Dissipation Profiles Research Articles

Theoretical study of the ultimate resolution in electron beam lithography by Monte Carlo simulation, including secondary electron generation: Energy dissipation profile in polymethylmethacrylate

A new Monte Carlo simulation including generation of secondary electrons has been performed to study ultimate resolution in electron beam lithography. With respect to the simulations of inelastic scattering process of the primary electrons we used Gryzinski’s excitation function for single electron excitation processes, generating secondary electrons, while the inelastic mean free path proposed by Seah and Dench for organic material and energy loss spectrum obtained by Ritsko were used for simulating the inelastic scattering processes of the secondaries. The calculations were made to obtain energy dissipation profile for 20-kV electrons, particularly, in the vicinity of the point of incidence on nanometer-scale in 3000-Å-thick films of polymethylmethacrylate (PMMA) on a silicon substrate. The result clearly indicates that the secondary electrons play a most important role in determining the energy dissipation profile in the vicinity of the point of incidence, being the significant source of broadening of the energy dissipation profile. The blurring due to secondary electrons at the surface of the PMMA resist is of the order of 10 nm.

Spatial energy dissipation profiles, W values, backscatter coefficients, and ranges for low-energy electrons in methane

In the energy range from 25 eV to 5 keV the spatial energy dissipation of electrons in methane has been studied experimentally by ionization chamber measurements as well as theoretically by Monte Carlo calculations. Using the measured and calculated spatial ionization and energy transfer distributions, the average energy W required to produce an ion pair, practical ranges, and backscatter coefficients with respect to ionization, energy, and particle number have been determined. The standard deviations of the measured W values are less than 1% for energies T ≧ 30 eV . Because of this, the differential ω values could also be derived from the energy dependence of the experimental W values. The agreement between our experimental and theoretical data is very satisfactory over the whole energy range. The theoretical results were therefore used to determine some other quantities useful in the fields of microdosimetry, such as, for instance, the energy absorption within thin layers of mass per area between 0.1 μg/cm 2 and 50 μg/cm 2 and the probability of ionization along an electron track.

Schumann resonance effects of electrical conductivity perturbations in an exponential atmospheric/ionospheric profile

Eigenmode solutions are computed for the n = 1 … 3 Schumann resonances in a perturbed, unmagnetized vertical atmospheric conductivity profile σ = 10 −16 exp ( z/3.1) mho m −1 for z ⩽ 100 km and σ = 10 −2 mho m −1 for z > 100 km. For the unperturbed exponential profile the radial electric field E r is nearly constant z ≲ 40 km, and decreases rapidly above 50 km. The tangential field E ϑ > E r for z ≳ 65 km. The Joule dissipation profile in this case has an absolute maximum at about 50 km and a smaller relative maximum at 90 km with a deep relative minimum at 65 km. The maximum dissipation thus occurs in the middle atmosphere, making the Schumann resonances particularly susceptible to conductivity perturbations in this region. The perturbations of this study comprise Gaussian-shaped enhancements or depressions of FWHM ≈ 10 km impressed on the unperturbed profile. Eigenfrequencies and Q-values are computed for the full range of perturbation amplitudes 10 −3−10 3 and altitudes 30–90 km. The perturbations induce overall eigenfrequency variations of ± 1.0, ±1.5, and ±2.5 Hz in the n = 1, 2, and 3 modes, respectively, and Q-values spanning the range 3.5–11.0. The results of this calculation extend those of previous works investigating the Schumann resonance response to atmospheric conductivity perturbations, and may be useful for interpreting experimental observations in terms of external ionization source intensities of GCR, Lyman-α, or solar cosmic or X-rays, or variations in middle atmospheric chemical constituents.

