Dissipation Imaging with Low Amplitude oﬀ-Resonance Atomic Force Microscopy H. O ¨ zgu ¨r O ¨ ZER  , Simon J. O’BRIEN, Andrew NORRIS, John E. SADER 1 and John B. PETHICA SFI Trinity Nanoscience Laboratory, Trinity College Dublin, Dublin 2, Ireland 1 Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia (Received February 7, 2005; accepted April 11, 2005; published July 26, 2005) A small amplitude non-contact atomic force microscope/scanning tunnelling microscope (nc-AFM/STM) is used to study dissipative interactions at atomic resolution on Cu(100) and Si(111) surfaces. For Cu(100) atomic resolution images of phase contrast are obtained, showing energy dissipation as high as 100 meV/cycle at each atomic site during constant tunnel current scans. In contrast, the Si(111) 7  7 surface usually did not exhibit signiﬁcant phase contrast during normal STM operating conditions. However, when the driving oscillation frequency was set to a sub-harmonic of the lever resonant frequency, atomic contrast in phase could be readily observed. We believe this harmonic coupling is due to the nonlinearity of the tip- sample interaction, and at these frequencies part of the energy is dissipated via the lever Q. [DOI: 10.1143/JJAP.44.5325] KEYWORDS: Atomic force microscopy, scanning tunneling microscopy, low amplitude, force gradient, dissipation, phase, harmonic coupling 1. Introduction Atomic force microscopy is widely used as a mechanical characterization probe as well as an imaging tool. With the advent of atom resolved nc-AFM, this capability has been extended to the atomic scale. An important resulting question is the extent to which energy is dissipated during these atom resolved measurements. In principle, for weak enough interactions, purely conservative processes and hence no dissipation should be involved. However, it has been known since the earliest nc-AFM results that signiﬁcant mechanical energy is actually dissipated, 1–3) and the loss signal can even be used for imaging. 4) There have been theoretical studies proposing possible mechanisms for observed dissipation, amongst which are adhesion hystere- sis, 3) atomic instabilities 5) and Brownian dissipation. 6) However, the actual origin remains uncertain. It is important, not only for a proper understanding of the interactions in imaging, but also because of its signiﬁcance for atom motion and manipulation, and the relation between atom motion and local atomic and chemical structure. The type of exper- imental setup used is signiﬁcant. 7) In this paper we present atom resolved dissipation images from an apparatus which uses very small oscillation amplitudes, and whose frequency can be varied independently of the lever resonance. This minimizes uncertainties about tip-surface separation, does not need deconvolution of interaction, and allows independ- ent investigation of resonance eﬀects. We show that non- linear coupling into the lever Q can be a signiﬁcant dissipative eﬀect. 2. Experiments and Results We investigated Cu(100) and Si(111) surfaces using a UHV-AFM/STM which employs a high resolution ﬁbre interferometer. Full details are given elsewhere. 8) The lever is oscillated with very small amplitudes (< 0:25  A) at a frequency below its resonance, while it is scanned across the surface under tunnelling current feedback control. The changes in the oscillation amplitude are recorded via a lock-in ampliﬁer. The oscillation amplitude gives the quantitative force gradient image directly, without deconvo- lution or assumptions about conservative interaction, as occur in large amplitude resonance AFM. Furthermore, the phase diﬀerence between the oscillation of the lever and the driving excitation is simultaneously recorded. This is a measure of the energy dissipation due to the tip-sample interaction. 1) In the case of very small oscillation amplitudes applied at frequencies far below resonance, the force gradient interaction between tip and sample can simply be expressed as: dF=dz ¼ k 0 1  A 0 A cos ’   ; ð1Þ where k 0 , A 0 , A, ’ are lever stiﬀness, free oscillation amplitude, the measured amplitude of the cantilever, and phase between the oscillations of the lever and its drive, respectively. The energy dissipated per cycle can be calculated, based on the model proposed by Anczykowski et al., 9) using the following expression: 1) E loss ¼ k 0 A 0 A sin ’: ð2Þ Home-made tungsten cantilevers with spring constants of 50 to 200 N/m were used in the experiments. The preparation and calibration of the cantilevers are reported elsewhere. 8) The Cu(100) sample, a 10 mm diameter disc of 3 mm thickness, was cleaned by repeated cycles of Ar ion bombardment at 1 kV for 30 min followed by an anneal for 30 min at 600  C. The (1  1) structure of the clean surface was veriﬁed independently by LEED investigation prior to AFM experiments. Si(111) sample was cut from P-doped, n- type wafer with 0.7 – 0.9 cm resistivity, oriented to within 0.20  of (111) plane. It was cleaned by ﬂash annealing to 900 and 1200 deg for a few tens of seconds following an overnight degas at about 600  C. Figure 1 shows an example of a simultaneous STM, force gradient and phase shift image, taken using an oscillation amplitude A 0 of 0.25  A. Both phase and force gradient exhibit atomic contrast whereas the corrugation in STM topography is less than 0.1  A. The lack of atomic scale contrast in the STM signal means we have essentially a ﬂat tip trajectory during imaging. This is expected for low index metals, and is shown by Eigler et al. 10) In turn, this means that the long-range component of tip-surface interaction force 11,12) is constant throughout the measurement. Hence  Corresponding author. E-mail address: ozero@tcd.ie Japanese Journal of Applied Physics Vol. 44, No. 7B, 2005, pp. 5325–5327 #2005 The Japan Society of Applied Physics 5325