Measurement of electrostatic tip–sample interactions by time-domain Kelvin probe force microscopy

• Christian Ritz,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2020, 11, 911–921, doi:10.3762/bjnano.11.76

• , are introduced by the vector This vector, the so-called transition noise vector, is anticipated to be Gaussian white noise (0,QK) with the covariance matrix The output of the Kelvin system is the scalar value of the intrinsic frequency shift . It is defined by using the definition in Equation 10. The

• measurement noise is assumed to be Gaussian white noise and is defined by . This is the case for measurements where thermal noise is the dominating noise source, i.e., when the modulation frequency is below the crossover of thermal white noise and (with increasing frequency) detection noise [29]. The power

• DD: The observed frequency shift Δfk corresponds to the output of the detection system, . If a PLL is used as a detection technique, the above system can be approximated by a low-pass filter. The noise introduced at the output of the detection system is modeled by Gaussian white noise with . Merging

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

• Edgar Cruz Valeriano,
• José Juan Gervacio Arciniega,
• Christian Iván Enriquez Flores,
• Susana Meraz Dávila,
• Joel Moreno Palmerin,
• Martín Adelaido Hernández Landaverde,
• Yuri Lizbeth Chipatecua Godoy,
• Aime Margarita Gutiérrez Peralta,
• Rafael Ramírez Bon and
• José Martín Yañez Limón

Beilstein J. Nanotechnol. 2020, 11, 703–716, doi:10.3762/bjnano.11.58

• that gives a qualitative relationship between a set of contact resonance frequencies and the indentation modulus. It is based on white-noise excitation of the tip–sample interaction and uses system theory for the extraction of the resonance modes. During conventional scanning, for each pixel, the tip

• –sample interaction is excited with a white-noise signal. Then, a fast Fourier transform is applied to the deflection signal that comes from the photodiodes of the atomic force microscopy (AFM) equipment. This approach allows for the measurement of several vibrational modes in a single step with high

• compared to conventional techniques. Keywords: atomic force microscopy; fast Fourier transform; mechanical properties; system theory; white noise; Introduction There are several methods to measure mechanical properties at the nanoscale level, based on, e.g., nanoindentation or on other physical phenomena

Coexisting spin and Rabi oscillations at intermediate time regimes in electron transport through a photon cavity

• Vidar Gudmundsson,
• Hallmann Gestsson,
• Nzar Rauf Abdullah,
• Chi-Shung Tang,
• Andrei Manolescu and
• Valeriu Moldoveanu

Beilstein J. Nanotechnol. 2019, 10, 606–616, doi:10.3762/bjnano.10.61

• it like is seen in Figure 8. Interestingly, “pink” or white noise is seen in Sx when current flows through the system. The same type of noise is seen in the Fourier power spectra of the current–current correlation functions, not shown here. The occurrence of pink or white noise is well known in

Intrinsic ultrasmall nanoscale silicon turns n-/p-type with SiO₂/Si₃N₄-coating

• Dirk König,
• Daniel Hiller,
• Noël Wilck,
• Birger Berghoff,
• Merlin Müller,
• Sangeeta Thakur,
• Giovanni Di Santo,
• Luca Petaccia,
• Joachim Mayer,
• Sean Smith and
• Joachim Knoch

Beilstein J. Nanotechnol. 2018, 9, 2255–2264, doi:10.3762/bjnano.9.210

• from the sample surface prior to the measurements. Single scans of spectra were recorded over 12 h per NWell sample and subsequently added up for eliminating white noise. Scans for the Si-reference sample were recorded over 2 h and subsequently added up. All NWell samples were exited with a photon

Disorder-induced suppression of the zero-bias conductance peak splitting in topological superconducting nanowires

• Jun-Tong Ren,
• Hai-Feng Lü,
• Sha-Sha Ke,
• Yong Guo and
• Huai-Wu Zhang

Beilstein J. Nanotechnol. 2018, 9, 1358–1369, doi:10.3762/bjnano.9.128

• the case of a clean wire, we set μi = μ0, Δi = Δ0, and ti = t0 for all sites. For each single disordered configuration of the system, the on-site disorder are modeled by the white noise and their strength is assumed to be randomly distributed in the range [−δW, +δW], where the W = t, μ, Δ denotes the

A review of demodulation techniques for amplitude-modulation atomic force microscopy

• Michael G. Ruppert,
• David M. Harcombe,
• Michael R. P. Ragazzon,
• S. O. Reza Moheimani and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

• tracking bandwidth can be achieved for a pure sinusoid by integrating over one period M = 1, in order to reject white noise, multiple oscillation periods must be integrated which reduces the tracking bandwidth and increases the latency [42]. In this work, the trapezoidal numerical integration method with

• that the off-mode rejection is maximized at frequencies corresponding to the zeros of the sinc2 function. This in turn means that broadband white noise or noise at frequencies other than at these zeros cannot be sufficiently suppressed. This is in contrast to the lock-in amplifier and high-bandwidth

• estimate is evaluated as a function of the tracking bandwidth. The responses are compared against the theoretical and experimental response of an “ideal demodulator” represented by a low-pass filtered white noise process. A schematic block diagram of the reference experiment is shown in Figure 14. The band

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

• Alberto Nocera,
• Carmine Antonio Perroni,
• Vincenzo Marigliano Ramaglia and
• Vittorio Cataudella

