ch5

• Diffusion


  The phenomenon of material transport by atomic motion
• Many reactions and processes that are important in the treatment of materials rely on the transfer of mass either within a specific solid (ordinarily on a microscopic level) or from a liquid, a gas, or another solid phase
• Diffusion couple


  Formed by joining bars of two different metals together so that there is intimate contact between the two faces
• Interdiffusion


  The process by which atoms of one metal diffuse into another
• Self-diffusion


  Diffusion where all atoms exchanging positions are of the same type
• Diffusion is the stepwise migration of atoms from lattice site to lattice site
• Vacancy diffusion


  Mechanism where an atom interchanges with an adjacent vacant lattice site or vacancy
• Interstitial diffusion


  Mechanism where atoms migrate from an interstitial position to a neighboring one that is empty
• Diffusion flux (J)


  The mass (or number of atoms) M diffusing through and perpendicular to a unit cross-sectional area of solid per unit of time
• Fick's first law


  The flux is proportional to the concentration gradient, with the diffusion coefficient as the constant of proportionality
• Steady-state diffusion


  A state where the diffusion flux does not change with time, the mass of diffusing species entering equals the mass exiting
• Concentration profile


  The curve of concentration C versus position (or distance) within the solid
• Concentration gradient


  The slope of the concentration profile at a particular point
• Fick's second law


  The partial differential equation that describes non-steady-state diffusion
• Under conditions of nonsteady state, use of Equation 5.2 is possible but not convenient; instead, the partial differential equation ∂C/∂t = ∂/∂x(D∂C/∂x) (Fick's second law) is used
• Concentration profiles for nonsteady-state diffusion are taken at three different times, t1, t2, and t3, where t3 > t2 > t1
• Driving force


  What compels a reaction to occur. For diffusion reactions, the concentration gradient is the driving force
• One practical example of steady-state diffusion is found in the purification of hydrogen gas using a thin sheet of palladium metal
• Fick's second law, ∂C/∂t = D∂2C/∂x2, is used for nonsteady-state diffusion if the diffusion coefficient is independent of composition
• The solution to Fick's second law for a semi-infinite solid with constant surface concentration is Cx - C0/Cs - C0 = 1 - erf(x/2√Dt)
• Gaussian error function


  The function erf(x/2√Dt) used in the solution to Fick's second law
• If a specific concentration C1 is desired, then x/2√Dt = constant
• As time increases


  The position x where a specific concentration is achieved increases proportionally to √Dt
• The diffusion coefficient D depends on the diffusing species and the host material
• Self-diffusion


  Diffusion of a species into itself, occurs by a vacancy mechanism
• Interstitial diffusion


  Diffusion of a species that fits into the interstitial sites of the host material
• The diffusion coefficient D increases exponentially with increasing temperature according to D = D0 exp(-Qd/RT)
• Activation energy Qd


  The energy required to produce the diffusive motion of one mole of atoms
• A plot of log D vs 1/T gives a straight line with slope -Qd/2.3R and intercept log D0
• Diffusion equation


  1. log D = log D0 - (log e)(Qd/RT)

  2. log D = log D0 - (0.434)(Qd/RT)

  3. log D = log D0 - (1/2.3)(Qd/RT)

  4. log D = log D0 - (Qd/2.3R)(1/T)
• Equation 5.9b takes on the form of an equation of a straight line: y = b + mx
• If log D is plotted versus the reciprocal of the absolute temperature, a straight line should result, having slope and intercept of -Qd/2.3R and log D0, respectively
• Linear relationships exist for all cases shown in Figure 5.6
• Diffusion is used in the fabrication of semiconductor integrated circuits (ICs)
• Predeposition step


  Impurity atoms are diffused into the silicon, often from a gas phase, the partial pressure of which is maintained constant
• Drive-in diffusion


  Used to transport impurity atoms farther into the silicon in order to provide a more suitable concentration distribution without increasing the overall impurity content
• Diffusion rates through the SiO2 layer are relatively slow, such that very few impurity atoms diffuse out of and escape from the silicon
• The solution to Fick's second law for drive-in diffusion takes the form: C(x,t) = Q0/sqrt(πDt) exp(-x^2/4Dt)
• Q0 = 2Cs*sqrt(Dp*tp/π)
• Junction depth (xj)


  Depth at which the diffusing impurity concentration is just equal to the background concentration of that impurity in the silicon