THE 300-mm IMPERATIVE

Examining scale-up and computer simulation in tool design for 300-mm wafer processing

Demetre J. Economou and Theodoros L. Panagopoulos, University of Houston; and M. Meyyappan, NASA Ames Research Center

Plans to introduce pilot lines and fabs for 300-mm wafer processing are well under way. A 300-mm wafer allows 2.4 to 2.7 times more die per wafer, and a 25—40% reduction in per-die cost.¹ At the same time, IC technology is moving toward 0.18-, 0.15-, and 0.13-µm linewidths. The combination of these two trends places unprecedented demands on wafer processing equipment and presents enormous challenges to equipment manufacturers. Their role in the IC business involves design and development of new-generation equipment as well as development and demonstration of processes compatible with such equipment. As a result, computational modeling is called on now more than ever to play a complementary role in equipment and process design. The development of models and computer simulation codes is being pursued vigorously at universities, government laboratories, and commercial vendors. The virtual reactor concept is close to becoming a reality.

Scale-Up Principles

The transition from 200- to 300-mm wafer processing tools presents a clear problem in scale-up. Chemical engineers have had years of experience in scaling up chemical reactors from laboratory to pilot to full-production scale. When a system is too complicated to be analyzed by direct computer simulation, semiempirical methodologies may be implemented. One such methodology involves the use of dimensionless numbers or groups that describe the system's behavior.² These numbers show the relative importance of one physical phenomenon versus another and appear naturally when the governing equations that describe the conservation of momentum, energy, and mass, and their respective boundary conditions are nondimensionalized.² Dimensionless groups can be used as a guide for scale-up even when direct numerical simulation is possible.

One simple example relates to the multiple-wafer-in-tube low-pressure chemical vapor deposition (LPCVD) reactor.³ In this system, wafers are placed in a tube parallel to one another, with the wafer axis collinear to the tube axis. One of the design parameters in such a system is the spacing between the wafers, such that the deposited film thickness is uniform across the wafer and the throughput (wafers per hour) is maximized. If there is too much spacing, the coating thickness is uniform but the throughput falls because there are too few wafers per batch. If there is too little spacing, there are many wafers per batch but the deposit thickness is very nonuniform and is thickest at the wafer edges. The dimensionless number that governs thickness uniformity in this system is the Thiele modulus.³ The scale-up problem is simple here: the modulus should be kept constant when scaling up from 200- to 300-mm wafers. When other conditions (pressure, temperature, and the like) are kept the same, this translates to a spacing for 300-mm wafers that is (300/200)² times the spacing used for the 200-mm substrates. After this semiempirical approach identifies the proper spacing, computer simulation can verify the acceptability of the design. Photoresist ashing in barrel etchers presents similar scaling and optimization issues.⁴ Another advantage of using dimensionless groups is that different parameters are grouped together, thus reducing the parameter space. For example, instead of considering the effect of wafer radius, reaction rate, wafer spacing, and system diffusivity individually, one has to consider only the Thiele modulus.

Figure 1: Schematic of a CVD reactor: (a) with streamlined flow pattern, and (b) with gas recirculation cells.

Compound semiconductor (III-V and II-VI) CVD presents another example.⁵ A central issue in such systems is the thickness uniformity and composition of the layers grown across the wafer. Figure 1 shows a frequently used reactor configuration. The spindle sometimes rotates at high speeds, often thousands of revolutions per minute. Because the operating pressure and wafer temperature tend to be relatively high, the flow forms buoyancy-driven recirculating patterns (natural convection), as shown in Figure 1b. These patterns are detrimental to the quality of the grown material. Computer simulation can help in identifying reactor designs (dimensions) and operating conditions (gas flow rate, pressure, wafer temperature, and the like) so that the flow streamlines are smooth and there are no recirculations (see Figure 1a). Simulations can be used to screen design alternatives, thus avoiding the construction and testing of prototypes that may cost hundreds of thousands of dollars. Dimensionless groups can again be used as a guide for scale-up.

For the flow problem at hand, the two most important dimensionless groups are the Reynolds number (Re) and the Grashof number (Gr). It has been suggested, for example, that when Re/Gr² is <<1, natural convection rolls are suppressed; that is, the forced convective flow coming from above is strong enough not to allow recirculating rolls to form. The 300-mm system should be designed so that both numbers are the same in the scale-up version as in the smaller one. Computer simulation can then be used to verify the adequacy of the new design.

