CHAPER 3 The Semiconductor in Equilibrium Solution The parameter values at T = 350 K are found as ?350?Nv?(1.04?10)???300?1932?1.31???19cm?3 And ?350?kT?(0.0259)???0.0302eV 300??The probability that an energy state at E = Ev –kT is empty is given by 1?fF(Ev?kT)?1?1??(EF?(Ev?kT))??exp? ?Ev?kT?EkT???F?1?exp??kT??Or ??(0.25?0.0302)??51?fF(Ev?kT)?exp??9.34?10 ?0.0302??The hole concentration is ??(EF?Ev)???0.25?19po?Nvexp??(1.31?10)exp ???kT0.0302????Or po?3.33?1015cm?3 ■ Comment The parameter values at any temperature can easily be found using the 300K values and the temperature dependence of the parameter. Exercise Problem Calculate the thermal-equilibrium hole concentration in silicon at T = 300 K for the case when the Fermi level is eV above the valence-band energy Ev. The effective density of states functions , Nc and Nv,are constant for a given semiconductor material at a fixed temperature. Table gives the valus of the density of states function and of the effective masses for silicon,gallium arsenide,and that value of Nc for gallium arsenide is smaller than the typical difference is due to the small electron effective mass in gallium arsenide. The thermal-equilibrium concentrations of electrons in the conduction band and of holes in the valence band are directly related to the effective density of states constants and to the Fermi energy level. Charge Carriers in Semiconductors Table Effective density of states function and effective mass values ?3?3** Nc(cm) Nv(cm) mn/m0 mp/m0 Silicon 2.8?10 1.04?10 Gallium arsenide ????10 ????10 Germanium ?????10 ????10 3.1.3 The Intrinsic Carrier Concentration For an intrinsic semiconductor,the concentration of electrons in the conduction band is equal to the concentration of holes in the valence can denote Ni and Pi as the electron and hole concentrations，respectively,in the intrinsic parameters are usually referred to as the intrinsic electron concentration and intrinsic hole , ni=pi,so normally we simply use the parameter Ni as the intrinsic carrier concentration,which refers to either the intrinsic electron or hole concentration. The Fermi energy level for the intrinsic semiconductor is called the intrinsic Fermi energy,or EF= 191817181919EFi.If we apply Equationsandto the intrinsic semiconductor,then we can write ??(Ec?EFi)?n0?ni?Ncexp?? （） kT??And ??(EFi?Ev)?p0?pi?ni?Nvexp?? （） kT??If we take the product of Equationsand,we obtain ??(Ec?Ev)???(EFi?Ev)?ni2?NcNvexp?.exp （） ???kTkT????or ??Eg???(Ec?Ev)?n?NcNvexp???NcNvexp?kT? （） kT????2iwhere Eg is the bandgap a given semiconductor material at a constant temperature,the value of ni is a constant,and independent of the Fermi energy. The intrinsic carrier concentration for silicon at T = 300 K can be calculated by using the effective density of states function values from Table . The value of calculated from Equationfor Eg = eV is ni = 6.95 ?10cm . The commonly accepted value 29 of ni for silicon at T = 300 K is approximately 2Various references may list slightly different valus of the intrinsic silicon concentration at room general,they are all between 1?1010and 1.5?10cm10?3.This difference is,in most cases,not significant. 第三章 半导体中的平稳 解决方案 在T = 350 K时的参数值可写成 ?350?Nv?(1.04?1019)???300? 而 32?1.31???19cm?3 ?350?kT?(0.0259)???0.0302eV 300??
879A39饶晓仕
