Published by Prentice Hall, NJ in 2000. This book starts with introduction to modern CMOS technology and continue with details about crystal growth, wafer fabrication and basic properties of silicon wafers. It also covers several fabrication steps, such as thermal oxidation, dopant diffusion and thin film deposition.
52) must be computed numerically. Experimentally, it often appears that the profile can be well modeled by assuming that the diffusivity is directly proportional to the free carrier profile as illustrated in Figure 7-28 where D (n/ni) or D (n/ni)?. The box-shaped profiles characteristic of concentration dependent diffusion are evident.
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Information on the concentration dependence of the diffusivity can be obtained from isoconcentration experiments, which we now describe. Boron is a particularly interesting element on which to perform isoconcentration experiments, because there are two common isotopes B'? and B". If a high-concentration background doping is set by one isotope, and a profile of the other isotope is introduced into the background, the diffusivity of the tracer can be measured as a function of the background concentration. This is a particularly nice experiment, because it is all boron diffusion, albeit different isotopes. Any complications that might occur due to dopant-dopant interactions are [te moved. SIMS is a particularly convenient analysis tool because its mass sensitivity al kind of experiment are a aed inside a uniform B" background, for example. This
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52) can be written as a function of concentration. the diffusivity of the common dopants in silicon has Pend linearly or sometimes quadratically on the cat ure 7-28. The effective diffusivity to be used in E4Models and Simulation | att | Dt =D? + p-() + p-(") for Ntype dopants (7.53) ny are
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D%f= p? + p(2) + pt*(2p for Ptype dopants (7.54) P i The superscripts D, D*, and so forth, are chosen, because on an atomic level, these different terms are thought to occur because of interactions with neutral and charged point defects, The diffusivity under intrinsic conditions for an n-type dopant (when p = n = ni) is Di, = D + D7 + D* (7.55) Each of these individual diffusivities can be written in Arrhenius form D.E D=DO0 -> exp kT ) (7.56) with a preexponential factor and an activation energy. By rewriting the above equations, the diffusion coefficient measured under extrinsic conditions can be elegantly described as 1+p-+ (2) Di = D4 io Y Ni, 1+Bt+y (7.57)
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