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Hysteresis is treated as a history dependent branching, and the use of the classical Preisach model for the analysis of macroeconomic hysteresis is first discussed. Then, a new Preisach-type model is introduced as a macroeconomic aggregation of more realistic microeconomic hysteresis than in the case of the classical Preisach model. It is demonstrated that this model is endowed with a more general mechanism of branching and may account for the continuous evolution of the economy and its effect on hysteresis. Furthermore, it is shown that the sluggishness of economic recovery is an intrinsic manifestation of hysteresis branching.

A new hysteresis-based technique for random number generation is presented which can be efficiently implemented by using modern spintronics based nano-technology. Thermal fluctuation induced random switchings of rectangular hysteresis loops are utilized whose outputs result in the generation of random binary numbers. Mathematically, the random switching is treated as a repeated sequence of two exit problems for stationary stochastic processes, which are shown to be reduced to the solution of initial boundary value problems for the appropriate backward Kolmogorov equations. Analytical solution of these boundary value problems are carried out for the stationary Gaussian Markov Ornstein-Uhlenbeck process. An alternative approach to the analysis of the random switching based on stochastic processes on graphs is also discussed with special attention paid to the trade-offs between the strength of thermal noise and the widths of the hysteresis loops.

A novel rectangular shape differential CMOS split-drain Hall Effect magnetic field-effect transistor (MAGFET) was designed and fabricated employing a CMOS 0.5 μm process. The detection and monitoring of single 2.8 μm diameter magnetic beads was successfully performed using this MAGFET design. Based on the device modeling, simulation and the signal to noise ratio analysis, it was found that the optimal sensitivity can be achieved when the MAGFET channel width to length ratio is equal to 1.3. Further, it is shown through that when the MAGFET is scaled down, its SNR performance can sustain its peak, while being more sensitive to the geometry variations.

A novel circular CMOS MAGFET (Magnetic Field Effect Transistor) design is introduced and a novel device geometry design methodology is proposed to optimize the magnetic particle detection sensitivity of such devices. In order to optimize the signal to noise ratio, it was determined that the geometry of the MAGFET is required to have specific ratios, where its sector angle θ and its inner and outer radii r1 and r2 are optimized when θ/ln(r2/r1) = 1.3 . Compared to the more traditional rectangular MAGFET, the circular MAGFET has compatible SNR peak performance with rectangular MAGET. However, when the size of the MAGFET is scaled down in order to detect smaller magnetic particles, the proposed circular MAGFET has more robust SNR performance, design flexibility and tolerance to processing variations.

A new model to semiconductor device electronic noise is presented in the framework of semiclassical transport theory. The salient feature of this model is that it connects the current noise characteristics directly to the physics of scattering of the semiclassical transport theory and makes no additional assumption regarding the nature of noise. Employing this approach, this work investigates the spatial origin of the current noise across two semiconductor structures. In this approach the terminal current noise is directly related to carrier scattering inside the device, which is accounted for in the Boltzmann transport equation (BTE), without the need to add Langevin noise terms to the calculations. Accordingly, it utilizes the well-established spherical harmonics expansion (SHE) technique to solve the BTE, and it combines analytical and numerical methods, in contrast with the Monte Carlo (MC) approach that employs ensemble averages of randomly generated events. The model leads to the solution of a time-dependent transient solution of the BTE with special initial and Ohmic boundary conditions that is solved in the frequency domain to directly compute the terminal current noise spectral density. It is also shown that with this approach the Nyquist theorem under thermal equilibrium conditions is recovered.

A special measurement system is developed to measure the combined noise and reliability of a three-axis micro-accelerometer. Three parametric tests are provided: gravitational, thermal and acoustical. The measurements were performed on both the in-plane and the out-of-plane axes. The temperature-dependence and acceleration-dependence of the noise was found, in agreement and contrast to the theories. The device is found to be very reliable when subjected to individual tests, but exhibits slight deviations during the combined tests.

