This paper continues a study on the initial-boundary value problem 
for a nonlinear parabolic equation of forth order which was presented by 
Johnson-Orme-Hunt-Graff-Sudijono-Sauder-Orr \cite{Jo} for describing the process of 
growth of a crystal surface under molecular beam epitaxy(MBE). In the previous papers \cite{FuYa,FuYa2},
we have constructed a dynamical system determined from the model equation
and have studied asymptotic behavior of solutions. 
This paper is then devoted to investigating stability or instability of homogeneous stationary solution.
Using the instability dimension, we will make a lower dimension estimate for the attractor 
of the dynamical system constructed in \cite{FuYa}.