TITLE: Epitaxy NAME: Dan Connelly COUNTRY: United States EMAIL: djconnel@flash.net WEBPAGE: http://www.flash.net/~djconnel/ TOPIC: Elements COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT. JPGFILE: epitaxy.jpg ZIPFILE: epitaxy.zip RENDERER USED: POVRay Windows 3.0 TOOLS USED: Paint Shop Pro 5.01, JPEG Optimizer, ImageMagick RENDER TIME: 4 CPU-days HARDWARE USED: PII 266 MHz, 128 MB memory (primary) HP Worksation, 100 MHz, 128 MB memory (secondary) IMAGE DESCRIPTION: see below DESCRIPTION OF HOW THIS IMAGE WAS CREATED: see below tools used detail: POV-Ray : rendering and modeling Paint Shop Pro 5: signature JPEG Optimizer: JPEG conversion ImageMagick: combine ====================================================================== NOTES theme notes: introduction ------------- The ruling class of the periodic table is column IV. Carbon, the lightest member, is the basis for life in its incredible diversity of molecular forms. As a crystal, it mechanical and aesthetic properties make it among the most values substances throughout human history. But as a crystal, it places second to the next member of the IV family : silicon. Developments of silicon technology have revolutionalized human society during the past 40 years. This image shows the interior of a chemical vapor deposition system for silicon epitaxy -- the thermally activated growth of crystalling material from hydrides. However, what is being formed isn't exactly silcon, but something newer : a zincblend germanium silicon crystal. GeSi as an alloy has received considerable attention over the past 15 years due to its superior electronic transport properties and due its application in "band engineering". However, as an alloy, it presents some difficulties. An ordered crystal would solve some of these, and would provide a clear advantage in CMOS technology. Yet its formation is too difficult -- entropy's pull is too strong. So it remains an idea.... a concept.... a goal. chamber ------- The distant background is dominated by the quartz reaction chamber. It must be transparent to allow penetration of the light from the lamp array above and below. This light is the heat source which controls the reaction rate. It is perhaps ironic that quartz is itself a compound of silicon -- silicon begets silicon. gas --- The reaction is generated from SiH4, GeH4, and trace amounts of B2H4 in an ambient of H2. Atoms are colored according to a scale based in spectral theory : red for the less tightly bound germanium valence electrons, and blue for the more strongly bound silicon atoms. Hydrogen, with its relatively neutral role, is white. Boron, being metallic, is also colored white (slightly transparent due to its reduced valence). In the foreground the rather large tetrahedral SiH4 and GeH4 molecules are clearly visible. Due to its lesser reactivity, more SiH4 must be used than GeH4, and thus these are shown in 2:1 molecular concentration ratio. The H2, despite being more numerous still, are more difficult to spot due to their small size. The B2H4 is considered too rare (its high reactivity and trace concentration in the crystal means very little is needed) to be seen and thus is not rendered. As the nanometers of the foreground give way to the decimeter-distances to the chamber, the gas loses its discrete visibility and becomes a gaseous continuum. The red and blues of the Ge and Si average into a purplish haze which pervades the scene. crystal ------- This, clearly, is the focus of the image. The zincblend lattice (an extension of the diamond lattice), despite the simplicity of its specification, is a wonderful mix of cubic and hexagonal symmetries which the raytracer is excellently suited to reveal. Here is a viewpoint quite close (approx 13 nm) from the edge of the wafer. To the right is visible a step on the surface -- it is via such steps that epitaxy typically occurs, due to the catalytic effect of the corners. The corner of the step is visible in the distance -- it hasn't yet reached the wafer edge. The step in this case is a double one -- quite rare in practice, but this is our lucky day :). The structure is formed from sp3 hybrid orbitals -- four ellipsoids per atom. The ellipsoids from adjacent atoms merge in a covalent bond with two electron states of complementary spin. Layers of germanium and silicon atoms alternate -- again the same colors are used : red for germanium and blue for silicon. The reaction is limited by hydrogen atoms terminating dangling surface bonds. The surface layer is here silicon, with approximately 800f the surface bonds H-tied. Note the crystal surface is highly simplified -- in reality there are complex surface reconstructions which reduce the number of free states per atom to one from the two shown here. Additionally, in current alloy deposition technology, there are other complex surface reactions taking place which are neglected. The perfection of the lattice is broken, however, by the presence of an occasional boron atom (here represented as white). With only three available valence electrons, boron creates a net electron deficiency which manifests itself as extended quantum states called "holes". These act as the conduction quanta in "p-type" material, shown here. The hole gas is shown as a green cloud permeating the crystal, fading exponentially away from the surface. Even though the doping level in this crystal is quite high, the hole gas is still quite dilute relative to the free carrier gas found in metals. It is the control of this carrier gas, the ability to attract and repel it, that makes it so useful in semiconductor switches. * * * * * * * * * * * * * * * * * * * * * * * * technical notes: First, the boring stuff... The chamber is CSG from superellipsoids textured with a modified quartz texture. An array of six lights placed at the top surface of the chamber interior lights the scene. They are visibly represented by toroids at over the top of the chamber... they affect the scene only in reflections. The hole gas is done