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Silicon has a bandgap of 1.1 eV, whereas germanium has 0.65 eV. Silicon has an indirect bandgap, whereas gallium arsenide has a direct bandgap. Still silicon is mainly used for making solar cells. Why?

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    $\begingroup$ My thesis advisor, who was a professor of materials science & engineering, once told me that silicon is actually not a very good semiconductor compared to germanium and some other semiconductors. For example, silicon doesn't have a particularly high carrier mobility. Like the answers below state, the reason silicon has remained popular in the semiconductor industry for so long is due to other factors than its electronic properties. $\endgroup$ – Samuel Weir Nov 3 '18 at 18:46
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    $\begingroup$ What are those other factors? $\endgroup$ – Shaona Bose Nov 3 '18 at 19:56
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    $\begingroup$ Gallium arsenide is surely something everyone wants on their roofs $\endgroup$ – PlasmaHH Nov 3 '18 at 20:24
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    $\begingroup$ @ShaonaBose - The answers below already list several reasons. Another is that it's relatively easy to make an insulating layer on top of silicon by exposing it to oxygen while heating it to form an SiO2 layer, which is a good, strong insulating material. I don't believe that anything comparable to that is possible with germanium. $\endgroup$ – Samuel Weir Nov 3 '18 at 21:34
  • $\begingroup$ By the way, a very relevant answer here: physics.stackexchange.com/a/162348/94257 $\endgroup$ – Yuriy S Nov 4 '18 at 0:36
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Si is among the most abundant materials on Earth and widely used for processors as well. There are very few other materials that can even theoretically compete with that. Germanium and GaAs won't be ever able to. Organic solar cells were promising due to low fabrication cost (just ask bacteria or whatever to make your solar cells), but failed. Now perovskites and especially perovskite-silicon tandems are the hot topic in research.

Back in the day, thin film technologies like CdTe, CIGS etc also looked promising and started gaining meaningful market share - the highest was about 13% or so, and many believed they will reach 20%+ of the market as they almost caught silicon efficiency. But then Chinese entered the market and killed other tech by dramatically lowering Si prices.

GaAs and closely related other III-V technology is used where mass or area efficiency matters the most as this tech offers the highest efficiency - therefore, it is used for satellites and other space craft. However, ISS still uses silicon (even though GaAs had higher efficiency even back then). From Tristan's comment, they will be upgrading to the state of the art GaAs tandems fairly soon - the tandems here will be GaInP/GaAs/Ge. This tandem is the most typical, but various other configurations are possible. Such tandems are usually (but not always) lattice matched and combine Ga/In with N/P/As in various ratios to achieve variable bandgap.

Now more specifically for the mentioned technologies in the question:

