The use of optimal parameter estimation for the online regulation of final etch depth in an ion milling process is described. A model-based control system utilizes a 3-D surface evolution model to predict dynamic surface profiles and etch depth. A heterodyne laser interferometer is used to measure trench height in situ for calculation of the difference in etch rates between the photoresist layer and the exposed portion of the underlying substrate layer. Adaptive material-specfic etch rate parameters and operating parameters such as ion beam strength and angle of incidence are estimated optimally with an extended Kalman filter. Optimal estimates of the in situ etch depth are calculated from the adaptive model, allowing the stopping time of the milling process to be varied from run to run to regulate final etch depth in the presence of disturbances. The system installed on an ion milling machine shows that the controller is capable of accurately regulating final etch depth in the presence of large process faults.

An important recent advance in the solution of the optimal regulator control problem for time-delayed systems is extended here to multivariable systems and to systems which exhibit multiple time delays. The state equations are partitioned into discrete and continuous portions through a state transformation such that the solution of the optimal regulator problem reduces to finding a steady-state controller gain based on both a discrete and continuous Riccati matrix. The discrete Ricatti matrix is found independently of the continuous solution due to the partitioning of the state equations, and it is not necessary to solve the system of partial differential Riccati equations which arise in the traditional solution of the linear quadratic regulator (LQR) problem for time-delayed systems. In addition, through this state transformation it becomes possible to extend the standard state controllability tests to time-delayed systems. It is shown that the controllability of the transformed state space is necessary for a feasible solution to the optimal regulator problem for time-delayed systems. This is an important test to determine the practicality of various time-delayed system realizations. Numerical examples illustrate the application of the technique to systems exhibiting multiple time delays, multivariable systems and time-series models. It is shown that the classic Wood-Berry distillation model realization does not possess state controllability properties which explains why this system has been historically difficult to control using feedback techniques.

We describe the design of a common-path heterodyne laser interferometer for the surface profiling of micron-sized photopatterned features during the microelectronic fabrication process. The common-path design of the interferometer’s reference and measurement arms effectively removes any path length difference in the measurement which can be attributed to the movement of the target surface. It is shown that repeated surface profiling during the ion milling process allows the difference in etch rates between the photoresist layer and the exposed portions of the underlying substrate layer to be monitored online. A prototype apparatus has been assembled and results demonstrating the usefulness of the device are reported. The surface profiles of both a photopatterned nickel–iron trench and an unmasked aluminum trench are measured and compared to those obtained using a stylus-based scanning profiler and an atomic force microscope.

Ion milling applications in the micro-electronics industry are becoming more challenging due to decreasing feature sizes and increasing aspect ratios. A simulation of the milling problem which is capable of predicting surface evolution in the presence of high aspect ratios where local shadowing of the substrate surface becomes an important issue is described. A method of characteristics solution based on surface inclination angles is derived for a three-dimensional surface evolution model. An algorithm is developed to account for local shadowing effects, where raised areas of the substrate surface (i.e., the photomask) prevent the ion beam from reaching hidden or shadowed portions of the surface. The yield (sputtering) function is modified to account for beam voltage as well as the angle of beam incidence. Yield function parameters are determined experimentally for Al2O3, Ti, permalloy (83/17 wt % Ni–Fe) and postbaked AZ P4400 photoresist. Model predictions are in good agreement with experimental results for the surface evolution of a photopatterned Al2O3 substrate.