In this work, a noise measurement of capacitive micro-accelerometers incorporating temperature effect is presented. In the setup, a hot plate is used to heat the device up to temperatures in the 75 degree C range. A thermo couple attached to the enclosure is used to assess its temperature. The data show that the noise power increases at high temperature, but not as significant as predicted by the theory.

Noise measurements of micro-accelerometers were performed using a special measurement system. A common spectral behavior of noise is found, with 1/f noise dominating at low frequencies and white thermal noise being the limiting factor at higher frequencies. Unexpected resonances are also observed in the commercial devices. Most importantly, an acceleration dependent of the noise is found in analog devices and freescale accelerometers, in contrast to prevailing theory.

The operation of a nonlinear binary detector with hysteresis is investigated. Prior models developed for continuous time inputs are extended for the computationally more efficient discrete-time inputs. The input to the rectangular hysteresis detector is modeled to be a binary signal in the presence of additive independent identically distributed noise. The rectangular hysteresis loop models one of a number of rate independent repeaters in an optical communication link. The link is terminated by a binary discriminator that is tuned to a particular bit duration. The study shows that key calculations to compute the bit error probability can be performed by employing the formalism of discrete Markov chains.

Processes of origin and relaxation of fluctuations of the conduction electrons’ distribution function in space-homogenous and non-degenerate thermal equilibrium semiconductors are discussed. It is shown that in low-frequency region the Fourier-component of the long-wavelength electrons and phonons distribution function's fluctuating component is directly proportional to ω - 1 / 2 . It is shown that electron energy and/or quasi-momentum fluctuations may contain the Schonfeld pulse and that the Schonfeld model can directly be incorporated into physical model describing 1 / f -type noise formation in semiconductors. It is suggested that the concept of “Thermal Equilibrium Semiconductor” can be reconsidered when one studies fluctuation phenomena, in particular 1 / f -noise. It is demonstrated that the electron–phonon system always stays in non-equilibrium condition from point of view of the fluctuation theory.

Microelectromechanical systems (MEMS) are devices that have static or movable components with dimensions on the scale of a micrometer. One particular device that is widely used commercially is the MEMS accelerometer. Such accelerometers typically contain some movable micro beams that measure acceleration in one or two orthogonal directions. Major markets for MEMS accelerometers are automobile airbag triggers, earthquake detection circuits and health care. MEMS accelerometers have advantages over conventional accelerometers because they are smaller, lighter and cheaper. Since MEMS accelerometers are used in many systems, the noise characteristics of these devices are very important. The noise characteristics will influence the performance of the accelerometers especially when operating at lower g conditions. In this work, we report on the noise characteristics and special measurement techniques for Analog Devices ADXL202, ADXL 105 and ADXL 190 accelerometers.

A binary detector with hysteresis-type nonlinearity is investigated. The detector is proposed as a suboptimal solution for a bit rate transparent midspan repeater in all optical networks. It is shown that key computations for the bit error rate are reduced to the well-known "exit problem" of stochastic differential equation theory. This formalism is employed to derive closed form expressions in the transform domain for the probability density function of the detector output in the presence of additive noise. Applying inverse transformations, these expressions can be utilized to determine various performance measures of binary detectors with hysteresis.

A nonlinear filter with hysteresis is presented to detect binary signals. It is shown that key calculations for the bit error rate are reduced to the “exit problem” of stochastic differential equation theory. Employing this formalism, closed form expressions are derived in the transform domain for the probability density function of the filter output in the presence of additive white Gaussian noise. By taking inverse transformations, such expressions can be used to compute several performance measures of binary detectors with hysteresis nonlinearity.

Preisach-based aftereffect models are employed to define the ground state of a magnetic system. Four different types of processes due to thermal perturbations, AC demagnetization, Curie point demagnetization and DC demagnetization are reviewed and compared with each other. By modeling the time evolution of the magnetization and magnetic field on the Preisach plane, it is shown that the asymptotic state of the system due to thermal perturbations is the true magnetic ground state.