  1. GaAs is crazy expensive. A single wafer costs several hundred euros, while even floatzone silicon wafer costs tens, and typical solar cells are made of dirt cheap silicon, costing far below 1€ for the wafer (unprocessed wafer costs). Add tons of Si tech from CPU industry. Getting tools that can do magic on silicon is easy and cheap, tooling for III-V is expensive and much more problematic, so processing again favors Si.
  2. Germanium alone isn't a good solar cell material - too low bandgap. But great for tandems. Sure, it will collect tons of photons, but all photon energy beyond the bandgap will get wasted and you won't end up with a lot of energy. Unless you try (and eventually fail) to make viable downconverters to split the high energy photons in 2, each with half the energy. Si is actually pretty good regarding bandgap, only ~1% (absolute) below the maximum.
  3. Indirect bandgap just means that your absorption coefficient severely drops near the bandgap. This has a single consequence optically: you require a thicker layer of absorber to get the same absorption. But, as silicon is cheap, it isn't much of a problem. As it turns out, move to say 100 μm wafers was postponed due to wafer handling more than the efficiency - it turns out you can break them easily unlike the robust 180 μm ones. Plus, even as thin as 1 μm of silicon would still absorb surprisingly large amount of light if it gets heavily scattered on each interface.
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    $\begingroup$ Small nit (since this is actually in my line of work): ISS presently uses silicon cells because they were built more than 20 years ago. The ISS solar cells at my desk were manufactured October 1993. The current spaceborne solar power state of the art (which ISS will be adding as an upgrade fairly soon) is based on triple-junction cells that use three separate junction materials: Gallium-Indium-Phosphide, Indium-Gallium-Arsenide, and Germanium, built on a Germanium substrate. See spectrolab.com/photovoltaics.html $\endgroup$ – Tristan Nov 5 '18 at 16:22
  • $\begingroup$ @Tristan Thanks for the comment. I have edited that bit, hopefully less wrong now. Though, GaAs had efficiency above Si since the beginning - do you perhaps know why didn't ISS start with GaAs? Was it not THAT much better back then, or were there some other issues? $\endgroup$ – Zizy Archer Nov 5 '18 at 20:10
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    $\begingroup$ Space-based hardware tends to lag the terrestrial state of the art. While GaAs cells were used some in the 60s, they didn't get used broadly in orbit until the 90s. The cells I have were built in 1993, but they were specced out and selected in 1986. At that time, there weren't really any commercially viable GaAs cells to use, and ISS needed more than a quarter million of them to fly. $\endgroup$ – Tristan Nov 5 '18 at 20:58
  • $\begingroup$ Good answer. -- Another significant factor is the brittleness of GaAs compared to Si wafers. Si is plenty brittle but nothing compared to GaAs. -- GaAs is also much harder to work with (which is one of the reasons it is, as you say, "crazy expensive"). -- GaAs is about 50% pure Arsenic - and Arsenic is a major biocide. Si is a little sharp when it breaks but otherwise inert to most life. Si is doped with Boron for solar and Boron doped Si is no more toxic than just Si. -- Hope this helps improve your answer. $\endgroup$ – user23715 Nov 5 '18 at 20:59
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    $\begingroup$ A gripe: thin film tech (you mention CdTe and CIGS, specifically) is not "dead" by any means. First Solar series 4 has 10 GW installed by itself, and that's cad-tel. $\endgroup$ – kevinsa5 Nov 5 '18 at 22:22
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On the topic of germanium versus silicon, a smaller band gap is not a good thing in a solar cell.

The maximum theoretical efficiency of a single-junction solar cell in natural, unfocused sunlight is called the Shockley-Queisser limit, and is a function of band gap. It turns out that this limit has a maximum at a band gap of $1.34~\rm eV$, which makes gallium arsenide ($1.42~\rm eV$) excellent and silicon ($1.1~\rm eV$) still pretty good. Germanium is far enough away that its efficiency is much lower.

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    $\begingroup$ GaAs has 1.42 eV bandgap, which of course, doesn't invalidate your argument $\endgroup$ – Yuriy S Nov 4 '18 at 0:34
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    $\begingroup$ This is specific to sunlight and Earth though, isn't it? Could germanium make sense for some space applications? $\endgroup$ – leftaroundabout Nov 4 '18 at 11:14
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    $\begingroup$ @leftaroundabout Potentially. The general idea is that lower band gap corresponds to higher efficiency for higher wavelengths. The frequency spectrum of sunlight isn't so different in space to make germanium useful with sunlight. In principle it could be useful somewhere more opaque to low wavelengths, though, or with a source of light besides the sun. $\endgroup$ – Chris Nov 5 '18 at 2:38
  • $\begingroup$ A combination of both would likely be better in space, to capture light at a wider bandwidth overall. On Earth we are shielded from a lot of shorter wavelength light by our atmosphere, but those wavelengths can be harvested in space... $\endgroup$ – Drunken Code Monkey Nov 5 '18 at 12:49
  • $\begingroup$ @DrunkenCodeMonkey Silicon is better for shorter wavelengths. A combination of various semiconductors can be more effective anywhere, but it is not typically cost effective considering the very marginal improvement over using just a single technology. $\endgroup$ – Chris Nov 5 '18 at 15:39
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Since silicon exists in abundance (I believe around circa 25 % of Earth's crust is made from silicon), the industry has come to accept it as a standard. International Technology Roadmap for Semiconductors say that a lot of new materials will change the industry but they also believe that silicon will be the dominant material in the field.

A big number of methods have just been developed for silicon. The Czochralski process, doping with ion implantation, wafer dicing techniques etc. are all complicated processes and methods that are used in the industry. A lot of the appliances used for semiconductor fabrication costs billions of dollars and they are usually optimized for working with silicon. Processing of other materials is of course possible but due to restricted knowledge and economic costs these methods are usually confined to academic research.