A Note on the Interaction Between a Thermally Forced Standing Internal Gravity Wave and the Mean Flow, With an Application to the Theory of the Quasi-Biennial Oscillation

A numerical model of the interaction of the mean flow with a two-dimensional standing internal gravity wave was constructed. This model was similar to the quasi-biennial oscillation “analogue” model of Plumb (1977), except that it did not employ the WKB approximation and it included thermal excitation of the waves near the lower boundary (the wave forcing region extended over a region meant to correspond to the tropical troposphere). Calculations of the mean flow evolution in the model were performed with values of the wave parameters comparable to those appropriate for the equatorial waves which are believed to force the quasi-biennial oscillation in the real atmosphere. It was found that, when a realistic profile of mean flow dissipation was included, the results of these calculations in the portion of the model corresponding to the stratosphere were strikingly similar to those obtained with the original version of the Plumb model together with an artificial no-slip boundary condition imposed at the level of the tropopause. These calculations thus support the validity of the no-slip lower boundary condition which is used in current theoretical models of the quasi-biennial oscillation.

Lateral spreads of energy dissipation profiles of 20-kV electrons in polymethylmethacrylate: Functional representation and its application to proximity effect

Monte Carlo calculations have been used extensively to study the energy dissipation of electrons penetrating into solid materials both in the direction of the initial electron trajectory and lateral to it. Knowing the lateral energy dissipation is important for the prediction of proximity effects in electron-beam lithography and limiting resolution in scanning electron microscopy. The Weibull probability density functions are shown to approximate the lateral energy dissipation profiles determined by Monte Carlo calculations of 20-keV electrons in polymethylmethacrylate (PMMA), and their application to simple line and square patterns of electron-beam exposure are also discussed.

The scaling of vertical temperature gradient spectra

Tests of a formula derived for the cutoff wave number of vertical temperature gradient spectra, using data taken in the upper layers of the North Pacific, show encouraging results. To derive this formula, the cutoff wave number is assumed to be the Batchelor wave number, with kinetic energy dissipation calculated by combining a form used in the atmosphere for calculating the vertical eddy diffusivity in terms of the dissipation with the Osborn‐Cox formula for calculating eddy diffusivity from the variance of the temperature gradient spectrum. Kinetic energy dissipation in the water column can be determined in this way; a vertical profile of dissipation shows values of the order of 10−3 cm2 s−3 at the base of a stormtossed mixing layer. In the thermocline below, dissipation occurs in patches.

Gravity waves of short period (5–90 min), in the lower thermosphere at 52°N (Saskatoon, Canada)

Winds data from a partial reflection D 1 drifts (P.R.D.) system are obtained from two 2–3 h soundings during summer and winter months. Sampling at 1 min intervals allows the resolution of frequencies as high as the Väisälä-Brunt frequency ( − 5 min), and on both occasions wind oscillations with periods − from ~5 to 90 min were observed. Selected time series and spectra of east-west and north-south winds within the lower thermospere are used to identify these oscillations as gravity waves. Polarization of the waves is present during both soundings. The autocorrelation functions of the reflected radiowaves (amplitude) are used to calculate a turbulent velocity parameter, and also the related rate of energy dissipation from ~70–100 km. The resulting energy dissipation profiles, with maximum values of ~0.05 W kg −1 near 90 km, are compared with those obtained from the r.m.s. deviations of the winds.

High‐resolution altitude profiles of the auroral zone energy dissipation due to ionospheric currents

The first height‐resolved altitude profiles of the Joule heating rate obtained by using the Chatanika, Alaska, incoherent scatter radar are presented. The measured Joule heating rate typically maximizes at an altitude that is well above the altitude of the current density maximum. For a reasonable model neutral atmosphere, it is also found that the maximum Joule heating rate occurs above the altitude of the corresponding Pedersen conductivity maximum. For these data the eastward auroral electrojet was centered near 130 km, while the westward electrojet was centered 10 km lower in altitude during its most intense period. It is inferred that this large difference in height between the two electrojets and the corresponding altitude change in the Joule heating will have a significant effect on the source mechanisms for such phenomena as atmospheric gravity waves, infrasonic waves, and spread F irregularities. One should expect an asymmetry in the occurrence and structure of such events with respect to the Harang discontinuity. This asymmetry is noted for aurorally excited gravity waves. A tentative calibration of the total Joule dissipation in the neutral atmosphere relative to the magnetic field disturbance vector measured by a nearby ground‐based magnetometer has been performed. The heating efficiency was found to be 10 times larger in a positive bay than in a negative bay. The heating efficiency for the negative bay event is close to the value deduced by Cole (1971) on theoretical grounds.

