Lorentzian Spectrum Research Articles

Modeling of 1/f noise due to thermally induced magnetic switches of anti-ferromagnetic grains in magnetic tunneling readers

Magnetic 1/f noise is one of the major noise sources in state-of-the-art magnetic tunneling read heads for hard disk drive applications. The 1/f noise can be induced by thermally activated magnetic switching of antiferromagnetic (AFM) grains in the reader stack. This noise mechanism is studied here by micro-magnetic modeling. The modeling shows that the 1/f like noise power spectrum can come from the addition of several Lorentzian type noise spectra corresponding to the switching of individual AFM moments that are most likely located near the edges of the AFM layer. Additionally, the modeling shows that magnetic glitches can be generated by the switching of the reference layer edge curling state at the top or bottom edge of the layer, which is induced by the switching of one or more AFM moments in those areas.

Defect-Related Excess Low-Frequency Noise in Ge-on-Si pMOSFETs

The low-frequency noise in strained and relaxed Ge pMOSFETs is characterized to investigate more closely the anomalously large current spectral density at low drain currents. As shown, the dominant Lorentzian spectrum found in weak inversion points to fluctuations by generation-recombination (GR) events at substrate defects. This is confirmed by the fact that strained Ge transistors, having a significantly lower threading dislocation density, also exhibit lower excess GR noise. The usual number-fluctuation 1/f noise becomes more pronounced above threshold and also for shorter gate lengths.

Temperature dependence of 1/f noise mechanisms in silicon nanowire biochemical field effect transistors

The 1∕f noise of silicon nanowire biochemical field effect transistors is fully characterized from weak to strong inversion in the temperature range 100-300 K. At 300 K, our devices follow the correlated Δn-Δμ model. As the temperature is lowered, the correlated mobility fluctuations become insignificant and the low frequency noise is best modeled by the Δn-model. For some devices, evidence of random telegraph signals is observed at low temperatures, indicating that fewer traps are active and that the 1∕f noise due to number fluctuations is further resolved to fewer fluctuators, resulting in a Lorentzian spectrum.

Spectrum in spontaneous emission: Beyond the Weisskopf-Wigner approximation

The theory of spontaneous emission presented by Weisskopf and Wigner [V. Weisskopf and E. Wigner, Z. Phys. 63, 54 (1930)] provides an excellent approximation of the actual decay that atoms undergo on optically allowed transitions. However, the theory cannot be rigorously correct since it leads to a Lorentzian spectrum that extends to negative frequencies. Within the rotating-wave approximation, we derive a closed-form expression for the spectrum that is valid for all frequencies.

Frequency Domain Detection of Biomolecules Using Silicon Nanowire Biosensors

We demonstrate a new protein detection methodology based upon frequency domain electrical measurement using silicon nanowire field-effect transistor (SiNW FET) biosensors. The power spectral density of voltage from a current-biased SiNW FET shows 1/f-dependence in frequency domain for measurements of antibody functionalized SiNW devices in buffer solution or in the presence of protein not specific to the antibody receptor. In the presence of protein (antigen) recognized specifically by the antibody-functionalized SiNW FET, the frequency spectrum exhibits a Lorentzian shape with a characteristic frequency of several kilohertz. Frequency and conventional time domain measurements carried out with the same device as a function of antigen concentration show more than 10-fold increase in detection sensitivity in the frequency domain data. These concentration-dependent results together with studies of antibody receptor density effect further address possible origins of the Lorentzian frequency spectrum. Our results show that frequency domain measurements can be used as a complementary approach to conventional time domain measurements for ultrasensitive electrical detection of proteins and other biomolecules using nanoscale FETs.

1/fnoise from nonlinear stochastic differential equations

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

CRACKING THE LIU KEY EXCHANGE PROTOCOL IN ITS MOST SECURE STATE WITH LORENTZIAN SPECTRA

We have found a security risk in the Liu's cypher based on random signals and feedback, when it utilizes a large class of noises for communication in its most secure state, the steady state. For the vulnerability to exist, the noise must have a spectrum which can be transformed to white-like noise by linear filtering. For the cracking, we utilize the natural properties of power density spectra and autocorrelation functions. We introduce and demonstrate the method for Lorentzian spectra. Some of the implications of the results concern the transient operation during changing bits, where the modulation products of noise cannot be band-limited therefore the cypher is vulnerable. We propose the application of line filters to provide a proper spectral shape and to improve the security.

