Exponential Ramp Research Articles

Shrinkage stress in light-cured composite resins: Influence of material and photoactivation mode

Objectives The aim of this study was to record the effect of composite type and photoactivation mode on the stresses resulting from polymerization of five established composite resins: packable (Solitaire, Solitaire 2), micro-hybrid (Aelitefil, Z100) and hybrid (Clearfil AP-X). Methods A mechanical testing machine was used to record the polymerization contraction stress (MPa) of cylindrical composite specimens ( d = 5 mm; h = 2 mm; C-factor = 1.25) at 0.1 s intervals over a period of 400 s. The samples were photopolymerized using a halogen light curing device under two types of light exposure: group 1, Standard (800 mW·cm −2 × 60 s); group 2, Exponential (logarithmic increase from 150 to 800 mW·cm −2 over 15 s + 800 mW·cm −2 × 45 s). The stress rate (SR: slope MPa>0–60 s ) and the maximum shrinkage stress (MSS: MPa 400 s ) of each material (five replications) were statistically analysed by one-way ANOVA/Scheffe's test and Pearson's correlation procedure ( α = 0.05). Finally, Student's t-test (two matched series) enabled the assessment of the effect of the irradiation method on the results. Results For group 1, in decreasing order, the MSS was 1.51 ± 0.07 MPa (Solitaire) statistically equivalent to 1.45 ± 0.06 MPa (Aelitefil), 1.29 ± 0.08 MPa (Solitaire 2), and 1.04 ± 0.03 MPa (Z100) statistically equivalent to 0.92 ± 0.05 MPa (Clearfil AP-X). Z100 showed the highest SR (0.045 ± 6 × 10 −3) and Solitaire, the lowest (0.017 ± 2 × 10 −3). There was no correlation between SR and MSS ( r < −0.33, p < 0.05). For group 2, the MSS and SR values were distributed in a similar way to those from group 1. There was a negative correlation between SR and MSS ( r < −0.43 and p < 0.01). The exponential ramp successfully reduced the MSS (−3.9%) and SR (−11%) values. Significance There is no relationship between composite resin type, stress rate and shrinkage stress levels. The slower stress rate development, resulting from ramped light intensity, helped slightly to reduce the maximum polymerization stress.

The Scanning DMA Transfer Function

The scanning differential mobility analyzer (DMA) has been widely employed for measurement of rapidly evolving aerosol size distributions. Interpretation of data from scanning DMAs is greatly facilitated when an exponential voltage ramp is prescribed, since the shape of the instrumental transfer function remains constant throughout a scan. However, that transfer function may differ significantly from that expected for fixed voltage operation. Because no simple analytical description of the scanning DMA transfer function exists, it has been evaluated numerically by simulating particle trajectories within a TSI 3081 cylindrical DMA. These computations yield transfer functions for the DMA up scan that are roughly triangular but with widths significantly greater than those for fixed voltage operation, and transfer functions for the down scan that are highly asymmetric. The impact of these distortions is most obvious when the size distribution of the measured aerosol is narrow, but errors in recovered size and concentration can be significant even when the aerosol size distribution is much broader than the transfer function. The magnitude of these errors is dependent upon the ratio of the mean gas residence time to the exponential voltage time constant, the sheath-to-aerosol-flow ratio, and the technique used to determine the instrument plumbing time. Experimental results for scans across broad and narrow size distributions compare favorably with predictions based on the simulated transfer functions. Simplified corrections are provided that can be used to adjust the concentration and mobility of size distributions recovered using a fixed voltage transfer function.

An introduction to fast wafer level reliability monitoring for integrated circuit mass production

The continuous verification of process reliability is essential to semiconductor manufacturing. The tool that accomplishes this task in the required short time is the fast wafer level reliability monitoring (fWLR). The basic approaches for this task are described in this introductory overview. It summarizes sampling plans, discusses the feasibility of using fWLR for screening and describes the data assessment and application of control cards. Beyond these general topics many of the fWLR stress methods are described in detail: Dielectric stressing by means of an exponential current ramp is compared to ramped voltage stress. Especially for thin oxides the methods differ regarding the soft breakdown detection and the time they consume. Another task of fWLR is the detection of plasma induced damage, which can be achieved by applying a revealing stress to MOSFETs with antenna. The design challenges of the structures and the test method as well as the data assessment are described in detail. An important section deals with fWLR for interconnects. In this section the appropriate test structures (including thermal simulations) are illustrated and fast electromigration stresses are discussed and the details of standard wafer level electromigration accelerated test (SWEAT) are included. For contacts and vias a simple method to check reliability is presented. Finally the monitoring of device reliability is treated. It is shown that using indirect parameters that correlate well to standard parameters such as the drain current can be beneficial for fWLR. For both, the interconnects and the devices, it is essential to have locally heated test structures in order to keep the stress time low. The detection and verification of mobile ions can also be performed with such a self-heated structure. For the described methods examples are given to illustrate the usefulness.

