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Notes: A formalism is developed for numerically calculating reflection and absorption of right-hand polarized waves and reflection of left-hand polarized waves propagating into a cyclotron resonance zone in a medium in which both magnetic field and plasma density are varying. The results are shown to agree with previous analytic calculations in the limit of constant density, weak collisionality, and linearly varying magnetic field, where the analytic calculation applies. The formalism is then applied to a plasma with general field and density variations, and arbitrary collisionality. The absorption and reflections are calculated for various boundary conditions along the propagation path, showing that there is an optimum density for power absorption. The collisionless absorption in the resonance zone, calculated from the single particle heating averaged over the flux is shown to be consistent with the linear wave absorption at low absorption and collisionality. At high absorption a prescription for bringing the two calculation methods into agreement is advanced. The results are used to qualitatively explain some previously puzzling experimental observations.

Notes: Thin (3–300-nm) oxides were grown on single-crystal silicon substrates at temperatures from 523 to 673 K in a low-pressure electron cyclotron resonance (ECR) oxygen plasma. Oxides were grown under floating, anodic or cathodic bias conditions, although only the oxides grown under floating or anodic bias conditions are acceptable for use as gate dielectrics in metal-oxide-semiconductor technology. Oxide thickness uniformity as measured by ellipsometry decreased with increasing oxidation time for all bias conditions. Oxidation kinetics under anodic conditions can be explained by negatively charged atomic oxygen, O−, transport limited growth. Constant current anodizations yielded three regions of growth: (1) a concentration gradient dominated regime for oxides thinner than 10 nm, (2) a field dominated regime with ohmic charged oxidant transport for oxide thickness in the range of 10 nm to approximately 100 nm, and (3) a space-charge limited regime for films thicker than approximately 100 nm. The relationship between oxide thickness (xox), overall potential drop (Vox) and ion current (ji) in the space-charge limited transport region was of the form: ji ∝ V2ox/x3ox. Transmission electron microscopy analysis of 5–60-nm-thick anodized films indicated that the silicon-silicon dioxide interface was indistinguishable from that of thermal oxides grown at 1123 K.High-frequency capacitance-voltage (C-V) and ramped bias current-voltage (I-V) studies performed on 5.4–30-nm gate thickness capacitors indicated that the as-grown ECR films had high levels of fixed oxide charge ((approximately-greater-than)1011 cm−2) and interface traps ((approximately-greater-than)1012 cm−2 eV−1). The fixed charge level could be reduced to ≈4×1010 cm−2 by a 20 min polysilicon gate activation anneal at 1123 K in nitrogen; the interface trap density at mid-band gap decreased to ≈(1–2)×1011 cm−2 eV−1 after this process. The mean breakdown strength for anodic oxides grown under optimum conditions was 10.87±0.83 MV cm−1. Electrical properties of the 5.4–8-nm gates compared well with thicker films and control dry thermal oxides of similar thicknesses.

Notes: Spherical and cylindrical many-particle models are used to simulate rf (radio frequency) discharges in which the rf powered and the grounded electrodes have different areas. This asymmetry determines the magnitude of the average plasma-to-electrode voltage Va (the ion bombarding energy) at the smaller powered electrode, which is a critical process parameter. A collisionless uniform ionization discharge model predicts that the voltage ratio Va/Vb scales as the fourth power of the electrode area ratio Ab/Aa, where Vb is the potential drop at the other electrode. However, measurements indicate a much weaker dependence of Va/Vb on the area ratio, which is also observed in our simulations. Over a limited range of area ratios it was found that the power dependence was close to one, in agreement with a local ionization discharge model. The simulation codes used are PDC1 (plasma device cylindrical one-dimensional) and PDS1 (plasma device spherical one-dimensional).

Notes: An electron-beam probe has been used to make time- and space-resolved measurements of the electric field in a parallel plate rf discharge. Measurements were taken at a time resolution of 5 ns and a field resolution ±1 V/cm at increments of 0.32 cm from the powered electrode. The detection method provides the weighted average of the electric field along the beam trajectory. Measurements of fields less than 20 V/cm were made throughout the entire discharge. Data were obtained for 13.6-MHz argon discharges at 2.3 and 20 mTorr, and at rf voltage amplitudes of 100 and 600 V at each pressure. The data for the 2.3-mTorr, 600-V case show (1) that a propagating double layer forms during the collapse of the sheath, (2) that the field near the electrode points in toward the plasma at the extreme collapse of the sheath, (3) that the collapse and expansion of the sheath proceeds asymmetrically for measurable field values, and (4) that the trajectory averaged electric field in the plasma has an anomalous phase shift and magnitude. Similar phenomena are observed for the remaining three discharge cases.