Dimensionless Groups

In general, similarity—geometric, dynamic, and chemical—should be retained in scale-up. Geometric similarity implies that all geometric dimensions of the bigger system are a constant (>1) multiplier of the corresponding dimensions of the smaller system. For example, the reactor aspect ratio should be kept the same. Dynamic similarity refers to maintaining the same flow characteristics as in the smaller system. For example, the Reynolds and Grashof numbers in the two reactors must be the same. Chemical similarity alludes to maintaining the same mass transfer and chemical reaction characteristics as in the smaller system. The most important dimensionless numbers describing mass transport and chemistry are the Peclet number (Pe), the Thiele modulus, and the Damkohler number (Da). In plasma processes additional dimensionless groups come into play that are associated with the plasma and electrical dynamics of the system.

The Reynolds number characterizes the importance of inertial forces compared to viscous forces. For many systems of interest, this number is low enough for the flow to be laminar, in the absence of recirculations. The Peclet number shows the relative importance of mass or heat transport by convective flow compared to molecular or gas-phase diffusion. The Damkohler number shows the relative importance of species production or loss by gas-phase (in the reactor volume) mechanisms relative to their ability to diffuse away from the source or sink. The Da/Pe ratio is actually a dimensionless residence time. When Da is >>1, large concentration gradients may be expected. The Thiele modulus shows the relative importance of surface reaction on the wafer compared to gas-phase diffusion. Large values of the modulus imply a diffusion-controlled situation and strong density gradients; the modulus decreases as pressure is decreased. However, even at pressures as low as 10 mtorr, the modulus can be high enough for substantial concentration gradients and nonuniformities to develop.⁶

Computer Simulation

There are three kinds of computer simulations: fluid, kinetic, and hybrid. Fluid simulations solve partial differential equations of continuity for the conservation of momentum, energy, and concentration of chemical species.⁷ All commercial computational fluid dynamics (CFD) software (Fluent, CFD-ACE, Phoenics, and the like) uses the fluid approach. Such packages have been used extensively by the microelectronics industry for applications such as thermal CVD and rapid thermal processing (RTP). However, as the operating pressure is reduced and the species' mean free path becomes comparable to or larger than a characteristic vessel dimension, the fluid approximation breaks down. The dimensionless group that characterizes the degree of flow rarefaction is the Knudsen number (kn). The fluid approximation is suspect if Kn is >0.2. High-Knudsen-number flows are encountered in LPCVD, high-plasma-density/low-gas-pressure reactors, physical vapor deposition (PVD), molecular beam epitaxy (MBE), and high-vacuum processes. For such high numbers, direct simulation Monte Carlo (DSMC) and other kinetic simulations become necessary.² The actual flow field in DSMC is represented by a collection of computation particles (superparticles) that are allowed to move and collide with one another and with the container walls. Collisions can be simple momentum transfer events or chemical reactions in which new species are generated. The simulations calculate the fluid velocity, temperature, and concentration profiles in the system and then output figures of merit such as etch or deposition rate and uniformity.

To be used as a technology computer-aided design (TCAD) tool, a computer simulation must be accurate, user-friendly, and rapidly executable on a desktop computer. These features allow one to conduct parametric investigations easily, in order to study the effect of different reactor designs and operating conditions on the figures of merit. Although DSMCs are considered more accurate at low pressures, compared to fluid simulations they are also computationally more expensive. For that reason, fluid simulations are thought to be more suitable for TCAD applications. As computing power increases, given DSMC's inherent robustness compared to fluid approaches, the Monte Carlo approach is expected to become more useful as a design tool. Finally, hybrids between fluid and kinetic simulations are often used in an effort to preserve accuracy while reducing the computational burden.