The sigmoidal decay of the magnetization in log time, which is geometrically similar to the major loop, starts at the major loop and decays to the anhysteretic magnetization for a given holding field. The linear displacement of these curves after normalization with holding field can be used to compute the fluctuation field. This paper discusses the errors in computing this field.

Numerical simulation results for the spectral density of noise due to current fluctuations are presented. The mathematical framework is based on the interpretation of the equations describing electron transport in the semiclassical transport model as stochastic differential equations (SDE). Within this framework, it was previously shown that the autocovariance function of current fluctuations can be obtained from the transient solution of the Boltzmann transport equation (BTE) with special initial conditions. The key aspect which differentiates this approach from other noise models is that this approach directly connects noise characteristics with the physics of scattering in the semiclassical transport model and makes no additional assumptions regarding the nature of noise. The solution of the BTE is based on the Legendre polynomial method. A numerical algorithm is presented for the solution of the transient BTE. Numerical results are in good agreement with Monte Carlo noise simulations for the spectral density of current fluctuations in bulk silicon.

The article reviews a novel approach to the modeling of after-effect phenomena in hysteretic systems. The after-effect model is based on Preisach-type models driven by stochastic inputs. Random thermal perturbations which result in the gradual loss of memory in hysteretic systems are modeled by discrete and continuous-time stochastic processes. The important properties of the after-effect model are summarized and compared with the traditional thermal activation-type models and with some known experimental facts.

We have demonstrated flexible packaging and integration of CMOS IC chips with PDMS microfluidics. Microfluidic channels are used to deliver both liquid samples and liquid metals to the CMOS die. The liquid metals are used to realize electrical interconnects to the CMOS chip. As a demonstration we integrated a CMOS magnetic sensor die and matched PDMS microfluidic channels in a flexible package. The packaged system is fully functional under 3cm bending radius. The flexible integration of CMOS ICs with microfluidics enables previously unavailable flexible CMOS electronic systems with fluidic manipulation capabilities, which hold great potential for wearable health monitoring, point-of-care diagnostics and environmental sensing.

The paper describes an approach to semiconductor noise analysis that is entirely within the framework of the semiclassical transport theory. The key aspect that differentiates this approach from other noise models is that this approach directly connects noise characteristics with the physics of scattering in the semiclassical transport model and makes no additional assumptions regarding the nature of noise. Employing the machinery of stochastic differential equation theory, a method is developed to compute the autocovariance function and spectral density of current fluctuations from the solutions of the Boltzmann transport equation (BTE). As a result, current fluctuations due to scattering are directly accounted for without the usual ad hoc addition of the "Langevin source term" to the transport equation. Simulation results are presented for the noise spectral density and autocovariance functions in silicon due to elastic-acoustic and optical-phonon scattering. The autocovariance and spectral density are computed in bulk silicon for different electric fields and temperatures based on the space-independent solutions of the BTE. In the practical case of Ohmic contacts, an explicit expression for the current noise spectral density is derived in terms of the scattering transition rate, the steady-state distribution function, and the average current density.

This review article summarizes our work during the past five years on a new approach to the modeling of aftereffect phenomena in hysteretic systems, This approach is based on Preisach type models driven by stochastic inputs. Both the classical and nonlinear Preisach models are employed in this approach. Thermal perturbations which result in the gradual loss of memory in hysteretic systems are modeled by discrete and continuous time stochastic inputs. The important properties of the aftereffect model are highlighted and compared with the traditional thermal activation type models and with some known experimental facts.

