陈壮锐-76-77-A38.doc

CHAPTER 3 The Semiconductor in EquilibriumOr The electron concentration is given by Or CommentThe probability of a state being occupied in the conduction band can be quite small，but the thermal equilibrium value of electron concentration can be a reasonable value since the density of States large.Exercise ProblemEX3.1 Calculate the thermal equilibrium electron concentration in silicon at T=300K for the case when the Fermi level is 0.25eV below the conduction-band energy,. The thermal-equilibrium concentration of holes in the valence band is found by integrating Equation （3.2）over the range of energies in the valence-band energy,orDensity of holes. (3.12)Where is the maximum energy of the valence band and is the minimum energy of the valence band .However,the function approaches zero very quickly as the energy decreases,as seen in Figure 3.1d,so we may let we can note that (3.13a)For energy states in the valence band,.IF(kT)(the Fermi function is still assumed to be within bandgap),then we have a slightly different form of the Boltzmann approximation.Equation（3.13a）can be written as (3.13b)Applying the boltzmann approximation of Equation (3.12), we find the thermal-equilibrium concentration of holes in the valence band is Where the lower of integration is taken as minus infinity of the bottom of the valence band.The exponential term decays fast enough so that this approximation is valid. Equation（3.14）can be solved more easily by again making a change of variable If we let Then Equation （3.14）becomes Where the negative sign comes from the differential dE=.Note that the lower limit ofbecomes +when If we change the of integration,we introduce another minus sign. From Equation（3.8）Equation （3.16）becomes We may define a parameter as Which is called the effective density of states function in the valence band.The thermal-equilibrium concentration of holes in the valence band canNow be written as The magnitude of is also on the order of at T=300K for most semiconductor.OBJECTIVE Calculate the probability that energy state in the valence band at is empty of an electron and calculate the thermal-equilibrium hole concentration in silicon at T=350K. Assume the energy is 0.25eV above the valence-band energy.The value of for silicon at T=300K is . 第三章 半导体中的平衡电子浓度可以表示为OR 评论在传导带被占领的状态的可能性可以是相当小的，但是电子集中的热平衡价值可以是合理的价值从大密度状态。运动问题：EX3.1计算在硅的热平衡电子集中在案件的T=300K，当费密水平是0.25eV在传导带能量之下时。孔的热平衡价带中的浓度发现，结合对在价带能量的能量范围或者是孔的密度。方程（3.2）(3.12)的最大能源在哪里的,是价带能量最小价带。然而,很快接近零功能的精力减少,例如图3.1d,所以从我们可可以看到对于在价带能级，如果kT费米函数一直假设为内带隙。然后我们稍微不同形式的的玻尔兹曼的近似而已。方程(3.13a)可以写成：(3.13b)运用玻尔兹曼近似方程(第3.12章),我们发现了孔热平衡价带中的浓度是：在低的整合是减去了无限底部的价带。该指数足够快，使这一近似是有效的长期衰变。方程（3.14）又可以更容易解决的变量的变化，如果我们知道 然后方程(3.14)为： 那里负号来自有差别的dE=请注意，下限变成+时，如果我们整合的变化，我们介绍另一个减号。从公式（3.8）式（3.16）变为： 我们可以定义一个参数