Equipment Design Applications

Electron cyclotron resonance (ECR) reactors, helicon plasma reactors, and sometimes inductively coupled plasma (ICP) reactors employ a dual-chamber design, with a source chamber in which plasma is generated and a process chamber in which the wafer is located some distance from the source (see Figure 2). The design is similar to that of the CVD reactor shown in Figure 1.The source chamber dimensions are primarily determined by the hardware associated with power coupling, such as RF coils or microwave equipment and magnet design. The question then arises as to the optimum diameter (d^_p) of the process chamber for 300-mm wafers. The semiempirical method using dimensionless groups and similarity mentioned earlier can be used at first to scale up from existing to larger equipment. Computer simulation can then be employed to verify and improve preliminary designs.

Figure 2: Schematic of high-charge-density, low-gas-pressure plasma reactor. Numerical simulations were performed to determine the diameter of the process chamber (d^_P) that results in optimum uniformity over a 300-mm wafer located at a distance h^_w from the source.

An example of using the DSMC method to study the effect of process chamber design on the uniformity of silicon etching in chlorine is illustrated in Figure 3. The flux of silicon bichloride emanating from a 300-mm silicon wafer, proportional to the etch rate, is plotted versus the radial position across the wafer. This is an axisymmetric system ensuring uniformity in the azimuthal direction. The wafer is located 17 cm away from the source and is supported on a 340-mm substrate. By increasing the process chamber diameter, the flow contraction around the edge of the substrate is attenuated, thus improving uniformity. For a wide range of pressures and wafer locations, a 45-cm-diam. process chamber appeared to yield the best uniformity in this case.⁸

Figure 3: Etch reaction uniformity over the 300-mm wafer for different values of the process chamber diameter and for two pressures.

Another application calls for selecting the position of the RF coil in a dome-shaped ICP reactor used for etching 300-mm wafers. The modular plasma reactor simulator (MPRES), an experimentally verified finite element—based fluid simulation package for ICP tools developed at the University of Houston, was used for the study described here.⁹ A four-turn solenoidal coil wound around the quartz dome powers the plasma (Figure 4). The coil can be positioned in one of four different locations designated in Figure 4 as high, middle, low, and bottom positions, in descending order from the top of the dome (for each position only half of the coil is shown). The finite element grids used for argon and chlorine plasma simulations are also depicted in the figure.

Figure 4: A dome-shaped ICP reactor showing four different positions of the coil. For each position only half of the coil is shown. The finite element grids used for numerical simulations of argon and chlorine plasmas are also shown.

Figure 5: Normalized ion flux versus radial position on a 300-mm wafer for different coil positions corresponding to Figure 4.

Figure 5 illustrates the effect of coil location on ion flux uniformity in an argon plasma under typical operating conditions. The peak values of the ion flux are 4.20 x 10²⁰, 4.23 x 10²⁰, 4.56 x 10²⁰ , and 4.64 x 10²⁰ m^—2/sec^—1, respectively, for the high, middle, low, and bottom coil positions. The uniformity improves steadily and dramatically in going from the high to bottom coil positions. This results from altering the location of the plasma generation zone (plasma is mainly generated in a torous centered several centimeters from the coil) and the ion diffusion length as the coil position is varied. Under the conditions of Figure 5 the ion density always peaks on axis. However, having the plasma production zone near the wafer edge, when the coil is at the bottom position, results in more uniform ion density profiles. The optimum coil placement is different for an argon plasma than for a chlorine plasma, mainly because the chemistry differs in the two systems. Placing the coils at the bottom position in a chlorine plasma would result in an etch rate highest at the wafer edge, while a center fast etch would be predicted based on the argon results shown.

In general, the ion flux uniformity depends on the ion production rate; ion diffusion length, which depends not only on the geometry of the system but also on the location of plasma production; reactor aspect ratio; and pressure, which determines the diffusivity value. These parameters can be lumped into two dimensionless groups—Damkohler number and aspect ratio—that characterize the system behavior. This number in plasma systems varies, depending on the plasma power and pressure. When Da is >>1, large concentration gradients and nonuniformities may be expected. The effect of aspect ratio is shown schematically in Figure 6. Given a localized source of species (for example, etching radicals or ions), the spatial distribution of these species at steady state will depend on the reactor aspect ratio. Low-aspect-ratio reactors (tall, small radius) yield a distribution that peaks on axis, while large-aspect-ratio systems (short, large radius) yield a distribution that peaks off axis. This is because, as the species diffuse radially away from the localized source to try to fill in the central regions of the reactor, they also diffuse toward and are lost onto the axial end walls. The final profile is dictated by the relative magnitude of the diffusion lengths, that is, the aspect ratio. It is actually the square of the aspect ratio that governs behavior because the diffusion loss rate is inversely proportional to the square of the diffusion length. A flat ion flux profile should be obtained at an intermediate aspect ratio.