Notes: In plasma immersion ion implantation, a target is immersed in a plasma and a series of negative, high-voltage pulses are applied to implant ions into the target. An approximate analytical model in one-dimensional planar geometry is developed to determine the time-varying implantation current, the total dose, and the energy distribution of the implanted ions for a voltage pulse with finite rise and fall times. Scaling rules are presented for the implanted current and energy distribution with respect to plasma density, peak applied voltage, and ion mass. Comparisons with numerical simulations are used to demonstrate that the accuracy of the model is well characterized by a single parameter: the ratio of the ion flight time to the pulse rise time.

Notes: Plasma-immersion ion implantation (also known as plasma-source ion implantation) is a process in which a target is immersed in a plasma and a series of large negative-voltage pulses are applied to it to extract ions from the plasma and implant them into the target. A general one-dimensional model is developed to study this process in different coordinate systems for the case in which the pressure of the neutral gas is large enough that the ion motion in the sheath can be assumed to be highly collisional.

Notes: An electron cyclotron resonance plasma processing system was used to etch hardbaked KTI-820 photoresist from single crystal silicon wafers, silicon dioxide films and patterned multilayer structures. Etch rates of 1500 nm/minute were observed at a substrate temperature below 373 K in a Pforward=750 W, 0.13-Pa ECR oxygen plasma with no applied substrate bias. The etch rate increased linearly with increasing power from Pforward=300–750 W. Etch rate was a complicated function of pressure and residence time, but a modified adsorption-reaction-ion-stimulated desorption rate expression could be used to fit the data. Etch rates decreased for increasing oxygen residence time at low operating pressures due to a combination of polymeric film formation of reaction products and reactant (atomic oxygen) depletion. Maximum etch rates were observed at approximately 0.13 Pa for all residence times. Multilayer photoresist structures were etched at various pressures as well as at a 45° angle to the incident plasma stream. Etch profiles for the variable angle runs indicated that the etch rate was strongly dependent on ion flux. Etch anisotropy increased with decreasing pressure, consistent with increased ion bombardment energy. The degree of anisotropy was, however, limited due to a non-normal component of ion energy, which has been interpreted previously as an ion temperature.

Notes: We report on the effect of Ar addition to an O2 plasma on photoresist etching in an inductively coupled, traveling wave driven, large area plasma source (LAPS). We also develop a simplified spatially varying O2/Ar mixture discharge model corresponding to the LAPS in a two-dimensional geometry in order to account for the effect of Ar addition. A photoresist etch kinetics model and spatially varying O2/Ar mixture discharge model are used to explain the experimental data. We find that the addition of 50% Ar increases the plasma density and etch rate approximately by a factor of 2. From the simulation we find that argon metastables (Ar*) play an important role in the mixture plasma. The simulation predicts an enhancement in O-atom density due to Ar addition, even in the presence of dilution of the feed gas. The experimental data and predicted etch rates from the simulation are generally in good agreement, indicating that the increase in the etch rate with Ar addition is due to both the increase in the plasma density and the enhancement in O-atom density attributable to the dissociation of O2 by Ar*. © 2001 American Institute of Physics.

Notes: Measurements of the rf electric field have been made along the z axis of a helicon reactor using a retarding field energy analyzer. A fluid code and a simple analytical model have been developed to analyze the ion energy distribution functions, especially in the case of bimodal distributions where the ion transit time through the sheath in front of the analyzer is comparable to the rf period. A generalized curve (and an analytical approximation to that curve) has been developed from the analytical model and confirmed by the self-consistent fluid model for high, low, and intermediate ion transit time, which can be used by experimenters to quickly convert the experimental results (energy peak separation, plasma potential and density, electron temperature), which are related to rf sheath oscillations, to absolute values of the rf electric field. An analysis of the errors involved in the derivation of the field is given. The results agree qualitatively with rf pickup measured with a floating Langmuir probe. © 2000 American Institute of Physics.

Notes: We study the approach to near-equipartition in the N-dimensional Fermi–Pasta–Ulam Hamiltonian with quartic (hard spring) nonlinearity. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy which is independent of N, one can reach equipartition if one waits for a time proportional to N2. Below this critical energy the time to equipartition is exponentially long. We develop a theory to determine the time evolution and the excitation of the nonlinear modes based on a resonant normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for equipartition, the time scale to equipartition, and the form of the nonlinear modes below equipartition, in qualitative agreement with the numerical results. © 1995 American Institute of Physics.