1 of 13 The Structure of AI By Ian Beardsley © 2016
2 of 13 In my book “The Chemistry of AI and Natural Life” we dealt with: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
The structure of Silicon (Si) How Si forms crystals How doping it with Boron makes p-type Si How doping it with Phosphorus makes n-type Si The active region of the Period Table for AI and Natural Life The Octet Rule and its pertinence to AI and Natural Life Ionic and Covalent bonding. Electron Orbitals Hydrocarbon Structure and Si Crystal Structure How Semiconductors Work How Semiconductors allow for logic gates AI and Natural Life equations for completing an Octet
In my book “The AI Matrices” 1. We demonstrated an AI Cookbook written into Nature by a Mysterious Force 2. We derived a set of AI Equations: a) The Isocyanic Matrix b) The Silexic Matrix c) The Skellein Matrix These were derived from molar masses of the AI and Natural Life elements. Now we turn to densities, dimensions, and doping proportions (numbers of atoms) in the AI elements and densities of the Natural Life elements. There are many different kinds of electronics components, so we will choose one kind of component, and, that will be a rectifier diode, to study these aforementioned aspects of doped silicon. Luckily for us, the elements that make up AI exist at or near standard temperature and pressure (STP) and, their densities vary little for a big range around that temperature and pressure. This will allow the study to be quite feasible. A rectifier diode converts an AC (alternating current signal) into a DC direct current signal: — — / \ / \ + —————————— \ / \ /— — AC IN
_ _ / \ / \ + -—-|>—— —————————— ———>
DC OUT


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4 of 13 We start with the most basic thing we can do and, that is, compare the density of silicon (Si) to the density of boron (B) and the density of silicon (Si) to the density of phosphorus (P), and following in suit with our earlier work, compare the density of germanium (Ge) to gallium (Ga) and the density of germanium (Ge) to the density of arsenic (As). Phosphorus has two elemental forms: white phosphorus and red phosphorus. Red phosphorus can be obtained by heating it to 250 degrees C, or by exposing it sunlight. It is the most stable allotrope of phosphorus, but can return back to white phosphorus simply under frictional heating. We will look at white phosphorus, as its density is well defined: Si: 2.57 grams per cubic centimeter P: 1.823 grams per cubic centimeter B: 2.37 grams per cubic centimeter Ge: 5.323 grams per cubic centimeter Ga: 5.91 grams per cubic centimeter As: 5.727 grams per cubic centimeter Si/P = 1.41 Si/B = 1.08 ~ 1 Ge/Ga = 5.323/5.91 = 0.90 ~ 1 Ge/As = 5.323/5.727 = 0.929 ~ 1 Everything except Si/P approximately equals one. Si/P = 1.41 = the square root of 2 (sqrt(2)). Phosphorus is sometimes replaced with arsenic (As) as a n-type dopant: Si/As = 2.57/5.727 = 0.44875 Let us compare Si to Ge, the semiconductors: Si/Ge = 2.57/5.323 = 0.4828 The result is their is nothing there interesting but Si/P because it is to two places after the decimal, the square root of two. The rest are actually interesting in that they are almost one. We can take the means, geometric, harmonic, and arithmetic: sqrt(PB)/Si = [sqrt(1.823*2.37)]/2.57 = 0.80878741 sqrt(Ga*As)/Ge = [sqrt(5.91*5.727)]/5.323 = 1.09 It is at once clear there is not much here and we don’t need to pursue the other means. But, this is good; it gives more meaning to the AI matrices in that it shows they are probably not a coincidence in that such calculations don’t alway have structure. That is we found that structure existed in the molar masses but not in these densities for the same materials. Furthermore we have shown that this avenue reveals very little, so we can eliminate it from our studies. Here, there is no golden ratio, just the square root of two and unity in everything else. The unity factor is not surprising in that, many of these elements are close to one another in the periodic table and therefore are approximately equivalent and that, is why we get unity in so many of the ratios.
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At this point I should like to say: the crystal wafers of silicon and germanium are doped as they are grown meaning, each wafer has an almost uniform doping with itself and the others. Further doping changes are made after the wafer is done with diffusion doping and implantation doping. The interesting thing here is there only on the order of one dopant atom per 100 million atoms in low or light doping, and there is only on the order of one dopant atom per 10 thousand atoms in the case of heavy or high doping. Thus we can consider the dopant atoms as negligible and use the the density of silicon alone in calculating the mass of our IN4007 rectifier diode whose dimensions we have already calculated. Most diodes are encased in glass but, clearly, this diode, is not. And, being a cylinder, we are ready to calculate its volume. The volume of a cylinder is V=Bh where B=2(pi)r: We have: V=2(pi)(5 mm)(1)^2 = 31.41 cubic millimeters The density of white silicon is 2.57 grams per cubic centimeter. 2.56 g | 100^3 cm^3 | m | —————- ————————————— = 0.00256 g/mm^3 cm^3 | m^3 | 1000^3 mm^3 |
(31.41 cubic millimeters)(0.00256 grams cubic millimeter) =0.080 grams or Mass of IN4007 Rectifier Diode = 8 centigrams There are 6.02E23 atoms per mole and 28.09 grams per mole of Si. (0.08 g Si)(mol Si)/(28.09 g Si) = 2.2472 moles of Si in the diode (2.2472 mol Si)(6.02E23 atoms Si) = 1.35E24 atoms of silicon in the diode. The precise calculation: 1/10,000 = 0.0001 99.9999 (2.57 g/cm^3) + 0.0001 (1.823 g/cm^3) ———————————— 256.9997 + 0.0001823 = 256.99988 grams per cubic centimeter of doped silicon And, we see there is no need to do the precise calculation; the weighted density of doped silicon has very little difference from the density of pure silicon. And, just because we have found no structure in the densities of the AI elements using the same template we use the the molar masses of the AI elements, does not mean structure does not exist in them. As Einstein said, “The truth is well hidden”. We need to take another approach in that, I feel, Nature is sublime.
6 of 13 It is my feeling, where the densities are concerned, we need to find a “magic volume” as opposed to dealing with ratios and means. And further I don’t believe that volume is to be found in the IN4007 rectifier diode because it is human contrived, not Nature produced. Why didn’t I see it before? With all those ones and the square root of two, P, B, Si, Ga, As, Ge, … are a unit square with its diagonal drawn in with the following scenario:
1 ——————————|| | | | | | - Si/P | Ge/As | Si/B | | | | | | | - | ——————————Ge/Ga We will call it The AI Density Matrix, which is:


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13 of 13 The Author