Effects of nearest and next-nearest neighbour interaction parameters on atomic correlation functions of stepped surfaces

We extend the range of the interaction between the surface scatterers to the next-nearest neighbours and thus treat the stepped surface as a second-order Markov chain. We employ two interaction parameters to describe the behaviour of the atomic pair correlation function for a two-level system and derive an exact expression for this function. This expression is then used to calculate the profile of the diffracted intensity. The effects of the interaction parameters on the intensity profiles as well as on the terrace width distributions are investigated in detail and compared to the molecular beam epitaxy measurement of Si on a Si(111) surface. The physical meaning of the interaction parameters is also interpreted in terms of the Ising model.