方茹辉144-145-B20

CHAPTER 4 Carrier Transport and Excess CarrIer Phenomena The drift velocity versus electric field characteristic of gallium arsenide is more complicated than for silicon or germanium. At low fields, the slope of the drift velocity versus ε-field is constant and is thc low-field electron mobility, which b approximately 85002/cm V s - for gallium arsenide. The low-field electron mobility in gallium arsenide is much larger than in silicon. As the field increases, the electron drift velocity in gallium arsenide reaches a peak and then decreases. A differential mobility is the slope of the d υ versus ε-field at a particular point on the curve and the negative slope of the drift velocity versus electric field represents a negative differ- ential mobility. The negative differential mobility produces a negative differential resistance; this characteristic is used in the design of oscillators. Negative differentialThe negative differential mobility can be understood by considering the E versus Mobilityκ diagram for gallium arsenide, which is shown again in Figure 4.8. The density of States effective mass of the electron in the lower valley is *00.067n m m = The small effective mass leads to a large mobility. As the ε-field increases, the energy of the electron increases and the electron can be scattered into the upper valley, where tbe density of states effective mass is 00.55m . The larger effective mass in the upper valley 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 2150/drf j A cm = is required in a sendconductordevice using n-type silicon with an applied electric field of ε = 25V/cm.Determine the impurity doping concentration that will achieve thisspecification. (Ans. if 1633.1310d N cm -≈⨯,then 21200/n cm V s μ≈-)TYU4.2 Silicon at T = 300 K is doped with impurity doping concentrations of163510a N cm -=⨯ and 163210d N cm -=⨯. (a) What are the electron andhole mobilities? (b) Determine the resistivity and conductivity of the material.[Ans.(a)21000/n cm V s μ≈-,2350/p cm V s μ≈-;(b)11.68()cm σ-=Ω-,0.595()cm ρ=Ω-]TYU4.3 Repeat TYU4.1 for GaAs.(Ans.If 53404110d N cm -≈⨯,then 28500/n cm V s μ≈-)TYU4.4 Repeat TYU4.2 fOr GaAs.[Ans.(a)2250/p cm V s μ≈-,24500/n cm V s μ≈-;(b)11.2()cm σ-=Ω-,0.833()cm ρ=Ω-]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 process is 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 veloc ity of electrons is indePendent of χ. To calculate the current, we willdetermine the net flow of electrOns per unit time per unit area crossing the plane at0χ=.If the distance l shown in Figure 4. l0 is the mean-free path of an electron, thatis, the average distance an electron travels between collisions (th cn l υτ=), then onthe average, electrons moving to the right at l χ=- and electrons moving to the leftat l χ=+ will cross the 0χ= plane. One half of the electrons at l χ=- will beiraveling to the right at any instant of time and one half of the electrons at l χ=+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ε -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85002/cm V s - 镓砷化物。