Control of dynamics and hysteresis in electromagnetic lenses (2011)

A comparison of control strategies is presented for fast and accurate switching of the operating point of electromagnetic lenses as used in electron microscopy. Electron microscopes are valuable tools for inspection and manipulation of specimens at the micrometer down to the nanometer scale. They enable further development of the next generation semiconductors, solar panels, fuel cells and chemical production processes of for instance polymers and medicines. From its invention in 1931 the electron microscope has traditionally been an imaging instrument used by highly experienced operators. More and more new applications arise in which the microscope is transformed from an imaging instrument into an automated measurement and manipulation tool. Next to a high quality image at a high magnification, the throughput of automated applications has become important. One of the throughput limiting factors is the time involved with switching the operation point of the electromagnetic lenses. Such transitions are required when images are recorded at different magnifications, with different electron energies or using different imaging and specimen manipulation principles. A transition consists of a two step procedure: In step 1, which is the main topic of this research, the magnetic flux density within the lens is brought as fast as possible to a steady level very close to the new operating point. In step 2 the focal settings of the lens are optimized using image based feedback techniques. The primary aim of research is to design and compare control strategies that are able to decrease both the maximum transition error and the maximum transition time involved with switching the operating point of electromagnetic lenses. To guarantee performance of image based focus optimization the error made in step 1 has to be smaller than 1% of the full range of possible set points. This bound was estimated by means of experiments carried out on a state-of-the-art scanning electron microscope. Feed forward controlled set point changes were evaluated with the help of the recorded image series. Besides experiments, the requirements for control were extracted from first principle electron optical models in combination with an analysis of the most dominant magnetization dynamics. An electromagnetic lens taken from a scanning electron microscope is extended with power electronics, magnetic flux density sensors and a data acquisition and rapid prototyping system. With this setup the controller performance can be evaluated experimentally. Instead of image quality the performance is based on measured behavior of the electromagnetic field. To meet the specifications for electron microscopy applications, the most accurate, large range, high bandwidth magnetic-flux-density-sensors available were placed within the lens geometry. Feed forward control is presently used in many microscopes and serves as the benchmark situation. The open loop magnetization dynamics in combination with ferromagnetic hysteresis result in a maximum transition time around 0.5s and a maximum transition error of 5% of the full range. Since the maximum error allowed is 1% there is a need for more advanced control. Analysis and design of control strategies is complicated due to spatially distributed dynamics and hysteresis in combination with both the demand for high accuracy and the restrictions on sensor positioning in the lens geometry. The implemented feedback controller reduces the maximum transition time down to 50ms, an improvement of a factor 10 when compared to feed forward. Next to that, feedback control is capable of dealing with the error introduced by hysteresis. However, restrictions on the sensor positioning imply that the sensor may not be placed in, or very close to, the electron optic volume during online operation of electron microscope. Because of this restriction the relation between the magnetic flux density at the position of the sensor and the magnetic flux density in the electron optical volume has to be controlled in feed forward. The experimental results obtained with this controller scheme show that hysteresis is again the dominant cause of the transition error. Due to the restrictions on the sensor position in combination with the spatially distributed hysteresis effect, the performance of this controller layout in terms of maximum transition error is at the critical boundary of 1%. Despite these restrictions, very fast switching is still guaranteed since the maximum transition times estimated at the sensor position and in the electron optic volume are both equal to 50ms. Feed forward initialization is introduced as a technique that specifically deals with reducing the error involved with hysteresis. By means of a forced reset of the state of the system, the error level is brought down to 0.05% of the full range, an improvement of 100 times when compared with conventional feed forward. The price being paid is the extra time (0.1s to 0.5s) needed for the applied input profile to enable the reset. Requirements on initialization trajectories for hysteretic systems are investigated by means of a model based analysis in combination with experiments carried out at both the electromagnetic lens setup and a scanning electron microscope. The optimal initialization trajectory for a specific trade-off between duration of initialization and the level of error reduction is obtained by an experimental procedure. The performance of all the different control techniques along with the performance limiting factors are indicated in a mapping of maximum transition time versus maximum transition error.