I'm going to assume a capacity factor of 20% for solar PV. That's significantly lower than the 28.6% capacity factor recorded for utility scale PV in the US last year, much higher than the ~10% you might expect in Germany. Choosing a high-ish solar capacity factor I'm going to note that most of the world's population lives in countries with better solar resources than Germany and that more solar PV is being installed on the utility scale than on e.g. household rooftops. Utility scale projects are sited for better sun resources and can use mechanical trackers that aren't suited for rooftops; both of those contribute to higher capacity factors than you can get out of opportunistic installations on existing rooftops, whichever country you're building in.

I'm also going to assume that modules have 25 years of factory-spec-power-equivalent output. Data from real-world solar installations show that the median module lasts about 30 years before it needs replacement (and more rigorous pre-sale testing may be pushing that number up in recent years), but maximum power output also declines over time due to a variety of degradation mechanisms, so I'm fudging these two factors together for 25 years' equivalent of "like new" power output.

Multiplying the capacity factor of 0.2 by the expected 25 years of like-new-power-output, we see that each nameplate watt of solar power installed is expected to provide 5 watt-years of energy output. The steady-state production rate you need for the world to have X watts of solar-generated power over the course of the year is then X/5.

Concrete numbers time: world electricity consumption in 2013 averaged about 2.28 terawatts. The world would need to produce about 457 gigawatts-peak of solar modules per year to produce this much electricity over the course of a year, consuming about 2,285,000 tonnes of silicon. World primary energy consumption in 2015 averaged about 17.3 terawatts. To match that on an annualized basis you'd need to produce 3.46 terawatts-peak of solar modules per year for a silicon consumption of about 17,340,000 tonnes.

Silica is about 46% silicon, so you'd need to mine ~5,000,000 to 38,000,000 tonnes of silica per year in order to produce enough silicon for solar PV to take over world electricity production or all world energy consumption respectively. For comparison, world sand consumption in 2014 was estimated at 15 billion tonnes, roughly 3 orders of magnitude greater. (Silicon producers usually don't start with sand anyway; they use coarsely crushed lumps of silica-rich materials like quartzite, quartz, or chert, which are even more abundant than clean sand.)

Note that I am NOT claiming that you could actually replace all the world's diverse energy sources with electricity from silicon based solar PV. There are of course no oceangoing ships that can be powered by electricity, no electrical passenger aircraft, etc. And even if we were just trying to replace fossils for current electricity generation, storage remains a hard open problem. Without cheap, abundant electricity storage it will be impossible for solar PV to take even a 40% share of world electricity consumption. But I hope that the numbers make it clear that silica availability is not a material constraint on solar PV deployment scale.

Silica is not the bottleneck