Optimal conditions for imaging in scanning tunneling microscopy: Theory

The scanning tunneling microscopy ~STM! feedback system is analyzed to look for the optimal conditions for measurement. The typical feedback circuit normally used in STM and the parameters involved on it are studied, and their relative importance into the loop are discussed. The analysis of the role of each parameter demonstrated the importance of a detailed knowledge of the instrument to assure that the images obtained are reliable. We obtained equations that involve the main parameters of the loop, and yield the optimal conditions for imaging taking into account stability, signal amplitude, and phase shift. Combining the stability conditions with the imaging conditions obtained in this work, we found values for the feedback parameters to perform optimal STM measurements. Moreover, with this work, we highlight the importance to include in further publications the value of the main parameters used to obtain STM images. The conclusion of our work is that in some cases ~in particular atomic resolution and fractal analysis ! STM users should pay more attention to the setting of the instrument. © 1998 American Institute of Physics. @S0034-6748~98! 02411-3# Scanning probe microscopy ~SPM! techniques, mainly scanning tunneling microscopy ~STM! and atomic force microscopy ~AFM! , have become today the standard techniques for characterization of surface materials with atomic resolution. Commercial instruments are widely disseminated around the world and their use and importance cover many fields of science. These instruments become increasingly compact and complex. Consequently, the users look to them as ‘‘black boxes. ’’ In this way, the parameters in the feedback loop are most of the time obtained by trial and error. However, to obtain ‘‘real copies’’ of the surface topography, it is necessary to keep in mind the main characteristics and the limits of the instrument. Pioneering efforts on the STM feedback system analysis were made on the base to find out the stability region 1 and the transfer function to obtain the conditions for a critical damping 2 to avoid instabilities. Other works proposed finding out the optimal feedback conditions experimentally—obtaining the critical damping conditions 3 —or using a mathematical model with complex equations, 4 without clear conclusions about how to use their results under real conditions. Park and Barret 5 studied the stability of the tunnel loop by using a resonant model but finally they were not able to acquire the stability region for imaging. Along this line, we discussed in previous works the optimal conditions in which to have stability, during scanning in the STM, in order to avoid artifacts, instabilities, resonance, or noise in the image. 6 We emphasized the real parameters involved in it and their experimental determination. 7 Therefore, an extensive analysis of a typical feedback circuit was made, finding conditions and rules for stability during imaging. Because ‘‘an image says more than a thousand words,’’ it is important to be sure of the image quality. Thus, a second part was missing in our previous work: the measurement conditions when the feedback loop is under conditions of stability. Therefore, the aim of this work is to present a study on the correct use of the STM feedback system from the point of view of the measurement conditions. As far as we know, this is the first study where the physical parameters used for measurement and the mechanical properties of the STM device have been related between them and with the images obtained.