So to conclude: Silicon might not be the best material for solar cells, but due to economic and techonological restrictions it is preferred by the industry.

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I am not an expert on semiconductor physics but from some internet research I have found out that money is not always the deciding factor. Germanium is also sometimes used in semiconductors and has been used as such even before silicon. Germanium is apparently less stable at high temperatures and doesn't handle high power levels as well as silicon does. Also, germanium is less abundant in Earth's crust than silicon.

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Raw material of germanium is about 100 to 1000 times more expensive than silicon.

Furthermore, the science and engineering of silicon is well established.

Also, you don't actually use silicon to make the solar cells, one uses doped silicon p-n junctions to make the cell, and if you want to use solar panel for powering things up, you need some voltage difference.

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    $\begingroup$ Doped silicon still remains silicon. And the N-P junctions are only a very thin layer of additional doping. $\endgroup$ – Ruslan Nov 3 '18 at 22:53
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    $\begingroup$ Part of the reason why high-purity silicon is so cheap is because it's made in huge volumes, and has been for about half a century. If germanium or gallium were used in that sort of volume, they'd also be a good bit cheaper than they currently are. $\endgroup$ – Mark Nov 4 '18 at 1:17
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    $\begingroup$ @Mark: Greater demand would not negate the fact that gallium's abundance in the Earth's crust is only about 1/10,000 of silicon, and germanium and arsenic both an order of magnitude rarer still. You need to prospect and mine for it, then isolate it from meager amounts in ores. Silicon, in contrast, is everywhere. $\endgroup$ – Henning Makholm Nov 4 '18 at 23:23
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Infrastructure

Sorry. But the answer is really boring and has nothing to do with Physics.

The answer is simply because we have an entire industry set up to manufacture high quality, high purity, low defect Silicon.

The electronics industry has been churning out pure silicon ingots for years. Interestingly it is the same reason why silicon was chosen for the Avogadro Project.

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    $\begingroup$ Spot on, Technology includes processing machines, the manufacturing industry goes beyond the physics of semiconductors and even the economics of the raw materials. For lack of a better word, we are better at printing intricate structures using silicon as the substrate, thereares many billions invested in tools to do that end-to-end process. Any new technology would need to come to the table with a conceivable mass production process to be considered. $\endgroup$ – crasic Nov 6 '18 at 2:48
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    $\begingroup$ Not so true in my opinion: Solar doesn't require the quality of Si required in chip manufacturing, and if it was, it would cost so much more: The main reason is that silicon is cheap, but the cost of purifying Si for chip fabrication is extremely high. The tooling involved in making solar cell has nothing to do with the tooling for making chips. $\endgroup$ – MrE Nov 6 '18 at 5:57
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    $\begingroup$ @MrE you are correct that the quality is not critical, but the processing technology is not restricted to high purity, there is a lot of basic research in the underlying material physics outside of electrical properties, just basic manipulation. It is (now) easy to work with and has extremely well characterized properties. While the equipment is not shared, by and large it is the same players involved in producing the equipment and they share many general processes $\endgroup$ – crasic Nov 6 '18 at 6:42
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    $\begingroup$ Its easy to discount the sort of brute force empirical cataloging research of material scientists.However, there is a lot of existing real science and technology behind the minutea of silicon processing at every scale, That is what I believe @Aron is refering to "Infrastructure" that goes beyond the raw price of silicon $\endgroup$ – crasic Nov 6 '18 at 6:53
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    $\begingroup$ @MrE high purity isn't important, but monocrystaline is important. $\endgroup$ – Aron Nov 6 '18 at 9:27
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Most important

Si is much cheaper.

Though GaAs is much better than si in terms of efficiency, it is very costly so dallar/watt goes up. Thus GaAs is used only in certain applications like space projects.

Ge's very small bandgap results in several loss mechanism that reduce the efficiency of Ge cells.

Further reading https://en.m.wikipedia.org/wiki/Solar_cell

https://scholar.google.co.in/scholar?q=gaas+on+silicon&hl=en&as_sdt=0&as_vis=1&oi=scholart

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