J. Phys.: Condens. Matter 11 (1999) 4367–4380. Printed in the UK PII: S0953-8984(99)99821-1 A new class of coupled continuum equations for atomic growth on surfaces Biplab Sanyal†, Anita Mehta‡‖ and Abhijit Mookerjee† † S N Bose National Centre for Basic Sciences, JD-Block, Sector-III, Salt Lake, Calcutta 700091, India ‡ Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK E-mail: biplab@boson.bose.res.in, anita@boson.bose.res.in and abhijit@boson.bose.res.in Received 4 December 1998, in final form 23 April 1999 Abstract. We propose a new class of coupled equations for describing interfacial growth by molecular beam epitaxy and, additionally, present some ab initio electronic structure calculations for energetics in support of our equations. Finally, we present our results for the critical spatial (α) and temporal (β) roughening exponents for our model and analyse our results in the context of atomic interfaces. 1. Introduction The study of kinetic growth equations [1] and their relevance to real experimental deposition techniques has become a challenging and fascinating topic. Such deposition processes are particularly important for the understanding of physical properties of the resulting surfaces. This is vital for technological reasons. In this communication we modify a class of coupled stochastic differential equations suggested earlier by Mehta et al [2, 3] for driven sandpiles, and study them as models for surface epitaxial growth of metals on metallic substrates. While non-equilibrium growth has been extensively studied by means of coarse-grained classical stochastic equations (see [1]), it is not obvious a priori that the microscopic constraints relevant to atomic surfaces would automatically be satisfied by largely heuristic classical terms. In this communication we therefore present electronic energy calculations in support of our model. The plan of this paper is as follows: (i) First, we shall adopt ideas introduced earlier in the field of granular media and modify them to model atomistic deposition processes. We shall therefore qualitatively justify each term in our deposition equations. (ii) Second, we shall numerically solve the equations for model situations to study the morphology of the rough surfaces which result from them. We shall vary parameters in our model equations to see their effect on the resulting surfaces and observe whether the results tally with the qualitative ideas put forward earlier. ‖ On leave from: S N Bose National Centre for Basic Sciences, Calcutta, India. 0953-8984/99/224367+14$19.50 © 1999 IOP Publishing Ltd 4367