We develop a theory for the surface ripples produced by near-normal-incidence ion bombardment of a (001) GaAs surface with a small miscut along the [110] direction. We restrict our attention to the case in which the energy of the incident ions is below the sputter yield threshold and the sample temperature is just above the recrystallization temperature. Highly ordered, faceted ripples with their wave vector aligned with the [110] direction form when the ion beam is normally incident and there is no miscut. Two additional terms appear in the equation of motion when the beam is obliquely incident and/or there is a miscut: a linearly dispersive term and a nonlinearly dispersive term. The coefficients of these terms can become large as the threshold temperature for pattern formation is approached from above. In the absence of strong nonlinear dispersion, strong linear dispersion leads to ripples with a dramatically increased degree of order. These ripples are nearly sinusoidal even though they are on the surface of a single crystal. The exceptionally high degree of order is disrupted by nonlinear dispersion if the coefficient of that term is sufficiently large. However, by choosing the angle of ion incidence appropriately, the coefficient of the nonlinearly dispersive term can be made small. Ion bombardment will then produce highly ordered ripples. For a different range of parameter values, nucleation and growth of facets and spinodal decomposition can occur.

• Received 8 September 2021
• Revised 11 January 2022
• Accepted 6 February 2022

DOI:https://doi.org/10.1103/PhysRevE.105.024801