (3.25) From the definitions for and given by Equations (3.10)and (3.18),respectively,Equation(3.25) can be written as (3.26a) The first term, ,is the energy exactly midway between and , or the midgap energy.We can define so that (3.26b) If the electron and hole effective masses are equal so that ,then the intrinsic Fermi level is exactly in the center of the .If ,the intrinsic Fermi level is slightly above the center,and if ,it is slightly below the center of the bandgap.The density of states function is directly related to the carrier effective mass; thus,a larger effective mass means a larger density of states function .The intrinsic Fermi level must shift away from the band with the larger density of states in order to maintain equal numbers of electrons and holes. EXAMPLE3.4 OBJECTIVE Determine the positon of the intrinsic Fermi level with respect to the center of the bandgap in silicon at T=300 K. The density of states effective mass of the electron is =1.08 and that of the hole is =0.56. Solution The intrinsic Fermi level with respect to the center of the bandgap is or Comment For silicon,the intrinsic Fermi level is 12.8 below the midgap engegy.If we compare 12.8 to 560 ,which is one-half of the bandgap energy.of silicon, we can, in