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In the molecular-beam epitaxy (MBE) process precise control over thickness, composition, and doping profiles are critical for end device performance. This article addresses the problem of accurately modeling and controlling the flux sources (effusion cells) used in MBE. A first-principles nonlinear dynamic model of an effusion cell is derived, investigated, tuned, and used for designing advanced closed-loop feedback schemes. The model is a coupled set of driven nonlinear ordinary differential equations. It provides the transient and steady-state time-dependent response of the cell to a given (heater power) input. Further, it provides output predictions of the produced molecular flux and the temperature read by a thermocouple built into all modern effusion cells. We show how to tune parameters in the model from actual experimental data using a nonlinear least squares identification algorithm. Simulations show excellent agreement with experimental data and empirical experience including reproduction of the well-known shutter transient event when the thermocouple temperature is regulated with a proportional-integral-derivative (PID) controller. The model further can be used to explore interesting effects. For example, the magnitude and duration of a shutter transient under PID regulation is different for gallium versus indium charged cells. This leads to a thin indium rich initial layer in the growth of InGaAs. The tuned model is used to investigate the efficacy of nested PID control designs and, finally, is used in an advanced feedback controller we design using differential geometric design methods of nonlinear control theory. Simulations show our advanced nonlinear controller eliminates flux transients over a wide range of operating conditions without the need for any recalibration or adjustment and provides superior tracking. The latter feature of superior tracking will become increasingly important as future devices call for new growth regimes and methods such as - - layers with continuously graded composition. © 1998 American Vacuum Society.
Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films (Volume:16 , Issue: 6 )
Date of Publication: Nov 1998