Our implementation of a fixed-point iteration technique for the three-dimensional (3D) steady-state simulation of MOSFET devices is presented. The simulation program is employed to investigate narrow channel effects on the device current-voltage characteristics. Particularly, the effects of impact ionization and the effects of variations in channel width and the field oxide bird's beak angle are evaluated. The degree to which various field oxide configurations isolate the device from the gate contact over the oxide transition region is determined by comparing the current-voltage characteristics with those of an idealized device with perfect isolation. Perfect isolation is simulated by setting the normal component of the electric field to zero at the semiconductor-field oxide interface. Simulation results show that the 3D computations are essential to account for rapidly varying charge densities and generation rates near the channel edge. Moreover, it is observed that the isolation effects of field oxides increase for larger bird's beak angles.

This paper presents a new approach to model hysteresis and aftereffect phenomena. A dynamic approximation of rectangular hysteresis loops is employed that leads to the representation of the input-output relationship as a first-order dynamical system driven by white noise. Closed-form expressions are derived for the output of rectangular loops in terms of convolution-type integrals. The formalism allows one to circumvent some of the mathematical challenges associated with history-dependent switching of rectangular hysteresis loops driven by stochastic processes.

We present a numerical technique which employs a local-in-time initial guess for the transient simulation of SOI MOSFETs. Specifically, the goal of this work is to compute the transient drain current which exhibits overshoot. A critical factor in such computations is the choice of the initial guess at each time point after the gate ramp. Our numerical simulations have shown that the use of the previous time point solution as an initial guess in the Gummel iterations fails to predict the decay in the drain current from its maximum overshoot value. This difficulty is circumvented when the steady-state solution is used as a local-in-time initial guess. We use the diagonally implicit Runge-Kutta method for the time domain discretization. A fixed-point iteration technique is employed for the space domain iterations. To demonstrate the usefulness of the local-in-time method, numerical results of the transient drain current for various device parameters, such as the silicon film doping, silicon film thickness and back-gate bias are presented.

This paper presents a new parallel-in-time algorithm for the two dimensional transient simulation of SOI devices. With this approach, simulation in both space and time domains is performed in parallel As a result, the CPU time is reduced significantly from the conventional serial-in-time method. This new approach fully exploits the inherent parallelism of the finite difference formulation of the basic semiconductor device equations and the massively parallel architecture of SIMD computers. The space domain computations are inherently parallel due to the nature of our technique of solving the finite-difference equations. Time domain parallelism is achieved by shifting the potentials from previous time points to subsequent points one-step forward along the time axis with each Gummel iteration. This algorithm employs a fixed-point iteration technique, therefore a direct solution of matrix equations is avoided. The algorithm is especially suitable for the transient simulation of SOI devices that exhibit transient drain current overshoot. Numerical experiments show that the new parallel-in-time method is up to eight times faster than the conventional serial-in-time method in SOI transient simulations. The program is coded in CM Fortran for the Connection Machine. >

We present an efficient method to compute the maximum transient drain current overshoot in silicon‐on‐insulator metal‐oxide‐silicon field effect transistors. The method is based on the physical idea that the number of majority carriers remains unchanged immediately after a change in the applied gate bias. The maximum overshoot is computed by solving the Poisson and the stationary minority carrier transport equations under the constraint that the number of majority carriers is conserved. Hence, the novel aspect of the method is that it allows one to compute the maximum drain current overshoot without resorting to a computationally costly transient simulation. The accuracy of the method is verified by comparing the value of the drain current computed by this method with the maximum value of the drain current computed by transient simulations. The comparisons show that, with this method, the maximum transient drain current overshoot can be computed quite accurately for fast changes in the gate bias.

The development of a shear horizontal surface acoustic wave (SH-SAW) liquid sensor with identification (ID) for wireless applications is described. Moreover, a novel feature of "write capability" for this sensor is proposed. The SH-SAW passive sensor has a delay line configuration with a sensing area. The sensor is fabricated on a lithium tantalate (LiTa03) substrate, which is Y-cut with rotations specified between about 36° around the X-axis. The principle of detection is based on the attenuation and time delay between the signals. The sensor is encoded according to partial reflections of an interrogation signal by metal reflectors placed on both side of the interdigital transducers (IDT). The structure of the sensor, the principle of the wireless communication, the detection process and testing results are presented.

