Modeling and Simulation of Plasma Processing
Requirements of the Microelectronics Fabrication Industry
The microelectronics fabrication industry must reduce the cost and time required to produce new plasma equipment and new processes in order to remain competitive with Japanese and other offshore suppliers. The industry is looking primarily toward modeling and simulation (M&S) to aid in this endeavor. It is generally acknowledged that M&S will not, in the foreseeable future, be reliable and accurate enough to produce “machine drawings” for plasma equipment that “works” with no further experimental development. Rather, the industry is looking toward M&S to reduce the number of hardware iterations required to develop new plasma tools, thereby producing great savings in cost and time.
The two spatial scales of interest to M&S are reactor scale and feature scale. The goal of reactor scale modeling is to optimize the uniformity of reactive fluxes (ions and radicals) to the wafer being processed. The goal of feature scale modeling is to predict etching profiles and rates as functions of the magnitude and composition of the reactive flux and as functions of the aspect ratio of the trench. The requirements for relevant reactor scale models are discussed briefly below.
The phenomena of interest in plasma tools for microelectronics fabrication are inherently multidimensional, and so models must be at least two-dimensional to significantly affect the design of plasma equipment. One might argue that three-dimensional models will ultimately be required. It is doubtful that in the next few years our limited knowledge of the plasma chemistry (see below) will warrant this additional effort.
Although the uniformity of volumetric plasma generation is largely a plasma physics problem, virtually all other characteristics of interest (e.g., etch rate, lag in reactive ion etching [RIE], anisotropy, selectivity) are driven by the details of the plasma chemistry. Very subtle aspects of plasma chemistry can have a large influence on the final product. For example, the sputtering of oxygen atoms from quartz liners in electron-cyclotron resonance (ECR) reactors can be responsible for producing desirable passivation layers on the sidewalls of trenches. Relevant plasma equipment models must therefore have the capability of including complex plasma chemistry. This presupposes, of course, the availability of fundamental cross-section and rate coefficient data.
In low-pressure, high-plasma-density tools, the flux of reactants from the wafer is a nonnegligible fraction of the total mass flux through the reactor. Many plasma equipment design issues may ultimately depend on the disposition of the reactant flux returning to the plasma. At gas pressures of less than tens of mTorr, the collision frequency of radicals or ions with the walls is greater than with the gas molecules. One could argue that, under these conditions, the “plasma” chemistry is indeed dominated by reactions occurring on the surfaces of the chamber and the wafer.
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 (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 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 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
coefficients. A fluid model uses those values to produce densities and electric fields. The fields and densities are cycled back to the kinetic model and the process iterated to convergence. Most advanced equipment models use hybrid techniques of one sort or another.
Two-dimensional models of ECR, RIE, and ICP reactors have been developed by a number of groups in the United States and abroad. These groups include Sandia National Laboratories, Lawrence Livermore National Laboratory, IBM T.J. Watson Research Center, Auburn University, University of California at Berkeley, University of Houston, University of Illinois, University of Wisconsin, Eindhoven University (Netherlands), Paul Sabatier University (France), and the Australian National University (Australia). The general weaknesses of these models are that they lack detailed plasma chemistry, plasma surface interactions, full electromagnetic capabilities, and geometrical flexibility. However, in at least three instances, these models are being used by plasma equipment manufacturers to iterate new designs and to hone existing designs of a low-pressure ICP system. These equipment-design-capable models are hybrid models that have separate electromagnetic, kinetic, and fluid modules and have the capability to rapidly vary geometry and materials.
A ROLE FOR NRL
NRL has embarked on a modeling program for ECR reactors. The intent of this effort appears, initially, to be to provide a learning platform for the NRL M&S team and to complement the experimental diagnostics program. The personnel and techniques employed in this effort are excellent, and in general the work is progressing toward an equipment-design-capable model. The program has had a good start.
