This article describes work I did to improve an existing infrared lamp heater in a so called horizontal geometry MOCVD reactor. Zemax was used to model and optimize the heater geometry using non-sequential ray-tracing.
Authored By: Oliver Stier
My Initial Problem
I wanted to improve an existing infrared lamp heater in a so called horizontal geometry MOCVD reactor, where MOCVD stands for metal-organic compound vapour deposition. This is an epitaxy process for the fabrication of a variety of semiconductor heterostructures. The reactor stands in the Institute of Solid State Physics of Technical University Berlin and is used for research purposes described on their homepage: http://sol.physik.tu-berlin.de/htm_group/research/pg_nanostrukturen_e.html
The reactor comes from the company Aixtron AG, and you will find details on it by visiting their page, http://www.aixtron.com and navigating to Products&Services / Products / AIX 200/4.
In my Zemax files (attached at the end of this article) you find a big glass tube around which six reflecting elements are arranged. In real life, this glass tube and the surrounding lamp heater look similar to that shown in http://www.fbh-berlin.de/images/downl/300/Horizontalreaktor.jpg (this picture is copyright Ferdinand-Braun-Institute).
The glowing item in the middle of the reactor tube is a graphite block, called the susceptor, and has the shape shown in the Zemax files by the detector surfaces:
The circular object in the center is a rotating tray carrying three circular subtrays (not really visible in this graphic). Those accommodate one 2” wafer each. On the wafer, the epitaxial layers will be deposited by a flow of so called precursor gases of metal-organic compounds. The wafers are heated by the lamp heater beneath the susceptor, and their temperature is a crucial parameter in the entire process. It is of interest to be able to (i) rapidly change the temperature and (ii) reach a high end temperature.
The Aixtron heater works well, but still has potential for improvement, as it is suited to a variety of Aixtron reactors. We wanted to optimize it for use in our specific application. Aixtron use parabolic reflectors which are good but not optimal for our specific task. Obviously, elliptic mirrors would enhance the radiation transfer to the detector surfaces representing the bottom side of the graphite susceptor. This was my task!
How I entered the design in Zemax
The design of a single heater element is shown in one_lamp.zmx, which is included in the attached zip archive on the last page of this article.
The mirrors were entered using Zemax's built-in TOROIDAL SURFACE object. This is a parametric object, and it uses facets only for drawing on screen and to provide an initial guess for the ray-object intersection point. For rendering purposes, I used a large number of drawing facets (400) but this can easily be set much smaller (10 is sufficient). Remember that the toroidal surface is smooth, and facets are only used for drawing purposes!
The sides of the parabolic mirrors are modelled using RECTANGULAR SURFACE objects. The sources are modelled as SOURCE FILAMENT objects. Finally, the glass tube was modelled using two CYLINDER VOLUME objects, one inside the other. The outer cylinder is made of fused silica, and the inner is made of air. The source filament is then placed inside of the air cylinder.
Here is a cross-section of the lamp:
and here is a fully rendered image:
This unit was then copied and pasted five times, and positioned relative to a dummy object to get the orientation correct. Detector objects were entered to model the susceptor. Finally the whole assembly was placed inside the external oven assembly:
As the above plot shows, rays from a lamp on the right-hand side may find their ways to the left-hand side of the structure. Therefore, the heater is represented entirely, rather than as a half structure only. For symmetry reasons it is sufficient, nevertheless, to have SOURCE FILAMENT objects only on the right-hand side and to use empty glass tubes on the left hand side. To ensure automatic symmetry of the structure in the course of optimisation, the left-hand side is entirely represented by PICK-UP SOLVES mirroring the right-hand side, so that the optimisation parameters only refer to the surfaces on the right-hand side.
How I optimized the design
The problem is intrinsically hierarchic, allowing the global optimisation to be broken down into three partial optimisations. The outermost lamp pair sees the smallest silhouette of the susceptor, so that the focussing of as much light as possible is most complicated here. The optimisation of these lamps should not be constrained by the properties of the neighbouring lamps. To start, the initial parabolic design is kept for the two inner pairs of lamps, their filaments are turned off, and only the outermost reflectors are optimised with the right lamp burning at 1000W. 5000 or 10000 rays are used. The only relevant constraint is that the reflector surface must not touch the reactor tube.
As the homogeneity of the illumination does not matter, and only the total power transmistted matters, the merit function is quite simple. Please see the file optimized result.zmx in the zip archive at the end of this article, and open the merit fuction editor. First, some NT** operands constain the total tilt so that the lamp does not hit the reactor wall or the susceptor. Then detectors are cleared, a non-sequential ray-trace is performed, and then the total power on all detectors is targeted to 1000W, this being the lamp power.
I fixed the width of the ellipse manually and let the remaining parameters (position, radius of curvature, conic constant and r^2 aspheric coefficient) be optimised by Zemax, using default settings. Thus I nested an inner, automatic optimisation in an outer, manual optimisation where I increased the width of the reflector until the ellipse scratched the reactor tube. At this point, the outermost lamp pair was done.
These reflectors were now fixed and their SOURCE FILAMENTs switched off, and the same procedure as above was conducted with the adjacent lamps. Importantly, the outer sidewalls of the outer lamps serve as prolongation to the elliptic surface which allows the ellipse to be intentionally tilted away from the direct incident. By this, the angular closure of this reflecting element could be raised in total, yielding a maximum of power transmission. This, honestly unexpected, solution was found by Zemax, not me! Again, the final design was fixed, the lamp switched off, and the innermost lamps were optimised straight-forwardly.
The toroidal surfaces' surface function was transformed into CNC milling data files using Mathematica (http://www.wolfram.com/products/mathematica/index.html), and that was it!
The Performance Improvement
The resulting increase in transmission efficiency is as follows:
The increase in transmitted power is very significant:
| |
Original |
Optimized |
| Outer lamps |
69% |
77% |
| Middle Lamps |
71% |
80% |
| Inner Lamps |
73% |
89% |
My total work time from getting started with the non-sequential mode, entering the initial structure (i. e. the original design), doing the optimisation, and exporting the graphics and result parameters of the TOROIDAL SURFACES was exactly 22 hours of work. Jenny Warwick of Optima Research (the European distributor of Zemax) had given me the appropriate pointers to the Zemax manual so that I could enter my problem without delay. I would like to mention that I had never used Zemax before.
I had done such optimisations three times before, from scratch, using Mathematica and my own C code, and that took a couple of weeks, as can be understood. I admit I was surprised to be ready with the task this time on day 3!