Etching models for A {111} diamond surface: Calculation of trigon slopes

Abstract

A mathematical analysis of the etching of {111} diamond surfaces is developed. The slopes of etch pit faces are computed in terms of the specific rate constants, k 2 and k 3, for removal of two- and three-bonded atoms along 〈1̄10〉 steps and the specific rate constant, k d, for step nucleation at the central initiating defect. Interactions between neighboring steps are neglected. Two limiting etching regimes are found, i.e., one in which the step velocity increases linearly with step length and a regime of constant step velocity. If k d is limited by a no overhang criterion, i.e., nucleation of a new step cannot occur until the prior step has moved out of the way, k d and etch pit slope are functions of the size of the initiating defect. This allows etch pits of vastly different slope to be formed at the same k 2 k 3 ratio. Point bottom pits with shallow (less than 2°) slopes form from small initiating defects, e.g., dislocation outcrops. At the same k 2 k 3 ratio flat bottom pits with steep (70° 32') outer faces are formed by etching from large shallow defects, e.g., ring cracks or inclusions. Some preliminary conclusions are drawn about the chemical environment present during the latter stages of diamond genesis.