Electron-beam exposure profiles in polymer films for metallic film mask fabrication

The effect of the metallic thin film on energy dissipation profiles in a resist polymer film on a metallic film-clad glass plate as in mask fabrication was investigated experimentally and by Monte Carlo calculations which take an exact account of the above boundary condition for a specific geometry. The thicknesses of the polymer film and metallic films are 8000 Å and 500–800 Å, respectively. Various metals such as Al, Cr, Mo, and Ta are used as mask materials. Both experimental and theoretical results show that the width of the developed profile increases with an increasing atomic number of the metallic film element depending on exposure density as expected due to increasing backscattering from the metallic film. It is concluded that even a very thin metallic film has an appreciable effect on the profile and its effect is exaggerated either by a large dose or by a strong development.

A MODEL STUDY OF ALONGSHORE SEDIMENT TRANSPORT RAT

Alongshore sediment transport rate was studied in a 3-dimensional mobile bed coastal model and was found to depend on the beach profile and rate of wave energy dissipation in addition to the normal wave and sediment parameters. Alongshore sediment transport rate was found to be strongly related to the surf similarity parameter, a single parameter simplistically describing beach profile and breaker type.

Experimental and theoretical study of energy dissipation profiles of keV electrons in polymethylmethacrylate

Energy dissipation profiles of keV electron beams in polymethylmethacrylate (PMM) were investigated both in theory and experiment. The results measured using a scanning electron microscope as a source of the electron beam were followed by the Monte Carlo calculations which were performed for the same conditions as the experiment. Good agreement was obtained not only for equidissipation profiles but also for absolute values of the energy dissipation between the experiment and the calculation. This encourages us to apply the Monte Carlo calculations to problems of electron resist exposure important for microelectronics.

Computer-controlled resist exposure in the scanning electron microscope

In modern microelectronics, complicated structures with very small dimensions must be fabricated on active-device materials. This task has been traditionally accomplished by photolithographic techniques, but electron-beam exposure of resist materials has recently been explored [1]-[3]. Submicron electron devices have been fabricated in several laboratories, often featuring a flying-spot scanner to generate the pattern being exposed [4]-[7]. Paper tape drives have been used for repetitive patterns [8], and computer control of the electron beam has been reported also [1], [9]. The electron resist that has shown the highest resolution to date appears to be poly-(methyl methacrylate) (PMM). We have used this material in a resist form for microelectronic device fabrication, and in bulk form to determine energy dissipation profiles. The exposure is performed with a computer-controlled scanning electron microscope (CCSEM). In this paper, we describe the electron beam system briefly, discuss the processes involved in resist exposure and development, describe our exposure procedures using the CCSEM, and show results of fabricated devices and energy dissipation studies.

The Effects of Ions on Very‐Low‐Frequency Propagation During Polar‐Cap Absorption Events

The propagation of electromagnetic waves in the VLF range in the earth‐ionosphere waveguide has been theoretically analyzed. The results of full‐wave calculations indicate that transpolar VLF waves suffer considerably more attenuation during a moderately strong polarcap absorption (PCA) event than during the undisturbed daytime. Computed height profiles of dissipation and field strengths show clearly that this increased attenuation is due mainly to ohmic losses associated with ion heating. Calculations based on a model of a relatively weak PCA event indicate no pronounced increase in attenuation at most VLF frequencies. For this model, ions are found not to be an important factor. The calculations do not include the possible effects of the Greenland ice cap. During a moderately strong PCA event, the height range over which long‐path VLF waves interact strongly with the ionosphere is substantially lower than in the undisturbed daytime. For all ionospheric models considered, the width of the height range of substantial wave‐ionosphere interaction at a given frequency was less than about 20 km. VLF probing experiments must therefore use several frequencies and incidence angles if a broader ionospheric height range is to be sampled effectively.

Stability of turbulent channel flow, with application to Malkus's theory

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkus's theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkus's theory is offered.