with halos. The main crystal has a single large halo with an exponential density function at the top surface. The atoms in the step have a separate halo, each with a simple spherical density function combined into a single, very expensive, halo field. Rendering of the middle part of the image is at under 2 lines per hour as a result of this structure. The rest is blobs. To assist with the definition of the structure, TMPOV (http://twysted.net/) was used for its array support (POV 3.1 Beta also has arrays, but I chose 3.0 instead due to its UNIX support and for my greater familiarity with halos at the time). Arrays were used to define an extended unit cell, which was stepped to create the entire crystal. The dimensions of the crystal are 25 x 50 x 10 of these extended unit cells, each containing four atoms, each containing four sp3 orbitals. This would be 200k blob components -- way too much for practice. Thus several optimizations needed to be made: 1. the depth of the crystal was made nonuniform : it increases linearly from zero to 10, then decreases exponentially to the wafer edge. This strategy was chosen to make sure there was reasonable depth along channeled directions (those with long lines of site without obscuring atoms).... at shallow angles, only atoms near the surface are visible anyway. 2. The breadth of the crystal was reduced by making the x extent in proportion to the z distance -- this more efficiently handles the field of view. 3. It was rendered in two pieces, which were assembled The first phase rendered the top of the scene, including only the top 1-2 layers of atoms. The second phase handled the foreground and those gas molecules close enough to cast shadows -- the full depth of the crystal was rendered, but it wasn't rendered to full distance. This two-phase scheme required some care in use of random number streams. The first phase was done on an HP workstation, while the second was done on my home PC. Each took close to 48 hours with full CPU usage. Note this isn't in violation of the IRTC rules. Glenn McCarter used a similar "layered" technique in the nature round ( http://www.irtc.org/ftp/pub/stills/1998-06-30/dominion.txt ). The source code also has a "phase 0" for the rendering of the whole thing in one shot.... 256MB is needed, I suspect. The gas is handled by blobs for the foreground molecules, spheres for the more distant molecules, and a fog for the continuum in the far distance. Atmosphere was tried, here, for greater effect, but it interacted in undesirable ways with the halos. The fog is much faster, as well. Of interest is the strange coloration of the bonds between the silicon and germanium atoms. These were intended to be a smooth fade from red to blue, due to the "as advertised" nature of blobs. However, I suspect the approximations imposed by the POV root solver resulted in some anomalous coloration. A bug? No -- a feature! These are but quantum mechanical fluctuations in the valence field :). * * * * * * * * * * * * * * * * * * * * * * * * artistic notes: The composition of this scene actually is quite similar to my last entry -- http://www.flash.net/~djconnel/POV/baseball.jpg . A strong foreground with a right focus extends into the distance, where the background has a left focus. Asymmetry with a touch of balance... * * * * * * * * * * * * * * * * * * * * * * * * footnote on camera : Assuming a chamber temperature in the range of 600C, the mean speed of the silane molecules is approximately 860 m/sec. Since the width of the near field of view is approximately 10^-8 meters, each pixel is approximately 10^-11 meters in width. This means the shutter on the camera is open on order 10^-14 seconds. With light speed at 3 10^10 cm/sec, this means the shutter can move no more than 1.5 micrometers in each direction. Clearly this camera doesn't have a mechanical shutter.... ======================================================================= APPENDIX I : source files camera.inc : generic definitions of camera parameters camera.pov : generic definition of cameras epitaxy.txt : this file final.ini : a file with some settings used in the final rendering (phase 2, in this case) header.inc : a generic header file main.pov : the main scene ======================================================================= APPENDIX II : rendering stats (phase 2 only) main.pov Statistics (Partial Image Rendered), Resolution 800 x 600 ---------------------------------------------------------------------------- Pixels: 320800 Samples: 1312272 Smpls/Pxl: 4.09 Rays: 1474661 Saved: 1768 Max Level: 5/12 ---------------------------------------------------------------------------- Ray->Shape Intersection Tests Succeeded Percentage ---------------------------------------------------------------------------- Blob 17821938 8307319 46.61 Blob Component 1168266263 122375575 10.47 Blob Bound 14463783035 3935823745 27.21 Box 40610483 40610483 100.00 CSG Intersection 46996820 43564302 92.70 CSG Merge 23498410 23498357 100.00 Superellipsoid 93993640 83748302 89.10 Torus 11783144 0 0.00 Torus Bound 11783144 0 0.00 Bounding Box 2008677095 33595489 1.67 Light Buffer 2928364429 2928359137 100.00 Vista Buffer 22068446 21562807 97.71 ---------------------------------------------------------------------------- Roots tested: 15145420 eliminated: 0 Calls to Noise: 12902610 Calls to DNoise: 10 ---------------------------------------------------------------------------- Halo Samples: 16843657970 Supersamples: 0 Shadow Ray Tests: 25806648 Succeeded: 16861490 Reflected Rays: 312 Refracted Rays: 240 Transmitted Rays: 161909 ---------------------------------------------------------------------------- Smallest Alloc: 26 bytes Largest: 9120716 Peak memory used: 114422529 bytes ---------------------------------------------------------------------------- Time For Parse: 0 hours 3 minutes 39.0 seconds (219 seconds) Time For Trace: 45 hours 23 minutes 35.0 seconds (163415 seconds) Total Time: 45 hours 27 minutes 14.0 seconds (163634 seconds)