Figure 6: Schematic of species flux uniformity for different aspect ratios. Tall reactors yield a center-peaked profile; short reactors yield an edge-peaked profile.

Although equipment designers are striving to achieve uniform processing, design trade-offs are sometimes forcing nonsymmetric reactors, such as the example shown in Figure 7. Gas enters through four portholes arranged symmetrically around the reactor and is pumped through a single exit port, a clearly azimuthally nonsymmetric configuration. An inductive coil generates plasma by applying 13.56 MHz to the coil. A focus ring may encircle the 300-mm wafer resting on the reactor floor. Even with geometrically symmetric reactors, azimuthal asymmetries may be introduced because the coil current is a function of length along the coil caused by capacitive coupling to the plasma and surrounding structures. As a result, the induced electric field and power deposition in the plasma may end up being azimuthally nonsymmetric.¹⁰ Asymmetries caused by gas flow or electrical characteristics of the coil require the use of three-dimensional simulations. Symmetric gas distribution is particularly important in relatively high-pressure systems since diffusion is not as facile. It was thought that gas distribution and the location of the pumping ports should not be important in low-pressure systems since diffusion should be fast enough to homogenize the gas. As it turns out, this is not always the case.

Figure 7: Schematic of gas injection and pumping port in a three-dimensional ICP reactor.

Figure 8: (a) Flux of molecular chlorine on the floor of a reactor without a focus ring. The solid line is the outline of a 300-mm wafer. (b) Flux of molecular chlorine on the floor of the reactor with a focus ring. The wafer is completely encircled by the focus ring shown here as a white ring.

Results of a 3-D simulation of a chlorine plasma sustained in an inductively coupled tool of the type depicted in Figure 7 are shown in Figure 8. The flux of molecular chlorine to the reactor floor without a focus ring is illustrated in Figure 8a. Large gradients can be seen over the 300-mm wafer, shown in solid outline. These are a result of molecular chlorine production caused by a recombination of chlorine atoms on the reactor sidewalls and pumping from the lower left-hand side of the figure. For a process in which the etch rate depends on the molecular chlorine concentration (for example, aluminum etching), this worst-case scenario would result in completely unacceptable nonuniformity—about 60% variation—of etching. When a focus ring is used (Figure 8b), the flux nonuniformity is reduced dramatically to <30% variation (note the different scales used in Figures 8a and 8b). Further improvement can be achieved by using a taller focus ring. The effect of a focus ring in a two-dimensional axisymmetric system has been examined previously.¹¹

Conclusion

Because equipment manufacturers face the dual challenge of developing the next-generation reactors and the processing recipes compatible with these reactors, modeling and simulation are playing increasingly important roles in equipment and process design. Computer simulation can help screen design alternatives, thereby reducing design cycle and cost. It can also be used for process optimization and control. Further understanding of the physics and chemistry of semiconductor processes as well as developments in numerical methods and in parallel computing will have a profound impact on multidimensional simulations of semiconductor processing equipment, culminating in a virtual reactor. This will be based on an integrated systems approach in which the reactor design, control, and optimization problems are solved simultaneously, not separately. At some point in the near future a simulation package for the tool will accompany the sale of that tool.

Comparison of simulation predictions to experiments must be an integral part of any 300-mm modeling and simulation program. Unfortunately, there are very few published experimental data pertaining to 300-mm wafers; an exception is the study that suggests that computer simulation can indeed be used to design the next generation of process tools.¹²

For complex chemical systems the simulation's accuracy is limited by the lack of knowledge about the chemistry in the gas phase and on surfaces. The latter is especially true at low pressures. However, one does not need to know everything about a complex system in order to build a useful model of that system. Dominant chemical reactions can be identified that, when incorporated into the simulation tool, capture the main features of the system. The "tuning" of model parameters can then be used based on experimental data to extend the range of the simulation's validity.