Preisach models driven by stochastic inputs are employed to model magnetic aftereffect in the presence of demagnetizing fields. As a result of thermal relaxation, the magnetization and, consequently, the demagnetizing field vary in time. The new model generalizes earlier work and self-consistently accounts for the effect of time varying demagnetizing fields on the relaxation process. Three practical numerical techniques are proposed to compute the time variation in the magnetic field and the state of the Preisach plane.

MEMS accelerometers are extensively employed in various consumer applications due to their rapidly decreasing costs. In order to meet the low-cost requirements, manufacturers are forced to sacrifice some design parameters that may degrade their accelerometers' reliabilities. Interestingly, there is not much published works on the reliability aspects of MEMS accelerometers. Two reports detailed the reliability qualitative assessment on commercial devices [1–2]. Both works concluded that MEMS accelerometers are high reliable devices with low failure rates. In a recent study [3], a procedure to perform the quantitative accelerated life testing (QALT) on tri-axis accelerometer from STM was proposed, with a crude setup to vary the accelerations and temperatures. The purpose of this paper is to employ the QALT procedure on single axis accelerometers from Analog Device and Freescale. Laser-precision apparatus was designed, built, and employed to provide three types of excitations with great accuracy; mechanical (gravitational) test, thermal test and acoustical test. These tests are designed to mimic the operating conditions of the system, where the devices are employed.

Performance of an electronic system can be greatly limited by its internal noise and can be employed as a measure to characterize the effectiveness of such systems. As a result, it is important to investigate electronic noise in semiconductor devices. Electronic noise is due to random events that take place inside electrical devices and the theoretical interpretation of these stochastic events is very important in order to accurately match a noise model to the observed results in experimental studies [1].

The viscosity phenomenon in hysteretic systems has been traditionally studied by using thermal activation‐type models. In this paper, a new approach to viscosity modeling is explored. This approach is based upon the use of the Preisach hysteresis models driven by stochastic inputs. First, the scalar case is discussed, and the obtained results are compared with thermal activation‐type models and with some known experimental facts. The paper is concluded by the discussion of the vector models for viscosity.

This article presents experimental evidence for scaling and data collapse in magnetic viscosity. It is demonstrated that, by using appropriate scaling, the “bell-shaped” viscosity coefficient curves observed for different temperatures collapse onto one universal curve. This data collapse reveals a self-similar structure of the viscosity coefficient as a function of two variables: magnetic field and temperature.

An iterative method for solving the discretized steady‐state semiconductor device equations is presented. This method uses Gummel’s block iteration technique to decouple the nonlinear Poisson and electron‐hole current continuity equations. However, the main feature of this method is that it takes advantage of the diagonal nonlinearity of the discretized equations, and solves each equation iteratively by using the nonlinear Jacobi method. Using the fact that the diagonal nonlinearities are monotonically increasing functions, it is shown that this method has two important advantages. First, it has global convergence, i.e., convergence is guaranteed for any initial guess. Second, the solution of simultaneous algebraic equations is avoided by updating the value of the electrostatic and quasi‐Fermi potentials at each mesh point by means of explicit formulae. This allows the implementation of this method on computers with small random access memories, such as personal computers, and also makes it very attractiv...

Simulation results are presented for a MOSFET with position- and energy- (potential-) dependent interface trap distributions that may be typical for devices subjected to interface-trap-producing processes such as hot-electron degradation. The interface-trap distribution is modeled as a Gaussian peak at a given position along the channel, and the energy dependence is derived from C-V measurements from an MOS capacitor exposed to ionizing radiation. A novel fixed-point technique is used to solve the two-dimensional boundary-value problem. The technique is shown to be globally convergent for arbitrary distributions of interface traps. A comparison of the convergence properties of the Newton and fixed-point methods is presented, and it is shown that for some important cases the Newton technique fails to converge while the fixed-point technique converges with a geometric convergence rate. >

The authors performed the low frequency noise measurement (LFNM) technique to study noise characteristics of commercial accelerometers with single and dual axis. In this work, we studied the noise characteristics of a three-axis accelerometer using an improved and sensitive test setup to avoid cross-axis distortion.

