Nonlinear modeling and control design for substrate temperature in molecular beam epitaxy

Molecular beam epitaxy (MBE) is a process for growing exotic, high speed semiconductors. In an MBE process the performance of the resultant devices depends heavily on the composition and morphology of layers deposited. They in turn depend on the substrate temperature and the effusion cell fluxes, neither of which have historically been controlled especially well. Recent advances in sensor technology coupled with the realization of the impact on performance of poorly controlled process parameters has lead to a desire for better control methods.; This thesis presents a novel model for substrate temperature derived from first principles. The model is a coupled set of nonlinear ordinary differential equations which gives a complete time history of the evolution of the states due to some exogenous input. In the derivation of the model we extend the standard theory of nodal representation of radiative heat transfer to include semitransparent bodies. From the model we derive a gain scheduled modified linear quadratic regulator based control law. We use the LQR methodology to derive feedback gains for all the measurable states and gain schedule the result. We examine some of the current issues that surround gain scheduling and suggest rules of thumb to insure the highest likelihood of success with a gain scheduled control for systems similar to the substrate thermal model. We also show that any system that is designed using our algorithm is guaranteed to be stable for sufficiently slow variations of its input. We examine the performance of a number of different control architectures and compare those to the current method of PID. We show that the current method of PID is inferior compared with the methods derived in this thesis. Finally we present some preliminary implementation results.