The Spectrum of a Noisy Free-Running Oscillator Explained by Random Frequency Pulling

We show that the Lorentzian spectrum of a free-running LC oscillator arises from the random pulling of its frequency by circuit noise sources. To prove this, we analyze the oscillator's spectrum using Adler's differential equation, first in response to pulling by a single injected tone and then by two tones mirrored around the free-run frequency. A novel analysis predicts the frequencies and amplitudes of the sidebands caused by the phase modulation that results. Ultimately, we show that frequency pulling by white noise accounts for the Lorentzian broadening of the oscillator spectrum, and that a complete pulling analysis predicts the same linewidth as a simple circuit analysis.

Spectral measurement of the thermal excitation of a superconducting qubit

We report the measurement of the fluctuations of a transmon qubit through the noise spectrum of the microwave signal that measures its state. The amplitude of the Lorentzian noise power spectrum allows us to determine the average qubit excitation, in agreement with the estimated thermal radiation reaching the sample. Its width yields the qubit energy relaxation rate that decreases with temperature, contrary to the predictions for a two-level system solely coupled to thermal radiation. This indicates the existence of another non-radiative energy relaxation channel for the qubit.

Spectrally selective thermal radiation based on intersubband transitions and photonic crystals

We propose to use a combination of intersubband transitions in semiconductor quantum wells with a two dimensional photonic crystal cavity to obtain narrow, strong thermal radiation spectra. Single peak thermal radiation is obtained due to the Lorentzian shape absorption spectrum of the intersubband transition and the single mode cavity embedded within the photonic band gap. We present an analysis based on the quantum Langevin theory. It is shown that local radiance of the narrow emission peak can be maximized to approximately 80% of the radiation from the blackbody devices when the photon dissipation rates of the cavity mode due to the intersubband absorption and that due to the radiation to the free space modes are equal. Guidelines for concrete device design are introduced, and an example device structure is shown.

Studies of polar mesosphere summer echoes with the EISCAT VHF and UHF radars: Information contained in the spectral shape

The nature of PMSE in the VHF and UHF frequency range is considered taking into account the shape of corresponding Doppler spectra. Assuming a turbulence-based model of PMSE it is argued that for cases where a VHF radar detects strong PMSE, the UHF radar could either detect enhanced coherent scattering caused by the same physical process as in the VHF (i.e., turbulence with large charged ice particles), there could be incoherent scattering modified by the charged ice particles, or there could be a mixture of both. In order to distinguish these cases a simple but robust method is introduced to characterize the shape of the Doppler spectra derived from observations at both frequencies. Spectral shapes are quantified with one simple fitting parameter of a generalized fit to the autocorrelation function (=Fourier transform of the Doppler spectrum). This parameter takes a value of 1 for a Lorentzian spectrum indicative of pure incoherent scatter from the D-region, a value of 2 for coherent scatter owing to turbulence, and a value of less than 1 for incoherent scatter modified by the presence of charged aerosol particles. This method is applicable to observations at altitudes between ∼70 and ∼90 km. Simultaneous observations with the EISCAT VHF and UHF radar are presented in which all three cases mentioned above are identified. For the case of incoherent scatter modified by the presence of charged aerosol particles we quantify the radius of the involved ice particles to exceed ∼5 nm. Most importantly, however, for the case where the UHF-signal exceeded the incoherent scatter signal significantly, the spectrum revealed a clear Gaussian shape indicative of a coherent scattering process with identical spectral width as for the VHF-observations. This finding gives strong support that both echoes are created by the same turbulence-based mechanism and not by different mechanisms as speculated by several previous authors.

Inter-particle interaction induced by broadband radiation

The recent fabrication of optical traps using super-continuum light impresses the need for a theory of inter-particle interactions under such conditions. Development of the theory provides a basis for calculation of the observations expected under experimental conditions. An expression for the inter-particle potential energy induced by continuum states of light is first derived using quantum electrodynamics. This energy expression is cast as a function of the spectral irradiance of the light, and the electric susceptibility of the interacting particles. Specific results are derived for light with a Lorentzian spectrum. It is shown that by filtering part of the spectrum, it is possible to exert control over the length of linear particle chains organized along the Poynting vector. The results exhibit scope for the optical fabrication of moldable structures using broadband light.

Magnetic-Field Induced Crossover of Superconducting Percolation Regimes in the Layered Organic Mott Systemκ−(BEDT−TTF)2Cu[N(CN)2]Cl

Fluctuation spectroscopy is used to investigate the organic bandwidth-controlled Mott system kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. We find evidence for percolative-type superconductivity in the spatially inhomogeneous coexistence region of antiferromagnetic insulating and superconducting states. When the superconducting transition is driven by a magnetic field, percolation seems to be dominated by instable superconducting clusters upon approaching T(c)(B) from above, before a "classical" type of percolation is resumed at low fields, dominated by the fractional change of superconducting clusters. The 1/f noise is resolved into Lorentzian spectra in the crossover region, where the action of an individual fluctuator is enhanced, pointing to a mesoscopic phase separation.

