Finite-source Effects Research Articles

Simulation of bent crystal spectrometers

In crystal spectrometers one traditionally labels each position in the dispersion/recording plane by a single wavelength value. A simple examination of the crystal spectrometers shows that different areas of the crystal contribute different wavelengths at the same position in the recording plane. Using collimators and apertures one may reduce these effects, as well as reduce the collected signal. Convolving the system response, in that case, may not allow simple analytic estimates of the sensitivity/responsivity of the system. A Monte-Carlo ray-trace program was written in order to study and simulate the real geometry including finite-source size effects. The results of the code are presented, demonstrating the contributions to the resolution and absolute responsivity, for a particular parabolically bent crystal spectrometer.

Monte Carlo simulation of line edge profiles and linewidth control in x-ray lithography

X-ray lithography exposures of PMMA on silicon have been simulated with a Monte–Carlo method including the energy backscattering from the substrate. The line-edge acuity of the resist image has been modeled with experimentally determined x-ray spectra of various sources (aluminum, tungsten, and palladium) and various source diameters (0.1, 1.5, and 3 mm). The intrinsic line-edge degradation due to secondary electron exposure is derived from the point source images while the finite-source effect (penumbra) is extracted from the additional degradation at finite source diameters. The penumbra effect is found to be rather small in PMMA. Depth profiles of the energy absorbed in PMMA demonstrate the significance of the energy backscattering from the substrate for energetic x rays. This effect can be significantly reduced by an organic spacer layer. The extent of the geometric projection effect has been modeled with the aluminum source. The results show that a finite angle of incidence of the x rays causes a sizable enlargement of the mask shadow due to the finite absorber thickness ultimately restricting the usable field size. The resultant linewidth variation is more pronounced for a mask with vertical profiles than for one with 20° wall angle. It can be reduced by thinning the absorber although at the expense of the mask contrast. The angle of incidence is replicated in the resist profiles causing an increasing tilt of the lines further away from the center of the wafer. This also restricts the field size but can be controlled to some extent by the thickness of the imaging resist layer.

Inversion of teleseismic body waves for the moment tensor of the 1978 Thessaloniki, Greece, earthquake

abstractSeismograms from WWSSN and Canadian network stations were modeled to determine the source parameters of the 20 June 1978 Thessaloniki, Greece, earthquake (Ms = 6.4). The depth of the initial rupture was constrained to 11 ± 1 km by comparison of the arrival times of surface reflections with synthetic short-period seismograms. A focal sphere plot of first motion polarities provided little constraint on other focal parameters, except to indicate that predominantly normal faulting was involved. A generalized inverse technique utilizing the moment tensor formalism was applied to teleseismic P and SH waves for six increments of depth. The moment tensor obtained indicated a nearly horizontal, N-trending tension axis and a nearly vertical compression axis, and yielded the following double-couple source parameters: strike 280° ± 7°; dip 55° ± 3°; rake −65° ± 5°; seismic moment 5.7 × 1025 dyne-cm; and a skewed triangular source time function with a rise time of about 1 sec and duration of 6 to 8 sec. Due to indications of multiple or finite source effects for this event, and the assumption in the moment tensor formalism of a point source, a low-pass filter was applied to the data and the inversions were repeated. The results were nearly identical with those of the original inversion, suggesting that any individual sources had similar mechanisms, or that the point source model is sufficient for this earthquake.

Inherent Load-Balancing in Step-By-Step Switching Systems

Questions have been raised over the years regarding the validity of the traffic-engineering tables used by the Bell System and others for the graded-multiple trunk groups within the step-by-step switching system. The tables indicate that the capacity of a graded multiple is increased when it is imbedded in the step-by-step system, the increase becoming larger as the number of switches connected to the graded multiple decreases. The increase in capacity supposedly occurs because of a “finite-source effect.” In this paper, we investigate in detail the flow of traffic through the step-by-step system to determine the validity of the tables. By a combination of simulation and analysis, we show that the increase in capacity arises not from a finite-source effect but from an inherent load-balancing that results from the clever manner in which the switches and trunks are interconnected. We conclude that, when used for engineering in the presence of day-to-day variations, the tables are adequate when the gradings are used with the large selector groups. For the minimum number of selectors, the tables estimate fairly accurately the capacity of the larger gradings, slightly overestimate the capacity for the medium-sized gradings, and overestimate the capacity of some of the smaller gradings by about 20 percent.