In this paper we show an approach to couple two stochastic processes to describe the dynamics of independent carriers in semiconductor devices: the launch time of carriers from the contacts is described by independent Poisson launch processes, and the stochastic motion of carriers due to scattering inside the device is described by inhomogeneous Poisson type Markov processes according to the semiclassical transport theory. The coupling of the Poisson type stochastic launch process to the semiclassical dynamics will be shown, and the resulting Ohmic contact boundary conditions will be derived. For proof of concept, an expression for the autocovariance for terminal current noise for one point contact will be shown which can be easily extended to a real semiconductor device with multiple contacts.

Investigations of the static characteristics, responsivity, internal noises, and detectivity of the forward biased p-i-n photodetectors made on wide bandgap compensated semiconductors operating in double injection regime are presented. Noise related calculations are performed by utilizing "Impedance Field Method". Numerical simulations are made assessing 4H-SiC and GaN biased p-i-n photodiodes noise related characteristics. It is shown that forward biased p-i-n photodiodes have low level of thermal and generation-recombination noises and high values of sensitivity and detectivity at the room temperature.

Recently, several aftereffect models were proposed in which Preisach type hysteresis transducers are driven by stochastic inputs. Such inputs represent random thermal perturbations which are the source of the aftereffect phenomenon. According to these models, aftereffect is completely characterized by the magnetization history, the Preisach function and noise parameters. In this article, we present an identification of model parameters in which temperature-dependence is incorporated into the aftereffect model. The temperature variation of the noise parameters are investigated in order to predict the aftereffect decay coefficient. Comparison of numerical results with experimental ones observed in metal particle tape (MPT) magnetic recording media show a good agreement. As a result, based on the magnetization history, the Preisach function and noise parameters, it is shown that the model can be used to predict aftereffect characteristics of magnetic recording media of arbitrary magnetization history and temperature.

The design of CMOS compatible thin ZnO film base, and LiNbO/sub 3/ wafer base, surface acoustics wave (SAW) gas sensors, that are highly selective and sensitive, is described. Furthermore, design and post-CMOS processing fabrication steps that utilises micro-electro-mechanical systems (MEMS) techniques to implement the SAW gas sensor are presented. The Rayleigh wave velocity for various ZnO film thicknesses is simulated and results are presented. The velocity calculation is based on a computer simulation of a multilayer (ZnO/SiO/sub 2//Si) structure that uses wave equations. Simulation results and experimental measurements of SAW sensors with a single layer bulk LiNbO/sub 3/ wafer are shown, and compared. Moreover, results of experimentation and simulation of wave velocity for a yz-cut LiNbO/sub 3/ wafer are shown.

ZnO, a well-known piezoelectric material, is used to develop micro-scale surface acoustic wave (SAW) delay line sensor. In this work, SAW delay line sensors are fabricated employing ZnO films that are deposited by RF sputtering technique. Films are characterized prior to device fabrication by X-ray diffraction (XRD) for film crystalline quality, UV-visible transmission spectroscopy for optical characteristics, and atomic force microscopy (AFM) for surface morphology. Interdigital electrodes producing surface acoustic waves in the hundreds of MHz are developed by photolithography and metallization techniques. SAW delay line sensor device testing, measurement and characteristics on RF sputtered ZnO films are presented and compared.