Perception of duration of ramped and damped sounds with exponential and raised cosine ramps

In the first experiment listeners were asked to adjust the duration of a steady-level sound in order to match the duration of 250-, 500-, 750-, or 1000-ms targets. Targets could be either steady in level, increasing in level with either a raised-cosine or an exponential ramp (ramped sounds), or the ramped sounds reversed in time (damped sounds). The results extended to longer durations than those reported by Schlauch et al. [J. Acoust. Soc. Am. 109, 2880–2887 (2001)]: damped sounds were matched as much shorter (∼35% for exponential ramps, ∼30% for raised-cosine ramps) and ramped sounds as slightly shorter (∼10%) than steady-level sounds. In the second experiment, the subjective duration of all targets used in the first experiment was measured as the difference between reaction times to their onsets and their offsets. Although delays in reaction times to onsets of ramped targets could explain their slight underestimation, anticipations to offsets of damped targets were too small to explain their underestimation. The results of the research contradict the predictions of the AIM model [R. D. Patterson and T. Irino, J. Acoust. Soc. Am. 104, 2967–2979 (1998)], where ramped and damped sounds longer than 200 ms should be perceived as possessing similar subjective durations.

Effects of head field pulse shape and rise time on subnanosecond magnetization reversal in longitudinal thin film media

Micromagnetic simulations of planar isotropic magnetic thin film recording media are performed to study initial magnetization reversal processes in response to pulses with linear and exponential ramps. Linear ramps lead to smaller zero-crossing times T0 than exponential ramps due to the more rapid field increase during the pulse ramps. It is shown that T0 increases substantially when the pulse amplitude is less than about half the anisotropy field, in which case pulse overshoots are effective to reduce T0. In addition, the effects of exchange coupling and gyromagnetic damping are examined.

A new algorithm for transforming exponential current ramp breakdown distributions into constant current TDDB space, and the implications for gate oxide QBD measurement methods

Abstract Charge-to-breakdown (QBD) is one of the manufacturing parameters that is used as a measure of oxide quality. In this work the influence of the measurement conditions on QBD is examined, as well as the relationship between QBD and oxide thickness. Using oxides ranging from 45 to 80 A, two QBD measurement methods are employed: constant current stress (CCS) and an exponential current ramp (ECR). A variety of current densities (for the constant current stress) and step durations (for the exponential current ramp) are studied. It is shown that not only does QBD depend on oxide thickness, but that QBD depends strongly on the measurement conditions, and that, depending on the test conditions, QBD can increase or decrease as the oxide thickness decreases. It is also shown that there is a strong agreement between the QBD measured with a constant current stress and the QBD measured with an exponential current ramp. Finally, an algorithm is proposed for transforming the QBD distribution obtained from a series of exponential current ramps into the QBD and/or tBD domains of constant current stressing.

Dielectric testing for integrated power devices

The integrated power devices inter-layer isolation needs an over micron thick dielectric. The reliability testing of dielectric films need to apply high voltages, incompatible with wafer probing. We show that, exponential ramp current charge injection into a dielectric and the dV dt measurements offer an alternative method to test reliability of thick dielectrics.

Thin SiO 2 films nitrided in N 2O

Thin oxide nitridation in N 2O has been demonstrated to improve the dielectric characteristics in terms of charge to breakdown and trapping under current injection. In this work we compare the results obtained with the RTP and conventional oven nitridation technologies. Both reference oxide and nitrided oxide samples have been considered. Auger electron spectroscopy provided the nitrogen depth profiles. The electrical characterization has been performed by means of the constant current stress and exponential current ramp stress techniques, as well as high-frequency and quasi-static capacitance-voltage (C-V) measurements for interfacial state density determination as a function of the injected charge.

Linear, polynomial and exponential ramp generators with automatic slope adjustment

A novel method for an automatic slope adjustment of ramp generators is presented. The method has been verified by functional chip implementations of both a linear and an exponential ramp generator in a 2 /spl mu/m standard CMOS process. Applying start and stop voltages to the ramp generator, the ramp will automatically adjust itself, and the time for a complete ramp is set by the pulse length of a clock signal. Such a ramp generator needs no trimming, and is insensitive to component values and ratios. Ramp forms that are functions of a linear ramp are obtainable, such as linear, exponential, and polynomial increasing ramp shapes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Implosion of reactor-size, gas-filled spherical shell targets driven by shaped pressure pulses

The implosion of a family of reactor-size targets for inertial confinement fusion (ICF) is studied analytically and numerically. The targets consist of a deuterium–tritium (D–T) shell filled with D–T vapor and they are imploded by a multistep pressure pulse designed in such a way that the final hot spot is formed mainly from the initially gaseous fuel. The formation of the hot spot is described by means of a relatively simple model, and scaling laws for the quantities that characterize the state of the initially gaseous part of the fuel prior to ignition are derived. The results of the model are compared with one-dimensional fluid simulations, and good agreement is found. A parametric study of the fuel energy gain is then presented; the dependence of the gain and of the hot spot convergence ratio on the pulse parameters and on the filling gas density is analyzed. It is also shown that a substantial increase in the gain (for a given target and pulse energy) can be achieved by replacing the last step of the pulse with an exponential ramp.

