IN the fast-paced semiconductor industry, staying ahead means optimizing and controlling the manufacturing processes down to the atomic level wherever possible. At stake is the $44-billion market in integrated circuits that power computers, communication devices, and consumer electronics.
INDUCT95, a unique simulation code developed by Livermore physicist Peter Vitello (Figure 1), may give the U.S. a leg up in the race. INDUCT95 helps designers of plasma-aided semiconductor manufacturing to optimize the process and equipment. Such tools are also used in the aerospace, automotive, steel, and biomedical industries.
Plasmas--gases containing ions and electrons--are widely used to fabricate microelectronic devices. Out of the nearly 800 steps to create today's intricate integrated circuits, nearly one-third use plasmas.
The increasing use of plasmas for etching, deposition, and other processes reflects the advantages of this technique. First, the plasma breaks down the gas molecules into chemicals that etch materials very rapidly. Second, the plasma ionizes chemicals, giving them an electrical charge that renders them maneuverable. Finally--and of key interest to chip manufacturers--plasma etching produces nearly perfect vertical etching profiles. Getting exact profiles of uniform depth is extremely important: uniform, sharp features in the final product mean that each chip can yield more usable circuits.
However, controlling a plasma--particularly at sub-micrometer levels--is not easy. The plasma gases used in semiconductor manufacturing are usually highly reactive ones such as chlorine and oxygen. The interactions between these gases and the surface of the chamber walls, as well as the material being etched, are complex and not entirely understood. For the manufacturing process to be most efficient, the ion energy of the plasma must be carefully controlled, and the flux of plasma ions onto surfaces must be uniform.
Until now, designing plasma-aided manufacturing tools has been done mostly by trial and error. But as integrated circuits began to incorporate smaller and smaller features--some now approach the nanometer scale--a more rigorous process for designing tools was needed.

Designing the Best Plasma Tools Possible
INDUCT95 models plasma chemistry and transport, keeping track of the average density, temperature, and velocity of each type of particle. The code provides numerical solutions for how the plasma evolves over space and time--in terms of its density, velocity, temperature, and electric field--and analyzes the plasma in two dimensions. It is unique in its robustness, speed, and key modeling capabilities.
The code also models the chemical reactions of the plasma with the neutral gas. In fact, INDUCT95 examines all reactions between all the types of particles in the bulk of the plasma system and on all the surfaces involved.
INDUCT95 takes the fluid modeling approach to the plasma. "Treating the plasma as a fluid of ions and electrons is very accurate for the conditions used in commercial plasma-aided manufacturing systems," says Vitello. "The fluid approach to computation is hundreds of times faster and more stable than a treatment of the plasma as a system of discrete particles." The approach allows many physical processes to be included, yet the code can often be run in a matter of hours. Tight integration of all physical processes results in unmatched code stability.
As Vitello points out, the chemistry in the plasma reactor chamber is extremely complex. Dozens of different types of neutral and ion species lead to hundreds of rate equations (i.e., two-dimensional, time-dependent, chemical equations). INDUCT95 was designed to excel in this environment.
"Sometimes, the other codes--which are designed for academic research and not for extremely complex situations--cannot complete the computation," Vitello explains. "For INDUCT95, I had this application in mind from the start. I was also concerned with quality control from day one. As a result, INDUCT95 runs fast and efficiently from a basic desktop PC and requires no special computer equipment" (Figure 2).
"A reactor chamber is made of different materials--stainless steel, aluminum, quartz for the window, and so on," says Vitello. "The plasma gases react chemically with these materials at the surfaces. Etch rates depend on the surface material of the chamber and the chip. The microstructures often require geometric structures composed of different material types. INDUCT95 models these complicated systems easily, reducing the amount of memory and run time needed."
In addition, INDUCT95 is the only plasma reactor code that successfully models applied, time-dependent high-voltage effects in complex geometries and effectively models high-density electronegative plasmas.

Designing Plasma Electrodes for High Voltages
Accurately modeling high voltages is important to the design of the electrodes that apply these voltages to the plasma. This voltage controls two critical aspects of the plasma: shaping the plasma's density in space and accelerating the ions onto the etching surfaces.
Manufacturers want a semiconductor device that is etched uniformly or that has a uniform deposit across the surface. To achieve this, the shape, position, frequency, and voltage of each electrode must be finely controlled.
"For example," said Vitello, "the use of multiple electrodes with wildly differing properties may lead to great variations in the plasma behavior, which can degrade the final product. These conditions are very difficult to accurately follow in semiconductor processing. INDUCT95 is the only software capable of modeling this environment."

Modeling Electronegative Plasmas
Highly reactive electronegative plasmas--plasmas containing a large fraction of negative ions--are commonly used in plasma-aided manufacturing. At high plasma densities and low neutral gas pressures, which are the design goals of new plasma processing equipment, the scattering of ions with ions dominates the scattering of ions with neutral gas particles. The ion-ion scattering thus governs behavior of the plasma current.
"No one else has considered the problem of ion-ion coupling in this environment," said Vitello. "Most computer-aided design codes for this particular application make simple assumptions about the interactions. INDUCT95 is the only code that has successfully modeled the turbulence and instabilities of ion-ion coupling in the plasma reactor."

Other Ventures for Plasma Modeling
The code's applications at Livermore extend beyond commercial uses. For example, INDUCT95 simulations will provide engineers with a better understanding of the plasma discharge process so they can improve the design of a unique high-voltage insulator for Livermore's Advanced Hydrotest Facility.
INDUCT95 can be applied to areas outside the semiconductor industry as well. The code can model a wide range of plasma discharges, including plasma sources for flat panel displays, glow discharges (such as those in fluorescent lamps), and filament streamer propagation used in hazardous waste treatments.
"The modeling software has matured and can make a significant contribution to industry," says Vitello. "No longer does a plasma tool designer have to design 'by guess or by golly.' This code allows us to explore the complex chemistry and physics of these little understood, but important, processes. In a sense, INDUCT95 provides another window into the physics of plasmas."
--Ann Parker

Key Words: computer-aided design, INDUCT95, plasma, plasma simulation, semiconductor.

For further information contact Peter Vitello (925) 422-0079 (

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