The NRL effort must, however, address the same weaknesses that are inherent in many of the other plasma equipment modeling activities: lack of robust plasma chemistry, lack of plasma surface interactions, and lack of relevance to the needs of the microelectronics fabrication industry. The NRL M&S team could also greatly leverage their code development efforts by adapting simulation techniques for plasma equipment that have been previously developed by others. This is particularly true with respect to plasma chemistry and plasma surface interactions. It is ultimately the flux of radicals and ions onto the wafer that determines the etch or deposition rate; therefore, determining their properties should occupy a significant portion of the effort. The existing computational effort on molecular dynamics should be an integral part of this program.
Many physics issues should be addressed with respect to the use of ECR tools in microelectronics fabrication, and in this regard the NRL effort is on track, even though the microelectronics industry is disenchanted with this technology. In spite of the promise and unresolved issues of ECR plasma tools, the U.S. semiconductor industry is moving away from ECR for microelectronics fabrication and moving toward other technologies such as ICP and helicon sources for 200-mm wafers. This situation is largely dictated by issues related to the cost of ownership of ECR equipment and the fact that Hitachi (a Japanese plasma equipment manufacturer) currently dominates the world market for ECR plasma tools and owns the majority of the patents. Attempts by U.S. equipment vendors to penetrate the ECR market for very large scale integrated (VLSI) circuit fabrication have had limited economic impact. As a result, investigations are being conducted on “nontraditional ” configurations of ECR, such as distributed sources, that do not conflict with current patents and may offer advantages with respect to plasma uniformity.
The lack of U.S. vendors offering ECR products does not imply that development of models for ECR microelectronics fabrication has no relevance to the U.S. semiconductor industry, since the use of ECR is still being considered as an alternative technology. This situation does imply, however, that development of models for ECR will not likely gain mainstream attention with either the tool
vendors or the end-users. ECR is, however, finding application for other materials processing applications outside the arena of fine line etching for microelectronics fabrication. For example, ECR is currently being investigated for diamond deposition, deposition of thin dielectric films for flat panel displays, and optical coatings. ECR discharges for these applications operate in a different parameter space (in terms of power, pressure, and gas mixture) from microelectronics fabrication, and therefore modeling of those systems should address the appropriate parameters.
The NRL M&S team would profit from interaction and visits with Sematech, Semiconductor Research Corporation, plasma equipment vendors (e.g., Lam Research, Applied Materials, PMT), and end-users to become familiar with the problems facing the microelectronics industry and to learn what is expected of M&S. For example, understanding and remediating the RIE lag (the phenomenon that features having different aspect ratios etch at different rates) have a high priority with almost all equipment vendors. There is an expectation by the vendors and end-users that any plasma equipment model “worth its salt” should be able to shed some light on these topics. There is also great concern about the effects of specific types of construction materials on the uniformity of the plasma and generation of particles. The details of these latter issues may be specific to particular equipment vendors or end-users. One should also appreciate the extremely short time scales of interest to the industry. For example, Sematech Equipment Improvement Programs, in which specific plasma equipment tools are “improved,” have durations of less than 1 year.
There are currently two, and soon to be a third, major modeling efforts for plasma equipment for microelectronics fabrication at other national laboratories. Sandia National Laboratories has a CRADA with Sematech to develop plasma equipment models for low-gas-pressure, high-plasma-density tools with emphasis on ICPs. Lawrence Livermore National Laboratory has a CRADA with AT&T Bell Laboratories and IBM T.J. Watson Research Center, as well as many “side agreements” with individual vendors, for plasma equipment modeling with emphasis on ICPs, helicons, and alternate configurations. Los Alamos National Laboratory is currently negotiating a CRADA with Semiconductor Research Corporation to perform similar modeling with emphasis on feature scale issues and may team with one of the other national laboratories. The greatest contribution that the NRL M& S effort can make to the micro-electronics industry will most likely come as a contributing member to this growing team of national laboratories, a task that will require significant coordination on both the scientific and managerial levels. The panel strongly urges the NRL M&S team to leverage and coordinate its efforts with those of the other national labora-tories and universities engaged in plasma equipment modeling.