A one-dimensional piezoelectric-driven inertial micropositioner with vertical capabilities

The authors have developed a novel piezoelectric-based linear inertial slider to achieve remote micropositioning in any orientation. It is particularly suitable for SPM in cryogenic and ultra-high vacuum environments and the simple, coaxial design results in a rigid structure. Speeds of up to 2 mm s-1 have been achieved vertically against gravity, and the ability to lift up to 100 g has been demonstrated. A computer simulation for the system has been developed and used to investigate the effects of different driving waveforms. In particular an exponential ramp was shown to be most effective, this was corroborated by experimental results.

Scanning Electrical Mobility Spectrometer

The measurement of particle size distributions using electrical mobility can be accelerated significantly by an alternate mode of operating mobility instruments. Rather than changing the electric field in discrete steps to select particles in a given mobility range, the electric field can be scanned continuously. The particles are classified in a time-varying electric field, but for an exponential ramp in the field strength there remains a one-to-one correspondence between the time a particle enters the classifier and the time it leaves. By this method, complete scans of mobility with as many as 100 mobility measurements have been made in 30 seconds using a differential mobility classifier with a condensation nuclei counter as a detector.

Scanning electrical mobility spectrometer

The measurement of particle size distributions using electrical mobility can be accelerated significantly by an alternate mode of operating mobility instruments. Rather than changing the electric field in discrete steps to select particles in a given mobility range, the electric field can be scanned continuously. The particles are classified in a time-varying electric field, but for an exponential ramp in the field strength there remains a one-to-one correspondence between the time a particle enters the classifier and the time it leaves. By this method, complete scans of mobility with as many as 100 mobility measurements have been made in 30 seconds using a differential mobility classifier with a condensation nuclei counter as a detector.

Coherent backscatter‐induced noise in optical fiber gyroscopes with serrodyne modulation

AbstractCoherent backscattered light produces considerable noise in optical fiber gyroscopes. The noise in serrodyne‐modulated optical‐fiber gyroscopes with a low‐coherence source is studied theoretically for various forms of serrodyne‐modulation functions. The noise in output signals from the lock‐in amplifier is analyzed for the closed‐loop gyroscope. The coherent backscatter‐induced noise against the maximum phase of serrodyne‐modulation is estimated for finite flyback time or exponential ramp. It is found that the ideal serrodyne‐modulation function with the maximum phase of π and without flyback time cancels the noise in the signals of these gyroscopes.

General solutions of Maxwell's equations for signals in a lossy medium. I. Electric and magnetic field strengths due to electric exponential ramp function excitation

Modification of Maxwell's equations to obtain general solutions for a lossy medium is reviewed. It is done by adding an extra term, referred to as the fictitious magnetic charge density. The solutions, which are in integral form, are solved numerically by computer for an exponential ramp function excitation. Computer plots for the electric and magnetic field strengths as functions of time at different locations in a lossy transmission medium are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

General solutions of Maxwell's equations for signals in a lossy medium. III. Electric and magnetic field strengths due to electric and magnetic sinusoidal pulse excitation

For pt.II see ibid., vol.30, no.1, p.37-40 (1988). The representation of a function with a general time variation by a series expansion of time-shifted transients is discussed. On the basis of this representation, numerical solutions of Maxwell's equations are presented for the electric and magnetic field strengths in a lossy medium due to electric and magnetic excitation functions consisting of a finite number of sinusoidal cycles. The solutions are derived by means of a time-series expansion of the available solutions for the electric and magnetic exponential ramp function excitations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

General solutions of Maxwell's equations for signals in a lossy medium. II. Electric and magnetic field strengths due to magnetic exponential ramp function excitation

For pt.I see ibid., vol.30, no.1, p.29-36 (1988). Solutions for the electric and magnetic field strengths in a lossy medium due to a magnetic exponential ramp function excitation are presented. The solutions are in integral form and are evaluated by numerical integration methods using a digital computer. Computer plots for the electric and magnetic field strengths at different locations in the propagation medium are given. The plots obtained for the transients can be used to represent solutions in lossy media for signals that can be represented in terms of a time-series expansion of the transients. >

A ramp model for turbulent temperature fluctuations

Temperature fluctuations in a turbulent shear flow are modeled by a ramp-like signal on which relatively high frequency Gaussian fluctuations are superimposed. Both linear ramps with fixed height and length and exponential ramps of variable length are considered. Parameters which characterize the exponential ramps are obtained from experimental data in a heated jet. High order moments of temperature calculated with the use of the ramp model are in reasonable agreement with available experimental measurements.