Analysis of scanning tunneling microscopy feedback system

A theoretical analysis of the feedback system in the scanning tunneling microscope (STM) is presented. The proposed model includes all the elements involved in the STM loop. The knowledge of its behavior allow one to accurately determine the region where the unstable STM operation could affect the measurements, and also to set the optimal working parameters. Each element of the feedback circuitry is analyzed and discussed as well as their mutual interactions. Thus the stability region of a STM has been obtained analytically, using all the possible elements in the feedback loop and without using simplifications or rare models for the system. The mathematical models for each element of the loop has been used and the problem has been solved using control theory. Different working conditions are simulated and analyzed. Some relations for stability conditions, considering the value of each component involved in the feedback loop, are proposed and analyzed. The good agreement between theory and experimentation is shown by comparing images taken under conditions of good stability and of instability.