Beilstein J. Nanotechnol. 2016, 7, 439–464, doi:10.3762/bjnano.7.39

• electronic fluctuations act on short time scales only. For this reason the total forces ξs(t) are locally correlated in time and one has to only retain the low-frequency limit of their stochastic variance. One thus obtains a multiplicative white-noise term where The fluctuating forces coming from the

Molecular machines operating on the nanoscale: from classical to quantum

• Igor Goychuk

Beilstein J. Nanotechnol. 2016, 7, 328–350, doi:10.3762/bjnano.7.31

• classical limit, , δT(t) becomes a delta function. Notice also that the real part of the first complex-valued term in Equation 9, which corresponds to zero-point quantum fluctuations, starts from a positive singularity at the origin t = 0 in the classical, white noise limit, ωc→∞, and becomes negative for

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• output G(s)(Udc − Ulcpd). Based on the transfer function, we find a state-space model of the system, in which we incorporate Ulcpd as a hidden state, and Udc is the control signal. We further model the uncertainties of state transitions () and our measurements as uncorrelated, zero-mean white noise with

• to the electrostatic force gradient instead of the electrostatic force. Although we have found our feedback loop superior to existing controllers, we see several aspects for improvement in the future. For example, the dynamics of Ulcpd are currently modelled as white noise. Since successive lines in

• -integral controller (red) to steps in Ulcpd and K. Both controllers incorporate the separately measured static gain, K, and are tuned for similar step responses at high K. Noise in K and at the inputs is artificial white noise lowpass-filtered with τfcut = 1 and the filter order n = 4, corresponding to the

Methods for rapid frequency-domain characterization of leakage currents in silicon nanowire-based field-effect transistors

• Tomi Roinila,
• Xiao Yu,
• Jarmo Verho,
• Tie Li,
• Pasi Kallio,
• Matti Vilkko,
• Anran Gao and
• Yuelin Wang

Beilstein J. Nanotechnol. 2014, 5, 964–972, doi:10.3762/bjnano.5.110

• frequency response is obtained by Fourier transform. The method tends to cancel out the effect of external noise in output provided that the excitation resembles ideal white noise. The method requires, however, that the measured perturbation is noise free. Considering a system shown in Figure 2, the ideal

• -correlation method requires that the excitation resembles ideal white noise (or more specifically, the auto correlation of the excitation resembles Dirac delta function), the logarithmic averaging procedure does not have this requirement. The method tends to cancel out the effect of uncorrelated noise both

• signal length and a sufficiently short clock cycle, the spectral and auto-correlation properties of the IRS are very close to the corresponding properties of a pure white noise. The sequence has the lowest possible peak factor, which means that the signal energy is very high in relation to the signal

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• as defined in Equation 1 is displayed in Figure 3a for typical experimental parameters exhibiting a sharp peak at f0 = 70 kHz (note the logarithmic scale of the ordinate) sticking far out of the white-noise floor when using low-noise detection electronics. The sharp peak in results from the

• treated here as a constant. This is fully justified by its white-noise character around the cantilever resonance. Note that this bandwidth limitation is solely based on noise considerations and does not reflect other bandwidth requirements, such as the stable operation of the PLL. However, there is a

• dashed lines are identical). For a study on how the noise of the detection system propagates through the demodulation system, different noise levels are artificially created by using white noise from a waveform generator DS345 (Stanford Research Systems, Inc., Sunnyvale, CA, USA) added to the

Characterization of the mechanical properties of qPlus sensors

• Jan Berger,
• Martin Švec,
• Martin Müller,
• Martin Ledinský,
• Antonín Fejfar,
• Pavel Jelínek and
• Zsolt Majzik

Beilstein J. Nanotechnol. 2013, 4, 1–9, doi:10.3762/bjnano.4.1

• subtracting the electrical noise density from it, thus . The electrical noise density, , should have white-noise character around the resonance, as a consequence, does not depend on the frequency. This requirement is usually well fulfilled around the resonant frequency of our homemade sensors. In order to

Wavelet cross-correlation and phase analysis of a free cantilever subjected to band excitation

• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2012, 3, 294–300, doi:10.3762/bjnano.3.33

• correlation between white noise and a sinusoidal signal, without implying any causal connection between the two time series. For this reason it is important to observe the phase relationship: A strong causal connection implies that the oscillations of the two series must be phase locked. Results As an example

Current-induced dynamics in carbon atomic contacts

• Jing-Tao Lü,
• Tue Gunst,
• Per Hedegård and
• Mads Brandbyge

Beilstein J. Nanotechnol. 2011, 2, 814–823, doi:10.3762/bjnano.2.90

• white noise in the high-bias and wide-band limits, where variations in the electronic DOS are neglected [47]. The assumption of a white-noise spectrum implies neglect of the equilibrium zero-point motion of the atoms, but most importantly here, it includes the Joule heating effects, A factor of 2 should

• ). Within the time-local white-noise approximation it is possible to address the effect of changes of electronic Hamiltonian and, especially, electron-phonon coupling on the motion, which was both included in the nonequilibrium force calculations here. This amounts to updating the nonconservative force

• compared to the static electronic structure approximation. A method which goes beyond white noise and includes the change in electron–phonon coupling when the system is far from the equilibrium positions, e.g., close to bond breaking, remains a challenge for the future. Conclusion We have developed a