Observations of polar mesospheric summer echoes using PFISR during the summer of 2007

The Poker Flat Incoherent Scatter Radar (PFISR) has been running nearly continuously throughout the summer of 2007, which permits an unprecedented, long-term study of polar mesospheric summer echoes (PMSE) at UHF. When not being used for other operations, PFISR runs in its International Polar Year (IPY) mode. 176 examples of PMSE have been identified in the IPY dataset during the summer of 2007 on 42 different days. IPY data were examined from March through mid-September. The first event was observed on May 27, and the last on August 10. During the four months from May 14 through September 14 the IPY mode was run 57% of the time and PMSE was detected 3.3% of the time the mode was running. Thirty-eight percent of the days with data during these four months had at least one PMSE event. Seventy-three percent of the events occurred during the daytime, and of the 48 events at night, 31 were accompanied by auroral precipitation. The events that did not occur with aurora show a strong correlation with solar zenith angle, which suggests a dependence on background ionization. Events were observed in range gates centered at 81.2 and 85.5 km, with 141 of the 176 events in the lower gate. The events have a mean duration of 19.6 min, but events lasting as long as 106 min have been observed. The events have a mean reflectivity of 1.3 × 10 - 17 m - 1 , which is a lower bound due to the possibility that the beam is not filled. A Lorentzian power spectrum was assumed to fit for the half-power half-width (HPHW) of the measured autocorrelation functions. The HPHWs which could be measured have a mean of 14.8 m/s, with a standard deviation of 11.1 m/s.

Analysis of electrical and optical fluctuations of light-emitting diodes by correlation method

A detailed analysis of electrical and optical uctuations of high power (3 W) light-emitting diodes (LEDs) is presented. A special attention was paid to the measurement and interpretation of simultaneous correlation coefcient between electrical and optical uctuations. The simultaneous correlation coefcient was measured not only over frequency range from 10 Hz to 20 kHz, but for the rst time in every one-octave frequency band. The presented technique not only permitted to determine the correlation coefcient dependence on frequency, but also to estimate what part to correlation coefcient is produced by low-frequency uctuations with 1=f , 1=f fi , and Lorentzian type spectra, respectively. From the obtained experimental and calculation results it is determined that the simultaneous correlated part of electrical and optical uctuations for these LEDs is related with the defect presence in the active layer or at its interfaces, while the uncorrelated part of electrical noise is caused by parallel leakage channel in other places, and the resistance of this channel is many times higher than that of pnn junction.

Impact of carbon concentration on 1∕f noise and random telegraph signal noise in SiGe:C heterojunction bipolar transistors

The influence of carbon concentration on the low-frequency noise (LF noise) of Si∕SiGe:C∕Si heterojunction bipolar transistors (HBTs) is investigated. When carbon is incorporated into these HBTs, representative noise spectra of the input current spectral density SIB show significant generation-recombination (GR) components. On the other hand, for transistors without carbon incorporation, no GR components were observed. When only 1∕f noise component is observed, the 1∕f noise level is found to be independent of the carbon concentration and the associated figure of merit of the normalized noise magnitude KB has a very good value of ∼4×10−10μm2. In order to relate the 1∕f noise and the high-frequency performance of the transistor, we studied and modeled the figure of merit defined as the ratio fc∕fT (fc is the low-frequency corner frequency and fT the unity current-gain frequency). Then we performed a detailed analysis of the GR components associated with the presence of the carbon. We found that the observed Lorentzian spectra are associated with random telegraph signal (RTS) noise. However, no RTS noise was measured in carbon-free devices. It is believed that the RTS noise is due to electrically active defects formed by the addition of carbon, typically observed for concentrations above the bulk solid solubility limit in silicon. The RTS amplitude (ΔIB) is found to scale with the base current, to decrease exponentially with temperature, and to be independent of the carbon concentration. The mean pulse widths (tH,tL) of the RTS are found to decrease rapidly with bias voltage, as 1∕exp(qVBE∕kT) or stronger. Our results confirm that electrically active C-related defects are located in the base-emitter junction, and the RTS amplitude is explained by a model based on voltage barrier height fluctuations across the base-emitter junction induced by trapped carriers in the space charge region. The observed bias dependence of mean pulse widths seems to indicate that two capture processes are involved, electron and hole capture. These C-related defects behave like recombination centers with deep energy levels rather than electron or hole traps involving trapping-detrapping processes.