This chapter investigates a binary detector with hysteresis-type nonlinearity and derives closed-form expressions in the Laplace transform domain for probability density functions that are necessary to compute bit error rates and probability of error. Naturally, in a typical communication system there are several other important issues related to system performance, such as jitter and clock recovery. In this discussion the system is considered to have perfect synchronization between the detector and the noisy input data. Therefore, it is assumed that there is no performance degradation in the receiver because of errors in the timing of bit intervals. The machinery of the “exit problem” and the associated techniques presented in the chapter may be very useful in determining jitter error, hence, overall system performance. Hysteresis is present in many engineering and scientific problems. Therefore, it is expected that the mathematical framework presented in this work may form the basis for several future directions of research and not simply be limited to the application of bit-rate transparent detection in optical-network links.

Previously, several aftereffect models were proposed in which Preisach type hysteresis transducers are driven by stochastic inputs. Such inputs model random thermal perturbations which are the source of aftereffect phenomena. In this article, we compare experimental and numerical simulation results for the first time in order to verify the proposed models, and present an identification procedure to determine aftereffect model parameters. Numerical simulations of the aftereffect model show the well known log t-type decay in magnetization whose rate reaches a maximum near the coercive field. Comparison of these with experimental results from /spl gamma/-Fe/sub 2/O/sub 3/ recording media show excellent agreement. Based on this comparison, we propose a practical procedure to identify the stochastic parameters of the aftereffect model.

In this paper we describe the design and implementation of a CMOS surface acoustic wave (SAW) oscillator. The oscillator utilizes surface acoustic wave resonators implemented in both 1.6micron and 0.5micron AMI CMOS process and fabricated through MOSIS. When connected to Pierce oscillator circuits, these resonators are capable of synthesizing frequencies in the range of 400MHz to 1GHz. This paper also addresses the design issues involving codesigning micromachined resonators with CMOS circuitry to optimize the oscillator design

The switching characteristics of ultra-thin SOI CMOS inverters with hot-carrier-induced degradations are examined by using device simulations. The simulator employs a robust fixed-point iteration method to avoid conventional matrix solutions. Potential-dependent interface traps and oxide trapped charges are used to model the degradations. The effects of front and back channel degradations in an nMOS device of a CMOS inverter are investigated in steady-state and transient regimes. The nonlinear variation of interface charges cannot be simulated by using a single nMOS device alone since the transition of the inverter is also determined by the pMOS transistor. It is found that the stagnant holes generated by impact ionization have a much greater effect on the rate of the pull-down transient than that of interface charges.

Process of the origin and relaxation of the fluctuation of distribution function of conduction electrons in space-homogenous and non-degenerate equilibrium semiconductors is discussed. The fluctuations of electron distribution function, formed as result of the internal fluctuations of the phonon system, are studied. The physical mechanisms of the origin and following slow (diffusion) damping of the equilibrium fluctuations of the electron and phonon distribution functions are represented. It is shown that in low frequency region the Fourier-component of distribution function fluctuations of predominantly long wavelength electrons and phonons are depends on frequency by law ω -1/2 .

Previously, it has been shown that Preisach type models driven by stochastic inputs can be employed to model aftereffect. In this model, the machinery of the "exit problem" is instrumental in computing the time evolutions of the expected value and the distributions of switching times. Here, for the first time, we present numerical simulation results of the aforementioned viscosity models and demonstrate that these models can be employed to compute switching times and time evolutions of the expected value of magnetization.

The development of inexpensive and miniaturized SAW gas sensors that are highly selective and sensitive is introduced. These sensors are implemented with micro-electro-mechanical systems (MEMS) in CMOS technology. Since the sensors are fabricated on a silicon substrate, additional signal processing circuitry can easily be integrated into the chip thereby readily providing functions such as multiplexing and analog-to-digital conversion that are needed for integration into a network.

The two main causes of origin of the mobility fluctuation of the electrons in homogeneous, unlimited, and non-degenerated semiconductors are discussed. It is shown that the mobility fluctuation is conditioned by the symmetric component of the fluctuation of the distribution function, i.e. by the fluctuations of the conduction electrons energy. On the base of the developed quasi-classical model the spectrum of electrons lattice mobility fluctuations is calculated. In the frequency wide variation range it has 1/f form.