Thermal frequency noise in dynamic scanning force microscopy

Colchero, J.; Cuenca, M.; Martínez, Juan Francisco González; Abad, José Antonio; García, B. Pérez; Palacios-Lidón, E.; Abellán, J.

doi:10.1063/1.3533769

Cited by 14 publications

(25 citation statements)

References 28 publications

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“…A deflection shifts the reflected beam, causing an unequal illumination, which can be quantified by measuring the photocurrents of the different quadrants. Current implementations reach deflection sensitivities on the order of 10 À12 m Hz À1/2 [77]. The adjustment of the light lever method is very convenient and user-friendly, and the setup is relatively robust and cheap, making this implementation the most used one reported in literature.…”

Section: Detection Of Cantilever Oscillationmentioning

confidence: 98%

Imaging and Characterization of Magnetic Micro- and Nanostructures Using Force Microscopy

Block

2015

Surface Science Tools for Nanomaterials Characterization

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Section: Detection Of Cantilever Oscillationmentioning

confidence: 98%

Imaging and Characterization of Magnetic Micro- and Nanostructures Using Force Microscopy

Block

2015

Surface Science Tools for Nanomaterials Characterization

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“…This is in contrast to the driven Q, , which is defined by the slope of the phase versus frequency curve for an actuated cantilever. Equation 1 has been experimentally verified in numerous FM-AFM [27][28][29][30] and micromechanical cantilever sensor studies [31][32][33]. Originally derived for UHV experiments, it incorporates two assumptions: i)…”

Section: Introductionmentioning

confidence: 99%

“…Recently, several authors have presented noise calculations that focused on frequency noise in FM-AFM [29,30,39,40]. Here, we investigate the thermal noise limited performance of all dynamic AFM modes by deriving expressions for the measured amplitude noise, 〈 〉, phase noise, 〈 〉, frequency noise, 〈 〉, minimum detectable force, , and force gradient ′ , arising due to the thermal motion of the cantilever under both low Q ( ≪ ) and high Q ( ≫ ) approximations (See Section 2.1).…”

Section: Introductionmentioning

confidence: 99%

High viscosity environments: an unexpected route to obtain true atomic resolution with atomic force microscopy

et al. 2014

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Atomic force microscopy (AFM) is widely used in liquid environments, where true atomic resolution at the solid-liquid interface can now be routinely achieved. It is generally expected that AFM operation in more viscous environments results in an increased noise contribution from the thermal motion of the cantilever, thereby reducing the signal-to-noise ratio (SNR). Thus, viscous fluids such as ionic and organic liquids have been generally avoided for highresolution AFM studies despite their relevance to, e.g. energy applications. Here, we investigate the thermal noise limitations of dynamic AFM operation in both low and high viscosity environments theoretically, deriving expressions for the amplitude, phase and frequency noise resulting from the thermal motion of the cantilever, thereby defining the performance limits of amplitude modulation (AM), phase modulation (PM) and frequency modulation (FM) AFM. We show that the assumption of a reduced SNR in viscous environments is not inherent to the technique and demonstrate that SNR values comparable to ultra-high vacuum systems can be obtained in high viscosity environments under certain conditions. Finally, we have obtained true atomic resolution images of highly ordered pyrolytic graphite and mica surfaces, thus revealing the potential of high-resolution imaging in high viscosity environments.High viscosity environments: an unexpected route to obtain true atomic resolution with atomic force microscopy 2

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“…The equipartition theorem is also used in FM-AFM to calculate the fundamental noise limits in force detection due to thermal excitation. 13,14 Understanding the fundamental noise limits is very important for judging and improving a system's performance. In this paper, we show the validity of using the equipartition theorem in the temperature range from 140 K to 300 K and discuss its application at liquid helium temperatures.…”

mentioning

confidence: 99%

“…It must be ensured that there are no mechanical excitations due to vibrations. In order to compare mechanical noise with the thermal noise, the equivalent white noise drive 14 a th ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2k B T=ðpf 0 kQÞ p…”

mentioning

confidence: 99%

Application of the equipartition theorem to the thermal excitation of quartz tuning forks

2011

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The deflection signal of a thermally excited force sensor of an atomic force microscope can be analyzed to gain important information about the detector noise and about the validity of the equipartion theorem of thermodynamics. Here, we measured the temperature dependence of the thermal amplitude of a tuning fork and compared it to the expected values based on the equipartition theorem. In doing so, we prove the validity of these assumptions in the temperature range from 140 K to 300 K. Furthermore, the application of the equipartition theorem to quartz tuning forks at liquid helium temperatures is discussed. Over the last decades, quartz tuning forks have been used to build self-sensing sensors in many research fields, for example, hydrodynamics of quantum fluids, 1,2 spectroscopic gas sensing, 3,4 and scanning probe microscopy. [5][6][7] In this paper, we focus on quartz tuning forks used in frequency modulation atomic force microscopy (FM-AFM), although the results are also applicable to other fields utilizing quartz tuning forks. FM-AFM with quartz tuning forks has put forth a number of impressive results, [8][9][10] e.g., FM-AFM was used to resolve the chemical structure of a molecule.10 In FM-AFM, the frequency shift Df of an oscillator measures the local interaction of the microscope tip with the sample. The force between tip and sample can be calculated from the frequency shift Df if the sensor's resonance frequency, stiffness, and oscillation amplitude are known.11,12 Thus, for determining relevant physical quantities out of the observed frequency shift, those properties must be well-characterized.A tuning fork is a cut piezoelectric quartz crystal with two prongs and gold electrodes along the prongs. When one or both prongs are deflected, charge accumulates on the electrodes. The sensitivity describes the relation between the piezoelectric output signal and the deflection of a tuning fork. It is therefore essential to know in order to determine the deflection amplitude. One method to determine the sensitivity is to compare the output of the tuning fork due to thermal excitation with the expected result based on the equipartition theorem and the assumption that the first harmonic mode is the only mode significantly excited. The equipartition theorem is also used in FM-AFM to calculate the fundamental noise limits in force detection due to thermal excitation. 13,14 Understanding the fundamental noise limits is very important for judging and improving a system's performance. In this paper, we show the validity of using the equipartition theorem in the temperature range from 140 K to 300 K and discuss its application at liquid helium temperatures.The equipartition theorem states that each degree of freedom holds a thermal energy of 1 2 k B T, where k B is Boltzmann's constant and T is the temperature in Kelvin. For a coupled oscillator like the tuning fork with one degree of freedom, this leads to the relationwhere k is the spring constant and A EqT th is the thermal deflection amplitude of one prong.Exper...

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Thermal frequency noise in dynamic scanning force microscopy

Cited by 14 publications

References 28 publications

Imaging and Characterization of Magnetic Micro- and Nanostructures Using Force Microscopy

Imaging and Characterization of Magnetic Micro- and Nanostructures Using Force Microscopy

High viscosity environments: an unexpected route to obtain true atomic resolution with atomic force microscopy

Application of the equipartition theorem to the thermal excitation of quartz tuning forks

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