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CHAPTER 4 Carrier Transport and Excess CarrIer PhenomenaThe drift velocity versus electric field characteristic of gallium arsenide is morecomplicated than for silicon or germanium. At low fields, the slope of the driftvelocity versus -field is constant and is thc low-field electron mobility, which bapproximately 8500 for gallium arsenide. The low-field electron mobility ingallium arsenide is much larger than in silicon. As the field increases, the electrondrift velocity in gallium arsenide reaches a peak and then decreases. A differentialmobility is the slope of the versus -field at a particular point on the curve and thenegative slope of the drift velocity versus electric field represents a negative differ-ential mobility. The negative differential mobility produces a negative differentialresistance; this characteristic is used in the design of oscillators.Negative differential The negative differential mobility can be understood by considering the E versusMobility diagram for gallium arsenide, which is shown again in Figure 4.8. The density ofStates effective mass of the electron in the lower valley is The smalleffective mass leads to a large mobility. As the -field increases, the energy of theelectron increases and the electron can be scattered into the upper valley, where tbedensity of states effective mass is . The larger effective mass in the uppervalley yields a smaller mobility. This intervalley transfer mechanism results ln a de-creasing average drift velocity of electrons with electric field, or the negative differ-ential mobility characteristic. Figure 4.8 | Energy-band structurefor gallium arsenide showing theupper valley and lower valley inthe conduction band.(From Sze 15)TYU4.1 A drift current density of is required in a sendconductordevice using n-type silicon with an applied electric field of = 25V/cm.Determine the impurity doping concentration that will achieve thisspecification. (Ans. if,then)TYU4.2 Silicon at T = 300 K is doped with impurity doping concentrations of and . (a) What are the electron andhole mobilities? (b) Determine the resistivity and conductivity of the material.Ans.(a),;(b),TYU4.3 Repeat TYU4.1 for GaAs.(Ans.If,then)TYU4.4 Repeat TYU4.2 fOr GaAs.Ans.(a),;(b),4.2 I CARRIER DIFFUSIONObjective: Describe the mechanism of carrier diffusion and diffusion currentdue to a gradient in the carrier concentration.There is a second mechanism, in addition to drift, that can induce a current in a semi-conductor We can consider a classic physics example in which a container, as shownin Figure 4.9, is divided into two pats by a membrane. The left side contains gas mol-ecules at a particular temperature and the right side is initially empty. The gas mole-cules are in continual random thermal motion so that, when the membrane is broken,there will be a net flow of gas molecules into the right side of the container. DiffusionDiffusion processis the process whereby Particles flow from a region of high concentration toward aregion of low concentration. If the gas molecules were electrically charged, the netflow of charge would result in a diffusion current.4.2.1 Diffusion Current DensityTo begin to understand the diffusion process in a semiconductor, we will consider asimplified analysis. Assume that an electron concentration varies in one dimension asshown in Figure 4.10. The temperature is assumed to be uniform so that the averagethermal velocity of electrons is indePendent of . To calculate the current, we willdetermine the net flow of electrOns per unit time per unit area crossing the plane at.If the distanceshown in Figure 4. l0 is the mean-free path of an electron, thatis, the average distance an electron travels between collisions (), then onthe average, electrons moving to the right at and electrons moving to the left at will cross the plane. One half of the electrons at will beiraveling to the right at any instant of time and one half of the electrons at 第四章承运人运输及过量载流子现象与砷化镓的电场漂移速度的特点是更复杂的比硅或锗.在低的领域，在与架 -场的漂移速度是常数，斜坡码头处理费低场电子迁移率，其中B约为8500 镓砷化物。在砷化镓低场电子迁移率比在较大的硅。作为字段的增加，在砷化镓电子漂移速度达到一个高峰，然后下降。一个流动性差是 与-场在曲线上和漂移速度与电场负斜率代表一个特定点的斜率负微分迁移率。负微分迁移率产生负微分电阻，这一特点是在振荡器的设计。负微分负微分迁移率是可以理解的，考虑电子与 镓砷化物，这是再次显示在迁移率图4.8图。对各国的电子有效质量在较低的河谷密度 。小有效量产生了大量的流动性。场的增加，增加了电子和电子能量可以被分散到上游在国家的有效质量，简称TBE密度为。在较大的上游产生了一个有效的质量较小的流动性。这谷间转移机制的结果与法律公告一电场，或负微分迁移率下降的特征电子平均漂移速度。 图4.8 |能带结构镓砷化物展示上游河谷中，下导带。（从事15）TYU4.1 漂移电流密度为 中需要使用一个应用半导体为 = 25V/cm。电场n型硅器件。确定杂质的掺杂浓度，将实现此规范。 (答。如，然后)TYU4.2 硅在T = 300 K的掺杂杂质掺杂浓度的 和 .。(a) 什么是电子和空穴迁移率？ (b) 确定了材料的电阻率和电导率。答。(a),;(b),TYU4.3 重复TYU4.1砷化镓。(答。如，然后)TYU4.4 重复TYU4.2砷化镓。答。(a),;(b),4.2 余载流子扩散目的：描述了载流子扩散电流和扩散机制由于在载流子浓度梯度。还有第二个机制，除了漂流，可以诱导半导体，我们可以考虑一个典型的例子，物理学的一个容器，如图4.9所示，分为两拍除以膜电流。在左侧包含在特定温度下气体分子，右边最初是空的。气体分子热运动中不断随机如此，当膜被破坏，有将容器的右侧净流量的气体分子。扩散是一个过程，即从一个粒子对低浓度区的高浓度 扩散过程区域流动。如果气体分子带电，净流量收费将导致扩散电流。4.2.1扩散电流密度首先要了解在半导体扩散过程中，我们将考虑简化分析。假设一个在一维电子浓度变化，如图4.10所示。温度是假设要均匀，使电子的热速度平均是。计算当前，我们将确定在电子的净流量每单位面积单位时间内穿过平面。如果距离图所示4.l0。 是一个电子平均自由路径，也就是说，平均距离在()，电子之间的碰撞 然后在平均，电子正以 的权利和电子移动到左侧旅行将穿越 飞机。一个 的电子一半将前往在任何一个瞬间的权利和电子一半。
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