Acknowledgments

Work performed at the University of Houston was sponsored by the National Science Foundation (CTS-9713262). The authors would like to thank Vikas Midha of the university's plasma processing lab for developing the electromagnetics code used as one of the modules of MPRES. They would also like to thank David Hash for his DSMC results in Figure 3.

References

1. Tandon S, "Challenges for 300-mm Plasma Etch System Development," Semiconductor International, 21(3):75—82, 1998.

2. Bird B, Stewart W, and Lightfoot E, Transport Phenomena, New York, Wiley & Sons, 1960.

3. Yeckel A, and Middleman S, "On the Origin of Nonuniform Growth of LPCVD Films from Silane Gas Mixtures," Journal of the Electrochemical Society, 136(7):2038— 2050, 1989.

4. Alkire R, and Economou D, "Transient Behavior during Film Removal in Diffusion-Controlled Plasma Etching," Journal of the Electrochemcial Society, 132(3):648—656, 1985.

5. Walker R, and Zawadski P, "Using CFD to Scale Up Production Process," Process Simulation, 15(5):39—42, 1998.

6. Economou DJ, Bartel T, Wise R, and Lymberopoulos D, "Two-Dimensional Direct Simulation Monte Carlo (DSMC) of Reactive Ion and Neutral Flow in a High-Density Plasma Reactor," IEEE Transactions on Plasma Science, 23(4):581—590, 1995.

7. Meyyappan M (ed), Computational Modeling in Semiconductor Processing, Boston, Artech House, 1994.

8. Hash D, and Meyyappan M, "A Direct Simulation Monte Carlo Study of Flow Considerations in Plasma Reactor Development for 300-mm Processing," Journal of the Electrochemical Society, 144(10):3999—4004, 1997.

9. Wise R, Lymberopoulos DJ, and Economou D, "A TCAD Simulation Tool for Inductively Coupled Plasma Reactors and Comparison with Experiments," in Proceedings of the 11th Plasma Processing Symposium, Mathad GS, Meyyappan M, and Hess DW (eds), PV-96-12, Pennington, NJ, Electrochemical Society, pp 11—19, 1996.

10. Kushner M, Collison W, and Grapperhaus M, "A Three-Dimensional Model for Inductively Coupled Plasma Etching Reactors: Azimuthal Symmetry, Coil Properties, and Comparison to Experiments," Journal of Applied Physics, 80(3):1337—1344, 1996.

11. Singh V, Outka D, and Yang R, "Application of Plasma and Flow Modeling to the Design of Optimized Aluminum Etch Equipment, Electrochemical Society Proceedings, Meyyappan M, Economou DJ, and Butler S (eds), PV-97-9, Pennington, NJ, Electrochemical Society, pp 251—259, 1997.

12. Collison W, Ni T, and Barnes M, "Studies of the Low-Pressure Inductively Coupled Plasma Etching for a Larger Area Wafer Using Plasma Modeling and Langmuir Probe," Journal of Vacuum Science and Technology A, 16(1):100—107, 1998.

Demetre J. Economou, PhD, is a John and Rebecca Moores Professor and the associate chairman of the department of chemical engineering at the University of Houston. His research interests include plasma processing (simulation, diagnostics, and process control), energetic neutral beams, and atomic layer etching. His PhD in chemical engineering is from the University of Illinois (Urbana-Champaign). A member of AIChE, Economou is the author or coauthor of more than 90 scientific papers, and he holds one U.S. patent.

Theodoros L. Panagopoulos is pursuing a PhD in chemical engineering at the University of Houston. His research interests include two- and three-dimensional simulations of ICP reactors, sheath dynamics, and ion energy distribution at target electrodes. He earned a BS in chemical engineering at the National Technical University of Athens, Greece.

M. Meyyappan, PhD, is a project manager of devices and nanotechnology at NASA Ames Research Center (Moffett Field, CA). His group is involved in modeling of ultrasmall semiconductor devices and processing equipment, chemistry database development for semiconductor processing, and carbon nanotubes—based nanotechnology. He holds a PhD in chemical engineering from Clarkson University. He is a member of IEEE, AICHE, AVS, ECS, and MRS. (Meyyappan can be reached at 650/604-2616 or meyya@orbit.arc.nasa.gov.)

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