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The vertical gradient freeze crystal growth process is the main technique forthe production of high quality compound semiconductors that are vital fortoday's electronic applications. A simplified model of this process consists oftwo 1D diffusion equations with free boundaries for the temperatures in crystaland melt. Both phases are coupled via an ordinary differential equation thatdescribes the evolution of the moving solid/liquid interface. The control ofthe resulting two-phase Stefan problem is the focus of this contribution. Aflatness-based feedforward design is combined with a multi-step backsteppingapproach to obtain a controller that tracks a reference trajectory for theposition of the phase boundary. Specifically, based on some preliminarytransformations to map the model into a time-variant PDE-ODE system,consecutive decoupling and backstepping transformations are shown to yield astable closed loop. The tracking controller is validated in a simulation thatconsiders the actual growth of a Gallium arsenide single crystal.

Backstepping-based tracking control of the vertical gradient freeze crystal growth process