Electromagnetics

It is generally accepted by industry that the traditional RIE plasma tool will not be adequate for feature sizes of < 0.5 µm and wafer sizes > 200 mm. ECR plasma tools have been investigated in recent years as a low-gas-pressure, high-plasma-density alternative to RIE. Issues related to uniformity over large wafers and to cost of ownership have motivated the investigation of other plasma sources, particularly inductively coupled plasmas (ICPs) and helicon sources. Since all of these advanced reactors are electromagnetically driven devices, plasma equipment models must have the capability to couple wave propagation with plasma chemistry self-consistently.

Current Status of Modeling and Simulation

Modeling and simulation (M&S) of plasma processing reactors and plasma-assisted materials processing (PAMP) have progressed significantly during the past 5 years. This rapid progress has resulted from the maturity of new modeling techniques and the availability of high-performance computers, in the form of both remote mainframes and desktop workstations. At a minimum, plasma equipment models must solve the continuity equations for charged and neutral species and Poisson's equation for the electric potential. At best, plasma equipment models include a full kinetic description for all charged particles and neutrals (hot atoms having energies exceeding 100 eV have been observed in RIE tools). Four classes of models for PAMP are being developed for advanced plasma equipment — particle-in-cell simulations, kinetic models, fluid or hydrodynamic models, and hybrid models.

Particle-in-Cell Simulations

Particle-in-cell (PIC) simulations coupled with electromagnetics are, in principle, exact representations of plasma equipment subject to limitations in our knowledge of the details of the plasma chemistry. PIC simulations have the advantage of easily addressing complex geometries. They suffer from being extremely computer intensive, particularly in multiple dimensions, and being poor at resolving large dynamic ranges in the densities of reactants. For example, one can easily have a dynamic range of 104 in important reactants, making it difficult to have a statistically meaningful number of pseudoparticles for all species.

Kinetic Models

Kinetic models are, in principle, direct solutions of Boltzmann's equation for all pertinent species. An example of a kinetic model is the “convective scheme,” which uses a Green's function propagator to advance fluidlike elements in a velocity-position phase space. Kinetic models have advantages (exact solutions of the problem) and disadvantages (computer-intensive applications) similar to those of PIC simulations. They have the additional advantage that they are not statistical and therefore do not suffer from noise in the solution of Poisson's equation. They are also able to address large dynamic ranges in densities.

Fluid or Hydrodynamic Models

Fluid models solve the hydrodynamic equations of motion (continuity, momentum, energy) for charged and neutral species coupled with Poisson 's and Maxwell's equations. Fluid models have the advantage of being relatively mature and often borrow numerical techniques from similar models developed for fusion and combustion. They suffer from the inability to produce kinetic information, such as energy distributions of ions. They also suffer from having questionable applicability at gas pressures less than tens of mTorr.

Hybrid Models

Hybrid models combine kinetic and fluid simulations in an iterative fashion. Typically, a kinetic simulation is used to generate energy or velocity distributions, which, in turn, are used to generate source functions and transport



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement