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?
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:
- 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.
- 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.
- 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.
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.
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.
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.
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.
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.
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