Effects of impurities on lateral growth of crystals

摘要

The effect of impurities on the step velocity of a growing crystal and, hence, the growth rate of the crystal is formulated on the basis of step pinning theory for the growth from dilute nutrients. The step velocity is obtained by solving two simultaneous equations i.e. one gives step velocity as a function of supersaturation and impurity density, and the other gives impurity density as a function of step velocity and impurity current. A graphical solution of the equation gives us clear explanation about pairing and instability of step trains. The minimum supersaturtion needed for crystal growth is proved to be approximated by 1:3-1:2 power of the current of impinging impurity molecules. Monte Carlo simulation of solid on solid model also verified the step bending and the dependence of the minimum supersaturation vs. current of impinging impurity molecules.