Growth equations for the Wolf-Villain and Das Sarma-Tamborenea models of molecular-beam epitaxy

We derive the growth equations for the Wolf-Villain and Das Sarma- Tamborenea models based on the master-equation method. The Wolf-Villain model is shown to obey the conserved growth equation ${{∂}h}{{∂}t}={-}{{ν}}₄{{∇}}⁴h+{{λ}}₂₂{{∇}}²{({∇}h)}²+{Σ}{n=1}^{{∞}}{{λ}}₁₂ₙ₊₁{∇}·{}{({∇}h)}²ⁿ⁺¹+F+{η}$, which is expected to exhibit the scaling behavior of the Edwards-Wilkinson universality class. We find that the Das Sarma- Tamborenea model is governed by the Villain-Lai-Das Sarma equation ${{∂}h}{{∂}t}={-}{{ν}}₄{{∇}}⁴h+{{λ}}₂₂{{∇}}²{({∇}h)}²+F+{η}$ in contrast to former results. The physical origin of the difference between these two similar models is also discussed.