Automated Optimization Techniques Improve Illumination
A group at the Institute of Solid State Physics at Technische Universität Berlin in Germany is using a metallorganic chemical vapor deposition reactor for the fabrication of a variety of semiconductor heterostructures. The wafers under fabrication are heated with an infrared lamp, which could not change temperature fast enough for a particular application and could not reach sufficiently high temperatures.
The reactor, an AIX 200/4 from Aixtron AG of Aachen, Germany, consists of a big glass tube, around which six reflecting elements are arranged. In the middle of the reactor tube is a graphite block called the susceptor. In the center, a rotating tray carries three circular subtrays, each of which accommodates a 2-in. wafer. A flow of precursor gases of metallorganic compounds deposits epitaxial layers on the wafers.
The lamps beneath the susceptor heat the wafers. Their temperature is a crucial parameter in a specific process: It is important to be able to rapidly change the temperature and to reach a high final temperature.
The heater was found to work well, but to achieve higher temperatures and more uniform distributions of temperature along the wafers, the researchers wanted to improve the illumination optics. The heater used parabolic reflectors, which are good but not optimal. Elliptical mirrors would enhance the radiation transfer to the graphite susceptor, but it was necessary to compute the exact shape of the mirrors.
The first step was to build a model of the existing design in Zemax, produced by Zemax Development Corp. of Bellevue, Wash. The ray-tracing software modeled the flow of light and the light/mirror/susceptor interactions. The graphite susceptor was modeled as a detector object, and the design goal was to maximize the energy transfer from the helical lamps to the susceptor. The lamp reflectors were modeled as toroidal mirrors with infinite bending radii.
The new surface shape was determined by setting the software to maximize energy transport. The original heater design had featured just one type of parabolic mirror, with the filament in the focus. The new design had three reflector surfaces, each duplicated for either half of the symmetric structure (Figure 1). All were elliptical, but they featured different semiaxes and angular orientations. The filaments were not necessarily centered in the foci.
Figure 1. Redesigning the illumination optics enhanced the power of the lamp heaters used in an epitaxy reactor for the fabrication of semiconductor heterostructures. In this ray-trace simulation, the susceptor carrying the wafers is irradiated by three of the six lamps.
The constraints were that the absolute positions of the lamps should remain unaltered relative to the susceptor and reactor tube and that the mirrors should not touch either one another or the glass tube. The design goals and constraints were expressed within the software, which optimized each set of two opposite reflectors.
The outermost lamp pair saw the smallest cross section of the susceptor, so it was difficult to focus the desired light there. The original parabolic design was retained for the two inner pairs of reflectors, their filaments were turned off in the software, and the outermost reflectors were optimized with their lamps simulated as burning at 1000 W. Tens of thousands of rays were used to get accurate simulations.
Because the only relevant constraint was that the reflector surface should not touch the reactor tube, the reflector could be as wide as needed. The width of the ellipse was fixed manually, and the software optimized the remaining parameters using default settings. With an inner, automatic optimization nested in an outer, manual optimization, the width of the reflector was increased until the ellipse almost touched the reactor tube. These reflectors were now fixed, and their source filaments were switched off.
Figure 2. The heater consists of six infrared lamps beneath the susceptor. They initially were inside parabolic reflectors. The design challenge was to compute the best mirror shape for each lamp individually. Image by Armin Dadgar, Universität Magdeburg.
The same procedure was conducted with the adjacent lamps. Because the planar sidewalls of the outermost reflector elements also reflect light from inner lamps, the ellipse could be tilted away from the direct incident light, toward the neighboring lamp. This could raise the angular extent of this reflecting element, yielding maximum power transmission. After the software arrived at this solution, the final design was fixed, the middle lamp switched off, and the innermost reflectors were optimized using the same approach.
The result was an increase in efficiency of more than 20 percent. More importantly, the outer edges of the susceptor were heated by 89 percent of one lamp’s power, versus 73 percent in the original design. This allowed an increase of up to 50 °C in the outer susceptor region, changing its function from “heat sink” to “flow neutral” or even “heat source.” As a consequence, the heat conduction away from the tray center to the susceptor margins has been reduced, contributing to a more homogeneous temperature profile.
Using the optical design software, this optimization took only three days, whereas it would have taken three weeks to write the code from scratch.
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