| The scan probe microscopy (SPM), a technology based on the scan tunneling microscope (STM), the atomic force microscope (AFM), and various offsprings, has claimed quite a few scientific breakthroughs since its invention in 1981 and demonstrated itself as one of the most promising technologies for the current and future science and engineering applications. However, together with the impressive images experimentally obtained with the SPMs, there also arise many questions in interpreting the physical meaning of the obtained images, for instance, the well-known "missing every other atom" on graphite surface. Clarifying these issues by modeling the SPM imaging mechanism is essential to interpreting current experiments and advising future development of the SPMs.; The three studies presented in this thesis focus on a key issue in the SPM imaging mechanism: the modeling of the cantilever force sensor in an AFM and the atomically sharp SPM tips. The first study is motivated by the so-called "missing every other atom" problem in a contact AFM. A coupling mechanism is proposed to show how the three dimensional atom forces on the graphite surface cause a residual linear deflection of the cantilever, leading to a "topography" with seemingly only three atoms per unit cell. Various previous experimental results are found consistent with such an explanation. The design principles of the contact AFM are then discussed.; The second study is on the noncontact AFM. In contrast to the often postulated point mass assumption, in this paper, the motion of a cantilever is formulized by superimposing the time responses of all modal oscillations. An efficient simulation method was derived and used to clarify the conditions under which the point mass assumption is not valid and the corresponding consequences, which sheds light on the design and operation of a noncontact AFM. It is also shown that such formulation leads to an analytical solution to the frequency shift problem within the first order approximation.; Finally, sharp SPM tips produced by crushing a single diamond crystal are studied systematically at the atomic level. Various possible tip front structures are modeled. Their electronic structures and mechanical properties are calculated with semi-empirical algorithm based on the molecular orbital theory. By comparison, the tips are classified and the best tip structures are identified in terms of producing stable and un-ambiguous SPM images. |