Complexity in the high latitude HF radar spectral width boundary region

Abstract. SuperDARN radars are sensitive to the collective Doppler characteristics of decametre-scale irregularities in the high latitude ionosphere. The radars routinely observe a distinct transition from large spectral width (>100 m s−1) located at higher latitudes to low spectral width (<50 m s−1) located at lower latitudes. Because of its equatorward location, the TIGER Tasmanian radar is very sensitive to the detection of the spectral width boundary (SWB) in the nightside auroral ionosphere. An analysis of the line-of-sight velocities and 2-D beam-swinging vectors suggests the meso-scale (~100 km) convection is more erratic in the high spectral width region, but slower and more homogeneous in the low spectral width region. The radar autocorrelation functions are better modelled using Lorentzian Doppler spectra in the high spectral width region, and Gaussian Doppler spectra in the low spectral width region. However, paradoxically, Gaussian Doppler spectra are associated with the largest spectral widths. Application of the Burg maximum entropy method suggests the occurrence of double-peaked Doppler spectra is greater in the high spectral width region, implying the small-scale (~10 km) velocity fluctuations are more intense above the SWB. These observations combined with collective wave scattering theory imply there is a transition from a fast flowing, turbulent plasma with a correlation length of velocity fluctuations less than the scattering wavelength, to a slower moving plasma with a correlation length greater than the scattering wavelength. Peak scaling and structure function analysis of fluctuations in the SWB itself reveals approximately scale-free behaviour across temporal scales of ~10 s to ~34 min. Preliminary scaling exponents for these fluctuations, αGSF=0.18±0.02 and αGSF=0.09±0.01, are even smaller than that expected for MHD turbulence.

Line Shape Distortion in a Nonlinear Auto-Oscillator Near Generation Threshold: Application to Spin-Torque Nano-Oscillators

The power spectrum of an auto-oscillator with a large frequency nonlinearity in a noisy environment is calculated. The power spectrum becomes strongly non-Lorentzian, broadened, and asymmetric near the generation threshold. A Lorentzian spectrum is recovered far below and far above the threshold, which suggests that line shape distortions provide a signature of the threshold. We show that the developed theory adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.

Quasiparticle Lifetime and Noise in Tantalum High Q Superconducting Resonators

We present measurements of the quasiparticle lifetime using optical pulses in the temperature range of 50 mK–1 K as well as measurements of the noise spectrum under continuous illumination in planar tantalum resonators. When decreasing the temperature the quasiparticle lifetime increases until it enters a saturation regime, reaching lifetime values of up to 35 μs at around 650 mK which decrease to a value of around 25 μs below a temperature of 350 mK. The noise spectrum follows a single pole Lorentzian spectrum, indicating that the quasiparticle lifetime is the only relevant timescale.

Dynamic structures of the time correlation functions of chaotic nonequilibrium fluctuations

Using the projection operator formalism we explore the decay form of the time correlation function U_(n)(t) identical with < û_(n)(t)û*_(n)(0)> of the state variable û_(n)(t) in the chaotic Kuramoto-Sivashinsky equation. The decay form turns out to be the algebraic decay 1/[1+(gamma_(na)(t)2] in the initial regime t<1/gamma_(ne) and the exponential decay exp(-gamma_(ne)t) in the final regime t>1/gamma_(ne) . The memory function Gamma_(n)(t) that represents the chaos-induced transport is found to obey the Gaussian decay exp[-(beta_(ng)t)2] in the case of large wave numbers, but the 3/2 power decay exp[-(beta_(n3)t)3/2] in the case of small wave numbers. The power spectrum of û_(n)(t) is given by the real part U'_(n)(omega) of the Fourier-Laplace transform of U_(n)(t) and has a dominant peak at omega=0 . This peak within the linewidth (-)gamma_(ne) (approximately equal to gamma_(ne)) is given by the Lorentzian spectrum (-)gamma2_(ne)/(omega2+(-)gamma2_(ne)) . However, the wings of the peak outside the width (-) gamma_(ne) turn out to take the exponential spectrum exp(-omega/gamma_(na)) . Thus it is found that the exponential decay exp(-gamma_(ne)t) appears to lead to the universal Lorentzian peak, while the algebraic decay 1/[1+(gamma_(na)t)2] arises to bring about the exponential wing.